Bosonic Formulas for \widehat{\mathfrak{s}\mathfrak{l}} 2 Coinvariants

We derive bosonic-type formulas for the characters of ₂ coinvariants.     

Conservative Means of Orthogonal Series and the Spaces $$L^p [0;1] $$ , $$p \in (1;\infty ) $$

Necessary and sufficient conditions for an orthogonal series to be the Fourier series of a function in the space , , are obtained. In the special case of regular summation methods we recover the classical results of Orlicz and Lomnicki.     

Multi-component C-KdV Hierarchy of Soliton Equations and Its Multi-component Integrable Coupling System

A new simple loop algebra G M is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component C-KdV hierarchy is obtained. Further, an expanding loop algebra FM of the loop algebra G M is presented. Based on FM , the multi-component integrable coupling system of the multi-component C-KdV hierarchy is worked out. The method can be used to other nonlinear evolution equations hierarchy.     

高阶奇性常微分方程的边值问题（Ⅰ）──—非退化情形

本文对高阶奇性常微分方程的非退化边值问题建立了非共轭性存在定理和上、下解型存在定理．     

满足右零化子特殊升链条件的环

本文讨论了满足右零化子特殊升链条件的环的性质以及与左、右完备环，ＱＦ－环的关系；给出了满足右零化子特殊升链条件的环中素理想是完全素理想的条件，从而给出了Ｇｏｌｄｉｅ定理的一个应用．     

一种完备完全分配格上矩阵方程的求解方法

模糊理论已经在决策、模式识别、故障诊断、过程控制等许多方面得到了广泛应用，在这些应用问题求解中往往要遇到求解模糊关系方程。本文从完备完全分配格的角度给出了一种求解模糊关系方程极小解的完备解法，并用计算机实现了提出的算法，为实际问题求解计算机化打下了基础。     

Completely Positive Definite Maps Over Topological^＊—algebras

ＣｏｍｐｌｅｔｅｌｙＰｏｓｉｔｉｖｅＤｅｆｉｎｉｔｅＭａｐｓＯｖｅｒＴｏｐｏｌｏｇｉｃａｌ－ａｌｇｅｂｒａｓＸｕＴｉａｎｚｈｏｕ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｆｏｇｙ，...     

Remarks on the star-triangle relation in the Baxter-Bazhanov model

We show that the restricted star-triangle relation introduced by Bazhanov and Baxter can be obtained either from the star-triangle relation of the chiral Potts model or from the star-square relation proposed by Kashaev, Mangazeev, and Stroganov, and give a response to a guess of Bazhanov and Baxter.     

Hamilton–Jacobi Quantization of Singular Lagrangians with Linear Velocities

In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton–Jacobi method. The integrablity conditions are considered on the equations of motion and the action function as well in order to obtain the path integral quantization of singular Lagrangians with linear velocities.     

New Simple Method for Obtaining Integrable Hierarchies of Soliton Equations with Multicomponent Potential Functions

A new simple method for obtaining integrable hierarchies of soliton equations is proposed. First of all, a new loop algebra is constructed, whose commutation operation is clear as that in loop algebra . Second, by making use of the Tu scheme, many of integrable hierarchies with multicomponent potential functions can be produced. As a specific application of our method, a multicomponent AKNS hierarchy is obtained. Finally, an expanding loop algebra of the loop algebra is constructed. Taking advantage of above, a type of integrable coupling system of the multicomponent AKNS hierarchy is worked out.