■ #Books and Articles
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Book
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Advanced Computational Applications of Geometric Algebra Springer Proceedings in Mathematics & Statistics (Collaboration) 2024
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| Language | English | | Publication Date | 2024 | | Type | Scholarly Book | | Peer Review | With peer review | | Title | Advanced Computational Applications of Geometric Algebra | | Contribution Type | Joint Editor | | Journal | Springer Proceedings in Mathematics & Statistics | | Journal Type | Another Country | | Publisher | Springer | | Responsible for | Editorial work | | International coauthorship | International coauthorship | | Author and coauthor | David DaSilva, Dietmar Hildenbrand, Eckhard Hitzer | | Details | David DaSilva, Dietmar Hildenbrand, Eckhard Hitzer (eds.), Advanced Computational Applications of Geometric Algebra, Springer Proceedings in Mathematics & Statistics, Springer Nature Switzerland AG, Cham, Switzerland, expected 2024. |
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Advanced Computational Applications of Geometric Algebra - First International Conference, ICACGA 2022, Colorado Springs, CO, USA, October 2-5, 2022, Proceedings Lecture Notes in Computer Science 13771 (Collaboration) 2023/12
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| Language | English | | Publication Date | 2023/12 | | Type | Scholarly Book | | Peer Review | With peer review | | Title | Advanced Computational Applications of Geometric Algebra - First International Conference, ICACGA 2022, Colorado Springs, CO, USA, October 2-5, 2022, Proceedings | | Contribution Type | Joint Editor | | Journal | Lecture Notes in Computer Science | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 13771 | | Responsible for | Editing | | International coauthorship | International coauthorship | | Author and coauthor | D. DaSilva, D. Hildenbrand, E. Hitzer | | Details | D. DaSilva, D. Hildenbrand, E. Hitzer (eds.), Advanced Computational Applications of Geometric Algebra - First International Conference, ICACGA 2022, Colorado Springs, CO, USA, October 2-5, 2022, Proceedings, LNCS Vol. 13771, SpringerNature, Cham, Switzerland, 24 Dec. 2023, ISBN: 978-3-031-34030-7, URL: https://link.springer.com/book/9783031340307 | | URL for researchmap | https://link.springer.com/book/9783031340307 |
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Book
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Quaternionic Integral Transforms - A Machine-Generated Literature Overview Trends in Mathematics (Research Summaries) 1 (Collaboration) 2023/08
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| Language | English | | Publication Date | 2023/08 | | Type | Scholarly Book | | Title | Quaternionic Integral Transforms - A Machine-Generated Literature Overview | | Contribution Type | Editor | | Journal | Trends in Mathematics (Research Summaries) | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 1 | | Total page number | 177 | | Responsible for | All editing, introduction, chapter introductions | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer (editor), S.J. Sangwine (foreword), Quaternionic Integral Transforms - A Machine-Generated Literature Overview, Trends in Mathematics (Research Summaries), Birkhauser, Cham, Switzerland, 177 pages, Aug. 2023. DOI: https://link.springer.com/book/10.1007/978-3-031-28375-8 | | URL for researchmap | https://link.springer.com/book/10.1007/978-3-031-28375-8 |
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Book
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Empowering Novel Geometric Algebra for Graphics and Engineering - 7th International Workshop, ENGAGE 2022, Virtual Event, September 12, 2022, Proceedings Lecture Notes in Computer Science 13862,pp.1-135 (Collaboration) 2023/04
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| Language | English | | Publication Date | 2023/04 | | Type | Scholarly Book | | Peer Review | With peer review | | Title | Empowering Novel Geometric Algebra for Graphics and Engineering - 7th International Workshop, ENGAGE 2022, Virtual Event, September 12, 2022, Proceedings | | Contribution Type | Joint Editor | | Journal | Lecture Notes in Computer Science | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 13862,pp.1-135 | | Total page number | 135 | | Responsible for | Editing | | International coauthorship | International coauthorship | | Author and coauthor | Eckhard Hitzer, George Papagiannakis, Petr Vasik | | Original author(s) | Eckhard Hitzer, George Papagiannakis, Petr Vasik | | Details | Eckhard Hitzer, George Papagiannakis, Petr Vasik (eds.), Empowering Novel Geometric Algebra for Graphics and Engineering - 7th International Workshop, ENGAGE 2022, Virtual Event, September 12, 2022, Proceedings, Springer, Cham, LNCS, Vol. 13862, 135 pages, April 2023, ISBN: 978-3-031-30922-9, DOI: https://doi.org/10.1007/978-3-031-30923-6 | | URL for researchmap | https://doi.org/10.1007/978-3-031-30923-6 |
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Book
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Quaternion and Clifford Fourier Transforms (Single) 2021/09
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| Language | English | | Publication Date | 2021/09 | | Type | Scholarly Book | | Title | Quaternion and Clifford Fourier Transforms | | Contribution Type | Single Work | | Journal Type | Another Country | | Publisher | Chapman and Hall/CRC | | Total page number | 472 | | Responsible for | Evertything | | Author and coauthor | Eckhard Hitzer, Foreword by S.J. Sangwine, | | Details | Quaternion and Clifford Fourier Transforms describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive, self-contained book covering this vibrant new area of pure and applied mathematics in depth.
The book begins with a historic overview, followed by chapters on Clifford and quaternion algebra and geometric (vector) differential calculus (part of Clifford analysis). The core of the book consists of one chapter on quaternion Fourier transforms and one on Clifford Fourier transforms. | | URL for researchmap | https://www.routledge.com/Quaternion-and-Clifford-Fourier-Transforms/Hitzer/p/book/9780367774660 |
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Book
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ebook: For a Sustainable World (Collaboration) 2021/08
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| Language | English and Japanese | | Publication Date | 2021/08 | | Type | Scholarly Book | | Title | ebook: For a Sustainable World | | Contribution Type | Joint Editor | | Journal Type | Another Country | | Publisher | Independently published – KDP, Seattle (US) | | Total page number | 286 | | Author and coauthor | Editors: E. Hitzer, G.C. Kimura, M. Shukuya, A. Takeuchi,
Foreword by P. Hastings | | Details | This volume is the result of three international workshops (2017-2020) on Sustainable University Development held at International Christian University in Tokyo, Japan.
In 2017 the focus was on renewable energy, in 2018 on energy efficiency and in 2020 on management and education. Colleagues from ICU, Sophia University, Ritsumeikan University, Tokyo City University, Tokyo Kasei University, Toho University and Chiba University of Commerce jointly organized these workshops. The workshops received generous financial support from Japan ICU Foundation in New York, and from the German JSPS Alumni Association. A key motivation for organizing these workshops was the urgent need for Japan to replace nuclear energy by sustainable forms of energy, and to aim at a reduction of expensive fossil fuel imports. Universities that try to prepare young people for social and life challenges, need to both teach about alternatives and become credible role models for students and society in general. | | URL for researchmap | https://www.amazon.com.au/%E6%8C%81%E7%B6%9A%E5%8F%AF%E8%83%BD%E3%81%AA%E4%B8%96%E7%95%8C%E3%81%AE%E3%81%9F%E3%82%81%E3%81%AB-Sustainable-World-%E7%9C%81%E3%82%A8%E3%83%8D%E3%83%BB%E5%86%8D%E3%82%A8%E3%83%8D%E3%81%AE%E5%8F%AF%E8%83%BD%E6%80%A7-Universitie |
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Book
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For a Sustainable World (Collaboration) 2021/08
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| Language | English and Japanese | | Publication Date | 2021/08 | | Type | Scholarly Book | | Title | For a Sustainable World | | Contribution Type | Joint Editor | | Journal Type | Another Country | | Publisher | Bookmundo Osiander, Tuebingen, Germany | | Total page number | 286 | | Responsible for | Coordinating Editor | | Author and coauthor | E. Hitzer, G.C. Kimura, M. Shukuya, A. Takeuchi (eds.), Foreword by P. Hastings | | Details | In 2017 the focus was on renewable energy, in 2018 on energy efficiency and in 2020 on management and education. Colleagues from ICU, Sophia University, Ritsumeikan University, Tokyo City University, Tokyo Kasei University, Toho University and Chiba University of Commerce jointly organized these workshops. The workshops received generous financial support from Japan ICU Foundation in New York, and from the German JSPS Alumni Association. A key motivation for organizing these workshops was the urgent need for Japan to replace nuclear energy by sustainable forms of energy, and to aim at a reduction of expensive fossil fuel imports. Universities that try to prepare young people for social and life challenges, need to both teach about alternatives and become credible role models for students and society in general. | | URL for researchmap | https://publish.bookmundo.de/site/?r=userwebsite/index&id=eckhardhitzer/bookdetails/270157 |
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Book
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Christ Centered Stewardship for the Environment – Responsibility, Energy, Care and Architecture (Single) 2021/03
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| Language | English | | Publication Date | 2021/03 | | Type | Scholarly Book | | Title | Christ Centered Stewardship for the Environment – Responsibility, Energy, Care and Architecture | | Contribution Type | Single Work | | Journal Type | Another Country | | Publisher | Bookmundo Osiander, Tuebingen, Germany | | Total page number | 72 | | Responsible for | The whole book. | | Author and coauthor | Author: Eckhard Hitzer
Foreword: Prof. Dr. Goro C. Kimura | | Details | Post Fukushima, there are rich opportunities in Japan for renewable energy and energy efficiency, yet without proper ethics humanity may stumble again. The book begins with Christ Centered Stewardship for the Environment. Then it shows the great opportunities particularly in Japan regarding full renewable energy supply. To begin sweeping in front of his own door, the author presents a feasibility study for wood gas co-generation at his university in suburban Tokyo. As for sustainable energy efficient architecture, Kaufmann Bausysteme GmbH (KBS) equipped a Social Center in Austria with cross laminated timber (CLT) modules. ... Foreword by Prof. Goro C. Kimura. | | URL for researchmap | https://osiander.bookmundo.de/site/index.php?r=userwebsite/index&id=eckhardhitzer/ |
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Book
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Space Group Visualizer (Collaboration) 2021/03
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| Language | English | | Publication Date | 2021/03 | | Type | Scholarly Book | | Title | Space Group Visualizer | | Contribution Type | Joint Work | | Journal Type | Another Country | | Publisher | Independently published – KDP, Seattle (US) | | Total page number | 162 | | Responsible for | Most of the text and graphics. | | Author and coauthor | Eckhard Hitzer, Christian Perwass | | Details | Prof. Dr. Davide M. Proserpio (foreword): "This 'great software project', as it was called by Prof. Frank Hoffmann in his recent book [F. Hoffman, Introduction to Crystallography (2020) Springer Nature Switzerland AG], is very powerful and is an ideal support to teach how to read the International Tables in a more interactive way than usually taught. This collection of papers allows to follow the many possibility of the program to explore the richness of the space group symmetries and for the more math oriented may suggest further reading in geometric algebra, as pointed out recently in Acta Crystallographica." Inspired by the work of David Hestenes and his student Jeremy Holt representing point groups and space groups byway of conformal geometric algebra as learned in a lecture from David Hestenes at the international conference Applied Geometric Algebra in Computer Science and Engineering (AGACSE 2001) held in Trinity College of Cambridge, UK, ... | | URL for researchmap | https://www.amazon.com/dp/B08YRYMPR5 |
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Book
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Advances in Computer Graphics, Proceedings of 36th Computer Graphics International Conference, CGI 2019, Calgary, AB, Canada, June 17–20, 2019 Lecture Notes in Computer Science 11542 (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Scholarly Book | | Invitation | With invitation | | Title | Advances in Computer Graphics, Proceedings of 36th Computer Graphics International Conference, CGI 2019, Calgary, AB, Canada, June 17–20, 2019 | | Contribution Type | Joint Editor | | Journal | Lecture Notes in Computer Science | | Journal Type | Another Country | | Publisher | Springer, New York | | Volume, Issue, Pages | 11542 | | Total page number | 587 | | Responsible for | Editing part of this conference proceedings. | | Author and coauthor | Gavrilova, M., Chang, J., Magnenat-Thalmann, N., Hitzer, E., Ishikawa, H. (eds.) |
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Book
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Quaternion and Clifford Fourier Transforms and Wavelets (Collaboration) 2013
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| Language | English | | Publication Date | 2013 | | Type | Scholarly Book | | Title | Quaternion and Clifford Fourier Transforms and Wavelets | | Contribution Type | Joint Editor | | Publisher | Springer/Birkhauser | | Author and coauthor | Eckhard Hitzer and Stephen Sangwine | | Details | Trends in Mathematics, Vol. 27 |
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Book
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Proc. of the Symposium Innovative Teaching of Mathematics with Geometric Algebra 2003, Nov. 20-22, 2003, RIMS, University of Kyoto, Japan. Proc. of the Symposium Innovative Teaching of Mathematics with Geometric Algebra 2003 1378 (Collaboration) 2003
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| Language | English | | Publication Date | 2003 | | Type | Book (Other) | | Title | Proc. of the Symposium Innovative Teaching of Mathematics with Geometric Algebra 2003, Nov. 20-22, 2003, RIMS, University of Kyoto, Japan. | | Contribution Type | Joint Editor | | Journal | Proc. of the Symposium Innovative Teaching of Mathematics with Geometric Algebra 2003 | | Journal Type | Japan | | Publisher | Kyoto University RIMS. | | Volume, Issue, Pages | 1378 | | Responsible for | Part of editorial work. | | Author and coauthor | E. Hitzer, R. Nagaoka, H. Ishi | | Details | E. Hitzer, R. Nagaoka, H. Ishi (work as editors), Proc. of the Symposium Innovative Teaching of Mathematics with Geometric Algebra 2003, Nov. 20-22, 2003, RIMS, University of Kyoto, Japan. Online edition: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/1378.html . |
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Article
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Inner product of two oriented points in conformal geometric algebra in Detail Springer Proceedings in Mathematics & Statistics (Single) 2024
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| Language | English | | Publication Date | 2024 | | Type | Research Paper | | Peer Review | With peer review | | Title | Inner product of two oriented points in conformal geometric algebra in Detail | | Contribution Type | Single Work | | Journal | Springer Proceedings in Mathematics & Statistics | | Journal Type | Another Country | | Publisher | Springer | | Total page number | 18 | | Responsible for | all | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer, Inner product of two oriented points in conformal geometric algebra in Detail, accepted for D. DaSilva, D. Hildenbrand, E. Hitzer (eds.), Proceedings of ICACGA 2022, Springer Proceedings in Mathematics & Statistics, Springer, Heidelberg, 18 pages, expected 2024. Preprint: https://vixra.org/abs/2308.0129 | | URL for researchmap | https://vixra.org/abs/2308.0129 |
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Introduction to Geometric Algebra Springer Proceedings in Mathematics & Statistics (Collaboration) 2024
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| Language | English | | Publication Date | 2024 | | Type | Research Paper | | Title | Introduction to Geometric Algebra | | Contribution Type | Joint Work | | Journal | Springer Proceedings in Mathematics & Statistics | | Journal Type | Another Country | | Publisher | Springer | | Total page number | 30 | | Responsible for | Concept and most of the text | | Authorship | Lead author,Corresponding author | | International coauthorship | International coauthorship | | Author and coauthor | E. Hitzer, D. Hildenbrand | | Original author(s) | E. Hitzer, D. Hildenbrand | | Details | E. Hitzer, D. Hildenbrand, Introduction to Geometric Algebra, accepted for D. DaSilva, D. Hildenbrand, E. Hitzer (eds.), Proceedings of ICACGA 2022, Springer Proceedings in Mathematics & Statistics, Springer, Heidelberg, 30 pages, publication expected 2024. |
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Article
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Quadratic Phase Quaternion Domain Fourier Transform Lecture Notes in Computer Science, Vols. 14495-14498 (Single) 2024
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| Language | English | | Publication Date | 2024 | | Type | Research Paper | | Peer Review | With peer review | | Title | Quadratic Phase Quaternion Domain Fourier Transform | | Contribution Type | Single Work | | Journal | Lecture Notes in Computer Science, Vols. 14495-14498 | | Journal Type | Another Country | | Publisher | Springer | | Total page number | 12 | | Responsible for | all | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer, Quadratic Phase Quaternion Domain Fourier Transform, accepted for Proceedings of ENGAGE 2023, in Bin Sheng, Lei Bi, Jinman Kim, Nadia Magnenat Thalmann, Daniel Thalmann (eds.), Advances in Computer Graphics, 40th Computer Graphics International Conference, CGI 2023, Shanghai, China, August 28–September 1, 2023, Proceedings, Parts I-IV, Lecture Notes in Computer Science, Vols. 14495-14498, 12 pages, publication due Feb. 2024. |
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Report on First Symposium of European Researchers in Japan Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. (Collaboration) 2024
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| Language | English | | Publication Date | 2024 | | Type | Conference Report, etc. | | Invitation | With invitation | | Title | Report on First Symposium of European Researchers in Japan | | Contribution Type | Joint Work | | Journal | Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Journal Type | Another Country | | Publisher | Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Total page number | 4 | | Responsible for | Most of the text | | Authorship | Corresponding author | | Author and coauthor | W. Wunderlich, E. Hitzer | | Original author(s) | W. Wunderlich, E. Hitzer | | Details | W. Wunderlich, E. Hitzer, Report on First Symposium of European Researchers in Japan, 4 pages, accepted for Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V., 2023 or 2024. |
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Scientific Research – Opportunities and Pitfalls Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. (Single) 2024
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| Language | English | | Publication Date | 2024 | | Type | Summary of Presentation (International Conference) | | Invitation | With invitation | | Title | Scientific Research – Opportunities and Pitfalls | | Contribution Type | Single Work | | Journal | Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Journal Type | Another Country | | Publisher | Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Total page number | 5 | | Responsible for | all | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer, Scientific Research – Opportunities and Pitfalls, 5 pages, accepted for Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V., 2023 or 2024. |
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Inner product of two oriented points in conformal geometric algebra Proceedings of ICACGA 2022, LNCS, SpringerNature 13771 (Single) 2023/12
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| Language | English | | Publication Date | 2023/12 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Inner product of two oriented points in conformal geometric algebra | | Contribution Type | Single Work | | Journal | Proceedings of ICACGA 2022, LNCS, SpringerNature | | Journal Type | Another Country | | Publisher | SpringerNature | | Volume, Issue, Pages | 13771 | | Total page number | 11 | | Responsible for | all | | Authorship | Lead author,Corresponding author | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | Inner product of two oriented points in conformal geometric algebra, in D. DaSilva, D. Hildenbrand, E. Hitzer (eds.), Advanced Computational Applications of Geometric Algebra - First International Conference, ICACGA 2022, Colorado Springs, CO, USA, October 2-5, 2022, Proceedings, LNCS, SpringerNature, Vol. 13771, ISBN 978-3-031-34030-7, 11 pages, Springer, Cham, 24 Dec. 2023, Chapter 5. DOI: https://doi.org/10.1007/978-3-031-34031-4_5 |
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Special affine quaternion domain Fourier transform Proceedings of "GOL 2021: International Conference “Applied Category Theory Graph-Operad-Logic”, Professor Zbigniew Oziewicz in memoriam", 12 pp., in Book Series: Series on Knots and Everything (SKAE), World Scientific, Singapore 75,pp.537-552 (Single) 2023/10
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| Language | English | | Publication Date | 2023/10 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Special affine quaternion domain Fourier transform | | Contribution Type | Single Work | | Journal | Proceedings of "GOL 2021: International Conference “Applied Category Theory Graph-Operad-Logic”, Professor Zbigniew Oziewicz in memoriam", 12 pp., in Book Series: Series on Knots and Everything (SKAE), World Scientific, Singapore | | Journal Type | Another Country | | Publisher | World Scientific, Singapore | | Volume, Issue, Pages | 75,pp.537-552 | | Total page number | 16 | | Responsible for | all | | Authorship | Lead author,Corresponding author | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer, Special affine quaternion domain Fourier transform, Hilda María Colín García, José de Jesús Cruz Guzmán, Louis H Kauffman, and Hanna Makaruk (eds.), Scientific Legacy of Professor Zbigniew Oziewicz, Series on Knots and Everything (SKAE), Vol. 75. World Scientific, Singapore, October 2023. pages 537–552, DOI: https://doi.org/10.1142/13275 | | URL for researchmap | https://doi.org/10.1142/13275 |
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Embedding of Octonion Fourier Transform in Geometric Algebra of R^3 and Polar Representations of Octonion Analytic Signals in Detail Mathematical Methods in the Applied Sciences (Single) 2023/09
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| Language | English | | Publication Date | 2023/09 | | Type | Research Paper | | Peer Review | With peer review | | Title | Embedding of Octonion Fourier Transform in Geometric Algebra of R^3 and Polar Representations of Octonion Analytic Signals in Detail | | Contribution Type | Single Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Total page number | 17 | | Responsible for | all | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | Embedding of Octonion Fourier Transform in Geometric Algebra of R^3 and Polar Representations of Octonion Analytic Signals in Detail, Mathematical Methods in the Applied Sciences, pp. 1-17, First published: 04 September 2023. DOI: 10.1002/mma.9639, URL: https://onlinelibrary.wiley.com/doi/10.1002/mma.9639 Preprint: https://vixra.org/abs/2308.0124 | | URL for researchmap | https://vixra.org/abs/2308.0124 |
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Survey of New Applications of Geometric Algebra Mathematical Methods in the Applied Sciences (Collaboration) 2023/07
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| Language | English | | Publication Date | 2023/07 | | Type | Research Paper | | Peer Review | With peer review | | Title | Survey of New Applications of Geometric Algebra | | Contribution Type | Joint Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Total page number | 21 | | Responsible for | Conception, most writing and final editing | | Authorship | Lead author,Corresponding author | | International coauthorship | International coauthorship | | Author and coauthor | E. Hitzer, M. Kamarianakis, G. Papagiannakis, P. Vašík | | Original author(s) | E. Hitzer, M. Kamarianakis, G. Papagiannakis, P. Vašík | | Details | E. Hitzer, M. Kamarianakis, G. Papagiannakis, P. Vašík, Survey of New Applications of Geometric Algebra, Mathematical Methods in the Applied Sciences/Early View, 21 pages, First published: 31 July 2023. DOI: https://doi.org/10.1002/mma.9575, Preprint: https://doi.org/10.22541/au.167687105.52780013/v1 , Full text share link: https://onlinelibrary.wiley.com/share/author/TNRNPQREN45UUXBVWDM5?target=10.1002/mma.9575 | | URL for researchmap | https://onlinelibrary.wiley.com/share/author/TNRNPQREN45UUXBVWDM5?target=10.1002/mma.9575 |
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Embedding of Octonion Fourier Transform in Geometric Algebra of R^3 and Polar Representations of Octonion Analytic Signals Lecture Notes in Computer Science 13862,pp.123-134 (Single) 2023/04
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| Language | English | | Publication Date | 2023/04 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Embedding of Octonion Fourier Transform in Geometric Algebra of R^3 and Polar Representations of Octonion Analytic Signals | | Contribution Type | Single Work | | Journal | Lecture Notes in Computer Science | | Journal Type | Another Country | | Publisher | SpringerNatur | | Volume, Issue, Pages | 13862,pp.123-134 | | Total page number | 12 | | Responsible for | all | | Authorship | Lead author | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer.,Embedding of Octonion Fourier Transform in Geometric Algebra of R3 and Polar Representations of Octonion Analytic Signals. In: Hitzer, E., Papagiannakis, G., Vasik, P. (eds) Empowering Novel Geometric Algebra for Graphics and Engineering. ENGAGE 2022. Lecture Notes in Computer Science, Vol. 13862, pp 123–134, Springer, Cham, 2023. DOI: https://doi.org/10.1007/978-3-031-30923-6_10 | | URL for researchmap | https://doi.org/10.1007/978-3-031-30923-6_10 |
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Special affine Fourier transform for space-time algebra signals in detail Advances in Applied Clifford Algebras 32:60(5),pp.1-18 (Single) 2022/10
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| Language | English | | Publication Date | 2022/10 | | Type | Research Paper | | Peer Review | With peer review | | Title | Special affine Fourier transform for space-time algebra signals in detail | | Contribution Type | Single Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhauser/SpringerNature | | Volume, Issue, Pages | 32:60(5),pp.1-18 | | Total page number | 18 | | Responsible for | all | | Authorship | Lead author | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer, Special affine Fourier transform for space-time algebra signals in detail, Adv. Appl. Clifford Algebras, Vol. 32:60, Iss. 5, 18 pages (October 2022). DOI: https://doi.org/10.1007/s00006-022-01228-w, Preprint: https://vixra.org/pdf/2206.0072v1.pdf | | URL for researchmap | https://doi.org/10.1007/s00006-022-01228-w |
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Extending Lasenby's embedding of octonions in space-time algebra Cl(1,3), to all three- and four dimensional Clifford geometric algebras Cl(p,q), n=p+q=3,4 Mathematical Methods in the Applied Sciences Special Issue (Single) 2022/08
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| Language | English | | Publication Date | 2022/08 | | Type | Research Paper | | Peer Review | With peer review | | Title | Extending Lasenby's embedding of octonions in space-time algebra Cl(1,3), to all three- and four dimensional Clifford geometric algebras Cl(p,q), n=p+q=3,4 | | Contribution Type | Single Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Volume, Issue, Pages | Special Issue | | Total page number | 24 | | Authorship | Lead author | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. H.itzer Extending Lasenby's embedding of octonions in space-time algebra Cl(1,3), to all three- and four dimensional Clifford geometric algebras Cl(p,q), n=p+q=3,4, Mathematical Methods in the Applied Sciences, pp. 1-24 (Early View: 04 Aug. 2022), DOI: http://doi.org/10.1002/mma.8577, Preprint: https://vixra.org/abs/2202.0109 | | URL for researchmap | http://doi.org/10.1002/mma.8577 |
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Current Survey of Clifford Geometric Algebra Applications Mathematical Methods in the Applied Sciences Special Issue (Collaboration) 2022/04
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| Language | English | | Publication Date | 2022/04 | | Type | Research Paper | | Peer Review | With peer review | | Title | Current Survey of Clifford Geometric Algebra Applications | | Contribution Type | Joint Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Volume, Issue, Pages | Special Issue | | Total page number | 31 | | Responsible for | Most of the text | | Authorship | Lead author | | International coauthorship | International coauthorship | | Author and coauthor | Eckhard Hitzer, Carlile Lavor, Dietmar Hildenbrand | | Original author(s) | Eckhard Hitzer, Carlile Lavor, Dietmar Hildenbrand | | Details | E. H.itzer, C. Lavor, D. Hildenbrand, Current Survey of Clifford Geometric Algebra Applications, Mathematical Methods in the Applied Sciences, 31 pages, (2022), DOI: https://onlinelibrary.wiley.com/doi/10.1002/mma.8316, Preprint: https://vixra.org/abs/2204.0062 | | URL for researchmap | https://onlinelibrary.wiley.com/doi/10.1002/mma.8316 |
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On Factorization of Multivectors in Cl(2,1), by Exponentials and Idempotents Mathematical Methods in the Applied Sciences 45(16),pp.9504-9519 (Single) 2022/04
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| Language | English | | Publication Date | 2022/04 | | Type | Research Paper | | Peer Review | With peer review | | Title | On Factorization of Multivectors in Cl(2,1), by Exponentials and Idempotents | | Contribution Type | Single Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Volume, Issue, Pages | 45(16),pp.9504-9519 | | Total page number | 16 | | Responsible for | Everything | | Authorship | Lead author | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | Eckhard Hitzer, On Factorization of Multivectors in Cl(2,1), by Exponentials and Idempotents, Mathematical Methods in the Applied Sciences, Vol. 45, Iss. 16, pp. 9504-9519, First published 24 April 2022, DOI: http://doi.org/10.1002/mma.8320, Preprint: https://vixra.org/abs/2204.0073
Abstract: In this paper, we consider general multivector elements of the Clifford algebra Cl(2,1) and look for possibilities to factorize multivectors into products of blades, idempotents, and exponentials, where the exponents are frequently blades of grades zero (scalar) to (pseudoscalar). We will succeed mostly, with a minor open case remaining. | | URL for researchmap | https://onlinelibrary.wiley.com/doi/10.1002/mma.8320 |
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27.
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Article
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New Applications of Clifford’s Geometric Algebra Adv. Appl. Clifford Algebras 32:17,pp.1-39 (Collaboration) 2022/02
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| Language | English | | Publication Date | 2022/02 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | New Applications of Clifford’s Geometric Algebra | | Contribution Type | Joint Work | | Journal | Adv. Appl. Clifford Algebras | | Journal Type | Another Country | | Publisher | SpringerNature | | Volume, Issue, Pages | 32:17,pp.1-39 | | Total page number | 39 | | Responsible for | Most of the text | | Authorship | Corresponding author | | International coauthorship | International coauthorship | | Author and coauthor | S. Breuils, K. Tachibana, E. Hitzer | | Original author(s) | S. Breuils, K. Tachibana, E. Hitzer | | Details | The new applications of Clifford’s geometric algebra surveyed in this paper include kinematics and robotics, computer graphics and animation, neural networks and pattern recognition, signal and image processing, applications of versors and orthogonal transformations, spinors and matrices, applied geometric calculus, physics, geometric algebra software and implementations, applications to discrete mathematics and topology, geometry and geographic information systems, encryption, and the representation of higher order curves and surfaces. | | URL for researchmap | https://link.springer.com/article/10.1007/s00006-021-01196-7 |
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28.
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On Factorization of Multivectors in Cl(3,0), Cl(1,2) and Cl(0,3), by Exponentials and Idempotents Complex Variables and Elliptic Equations (Single) 2021/12
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| Language | English | | Publication Date | 2021/12 | | Type | Research Paper | | Peer Review | With peer review | | Title | On Factorization of Multivectors in Cl(3,0), Cl(1,2) and Cl(0,3), by Exponentials and Idempotents | | Contribution Type | Single Work | | Journal | Complex Variables and Elliptic Equations | | Journal Type | Another Country | | Publisher | Taylor and Francis | | Total page number | 25 | | Responsible for | Everything | | Author and coauthor | E. Hitzer | | Details | In this paper we consider general multivector elements of Clifford algebras Cl(3,0), Cl(1,2) and Cl(0,3), and look for possibilities to factorize multivectors into products of blades, idempotents and exponentials, where the exponents are frequently blades of grades zero (scalar) to n (pseudoscalar). | | URL for researchmap | https://www.tandfonline.com/doi/full/10.1080/17476933.2021.2001462 |
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29.
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Foundations for strip adjustment of airborne laserscanning data with conformal geometric algebra Adv. Appl. Clifford Algebras 32(1),pp.1-34 (Collaboration) 2021/11
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| Language | English | | Publication Date | 2021/11 | | Type | Research Paper | | Peer Review | With peer review | | Title | Foundations for strip adjustment of airborne laserscanning data with conformal geometric algebra | | Contribution Type | Joint Work | | Journal | Adv. Appl. Clifford Algebras | | Journal Type | Another Country | | Publisher | SpringerNature | | Volume, Issue, Pages | 32(1),pp.1-34 | | Total page number | 34 | | Responsible for | Most of text and computations | | Authorship | Lead author | | International coauthorship | International coauthorship | | Author and coauthor | E. H.itzer, W. Benger, M. Niederwieser, R. Baran and F. Steinbacher | | Original author(s) | E. H.itzer, W. Benger, M. Niederwieser, R. Baran and F. Steinbacher | | Details | Typically, airborne laserscanning includes a laser mounted on an airplane or drone (its pulsed beam direction can scan in flight direction and perpendicular to it) an intertial positioning system of gyroscopes, and a global navigation satellite system. The data, relative orientation and relative distance of these three systems are combined in computing strips of ground surface point locations in an earth fixed coordinate system. Finally, all laserscanning strips are combined via iterative closes point methods to an interactive three-dimensional terrain map. In this work we describe the mathematical framework for how to use the iterative closest point method for the adjustment of the airborne laserscanning data strips in the framework of conformal geometric algebra. | | URL for researchmap | https://link.springer.com/article/10.1007/s00006-021-01184-x |
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30.
