On differential rational invariants of patches with respect to motion groups

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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Main Author: Bekbaev, Ural
Format: Conference or Workshop Item
Language:English
Published: American Institute of Physics 2015
Subjects:
QA Mathematics
Online Access: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
id iium-47300
recordtype eprints
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 Conference or Workshop Item 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
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Bekbaev, Ural
On differential rational invariants of patches with respect to motion groups
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.
format Conference or Workshop Item
author Bekbaev, Ural
author_facet Bekbaev, Ural
author_sort Bekbaev, Ural
title On differential rational invariants of patches with respect to motion groups
title_short On differential rational invariants of patches with respect to motion groups
title_full On differential rational invariants of patches with respect to motion groups
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_sort on differential rational invariants of patches with respect to motion groups
publisher American Institute of Physics
publishDate 2015
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
first_indexed 2023-09-18T21:07:19Z
last_indexed 2023-09-18T21:07:19Z
_version_ 1777411020077137920

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