Linear recurrence relations in the algebra of matrices and applications

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for Aⁿ (nr) and e^tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A^j, where 0jr−1.     

(∈,∈∨ q(λ,μ))-凸模糊集

给出(∈,∈∨q(λ,μ))-凸模糊集的定义,讨论它们的一些基本性质。     

Polynomial Approximation of Functions: Historical Perspective and New Tools

This paper examines the effect of applying symbolic computation and graphics to enhance students' ability to move from a visual interpretation of mathematical concepts to formal reasoning. The mathematics topics involved, Approximation and Interpolation, were taught according to their historical development, and the students tried to follow the thinking process of the creators of the theory. They used a Computer Algebra System to manipulate algebraic expressions and generate a wide variety of dynamic graphics; thus21st century technology was applied in order to “walk” with the students from the period of Euler in 1748 to the period of Runge in 1901. We describe some situations in which the combination of dynamic graphics,algorithms, and historical perspective enabled the students to improve their understanding of concepts such as limit, convergence, and the quality of approximation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Representations of q-analogue of the Virasoro Algebra

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Coherent states and infinite-dimensional lie algebras: An outlook

Summary The possible extension of the notion of generalized coherent state to the case of infinite-dimesional affine Lie algebras is discussed with special attention to the resulting topological structure of the coherent states manifold, and to its connection with the structure of the algebra. The relevance for the solution of nonlinear dynamical systems equations of motion is briefly reviewed. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

替换定理一些问题的讨论

本给出了替换定理的一种新的证法，此证法直观易懂。     

关于解析函数的一个易想象的不等式及其应用

本文关于解析函数给出了一个可作几何理解的不等式,由此易得出一个有关解析函数零点的命题,而代数学基本定理成为它的直接推论．     

TL-subrings and TL-ideals,Part3:Maximal TL-ideals and ireducible TL-ideals

ＴＬｓｕｂｒｉｎｇｓａｎｄＴＬｉｄｅａｌｓ，Ｐａｒｔ３：ＭａｘｉｍａｌＴＬｉｄｅａｌｓａｎｄｉｒｅｄｕｃｉｂｌｅＴＬｉｄｅａｌｓＹｕＹａｎｄｏｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＹａｎｃｈｅｎｇＴｅａｃｈｅｒｓＣｏｌｅｇｅ...     

A Geodesic Between the Hilbert Basis Theorem and Gordan''''s Lemma

Gordan's Lemma and Hilbert Basis theorem, both merging from establishing thefinite generation of invariants, are proved in one combinatorial set up, namely, thesemigroup N~n     

Multiplicative Maps With Specified (1, 1)-Entry

In this article, we will show that for many complex-valued maps f over a semigroup G of matrices, there exists a minimum k for the existence of a multiplicative map for which the (1, 1)-entry of ϕ( A ) is f ( A ). We obtain results on such multiplicative maps, and use them to classify all the multiplicative maps τon G such that f ( A ) = τ( g ( A )) for any A ε G , where f and g are given complex-valued maps.