Affine Differential Invariants of Functions on the Plane
A differential invariant is a function defined on the jet space of functions that remains the same under a group action. It is an important concept to solve the equivalence problem. This paper presents an effective method to derive a special type of affine differential invariants. Given some functio...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/868725 |
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| _version_ | 1849690823106494464 |
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| author | Yuanbin Wang Xingwei Wang Bin Zhang |
| author_facet | Yuanbin Wang Xingwei Wang Bin Zhang |
| author_sort | Yuanbin Wang |
| collection | DOAJ |
| description | A differential invariant is a function defined on the jet space of functions that remains the same under a group action. It is an important concept to solve the equivalence problem. This paper presents an effective method to derive a special type of affine differential invariants. Given some functions defined on the plane and an affine group acting on the plane, there are induced actions of the group on the functions and on the derivative functions of the functions. Affine differential invariants of these functions are useful in many applications. However, there has been little systematic study of this problem at present. No clear and simple results are available for application users to use directly. We propose a direct and simple method to construct affine differential invariants in this situation. Some useful explicit formulas of affine differential invariants of 2D functions are presented. |
| format | Article |
| id | doaj-art-ee9b8adbdbcf4579bfda2d8a41ea119a |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ee9b8adbdbcf4579bfda2d8a41ea119a2025-08-20T03:21:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/868725868725Affine Differential Invariants of Functions on the PlaneYuanbin Wang0Xingwei Wang1Bin Zhang2College of Information Science and Engineering, Northeastern University, Shenyang 110004, ChinaCollege of Information Science and Engineering, Northeastern University, Shenyang 110004, ChinaCollege of Information Science and Engineering, Northeastern University, Shenyang 110004, ChinaA differential invariant is a function defined on the jet space of functions that remains the same under a group action. It is an important concept to solve the equivalence problem. This paper presents an effective method to derive a special type of affine differential invariants. Given some functions defined on the plane and an affine group acting on the plane, there are induced actions of the group on the functions and on the derivative functions of the functions. Affine differential invariants of these functions are useful in many applications. However, there has been little systematic study of this problem at present. No clear and simple results are available for application users to use directly. We propose a direct and simple method to construct affine differential invariants in this situation. Some useful explicit formulas of affine differential invariants of 2D functions are presented.http://dx.doi.org/10.1155/2013/868725 |
| spellingShingle | Yuanbin Wang Xingwei Wang Bin Zhang Affine Differential Invariants of Functions on the Plane Journal of Applied Mathematics |
| title | Affine Differential Invariants of Functions on the Plane |
| title_full | Affine Differential Invariants of Functions on the Plane |
| title_fullStr | Affine Differential Invariants of Functions on the Plane |
| title_full_unstemmed | Affine Differential Invariants of Functions on the Plane |
| title_short | Affine Differential Invariants of Functions on the Plane |
| title_sort | affine differential invariants of functions on the plane |
| url | http://dx.doi.org/10.1155/2013/868725 |
| work_keys_str_mv | AT yuanbinwang affinedifferentialinvariantsoffunctionsontheplane AT xingweiwang affinedifferentialinvariantsoffunctionsontheplane AT binzhang affinedifferentialinvariantsoffunctionsontheplane |