BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, , , Mathematical model of representation of one-parameter curve and two-parameter surface as product integral representation // BSU Bulletin. Mathematics, Informatics. - 2016. №4. . - С. 43-49.
Title:
Mathematical model of representation of one-parameter curve and two-parameter surface as product integral representation
Financing:
Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (проекты 14-07-0027215 и 14-08-14-08-01132) и при под- держке Программы РАН по проекту «Математические методы распознавания образов и прогнозирования» (№0314-2014-2017) (№ госрегистрации 01201351843)
Codes:
Annotation:
Mathematical model for representing of one-parameter curve and two- parameter surface in the form of product integral is considered in the paper. The use of this model allows to synthesize a surface by means of elementary functions, which reduces amount of computational operations and numerical errors of integration. Representation of solutions of the Cauchy problem of dif- ferential equations by matrix-valued function ensures the absence of dependence on the coordinates (coordinate-free solutions).
Keywords:
parametric surface, product integral, invariant to vector state transformation.
List of references:
1. Abbena E., Salamon S., Gray A. Modern differential geometry of curves and surfaces with Mathematica. — CRC press. — 2006.
2. Aref'eva I. Y. Non-Abelian stokes formula // Theoretical and Mathematical Physics. — 1980. — Т. 43. — №. 1. — С. 353 – 356.
3. Baker A. Matrix groups: An introduction to Lie group theory. – Springer Science & Business Media. — 2012.
4. Chukanov S. N. Constructing invariants for visualization of vector fields defined by integral curves of dynamic systems // Optoelectronics, Instrumenta- tion and Data Processing. — 2011. — Т. 47. — №. 2. — С. 151 – 155.
5. Dollard J. D., Friedman C.N. Product Integration. – Addison Wesley, 1979.
6. Karp R. L., Mansouri F., Rno J. S. Product Integral Representations of Wilson Lines and Wilson loops and Non-Abelian Stokes Theorem // arXiv pre- print hep-th/9903221.
2. Aref'eva I. Y. Non-Abelian stokes formula // Theoretical and Mathematical Physics. — 1980. — Т. 43. — №. 1. — С. 353 – 356.
3. Baker A. Matrix groups: An introduction to Lie group theory. – Springer Science & Business Media. — 2012.
4. Chukanov S. N. Constructing invariants for visualization of vector fields defined by integral curves of dynamic systems // Optoelectronics, Instrumenta- tion and Data Processing. — 2011. — Т. 47. — №. 2. — С. 151 – 155.
5. Dollard J. D., Friedman C.N. Product Integration. – Addison Wesley, 1979.
6. Karp R. L., Mansouri F., Rno J. S. Product Integral Representations of Wilson Lines and Wilson loops and Non-Abelian Stokes Theorem // arXiv pre- print hep-th/9903221.
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