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Special affine Fourier transform for space-time algebra signals Lecture Notes in Computer Science 13002,pp.658-669 (Single) 2021/10
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| Language | English | | Publication Date | 2021/10 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Special affine Fourier transform for space-time algebra signals | | Contribution Type | Single Work | | Journal | Lecture Notes in Computer Science | | Journal Type | Another Country | | Publisher | SpringerNature | | Volume, Issue, Pages | 13002,pp.658-669 | | Total page number | 12 | | Responsible for | Everything | | Author and coauthor | E. Hitzer | | Details | We generalize the space-time Fourier transform (SFT) [9] to a special affine Fourier transform (SASFT, also known as offset linear canonical transform) for 16-dimensional space-time multivector Cl(3, 1)-valued signals over the domain of space-time (Minkowski space) R3,1. We establish how it can be computed in terms of the SFT, and introduce its properties of multivector coefficient linearity, shift and modulation, inversion, Rayleigh (Parseval) energy theorem, partial derivative identities, a directional uncertainty principle and its specialization to coordinates. | | URL for researchmap | https://link.springer.com/chapter/10.1007%2F978-3-030-89029-2_49 |
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31.
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Introduction to Clifford’s Geometric Algebra Vixra.org preprint archive 2021 (Collaboration) 2021/08
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| Language | English | | Publication Date | 2021/08 | | Type | Research Paper | | Title | Introduction to Clifford’s Geometric Algebra | | Contribution Type | Joint Work | | Journal | Vixra.org preprint archive | | Journal Type | Another Country | | Publisher | vixra.org | | Volume, Issue, Pages | 2021 | | Total page number | 10 | | Responsible for | Part of text and equations | | Authorship | Last author,Corresponding author | | International coauthorship | International coauthorship | | Author and coauthor | S. Breuils, K. Tachibana, E. Hitzer | | Original author(s) | S. Breuils, K. Tachibana, E. Hitzer | | Details | S. Breuils, K. Tachibana, E. Hitzer, Introduction to Clifford’s Geometric Algebra, 10 pp., 2021. Preprint URL: https://vixra.org/abs/2108.0145, last accessed: 27 Aug. 2021.
Abstract: A brief application-oriented introduction to W.K. Clifford's geometric algebras, including conformal geometric algebra (CGA). | | URL for researchmap | https://vixra.org/abs/2108.0145 |
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32.
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Article
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Generalized Uncertainty Principles associated with the Quaternionic Offset Linear Canonical Transform Complex Variables and Elliptic Equations (Collaboration) 2021/04
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| Language | English | | Publication Date | 2021/04 | | Type | Research Paper | | Peer Review | With peer review | | Title | Generalized Uncertainty Principles associated with the Quaternionic Offset Linear Canonical Transform | | Contribution Type | Joint Work | | Journal | Complex Variables and Elliptic Equations | | Journal Type | Another Country | | Publisher | Taylor and Francis | | Total page number | 20 | | Responsible for | part of computation, part of text | | Author and coauthor | Y. El Haoui, E.H.itzer | | Details | The quaternionic offset linear canonical transform (QOLCT) can be defined as a generalization of the quaternionic linear canonical transform (QLCT). In this paper, we define the QOLCT, we derive the relationship between the QOLCT and the quaternion Fourier transform (QFT). Based on this fact, we prove the Rayleigh formula and some properties related to the QOLCT. Then, we generalize some different uncertainty principles (UPs), including Heisenberg-Weyl's UP, Hardy's UP, Beurling's UP, and logarithmic UP to the QOLCT domain. | | URL for researchmap | https://www.tandfonline.com/doi/full/10.1080/17476933.2021.1916919 |
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33.
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Article
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Report on 3rd Workshop on Sustainable University Development with Focus on Education and Management 22nd Feb. 2020, ICU Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. 2021(85/4),pp.3-6 (Single) 2021/04
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| Language | English | | Publication Date | 2021/04 | | Type | Conference Report, etc. | | Title | Report on 3rd Workshop on Sustainable University Development with Focus on Education and Management 22nd Feb. 2020, ICU | | Contribution Type | Single Work | | Journal | Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Journal Type | Another Country | | Publisher | JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Volume, Issue, Pages | 2021(85/4),pp.3-6 | | Total page number | 4 | | Responsible for | All | | Authorship | Lead author,Corresponding author | | International coauthorship | International coauthorship | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer, Report on 3rd Workshop on Sustainable University Development with Focus on Education and Management 22nd Feb. 2020, ICU, 4 pages. Also available as Preprint: https://vixra.org/pdf/2004.0183v1.pdf | | URL for researchmap | https://www.jsps-club.de/veroeffentlichungen/neues-vom-club/2021/04#c6036 |
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34.
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Article
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Strip adjustment of airborne laserscanning data with conformal geometric algebra Joint 11th Int. Conf. on Soft Comp. & Intell. Systems & 21st Int.Symp. on Adv. Intell.Sys SCIS-ISIS pp.1-6 (Collaboration) 2020/12
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| Language | English | | Publication Date | 2020/12 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Strip adjustment of airborne laserscanning data with conformal geometric algebra | | Contribution Type | Joint Work | | Journal | Joint 11th Int. Conf. on Soft Comp. & Intell. Systems & 21st Int.Symp. on Adv. Intell.Sys SCIS-ISIS | | Journal Type | Another Country | | Publisher | IEEE | | Volume, Issue, Pages | pp.1-6 | | Total page number | 6 | | Responsible for | Computations and text | | Author and coauthor | E. Hitzer, W. Benger, M. Niederwieser, R. Baran and F. Steinbacher | | Details | In this work we describe how to use the iterative closest point method for the adjustment of airborne laser scanning data strips in the framework of conformal geometric algebra, using rotors, translators, motors and differentiating w.r.t. bivector angles and translation vectors. | | URL for researchmap | https://ieeexplore.ieee.org/document/9322694 |
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35.
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Article
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Heisenberg's and Hardy's uncertainty principles for special relativistic Space-Time Fourier transformation Adv. Appl. Clifford Algebras 30(69),pp.1-29 (Collaboration) 2020/09
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| Language | English | | Publication Date | 2020/09 | | Type | Research Paper | | Peer Review | With peer review | | Title | Heisenberg's and Hardy's uncertainty principles for special relativistic Space-Time Fourier transformation | | Contribution Type | Joint Work | | Journal | Adv. Appl. Clifford Algebras | | Journal Type | Another Country | | Publisher | SpringerNature | | Volume, Issue, Pages | 30(69),pp.1-29 | | Total page number | 29 | | Responsible for | part of computations and text | | Author and coauthor | Youssef El Haoui, E. H.itzer, Said Fahlaoui | | Details | The special relativistic (space-time) Fourier transform (SFT) in Clifford algebra Cl_{(3,1)} of space-time, first introduced from a mathematical point of view in Hitzer (Adv Appl Clifford Algebras 17:497–517, 2007), extends the quaternionic Fourier transform to functions, fields and signals in space-time. The purpose of this paper is to advance the study of the SFT and investigate important properties such as continuity, Plancherel identity, Riemann–Lebesgue lemma, and to establish the associated Hausdorff–Young inequality. Moreover, using the observer related space-time split several uncertainty inequalities are established, including Heisenberg’s uncertainty principle and Hardy’s theorem. | | URL for researchmap | https://doi.org/10.1007/s00006-020-01093-5 |
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36.
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Article
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Exponential Factorization of Multivectors in Cl(p,q), p+q < 3 Mathematical Methods in the Applied Sciences Early View,pp.1-15 (Single) 2020/07
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| Language | English | | Publication Date | 2020/07 | | Type | Research Paper | | Peer Review | With peer review | | Title | Exponential Factorization of Multivectors in Cl(p,q), p+q < 3 | | Contribution Type | Single Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Volume, Issue, Pages | Early View,pp.1-15 | | Total page number | 15 | | Responsible for | All | | Authorship | Lead author | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer, Exponential Factorization of Multivectors in Cl(p,q), p+q < 3, Mathematical Methods in the Applied Sciences, pp. 1-15, First published: 15 July 2020. DOI: https://doi.org/10.1002/mma.6629. Preprint: https://vixra.org/pdf/2004.0408v2.pdf
Abstract: In this paper, we consider general multivector elements of Clifford algebras Cl(p,q), p+q<3, and study multivector factorization into products of exponentials and idempotents, where the exponents are blades of grades zero (scalar) to n (pseudoscalar). | | URL for researchmap | https://onlinelibrary.wiley.com/doi/10.1002/mma.6629 |
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37.
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Article
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First Steps of Vector Differential Calculus rxiv.org preprint archive (Single) 2020/06
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| Language | English | | Publication Date | 2020/06 | | Type | Technical Report, Preprint, etc. | | Title | First Steps of Vector Differential Calculus | | Contribution Type | Single Work | | Journal | rxiv.org preprint archive | | Journal Type | Another Country | | Publisher | rxiv.org | | Total page number | 31 | | Responsible for | Everything | | Author and coauthor | Eckhard Hitzer | | Details | This pap er treats the fundamentals of the vector dierential calcu-
lus part of universal geometric calculus. Geometric calculus simpli es
and uni es the structure and notation of mathematics for all of science
and engineering, and for technological applications. In order to make the
treatment self-contained, I rst compile all imp ortant geometric algebra
relationships, which are necessary for vector dierential calculus. Then
dierentiation by vectors is intro duced and a host of ma jor vector dif-
ferential and vector derivative relationships is proven explicitly in a very
elementary step by step approach. The pap er is thus intended to serve
as reference material, giving details, which are usually skipp ed in more
advanced discussions of the sub ject matter. | | URL for researchmap | https://rxiv.org/pdf/2006.0105v1.pdf |
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38.
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Article
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Bericht über 3. Workshop zu Nachhaltiger Universitätsentwicklung mit Schwerpunkt auf Bildung und Verwaltung (SUDem2020) 22nd Feb. 2020, ICU Preprint archive vixra.org 2020 (Single) 2020/04
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| Language | English | | Publication Date | 2020/04 | | Type | Conference Report, etc. | | Title | Bericht über 3. Workshop zu Nachhaltiger Universitätsentwicklung mit Schwerpunkt auf Bildung und Verwaltung (SUDem2020) 22nd Feb. 2020, ICU | | Contribution Type | Single Work | | Journal | Preprint archive vixra.org | | Journal Type | Another Country | | Publisher | vixra.org | | Volume, Issue, Pages | 2020 | | Total page number | 4 | | Responsible for | All | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer, Bericht über 3. Workshop zu Nachhaltiger Universitätsentwicklung mit Schwerpunkt auf Bildung und Verwaltung (SUDem2020) 22nd Feb. 2020, ICU, 4 pages, Language: German. Preprint: https://vixra.org/pdf/2004.0182v1.pdf | | URL for researchmap | https://vixra.org/pdf/2004.0182v1.pdf |
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39.
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Article
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第 3 回持続可能な大学の発展 「教育とマネージメント」 ( ワークショップ報告 2020 年 2 月 22 日 ), Vixra preprint server vixra.org 2020 (Single) 2020/04
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| Language | English | | Publication Date | 2020/04 | | Type | Review Article and Commentary (International Conference Proceedings) | | Title | 第 3 回持続可能な大学の発展 「教育とマネージメント」 ( ワークショップ報告 2020 年 2 月 22 日 ), | | Contribution Type | Single Work | | Journal | Vixra preprint server vixra.org | | Journal Type | Another Country | | Publisher | Vixra.org | | Volume, Issue, Pages | 2020 | | Total page number | 4 | | Responsible for | All content | | Authorship | Lead author | | International coauthorship | International coauthorship | | Author and coauthor | Author: Eckhard Hitzer
Translators: 本報告の翻訳：萩原義久 、木村護郎クリストフ | | Original author(s) | Eckhard Hitzer | | Details | E. Hitzer, 第 3 回持続可能な大学の発展 「教育とマネージメント」 ( ワークショップ報告 2020 年 2 月 22 日 ), 本報告の翻訳：萩原義久 、木村護郎クリストフ。4 pages, Japanese translation of report preprint submitted to Neues vom JSPS Club (German JSPS Alumni Association), March 2020, 9 images. Preprint (Japanese): https://vixra.org/pdf/2004.0180v1.pdf | | URL for researchmap | https://www.vixra.org/pdf/2004.0180v1.pdf |
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40.
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Article
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Invited review of “An Introduction to Clifford Algebras and Spinors. By Jayme Vaz, Jr. and Roldã o da Rocha, Jr. Oxford University Press, 2019. pp 256. Paperback, ISBN 9780198836285 price GBP 34.99.” Acta Crystallographica Section A: Foundations and Advances (ISSN 2053-2733) 76(2),pp.269-272 (Single) 2020
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| Language | English | | Publication Date | 2020 | | Type | Review Article or Commentary (Scientific Journal) | | Peer Review | With peer review | | Title | Invited review of “An Introduction to Clifford Algebras and Spinors. By Jayme Vaz, Jr. and Roldã o da Rocha, Jr. Oxford University Press, 2019. pp 256. Paperback, ISBN 9780198836285 price GBP 34.99.” | | Contribution Type | Single Work | | Journal | Acta Crystallographica Section A: Foundations and Advances (ISSN 2053-2733) | | Journal Type | Another Country | | Publisher | International Union of Crystallography | | Volume, Issue, Pages | 76(2),pp.269-272 | | Total page number | 4 | | Author and coauthor | Eckhard Hitzer | | Details | Invited review of “An Introduction to Clifford Algebras and Spinors. By Jayme Vaz, Jr. and Roldã o da Rocha, Jr. Oxford University Press, 2019. pp 256. Paperback, ISBN 9780198836285 price GBP 34.99.”, Acta Crystallographica Section A: Foundations and Advances (ISSN 2053-2733), Volume 76, Part 2, pages 269-272. URL: http://journals.iucr.org/a/issues/2020/02/00/xo0142/index.html, DOI: https://doi.org/10.1107/S2053273319017030 | | URL for researchmap | https://journals.iucr.org/a/issues/2020/02/00/xo0142/index.html |
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41.
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Article
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Polar decomposition of complexified quaternions and octonions Adv. Appl. Clifford Algebras 30(2:23),pp.1-12 (Collaboration) 2020
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| Language | English | | Publication Date | 2020 | | Type | Research Paper | | Peer Review | With peer review | | Title | Polar decomposition of complexified quaternions and octonions | | Contribution Type | Joint Work | | Journal | Adv. Appl. Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhauser | | Volume, Issue, Pages | 30(2:23),pp.1-12 | | Total page number | 12 | | Responsible for | Part of computations, part of text | | Author and coauthor | S. J. Sangwine, E. Hitzer | | Details | S. J. Sangwine, E. Hitzer, Polar decomposition of complexified quaternions and octonions, Adv. Appl. Clifford Algebras 30(2):23 (2020), 12 pages. DOI: 10.1007/s00006-020-1048-y. Preprint: http://repository.essex.ac.uk/24443/ | | URL for researchmap | https://link.springer.com/article/10.1007%2Fs00006-020-1048-y |
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42.
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Article
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Book review of: Real spinorial groups - A short mathematical introduction Mathematical Reviews 2019 (Single) 2019
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| Language | English | | Publication Date | 2019 | | Type | Book Review, etc. | | Invitation | With invitation | | Title | Book review of: Real spinorial groups - A short mathematical introduction | | Contribution Type | Single Work | | Journal | Mathematical Reviews | | Journal Type | Another Country | | Publisher | American Mathematical Society | | Volume, Issue, Pages | 2019 | | Total page number | 3 | | Responsible for | all | | Authorship | Lead author,Corresponding author | | Author and coauthor | Eckhard Hitzer | | Details | E. Hitzer, book review of: Xambó-Descamps, Sebastià, Real spinorial groups - A short mathematical introduction, Springer Briefs in Mathematics, SBMAC SpringerBriefs, Springer, Cham, 2018, 161 pages. Mathematical Reviews, MR3839319 (https://mathscinet.ams.org/mathscinet/). | | URL for researchmap | https://mathscinet.ams.org/mathscinet/ |
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43.
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Article
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Book review. G. Kuby, R. Spaemann (forword), J. P. Kirchner (translation), The Global Sexual Revolution: Destruction of Freedom in the Name of Freedom, Angelico Press, Kettering, USA, 2015 Sophia Journal of European Studies 11,pp.125-135 (Single) 2019
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| Language | English | | Publication Date | 2019 | | Type | Book Review, etc. | | Peer Review | With peer review | | Title | Book review. G. Kuby, R. Spaemann (forword), J. P. Kirchner (translation), The Global Sexual Revolution: Destruction of Freedom in the Name of Freedom, Angelico Press, Kettering, USA, 2015 | | Contribution Type | Single Work | | Journal | Sophia Journal of European Studies | | Journal Type | Japan | | Publisher | Sophia University, Tokyo, Japan. | | Volume, Issue, Pages | 11,pp.125-135 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | Open Access |
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44.
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Article
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Conic and Cyclidic Sections in Double Conformal Geometric Algebra G_{8,2} with Computing and Visualization using Gaalop Mathematical Methods in the Applied Sciences 43(1),pp.334-357 (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Research Paper | | Peer Review | With peer review | | Title | Conic and Cyclidic Sections in Double Conformal Geometric Algebra G_{8,2} with Computing and Visualization using Gaalop | | Contribution Type | Joint Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Volume, Issue, Pages | 43(1),pp.334-357 | | Total page number | 24 | | Responsible for | Part of text and part of computations. | | Author and coauthor | Robert B. Easter, Eckhard Hitzer | | Details | R.B. Easter, E. Hitzer, Conic and Cyclidic Sections in Double Conformal Geometric Algebra G_{8,2} with Computing and Visualization using Gaalop, Mathematical Methods in the Applied Sciences, 43(1), pp. 334-357, 2020. DOI: 10.1002/mma.5887. | | URL for researchmap | https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.5887 |
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45.
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Article
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Conic and Cyclidic Sections in Double Conformal Geometric Algebra G_{8,2} with Computing and Visualization using Gaalop, Mathematical Methods in the Applied Sciences Mathematical Methods in the Applied Sciences (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Research Paper | | Peer Review | With peer review | | Title | Conic and Cyclidic Sections in Double Conformal Geometric Algebra G_{8,2} with Computing and Visualization using Gaalop, Mathematical Methods in the Applied Sciences | | Contribution Type | Joint Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Responsible for | Part of text and computations. | | Author and coauthor | Robert B. Easter, Eckhard Hitzer | | Details | DOI: 10.1002/mma.5887 |
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46.
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Article
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Conic Conformal Geometric Algebra and Simplified Versors for Rotation, Translation and Scaling Adv. of App. Cliff. Algs. 29(5),pp.96:1-96:16 (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Research Paper | | Peer Review | With peer review | | Title | Conic Conformal Geometric Algebra and Simplified Versors for Rotation, Translation and Scaling | | Contribution Type | Joint Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 29(5),pp.96:1-96:16 | | Responsible for | Most of text and computations. | | Author and coauthor | Eckhard Hitzer, Stephen J. Sangwine |
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47.
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Article
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Construction of multivector inverse for Clifford algebras over $2m+1$-dimensional vector spaces from multivector inverse for Clifford algebras over $2m$-dimensional vector spaces Adv. of App. Cliff. Algs. 29(2),pp.29:1-29:22 (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Research Paper | | Peer Review | With peer review | | Title | Construction of multivector inverse for Clifford algebras over $2m+1$-dimensional vector spaces from multivector inverse for Clifford algebras over $2m$-dimensional vector spaces | | Contribution Type | Joint Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 29(2),pp.29:1-29:22 | | Responsible for | Symbolic algebraic computations and part of text. | | Author and coauthor | Eckhard Hitzer, Stephen J. Sangwine |
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48.
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Cubic Curves and Cubic Surfaces from Contact Points in Conformal Geometric Algebra Proceedings of Workshop ENGAGE 2019 at CGI 2019 with Springer LNCS, April 2019 11542,pp.535-545 (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Cubic Curves and Cubic Surfaces from Contact Points in Conformal Geometric Algebra | | Contribution Type | Joint Work | | Journal | Proceedings of Workshop ENGAGE 2019 at CGI 2019 with Springer LNCS, April 2019 | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 11542,pp.535-545 | | Responsible for | Most of computations and text. | | Author and coauthor | Eckhard Hitzer, Dietmar Hildenbrand | | Details | in M. Gavrilova et al (eds.), Proceedings of Workshop ENGAGE 2019 at CGI 2019 with Springer LNCS, volume 11542, April 2019. In: Advances in Computer Graphics - 36th Computer Graphics International Conference, CGI 2019, Calgary, AB, Canada, June 17-20, 2019, Proceedings. 2019, pp. 535–545. DOI: 10.1007/978-3-030-22514-8\_53 |
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49.
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Article
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Exponential Factorization and Polar Decomposition of Multivectors in Cl(p,q), p+q <= 3 Preprint archive vixra.org (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Technical Report, Preprint, etc. | | Title | Exponential Factorization and Polar Decomposition of Multivectors in Cl(p,q), p+q <= 3 | | Contribution Type | Joint Work | | Journal | Preprint archive vixra.org | | Journal Type | Another Country | | Publisher | vixra.org | | Total page number | 18 | | Responsible for | Part of computations, part of text | | Author and coauthor | Eckhard Hitzer, Stephen J. Sangwine | | Details | E. Hitzer, S.J. Sangwine, Exponential Factorization and Polar Decomposition of Multivectors in Cl(p,q), p+q <= 3, 18 pages, Nov. 2019. Preprint: https://vixra.org/pdf/1911.0275v2.pdf | | URL for researchmap | https://vixra.org/pdf/1911.0275v2.pdf |
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50.
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Article
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Feature Extraction using Conformal Geometric Algebra for AdaBoost Algorithm based In-plane Rotated Face Detection Adv. of App. Cliff. Algs. 29(4),pp.61:1-61:19 (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Research Paper | | Peer Review | With peer review | | Title | Feature Extraction using Conformal Geometric Algebra for AdaBoost Algorithm based In-plane Rotated Face Detection | | Contribution Type | Joint Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 29(4),pp.61:1-61:19 | | Responsible for | Part of text. | | Author and coauthor | Tuan M. Pham, Danh C. Doan & Eckhard Hitzer | | Details | Adv. of App. Cliff. Algs. 29(4):61 (First Online: 02 July 2019), 19 pages, DOI: 10.1007/s00006-019-0976-x |
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51.
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Foundations of Conic Conformal Geometric Algebra and Compact Versors for Rotation, Translation and Scaling Adv. of App. Cliff. Algs. 29(5:96),pp.1-16 (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Research Paper | | Peer Review | With peer review | | Title | Foundations of Conic Conformal Geometric Algebra and Compact Versors for Rotation, Translation and Scaling | | Contribution Type | Joint Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhauser | | Volume, Issue, Pages | 29(5:96),pp.1-16 | | Total page number | 16 | | Responsible for | Theory, equations, text | | Author and coauthor | Eckhard Hitzer, Stephen J. Sangwine | | Details | E. Hitzer, S.J. Sangwine, Foundations of Conic Conformal Geometric Algebra and Compact Versors for Rotation, Translation and Scaling, Adv. of App. Cliff. Algs., (2019) 29(5):96 (First Online: 04 October 2019), 16 pages, DOI: 10.1007/s00006-019-1016-6. Preprint: http://vixra.org/pdf/1905.0030v2.pdf | | URL for researchmap | https://link.springer.com/article/10.1007%2Fs00006-019-1016-6 |
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52.
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Generalized Uncertainty Principles associated with the Quaternionic Offset Linear CanonicalTransform Preprint archive arxiv.org (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Technical Report, Preprint, etc. | | Title | Generalized Uncertainty Principles associated with the Quaternionic Offset Linear CanonicalTransform | | Contribution Type | Joint Work | | Journal | Preprint archive arxiv.org | | Journal Type | Another Country | | Publisher | Cornell University | | Total page number | 15 | | Responsible for | Part of computation, part of text | | Author and coauthor | Youssef El Haoui, Said Fahlaoui, Eckhard Hitzer | | Details | Youssef El Haoui, Said Fahlaoui, Eckhard Hitzer, Generalized Uncertainty Principles associated with the Quaternionic Offset Linear CanonicalTransform, 15 pages, Sep. 2019. Preprint: https://arxiv.org/pdf/1807.04068.pdf | | URL for researchmap | https://arxiv.org/pdf/1807.04068.pdf |
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53.
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Article
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Polar decomposition of complexified quaternions and octonions Technical Report, University of Essex, UK (CES-535),pp.1-8 (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Technical Report, Preprint, etc. | | Title | Polar decomposition of complexified quaternions and octonions | | Contribution Type | Joint Work | | Journal | Technical Report, University of Essex, UK | | Journal Type | Another Country | | Publisher | University of Essex, UK | | Volume, Issue, Pages | (CES-535),pp.1-8 | | Responsible for | Part of text and computations. | | Author and coauthor | Stephen J. Sangwine, Eckhard Hitzer | | Details | We present a hitherto unknown polar representation of complexified quaternions (also known asbiquaternions), also applicable to complexified octonions. The complexified quaternion is factored intothe product of two exponentials, one trigonometric or circular, and one hyperbolic. The trigonometricexponential is a real quaternion, the hyperbolic exponential has a real scalar part and imaginary vectorpart. This factorisation is shown to be isomorphic to the polar decomposition of linear algebra. |
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54.
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Report on Visit of Architects Sitka and Kaserer in Saalfelden, and Social Center Pillertal in Fieberbrunn Near St. Johann, in Tyrol, Austria, We. 13 Mar. 2019 Preprint server Vixra.org, category Social Science pp.1-6 (Single) 2019
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| Language | English | | Publication Date | 2019 | | Type | Technical Report, Preprint, etc. | | Title | Report on Visit of Architects Sitka and Kaserer in Saalfelden, and Social Center Pillertal in Fieberbrunn Near St. Johann, in Tyrol, Austria, We. 13 Mar. 2019 | | Contribution Type | Single Work | | Journal | Preprint server Vixra.org, category Social Science | | Journal Type | Another Country | | Publisher | Vixra.org | | Volume, Issue, Pages | pp.1-6 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | Part I. At the architect’s office Sitka and Kaserer, describes a meeting with Mr. A. Planegger, the architect of the Social Center Pillerseetal in Fieberbrunn, which is constructed with prefabricated modern cross laminated timber (CLT) modules, sustainable, cost efficient, and highly energy efficient. Part II: Visit of the Social Center Pillerseetal, describes a tour through the Social Center, guided by Director of Care Mr. Herbert Breitmayer. The biggest discovery is the unbelievable success of consequently putting Dr. Maria Riedl's "Integrative Care Concept" into practice. |
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55.
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Special relativistic Fourier transformation and convolutions Mathematical Methods in the Applied Sciences 42(7),pp.2244-2255 (Single) 2019
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| Language | English | | Publication Date | 2019 | | Type | Research Paper | | Peer Review | With peer review | | Title | Special relativistic Fourier transformation and convolutions | | Contribution Type | Single Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Volume, Issue, Pages | 42(7),pp.2244-2255 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | Mathematical Methods in the Applied Sciences, First published: 04 Mar. 2019, Vol. 42, Issue 7, pp. 2244–2255, 2019, DOI: 10.1002/mma.5502 |
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56.
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Three-dimensional quadrics in conformal geometric algebras and their versor transformations Adv. of App. Cliff. Algs. 29(3:46),pp.1-16 (Single) 2019
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| Language | English | | Publication Date | 2019 | | Type | Research Paper | | Peer Review | With peer review | | Title | Three-dimensional quadrics in conformal geometric algebras and their versor transformations | | Contribution Type | Single Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhauser | | Volume, Issue, Pages | 29(3:46),pp.1-16 | | Total page number | 16 | | Responsible for | Whole work. | | Author and coauthor | Eckhard Hitzer | | Details | [8] E. H. Three-dimensional quadrics in conformal geometric algebras and their versor transformations, Adv. of App. Cliff. Algs., 29(3):46, pp. 1-16, 2019. DOI: 10.1007/s00006-019-0964-1, preprint: http://vixra.org/pdf/1902.0401v4.pdf | | URL for researchmap | http://vixra.org/pdf/1902.0401v4.pdf |
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57.
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Three-dimensional quadrics in extended conformal geometric algebras of higher dimensions from control points, implicit equations and axis alignment Adv. of App. Cliff. Algs. 29(3),pp.57:1-57:22 (Collaboration) 2019
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| Language | English | | Publication Date | 2019 | | Type | Research Paper | | Peer Review | With peer review | | Title | Three-dimensional quadrics in extended conformal geometric algebras of higher dimensions from control points, implicit equations and axis alignment | | Contribution Type | Joint Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 29(3),pp.57:1-57:22 | | Responsible for | Part of computations and part of text. | | Author and coauthor | S. Breuils, L. Fuchs, E. Hitzer, V. Nozick and A. Sugimoto | | Details | DOI: 10.1007/s00006-019-0974-z |
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58.
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Offene Vorlesung am 4. Juni 2018 an der International Christian University in Tokyo zu „Building Energy Efficiency, Frameworks in Germany and Europe, Progress in Germany since 1970ies (oil crisis)“ und Executive Luncheon unterstützt vom JSPS-Club Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. 2018(72/3),pp.8-9 (Single) 2018/03
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| Language | English | | Publication Date | 2018/03 | | Type | Review Article or Commentary (Magazine) | | Title | Offene Vorlesung am 4. Juni 2018 an der International Christian University in Tokyo zu „Building Energy Efficiency, Frameworks in Germany and Europe, Progress in Germany since 1970ies (oil crisis)“ und Executive Luncheon unterstützt vom JSPS-Club | | Contribution Type | Single Work | | Journal | Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Journal Type | Another Country | | Publisher | Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Volume, Issue, Pages | 2018(72/3),pp.8-9 | | Total page number | 2 | | Responsible for | Everything. | | Authorship | Lead author | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer | | Details | Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V., Nr. 03 / 2018, Ausgabe 72, pp. 8-9. Open Access: https://www.jsps-club.de/veroeffentlichungen/neues-vom-club/2018/03/ , PDF: https://www.jsps-club.de/fileadmin/veroeffentlichungen/2018_NvC/2018_03_NvC.pdf | | URL for researchmap | https://www.jsps-club.de/fileadmin/veroeffentlichungen/2018_NvC/2018_03_NvC.pdf |
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59.
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Article
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Application of Conformal Geometric Algebra to In-plane Rotated Face Detection by AdaBoost-based Algorithm Early Proceedings of the AGACSE 2018 Conference pp.117-126 (Collaboration) 2018
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| Language | English | | Publication Date | 2018 | | Type | Research Paper | | Peer Review | With peer review | | Title | Application of Conformal Geometric Algebra to In-plane Rotated Face Detection by AdaBoost-based Algorithm | | Contribution Type | Joint Work | | Journal | Early Proceedings of the AGACSE 2018 Conference | | Journal Type | Another Country | | Publisher | ISBN: 978-84-9880-703-5, Printed in Barcelona (Spain), 2018 | | Volume, Issue, Pages | pp.117-126 | | Responsible for | Part of text and structure. | | Author and coauthor | [11] T. M. Pham. D. C. Doan, E. Hitzer | | Details | in Early Proceedings of the AGACSE 2018 Conference, Edt. by S. XAMBÓ-DESCAMPS, C. LAVOR, L. A. FERNANDES, M. JARDIM, ISBN: 978-84-9880-703-5, Printed in Barcelona (Spain), 2018, pp. 117-126. Open Access |
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60.
