The trees for which maximum multiplicity implies the simplicity of other eigenvalues

Among those real symmetric matrices whose graph is a given tree T, the maximum multiplicity is known to be the path cover number of T. An explicit characterization is given for those trees for which whenever the maximum multiplicity is attained, all other multiplicities are 1.     

Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians

It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.      

关于纤维锥的Hilbert系数

Let （R, m） be a Cohen-Macaulay local ring of dimension d, I an mprimary ideal and K an ideal containing I. Assuming that I has minimal （almost minimal） mixed multiplicity with respect to K, we get some results on the Hilbert coefficients of fiber cones.     

一类由可修,可靠的人与机器构成的系统解的渐近性质

运用C0-半群理论研究一类由可修,可靠的人与机器构成的系统解的渐近性质.首先证明在虚轴上除了0以外其他所有点都属于该算子的豫解集,其次证明0是对应于该系统的主算子及其共轭算子的几何与代数重数为1的特征值,由此推出该系统的时间依赖解当时刻趋向于无穷时强收敛于系统的稳态解.     

Multiplicity and Stability of Equilibrium States of Three-Dimensional Nonlinear System

The multiplicity and stability of the equilibrium states of a three-dimensional differential system with initial conditions and three cross terms are studied in this paper. The existence and multiplicity of equilibrium states are given under the different qualifications of parameters. Besides, the local stability of the equilibrium state is shown by analyzing the eigenfunction of the Jacobi matrix. The global stability of the equilibrium state is obtained by constructing the Lyapunov function. Furthermore, the numerical simulation intuitively reflected the relationship of variables and verified the correctness of theoretical analysis.     

渐近线性二阶Hamilton系统解的存在性和多重性

在实际问题中存在着Neumann边值情形.为实际需要,运用指标理论和Morse理论研究了渐近线性二阶Hamilton系统在这种情形下解的存在性和多重性问题。     

The multiplicity of abelian covers of splice quotient singularities

From a resolution graph with certain conditions, Neumann and Wahl constructed an equisingular family of surface singularities called splice quotients. For this class some fundamental analytic invariants have been computed from their resolution graph. In this paper we give a method to compute the multiplicity of an abelian covering of a splice quotient from its resolution graph and the Galois group.     

On multiplicities of simple subquotients in generalized Verma modules

We reduce the problem on multiplicities of simple subquotients in an -stratified generalized Verma module to the analogous problem for classical Verma modules.