On differential rational invariants of patches with respect to motion groups
This paper can be considered as a research on Algebraic Differential Geometry. It is about differential rational invariants of subgroups of the Affine group over the constant fields of partial differential fields (characteristic zero). The obtained results can be formulated in terms of Differentia...
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| Format: | Proceeding Paper |
| Language: | English |
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American Institute of Physics
2015
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| Online Access: | http://irep.iium.edu.my/47300/ http://irep.iium.edu.my/47300/4/47300-new.pdf |
| _version_ | 1848783121132027904 |
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| author | Bekbaev, Ural |
| author_facet | Bekbaev, Ural |
| author_sort | Bekbaev, Ural |
| building | IIUM Repository |
| collection | Online Access |
| description | This paper can be considered as a research on Algebraic Differential Geometry. It is about differential
rational invariants of subgroups of the Affine group over the constant fields of partial differential fields (characteristic
zero). The obtained results can be formulated in terms of Differential Geometry as follows: 1. For any motion group
represented by a subgroup H of the Affine group it is shown that systems of generators of a field of H-invariant (not
differential) rational functions can be used to construct systems of generators for the differential field of H-invariant
differential rational functions of parameterized surface (patch). 2. For some classic motion groups H the generating
systems of the field of H-invariant differential functions are presented. 3. For motion groups, including all classical
subgroups of the Affine group, separating systems of invariants, uniqueness and existence theorems are offered.
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| first_indexed | 2025-11-14T16:16:19Z |
| format | Proceeding Paper |
| id | iium-47300 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:16:19Z |
| publishDate | 2015 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-473002016-05-25T07:06:06Z http://irep.iium.edu.my/47300/ On differential rational invariants of patches with respect to motion groups Bekbaev, Ural QA Mathematics This paper can be considered as a research on Algebraic Differential Geometry. It is about differential rational invariants of subgroups of the Affine group over the constant fields of partial differential fields (characteristic zero). The obtained results can be formulated in terms of Differential Geometry as follows: 1. For any motion group represented by a subgroup H of the Affine group it is shown that systems of generators of a field of H-invariant (not differential) rational functions can be used to construct systems of generators for the differential field of H-invariant differential rational functions of parameterized surface (patch). 2. For some classic motion groups H the generating systems of the field of H-invariant differential functions are presented. 3. For motion groups, including all classical subgroups of the Affine group, separating systems of invariants, uniqueness and existence theorems are offered. American Institute of Physics 2015 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/47300/4/47300-new.pdf Bekbaev, Ural (2015) On differential rational invariants of patches with respect to motion groups. In: International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014, 28-30 May 2014, Penang. http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4926637 10.1063/1.4926637 |
| spellingShingle | QA Mathematics Bekbaev, Ural On differential rational invariants of patches with respect to motion groups |
| title | On differential rational invariants of patches with respect to motion groups
|
| title_full | On differential rational invariants of patches with respect to motion groups
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| title_fullStr | On differential rational invariants of patches with respect to motion groups
|
| title_full_unstemmed | On differential rational invariants of patches with respect to motion groups
|
| title_short | On differential rational invariants of patches with respect to motion groups
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| title_sort | on differential rational invariants of patches with respect to motion groups |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/47300/ http://irep.iium.edu.my/47300/ http://irep.iium.edu.my/47300/ http://irep.iium.edu.my/47300/4/47300-new.pdf |