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Article
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European Trends in Wood Biomass Energy Cogeneration Sophia Journal of European Studies 10,pp.191-205 (Single) 2018
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| Language | English | | Publication Date | 2018 | | Type | Research Paper (Bulletin of University/Institution) | | Peer Review | With peer review | | Title | European Trends in Wood Biomass Energy Cogeneration | | Contribution Type | Single Work | | Journal | Sophia Journal of European Studies | | Journal Type | Japan | | Publisher | Sophia University, Tokyo, Japan | | Volume, Issue, Pages | 10,pp.191-205 | | Responsible for | Everything | | Author and coauthor | Eckhard Hitzer |
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61.
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Quadric Conformal Geometric Algebra of R^{9,6} Adv. of App. Cliff. Algs. 28(2),pp.35:1-35:16 (Collaboration) 2018
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| Language | English | | Publication Date | 2018 | | Type | Research Paper | | Peer Review | With peer review | | Title | Quadric Conformal Geometric Algebra of R^{9,6} | | Contribution Type | Joint Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 28(2),pp.35:1-35:16 | | Responsible for | Algebraic framework, part of text | | Author and coauthor | [14] S. Breuils, V. Nozick, A. Sugimoto, E.Hitzer | | Details | DOI: https://doi.org/10.1007/s00006-018-0851-1 |
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62.
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Renewable Energy and Energy Efficiency for Japanese RE100 Universities program of 3rd Japanese-German Workshop on Renewable Energies, Tokyo, Japan, 17-19 Oct. 2018. (Single) 2018
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| Language | English | | Publication Date | 2018 | | Type | Summary of Presentation (International Conference) | | Title | Renewable Energy and Energy Efficiency for Japanese RE100 Universities | | Contribution Type | Single Work | | Journal | program of 3rd Japanese-German Workshop on Renewable Energies, Tokyo, Japan, 17-19 Oct. 2018. | | Journal Type | Japan | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | Abstract No. 1-20 in program of 3rd Japanese-German Workshop on Renewable Energies, Tokyo, Japan, 17-19 Oct. 2018. |
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63.
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Article
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Three-dimensional quadrics in hybrid conformal geometric algebra of higher dimensions Early Proceedings of the AGACSE 2018 Conference (Single) 2018
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| Language | English | | Publication Date | 2018 | | Type | Research Paper | | Peer Review | With peer review | | Invitation | With invitation | | Title | Three-dimensional quadrics in hybrid conformal geometric algebra of higher dimensions | | Contribution Type | Single Work | | Journal | Early Proceedings of the AGACSE 2018 Conference | | Journal Type | Another Country | | Publisher | ISBN: 978-84-9880-703-5, Printed in Barcelona (Spain), 2018 | | Responsible for | Everything | | Author and coauthor | Eckhard Hitzer | | Details | in Early Proceedings of the AGACSE 2018 Conference, Edt. by S. XAMBÓ-DESCAMPS, C. LAVOR, L. A. FERNANDES, M. JARDIM, ISBN: 978-84-9880-703-5, Printed in Barcelona (Spain), 2018, pp. 17-26. Open Access |
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64.
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Article
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Triple Conformal Geometric Algebra for Cubic Plane Curves Mathematical Methods in the Applied Sciences 41(11),pp.4088-4105 (Collaboration) 2018
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| Language | English | | Publication Date | 2018 | | Type | Research Paper | | Peer Review | With peer review | | Title | Triple Conformal Geometric Algebra for Cubic Plane Curves | | Contribution Type | Joint Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Volume, Issue, Pages | 41(11),pp.4088-4105 | | Responsible for | Part of: computations and text. | | Author and coauthor | Robert Benjamin Easter, Eckhard Hitzer | | Details | DOI: 10.1002/mma.4597 |
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65.
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Article
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Workshop Sustainable University Development mit Fokus auf Energieeffizienz (SUDee2018) an der International Christian University Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. 72(3),pp.10-11 (Single) 2018
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| Language | English | | Publication Date | 2018 | | Type | Conference Report, etc. | | Title | Workshop Sustainable University Development mit Fokus auf Energieeffizienz (SUDee2018) an der International Christian University | | Contribution Type | Single Work | | Journal | Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Journal Type | Another Country | | Publisher | Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Volume, Issue, Pages | 72(3),pp.10-11 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer |
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66.
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SUDre - Workshop über nachhaltige universitäre Energieversorgung in Mitaka/Tōkyō (German) Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. 2017(68/3),pp.3-5 (Collaboration) 2017/03
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| Language | English | | Publication Date | 2017/03 | | Type | Review Article and Commentary (International Conference Proceedings) | | Title | SUDre - Workshop über nachhaltige universitäre Energieversorgung in Mitaka/Tōkyō (German) | | Contribution Type | Joint Work | | Journal | Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Journal Type | Another Country | | Publisher | Deutsche Gesellschaft der JSPS Stipendiaten e.V. | | Volume, Issue, Pages | 2017(68/3),pp.3-5 | | Total page number | 3 | | Responsible for | Most part of text. | | Authorship | Last author | | International coauthorship | International coauthorship | | Author and coauthor | O. Karthaus, W. Wunderlich, E. Hitzer | | Original author(s) | O. Karthaus, W. Wunderlich, E. Hitzer | | Details | O. Karthaus, W. Wunderlich, E. Hitzer, SUDre - Workshop über nachhaltige universitäre Energieversorgung in Mitaka/Tōkyō (German), Neues vom JSPS-Club, Deutsche Gesellschaft der JSPS Stipendiaten e.V., Nr. 03 / 2017, Ausgabe 68, pp. 3-5. Open Access: https://www.jsps-club.de/veroeffentlichungen/neues-vom-club/2017/03/ , PDF: https://www.jsps-club.de/fileadmin/veroeffentlichungen/2017_NvC/2017_03_NvC.pdf | | URL for researchmap | https://www.jsps-club.de/fileadmin/veroeffentlichungen/2017_NvC/2017_03_NvC.pdf |
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67.
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Double Conformal Geometric Algebra Adv. of App. Cliff. Algs. 27(3),pp.2175-2199 (Collaboration) 2017
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| Language | English | | Publication Date | 2017 | | Type | Research Paper | | Peer Review | With peer review | | Title | Double Conformal Geometric Algebra | | Contribution Type | Joint Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Volume, Issue, Pages | 27(3),pp.2175-2199 | | Responsible for | Part of: computations and text. | | Author and coauthor | Robert Benjamin Easter, Eckhard Hitzer | | Details | DOI: 10.1007/s00006-017-0784-0 |
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68.
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Double Conformal Space-Time Algebra AIP Conf. Proc. 1798(020066),pp.1-10 (Collaboration) 2017
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| Language | English | | Publication Date | 2017 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Double Conformal Space-Time Algebra | | Contribution Type | Joint Work | | Journal | AIP Conf. Proc. | | Journal Type | Another Country | | Publisher | American Institute of Physics Publishing | | Volume, Issue, Pages | 1798(020066),pp.1-10 | | Responsible for | Algebraic computations and text (shared). | | Author and coauthor | Robert Benjamin Easter, Eckhard Hitzer | | Details | S. Sivasundaram (ed.), International Conference in Nonlinear Problems in Aviation and Aerospace ICNPAA 2016,
DOI: 10.1063/1.4972658 |
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69.
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Article
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General one-sided Clifford Fourier transform, convolution products in the spatial and frequency domains, and auto-correlation theorems Proceedings of the 17th International Conference on Computational and Math. Methods in Sci. and Eng. pp.1042-1053 (Single) 2017
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| Language | English | | Publication Date | 2017 | | Type | Research Paper | | Peer Review | With peer review | | Title | General one-sided Clifford Fourier transform, convolution products in the spatial and frequency domains, and auto-correlation theorems | | Contribution Type | Single Work | | Journal | Proceedings of the 17th International Conference on Computational and Math. Methods in Sci. and Eng. | | Journal Type | Another Country | | Volume, Issue, Pages | pp.1042-1053 | | Author and coauthor | Eckhard Hitzer |
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70.
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General steerable two-sided Clifford Fourier transform, convolution and Mustard convolution Adv. of App. Cliff. Algs. 27(1),pp.2215-2234 (Single) 2017
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| Language | English | | Publication Date | 2017 | | Type | Research Paper | | Peer Review | With peer review | | Title | General steerable two-sided Clifford Fourier transform, convolution and Mustard convolution | | Contribution Type | Single Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland | | Volume, Issue, Pages | 27(1),pp.2215-2234 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer |
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71.
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General two-sided quaternion Fourier transform, convolution and Mustard convolution Adv. of App. Cliff. Algs. 27(1),pp.381-395 (Single) 2017
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| Language | English | | Publication Date | 2017 | | Type | Research Paper | | Peer Review | With peer review | | Title | General two-sided quaternion Fourier transform, convolution and Mustard convolution | | Contribution Type | Single Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland | | Volume, Issue, Pages | 27(1),pp.381-395 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | DOI: 10.1007/s00006-016-0684-8 |
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72.
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Article
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Multivector and multivector matrix inverses in real Clifford algebras Appl. Math. and Comp. 311(C),pp.375-389 (Collaboration) 2017
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| Language | English | | Publication Date | 2017 | | Type | Research Paper | | Peer Review | With peer review | | Title | Multivector and multivector matrix inverses in real Clifford algebras | | Contribution Type | Joint Work | | Journal | Appl. Math. and Comp. | | Journal Type | Another Country | | Publisher | Elsevier | | Volume, Issue, Pages | 311(C),pp.375-389 | | Responsible for | Algebraic computations and text. | | Author and coauthor | Eckhard Hitzer, Stephen J. Sangwine | | Details | DOI: 10.1016/j.amc.2017.05.027 |
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73.
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Article
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Quaternionic Wiener-Khinchine theorems and spectral representation of convolution with steerable two-sided quaternion Fourier transform Adv. of App. Cliff. Algs. 27(2),pp.1313-1328 (Single) 2017
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| Language | English | | Publication Date | 2017 | | Type | Research Paper | | Peer Review | With peer review | | Title | Quaternionic Wiener-Khinchine theorems and spectral representation of convolution with steerable two-sided quaternion Fourier transform | | Contribution Type | Single Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland | | Volume, Issue, Pages | 27(2),pp.1313-1328 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | DOI: 10.1007/s00006-016-0744-0 |
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74.
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Christ Centered Stewardship for the Environment Vixra Preprint Server, General Science and Philosophy. (Single) 2016
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| Language | English | | Publication Date | 2016 | | Type | Technical Report, Preprint, etc. | | Peer Review | With peer review | | Title | Christ Centered Stewardship for the Environment | | Contribution Type | Single Work | | Journal | Vixra Preprint Server, General Science and Philosophy. | | Journal Type | Another Country | | Publisher | Vixra Preprint Server. | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | The recent Encyclical Laudato Si by Pope Francis also highlights environmental stewardship in broad terms. In contrast to this generality, our reflections particularly advance with a fresh look at the person of Christ, his role in the creation of our world as portrayed in the Bible, the origin and commission of man, and the relation of man and Christ. In this triangle of Christ, world and man, all three are appear related in the principle of Christ centered stewardship (of man) for the (created) environment. To gain insight we review some essential Biblical passage from both the Old and New Testaments. The second half of this work endeavors initial application in the fields of purchasing, building, energy, policy and education. Our approach is that of a natural scientist (of theoretical physics) and convinced Christian with interest in environmental questions. |
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75.
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Clifford Multivector Toolbox (for MATLAB) Adv. of App. Cliff. Algs. (Collaboration) 2016
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| Language | English | | Publication Date | 2016 | | Type | Research Paper | | Peer Review | With peer review | | Title | Clifford Multivector Toolbox (for MATLAB) | | Contribution Type | Joint Work | | Journal | Adv. of App. Cliff. Algs. | | Journal Type | Another Country | | Publisher | Birkhauser / Springer |
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76.
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Conic and Cyclidic Sections in Double Conformal Geometric Algebra G8,2 Proceedings of 計測自動制御学会システム・情報部門学術講演会2016 (SSI 2016), Session SS11 pp.866-871 (Collaboration) 2016
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| Language | English | | Publication Date | 2016 | | Type | Research Paper (Material for Workshop, Symposium, etc.) | | Title | Conic and Cyclidic Sections in Double Conformal Geometric Algebra G8,2 | | Contribution Type | Joint Work | | Journal | Proceedings of 計測自動制御学会システム・情報部門学術講演会2016 (SSI 2016), Session SS11 | | Journal Type | Japan | | Publisher | The Society of Instrument and Control Engineers, Japan | | Volume, Issue, Pages | pp.866-871 | | Responsible for | Part of computations and text. | | Author and coauthor | Robert B. Easter, Eckhard Hitzer | | Details | Proceedings of 計測自動制御学会システム・情報部門学術講演会2016 (SSI 2016), Session SS11, pp. 866-871, 6-8 Dec. 2016, Otsu, Shiga, Japan. |
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77.
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Double Conformal Geometric Algebra for Quadrics and Darboux Cyclides Association for Computing Machinery Digital Library pp.93-96 (Collaboration) 2016
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| Language | English | | Publication Date | 2016 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Double Conformal Geometric Algebra for Quadrics and Darboux Cyclides | | Contribution Type | Joint Work | | Journal | Association for Computing Machinery Digital Library | | Journal Type | Another Country | | Publisher | Association for Computing Machinery | | Volume, Issue, Pages | pp.93-96 | | Responsible for | Algebraic computations. | | Author and coauthor | Robert Benjamin Easter, Eckhard Hitzer | | Details | CGI '16, Proceedings of the 33rd Computer Graphics International,
DOI: 10.1145/2949035.2949059 |
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78.
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Operator Exponentials for the Clifford Fourier Transform on Multivector Fields in Detail Advances in Applied Clifford Algebras 26(3),pp.953-968 (Collaboration) 2016
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| Language | Japanese | | Publication Date | 2016 | | Type | Research Paper | | Peer Review | With peer review | | Title | Operator Exponentials for the Clifford Fourier Transform on Multivector Fields in Detail | | Contribution Type | Joint Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhauser / Springer | | Volume, Issue, Pages | 26(3),pp.953-968 | | Author and coauthor | David Eelbode |
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79.
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The Quaternion Domain Fourier Transform and its Properties Advances in Applied Clifford Algebras 26(3),pp.969-984 (Single) 2016
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| Language | Japanese | | Publication Date | 2016 | | Type | Research Paper | | Peer Review | With peer review | | Title | The Quaternion Domain Fourier Transform and its Properties | | Contribution Type | Single Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhauser / Springer | | Volume, Issue, Pages | 26(3),pp.969-984 |
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80.
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Article
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Demystification of the Geometric Fourier Transforms and resulting Convolution Theorems Mathematical Methods in the Applied Sciences (Collaboration) 2015/09
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| Language | English | | Publication Date | 2015/09 | | Type | Research Paper | | Peer Review | With peer review | | Title | Demystification of the Geometric Fourier Transforms and resulting Convolution Theorems | | Contribution Type | Joint Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Author and coauthor | R. Bujack, E. Hitzer, G. Scheuermann |
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81.
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Moment Invariants for 3D Flow Fields via Normalization Proc The 8th IEEE Pacific Vis Symp (PacificVis 2015), Zhejiang Univ, Hangzhou, China, April 2015 pp.9-16 (Collaboration) 2015/04
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| Language | English | | Publication Date | 2015/04 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Moment Invariants for 3D Flow Fields via Normalization | | Contribution Type | Joint Work | | Journal | Proc The 8th IEEE Pacific Vis Symp (PacificVis 2015), Zhejiang Univ, Hangzhou, China, April 2015 | | Journal Type | Another Country | | Publisher | IEEE | | Volume, Issue, Pages | pp.9-16 | | Author and coauthor | R. Bujack, I. Hotz, G. Scheuermann, E. Hitzer | | Details | Journal Name: Proceedings of The 8th IEEE Pacific Visualization Symposium (PacificVis 2015), Zhejiang University, Hangzhou, China, 14-17 April 2015 | | DOI | 10.1109/PACIFICVIS.2015.7156350 |
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82.
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Prospects of Modern Wood Gas Cogeneration Renewable Energy Supply in Japan − Case Study of ICU Vixra preprint server, Economics and Finance. (Collaboration) 2015
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| Language | English | | Publication Date | 2015 | | Type | Technical Report, Preprint, etc. | | Title | Prospects of Modern Wood Gas Cogeneration Renewable Energy Supply in Japan − Case Study of ICU | | Contribution Type | Joint Work | | Journal | Vixra preprint server, Economics and Finance. | | Journal Type | Another Country | | Publisher | Vixra preprint server. | | Responsible for | Most of text. | | Author and coauthor | E. Hitzer, N. Miyazaki, M. Langager, T. Kibe | | Details | In this article we introduce scalable modern commercial wood gas cogeneration technology of micro scale, beginning at 35-45 kW electric power, scalable up to 800kW electric power, as offered by several international companies. Cogeneration means to use both electricity and heat, which leads to an overall efficiency of converting the chemical energy in wood of up to 90%. We discuss aspects of technology, sustainability, forest ecology, local and international fuel quality standards, long term cost efficiency, potential for attracting various forms of official financial support and potential risks involved. |
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83.
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The orthogonal planes split of quaternions and its relation to quaternion geometry of rotations Proc 30th Int Coll on Gr Th Met i Phys, 14-18 Jul 2014, Ghent, Belgium, IOP J Phys: Conf Ser (JPCS) 597 (Single) 2015
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| Language | English | | Publication Date | 2015 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | The orthogonal planes split of quaternions and its relation to quaternion geometry of rotations | | Contribution Type | Single Work | | Journal | Proc 30th Int Coll on Gr Th Met i Phys, 14-18 Jul 2014, Ghent, Belgium, IOP J Phys: Conf Ser (JPCS) | | Journal Type | Another Country | | Volume, Issue, Pages | 597 | | Author and coauthor | E. Hitzer | | DOI | 10.1088/1742-6596/597/1/012042 |
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84.
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The true riches of Japan: High tech and natural energy can secure Japan’s peace and prosperity, and give a new sustainable peace and prosperity dimension to its overseas development aid Peace Reports of the International Christian University Peace Research Institute 10(2),pp.9-11 (Single) 2015
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| Language | English | | Publication Date | 2015 | | Type | Research Paper | | Title | The true riches of Japan: High tech and natural energy can secure Japan’s peace and prosperity, and give a new sustainable peace and prosperity dimension to its overseas development aid | | Contribution Type | Single Work | | Journal | Peace Reports of the International Christian University Peace Research Institute | | Journal Type | Japan | | Publisher | International Christian University Peace Research Institute, Mitaka, Japan. | | Volume, Issue, Pages | 10(2),pp.9-11 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer |
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85.
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Moment Invariants for 2D Flow Fields via Normalization in Detail pp.916-929 (Collaboration) 2014/11
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| Language | English | | Publication Date | 2014/11 | | Type | Research Paper | | Peer Review | With peer review | | Title | Moment Invariants for 2D Flow Fields via Normalization in Detail | | Contribution Type | Joint Work | | Journal Type | Another Country | | Volume, Issue, Pages | pp.916-929 | | Details | DOI 10.1109/TVCG.2014.2369036 |
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86.
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Article
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Book review of: Foundations of Geometric Algebra Computing Mathematical Reviews 2014 (Single) 2014
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| Language | English | | Publication Date | 2014 | | Type | Book Review, etc. | | Invitation | With invitation | | Title | Book review of: Foundations of Geometric Algebra Computing | | Contribution Type | Single Work | | Journal | Mathematical Reviews | | Journal Type | Another Country | | Publisher | American Mathematical Society | | Volume, Issue, Pages | 2014 | | Total page number | 2 | | Responsible for | all | | Authorship | Lead author,Corresponding author | | Author and coauthor | Eckhard Hitzer | | Details | E. Hitzer, book review of: Hildenbrand, D., Foundations of Geometric Algebra Computing, Springer, Berlin, 2013, 196 pages. Mathematical Reviews, MR 3013683 (https://mathscinet.ams.org/mathscinet/). | | URL for researchmap | https://mathscinet.ams.org/mathscinet/ |
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87.
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Book review of: New foundations in mathematics. The geometric concept of number Mathematical Reviews (Single) 2014
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| Language | English | | Publication Date | 2014 | | Type | Book Review, etc. | | Invitation | With invitation | | Title | Book review of: New foundations in mathematics. The geometric concept of number | | Contribution Type | Single Work | | Journal | Mathematical Reviews | | Journal Type | Another Country | | Publisher | American Mathematical Society | | Total page number | 2 | | Responsible for | all | | Authorship | Lead author,Corresponding author | | Author and coauthor | Eckhard Hitzer | | Details | E. Hitzer, book review of: Sobczyk, G., New foundations in mathematics. The geometric concept of number, Birkhaeuser/Springer, New York, 2013, 384 pages. Mathematical Reviews, MR 3014720 (mathscinet.ams.org/mathscinet/). | | URL for researchmap | https://mathscinet.ams.org/mathscinet/ |
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88.
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Customized TRS Invariants for 2D Vector Fields via Moment Normalization Pattern Recognition Letters 46,pp.46-59 (Collaboration) 2014
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| Language | English | | Publication Date | 2014 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Customized TRS Invariants for 2D Vector Fields via Moment Normalization | | Contribution Type | Joint Work | | Journal | Pattern Recognition Letters | | Volume, Issue, Pages | 46,pp.46-59 | | Author and coauthor | R. Bujack, M. Hlawitschka, G. Scheuermann, E. Hitzer | | DOI | 10.1016/j.patrec.2014.05.005 |
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89.
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Detection of Outer Rotations on 3D-Vector Fields with Iterative Geometric Correlation and its Efficiency Adv. Appl. Clifford Alg. 24(2),pp.403-421 (Collaboration) 2014
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| Language | English | | Publication Date | 2014 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Detection of Outer Rotations on 3D-Vector Fields with Iterative Geometric Correlation and its Efficiency | | Contribution Type | Joint Work | | Journal | Adv. Appl. Clifford Alg. | | Publisher | Springer/Birkhauser | | Volume, Issue, Pages | 24(2),pp.403-421 | | Author and coauthor | R. Bujack, G. Scheuermann, E. Hitzer | | DOI | 10.1007/s00006-013-0411-7 |
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90.
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Moment Invariants for 2D Flow Fields Using Normalization Proceedings of IEEE Pacific Visualization Symposium (PacificVis) 2014 pp.41-48 (Collaboration) 2014
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| Language | English | | Publication Date | 2014 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Moment Invariants for 2D Flow Fields Using Normalization | | Contribution Type | Joint Work | | Journal | Proceedings of IEEE Pacific Visualization Symposium (PacificVis) 2014 | | Journal Type | Another Country | | Volume, Issue, Pages | pp.41-48 | | Author and coauthor | R. Bujack, I. Holz, G. Scheuermann, E. Hitzer | | DOI | 10.1109/PacificVis.2014.16 |
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91.
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New Developments in Clifford Fourier Transforms Advances in Applied and Pure Mathematics, Proceedings of the 2014 International Conference on Pure M 29,pp.19-25 (Single) 2014
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| Language | English | | Publication Date | 2014 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | New Developments in Clifford Fourier Transforms | | Contribution Type | Single Work | | Journal | Advances in Applied and Pure Mathematics, Proceedings of the 2014 International Conference on Pure M | | Journal Type | Another Country | | Volume, Issue, Pages | 29,pp.19-25 | | Details | N. E. Mastorakis, P. M. Pardalos, R. P. Agarwal, L. Kocinac (eds.), Advances in Applied and Pure Mathematics, Proceedings of the 2014 International Conference on Pure Mathematics, Applied Mathematics, Computational Methods (PMAMCM 2014), Santorini Island, Greece, July 17-21, 2014, Mathematics and Computers in Science and Engineering Series, |
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92.
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Operator Exponentials for the Clifford Fourier Transform on Multivector Fields Electronic proceedings of ICCA10, Tartu, Estonia, Aug. 2014. 2014
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| Language | English | | Publication Date | 2014 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Operator Exponentials for the Clifford Fourier Transform on Multivector Fields | | Contribution Type | - | | Journal | Electronic proceedings of ICCA10, Tartu, Estonia, Aug. 2014. | | Author and coauthor | D. Eelbode, E. Hitzer |
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93.
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Preprocessing quaternion data in quaternion spaces using the quaternion domain Fourier transform Proceedings of SICE Symposium on Systems and Information 2014 (SSI 2014), Session SS13-6, catalog No pp.834-839 (Single) 2014
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| Language | English | | Publication Date | 2014 | | Type | Research Paper (Material for Workshop, Symposium, etc.) | | Title | Preprocessing quaternion data in quaternion spaces using the quaternion domain Fourier transform | | Contribution Type | Single Work | | Journal | Proceedings of SICE Symposium on Systems and Information 2014 (SSI 2014), Session SS13-6, catalog No | | Journal Type | Japan | | Volume, Issue, Pages | pp.834-839 | | Author and coauthor | E. Hitzer | | Details | Proceedings of SICE Symposium on Systems and Information 2014 (SSI 2014), Session SS13-6, catalog No. SY0009/14/0000-0834©2014 SICE, Okayama University, Okayama, Japan, 21-23 Nov. 2014, pp. 834-839. |
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94.
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Quaternion Domain Fourier Transform Electronic proceedings of ICCA10, Tartu, Estonia, Aug. 2014 (Single) 2014
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| Language | English | | Publication Date | 2014 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Quaternion Domain Fourier Transform | | Contribution Type | Single Work | | Journal | Electronic proceedings of ICCA10, Tartu, Estonia, Aug. 2014 | | Journal Type | Another Country | | Author and coauthor | E. Hitzer |
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95.
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Article
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Two-sided Clifford Fourier transform with two square roots of −1 in Cl(p,q) Advances in Applied Clifford Algebras 24(2),pp.313-332 (Single) 2014
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| Language | English | | Publication Date | 2014 | | Type | Research Paper | | Peer Review | With peer review | | Title | Two-sided Clifford Fourier transform with two square roots of −1 in Cl(p,q) | | Contribution Type | Single Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 24(2),pp.313-332 | | Author and coauthor | HITZER Eckhard | | DOI | 10.1007/s00006-014-0441-9 |
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96.
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A General Geometric Fourier Transform Trends in Mathematics 27, Birkhauser, Basel, 2013, pp. 155-176. pp.155-176 (Collaboration) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | A General Geometric Fourier Transform | | Contribution Type | Joint Work | | Journal | Trends in Mathematics 27, Birkhauser, Basel, 2013, pp. 155-176. | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland | | Volume, Issue, Pages | pp.155-176 | | Author and coauthor | HITZER Eckhard, R. Bujack, G. Scheuermann | | Details | in E. Hitzer, S.J. Sangwine (eds.), "Quaternion and Clifford Fourier transforms and wavelets", Trends in Mathematics 27, Birkhauser, Basel, 2013, pp. 155-176. DOI: 10.1007/978-3-0348-0603-9_8 , Preprint: http://arxiv.org/abs/1306.2184 . First published in K. Guerlebeck (ed.), electronic Proc. of The 9th Int. Conf. on Clifford Algebras and their Applications, (2011). | | DOI | 10.1007/978-3-0348-0603-9_8 |
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97.
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A General Geometric Fourier Transform Convolution Theorem Adv. Appl. Clifford Alg. 23(1),pp.15-38 (Collaboration) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | A General Geometric Fourier Transform Convolution Theorem | | Contribution Type | Joint Work | | Journal | Adv. Appl. Clifford Alg. | | Journal Type | Another Country | | Volume, Issue, Pages | 23(1),pp.15-38 | | Author and coauthor | HITZER Eckhard, R. Bujack, G. Scheuerma | | Details | The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of “A General Geometric Fourier Transform” in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which constraints are additionally necessary to obtain certain features like linearity, a scaling, or a shift theorem. In this paper we extend the former results by a convolution theorem. | | DOI | 10.1007/s00006-012-0338-4 |
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98.
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Algebraic foundations of split hypercomplex nonlinear adaptive filtering Mathematical Methods in the Applied Sciences 36(9),pp.1042-1055 (Single) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Algebraic foundations of split hypercomplex nonlinear adaptive filtering | | Contribution Type | Single Work | | Journal | Mathematical Methods in the Applied Sciences | | Publisher | Wiley | | Volume, Issue, Pages | 36(9),pp.1042-1055 | | Author and coauthor | HITZER Eckhard | | Details | A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of hypercomplex algebra and hypercomplex calculus, some of which have been neglected in existing learning approaches (e.g., for quaternions). Already in the case of quaternions, we can predict improvements in performance of hypercomplex processes. The convergence of the proposed algorithms is rigorously analyzed. | | DOI | 10.1002/mma.2660 |
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99.
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Applications of Clifford's Geometric Algebra Adv. Appl. Clifford Alg. 23,pp.377-404 (Collaboration) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Applications of Clifford's Geometric Algebra | | Contribution Type | Joint Work | | Journal | Adv. Appl. Clifford Alg. | | Volume, Issue, Pages | 23,pp.377-404 | | Author and coauthor | HITZER Eckhard | | Details | We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly demonstrate the benefit of developing problem solutions in a unified framework for algebra and geometry with the widest possible scope: from quantum computing and electromagnetism to satellite navigation, from neural computing to camera geometry, image processing, robotics and beyond. | | DOI | 10.1007/s00006-013-0378-4 |
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100.
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Demystification of the Geometric Fourier Transforms AIP Conf. Proc. 1558,pp.525-528 (Collaboration) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Demystification of the Geometric Fourier Transforms | | Contribution Type | Joint Work | | Journal | AIP Conf. Proc. | | Volume, Issue, Pages | 1558,pp.525-528 | | Author and coauthor | R. Bujack, G. Scheuermann, E. Hitzer | | DOI | 10.1063/1.4825543 |
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101.
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Extending Fourier transformations to Hamilton’s quaternions and Clifford’s geometric algebras AIP Conf. Proc. 1558,pp.529-532 (Single) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Extending Fourier transformations to Hamilton’s quaternions and Clifford’s geometric algebras | | Contribution Type | Single Work | | Journal | AIP Conf. Proc. | | Volume, Issue, Pages | 1558,pp.529-532 | | Details | In T. Simos, G. Psihoyios and C. Tsitouras (eds.), Numerical Analysis and Applied Mathematics ICNAAM 2013, AIP Conf. Proc. 1558, pp. 529 -532 (2013). DOI: 10.1063/1.4825544 | | DOI | 10.1063/1.4825544 |
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102.
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History of Quaternion and Clifford-Fourier Transforms "Quaternion and Clifford Fourier Transforms and Wavelets", Trends in Mathematics (TIM) 27,pp.xi-xxvii (Collaboration) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (International Conference Proceedings) | | Title | History of Quaternion and Clifford-Fourier Transforms | | Contribution Type | Joint Work | | Journal | "Quaternion and Clifford Fourier Transforms and Wavelets", Trends in Mathematics (TIM) | | Publisher | Springer/Birkhauser | | Volume, Issue, Pages | 27,pp.xi-xxvii | | Author and coauthor | F. Brackx, E. Hitzer, S. Sangwine |
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103.
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Quaternionic Fourier-Mellin Transform Proceedings of 19th ICFIDCAA pp.123-131 (Single) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Quaternionic Fourier-Mellin Transform | | Contribution Type | Single Work | | Journal | Proceedings of 19th ICFIDCAA | | Publisher | Tohoku University Press, Sendai | | Volume, Issue, Pages | pp.123-131 | | Author and coauthor | HITZER Eckhard | | Details | in T. Sugawa (ed.), Proceedings of the The 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (ICFIDCAA), 11-15 December 2011, Hiroshima, Japan, Tohoku University Press, Sendai (2013), pp. ii, 123-131. Preprint: http://arxiv.org/abs/1306.1669 . |
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104.
