On differential rational invariants of classical motion groups

Bekbaev Ural Dj.; Rakhimov Isamiddin S.; Muminov Qabildjan K.

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On differential rational invariants of classical motion groups

机译：关于经典运动群的微分有理不变量

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摘要

A pure algebraic approach to differential invariants of curves and surfaces is presented. By the use of this approach the explicit formulae for the generating differential invariants and invariant differential operators for the generic curves in n-dimensional classical geometries are constructed.

机译：给出了曲线和曲面的微分不变式的纯代数方法。通过使用这种方法，构造了用于生成n维经典几何中一般曲线的微分不变量和不变微分算子的显式公式。

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《Journal of algebra and its applications》 |2015年第2期|共14页
作者
Bekbaev Ural Dj.; Rakhimov Isamiddin S.; Muminov Qabildjan K.;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
Differential rational function; differential invariant; curve; surface; affine group;

机译：微分有理函数;微分不变量;曲线;曲面;仿射群;

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专利

1. ON DIFFERENTIAL RATIONAL INVARIANTS OF THE CLASSICAL GROUPS OF MOTIONS OF A VECTOR SPACE [J] . U. D. Bekbaev, K. K. Muminov Methods of Functional Analysis and Topology . 2004,第3期

机译：向量空间的经典运动的微分有理不变性
2. On differential rational invariants of the classical motion groups of a vector space [J] . U. D. Bekbaev, K. K. Muminov Доклады Академии Наук Республики Узбекистан . 1998,第6期

机译：向量空间经典运动群的微分有理不变量
3. On differential rational invariants of the classical motion groups of a vector space [J] . U. D. Bekbaev, K. K. Muminov Доклады Академии Наук Республики Узбекистан . 1998,第6期

机译：关于矢量空间的古典运动组的差分Rational Invariants
4. The Peculiarities of the Structural Optimization of the Energy-Efficient Precision ARC-Filters on the Base of Classical and Differential Difference Operational Amplifiers [C] . S.G. Krutchinsky, N.N. Prokopenko, E.A. Zhebrun, IEEE East-West Design Test Symposium . 2015

机译：经典差分差分运算放大器基极节能精密灭弧器结构优化的特性
5. A New Method for Functional Decomposition of Rational Invariants, and the Solution of Abel's Differential Equation via the Equivalence Method. [D] . Roche, Austin Duncan. 2010

机译：有理不变量函数分解的新方法，以及通过等价法求解Abel微分方程的方法。
6. Differential Invariants and Invariant Partial Differential Equations Under Continuous Transformation Groups in Normed Linear Spaces [O] . Aristotle D. Michal 1951

机译：赋范线性空间中连续变换群下的微分不变量和不变性偏微分方程
7. Erratum: Approximate constants of motion for classically chaotic vibrational dynamics: Vague tori, semiclassical quantization, and classical intramolecular energy flow J. Chem. Phys. 77, 5204 (1982) [O] . Randall B. Shirts, William P. Reinhardt 1983

机译：错误：经典混沌振动动力学的近似常量：模糊的波特，半透明量化和经典的分子内能量流动J。化学。物理。 77,5204（1982）
8. An Invariant Infinitesimal Theory of Motions Superposed on a Given Motion [R] . Casey, J., Naghdi, P. M. 1980

机译：一个不变的无穷小运动理论叠加在给定运动上

On differential rational invariants of classical motion groups

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