边界条件都含有特征参数的四阶微分算子特征值的依赖性

本文考虑了区间[a,b]两端四个边界条件都含有特征函数的四阶微分算子特征值的依赖性问题,证明了特征值不仅连续依赖而且可微依赖于问题的各个参数(系数函数,权函数,区间端点,边界条件系数矩阵),并且给出了相应的微分表达式.特别地,给出特征值关于特征参数依赖的边界条件系数矩阵的Frechet导数.     

正则型Sturm-Liouville微分算子特征值关于边界条件的连续依赖性

本文以隐函数存在定理为主要工具,重新研究Sturm-Liouville微分算子特征值关于边界条件参数的连续依赖性问题.我们不仅给出了该结果一个简单的新证明,而且明确地呈现了第n个特征值关于边界条件参数的导数,进而得到了在实耦合型边界条件下二重特征值产生的位置及个数的新结果.     

边界条件中带有谱参数且在多个点不连续的Sturm-Liouville算子的特征问题

本文研究了边界条件中带有谱参数且在多个不连续点处具有转移耦合边条件的SturmLiouville特征问题,得到了该问题的特征值分布和特征值的渐近式.     

一类基于Robin边界条件变化的反传输特征值问题

本文研究具有Robin边界条件的Schr?dinger算子反传输特征值问题,旨在由传输特征值数据还原势函数.通过改变其中一个边界条件参数,可以获得有无穷多个能量有限的传输特征值.本文证明这样的传输特征值集合可以唯一地确定Schr?dinger算子的势函数及另一个边界条件参数.     

时标上具有非线性谱参数边界条件的Sturm-Liouville问题的特征值（英文）

本文考虑一类时标上带有非线性多项式谱参数边界条件的Sturm-Liouville问题的特征值.结果表明特征值的个数不仅依赖于对时标的分割,而且依赖于多项式谱参数边界条件.     

一类四阶边值问题的特征值对边界的依赖性[英文]

本文研究四阶边值问题的特征值对边界的依赖性问题,指出带有支撑边界条件的四阶边值问题的特征值连续且光滑地依赖于边界点,给出其第n个特征值关于一端点的一阶微分表达式,并证明当区间长度趋于零时,其所有的特征值会趋于无穷.     

带转移条件的四阶微分方程边值问题的特征值的依赖性

研究带转移条件的四阶微分方程边值问题的特征值对边界条件及转移条件的连续依赖性和可微依赖性,并给出了特征值关于这些参数所满足的微分表达式.     

求解一类不连续的Sturm-Liouville问题

研究一类边界条件中有谱参数的不连续的Sturm-Liouville问题.首先在Hilbert空间中定义了一个自共轭的线性算子A,使得该类Sturm-Liouville问题的特征值与算子A的特征值相一致.进一步证明了算子A是自共轭的,且这类Sturm-Liouville问题特征值是解析单的.最后展示了一个具体问题的特征值以及特征函数的逼近解.     

边界条件含谱参数并具有转移条件的Sturm-Liouville问题的格林函数（英文）

本文在与边界条件有关的修正Hilbert空间中考察一类边界条件含谱参数并具有转移条件的Sturm-Liouville问题.得到了λ为该问题特征值的等价条件,给出了该问题的格林函数.     

具有混合型边界条件的左定Sturm-Liouville问题特征值的下标计算(英文)

本文研究具有混合型边界条件的左定Sturm-Liouvile问题特征值的下标计算问题.首先给出具有分离型边界条件和混合型边界条件的左定Sturm-Liouville问题的特征值之间的不等式;然后利用这个结果给出一种计算混合型边界条件下左定Sturm-Liouville问题特征值下标的方法.     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Radius of convexity of certain classes of analytic functions

We consider the classes of analytic functions introduced recently by K.I. Noor which are defined by conditions joining ideas of close-to-convex and of bounded boundary rotation functions. We investigate coefficients estimates and radii of convexity.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。