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Representation of Crystallographic Subperiodic Groups in Clifford's Geometric Algebra Adv. Appl. Clifford Alg. 23(4),pp.887-906 (Collaboration) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Representation of Crystallographic Subperiodic Groups in Clifford's Geometric Algebra | | Contribution Type | Joint Work | | Journal | Adv. Appl. Clifford Alg. | | Journal Type | Another Country | | Publisher | Springer/Birkhauser | | Volume, Issue, Pages | 23(4),pp.887-906 | | Author and coauthor | E. Hitzer, D. Ichikawa | | DOI | 10.1063/1.4825543 |
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105.
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Square roots of -1 in real Clifford algebras Trends in Mathematics, Vol 27, Birkhauser, Basel, 2013. pp.123-153 (Collaboration) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Square roots of -1 in real Clifford algebras | | Contribution Type | Joint Work | | Journal | Trends in Mathematics, Vol 27, Birkhauser, Basel, 2013. | | Volume, Issue, Pages | pp.123-153 | | Author and coauthor | HITZER Eckhard, J. Helmstetter, R. Ablamowicz | | Details | Let Cl(p,q) be the universal Clifford algebra (associative with unit) generated over R by p + q elements e_k (with k = 1, 2, ... , p + q) with the relations e^2_k = 1 if k <= p, e^2_k = -1 if k > p and e_he_k + e_ke_h = 0 whenever h not equal k, see [6]. We set n = p + q and s = p - q. This algebra has dimension 2^n, and its even subalgebra Cl_0(p,q) has dimension 2^{n-1} (if n > 0). We are concerned with square roots of -1 contained in Cl(p,q) or Cl_0(p,q). If the dimension of Cl(p,q) or C_0(p,q) is less or equal 2, it is isomorphic to R or R^2 or C, and it is clear that there is no square root of -1 in R and R2 = R x R, and that there are two squares roots i and -i in C. Therefore we only consider algebras of dimension greater or equal 4. Square roots of -1 have been computed in [4] for algebras of dimension less or equal 16, and for Cl(3,0) in [7]. | | DOI | 10.1007/978-3-0348-0603-9_7 |
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106.
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The Clifford Fourier transform in real Clifford algebras Clifford Analysis, Clifford Algebras and their Applications 2(3),pp.227-240 (Single) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper | | Peer Review | With peer review | | Title | The Clifford Fourier transform in real Clifford algebras | | Contribution Type | Single Work | | Journal | Clifford Analysis, Clifford Algebras and their Applications | | Journal Type | Another Country | | Publisher | Cambridge Scientiic Publishers | | Volume, Issue, Pages | 2(3),pp.227-240 | | Responsible for | Everything | | Author and coauthor | HITZER Eckhard | | Details | in E. H., K. Tachibana (eds.), "Session on Geometric Algebra and Applications, IKM 2012", Special Issue of Clifford Analysis, Clifford Algebras and their Applications, Vol. 2, No. 3, pp. 223-235, (2013). First published in K. Guerlebeck, T. Lahmer and F. Werner (eds.), electronic Proc. of 19th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering, IKM 2012, Weimar, Germany, 04–06 July 2012. |
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107.
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The orthogonal planes split of quaternions Trends in Mathematics 27, Birkhauser, Basel, 2013, pp. 15-39. DOI: 10.1007/978-3-0348-0603-9_2 pp.15-39 (Collaboration) 2013
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| Language | English | | Publication Date | 2013 | | Type | Conference Report, etc. | | Peer Review | With peer review | | Title | The orthogonal planes split of quaternions | | Contribution Type | Joint Work | | Journal | Trends in Mathematics 27, Birkhauser, Basel, 2013, pp. 15-39. DOI: 10.1007/978-3-0348-0603-9_2 | | Journal Type | Another Country | | Publisher | Birkhauser, Basel, Switzerland. | | Volume, Issue, Pages | pp.15-39 | | Responsible for | Symbolic algebraic computations and part of text. | | Author and coauthor | HITZER Eckhard, S. J. Sangwine | | Details | The two-sided quaternionic Fourier transformation (QFT) was introduced in [2] for the analysis of 2D linear time-invariant partial-differential systems. In further theoretical investigations [3, 4] a special split of quaternions was introduced, then called plus minus split. In the current paper we analyze this split further, interpret it geometrically as orthogonal planes split (OPS), and generalize it. The new general form of the OPS split allows us to find new geometric interpretations for the action of the QFT on the signal. The second major result of this work is a variety of new forms of the QFT, their geometric interpretation, and for each form OPS split theorems, which allow fast and efficient numerical implementation with standard FFT software. | | DOI | 10.1007/978-3-0348-0603-9_2 |
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108.
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The quest for conformal geometric algebra Fourier transformations AIP Conf. Proc. 1558,pp.30-33 (Single) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | The quest for conformal geometric algebra Fourier transformations | | Contribution Type | Single Work | | Journal | AIP Conf. Proc. | | Journal Type | Another Country | | Publisher | American Institute of Physics | | Volume, Issue, Pages | 1558,pp.30-33 | | Responsible for | Everything | | DOI | 10.1063/1.4825413 |
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109.
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Vector field computations in Clifford's geometric algebra Proc. of the Third SICE Symposium on Computational Intelligence, August 30, 2013, Osaka University, Osaka pp.91-95 (Collaboration) 2013
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| Language | English | | Publication Date | 2013 | | Type | Research Paper (Material for Workshop, Symposium, etc.) | | Title | Vector field computations in Clifford's geometric algebra | | Contribution Type | Joint Work | | Journal | Proc. of the Third SICE Symposium on Computational Intelligence, August 30, 2013, Osaka University, Osaka | | Volume, Issue, Pages | pp.91-95 | | Author and coauthor | E. Hitzer, R. Bujack, G. Scheuerma |
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110.
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Clifford Fourier-Mellin transform with two real square roots of -1 in Cl(p,q), p+q = 2 AIP Conf. Proc. 1493,pp.480-485 (Single) 2012
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| Language | English | | Publication Date | 2012 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Clifford Fourier-Mellin transform with two real square roots of -1 in Cl(p,q), p+q = 2 | | Contribution Type | Single Work | | Journal | AIP Conf. Proc. | | Journal Type | Another Country | | Publisher | American Institute of Physics | | Volume, Issue, Pages | 1493,pp.480-485 | | Responsible for | Everything | | Author and coauthor | HITZER Eckhard | | Details | We describe a non-commutative generalization of the complex Fourier-Mellin transform to Clifford algebra valued signal functions over the domain mathp,q taking values in Cl(p,q),p+q = 2. | | DOI | 10.1063/1.4765531 |
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111.
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Detection of Outer Rotations on 3D-Vector Fields with Iterative Geometric Correlation electronic Proceedings of AGACSE 2012, La Rochelle, France, 2-4 July 2012. (Collaboration) 2012
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| Language | English | | Publication Date | 2012 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Detection of Outer Rotations on 3D-Vector Fields with Iterative Geometric Correlation | | Contribution Type | Joint Work | | Journal | electronic Proceedings of AGACSE 2012, La Rochelle, France, 2-4 July 2012. | | Author and coauthor | HITZER Eckhard, R. Bujack, G. Scheuermann |
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112.
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Detection of Total Rotations on linear 2D-Vector Fields with Iterative Geometric Correlation AIP Conf. Proc. 1493,pp.190-199 (Collaboration) 2012
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| Language | English | | Publication Date | 2012 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Detection of Total Rotations on linear 2D-Vector Fields with Iterative Geometric Correlation | | Contribution Type | Joint Work | | Journal | AIP Conf. Proc. | | Journal Type | Another Country | | Publisher | American Institute of Physics | | Volume, Issue, Pages | 1493,pp.190-199 | | Author and coauthor | HITZER Eckhard | | Details | Correlation is a common technique for the detection of shifts. Its generalization to the multidimensional geometric correlation in Clifford algebras additionally contains information with respect to rotational misalignment. It has been proven a useful tool for the registration of vector fields that differ by an outer rotation. In this paper we proof that applying the geometric correlation iteratively has the potential to detect the total rotational misalignment for linear two-dimensional vector fields. We further analyze its effect on general analytic vector fields and show how the rotation can be calculated from their power series expansions. | | DOI | 10.1063/1.4765489 |
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113.
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Introduction to Clifford's Geometric Algebra SICE Journal of Control, Measurement, and System Integration 51(4) (Single) 2012
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| Language | English | | Publication Date | 2012 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Introduction to Clifford's Geometric Algebra | | Contribution Type | Single Work | | Journal | SICE Journal of Control, Measurement, and System Integration | | Journal Type | Japan | | Volume, Issue, Pages | 51(4) | | Author and coauthor | HITZER Eckhard | | Details | Geometric algebra was initiated byW.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing, tracking, geographic information systems and neural computing. This tutorial explains the basics of geometric algebra, with concrete examples of the plane, of 3D space, of spacetime, and the popular conformal model. Geometric algebras are ideal to represent geometric transformations in the general framework of Clifford groups (also called versor or Lipschitz groups). Geometric (algebra based) calculus allows e.g. to optimize learning algorithms of Clifford neurons, etc. |
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114.
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Natural Science Education in Germany in 2012 after the 1999 European Bologna Reforms Proceedings of the Meiji University Symposium on Mathematical Education 2012, Meiji University, Toky pp.51-54 (Single) 2012
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| Language | English | | Publication Date | 2012 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | Natural Science Education in Germany in 2012 after the 1999 European Bologna Reforms | | Contribution Type | Single Work | | Journal | Proceedings of the Meiji University Symposium on Mathematical Education 2012, Meiji University, Toky | | Journal Type | Japan | | Publisher | Meiji University, Tokyo | | Volume, Issue, Pages | pp.51-54 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | High school teacher education - Education of University Teachers - Research at German Universities - The new structure of university degrees in Germany after the Bologna reforms - The new Bachelor degree - The new Master degree - Acknowledgments - Further literature. |
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115.
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Survey of Applications of Clifford Algebra SICE Journal of Control, Measurement, and System Integration (Collaboration) 2012
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| Language | Japanese | | Publication Date | 2012 | | Type | Research Paper (Scientific Journal) | | Title | Survey of Applications of Clifford Algebra | | Contribution Type | Joint Work | | Journal | SICE Journal of Control, Measurement, and System Integration | | Journal Type | Japan | | Author and coauthor | HITZER Eckhard, Y. Kuroe, T. Nitta | | Details | We survey the development of Cli ord's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly demonstrate the benefit of developing problem solutions in a unified framework for algebra and geometry with the widest possible scope: from quantum computing and electromagnetism to satellite navigation, from neural computing to camera geometry, image processing, robotics and beyond. |
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116.
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Crystal planes and reciprocal space in Clifford geometric algebra Math. Methods in the Applied Sciences 34(12),pp.1421-1429 (Single) 2011
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| Language | English | | Publication Date | 2011 | | Type | Research Paper (Scientific Journal) | | Title | Crystal planes and reciprocal space in Clifford geometric algebra | | Contribution Type | Single Work | | Journal | Math. Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Volume, Issue, Pages | 34(12),pp.1421-1429 | | Responsible for | Everything | | Author and coauthor | HITZER Eckhard | | Details | This paper discusses the geometry of kD crystal cells given by (k+ 1) points in a projective space ℝn+ 1. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual representation are related (and geometrically interpreted) in the projective geometric algebra Cl(ℝn+ 1) (see (Die Ausdehnungslehre von 1844 und die Geom. Anal. Teubner: Leipzig, 1894)) and in the conformal algebra Cl(ℝn+ 1, 1). The crystallographic notions of d-spacing, phase angle, structure factors, conditions for Bragg reflections, and the interfacial angles of crystal planes are obtained in the same context. | | DOI | 10.1002/mma.1442 |
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117.
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Geometric Roots of –1 in Clifford Algebras Cl(p,q) with p+q <= 4 Adv. In Appl. Cliff. Algebras 21(1),pp.121-144 (Collaboration) 2011
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| Language | English | | Publication Date | 2011 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Geometric Roots of –1 in Clifford Algebras Cl(p,q) with p+q <= 4 | | Contribution Type | Joint Work | | Journal | Adv. In Appl. Cliff. Algebras | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 21(1),pp.121-144 | | Responsible for | Symbolic computations and most of text. | | Author and coauthor | HITZER Eckhard, R. Abłamowicz | | Details | It is known that Clifford (geometric) algebra offers a geometric interpretation for square roots of -1 in the form of blades that square to minus 1. This extends to a geometric interpretation of quaternions as the side face bivectors of a unit cube. Research has been done [S. J. Sangwine, Biquaternion (Complexified Quaternion) Roots of -1, Adv. Appl. Cliford Alg. 16(1), pp. 63-68, 2006.] on the biquaternion roots of -1, abandoning the restriction to blades. Biquaternions are isomorphic to the Clifford (geometric) algebra C(3,0) of R^3. All these roots of -1 find immediate applications in the construction of new types of geometric Clifford Fourier transformations. We now extend this research to general algebras C(p,q). We fully derive the geometric roots of -1 for the Clifford (geometric) algebras with p+q <= 4. | | DOI | 10.1007/s00006-010-0240-x |
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118.
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Non-constant bounded holomorphic functions of hyperbolic numbers - Candidates for hyperbolic activation functions Proceedings of the First SICE Symposium on Computational Intelligence pp.23-28 (Single) 2011
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| Language | English | | Publication Date | 2011 | | Type | Research Paper (Material for Workshop, Symposium, etc.) | | Peer Review | With peer review | | Title | Non-constant bounded holomorphic functions of hyperbolic numbers - Candidates for hyperbolic activation functions | | Contribution Type | Single Work | | Journal | Proceedings of the First SICE Symposium on Computational Intelligence | | Journal Type | Japan | | Volume, Issue, Pages | pp.23-28 | | Responsible for | Everything. | | Author and coauthor | HITZER Eckhard | | Details | The Liouville theorem states that bounded holomorphic complex functions are necessarily constant. Holomorphic functions fulfill the socalled Cauchy-Riemann (CR) conditions. The CR conditions mean that a complex z-derivative is independent of the direction. Holomorphic functions are ideal for activation functions of complex neural networks, but the Liouville theorem makes them useless. Yet recently the use of hyperbolic numbers, lead to the construction of hyperbolic number neural networks. We will describe the Cauchy-Riemann conditions for hyperbolic numbers and show that there exists a new interesting type of bounded holomorphic functions of hyperbolic numbers, which are not constant. We give examples of such functions. They therefore substantially expand the available candidates for holomorphic activation functions for hyperbolic number neural networks. |
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119.
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OPS-QFTs: A new type of quaternion Fourier transforms based on the orthogonal planes split with one or two general pure quaternions AIP Conf. Proc. 1389,pp.280-283 (Single) 2011
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| Language | English | | Publication Date | 2011 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | OPS-QFTs: A new type of quaternion Fourier transforms based on the orthogonal planes split with one or two general pure quaternions | | Contribution Type | Single Work | | Journal | AIP Conf. Proc. | | Journal Type | Another Country | | Publisher | American Institute of Physics | | Volume, Issue, Pages | 1389,pp.280-283 | | Author and coauthor | HITZER Eckhard | | Details | We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions f,g. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to quaternion fields to conform with the OPS determined by f,g, or by only one pure unit quaternion f, comment on their geometric meaning, and establish inverse transformations. | | DOI | 10.1063/1.3636721 |
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120.
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A Note on Geometric Algebra and Neural Networks Proc. of 20th Intelligent Systems Symposium (FAN 2010), 25-26 Sep. 2010, Tokyo, Japan pp.116-117 (Collaboration) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (Material for Workshop, Symposium, etc.) | | Title | A Note on Geometric Algebra and Neural Networks | | Contribution Type | Joint Work | | Journal | Proc. of 20th Intelligent Systems Symposium (FAN 2010), 25-26 Sep. 2010, Tokyo, Japan | | Journal Type | Japan | | Volume, Issue, Pages | pp.116-117 | | Author and coauthor | K. Tachibana, E. Hitzer, M. T. Pham, T. Yoshikawa, T. Furuhashi |
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121.
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Angles between subspaces Workshop Proceedings: Computer Graphics, Computer Vision and Mathematics 2010, Sep. 07-10 (Single) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (International Conference Proceedings) | | Title | Angles between subspaces | | Contribution Type | Single Work | | Journal | Workshop Proceedings: Computer Graphics, Computer Vision and Mathematics 2010, Sep. 07-10 | | Publisher | UNION Agency, Plzen | | Author and coauthor | HITZER Eckhard | | Details | We first review the de nition of the angle between subspaces and how it is computed using matrix algebra. Then we introduce the Grassmann and Clifford algebra description of subspaces. The geometric product of two subspaces yields the full relative angular information in an explicit manner. We explain and interpret the result of the geometric product of subspaces gaining thus full access to the relative orientation information. |
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122.
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Angles Between Subspaces Computed in Clifford Algebra AIP Conf. Proc. 1281,pp.1476-1479 (Single) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (International Conference Proceedings) | | Title | Angles Between Subspaces Computed in Clifford Algebra | | Contribution Type | Single Work | | Journal | AIP Conf. Proc. | | Journal Type | Another Country | | Publisher | American Institute of Physics | | Volume, Issue, Pages | 1281,pp.1476-1479 | | Author and coauthor | HITZER Eckhard | | Details | We first review the definition of the angle between subspaces and how it is computed using matrix algebra. Then we introduce the Grassmann and Clifford algebra description of subspaces. The geometric product of two subspaces yields the full relative angular information in an explicit manner. We explain and interpret the result of the geometric product of subspaces gaining thus full practical access to the relative orientation information. | | DOI | 10.1063/1.3498043 |
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123.
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Classification and Clustering of Spatial Patterns with Geometric Algebra Geometric Algebra Computing, Springer, New York, 2010 pp.231-247 (Collaboration) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Classification and Clustering of Spatial Patterns with Geometric Algebra | | Contribution Type | Joint Work | | Journal | Geometric Algebra Computing, Springer, New York, 2010 | | Journal Type | Another Country | | Publisher | Spriner | | Volume, Issue, Pages | pp.231-247 | | Author and coauthor | M. T. Pham, K. Tachibana, E. Hitzer, T. Yoshikawa, T. Furuhashi |
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124.
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Directional Uncertainty Principle for Quaternion Fourier Transforms Advances in Applied Clifford Algebras 20(2),pp.271-284 (Single) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Directional Uncertainty Principle for Quaternion Fourier Transforms | | Contribution Type | Single Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland | | Volume, Issue, Pages | 20(2),pp.271-284 | | Responsible for | Everything. | | Author and coauthor | HITZER Eckhard | | Details | This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric algebras with quaternion subalgebras. We demonstrate this with the example of a directional spacetime algebra function uncertainty principle related to multivector wave packets. | | DOI | 10.1007/s00006-009-0175-2 |
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125.
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Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra Geometric Algebra Computing, Springer, New York, 2010 pp.385-400 (Collaboration) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra | | Contribution Type | Joint Work | | Journal | Geometric Algebra Computing, Springer, New York, 2010 | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | pp.385-400 | | Responsible for | Most of text and computations | | Author and coauthor | HITZER Eckhard, C. Perwass, D. Ichikawa | | Details | The Space Group Visualizer (SGV) for all 230 3D space groups is a standalone PC application based on the visualization software CLUCalc. We first explain the unique geometric algebra structure behind the SGV. In the second part we review the main features of the SGV: The GUI, group and symmetry selection, mouse pointer interactivity, and visualization options.We further introduce the joint use with the International Tables of Crystallography, Vol. A [7]. In the third part we explain how to represent the 162 socalled subperiodic groups of crystallography in geometric algebra. We construct a new compact geometric algebra group representation symbol, which allows to read off the complete set of geometric algebra generators. For clarity we moreover state explicitly what generators are chosen. The group symbols are based on the representation of point groups in geometric algebra by versors. |
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126.
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Interactive 3D Space Group Visualization with CLUCalc and the Clifford Geometric Algebra Description of Space Groups Adv. Appl. Clifford Alg. 20(3-4),pp.631-658 (Collaboration) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (Scientific Journal) | | Title | Interactive 3D Space Group Visualization with CLUCalc and the Clifford Geometric Algebra Description of Space Groups | | Contribution Type | Joint Work | | Journal | Adv. Appl. Clifford Alg. | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 20(3-4),pp.631-658 | | Responsible for | Most of text and computations. | | Author and coauthor | HITZER Eckhard, C. Perwass | | Details | A new interactive software tool is described, that visualizes 3D space group symmetries. The software computes with Clifford (geometric) algebra. The space group visualizer (SGV) is a script for the open source visual CLUCalc, which fully supports geometric algebra computation. Selected generators (Hestenes and Holt, JMP, 2007) form a multivector generator basis of each space group. The approach corresponds to an algebraic implementation of groups generated by reflections (Coxeter and Moser, 4th ed., 1980). |
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127.
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Interactive visualization of plane groups The Journal of the Int. Soc. For the Interdisc. Study of Symmetry (ISIS) 2010(1-4),pp.80-83 (Single) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Interactive visualization of plane groups | | Contribution Type | Single Work | | Journal | The Journal of the Int. Soc. For the Interdisc. Study of Symmetry (ISIS) | | Journal Type | Another Country | | Volume, Issue, Pages | 2010(1-4),pp.80-83 | | Author and coauthor | HITZER Eckhard | | Details | This contribution shows how to successfully display the 17 two-dimensional space groups (wallpaper groups) in the interactive crystal symmetry software Space Group Visualizer (SGV) (Perwass & Hitzer, 2005). We show examples of four wallpaper groups that contain (as sub patterns, i.e as subgroups) all other 13 wallpaper groups. The SGV is described in (Hitzer & Perwass, 2010). It is based on a new type of powerful geometric algebra visualization platform (Perwass, 2000). |
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128.
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Interactive Visualization of Plane Space Groups with the Space Group Visualizer Vixra Preprint Server, Condensed Matter. pp.1-36 (Single) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper | | Title | Interactive Visualization of Plane Space Groups with the Space Group Visualizer | | Contribution Type | Single Work | | Journal | Vixra Preprint Server, Condensed Matter. | | Journal Type | Another Country | | Publisher | Vixra Preprint Server. | | Volume, Issue, Pages | pp.1-36 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | This set of instructions shows how to successfully display the 17 two-dimensional (2D) space groups in the interactive crystal symmetry software Space Group Visualizer (SGV) [6]. The SGV is described in [4]. It is based on a new type of powerful geometric algebra visualization platform [5]. The principle is to select in the SGV a three-dimensional super space group and by orthogonal projection produce a view of the desired plane 2D space group. The choice of 3D super space group is summarized in the lookup table Table 1. |
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129.
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New views of crystal symmetry guided by profound admiration of the extraordinary works of Grassmann and Clifford From Past to Future: Graßmann's Work in Context, Graßmann Bicentennial Conference, September 2009 pp.413-422 (Single) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | New views of crystal symmetry guided by profound admiration of the extraordinary works of Grassmann and Clifford | | Contribution Type | Single Work | | Journal | From Past to Future: Graßmann's Work in Context, Graßmann Bicentennial Conference, September 2009 | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland | | Volume, Issue, Pages | pp.413-422 | | Author and coauthor | HITZER Eckhard | | Details | This paper shows how beginning with Justus Grassmann's work, Hermann Grassmann was influenced in his mathematical thinking by crystal- lography. H. Grassmann's Ausdehnungslehre in turn had a decisive influence on W.K. Clifford in the genesis of geometric algebras. Geometric algebras have been expanded to conformal geometric algebras, which provide an ideal framework for modern computer graphics. Within this framework a new visualization of three-dimensional crystallographic space groups has been created. The complex beauty of this new visualization is shown by a range of images of a diamond cell. Mathematical details are given in an appendix. |
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130.
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Reciprocal space and crystal planes in geometric algebra electronic conf. proc. of AGACSE 2010, Amsterdam, The Netherlands, 14-16 June 2010. (Single) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Reciprocal space and crystal planes in geometric algebra | | Contribution Type | Single Work | | Journal | electronic conf. proc. of AGACSE 2010, Amsterdam, The Netherlands, 14-16 June 2010. | | Journal Type | Another Country | | Author and coauthor | HITZER Eckhard | | Details | This contribution discusses the geometry of kD crystal cells given by (k + 1) points in a projective space R^{n+1}. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual representation are related (and geometrically interpreted) in the projective geometric algebra R_{n+1} (see [2]) and in the conformal algebra R_{n+1,1}. The crystallographic notions of d-spacing, phase angle (in structure factors), extinction of Bragg re ections, and the interfacial angles of crystal planes are obtained in the same context.
[2] H. Grassmann, edited by F. Engel, Die Ausdehnungslehre von 1844 und die Geometrische Analysis, Vol. 1, Part 1, Teubner, Leipzig, 1894. |
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131.
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Two-Dimensional Clifford Windowed Fourier Transform Geometric Algebra Computing, Springer, New York, 2010 pp.93-106 (Collaboration) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Two-Dimensional Clifford Windowed Fourier Transform | | Contribution Type | Joint Work | | Journal | Geometric Algebra Computing, Springer, New York, 2010 | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | pp.93-106 | | Author and coauthor | B. Mawardi, E. Hitzer, S. Adji | | Details | Recently several generalizations to higher dimension of the classical Fourier transform (FT) using Clifford geometric algebra have been introduced, including the two-dimensional (2D) Clifford Fourier transform (CFT). Based on the 2D CFT, we establish the two-dimensional Clifford windowed Fourier transform (CWFT). Using the spectral representation of the CFT, we derive several important properties such as shift, modulation, a reproducing kernel, isometry and an orthogonality relation. Finally, we discuss examples of the CWFT and compare the CFT and the CWFT. |
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132.
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Windowed Fourier transform of two-dimensional quaternionic signals Appl. Math. and Computation 216(8),pp.2366-2379 (Collaboration) 2010
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| Language | English | | Publication Date | 2010 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Windowed Fourier transform of two-dimensional quaternionic signals | | Contribution Type | Joint Work | | Journal | Appl. Math. and Computation | | Journal Type | Another Country | | Publisher | Elsevier | | Volume, Issue, Pages | 216(8),pp.2366-2379 | | Author and coauthor | HITZER Eckhard, B. Mawardi, R. Ashino, R. Vaillancourt | | Details | In this paper, we generalize the classical windowed Fourier transform (WFT) to quaternion-valued signals, called the quaternionic windowed Fourier transform (QWFT). Using the spectral representation of the quaternionic Fourier transform (QFT), we derive several important prop- erties such as reconstruction formula, reproducing kernel, isometry, and orthogonality relation. Taking the Gaussian function as window function we obtain quaternionic Gabor filters which play the role of coefficient functions when decomposing the signal in the quaternionic Gabor basis. We apply the QWFT properties and the (right-sided) QFT to establish a Heisenberg type uncertainty principle for the QWFT. Finally, we briefly introduce an application of the QWFT to a linear time-varying system. | | DOI | 10.1016/j.amc.2010.03.082 |
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133.
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Algorithm for conversion between geometric algebra versor notation and conventional crystallographic symmetry-operation symbols Vixra Preprint Server, Condensed Matter. pp.1-14 (Collaboration) 2009
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| Language | English | | Publication Date | 2009 | | Type | Research Paper | | Title | Algorithm for conversion between geometric algebra versor notation and conventional crystallographic symmetry-operation symbols | | Contribution Type | Joint Work | | Journal | Vixra Preprint Server, Condensed Matter. | | Journal Type | Another Country | | Publisher | Vixra Preprint Server | | Volume, Issue, Pages | pp.1-14 | | Responsible for | Most of text and tables. | | Author and coauthor | E. Hitzer, C. Perwass |
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134.
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Analysis of Point Clouds - Using conformal geometric algebra GRAPP 2008, 3rd Int. Conf. on Computer Graphics Theory and Applications. Proc. pp.99-106 (Collaboration) 2009
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| Language | English | | Publication Date | 2009 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Analysis of Point Clouds - Using conformal geometric algebra | | Contribution Type | Joint Work | | Journal | GRAPP 2008, 3rd Int. Conf. on Computer Graphics Theory and Applications. Proc. | | Journal Type | Another Country | | Volume, Issue, Pages | pp.99-106 | | Author and coauthor | HITZER Eckhard, D. Hildenbrand | | Details | This paper presents some basics for the analysis of point clouds using the geometrically intuitive mathematical framework of conformal geometric algebra. In this framework it is easy to compute with osculating circles for the description of local curvature. Also methods for the fitting of spheres as well as bounding spheres are presented. In a nutshell, this paper provides a starting point for shape analysis based on this new, geometrically intuitive and promising technology. |
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135.
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Carrier method for the general evaluation and control of pose, molecular conformation, tracking, and the like Advances in Applied Clifford Algebras 19(2),pp.339-364 (Collaboration) 2009
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| Language | English | | Publication Date | 2009 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Carrier method for the general evaluation and control of pose, molecular conformation, tracking, and the like | | Contribution Type | Joint Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland | | Volume, Issue, Pages | 19(2),pp.339-364 | | Author and coauthor | HITZER Eckhard, Kanta Tachibana, Sven Buchholz, Isseki Yu | | Details | The four basic geometric objects of points, point pairs, circles and spheres correspond to outer product null-spaces constructed by conformal points in conformal geometric algebra. Wedging with the infinity point we get four flat objects: finite-infinity point pairs, lines, planes and the whole 5D space. We show that all these basic geometric objects have the same algebraic structure. We then develop a single general algebraic method to quantify and interpolate the relative pose of the eight different classes of objects. As an explicit example we finally apply our framework to the conformation of organic macromolecules. | | DOI | 10.1007/s00006-009-0160-9 |
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136.
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Clifford (Geometric) Algebra Wavelet Transform Proc. of GraVisMa 2009, 02-04 Sep. 2009, Plzen, Czech Republic pp.94-101 (Single) 2009
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| Language | English | | Publication Date | 2009 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Clifford (Geometric) Algebra Wavelet Transform | | Contribution Type | Single Work | | Journal | Proc. of GraVisMa 2009, 02-04 Sep. 2009, Plzen, Czech Republic | | Journal Type | Another Country | | Volume, Issue, Pages | pp.94-101 | | Author and coauthor | HITZER Eckhard | | Details | While the Clifford (geometric) algebra Fourier Transform (CFT) is global, we introduce here the local Clifford (geometric) algebra (GA) wavelet concept. We show how for n = 2,3(mod 4) continuous Cl_n-valued admissible wavelets can be constructed using the similitude group SIM(n). We strictly aim for real geometric interpretation, and replace the imaginary unit i element of C (complex numbers) therefore with a GA blade squaring to -1. Consequences due to non-commutativity arise. We express the admissibility condition in terms of a Cl_n CFT and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the CliRord wavelet transform. As an explicit example, we introduce Clifford Gabor wavelets. We further invent a generalized Clifford wavelet uncertainty principle. Extensions of CFTs and Clifford wavelets to Cl(0,n') ; n' = 1,2(mod 4) appear straight forward. |
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137.
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New views of crystal symmetry The Journal of the Int. Soc. For the Interdisciplinary Study of Symmetry (Special),pp.112-115 (Single) 2009
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| Language | English | | Publication Date | 2009 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | New views of crystal symmetry | | Contribution Type | Single Work | | Journal | The Journal of the Int. Soc. For the Interdisciplinary Study of Symmetry | | Journal Type | Another Country | | Volume, Issue, Pages | (Special),pp.112-115 | | Author and coauthor | HITZER Eckhard | | Details | Already Hermann Grassmann's father Justus (1829, 1830) published two works on the geometrical description of crystals, influenced by the earlier works of C.S. Weiss (1780-1856) on three main crystal forces governing crystal formation. In his 1840 essay on the derivation of crystal shapes from the general law of crystal formation Hermann established the notion of a three-dimensional vectorial system of forces with rational coefficients, that represent the interior crystal structure, regulate its formation, its shape and physical behavior. |
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138.
