带裂纹十次对称二维准晶平面弹性的无摩擦接触问题

借助经典平面弹性复变函数方法，研究了单个刚性凸基底压头作用下，带任意形状裂纹十次对称二维准晶半平面弹性的无摩擦接触问题.利用十次对称二维准晶位移、应力的复变函数表达式, 带任意形状裂纹的准晶半平面弹性无摩擦接触问题被转换为可解的解析函数复合边值问题，进而简化成一类可解的Riemann边值问题.通过求解Riemann边值问题，得到了应力函数的封闭解, 并给出了裂纹端点处应力强度因子和压头下方准晶体表面任意点处接触应力的显式表达式.从压头下方接触应力的表达式可以看出, 接触应力在压头边缘和裂纹端点处具有奇异性.当忽略相位子场影响时, 该文所得结论与弹性材料对应结果一致.数值算例分别给出了单个平底刚性压头无摩擦压入带单个垂直裂纹和水平裂纹的十次对称二维准晶下半平面的结果.该文所得结论为准晶材料的应用提供了理论参考.     

材料各向异性对热弹性接触问题的影响

研究一个绝热刚性冲头和各向异性弹性传热半空间之间的稳态平面接触问题.由于冲头在半空间表面上的滑移,在接触区域内摩擦生热,并且热辐射到接触区域.之外的区域利用Fourier积分变换,将问题简化为两个奇异积分方程构成的方程组.利用Gauss-Jacobi梯形求积公式,数值地求解该方程组给出了各向异性和热效应的图例.     

复合材料弹性平面的周期接触问题

对于平面弹性理论的经典接触问题,即弹性体(作为占有下半平面)上压着有限个压头的情况,曾应用复变函数理论,得到了一些有效的解答。对于平面弹性理论的周期接触问题,即弹性体上压着无限个按周期排列的压头,在所指弹性体为各向同性体的情况,路见可和蔡海涛同样应用复变函数理论,得到了一些有效解答。     

不同材料拼接的半平面周期裂缝问题

在[1]中讨论了不同材料拼接平面裂缝中的数学问题,[2]中讨论了不同材料拼接的周期裂缝问题,在[3]中讨论了带周期裂缝的弹性长条基本问题。本文将讨论不同材料拼接的半平面周期裂缝问题,把问题化为某正则型的奇异积分方程,并采用分拆函数的方法,给出了周期直裂纹情况的封闭形式解,且导出了应力强度因子的公式。     

浅水中度振幅孤立波解的分支

利用平面动力系统分支方法研究浅水中度振幅方程的定性行为和孤立波解.给出了系统在不同参数条件下的相图.获得了光滑孤立波、cuspon解和周期波解的隐式表达式.对方程的光滑孤立波解、cuspon解和周期波解进行了数值模拟.获得的结果完善了相关文献已有的结果.     

弹性长条的周期基本问题

Howland、唐立民、Isida 等对一个周期带内含有一个圆孔的弹性平面周期基本问题作了研究.把具有一个任意形状周期孔的平面弹性问题化为 Fredholm 积分方程.森口繁一在文献[4]§10中给出了在应力是周期的条件下函数的一般表达式,并分离出周期部分和非周期部分.路见可教授在文献[1]中把弹性平面或半平面中     

方程(t)=-x〔t-π/(33~(1/2))〕-x〔t-2π/(33~(1/2))〕周期解的部分表达式

]文 [1 ]给出了一类具两个滞量的方程存在周期解的充分条件 ,但并没有给出周期解的表达式 .本文给出了方程 x( t) =-x t-π3 3-x t-2π3 3周期解的部分表达式 .     

方程(x·)(t)=-x[t-π/3√3]-x[t-2π/3√3]周期解的部分表达式

文[1]给出了一类具两个滞量的方程存在周期解的充分条件,但并没有给出周期解的表达式.本文给出了方程(x·)(t)=-x[t-π/3√3]-x[t-2π/3√3]周期解的部分表达式.     

带周期裂缝的弹性半平面问题

本文把具有任意形状和个数的周期裂缝的弹性半平面基本问题化为了某种特殊类型的奇异积分方程,证明了其解的存在和唯一。并对带周期共线直裂缝的弹性半平面问题,给出了封闭形式的解。     

一类非线性方程的行波解分支

运用平面动力系统的分支方法,研究了一类非线性方程的行波解,画出了在不同参数条件下的相图,证明方程存在周期行波解和周期尖波解.给出了有界波的精确的参数表达式,指出了周期尖波是周期波的极限形式,同时指出了方程不存在圈孤子解.     

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.     

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.     

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。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

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.     

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.