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Real Clifford Algebra Cl(n,0), n = 2,3(mod 4) Wavelet Transform AIP Conf. Proceedings 1168,pp.781-784 (Single) 2009
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| Language | English | | Publication Date | 2009 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Real Clifford Algebra Cl(n,0), n = 2,3(mod 4) Wavelet Transform | | Contribution Type | Single Work | | Journal | AIP Conf. Proceedings | | Journal Type | Another Country | | Publisher | American Institute of Physics | | Volume, Issue, Pages | 1168,pp.781-784 | | Author and coauthor | HITZER Eckhard | | Details | We show how for n = 2, 3(mod 4) continuous Clifford (geometric) algebra (GA) Cln‐valued admissible wavelets can be constructed using the similitude group SIM(n). We strictly aim for real geometric interpretation, and replace the imaginary unit i ∊ therefore with a GA blade squaring to −1. Consequences due to non‐commutativity arise. We express the admissibility condition in terms of a Cln Clifford Fourier Transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform. As an example, we introduce Clifford Gabor wavelets. We further invent a generalized Clifford wavelet uncertainty principle. |
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139.
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Visualization of fundamental symmetries in nature Proceedings of Fuzzy System Symposium (FSS 2009), Tsukuba, Japan, 14-16 Jul. 2009 (Collaboration) 2009
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| Language | English | | Publication Date | 2009 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Visualization of fundamental symmetries in nature | | Contribution Type | Joint Work | | Journal | Proceedings of Fuzzy System Symposium (FSS 2009), Tsukuba, Japan, 14-16 Jul. 2009 | | Journal Type | Japan | | Responsible for | Text (most) and graphics. | | Author and coauthor | HITZER Eckhard, C. Perwass | | Details | Most matter in nature and technology is composed of crystals and crystal grains. A full understanding of the inherent symmetry is vital. A new interactive software tool is demonstrated, that visualizes 3D space group symmetries. The software computes with Clifford (geometric) algebra. The space group visualizer (SGV) is a script for the open source visual CLUCalc, which fully supports geometric algebra computation. In our presentation we will first give some insights into the geometric algebra description of space groups. The symmetry generation data are stored in an XML file, which is read by a special CLUScript in order to generate the visualization. Then we will use the Space Group Visualizer to demonstrate space group selection and give a short interactive computer graphics presentation on how reflections combine to generate all 230 three-dimensional space groups. |
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140.
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An Uncertainty Principle for Quaternion Fourier Transform Computer & Mathematics with Applications 56,pp.2398-2410 (Collaboration) 2008
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| Language | English | | Publication Date | 2008 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | An Uncertainty Principle for Quaternion Fourier Transform | | Contribution Type | Joint Work | | Journal | Computer & Mathematics with Applications | | Journal Type | Another Country | | Publisher | Elsevier | | Volume, Issue, Pages | 56,pp.2398-2410 | | Author and coauthor | HITZER Eckhard, B. Mawardi, A. Hayashi, R. Ashino | | Details | We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternion signal minimizes the uncertainty. | | DOI | 10.1016/j.camwa.2008.05.032 . |
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141.
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Basic Multivector Calculus Proc. of 18th Intelligent Systems Symposium (FAN 2008), 23-24 Oct. 2008, Hiroshima, Japan pp.185-190 (Single) 2008
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| Language | English | | Publication Date | 2008 | | Type | Research Paper (Material for Workshop, Symposium, etc.) | | Title | Basic Multivector Calculus | | Contribution Type | Single Work | | Journal | Proc. of 18th Intelligent Systems Symposium (FAN 2008), 23-24 Oct. 2008, Hiroshima, Japan | | Volume, Issue, Pages | pp.185-190 | | Author and coauthor | E. Hitzer |
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142.
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Article
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Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions n = 2 (mod 4) and n = 3 (mod 4) Adv. App. Cliff. Alg. 18(S 3,4),pp.715-736 (Collaboration) 2008
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| Language | English | | Publication Date | 2008 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions n = 2 (mod 4) and n = 3 (mod 4) | | Contribution Type | Joint Work | | Journal | Adv. App. Cliff. Alg. | | Volume, Issue, Pages | 18(S 3,4),pp.715-736 | | Responsible for | Main part of text and computations. | | Author and coauthor | HITZER Eckhard, B. Mawardi | | Details | First, the basic concepts of the multivector functions, vector differential and vector derivative in geometric algebra are introduced. Second, we define a generalized real Fourier transform on Clifford multivector-valued functions ( f:Rn→Cln,0,n=2,3 (mod 4)). Third, we show a set of important properties of the Clifford Fourier transform on Cl n,0, n = 2, 3 (mod 4) such as differentiation properties, and the Plancherel theorem, independent of special commutation properties. Fourth, we develop and utilize commutation properties for giving explicit formulas for fx m , f ∇ m and for the Clifford convolution. Finally, we apply Clifford Fourier transform properties for proving an uncertainty principle for Cl n,0, n = 2, 3 (mod 4) multivector functions. | | DOI | 10.1007/s00006-008-0098-3 |
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143.
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Article
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Clustering of Questionnaire Based on Features Extracted by Geometric Algebra Proc. Joint 4th Int. Conf. on Soft Comp. and Intel. Sys., and 9th Int. Symp. on Adv. Intel. Sys. pp.798-803 (Collaboration) 2008
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| Language | English | | Publication Date | 2008 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Clustering of Questionnaire Based on Features Extracted by Geometric Algebra | | Contribution Type | Joint Work | | Journal | Proc. Joint 4th Int. Conf. on Soft Comp. and Intel. Sys., and 9th Int. Symp. on Adv. Intel. Sys. | | Journal Type | Japan | | Volume, Issue, Pages | pp.798-803 | | Author and coauthor | HITZER Eckhard, M. T. Pham, K. Tachibana, T. Yoshikawa, T. Furuhashi | | Details | Clustering is one of the most useful methods to understand similarity among data. However, most conventional clustering methods do not pay sufficient attention to geometric properties of data. Geometric algebra (GA) is a generalization of complex numbers and of quaternions, and it is able to describe spatial objects and relations between them. In this study we introduce GA to systematically extract geometric features from data. We propose a new clustering method by using various geometric features extracted with GA. We apply the proposed method to clarification of human impressions of a product. In the field of marketing, companies often carry out a questionnaire on consumers for grasping their impressions. Analyzing consumers through the obtained evaluation data enables us to know the tendency of the market and to find problems and/or to make hypotheses that are useful for the development of products. Finally, we discuss clustering results of a questionnaire with/without GA. |
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144.
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Article
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Coordinate independent update formulas for versor Clifford neurons Proc. Joint 4th Int. Conf. on Soft Comp. and Intel. Sys., and 9th Int. Symp. on Adv. Intel. Sys. pp.814-819 (Collaboration) 2008
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| Language | English | | Publication Date | 2008 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Coordinate independent update formulas for versor Clifford neurons | | Contribution Type | Joint Work | | Journal | Proc. Joint 4th Int. Conf. on Soft Comp. and Intel. Sys., and 9th Int. Symp. on Adv. Intel. Sys. | | Journal Type | Japan | | Volume, Issue, Pages | pp.814-819 | | Author and coauthor | S. Buchholz, HITZER Eckhard, K. Tachibana | | Details | We study the optimization of neural networks with Clifford geometric algebra versor and spinor nodes. For that purpose important multivector calculus results are introduced. Such nodes are generalizations of real, complex and quaternion spinor nodes. In particular we consider nodes that can learn all proper and improper Euclidean transformations with so-called conformal versors. Thus a single node can correctly compute full 3D screws and rotoinversions with off-origin axis and offorigin points of inversion. The latter is a unique property of our proposed versor neuron. Computing inversions by ordinary real-valued networks is not easily possible due to its nonlinear nature. Simulation on learning inversions illustrating these facts are provided in the paper. |
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145.
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Article
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Feature Extraction with Geometric Algebra from Geometric Data Proceedings of The Institute of Statistical Mathematics (Tokyo) pp.185-198 (Collaboration) 2008
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| Language | Japanese | | Publication Date | 2008 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Feature Extraction with Geometric Algebra from Geometric Data | | Contribution Type | Joint Work | | Journal | Proceedings of The Institute of Statistical Mathematics (Tokyo) | | Journal Type | Japan | | Volume, Issue, Pages | pp.185-198 | | Author and coauthor | HITZER Eckhard, M. T. Pham, K. Tachibana, S. Buchholz, T. Yoshikawa, T. Furuhashi | | Details | Most conventional methods of feature extraction for pattern recognition do not pay much attention to geometric properties of data, even in the case where the data have spatial features. In this study we introduce Geometric Algebra to undertake various kinds of feature extractions from spatial data. A Geometric Algebra is a generalization of complex numbers and of quaternions, and it is able to describe spatial objects and relations between them. This paper proposes to use Geometric Algebra to extract geometric features systematically from data given in a vector space. We show the results of classification of hand-written digits, which were classified by feature extraction with the proposed method. |
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146.
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Article
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Feature Extractions with Geometric Algebra for Classification of Objects Proc. of Int. Joint Conf. on Neural Networks (IJCNN/WCCI2008) Hong Kong, China, 1-4 Jun. 2008 pp.4069-4073 (Collaboration) 2008
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| Language | English | | Publication Date | 2008 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Feature Extractions with Geometric Algebra for Classification of Objects | | Contribution Type | Joint Work | | Journal | Proc. of Int. Joint Conf. on Neural Networks (IJCNN/WCCI2008) Hong Kong, China, 1-4 Jun. 2008 | | Journal Type | Another Country | | Publisher | IEEE | | Volume, Issue, Pages | pp.4069-4073 | | Author and coauthor | M. T. Pham, K. Tachibana, HITZER Eckhard, S. Buchholz, T. Yoshikawa, T. Furuhashi | | Details | Most conventional methods of feature extraction do not pay much attention to the geometric properties of data, even in cases where the data have spatial features. In this study we introduce geometric algebra to undertake various kinds of feature extraction from spatial data. Geometric algebra is a generalization of complex numbers and of quaternions, and it is able to describe spatial objects and relations between them. This paper proposes to use geometric algebra to systematically extract geometric features from data given in a vector space. We show the results of classification of hand-written digits, which were classified by feature extraction with the proposed method. |
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147.
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Article
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Geometric operations implemented by conformal geometric algebra neural nodes Proc. SICE Symposium on Systems and Information 2008, 26-28 Nov. 2008, Himeji, Japan pp.357 – 362 (Single) 2008
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| Language | English | | Publication Date | 2008 | | Type | Research Paper (Material for Workshop, Symposium, etc.) | | Peer Review | With peer review | | Title | Geometric operations implemented by conformal geometric algebra neural nodes | | Contribution Type | Single Work | | Journal | Proc. SICE Symposium on Systems and Information 2008, 26-28 Nov. 2008, Himeji, Japan | | Journal Type | Japan | | Volume, Issue, Pages | pp.357 – 362 | | Author and coauthor | HITZER Eckhard | | Details | Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this approach to elementary representations of arbitrary points, point pairs, lines, circles, planes and spheres. Apart from including curved objects, conformal geometric algebra has an elegant unified quaternion like representation for all proper and improper Euclidean transformations, including reflections at spheres, general screw transformations and scaling. Expanding the concepts of real and complex neuronswe arrive at the new powerful concept of conformal geometric algebra neurons. These neurons can easily take the above mentioned geometric objects or sets of these objects as inputs and apply a wide range of geometric transformations via the geometric algebra valued weights. |
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148.
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Article
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Representation of crystallographic subperiodic groups by geometric algebra in E. Bayro-Corrochano, G. Scheuermann (eds.), Electronic Proc. of AGACSE 3, Leipzig, Germany, 17-19 (Collaboration) 2008
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| Language | English | | Publication Date | 2008 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Representation of crystallographic subperiodic groups by geometric algebra | | Contribution Type | Joint Work | | Journal | in E. Bayro-Corrochano, G. Scheuermann (eds.), Electronic Proc. of AGACSE 3, Leipzig, Germany, 17-19 | | Journal Type | Another Country | | Author and coauthor | HITZER Eckhard, D. Ichikawa | | Details | We explain how following the representation of 3D crystallographic space groups in geometric algebra it is further possible to similarly represent the 162 socalled subperiodic groups of crystallography in geometric algebra. We construct a new compact geometric algebra group representation symbol, which allows to read off the complete set of geometric algebra generators. For clarity we moreover state explicitly what generators are chosen. The group symbols are based on the representation of point groups in geometric algebra by versors (Clifford group, Lipschitz elements). |
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149.
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Article
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Robust geometric feature extraction and classification Proceedings of ISAMPE 2008, Busan, South Korea, 9-11 Oct. 2008 pp.175-182 (Collaboration) 2008
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| Language | English | | Publication Date | 2008 | | Type | Research Paper (International Conference Proceedings) | | Title | Robust geometric feature extraction and classification | | Contribution Type | Joint Work | | Journal | Proceedings of ISAMPE 2008, Busan, South Korea, 9-11 Oct. 2008 | | Volume, Issue, Pages | pp.175-182 | | Author and coauthor | M. T. Pham, K. Tachibana, E. Hitzer, S. Buchholz, T. Yoshikawa, T. Furuhashi |
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150.
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Article
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Tutorial Note on Geometric Algebra Neural Networks pp.1-20 (Collaboration) 2008
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| Language | English | | Publication Date | 2008 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | Tutorial Note on Geometric Algebra Neural Networks | | Contribution Type | Joint Work | | Journal Type | Another Country | | Publisher | AGACSE 3, Leipzig, Germany | | Volume, Issue, Pages | pp.1-20 | | Author and coauthor | K. Tachibana, E. Hitzer | | Details | AGACSE 3, Leipzig, Germany, 17-19. Aug. 2008, 20 pages. |
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151.
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Article
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Clifford Algebra Cl(3,0)-valued Wavelet Transformation, Clifford Wavelet Uncertainty Inequality and Clifford Gabor Wavelets International Journal of Wavelets, Multiresolution and Information Processing 5(6),pp.997-1019 (Collaboration) 2007
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| Language | English | | Publication Date | 2007 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Clifford Algebra Cl(3,0)-valued Wavelet Transformation, Clifford Wavelet Uncertainty Inequality and Clifford Gabor Wavelets | | Contribution Type | Joint Work | | Journal | International Journal of Wavelets, Multiresolution and Information Processing | | Journal Type | Another Country | | Publisher | World Scientific Singapore | | Volume, Issue, Pages | 5(6),pp.997-1019 | | Author and coauthor | HITZER Eckhard, B. Mawardi | | Details | In this paper, it is shown how continuous Clifford Cl3,0-valued admissible wavelets can be constructed using the similitude group SIM(3), a subgroup of the affine group of ℝ3. We express the admissibility condition in terms of a Cl3,0 Clifford Fourier transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform of multivector functions. We invent a generalized Clifford wavelet uncertainty principle. For scalar admissibility constant, it sets bounds of accuracy in multivector wavelet signal and image processing. As concrete example, we introduce multivector Clifford Gabor wavelets, and describe important properties such as the Clifford Gabor transform isometry, a reconstruction formula, and an uncertainty principle for Clifford Gabor wavelets. | | DOI | 10.1142/S0219691307002166 |
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152.
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Article
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Introduction to Theory, Construction and Application of Clifford Neural Networks pp.1-14 (Collaboration) 2007
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| Language | English | | Publication Date | 2007 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | Introduction to Theory, Construction and Application of Clifford Neural Networks | | Contribution Type | Joint Work | | Journal Type | Japan | | Volume, Issue, Pages | pp.1-14 | | Author and coauthor | S. Buchholz, K. Tachibana, E. Hitzer | | Details | ICONIP 2007, 14th International Conf. on Neural Information Processing, Japan, 13 Nov. 2007, 14 pp. |
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153.
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Article
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Optimal Learning Rates for Clifford Neurons International Conference on Artificial Neural Networks, Springer, New York, LNCS 4668,pp.864-873 (Collaboration) 2007
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| Language | English | | Publication Date | 2007 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Optimal Learning Rates for Clifford Neurons | | Contribution Type | Joint Work | | Journal | International Conference on Artificial Neural Networks, Springer, New York, LNCS | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 4668,pp.864-873 | | Author and coauthor | S. Buchholz, K. Tachibana, HITZER Eckhard | | Details | Neural computation in Clifford algebras, which include familiar complex numbers and quaternions as special cases, has recently become an active research field. As always, neurons are the atoms of computation. The paper provides a general notion for the Hessian matrix of Clifford neurons of an arbitrary algebra. This new result on the dynamics of Clifford neurons then allows the computation of optimal learning rates. A thorough discussion of error surfaces together with simulation results for different neurons is also provided. The presented contents should give rise to very efficient second–order training methods for Clifford Multi-layer perceptrons in the future. | | DOI | 10.1007/978-3-540-74690-4_88 . |
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154.
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Article
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Quaternion Fourier Transform on Quaternion Fields and Generalizations Advances in Applied Clifford Algebras 17(3),pp.497-517 (Single) 2007
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| Language | English | | Publication Date | 2007 | | Type | Research Paper (Scientific Journal) | | Title | Quaternion Fourier Transform on Quaternion Fields and Generalizations | | Contribution Type | Single Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Springer. | | Volume, Issue, Pages | 17(3),pp.497-517 | | Author and coauthor | HITZER Eckhard | | Details | We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to the QFT of real signals. We research the general linear (GL) transformation behavior of the QFT with matrices, Clifford geometric algebra and with examples. We finally arrive at wide-ranging non-commutative multivector FT generalizations of the QFT. Examples given are new volume-time and spacetime algebra Fourier transformations. | | DOI | 10.1007/s00006-007-0037-8 |
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155.
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Article
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Symmetry of orthorhombic materials and interactive 3D visualization in geometric algebra Proceedings of the International Symposium on Advanced Mechanical and Power Engineering 2007 pp.302-312 (Collaboration) 2007
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| Language | English | | Publication Date | 2007 | | Type | Research Paper (International Conference Proceedings) | | Title | Symmetry of orthorhombic materials and interactive 3D visualization in geometric algebra | | Contribution Type | Joint Work | | Journal | Proceedings of the International Symposium on Advanced Mechanical and Power Engineering 2007 | | Journal Type | Japan | | Volume, Issue, Pages | pp.302-312 | | Author and coauthor | D. Ichikawa, E. Hitzer | | Details | Proceedings of the International Symposium on Advanced Mechanical and Power Engineering 2007, between University of Fukui (Japan), Pukyong National University (Korea) and University of Shanghai for Science and Technology (China), 22-25 Nov. 2007, 302-312 (2007). |
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156.
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Article
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The hidden beauty of gold Proceedings of the International Symposium on Advanced Mechanical and Power Engineering 2007 pp.157-167 (Collaboration) 2007
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| Language | English | | Publication Date | 2007 | | Type | Research Paper (International Conference Proceedings) | | Title | The hidden beauty of gold | | Contribution Type | Joint Work | | Journal | Proceedings of the International Symposium on Advanced Mechanical and Power Engineering 2007 | | Journal Type | Japan | | Volume, Issue, Pages | pp.157-167 | | Author and coauthor | E. Hitzer, C. Perwass | | Details | Proceedings of the International Symposium on Advanced Mechanical and Power Engineering 2007, between University of Fukui (Japan), Pukyong National University (Korea) and University of Shanghai for Science and Technology (China), 22-25 Nov. 2007, pp. 157-167 (2007). |
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157.
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Article
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Tutorial on Fourier Transformations and Wavelet Transformations in Clifford Geometric Algebra Lecture notes of the Int. Workshop for “Computational Science with Geometric Algebra” (FCSG pp.65-87 (Single) 2007
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| Language | English | | Publication Date | 2007 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | Tutorial on Fourier Transformations and Wavelet Transformations in Clifford Geometric Algebra | | Contribution Type | Single Work | | Journal | Lecture notes of the Int. Workshop for “Computational Science with Geometric Algebra” (FCSG | | Journal Type | Japan | | Publisher | University of Nagoya, Japan. | | Volume, Issue, Pages | pp.65-87 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | in K. Tachibana (ed.), Lecture notes of the International Workshop for “Computational Science with Geometric Algebra” (FCSGA2007), Nagoya University, Japan, 14-21 Feb. 2007, pp. 65-87 (2007). |
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158.
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Article
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Tutorial on Reflections in Geometric Algebra Lecture notes of the int. Workshop for “Computational Science with Geometric Algebra” (FCSG pp.34-44 (Single) 2007
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| Language | English | | Publication Date | 2007 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | Tutorial on Reflections in Geometric Algebra | | Contribution Type | Single Work | | Journal | Lecture notes of the int. Workshop for “Computational Science with Geometric Algebra” (FCSG | | Journal Type | Japan | | Publisher | University of Nagoya, Japan. | | Volume, Issue, Pages | pp.34-44 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer | | Details | in K. Tachibana (ed.), Lecture notes of the international Workshop for “Computational Science with Geometric Algebra” (FCSGA2007), Nagoya University, Japan, 14-21 Feb. 2007, pp. 34-44 (2007). |
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159.
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Article
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Clifford Algebra Cl(3,0)-valued Wavelets and Uncertainty Inequality for Clifford Gabor Wavelet Transformation Preprints of Meeting of the Japan Society for Industrial and Applied Mathematics, ISSN: 1345-3378 pp.64-65 (Collaboration) 2006
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| Language | English | | Publication Date | 2006 | | Type | Research Paper (Material for Workshop, Symposium, etc.) | | Title | Clifford Algebra Cl(3,0)-valued Wavelets and Uncertainty Inequality for Clifford Gabor Wavelet Transformation | | Contribution Type | Joint Work | | Journal | Preprints of Meeting of the Japan Society for Industrial and Applied Mathematics, ISSN: 1345-3378 | | Journal Type | Japan | | Volume, Issue, Pages | pp.64-65 | | Author and coauthor | B. Mawardi, E. Hitzer | | ISSN | 1345-3378 |
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160.
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Article
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Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl(3,0) Advances in Applied Clifford Algebras 16(1),pp.41-61 (Collaboration) 2006
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| Language | English | | Publication Date | 2006 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl(3,0) | | Contribution Type | Joint Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland | | Volume, Issue, Pages | 16(1),pp.41-61 | | Author and coauthor | HITZER Eckhard, B. Mawardi | | Details | First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions (f:\user2R3→Cl3,0). Third, we show a set of important properties of the Clifford Fourier transform on Cl 3,0 such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl 3,0 multivector functions. | | DOI | 10.1007/s00006-006-0003-x |
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161.
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Crystallographic space groups: Representation and interactive visualization by geometric algebra Vixra preprint server. (Collaboration) 2006
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| Language | English | | Publication Date | 2006 | | Type | Technical Report, Preprint, etc. | | Title | Crystallographic space groups: Representation and interactive visualization by geometric algebra | | Contribution Type | Joint Work | | Journal | Vixra preprint server. | | Journal Type | Another Country | | Publisher | Vixra preprint server. | | Responsible for | Symbolic computations and text. | | Author and coauthor | E. Hitzer, C. Perwass | | Details | contribution to Proceedings of the 26th Int. Conference on Group Theoretical Methods in Physics, New York, USA, 2006. |
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162.
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Foundations of Multidimensional Wavelet Theory: The Quaternion Fourier Transform and its Generalizations Preprints of Meeting of the Japan Society for Industrial and Applied Mathematics, ISSN: 1345-3378 pp.66-67 (Single) 2006
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| Language | English | | Publication Date | 2006 | | Type | Research Paper (Material for Workshop, Symposium, etc.) | | Title | Foundations of Multidimensional Wavelet Theory: The Quaternion Fourier Transform and its Generalizations | | Contribution Type | Single Work | | Journal | Preprints of Meeting of the Japan Society for Industrial and Applied Mathematics, ISSN: 1345-3378 | | Journal Type | Japan | | Volume, Issue, Pages | pp.66-67 | | Author and coauthor | E. Hitzer | | ISSN | 1345-3378 |
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163.
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Article
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Space Group Visualizer for Monoclinic Space Groups Bulletin of the Society for Science on Form 21(1),pp.38-39 (Collaboration) 2006
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| Language | English | | Publication Date | 2006 | | Type | Research Paper (Material for Workshop, Symposium, etc.) | | Title | Space Group Visualizer for Monoclinic Space Groups | | Contribution Type | Joint Work | | Journal | Bulletin of the Society for Science on Form | | Volume, Issue, Pages | 21(1),pp.38-39 | | Author and coauthor | C. Perwass, E. Hitzer |
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164.
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Article
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The Space Group Visualizer Proceedings of the International Symposium on Advanced Mechanical Engineering, Pusan, 2006. pp.172-181 (Collaboration) 2006
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| Language | English | | Publication Date | 2006 | | Type | Research Paper (International Conference Proceedings) | | Title | The Space Group Visualizer | | Contribution Type | Joint Work | | Journal | Proceedings of the International Symposium on Advanced Mechanical Engineering, Pusan, 2006. | | Journal Type | Another Country | | Volume, Issue, Pages | pp.172-181 | | Author and coauthor | E. Hitzer, C. Perwass |
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165.
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Article
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Three Vector Generation of Crystal Space Groups in Geometric Algebra Bulletin of the Society for Science on Form 21(1),pp.55-56 (Collaboration) 2006
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| Language | English | | Publication Date | 2006 | | Type | Research Paper (International Conference Proceedings) | | Title | Three Vector Generation of Crystal Space Groups in Geometric Algebra | | Contribution Type | Joint Work | | Journal | Bulletin of the Society for Science on Form | | Volume, Issue, Pages | 21(1),pp.55-56 | | Author and coauthor | E. Hitzer, C. Perwass |
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166.
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Article
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Uncertainty Principle for Clifford Geometric Algebras Cl_{n,0} , n = 3 (mod 4) based on Clifford Fourier Transform Springer (SCI) Book Series Applied and Numerical Harmonic Analysis pp.45-54 (Collaboration) 2006
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| Language | English | | Publication Date | 2006 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Uncertainty Principle for Clifford Geometric Algebras Cl_{n,0} , n = 3 (mod 4) based on Clifford Fourier Transform | | Contribution Type | Joint Work | | Journal | Springer (SCI) Book Series Applied and Numerical Harmonic Analysis | | Volume, Issue, Pages | pp.45-54 | | Author and coauthor | HITZER Eckhard, B. Mawardi | | Details | First, the basic concepts of the multivector functions, vector differential and vector derivative in geometric algebra are introduced. Second, we define a generalized real Fourier transform on Clifford multivector-valued functions (f : ℝn → Cl n,0, n = 3 (mod 4)). Third, we introduce a set of important properties of the Clifford Fourier transform on Cl n,0, n = 3 (mod 4) such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving a directional uncertainty principle for Cl n,0 n = 3 (mod 4) multivector functions. | | DOI | 10.1007/978-3-7643-7778-6_6 |
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167.
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Conic Sections and Meet Intersections in Geometric Algebra Springer, Lecture Notes in Computer Science, 3519 3519,pp.350-362 (Single) 2005
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| Language | English | | Publication Date | 2005 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Conic Sections and Meet Intersections in Geometric Algebra | | Contribution Type | Single Work | | Journal | Springer, Lecture Notes in Computer Science, 3519 | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 3519,pp.350-362 | | Author and coauthor | HITZER Eckhard | | Details | This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective spaces, and the conformal model of Euclidean space. Second the conformal model descriptions of a subset of conic sections are listed in parametrizations specific for the use in the main part of the paper. In the third main part the meets of lines and circles, and of spheres and planes are calculated for all cases of real and virtual intersections. In the discussion special attention is on the hyperbolic carriers of the virtual intersections. | | DOI | 10.1007/11499251_25 |
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168.
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Crystal Cell and Space Lattice Symmetries in Clifford Geometric Algebra International Conference on Numerical Analysis and Applied Mathematics 2005, Wiley-VCH, Weinheim, 20 pp.937-941 (Collaboration) 2005
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| Language | English | | Publication Date | 2005 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Crystal Cell and Space Lattice Symmetries in Clifford Geometric Algebra | | Contribution Type | Joint Work | | Journal | International Conference on Numerical Analysis and Applied Mathematics 2005, Wiley-VCH, Weinheim, 20 | | Journal Type | Another Country | | Publisher | Wiley-VCH | | Volume, Issue, Pages | pp.937-941 | | Author and coauthor | HITZER Eckhard, C. Perwass | | Details | The structure of crystal cells in two and three dimensions is fundamental for many material properties. Many elements, including Aluminium, Copper and Iron have e.g. cubic unit cells. ... Today some 80\% of crystal structure analysis is carried out on crystallized biomolecules with huge investments from pharmaceutical companies.
In two dimensions atoms (or molecules) often group together in triangles, squares and hexagons (regular polygons). Crystal cells in three dimensions have triclinic, monoclinic, orthorhombic, hexagonal, rhombohedral, tetragonal and cubic shapes (see Fig. 1). |
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169.
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Full Geometric Description of All Symmetry Elements of Crystal Space Groups by the Suitable Choice of Only Three Vectors for Each Bravais Cell or Crystal Family Proceedings of the International Symposium on Advanced Mechanical Engineering, Pusan, 2005. pp.19-25 (Collaboration) 2005
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| Language | English | | Publication Date | 2005 | | Type | Research Paper (International Conference Proceedings) | | Title | Full Geometric Description of All Symmetry Elements of Crystal Space Groups by the Suitable Choice of Only Three Vectors for Each Bravais Cell or Crystal Family | | Contribution Type | Joint Work | | Journal | Proceedings of the International Symposium on Advanced Mechanical Engineering, Pusan, 2005. | | Journal Type | Another Country | | Volume, Issue, Pages | pp.19-25 | | Author and coauthor | E. Hitzer, C. Perwass |
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170.
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Article
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Interactive Visualization of Full Geometric Description of Crystal Space Groups Proceedings of the International Symposium on Advanced Mechanical Engineering, Pusan, 2005. pp.276-282 (Collaboration) 2005
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| Language | English | | Publication Date | 2005 | | Type | Research Paper (International Conference Proceedings) | | Title | Interactive Visualization of Full Geometric Description of Crystal Space Groups | | Contribution Type | Joint Work | | Journal | Proceedings of the International Symposium on Advanced Mechanical Engineering, Pusan, 2005. | | Journal Type | Another Country | | Volume, Issue, Pages | pp.276-282 | | Author and coauthor | C. Perwass, E. Hitzer |
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171.
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Article
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Relativistic Physics as Application of Geometric Algebra Proceedings of the International Conference on Relativity 2005. pp.71-90 (Single) 2005
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| Language | English | | Publication Date | 2005 | | Type | Research Paper (International Conference Proceedings) | | Title | Relativistic Physics as Application of Geometric Algebra | | Contribution Type | Single Work | | Journal | Proceedings of the International Conference on Relativity 2005. | | Journal Type | Another Country | | Publisher | University of Amravati, India, 2005. | | Volume, Issue, Pages | pp.71-90 | | Author and coauthor | E. Hitzer |
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172.
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Article
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The GeometricAlgebra Java Package - Novel Structure Implementation of 5D Geometric Algebra R_(4,1) for Object Oriented Euclidean Geometry, Space-Time Physics and Object Oriented Computer Algebra Mem. Fac. Eng. Univ. Fukui 53(1),pp.47-59 (Collaboration) 2005
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| Language | English | | Publication Date | 2005 | | Type | Research Paper (Bulletin of University/Institution) | | Title | The GeometricAlgebra Java Package - Novel Structure Implementation of 5D Geometric Algebra R_(4,1) for Object Oriented Euclidean Geometry, Space-Time Physics and Object Oriented Computer Algebra | | Contribution Type | Joint Work | | Journal | Mem. Fac. Eng. Univ. Fukui | | Journal Type | Japan | | Publisher | University of Fukui | | Volume, Issue, Pages | 53(1),pp.47-59 | | Author and coauthor | E. Hitzer, G. Utama |
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173.
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Article
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Uncertainty Principle for the Clifford Geometric Algebra Cl(3,0) based on Clifford Fourier Transform International Conference on Numerical Analysis and Applied Mathematics 2005 pp.922-925 (Collaboration) 2005
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| Language | English | | Publication Date | 2005 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Uncertainty Principle for the Clifford Geometric Algebra Cl(3,0) based on Clifford Fourier Transform | | Contribution Type | Joint Work | | Journal | International Conference on Numerical Analysis and Applied Mathematics 2005 | | Journal Type | Another Country | | Publisher | Wiley-VCH | | Volume, Issue, Pages | pp.922-925 | | Author and coauthor | HITZER Eckhard, B. Mawardi | | Details | In the field of applied mathematics the Fourier transform has developed into an important tool. It is a powerful method for solving partial differential equations. The Fourier transform provides also a technique for signal analysis where the signal from the original domain is transformed to the spectral or frequency domain. In the frequency domain many characteristics of the signal are revealed. With these facts in mind, we extend the Fourier transform in geometric algebra. ...
In this paper we adopt and expand the generalization of the Fourier transform in Clifford geometric algebra G_3 recently suggested by Ebling and Scheuermann [5]. We explicitly show detailed properties of the real Clifford geometric algebra Fourier transform (CFT), which we subsequently use to define and prove the uncertainty principle for G_3 multivector functions. |
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174.
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Article
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6-[3-Hydroxy-17-oxoestra-1,3,5(10)-trien-7[beta]-yl]hexanenitrile Acta Crystallographica Section C 60(2),pp.o130-o132 (Collaboration) 2004
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| Language | English | | Publication Date | 2004 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | 6-[3-Hydroxy-17-oxoestra-1,3,5(10)-trien-7[beta]-yl]hexanenitrile | | Contribution Type | Joint Work | | Journal | Acta Crystallographica Section C | | Journal Type | Another Country | | Publisher | Wiley | | Volume, Issue, Pages | 60(2),pp.o130-o132 | | Responsible for | Computations. | | Author and coauthor | C. Yamamoto, T. Matsumoto, M. Watanabe, E. HITZER, S. Mataka and T. Thiema | | Details | In the title compound, C24H31NO2, ring B adopts a conformation between the boat and twisted-boat forms. This conformation best accommodates adverse intramolecular H...H interactions between the H atoms of the 7[beta]-substituent and the two nearest ring H atoms. The tilt angle between rings A and D is 28.6 (1)°. | | DOI | 10.1107/S010827010302866X |
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175.
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Article
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Crystal Cells in Geometric Algebra Proceedings of the International Symposium on Advanced Mechanical Engineering, Fukui, 2004. pp.290-295 (Collaboration) 2004
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| Language | English | | Publication Date | 2004 | | Type | Research Paper (International Conference Proceedings) | | Title | Crystal Cells in Geometric Algebra | | Contribution Type | Joint Work | | Journal | Proceedings of the International Symposium on Advanced Mechanical Engineering, Fukui, 2004. | | Journal Type | Japan | | Volume, Issue, Pages | pp.290-295 | | Author and coauthor | E. Hitzer, C. Perwass |
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176.
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Article
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English Education Reform University of Fukui, Fac. Dev. Forum 4,pp.11-11 (Single) 2004
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| Language | English | | Publication Date | 2004 | | Type | Technical Report, Preprint, etc. | | Title | English Education Reform | | Contribution Type | Single Work | | Journal | University of Fukui, Fac. Dev. Forum | | Journal Type | Japan | | Publisher | University of Fukui, Japan. | | Volume, Issue, Pages | 4,pp.11-11 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer |
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177.
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Article
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Euclidean Geometric Objects in the Clifford Geometric Algebra of {Origin, 3-Space, Infinity} Bulletin of the Belgian Mathematical Society - Simon Stevin 11(5),pp.653-662 (Single) 2004
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| Language | English | | Publication Date | 2004 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Euclidean Geometric Objects in the Clifford Geometric Algebra of {Origin, 3-Space, Infinity} | | Contribution Type | Single Work | | Journal | Bulletin of the Belgian Mathematical Society - Simon Stevin | | Journal Type | Another Country | | Publisher | Belgian Mathematical Society | | Volume, Issue, Pages | 11(5),pp.653-662 | | Author and coauthor | HITZER Eckhard | | Details | This paper concentrates on the homogeneous (conformal) model of Euclidean space (Horosphere) with subspaces that intuitively correspond to Euclidean geometric objects in three dimensions. Mathematical details of the construction and (useful) parametrizations of the 3D Euclidean object models are explicitly demonstrated in order to show how 3D Euclidean information on positions, orientations and radii can be extracted. |
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178.
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Article
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New Ways for Physics Education University of Fukui, Fac. Dev. Forum 5,pp.12-12 (Single) 2004
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| Language | English | | Publication Date | 2004 | | Type | Technical Report, Preprint, etc. | | Title | New Ways for Physics Education | | Contribution Type | Single Work | | Journal | University of Fukui, Fac. Dev. Forum | | Journal Type | Japan | | Publisher | University of Fukui, Japan. | | Volume, Issue, Pages | 5,pp.12-12 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer |
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179.
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Article
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What is an imaginary number? Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008 pp.1-4 (Single) 2004
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| Language | English | | Publication Date | 2004 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | What is an imaginary number? | | Contribution Type | Single Work | | Journal | Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008 | | Journal Type | Japan | | Volume, Issue, Pages | pp.1-4 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer |
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180.
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Article
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Axioms of Geometric Algebra Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008. pp.1-8 (Single) 2003
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| Language | English | | Publication Date | 2003 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | Axioms of Geometric Algebra | | Contribution Type | Single Work | | Journal | Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008. | | Journal Type | Japan | | Volume, Issue, Pages | pp.1-8 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer |
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181.
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Article
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Conic sections through five points - classical, projective, conformal Proceedings of the International Symposium 2003 of Advanced Mechanical Engineering, Pusan, 2003. pp.109-114 (Single) 2003
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| Language | English | | Publication Date | 2003 | | Type | Research Paper (International Conference Proceedings) | | Title | Conic sections through five points - classical, projective, conformal | | Contribution Type | Single Work | | Journal | Proceedings of the International Symposium 2003 of Advanced Mechanical Engineering, Pusan, 2003. | | Journal Type | Another Country | | Volume, Issue, Pages | pp.109-114 | | Author and coauthor | E. Hitzer |
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182.
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Article
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Determinants in Geometric Algebra Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008 pp.1-3 (Single) 2003
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| Language | English | | Publication Date | 2003 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | Determinants in Geometric Algebra | | Contribution Type | Single Work | | Journal | Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008 | | Journal Type | Japan | | Volume, Issue, Pages | pp.1-3 |
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183.
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Article
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Geometric Algebra illustrated by Cinderella Advances in Applied Clifford Algebras 13(2),pp.157-181 (Collaboration) 2003
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| Language | English | | Publication Date | 2003 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Geometric Algebra illustrated by Cinderella | | Contribution Type | Joint Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 13(2),pp.157-181 | | Responsible for | Most of text and graphics. | | Author and coauthor | HITZER Eckhard, Luca Redaelli | | Details | Conventional illustrations of the rich elementary relations and physical applications of geometric algebra are helpful, but restricted in communicating full generality and time dependence. Up till now very little animated and fully interactive, free, instant access, online material is available.
This report presents therefore a set of over 90 newly developed (freely online accessible) JAVA applets. These applets range from the elementary concepts of vector, bivector, outer product and rotations to triangle relationships, oscillations and polarized waves. A special group of 21 applets illustrates three geometrically different approaches to the representation of conics; and even more ways to describe ellipses. | | DOI | 10.1007/s00006-003-0013-x |
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184.
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Article
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Gram-Schmidt Orthogonalization in Geometric Algebra Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008 pp.1-2 (Single) 2003
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| Language | English | | Publication Date | 2003 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | Gram-Schmidt Orthogonalization in Geometric Algebra | | Contribution Type | Single Work | | Journal | Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008 | | Journal Type | Japan | | Volume, Issue, Pages | pp.1-2 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer |
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185.
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Article
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KamiWaAi - Interactive 3D Sketching with Java based on Cl(4,1) Conformal Model of Euclidean Space Advances in Applied Clifford Algebras 13(1),pp.11-45 (Single) 2003
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| Language | English | | Publication Date | 2003 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | KamiWaAi - Interactive 3D Sketching with Java based on Cl(4,1) Conformal Model of Euclidean Space | | Contribution Type | Single Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 13(1),pp.11-45 | | Author and coauthor | HITZER Eckhard | | Details | This paper introduces the new interactive Java sketching software KamiWaAi. Its graphical user interface enables the user without any knowledge of both mathematics or computer science, to do full three dimensional “drawings” on the screen. The resulting constructions can be reshaped interactively by dragging its points over the screen. KamiWaAi implements geometric objects like points, lines, circles, spheres, etc. directly as software objects (Java classes) of the same name. | | DOI | 10.1007/s00006-003-0004-y |
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186.
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Article
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Learning about Conic Sections with Geometric Algebra and Cinderella Proc. of the Symposium Innovative Teaching of Mathematics with Geometric Algebra 2003 pp.89-104 (Single) 2003
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| Language | English | | Publication Date | 2003 | | Type | Research Paper (International Conference Proceedings) | | Title | Learning about Conic Sections with Geometric Algebra and Cinderella | | Contribution Type | Single Work | | Journal | Proc. of the Symposium Innovative Teaching of Mathematics with Geometric Algebra 2003 | | Journal Type | Japan | | Publisher | Kyoto University RIMS | | Volume, Issue, Pages | pp.89-104 | | Author and coauthor | E. Hitzer |
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187.
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Article
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The geometric product and derived products Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008 pp.1-11 (Single) 2003
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| Language | English | | Publication Date | 2003 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | The geometric product and derived products | | Contribution Type | Single Work | | Journal | Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008 | | Journal Type | Japan | | Volume, Issue, Pages | pp.1-11 |
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188.
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Article
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The use of quadratic forms in geometric algebra Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008 pp.1-6 (Single) 2003
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| Language | English | | Publication Date | 2003 | | Type | Lecture Material (Seminar, Tutorial, Workshop, Lecture, etc.) | | Title | The use of quadratic forms in geometric algebra | | Contribution Type | Single Work | | Journal | Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008 | | Journal Type | Japan | | Volume, Issue, Pages | pp.1-6 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer |
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189.
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Article
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Geometric Calculus - Engineering Mathematics for the 21st Century Mem. Fac. Eng. Fukui Univ. 50(1),pp.127-137 (Single) 2002
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| Language | English | | Publication Date | 2002 | | Type | Research Paper (Bulletin of University/Institution) | | Title | Geometric Calculus - Engineering Mathematics for the 21st Century | | Contribution Type | Single Work | | Journal | Mem. Fac. Eng. Fukui Univ. | | Journal Type | Japan | | Publisher | University of Fukui | | Volume, Issue, Pages | 50(1),pp.127-137 | | Responsible for | Everything. | | Author and coauthor | Eckhard Hitzer |
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190.
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Article
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Multivector Differential Calculus Advances in Applied Clifford Algebras 12(2),pp.135-182 (Single) 2002
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| Language | English | | Publication Date | 2002 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Multivector Differential Calculus | | Contribution Type | Single Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 12(2),pp.135-182 | | Author and coauthor | HITZER Eckhard | | Details | Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential calculus part of geometric calculus. The multivector differential is introduced, followed by the multivector derivative and the adjoint of multivector functions. The basic rules of multivector differentiation are derived explicitly, as well as a variety of basic multivector derivatives. | | DOI | 10.1007/BF03161244 |
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191.
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Article
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Play with Geometry - Animated and Interactive, Free, Instant Access, Online Geometric Algebra Java Applets Proceedings of Fukui Univ. Int. Congress, Int. Symp. on Advanced Mech. Engineering, Fukui, 2002. pp.7-12 (Collaboration) 2002
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| Language | English | | Publication Date | 2002 | | Type | Research Paper (International Conference Proceedings) | | Title | Play with Geometry - Animated and Interactive, Free, Instant Access, Online Geometric Algebra Java Applets | | Contribution Type | Joint Work | | Journal | Proceedings of Fukui Univ. Int. Congress, Int. Symp. on Advanced Mech. Engineering, Fukui, 2002. | | Journal Type | Japan | | Publisher | University of Fukui, 2002. | | Volume, Issue, Pages | pp.7-12 | | Responsible for | Most of text and graphics. | | Author and coauthor | E. Hitzer, L. Redaelli |
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192.
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Article
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Vector Differential Calculus Mem. Fac. Eng. Fukui Univ. 50(1),pp.127-137 (Single) 2002
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| Language | English | | Publication Date | 2002 | | Type | Research Paper (Bulletin of University/Institution) | | Title | Vector Differential Calculus | | Contribution Type | Single Work | | Journal | Mem. Fac. Eng. Fukui Univ. | | Journal Type | Japan | | Publisher | University of Fukui. | | Volume, Issue, Pages | 50(1),pp.127-137 | | Author and coauthor | E. Hitzer |
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193.
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Article
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A real explanation for imaginary eigenvalues and complex eigenvectors Proc. of the Nat. Symp. on Mathematical Sciences, 1-5 March, 2001, Nagpur, India. 1,pp.1-26 (Single) 2001
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| Language | English | | Publication Date | 2001 | | Type | Research Paper (International Conference Proceedings) | | Title | A real explanation for imaginary eigenvalues and complex eigenvectors | | Contribution Type | Single Work | | Journal | Proc. of the Nat. Symp. on Mathematical Sciences, 1-5 March, 2001, Nagpur, India. | | Journal Type | Another Country | | Publisher | University of Nagpur, Nagpur, India. | | Volume, Issue, Pages | 1,pp.1-26 | | Author and coauthor | E. Hitzer |
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194.
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Article
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Antisymmetric Matrices are Real Bivectors Mem. Fac. Eng. Fukui Univ. 49(2),pp.283-298 (Single) 2001
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| Language | English | | Publication Date | 2001 | | Type | Research Paper (Bulletin of University/Institution) | | Title | Antisymmetric Matrices are Real Bivectors | | Contribution Type | Single Work | | Journal | Mem. Fac. Eng. Fukui Univ. | | Journal Type | Japan | | Publisher | University of Fukui. | | Volume, Issue, Pages | 49(2),pp.283-298 | | Author and coauthor | E. Hitzer |
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195.
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Article
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Early works on the Hagen-Poiseuille flow Mem. Fac. Eng. Fukui Univ. 49(1),pp.45-53 (Single) 2001
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| Language | English | | Publication Date | 2001 | | Type | Research Paper (Bulletin of University/Institution) | | Invitation | With invitation | | Title | Early works on the Hagen-Poiseuille flow | | Contribution Type | Single Work | | Journal | Mem. Fac. Eng. Fukui Univ. | | Journal Type | Japan | | Publisher | University of Fukui. | | Volume, Issue, Pages | 49(1),pp.45-53 | | Author and coauthor | E. Hitzer |
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196.
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Article
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Geometric Calculus for Engineers Proc. of the Pukyong National University - Fukui University International Symposium 2001 pp.59-66 (Single) 2001
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| Language | English | | Publication Date | 2001 | | Type | Research Paper (International Conference Proceedings) | | Title | Geometric Calculus for Engineers | | Contribution Type | Single Work | | Journal | Proc. of the Pukyong National University - Fukui University International Symposium 2001 | | Journal Type | Another Country | | Publisher | Pukyong National University, Busan, Korea | | Volume, Issue, Pages | pp.59-66 | | Author and coauthor | E. Hitzer |
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197.
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Article
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Imaginary eigenvalues and complex eigenvectors explained by real geometry Applied Geometrical Algebras in Computer Science and Engineering, AGACSE 2001, Birkhauser pp.145-153 (Single) 2001
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| Language | English | | Publication Date | 2001 | | Type | Research Paper (International Conference Proceedings) | | Peer Review | With peer review | | Title | Imaginary eigenvalues and complex eigenvectors explained by real geometry | | Contribution Type | Single Work | | Journal | Applied Geometrical Algebras in Computer Science and Engineering, AGACSE 2001, Birkhauser | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | pp.145-153 | | Author and coauthor | HITZER Eckhard | | Details | This paper first reviews how anti-symmetric matrices in two dimensions yield imaginary eigenvalues and complex eigenvectors. It is shown how this carries on to rotations by means of the Cayley transformation. Then a real geometric interpretation is given to the eigenvalues and eigenvectors by means of real geometric algebra. The eigenvectors are seen to be two component eigenspinors which can be further reduced to underlying vector duplets. The eigenvalues are interpreted as rotation operators, which rotate the underlying vector duplets. The second part of this paper extends and generalizes the treatment to three dimensions. Finally the four-dimensional problem is stated. |
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198.
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Classical and Semi-Classical Optics with MAPLE: Investigating a Two-dimensional Light Ray Geometry Proceedings of Teaching Computational Physics, 12th Summer School on Com. Techn. in Physics pp.54-56 (Single) 2000
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| Language | English | | Publication Date | 2000 | | Type | Research Paper (International Conference Proceedings) | | Title | Classical and Semi-Classical Optics with MAPLE: Investigating a Two-dimensional Light Ray Geometry | | Contribution Type | Single Work | | Journal | Proceedings of Teaching Computational Physics, 12th Summer School on Com. Techn. in Physics | | Journal Type | Another Country | | Volume, Issue, Pages | pp.54-56 | | Author and coauthor | E. Hitzer |
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199.
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Article
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Closed Light Paths in Equiangular Spiral Disks Advances in Applied Clifford Algebras 10(2),pp.225-257 (Single) 2000
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| Language | English | | Publication Date | 2000 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Closed Light Paths in Equiangular Spiral Disks | | Contribution Type | Single Work | | Journal | Advances in Applied Clifford Algebras | | Journal Type | Another Country | | Publisher | Birkhaeuser, Basel, Switzerland. | | Volume, Issue, Pages | 10(2),pp.225-257 | | Author and coauthor | HITZER Eckhard | | Details | A new type of deformation for microscopic laser disks, the equiangular spiral deformation is proposed. First a short review of the geometry of light paths in equiangular spirals in the language of real two-dimensional geometric calculus is given. Second, the constituting equations for closed paths inside equiangular spirals are derived. Third, their numerical solution is performed and found to yield two generic types of closed light paths. Degenerate closed paths that exist over large intervals of the deformation parameter, and nondegenerate closed paths which only exist over relatively small deformation parameter intervals spanning less than 1% of the nondegenerate intervals. Fourth, amongst the nondegenerate paths a stable asymmetric bow-tie shaped light trajectory was found. | | DOI | 10.1007/s00006-000-0005-z |
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200.
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Article
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The Geometry of Light Paths for Equiangular Spirals Advances in Applied Clifford Algebras 9(2),pp.261-286 (Single) 1999
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| Language | English | | Publication Date | 1999 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | The Geometry of Light Paths for Equiangular Spirals | | Contribution Type | Single Work | | Journal | Advances in Applied Clifford Algebras | | Volume, Issue, Pages | 9(2),pp.261-286 | | Author and coauthor | HITZER Eckhard | | Details | First geometric calculus alongside its description of equiangular spirals, reflections and rotations is introduced briefly. Then single and double reflections at such a spiral are investigated. It proves suitable to distinguish incidence from theright andleft relative to the radial direction. The properties of geometric light propagation inside the equiangular spiral are discussed, as well as escape conditions and characteristics. Finally the dependence of right and left incidence from the source locations are examined, revealing a well defined innercritical curve, which delimits the area of purely right incident propagation. This critical curve is self similar to the original equiangular spiral. | | DOI | 10.1007/BF03042381 |
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201.
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New Higgs Field Ansatz for Effective Gravity in Flat Space Time Acta Physica Polonica B 29(4),pp.971-980 (Collaboration) 1998
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| Language | English | | Publication Date | 1998 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | New Higgs Field Ansatz for Effective Gravity in Flat Space Time | | Contribution Type | Joint Work | | Journal | Acta Physica Polonica B | | Volume, Issue, Pages | 29(4),pp.971-980 | | Author and coauthor | HITZER Eckhard, A. Geitner, M. Hanauske | | Details | Regarding Pauli's matrices as proper Higgs fields one can deduce an effective approximation for gravity in flat space. In this work we extend this approximation up to the second order, reaching complete agreement in the special case of gravitational waves. Unification in view, we introduce isospinorial degrees of freedom. In this way the mass spectrum and chiral asymmetry can be generated with the help of an additional scalar Higgs field. The Higgs modes corresponding to gravity are discussed. |
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202.
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Integration of Einstein's Equations in the Weak-Field Domain Using the "Einstein" Gauge International Journal of Theoretical Physics 36(2),pp.559-567 (Collaboration) 1997
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| Language | English | | Publication Date | 1997 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Integration of Einstein's Equations in the Weak-Field Domain Using the "Einstein" Gauge | | Contribution Type | Joint Work | | Journal | International Journal of Theoretical Physics | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 36(2),pp.559-567 | | Author and coauthor | HITZER Eckhard, H. Dehnen | | Details | We propose a new alternative gauge for the Einstein equations instead of the de Donder gauge, which allows in the limit of weak fields a straightforward integration of these equations. The Newtonian potential plays a new and interesting role in this framework. The calculations are demonstrated explicitly for two simple astrophysical models. | | DOI | 10.1007/BF02435749 |
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203.
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The Higgs-Field Theoretic Extension of the Spin-Gauge Theory of Gravity (Single) 1996
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| Language | English | | Publication Date | 1996 | | Type | Doctoral Dissertation | | Title | The Higgs-Field Theoretic Extension of the Spin-Gauge Theory of Gravity | | Contribution Type | Single Work | | Journal Type | Another Country | | Publisher | Hartung-Gorre, Konstanz, Germany | | Total page number | 123 | | Responsible for | Everything | | Authorship | Lead author | | Author and coauthor | Eckhard Hitzer | | Original author(s) | Eckhard Hitzer |
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204.
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SU(2) x U(1) Gauge Gravity International Journal of Theoretical Physics 34(9),pp.1981-2001 (Collaboration) 1995
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| Language | English | | Publication Date | 1995 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | SU(2) x U(1) Gauge Gravity | | Contribution Type | Joint Work | | Journal | International Journal of Theoretical Physics | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 34(9),pp.1981-2001 | | Author and coauthor | H. Dehnen, E. Hitzer | | Details | We propose a Lorentz-covariant Yang-Mills “spin-gauge” theory, where the function-valued Pauli matrices play the role of a nonscalar Higgs field. As symmetry group we choose SU(2) × U(1) of the 2-spinors describing particle/antiparticle states. After symmetry breaking, a nonscalar Lorentz-covariant Higgsfield gravity appears, which can be interpreted within a classical limit as Einstein's metrical theory of gravity, where we restrict ourselves in a first step to its linearized version. | | DOI | 10.1007/BF00674079 |
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205.
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Spin-Gauge Theory of Gravity with Higgs-Field Mechanism International Journal of Theoretical Physics 33(3),pp.575-592 (Collaboration) 1994
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| Language | English | | Publication Date | 1994 | | Type | Research Paper (Scientific Journal) | | Peer Review | With peer review | | Title | Spin-Gauge Theory of Gravity with Higgs-Field Mechanism | | Contribution Type | Joint Work | | Journal | International Journal of Theoretical Physics | | Journal Type | Another Country | | Publisher | Springer | | Volume, Issue, Pages | 33(3),pp.575-592 | | Author and coauthor | H. Dehnen, E. Hitzer | | Details | We propose a Lorentz-covariant Yang-Mills spin-gauge theory, where the function-valued Dirac matrices play the role of a nonscalar Higgs-field. As symmetry group we chooseSU(2) xU(1). After symmetry breaking a nonscalar Lorentz-covariant Higgs-field gravity appears, which can be interpreted within a classical limit as Einstein's metrical theory of gravity, where we restrict ourselves in a first step to its linearized version. | | DOI | 10.1007/BF00670517 |
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206.
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Other
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Editorial of Applied Geometric Algebras in Computer Science and Engineering (AGACSE 21) Mathematical Methods in the Applied Sciences (Collaboration) 2023
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| Language | English | | Publication Date | 2023 | | Type | Other | | Title | Editorial of Applied Geometric Algebras in Computer Science and Engineering (AGACSE 21) | | Contribution Type | Joint Work | | Journal | Mathematical Methods in the Applied Sciences | | Journal Type | Another Country | | Publisher | Wiley | | Responsible for | Part of text | | International coauthorship | International coauthorship | | Author and coauthor | P. Vasik, E. Hitzer, C. Lavor | | Original author(s) | P. Vasik, E. Hitzer, C. Lavor | | Details | P. Vasik, E. Hitzer, C. Lavor, Editorial of Applied Geometric Algebras in Computer Science and Engineering (AGACSE 21), accepted for Special Issue of Mathematical Methods in the Applied Sciences, Wiley, 2023, DOI: 10.1002/mma.9783 |
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■ #Academic Conference Presentation
| 1. |
2023/10/21 |
Scientific Research - Opportunities and Pitfalls (First Symposium of European Researchers in Japan)
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| Date | 2023/10/21 | | Presentation Theme | Scientific Research - Opportunities and Pitfalls | | Conference | First Symposium of European Researchers in Japan | | Conference Type | Workshop/Symposium | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Country | Japan | | Venue | Tokyo | | Holding period | 2023/10/21～2023/10/21 | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | Invited Lecture: Eckhard Hitzer, Scientific Research - Opportunities and Pitfalls, First Symposium of European Researchers in Japan, 21 Oct. 2023, Europa House, Tokyo, Japan. |
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| 2. |
2023/10/01 |
Man’s Influence on Nature Viewed through the Lenses of Science and Old Testament (ICU ICC 60th Anniversary Symposium, Perspective on Nature and Environmental Ethics in the Old Testament)
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| Date | 2023/10/01 | | Presentation Theme | Man’s Influence on Nature Viewed through the Lenses of Science and Old Testament | | Conference | ICU ICC 60th Anniversary Symposium, Perspective on Nature and Environmental Ethics in the Old Testament | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Country | Japan | | Venue | Mitaka, Tokyo | | Holding period | 2023/09/29～2023/10/01 | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | Invited Lecture: Eckhard Hitzer, Man’s Influence on Nature Viewed through the Lenses of Science and Old Testament, ICU ICC 60th Anniversary Symposium, Perspective on Nature and Environmental Ethics in the Old Testament, September 29th - October 1st, 2023, ICU, Mitaka, Japan |
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| 3. |
2023/08/28 |
Quadratic Phase Quaternion Domain Fourier Transform (Computer Graphics International 2023 (CGI 2023), Workshop Empowering Novel Geometric Algebra for Graphics and Engineering 2023 (ENGAGE 2023))
|
| Date | 2023/08/28 | | Presentation Theme | Quadratic Phase Quaternion Domain Fourier Transform | | Conference | Computer Graphics International 2023 (CGI 2023), Workshop Empowering Novel Geometric Algebra for Graphics and Engineering 2023 (ENGAGE 2023) | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Country | China | | Venue | Shanghai | | Holding period | 2023/08/28～2023/08/28 | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | Quadratic Phase Quaternion Domain Fourier Transform, Computer Graphics International 2023 (CGI 2023), Workshop Empowering Novel Geometric Algebra for Graphics and Engineering 2023 (ENGAGE 2023), 12:00pm, 28 Aug. 2023, Marriott Hotel, Shanghai, China. |
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| 4. |
2023/08/23 |
Geometric Algebra, Airborne Laser Scanning and Oriented Points (The Second International Conference on W.K. Clifford's Geometric Algebra and Geographic Information Science (GAGIS II))
|
| Date | 2023/08/23 | | Presentation Theme | Geometric Algebra, Airborne Laser Scanning and Oriented Points | | Conference | The Second International Conference on W.K. Clifford's Geometric Algebra and Geographic Information Science (GAGIS II) | | Conference Type | International | | Presentation Type | Speech (Keynote) | | Contribution Type | Individual | | Invited | Invited | | Country | China | | Venue | Nanjing | | Holding period | 2023/08/23～2023/08/25 | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | Keynote Lecture: Geometric Algebra, Airborne Laser Scanning and Oriented Points, The Second International Conference on W.K. Clifford's Geometric Algebra and Geographic Information Science (GAGIS II), Nanjing Normal University, Nanjing, China, We. 23 Aug. 2023: 9:00-10:00 CST. |
|
| 5. |
2023/01/27 |
Octonion Fourier Transform in Geometric Algebra of R3 and Polar Representations of Octonion Analytic Signals (Workshop on High-dimensional and spatio-temporal neuro-dynamics and its application to the construction of related systems)
|
| Date | 2023/01/27 | | Presentation Theme | Octonion Fourier Transform in Geometric Algebra of R3 and Polar Representations of Octonion Analytic Signals | | Conference | Workshop on High-dimensional and spatio-temporal neuro-dynamics and its application to the construction of related systems | | Conference Type | Workshop/Symposium | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Country | Japan | | Venue | Tohoku, Sendai | | Holding period | 2023/01/27～2023/01/27 | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | Invited Lecture: Octonion Fourier Transform in Geometric Algebra of R3 and Polar Representations of Octonion Analytic Signals, Tohoku, Workshop on High-dimensional and spatio-temporal neuro-dynamics and its application to the construction of related systems, RIEC, Tohoku University, Sendai, Japan, 27 Jan. 2023. |
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| 6. |
2022/10/16 |
Quaternions in 2022 (Quaternions 179 (online))
|
| Date | 2022/10/16 | | Presentation Theme | Quaternions in 2022 | | Conference | Quaternions 179 (online) | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 7. |
2022/10/05 |
Inner product of two oriented points in conformal geometric algebra (International Conference of Advanced Computational Application of Geometric Algebra (ICACGA 2022))
|
| Date | 2022/10/05 | | Presentation Theme | Inner product of two oriented points in conformal geometric algebra | | Conference | International Conference of Advanced Computational Application of Geometric Algebra (ICACGA 2022) | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Country | United States | | Venue | Denver, Colorado | | Holding period | 2022/10/02～2022/10/05 | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 8. |
2022/09/12 |
Embedding of Octonion Fourier Transform in Geometric Algebra of R^3 and Polar Representations of Octonion Analytic Signals (Computer Graphics International 2022 (CGI 2022), Workshop Empowering Novel Geometric Algebra for Graphics and Engineering 2022 (ENGAGE 2022))
|
| Date | 2022/09/12 | | Presentation Theme | Embedding of Octonion Fourier Transform in Geometric Algebra of R^3 and Polar Representations of Octonion Analytic Signals | | Conference | Computer Graphics International 2022 (CGI 2022), Workshop Empowering Novel Geometric Algebra for Graphics and Engineering 2022 (ENGAGE 2022) | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Country | Switzerland | | Venue | Geneva | | Holding period | 2022/09/12～2022/09/12 | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 9. |
2022/07/01 |
Relating Clifford Algebras and Octonions (International Conference Day to pay Tribute to Outstanding Professor Ahmed ABOUELAZ)
|
| Date | 2022/07/01 | | Presentation Theme | Relating Clifford Algebras and Octonions | | Conference | International Conference Day to pay Tribute to Outstanding Professor Ahmed ABOUELAZ | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Country | Morocco | | Venue | Casablanca, Km 8 Route d’El Jadida, BP 5366 Maarif, Casablanca, Morocco | | Holding period | 2022/07/01～2022/07/01 | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 10. |
2022/03/23 |
Clifford algebra and octonions (Mathematical Colloquium)
|
| Date | 2022/03/23 | | Presentation Theme | Clifford algebra and octonions | | Conference | Mathematical Colloquium | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Country | Israel | | Venue | Tel Aviv, Israel | | Holding period | 2022/03/23～2022/03/23 | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 11. |
2021/09/21 |
Special affine quaternion domain Fourier transform (DMV-OeMG Annual Conference 2021, Session M7 Clifford Analysis and Phase Retrieval for Image Processing)
|
| Date | 2021/09/21 | | Presentation Theme | Special affine quaternion domain Fourier transform | | Conference | DMV-OeMG Annual Conference 2021, Session M7 Clifford Analysis and Phase Retrieval for Image Processing | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Venue | University of Passau, Germany | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | E. Hitzer, Special affine quaternion domain Fourier transform, DMV-OeMG Annual Conference 2021, Session M7 Clifford Analysis and Phase Retrieval for Image Processing, 11:30-12:00, 28 Sep. 2021, University of Passau, Germany | | URL for researchmap | https://www.uni-passau.de/en/dmv-oemg-jahrestagung-2021/home/ |
|
| 12. |
2021/09/06 |
Special affine Fourier transform for space-time algebra signals (Computer Graphics International 2021 (CGI2021), Workshop Geometric Algebra for Computing, Graphics and Engineering 2021 (ENGAGE2021))
|
| Date | 2021/09/06 | | Presentation Theme | Special affine Fourier transform for space-time algebra signals | | Conference | Computer Graphics International 2021 (CGI2021), Workshop Geometric Algebra for Computing, Graphics and Engineering 2021 (ENGAGE2021) | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Venue | Geneva, Switzerland | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | Eckhard Hitzer, Special affine Fourier transform for space-time algebra signals, Computer Graphics International 2021 (CGI2021), Workshop Geometric Algebra for Computing, Graphics and Engineering 2021 (ENGAGE2021), 06 Sep. 2021, Geneva, Switzerland. | | URL for researchmap | https://www.youtube.com/watch?v=f_dLM0yVHjQ |
|
| 13. |
2021/08/26 |
Special affine quaternion domain Fourier transform (GOL 2021: International Conference “Applied Category Theory Graph-Operad-Logic”, Professor Zbigniew Oziewicz in memoriam)
|
| Date | 2021/08/26 | | Presentation Theme | Special affine quaternion domain Fourier transform | | Conference | GOL 2021: International Conference “Applied Category Theory Graph-Operad-Logic”, Professor Zbigniew Oziewicz in memoriam | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Venue | Cuautitlan Izcalli, Mexico | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | Invited Lecture: Special affine quaternion domain Fourier transform, "GOL 2021: International Conference “Applied Category Theory Graph-Operad-Logic”, Professor Zbigniew Oziewicz in memoriam", Cuautitlan Izcalli, Mexico, 26 Aug. 2021. | | URL for researchmap | https://gaupdate.wordpress.com/2021/09/10/video-lecture-by-e-hitzer-at-gol-2021-special-affine-quaternion-domain-fourier-transform/ |
|
| 14. |
2021/08/06 |
Generalization of special affine Fourier transform to spacetime algebra Cl(3,1) (ISAAC2021, Session on Quaternionic and Clifford Analysis)
|
| Date | 2021/08/06 | | Presentation Theme | Generalization of special affine Fourier transform to spacetime algebra Cl(3,1) | | Conference | ISAAC2021, Session on Quaternionic and Clifford Analysis | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Venue | Ghent, Belgium | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | E. Hitzer, Generalization of special affine Fourier transform to spacetime algebra Cl(3,1), ISAAC2021, Session on Quaternionic and Clifford Analysis, Ghent, Belgium, 06 Aug. 2021. | | URL for researchmap | https://cage.ugent.be/isaac2021/ |
|
| 15. |
2021/03/21 |
Airborne laserscanning data adjustment with conformal geometric algebra (Workshop on “High-dimensional neuro-dynamics and neuro hardware structure development”)
|
| Date | 2021/03/21 | | Presentation Theme | Airborne laserscanning data adjustment with conformal geometric algebra | | Conference | Workshop on “High-dimensional neuro-dynamics and neuro hardware structure development” | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Invited | Invited | | Venue | RIEC, Tohoku University, Sendai, Japan | | Researchers and Co-Researchers | Presenter: E. Hitzer,
Copresenters: W. Benger, M. Niederwieser, R. Baran, F. Steinbacher | | Details | Invited Lecture: E.H., W. Benger, M. Niederwieser, R. Baran, F. Steinbacher, Airborne laserscanning data adjustment with conformal geometric algebra, Tohoku, Workshop on “High-dimensional neuro-dynamics and neuro hardware structure development”, RIEC, Tohoku University, Sendai, Japan, 02 Mar. 2021. |
|
| 16. |
2020/12/07 |
Strip Adjustment of Airborne Laserscanning Data with Conformal Geometric Algebra (Joint 11th International Conference on Soft Computing and Intelligent Systems and 21st International Symposium on Advanced Intelligent Systems (SCIS&ISIS2020), OS-14: Modern Applications of Clifford Algebra (online))
|
| Date | 2020/12/07 | | Presentation Theme | Strip Adjustment of Airborne Laserscanning Data with Conformal Geometric Algebra | | Conference | Joint 11th International Conference on Soft Computing and Intelligent Systems and 21st International Symposium on Advanced Intelligent Systems (SCIS&ISIS2020), OS-14: Modern Applications of Clifford Algebra (online) | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Venue | Hachijo Island, Tokyo, Japan | | Researchers and Co-Researchers | Presenter: E. Hitzer,
Copresenters: W. Benger, M. Niederwieser, R. Baran, F. Steinbacher | | Details | E.H., W. Benger, M. Niederwieser, R. Baran, F. Steinbacher, Strip Adjustment of Airborne Laserscanning Data with Conformal Geometric Algebra, Joint 11th International Conference on Soft Computing and Intelligent Systems and 21st International Symposium on Advanced Intelligent Systems (SCIS&ISIS2020), OS-14: Modern Applications of Clifford Algebra (online), Hachijo Island, Tokyo, Japan, Mo. 07 Dec. 2020. |
|
| 17. |
2020/08/07 |
Exponential Factorization of Multivectors in Cl(p,q), n = p + q <= 3 (Mini-Symposium Fourier and other Integral Transformations with Clifford Algebras, Quaternions and Octonions IV (FITCAQO 4) of The 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA12))
|
| Date | 2020/08/07 | | Presentation Theme | Exponential Factorization of Multivectors in Cl(p,q), n = p + q <= 3 | | Conference | Mini-Symposium Fourier and other Integral Transformations with Clifford Algebras, Quaternions and Octonions IV (FITCAQO 4) of The 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA12) | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Venue | Heifei, Anhui, China | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | In this talk we consider general multivector elements of
Cli ord algebras Cl(p; q), n = p + q = 3, and look for
possibilities to factorize multivectors into products of
blades, idempotents and exponentials, where the expo-
nents are frequently blades of grades zero (scalar) to n
(pseudoscalar). | | URL for researchmap | http://www.smartchair.org/hp/ICCA2020/ |
|
| 18. |
2020/08/04 |
Airborne Laser Scanning Registration and Conformal Geometric Algebra (Mini-Symposium Geometric Calculi and Deep Learning: a long-term relationship of The 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA12))
|
| Date | 2020/08/04 | | Presentation Theme | Airborne Laser Scanning Registration and Conformal Geometric Algebra | | Conference | Mini-Symposium Geometric Calculi and Deep Learning: a long-term relationship of The 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA12) | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Venue | Heifei, Anhui, China | | Researchers and Co-Researchers | Presenter: E. H.itzer
Copresenters: W. Benger, M. Niederwieser, R. Baran, F. Steinbacher | | Details | In this contribution we outlikne how to use the iterative
closest point method for the adjustment of airborne
laserscanning data strips in the framework of conformal
geometric algebra and calculus. | | URL for researchmap | http://www.smartchair.org/hp/ICCA2020/ |
|
| 19. |
2020/08/03 |
Opening Speech (The 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA12))
|
| Date | 2020/08/03 | | Presentation Theme | Opening Speech | | Conference | The 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA12) | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Venue | Heifei, Anhui, China | | Researchers and Co-Researchers | Eckhard Hitzer | | Details | Opening Speech as President of International Advisory Board | | URL for researchmap | http://www.smartchair.org/hp/ICCA2020/ |
|
| 20. |
2019/02/01 |
Energy saving wooden buildings (2019東京耐震博覧会)
|
| Date | 2019/02/01 | | Presentation Theme | Energy saving wooden buildings | | Conference | 2019東京耐震博覧会 | | Promoters | Prof. em. Tatsuaki Tanaka, President of Japanese Association for Housing Thermal Insulation Technology Corp. | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Venue | Tokyo Big Sight, Tokyo | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 21. |
2018/11/10 |
Geometric Transformations of Conics in Geometric Algebra (Workshop on Information Processing Capacity of High-dimensional Neural Networks, RIEC, Tohoku University, Sendai, Japan)
|
| Date | 2018/11/10 | | Presentation Theme | Geometric Transformations of Conics in Geometric Algebra | | Conference | Workshop on Information Processing Capacity of High-dimensional Neural Networks, RIEC, Tohoku University, Sendai, Japan | | Promoters | Prof. Akira Hirose (Univrsity of Tokyo), Prof. Shigeo Sato (RIEC, Tohoku University) | | Conference Type | Domestic | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Invited | Invited | | Venue | RIEC, Tohoku University, Sendai, Japan | | Researchers and Co-Researchers | Eckhard Hitzer, Stephen J. Sangwine |
|
| 22. |
2018/10/18 |
Renewable Energy and Energy Efficiency for Japanese RE100 Universities (3rd Japanese-German Workshop on Renewable Energies, Tokyo, Japan)
|
| Date | 2018/10/18 | | Presentation Theme | Renewable Energy and Energy Efficiency for Japanese RE100 Universities | | Conference | 3rd Japanese-German Workshop on Renewable Energies, Tokyo, Japan | | Promoters | Dr. Toru Okazaki (The Institute of Applied Energy) | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Venue | TEPIA Hall, Tokyo, Japan | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 23. |
2018/08/24 |
Conic Conformal Geometric Algebra (Conference Function Theories in Higher Dimensions 2018 (FTHD2018), University of Tampere, Tampere, Finland)
|
| Date | 2018/08/24 | | Presentation Theme | Conic Conformal Geometric Algebra | | Conference | Conference Function Theories in Higher Dimensions 2018 (FTHD2018), University of Tampere, Tampere, Finland | | Promoters | Prof. Heikki Orelma, Tampere University of Technology, Finnland. | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Venue | University of Tampere, Tampere, Finland | | Researchers and Co-Researchers | Eckhard Hitzer, Stephen J. Sangwine |
|
| 24. |
2018/07/25 |
Application of Conformal Geometric Algebra to in-plane rotated face detection by AdaBoost-based algorithm (The 7th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE2018), IMECC–UNICAMP, Las Campinas, Brazil)
|
| Date | 2018/07/25 | | Presentation Theme | Application of Conformal Geometric Algebra to in-plane rotated face detection by AdaBoost-based algorithm | | Conference | The 7th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE2018), IMECC–UNICAMP, Las Campinas, Brazil | | Promoters | Prof. Carlile Lavor, President of Association of Applied Mathematics in Brazil, Prof. Sebastia Xambo (University of Barcelona, Spain) | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Venue | MECC–UNICAMP, Las Campinas, Brazil | | Researchers and Co-Researchers | T. M. Pham, D. C. Doan, E. Hitzer |
|
| 25. |
2018/07/24 |
3D Quadrics in Hybrid CGA of Higher Dimensions (The 7th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE2018), IMECC–UNICAMP, Las Campinas, Brazil)
|
| Date | 2018/07/24 | | Presentation Theme | 3D Quadrics in Hybrid CGA of Higher Dimensions | | Conference | The 7th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE2018), IMECC–UNICAMP, Las Campinas, Brazil | | Promoters | Prof. Carlile Lavor, President of Association of Applied Mathematics in Brazil, Prof. Sebastia Xambo (University of Barcelona, Spain) | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Venue | IMECC–UNICAMP, Las Campinas, Brazil | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 26. |
2017/12/11 |
Developing Conformal Geometric Algebra for the Representation of Algebraic Curves and Surfaces (Workshop on Information Processing Capacity of High-dimensional Neural Networks, RIEC, Tohoku University, Sendai, Japan)
|
| Date | 2017/12/11 | | Presentation Theme | Developing Conformal Geometric Algebra for the Representation of Algebraic Curves and Surfaces | | Conference | Workshop on Information Processing Capacity of High-dimensional Neural Networks, RIEC, Tohoku University, Sendai, Japan | | Promoters | Prof. Akira Hirose (University of Tokyo), Prof. Shigeo Sato (RIEC, Tohoku University) | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Venue | RIEC, Tohoku University, Sendai, Japan | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 27. |
2017/09/27 |
Aspirations of Japanese Universities to Become Sustainable by Means of Energy Efficiency and Renewable Energy (Academic seminar of JSPS Club, Tsukuba, Japan)
|
| Date | 2017/09/27 | | Presentation Theme | Aspirations of Japanese Universities to Become Sustainable by Means of Energy Efficiency and Renewable Energy | | Conference | Academic seminar of JSPS Club, Tsukuba, Japan | | Promoters | Prof. Heinrich Menkhaus, President of JSPS Club. | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Venue | University of Tsukuba, Japan. | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 28. |
2017/08/08 |
Convolutions for Quaternionic and Clifford Fourier Transforms in spatial and spectral domains (ICCA11)
|
| Date | 2017/08/08 | | Presentation Theme | Convolutions for Quaternionic and Clifford Fourier Transforms in spatial and spectral domains | | Conference | ICCA11 | | Promoters | Prof. Fred Brackx, Prof. Hennie De Schepper | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Venue | University of Gent, Gent, Belgium | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 29. |
2017/08/08 |
Extending MATLAB to handle hypercomplex algebras (ICCA11)
|
| Date | 2017/08/08 | | Presentation Theme | Extending MATLAB to handle hypercomplex algebras | | Conference | ICCA11 | | Promoters | Prof. Fred Brackx, Prof. Hennie De Schepper | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Venue | University of Gent, Gent, Belgium | | Researchers and Co-Researchers | Stephen J. Sangwine, Eckhard Hitzer |
|
| 30. |
2017/08/07 |
Extended Conformal Geometric Algebra for the Representation of Algebraic Curves and Surfaces (ICCA11)
|
| Date | 2017/08/07 | | Presentation Theme | Extended Conformal Geometric Algebra for the Representation of Algebraic Curves and Surfaces | | Conference | ICCA11 | | Promoters | Prof. Fred Brackx, Prof. Hennie De Schepper | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Venue | University of Gent, Gent, Belgium | | Researchers and Co-Researchers | Eckhard Hitzer, Robert B. Easter |
|
| 31. |
2017/07/05 |
General one-sided Clifford Fourier transform, convolution products in the spatial and frequency domains, and auto-correlation theorems (CMMSE 2017, Session on Hypercomplex Methods in Applied Science, Costa Ballena, Cadiz, Spain)
|
| Date | 2017/07/05 | | Presentation Theme | General one-sided Clifford Fourier transform, convolution products in the spatial and frequency domains, and auto-correlation theorems | | Conference | CMMSE 2017, Session on Hypercomplex Methods in Applied Science, Costa Ballena, Cadiz, Spain | | Promoters | Prof. Wolfgang Sproessig. | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Venue | Costa Ballena, Cadiz, Spain | | Researchers and Co-Researchers | Eckhard Hitzer |
|
| 32. |
2017/06/27 |
Triple Conformal Geometric Algebra for Cubic Plane Curves (Workshop Empowering Novel Geometric Algebra for Graphics & Engineering Workshop (ENGAGE 2017) at Computer Graphics International (CGI 2017), Keio University, Yokohama, Japan)
|
| Date | 2017/06/27 | | Presentation Theme | Triple Conformal Geometric Algebra for Cubic Plane Curves | | Conference | Workshop Empowering Novel Geometric Algebra for Graphics & Engineering Workshop (ENGAGE 2017) at Computer Graphics International (CGI 2017), Keio University, Yokohama, Japan | | Promoters | International organizing committee of ENGAGE 2017 workshop. | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Venue | Keio University, Yokohama, Japan | | Researchers and Co-Researchers | Eckhard Hitzer, Robert B. Easter |
|
| 33. |
2016/12/07 |
Conic and Cyclidic Sections in Double Conformal Geometric Algebra G8,2 (SSI 2016, Session SS11, Otsu, Shiga, Japan, 7 Dec. 2016.)
|
| Date | 2016/12/07 | | Presentation Theme | Conic and Cyclidic Sections in Double Conformal Geometric Algebra G8,2 | | Conference | SSI 2016, Session SS11, Otsu, Shiga, Japan, 7 Dec. 2016. | | Conference Type | Domestic | | Presentation Type | Poster | | Contribution Type | Collaborative | | Venue | Otsu, Shiga, Japan | | Researchers and Co-Researchers | Robert B. Easter, Eckhard Hitzer |
|
| 34. |
2016/09/12 |
Double Conformal Geometric Algebra Surface Representation (Workshop on Information Processing Capacity of High-dimensional Neural Networks)
|
| Date | 2016/09/12 | | Presentation Theme | Double Conformal Geometric Algebra Surface Representation | | Conference | Workshop on Information Processing Capacity of High-dimensional Neural Networks | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Venue | RIEC, Tohoku University, Sendai, Japan | | Researchers and Co-Researchers | Robert Benjamin Easter |
|
| 35. |
2016/08/25 |
Modern Applications of Clifford Geometric Algebra (GAGIS Section at 33rd International Geographic Congress)
|
| Date | 2016/08/25 | | Presentation Theme | Modern Applications of Clifford Geometric Algebra | | Conference | GAGIS Section at 33rd International Geographic Congress | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Venue | Nanjing Normal University, Nanjing, PR China |
|
| 36. |
2016/07/08 |
Double Conformal Space Time Algebra (ICNPAA 2016)
|
| Date | 2016/07/08 | | Presentation Theme | Double Conformal Space Time Algebra | | Conference | ICNPAA 2016 | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Venue | La Rochelle, France | | Researchers and Co-Researchers | Robert Benjamin Easter |
|
| 37. |
2016/06/28 |
Double Conformal Geometric Algebra for Quadrics and Darboux Cyclides (GACSE Workshop at CGI 2016)
|
| Date | 2016/06/28 | | Presentation Theme | Double Conformal Geometric Algebra for Quadrics and Darboux Cyclides | | Conference | GACSE Workshop at CGI 2016 | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Venue | Heraklion, Crete, Greece | | Researchers and Co-Researchers | Robert Benjamin Easter |
|
| 38. |
2016/06/28 |
General steerable two-sided Clifford Fourier transform, convolution and Mustard convolution (GACSE Workshop at CGI 2016)
|
| Date | 2016/06/28 | | Presentation Theme | General steerable two-sided Clifford Fourier transform, convolution and Mustard convolution | | Conference | GACSE Workshop at CGI 2016 | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Venue | Heraklion, Crete, Greece |
|
| 39. |
2016/06/27 |
Conformal geometric algebra (Computer Graphics International 2016)
|
| Date | 2016/06/27 | | Presentation Theme | Conformal geometric algebra | | Conference | Computer Graphics International 2016 | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Venue | Heraklion, Crete, Greece | | Details | Tutorial |
|
| 40. |
2016/05/29 |
Christ centered environmental stewardship (Sustainable Management Forum Japan National Conference)
|
| Date | 2016/05/29 | | Presentation Theme | Christ centered environmental stewardship | | Conference | Sustainable Management Forum Japan National Conference | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Venue | Nihon University, Tokyo |
|
| 41. |
2015/10/24 |
Prospects of Modern Wood Gas Cogeneration Renewable Energy Supply in Japan – Case Study of ICU (Japanese Association of Social Accounting National Conference)
|
| Date | 2015/10/24 | | Presentation Theme | Prospects of Modern Wood Gas Cogeneration Renewable Energy Supply in Japan – Case Study of ICU | | Conference | Japanese Association of Social Accounting National Conference | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Invited | Invited | | Venue | Asia University Tokyo, Japan | | Researchers and Co-Researchers | Nobuyuki Miyazaki |
|
| 42. |
2015/07/31 |
Fourier Transformations in Conformal Geometric Algebra (6th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE 2015), Universitat Politècnica de Catalunya, Barcelona, Spain.)
|
| Date | 2015/07/31 | | Presentation Theme | Fourier Transformations in Conformal Geometric Algebra | | Conference | 6th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE 2015), Universitat Politècnica de Catalunya, Barcelona, Spain. | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer, D. Eelbode |
|
| 43. |
2015/07/28 |
Overview of the development of quaternionic Fourier transforms over three decades, from 1987 to 2015: Theory and application (Summer School of 6th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE 2015), Universitat Politècnica de Catalunya, Barcelona, Spain.)
|
| Date | 2015/07/28 | | Presentation Theme | Overview of the development of quaternionic Fourier transforms over three decades, from 1987 to 2015: Theory and application | | Conference | Summer School of 6th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE 2015), Universitat Politècnica de Catalunya, Barcelona, Spain. | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 44. |
2015/07/27 |
Basic Notions of Geometric Algebra (Summer School of 6th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE 2015))
|
| Date | 2015/07/27 | | Presentation Theme | Basic Notions of Geometric Algebra | | Conference | Summer School of 6th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE 2015) | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 45. |
2015/07/20 |
Modern Applications of Clifford Geometric Algebra (The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering (IKM 2015), Bauhaus University Weimar, Germany)
|
| Date | 2015/07/20 | | Presentation Theme | Modern Applications of Clifford Geometric Algebra | | Conference | The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering (IKM 2015), Bauhaus University Weimar, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 46. |
2015/03/27 |
Introduction to quaternion and Clifford Fourier transforms (Asian Workshop on Clifford's Geometric Algebra and Information Technology – AWCGAIT2015, University of Science and Technology – The University of Danang, Danang, Vietnam, 26-28 March 2015)
|
| Date | 2015/03/27 | | Presentation Theme | Introduction to quaternion and Clifford Fourier transforms | | Conference | Asian Workshop on Clifford's Geometric Algebra and Information Technology – AWCGAIT2015, University of Science and Technology – The University of Danang, Danang, Vietnam, 26-28 March 2015 | | Conference Type | International | | Presentation Type | Speech (Keynote) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 47. |
2014/11 |
Preprocessing quaternion data in quaternion spaces using the quaternion domain Fourier transform (SICE SSI 2014, Session SS13, Okayama, Japan, 21-23 Nov. 2014)
|
| Date | 2014/11 | | Presentation Theme | Preprocessing quaternion data in quaternion spaces using the quaternion domain Fourier transform | | Conference | SICE SSI 2014, Session SS13, Okayama, Japan, 21-23 Nov. 2014 | | Conference Type | Domestic | | Presentation Type | Poster | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 48. |
2014/07/19 |
New Developments in Clifford Fourier Transforms (International Conference on Pure Mathematics, Applied Mathematics, Computational Methods (PMAMCM 2014), Santorini Island, Greece)
|
| Date | 2014/07/19 | | Presentation Theme | New Developments in Clifford Fourier Transforms | | Conference | International Conference on Pure Mathematics, Applied Mathematics, Computational Methods (PMAMCM 2014), Santorini Island, Greece | | Conference Type | International | | Presentation Type | Speech (Keynote) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 49. |
2014/07/17 |
The orthogonal planes split of quaternions and its relation to quaternion geometry of rotations (The 30th International Colloquium on Group Theoretical Methods in Physics (Group30), Ghent University, Belgium)
|
| Date | 2014/07/17 | | Presentation Theme | The orthogonal planes split of quaternions and its relation to quaternion geometry of rotations | | Conference | The 30th International Colloquium on Group Theoretical Methods in Physics (Group30), Ghent University, Belgium | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 50. |
2014/07/04 |
Quaternion Domain Fourier Transform (Int. Conf. on Clifford Algs. and their Appls. in Math. Phys., Tartu, Estonia)
|
| Date | 2014/07/04 | | Presentation Theme | Quaternion Domain Fourier Transform | | Conference | Int. Conf. on Clifford Algs. and their Appls. in Math. Phys., Tartu, Estonia | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 51. |
2014/01/21 |
IYCR 2014 - Virtual reality, space groups and Clifford's geometric algebra (Int. Conference on Recent Advances in Mathematics, ICRAM 2014, Nagpur, India)
|
| Date | 2014/01/21 | | Presentation Theme | IYCR 2014 - Virtual reality, space groups and Clifford's geometric algebra | | Conference | Int. Conference on Recent Advances in Mathematics, ICRAM 2014, Nagpur, India | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 52. |
2013/09/22 |
The quest for conformal geometric algebra Fourier transformations (10th Symp. on Clifford Analysis and Appl. at the 11th Int. Conf. of Num. Anal. and Appl. Math. 2013, ICNAAM 2013, Rhodes, Greece)
|
| Date | 2013/09/22 | | Presentation Theme | The quest for conformal geometric algebra Fourier transformations | | Conference | 10th Symp. on Clifford Analysis and Appl. at the 11th Int. Conf. of Num. Anal. and Appl. Math. 2013, ICNAAM 2013, Rhodes, Greece | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 53. |
2013/09/21 |
Extending Fourier transformations to Hamilton’s quaternions and Clifford’s geometric algebras (11th Int. Conf. of Num. Anal. and Appl. Math. 2013, ICNAAM 2013, Rhodes, Greece)
|
| Date | 2013/09/21 | | Presentation Theme | Extending Fourier transformations to Hamilton’s quaternions and Clifford’s geometric algebras | | Conference | 11th Int. Conf. of Num. Anal. and Appl. Math. 2013, ICNAAM 2013, Rhodes, Greece | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 54. |
2013/08/13 |
Vector field computations in Clifford's geometric algebra (Third SICE Symposium on Computational Intelligence, Osaka University, Osaka)
|
| Date | 2013/08/13 | | Presentation Theme | Vector field computations in Clifford's geometric algebra | | Conference | Third SICE Symposium on Computational Intelligence, Osaka University, Osaka | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, R. Bujack, G. Scheuerma |
|
| 55. |
2013/03/09 |
New way of teaching geometry with physical point of view in mind (Meiji University Symposium on Mathematics Education, Meiji University, Tokyo, Japan)
|
| Date | 2013/03/09 | | Presentation Theme | New way of teaching geometry with physical point of view in mind | | Conference | Meiji University Symposium on Mathematics Education, Meiji University, Tokyo, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 56. |
2012/12/10 |
The Clifford Fourier Transform in Conformal Geometric Algebra (Workshop on Information Processing Capacity of High-dimensional Neural Networks, Tohoku University, Sendai, Japan)
|
| Date | 2012/12/10 | | Presentation Theme | The Clifford Fourier Transform in Conformal Geometric Algebra | | Conference | Workshop on Information Processing Capacity of High-dimensional Neural Networks, Tohoku University, Sendai, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 57. |
2012/11/07 |
Moderne geothermische Energienutzung am Beispiel Islands - Eine aktuelle Erkundungsreise (2. Treffen der in Japan tätigen Mitglieder des JSPS- Clubs Tokyo, Japan)
|
| Date | 2012/11/07 | | Presentation Theme | Moderne geothermische Energienutzung am Beispiel Islands - Eine aktuelle Erkundungsreise | | Conference | 2. Treffen der in Japan tätigen Mitglieder des JSPS- Clubs Tokyo, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 58. |
2012/09/30 |
Non-constant bounded holomorphic functions of hyperbolic numbers - Candidates for hyperbolic activation functions (First SICE Symposium on Computational Intelligence [Concentrating on Clifford Neural Computing], KIT, Kyoto, Japan)
|
| Date | 2012/09/30 | | Presentation Theme | Non-constant bounded holomorphic functions of hyperbolic numbers - Candidates for hyperbolic activation functions | | Conference | First SICE Symposium on Computational Intelligence [Concentrating on Clifford Neural Computing], KIT, Kyoto, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 59. |
2012/09/28 |
Quaternionic generalization of Fourier-Mellin Transform (2nd SICE Symposium on Computational Intelligence “High-Dimensional Approaches and Representations in the Computational Intelligence”, Okayama University, Okayama, Japan)
|
| Date | 2012/09/28 | | Presentation Theme | Quaternionic generalization of Fourier-Mellin Transform | | Conference | 2nd SICE Symposium on Computational Intelligence “High-Dimensional Approaches and Representations in the Computational Intelligence”, Okayama University, Okayama, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 60. |
2012/07/06 |
The Clifford Fourier transform in real Clifford algebras (IKM 2012, Session Geometric Algebra and Applications, Bauhaus University, Weimar, Germany)
|
| Date | 2012/07/06 | | Presentation Theme | The Clifford Fourier transform in real Clifford algebras | | Conference | IKM 2012, Session Geometric Algebra and Applications, Bauhaus University, Weimar, Germany | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 61. |
2012/07/03 |
Two-sided Clifford Fourier Transform with Square Roots of -1 in Cl(p,q) (AGACSE 2012, La Rochelle, France)
|
| Date | 2012/07/03 | | Presentation Theme | Two-sided Clifford Fourier Transform with Square Roots of -1 in Cl(p,q) | | Conference | AGACSE 2012, La Rochelle, France | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 62. |
2012/03/18 |
Discussion on Mathematical Experiences (Mathematics Education Symposium 2012, Meiji University, Tokyo, Japan)
|
| Date | 2012/03/18 | | Presentation Theme | Discussion on Mathematical Experiences | | Conference | Mathematics Education Symposium 2012, Meiji University, Tokyo, Japan | | Conference Type | Domestic | | Presentation Type | Panelist at Symposium/Workshop (Applied) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 63. |
2012/03/18 |
Natural Science Education in Germany in 2012 after the 1999 European Bologna Reforms (Mathematics Education Symposium 2012, Meiji University, Tokyo, Japan)
|
| Date | 2012/03/18 | | Presentation Theme | Natural Science Education in Germany in 2012 after the 1999 European Bologna Reforms | | Conference | Mathematics Education Symposium 2012, Meiji University, Tokyo, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 64. |
2012/03/17 |
English Presentation for Mathematics Students (Mathematics Education Symposium 2012, Meiji University, Tokyo, Japan)
|
| Date | 2012/03/17 | | Presentation Theme | English Presentation for Mathematics Students | | Conference | Mathematics Education Symposium 2012, Meiji University, Tokyo, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 65. |
2012/01/20 |
Introduction to William Kingdon Clifford’s geometric algebras (Research Meeting on Particle Filters, Nagoya University, Japan)
|
| Date | 2012/01/20 | | Presentation Theme | Introduction to William Kingdon Clifford’s geometric algebras | | Conference | Research Meeting on Particle Filters, Nagoya University, Japan | | Conference Type | Domestic | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 66. |
2012 |
Quaternionic generalization of Fourier Mellin Transform (ICNPAA 2012 Congress: Mathematical Problems in Engineering, Aerospace and Sciences, Vienna, Austria, 11-14 July 2012)
|
| Date | 2012 | | Presentation Theme | Quaternionic generalization of Fourier Mellin Transform | | Conference | ICNPAA 2012 Congress: Mathematical Problems in Engineering, Aerospace and Sciences, Vienna, Austria, 11-14 July 2012 | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 67. |
2011/12/14 |
Quaternionic Fourier Mellin transform (19th ICFIDCAA, Hiroshima, Japan)
|
| Date | 2011/12/14 | | Presentation Theme | Quaternionic Fourier Mellin transform | | Conference | 19th ICFIDCAA, Hiroshima, Japan | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 68. |
2011/09 |
The OPS-QFT: A new type of quaternion Fourier transform based on the orthogonal planes split with two general pure quaternions (8th Symp. on Clifford Analysis and Appl. at the 9th Int. Conf. of Num. Anal. and Appl. Math. 2011 (ICNAAM 2011), Halkidiki, Greece, 19-25 Sep. 2011.)
|
| Date | 2011/09 | | Presentation Theme | The OPS-QFT: A new type of quaternion Fourier transform based on the orthogonal planes split with two general pure quaternions | | Conference | 8th Symp. on Clifford Analysis and Appl. at the 9th Int. Conf. of Num. Anal. and Appl. Math. 2011 (ICNAAM 2011), Halkidiki, Greece, 19-25 Sep. 2011. | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 69. |
2011/08 |
Crystal planes in Clifford geometric algebra (IUCr Madrid, Spain, 22-29 Aug. 2011.)
|
| Date | 2011/08 | | Presentation Theme | Crystal planes in Clifford geometric algebra | | Conference | IUCr Madrid, Spain, 22-29 Aug. 2011. | | Conference Type | International | | Presentation Type | Poster | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 70. |
2011/07 |
Square roots of -1 in real Clifford algebras (The 9th Int. Conf. on Clifford Algebras and their Applications (ICCA 2011), Weimar, Germany)
|
| Date | 2011/07 | | Presentation Theme | Square roots of -1 in real Clifford algebras | | Conference | The 9th Int. Conf. on Clifford Algebras and their Applications (ICCA 2011), Weimar, Germany | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, J. Helmstetter, R. Ablamowicz |
|
| 71. |
2011/02/18 |
Mathematics education in the UK (Mathematics Education Symposium, Meiji University, Tokyo, Japan)
|
| Date | 2011/02/18 | | Presentation Theme | Mathematics education in the UK | | Conference | Mathematics Education Symposium, Meiji University, Tokyo, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 72. |
2010/12/22 |
Algebraic foundations of split hypercomplex nonlinear adaptive filtering (2nd Research Meeting of Cooperative Research Program at RIEC, Tohoku University, Sendai, Japan)
|
| Date | 2010/12/22 | | Presentation Theme | Algebraic foundations of split hypercomplex nonlinear adaptive filtering | | Conference | 2nd Research Meeting of Cooperative Research Program at RIEC, Tohoku University, Sendai, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 73. |
2010/09 |
Angles between subspaces computed in Clifford algebra (7th Symp. on Clifford Analysis and Appl. at the 8th Int. Conf. of Num. Anal. and Appl. Math. 2010 (ICNAAM 2010), Rhodes, Greece, 19-25 Sep. 2010)
|
| Date | 2010/09 | | Presentation Theme | Angles between subspaces computed in Clifford algebra | | Conference | 7th Symp. on Clifford Analysis and Appl. at the 8th Int. Conf. of Num. Anal. and Appl. Math. 2010 (ICNAAM 2010), Rhodes, Greece, 19-25 Sep. 2010 | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 74. |
2010/08/26 |
Interactive visualization of plane groups (Symmetry: Art and Science, 8th Congress of Int. Soc. For the Interdisc. Study of Symmetry (ISIS), Days of Harmonics, Gmünd, Austria)
|
| Date | 2010/08/26 | | Presentation Theme | Interactive visualization of plane groups | | Conference | Symmetry: Art and Science, 8th Congress of Int. Soc. For the Interdisc. Study of Symmetry (ISIS), Days of Harmonics, Gmünd, Austria | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, C. Perwass |
|
| 75. |
2010/08 |
Interactive 3D Visualization of Plane Groups and Layer Groups Using the SGV (MS46-T06, 26th European Crystallographic Meeting (ECM26), 29 Aug. – 2 Sep. 2010, Darmstadt, Germany)
|
| Date | 2010/08 | | Presentation Theme | Interactive 3D Visualization of Plane Groups and Layer Groups Using the SGV | | Conference | MS46-T06, 26th European Crystallographic Meeting (ECM26), 29 Aug. – 2 Sep. 2010, Darmstadt, Germany | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, C. Perwass |
|
| 76. |
2010/08 |
Introduction to Quaternions and Geometric Algebra and their applications in crystallography, (MaThCryst Satellite Conference at ECM 26 on Minimal Surfaces, Aperiodic Structures, Geometric Algebra, Darmstadt, Germany, 27 – 29 Aug. 2010)
|
| Date | 2010/08 | | Presentation Theme | Introduction to Quaternions and Geometric Algebra and their applications in crystallography, | | Conference | MaThCryst Satellite Conference at ECM 26 on Minimal Surfaces, Aperiodic Structures, Geometric Algebra, Darmstadt, Germany, 27 – 29 Aug. 2010 | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | H. Grimmer, E. Hitzer |
|
| 77. |
2010/06/15 |
Reciprocal space and crystal planes in geometric algebra (AGACSE 2010, Amsterdam, The Netherlands)
|
| Date | 2010/06/15 | | Presentation Theme | Reciprocal space and crystal planes in geometric algebra | | Conference | AGACSE 2010, Amsterdam, The Netherlands | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 78. |
2010/03/20 |
Interactive 3D graphics software as a new tool to teach space group symmetry (Meiji University, Tokyo, Japan)
|
| Date | 2010/03/20 | | Presentation Theme | Interactive 3D graphics software as a new tool to teach space group symmetry | | Conference | Meiji University, Tokyo, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 79. |
2010/03/19 |
Reflections on some aspects of mathematical education during the last two centuries and on how to bridge the gap between abstract mathematics and common experiential knowledge (Meiji University, Tokyo, Japan)
|
| Date | 2010/03/19 | | Presentation Theme | Reflections on some aspects of mathematical education during the last two centuries and on how to bridge the gap between abstract mathematics and common experiential knowledge | | Conference | Meiji University, Tokyo, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 80. |
2010/03 |
3D Space Group Visualization with Interactive Crystal Symmetry Software (Dipartimento di Chimica Strutturale e Stereochimica Inorganica, Seminari Chimici, University of Milan, Italy, 3+4 March 2010.)
|
| Date | 2010/03 | | Presentation Theme | 3D Space Group Visualization with Interactive Crystal Symmetry Software | | Conference | Dipartimento di Chimica Strutturale e Stereochimica Inorganica, Seminari Chimici, University of Milan, Italy, 3+4 March 2010. | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 81. |
2010/02/25 |
Clifford Fourier and Clifford Wavelet Transformations (Seminar on Functional Analysis, Ass. Prof. S. Siltanen, University of Helsinki, Finland)
|
| Date | 2010/02/25 | | Presentation Theme | Clifford Fourier and Clifford Wavelet Transformations | | Conference | Seminar on Functional Analysis, Ass. Prof. S. Siltanen, University of Helsinki, Finland | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 82. |
2010/02/24 |
Interactive 3D visualization of space group symmetry (Department of Chemistry, Prof. J. Pesonen, University of Helsinki, Finland)
|
| Date | 2010/02/24 | | Presentation Theme | Interactive 3D visualization of space group symmetry | | Conference | Department of Chemistry, Prof. J. Pesonen, University of Helsinki, Finland | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 83. |
2010/02/24 |
Introduction to Clifford Fourier and Clifford Wavelet Transformations (Department of Chemistry, Prof. J. Pesonen, University of Helsinki, Finland)
|
| Date | 2010/02/24 | | Presentation Theme | Introduction to Clifford Fourier and Clifford Wavelet Transformations | | Conference | Department of Chemistry, Prof. J. Pesonen, University of Helsinki, Finland | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 84. |
2010 |
Angles between subspaces (GraVisMa 2010, Brno, Czech Republic, 7-10 Sep. 2010)
|
| Date | 2010 | | Presentation Theme | Angles between subspaces | | Conference | GraVisMa 2010, Brno, Czech Republic, 7-10 Sep. 2010 | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 85. |
2009/12 |
Neural Computation with Clifford Algebra (Research Meeting of Cooperative Research Program at RIEC, Tohoku University, Sendai, Japan)
|
| Date | 2009/12 | | Presentation Theme | Neural Computation with Clifford Algebra | | Conference | Research Meeting of Cooperative Research Program at RIEC, Tohoku University, Sendai, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 86. |
2009/09/22 |
Real Clifford Algebra Cl(n,0), n=2,3(mod 4) Wavelet Transform (ICNAAM, Rethymno, Crete, Greece)
|
| Date | 2009/09/22 | | Presentation Theme | Real Clifford Algebra Cl(n,0), n=2,3(mod 4) Wavelet Transform | | Conference | ICNAAM, Rethymno, Crete, Greece | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 87. |
2009/09/07 |
Brief Introduction to Clifford Geometric Algebra (Faculty of Informatik and Mathematik, University of Leipzig, Germany)
|
| Date | 2009/09/07 | | Presentation Theme | Brief Introduction to Clifford Geometric Algebra | | Conference | Faculty of Informatik and Mathematik, University of Leipzig, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 88. |
2009/09/07 |
Clifford Wavelets (Faculty of Informatik and Mathematik, University of Leipzig, Germany)
|
| Date | 2009/09/07 | | Presentation Theme | Clifford Wavelets | | Conference | Faculty of Informatik and Mathematik, University of Leipzig, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 89. |
2009/09 |
Fourier and Wavelet Transformations in Geometric Algebra (Computer Graphics, Computer Vision and Mathematics, Plzeň, Czech Republic, 2-4 Sep. 2009)
|
| Date | 2009/09 | | Presentation Theme | Fourier and Wavelet Transformations in Geometric Algebra | | Conference | Computer Graphics, Computer Vision and Mathematics, Plzeň, Czech Republic, 2-4 Sep. 2009 | | Conference Type | International | | Presentation Type | Speech (Keynote) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 90. |
2009/09 |
New views of crystal symmetry (Symmetries of Forms and Structures, Wroclaw and Cracow, Poland, 14-19 Sep. 2009)
|
| Date | 2009/09 | | Presentation Theme | New views of crystal symmetry | | Conference | Symmetries of Forms and Structures, Wroclaw and Cracow, Poland, 14-19 Sep. 2009 | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 91. |
2009/09 |
New views of crystal symmetry guided by profound admiration of the extraordinary works of Grassmann and Clifford (Grassmann Bicentennial Conf., Potsdam (DE), Szczecin (PL), 16-19. Sep. 2009)
|
| Date | 2009/09 | | Presentation Theme | New views of crystal symmetry guided by profound admiration of the extraordinary works of Grassmann and Clifford | | Conference | Grassmann Bicentennial Conf., Potsdam (DE), Szczecin (PL), 16-19. Sep. 2009 | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 92. |
2009/08/07 |
Clifford Fourier and Clifford Wavelet Transformations (Department of Mathematics, Tampere University of Technology, Tampere, Finland)
|
| Date | 2009/08/07 | | Presentation Theme | Clifford Fourier and Clifford Wavelet Transformations | | Conference | Department of Mathematics, Tampere University of Technology, Tampere, Finland | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 93. |
2009/07 |
Geometric Algebra Wavelet Transforms (Workshop Clifford algebras and Lie Groups for multi-dimensional image processing, La Rochelle, France, 2-3 Jul. 2009.)
|
| Date | 2009/07 | | Presentation Theme | Geometric Algebra Wavelet Transforms | | Conference | Workshop Clifford algebras and Lie Groups for multi-dimensional image processing, La Rochelle, France, 2-3 Jul. 2009. | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 94. |
2009/07 |
Visualization of Fundamental Symmetries in Nature (Fuzzy System Symposium FSS 2009, University of Tsukuba, Tsukuba, Japan, 14-16 July 2009.)
|
| Date | 2009/07 | | Presentation Theme | Visualization of Fundamental Symmetries in Nature | | Conference | Fuzzy System Symposium FSS 2009, University of Tsukuba, Tsukuba, Japan, 14-16 July 2009. | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, C. Perwass |
|
| 95. |
2009/04/06 |
Space Group Visualizer – A Demonstration (Nanyang Technological University, Singapore)
|
| Date | 2009/04/06 | | Presentation Theme | Space Group Visualizer – A Demonstration | | Conference | Nanyang Technological University, Singapore | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 96. |
2008/12/26 |
Multivector calculus applied to pose estimation (University of Nagoya, FCS)
|
| Date | 2008/12/26 | | Presentation Theme | Multivector calculus applied to pose estimation | | Conference | University of Nagoya, FCS | | Conference Type | Domestic | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 97. |
2008/12/12 |
Geometric Algebra and Geometric Calculus with applications to crystal symmetry visualization, wave packets and neural computation (University of Kanazawa, Kanazawa, Japan)
|
| Date | 2008/12/12 | | Presentation Theme | Geometric Algebra and Geometric Calculus with applications to crystal symmetry visualization, wave packets and neural computation | | Conference | University of Kanazawa, Kanazawa, Japan | | Conference Type | Domestic | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 98. |
2008/11 |
Geometric operations implemented by conformal geometric algebra neural nodes (SICE SSI, Himeji, Japan, 26-28 Nov. 2008.)
|
| Date | 2008/11 | | Presentation Theme | Geometric operations implemented by conformal geometric algebra neural nodes | | Conference | SICE SSI, Himeji, Japan, 26-28 Nov. 2008. | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 99. |
2008/10/10 |
Robust geometric feature extraction and classification (ISAMPE 2008, Busan, South Korea)
|
| Date | 2008/10/10 | | Presentation Theme | Robust geometric feature extraction and classification | | Conference | ISAMPE 2008, Busan, South Korea | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, M. T. Pham, K. Tachibana, S. Buchholz, T. Yoshikawa, T. Furuhashi |
|
| 100. |
2008/10 |
Basic Multivector Calculus (18th Symposium on Intelligent Systems (FAN 2008), Hiroshima, 23-24 Oct. 2008.)
|
| Date | 2008/10 | | Presentation Theme | Basic Multivector Calculus | | Conference | 18th Symposium on Intelligent Systems (FAN 2008), Hiroshima, 23-24 Oct. 2008. | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 101. |
2008/09/19 |
Coordinate independent node computations of important spinor and versor Clifford neurons (SCIS&ISIS’08, Special Session Complex and Hypercomplex Numbers in Intel. Syst., Nagoya, Japan)
|
| Date | 2008/09/19 | | Presentation Theme | Coordinate independent node computations of important spinor and versor Clifford neurons | | Conference | SCIS&ISIS’08, Special Session Complex and Hypercomplex Numbers in Intel. Syst., Nagoya, Japan | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, S. Buchholz, K. Tachibana |
|
| 102. |
2008/08/25 |
Interactive 3D Space Group Visualizer (IUCr Osaka, Japan)
|
| Date | 2008/08/25 | | Presentation Theme | Interactive 3D Space Group Visualizer | | Conference | IUCr Osaka, Japan | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, C. Perwass |
|
| 103. |
2008/08/23 |
How to teach cubic symmetry groups, using the interactive Space Group Visualizer (Teaching Crystallography in the 21st Century, IUCr Osaka, Japan)
|
| Date | 2008/08/23 | | Presentation Theme | How to teach cubic symmetry groups, using the interactive Space Group Visualizer | | Conference | Teaching Crystallography in the 21st Century, IUCr Osaka, Japan | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, C. Perwass |
|
| 104. |
2008/08/19 |
Classification and Clustering of Spatial Patterns with Geometric Algebra (AGACSE 3, Leipzig, Germany)
|
| Date | 2008/08/19 | | Presentation Theme | Classification and Clustering of Spatial Patterns with Geometric Algebra | | Conference | AGACSE 3, Leipzig, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, M. T. Pham, K. Tachibana, S. Buchholz, T. Yoshikawa, T. Furuhashi |
|
| 105. |
2008/08/19 |
Interactive 3D Space Group Visualization with CLUCalc based on Geometric Algebra (AGACSE 3, Leipzig, Germany)
|
| Date | 2008/08/19 | | Presentation Theme | Interactive 3D Space Group Visualization with CLUCalc based on Geometric Algebra | | Conference | AGACSE 3, Leipzig, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, C. Perwass |
|
| 106. |
2008/08/18 |
Representation of Crystallographic Subperiodic Groups by Geometric Algebra (AGACSE 3, Leipzig, Germany)
|
| Date | 2008/08/18 | | Presentation Theme | Representation of Crystallographic Subperiodic Groups by Geometric Algebra | | Conference | AGACSE 3, Leipzig, Germany | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, D. Ichikawa |
|
| 107. |
2008/08/18 |
Two-Dimensional Clifford-Windowed Fourier Transform (AGACSE 3, Leipzig, Germany)
|
| Date | 2008/08/18 | | Presentation Theme | Two-Dimensional Clifford-Windowed Fourier Transform | | Conference | AGACSE 3, Leipzig, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, B. Mawardi, S. Adji |
|
| 108. |
2008/06 |
Feature Extractions with Geometric Algebra for Classification of Objects (WCCI, Hongkong, 1-6 June 2008)
|
| Date | 2008/06 | | Presentation Theme | Feature Extractions with Geometric Algebra for Classification of Objects | | Conference | WCCI, Hongkong, 1-6 June 2008 | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, Minh Tuan Pham, Kanta Tachibana, Sven Buchholz, Tomohiro Yoshikawa, Takeshi Furuhashi |
|
| 109. |
2008/05/29 |
Geometric Roots of –1 (ICCA8, Sao Paulo, Brazil)
|
| Date | 2008/05/29 | | Presentation Theme | Geometric Roots of –1 | | Conference | ICCA8, Sao Paulo, Brazil | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 110. |
2008/05/29 |
The interactive 3D space group visualizer based on Clifford geometric algebra description of space groups (ICCA8, Sao Paulo, Brazil)
|
| Date | 2008/05/29 | | Presentation Theme | The interactive 3D space group visualizer based on Clifford geometric algebra description of space groups | | Conference | ICCA8, Sao Paulo, Brazil | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer, C. Perwass |
|
| 111. |
2008/05/27 |
Geometric Algebra Feature Extraction and Classification (ICCA8, Sao Paulo, Brazil)
|
| Date | 2008/05/27 | | Presentation Theme | Geometric Algebra Feature Extraction and Classification | | Conference | ICCA8, Sao Paulo, Brazil | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, Minh Tuan Pham, Kanta Tachibana, Sven Buchholz, Tomohiro Yoshikawa, Takeshi Furuhashi |
|
| 112. |
2008/03/04 |
Clifford Algebra Neural Networks (Seminar of The Neural Network Study Group of The Society of Instrument and Control Engineers (SICE), Fukui, Japan)
|
| Date | 2008/03/04 | | Presentation Theme | Clifford Algebra Neural Networks | | Conference | Seminar of The Neural Network Study Group of The Society of Instrument and Control Engineers (SICE), Fukui, Japan | | Conference Type | Domestic | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 113. |
2008/03/04 |
Description and visualization of crystal structures by geometric algebra (Symposium on Frontiers of Computational Science, Nagoya, Japan)
|
| Date | 2008/03/04 | | Presentation Theme | Description and visualization of crystal structures by geometric algebra | | Conference | Symposium on Frontiers of Computational Science, Nagoya, Japan | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer, C. Perwass |
|
| 114. |
2007/11/23 |
The hidden beauty of gold (Int. Symp. on App. Mech. and Power Engin. 2007, Fukui, Japan)
|
| Date | 2007/11/23 | | Presentation Theme | The hidden beauty of gold | | Conference | Int. Symp. on App. Mech. and Power Engin. 2007, Fukui, Japan | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 115. |
2007/09/20 |
Directional uncertainty in Clifford algebra (for multivector integral transforms) (Chinese Academy of Science, Peking, China)
|
| Date | 2007/09/20 | | Presentation Theme | Directional uncertainty in Clifford algebra (for multivector integral transforms) | | Conference | Chinese Academy of Science, Peking, China | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 116. |
2007/09/14 |
Clifford geometric algebra description of space groups and interactive 3D space group visualizer (Department of Mathematics, University of Aveiro, Portugal)
|
| Date | 2007/09/14 | | Presentation Theme | Clifford geometric algebra description of space groups and interactive 3D space group visualizer | | Conference | Department of Mathematics, University of Aveiro, Portugal | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 117. |
2007/09/10 |
Optimal Learning Rates for Clifford Neurons (Special Session Complex-Valued Neural Networks, ICANN’07 International Conference on Artificial Neural Networks, Porto, Portugal)
|
| Date | 2007/09/10 | | Presentation Theme | Optimal Learning Rates for Clifford Neurons | | Conference | Special Session Complex-Valued Neural Networks, ICANN’07 International Conference on Artificial Neural Networks, Porto, Portugal | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | S. Buchholz, K. Tachibana, E. Hitzer |
|
| 118. |
2007/09/03 |
Carrier method for the general evaluation and control of pose, molecular conformation, tracking, etc. (WCAA 2007, Workshop on Clifford Analysis and Applications, "Het Pand", Ghent, Belgium)
|
| Date | 2007/09/03 | | Presentation Theme | Carrier method for the general evaluation and control of pose, molecular conformation, tracking, etc. | | Conference | WCAA 2007, Workshop on Clifford Analysis and Applications, "Het Pand", Ghent, Belgium | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Collaborative | | Researchers and Co-Researchers | E. Hitzer, K. Tachibana, S. Buchholz |
|
| 119. |
2007/09/03 |
Directional uncertainty principle for quaternion Fourier transform (WCAA 2007, Workshop on Clifford Analysis and Applications, "Het Pand", Ghent, Belgium)
|
| Date | 2007/09/03 | | Presentation Theme | Directional uncertainty principle for quaternion Fourier transform | | Conference | WCAA 2007, Workshop on Clifford Analysis and Applications, "Het Pand", Ghent, Belgium | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 120. |
2007/08/22 |
Multivector integral transforms for multi-dimensional signal processing (Institute of Computer Science and Applied Mathematics, Cognitive Systems, University of Kiel, Germany)
|
| Date | 2007/08/22 | | Presentation Theme | Multivector integral transforms for multi-dimensional signal processing | | Conference | Institute of Computer Science and Applied Mathematics, Cognitive Systems, University of Kiel, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 121. |
2007/08/17 |
Foundations of geometric algebra for geometric graph theory (Information Systems Engineering, Prof. Dr. H. J. Klein, University of Kiel, Germany)
|
| Date | 2007/08/17 | | Presentation Theme | Foundations of geometric algebra for geometric graph theory | | Conference | Information Systems Engineering, Prof. Dr. H. J. Klein, University of Kiel, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 122. |
2007/08/10 |
Computer visualization of crystallographic symmetries (Structure Investigation Group, Prof. Dr. H. Fuess, TU Darmstadt, Germany)
|
| Date | 2007/08/10 | | Presentation Theme | Computer visualization of crystallographic symmetries | | Conference | Structure Investigation Group, Prof. Dr. H. Fuess, TU Darmstadt, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 123. |
2007/08/09 |
Introduction to the Space Group Visualizer (Lab. for the Appl. of Synchrotron Radiation (LAS), Prof. em. Dr. H. Wondratschek, Univ. of Karlsruhe, Germany)
|
| Date | 2007/08/09 | | Presentation Theme | Introduction to the Space Group Visualizer | | Conference | Lab. for the Appl. of Synchrotron Radiation (LAS), Prof. em. Dr. H. Wondratschek, Univ. of Karlsruhe, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 124. |
2007/08/07 |
Introduction to geometric algebra with examples from computer vision and computer graphics (Center of Research Excellence for Computer Graphics, Darmstadt, Germany)
|
| Date | 2007/08/07 | | Presentation Theme | Introduction to geometric algebra with examples from computer vision and computer graphics | | Conference | Center of Research Excellence for Computer Graphics, Darmstadt, Germany | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 125. |
2007/02 |
Fourier and Wavelet Transformations in Geometric Algebra (FCS Colloquium, University of Nagoya, Japan)
|
| Date | 2007/02 | | Presentation Theme | Fourier and Wavelet Transformations in Geometric Algebra | | Conference | FCS Colloquium, University of Nagoya, Japan | | Conference Type | Domestic | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 126. |
2006/11 |
Applications of Clifford Algebra to Fourier Transformation, Wavelets and Crystal Symmetry (Seminar of Chinese Academy of Science, Peking, PR China)
|
| Date | 2006/11 | | Presentation Theme | Applications of Clifford Algebra to Fourier Transformation, Wavelets and Crystal Symmetry | | Conference | Seminar of Chinese Academy of Science, Peking, PR China | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 127. |
2006/11 |
Geometric Algebra Tools: 3D Visualization of Crystal Classes and Space Groups (AIST Diamond Institute, Tsukuba, Japan)
|
| Date | 2006/11 | | Presentation Theme | Geometric Algebra Tools: 3D Visualization of Crystal Classes and Space Groups | | Conference | AIST Diamond Institute, Tsukuba, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 128. |
2006/11 |
Interactive Space Group Visualizer (Theoretical Crystallography and Material Science, International Union of Crystallography, Commission on Mathematical and Theoretical Crystallography, Tsukuba, Japan)
|
| Date | 2006/11 | | Presentation Theme | Interactive Space Group Visualizer | | Conference | Theoretical Crystallography and Material Science, International Union of Crystallography, Commission on Mathematical and Theoretical Crystallography, Tsukuba, Japan | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 129. |
2006/10 |
The Space Group Visualizer (ISAME 2006, Shanghai, PR China)
|
| Date | 2006/10 | | Presentation Theme | The Space Group Visualizer | | Conference | ISAME 2006, Shanghai, PR China | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 130. |
2006/09 |
Foundations of Multidimensional Wavelet Theory: The Quaternion Fourier Transform and its Generalizations (JSIAM annual meeting, Tsukuba, Japan)
|
| Date | 2006/09 | | Presentation Theme | Foundations of Multidimensional Wavelet Theory: The Quaternion Fourier Transform and its Generalizations | | Conference | JSIAM annual meeting, Tsukuba, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 131. |
2006/06 |
Crystallographic Space Group Symmetry: Representation and Interactive Visualization by Geometric Algebra (26th International Colloquium on Group Theoretical Methods in Physics, New York, USA)
|
| Date | 2006/06 | | Presentation Theme | Crystallographic Space Group Symmetry: Representation and Interactive Visualization by Geometric Algebra | | Conference | 26th International Colloquium on Group Theoretical Methods in Physics, New York, USA | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 132. |
2006/06 |
Monoclinic Spacegroups in Geometric Algebra: The Spacegroup Visualizer (FTHD, Tampere, Finland)
|
| Date | 2006/06 | | Presentation Theme | Monoclinic Spacegroups in Geometric Algebra: The Spacegroup Visualizer | | Conference | FTHD, Tampere, Finland | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 133. |
2006/06 |
Quaternion Fourier Transforms on Quaternion Fields (FTHD, Tampere, Finland)
|
| Date | 2006/06 | | Presentation Theme | Quaternion Fourier Transforms on Quaternion Fields | | Conference | FTHD, Tampere, Finland | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 134. |
2006/06 |
Three vector generation of crystal space groups in geometric algebra (Symposium on Form 61, Nagoya, Japan)
|
| Date | 2006/06 | | Presentation Theme | Three vector generation of crystal space groups in geometric algebra | | Conference | Symposium on Form 61, Nagoya, Japan | | Conference Type | Domestic | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 135. |
2005/10 |
The GeometricAlgebra Java Package – Novel Structure Implementation of 5D Geometric Algebra R_4,1 for Object Oriented Euclidean Geometry, Space-Time Physics and Object Oriented Computer Algebra (ALGI 16, Fukuoka, Japan)
|
| Date | 2005/10 | | Presentation Theme | The GeometricAlgebra Java Package – Novel Structure Implementation of 5D Geometric Algebra R_4,1 for Object Oriented Euclidean Geometry, Space-Time Physics and Object Oriented Computer Algebra | | Conference | ALGI 16, Fukuoka, Japan | | Conference Type | Domestic | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 136. |
2005/09 |
Crystal Cell and Space Lattice Symmetries in Clifford Geometric Algebra (ICNAAM 2005, Rhodos, Greece)
|
| Date | 2005/09 | | Presentation Theme | Crystal Cell and Space Lattice Symmetries in Clifford Geometric Algebra | | Conference | ICNAAM 2005, Rhodos, Greece | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 137. |
2005/09 |
Uncertainty Principle for the Clifford Geometric Algebra Cl(3,0) based on Clifford Fourier Transform (ICNAAM 2005, Rhodos, Greece)
|
| Date | 2005/09 | | Presentation Theme | Uncertainty Principle for the Clifford Geometric Algebra Cl(3,0) based on Clifford Fourier Transform | | Conference | ICNAAM 2005, Rhodos, Greece | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 138. |
2005/05 |
Crystal Cell Symmetries in Geometric Algebra of Crystal Cell Vectors (Symposium on Form 59, Sapporo, Japan)
|
| Date | 2005/05 | | Presentation Theme | Crystal Cell Symmetries in Geometric Algebra of Crystal Cell Vectors | | Conference | Symposium on Form 59, Sapporo, Japan | | Conference Type | Domestic | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 139. |
2005/05 |
Geometric Algebra and Interactive Visualization of Crystal Groups (ICCA7, Toulouse, France)
|
| Date | 2005/05 | | Presentation Theme | Geometric Algebra and Interactive Visualization of Crystal Groups | | Conference | ICCA7, Toulouse, France | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 140. |
2005/01 |
Special Relativity as Application of Geometric Algebra (Int. Conference on Relativity 2005, Amravati, India)
|
| Date | 2005/01 | | Presentation Theme | Special Relativity as Application of Geometric Algebra | | Conference | Int. Conference on Relativity 2005, Amravati, India | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 141. |
2004/11 |
Crystal Cells in Geometric Algebra (International Symposium on Advanced Mechanical Engineering, Fukui, Japan)
|
| Date | 2004/11 | | Presentation Theme | Crystal Cells in Geometric Algebra | | Conference | International Symposium on Advanced Mechanical Engineering, Fukui, Japan | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 142. |
2004/05 |
Conic Sections in Geometric Algebra (Geometric Invariance and Applications in Engineering, Xian, PR China)
|
| Date | 2004/05 | | Presentation Theme | Conic Sections in Geometric Algebra | | Conference | Geometric Invariance and Applications in Engineering, Xian, PR China | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Invited | Invited | | Researchers and Co-Researchers | E. Hitzer |
|
| 143. |
2003/11 |
Conic Sections Through Five Points - Classical, Projective, Conformal (Pukyong National University - Fukui University, Symposium on Advanced Mechanical Engineering, 23-24 Nov. 2003, Pukyong National University, Busan, Korea)
|
| Date | 2003/11 | | Presentation Theme | Conic Sections Through Five Points - Classical, Projective, Conformal | | Conference | Pukyong National University - Fukui University, Symposium on Advanced Mechanical Engineering, 23-24 Nov. 2003, Pukyong National University, Busan, Korea | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 144. |
2003/11 |
Learning about Conic Sections with Geometric Algebra and Cinderella (Innovative Teaching of Mathematics with geometric algebra - New Concepts and Cutting Edge Technology Applied to Mathematical Education, Int. Symposium 2003.11.20-22, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan)
|
| Date | 2003/11 | | Presentation Theme | Learning about Conic Sections with Geometric Algebra and Cinderella | | Conference | Innovative Teaching of Mathematics with geometric algebra - New Concepts and Cutting Edge Technology Applied to Mathematical Education, Int. Symposium 2003.11.20-22, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan | | Conference Type | International | | Presentation Type | Speech (Invitation/Special) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
|
| 145. |
2003/07 |
Homogeneous Model of Euclidean Space in the Cl(4,1) Algebra of {origin, 3-space, infinity} and Java Implementation (The 5th Int. Cong. on Industrial and Appl. Math., Minisymposium: Clifford Algebras, Cliff. Analysis and Appl. I: Algebras, Extensions and Appl., Sidney, Australia)
|
| Date | 2003/07 | | Presentation Theme | Homogeneous Model of Euclidean Space in the Cl(4,1) Algebra of {origin, 3-space, infinity} and Java Implementation | | Conference | The 5th Int. Cong. on Industrial and Appl. Math., Minisymposium: Clifford Algebras, Cliff. Analysis and Appl. I: Algebras, Extensions and Appl., Sidney, Australia | | Conference Type | International | | Presentation Type | Speech (General) | | Contribution Type | Individual | | Researchers and Co-Researchers | E. Hitzer |
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