小周期型复合材料稳态热传导问题的一种双尺度渐近展开收敛性分析

给出一类具有某种对称性小周期复合材料稳态热传导问题解的渐近表示方法.区别于传统多尺度计算方法,将计算过程中需要求解的关于单胞Q的H_per¹(Q)周期边值问题改为齐次边值问题,这样数值方法求解时协调元空间容易构造;另一方面传统的多尺度渐近解不满足原始问题的边界条件,新构造的渐近形式不仅满足原始问题的物理边界条件,同时保持一定的收敛阶,更能被工程上所接受.     

一类时滞反应扩散方程的周期解和概周期解

通过构造上、下控制函数，结合上、下解方法及相应的单调迭代方法研究了一类时滞反应扩散方程，证明了在反应项非单调时，如果一雏边值问题存在一对周期（或概周期）上、下解，则方程一定存在唯一的周期（或概周期）解．并给出了二维边值问题周期（或概周期）解存在唯一性的充分条件．推广了已有的一些结果。     

基于双尺度渐近分析的有限元算法

1．引言正如文山所说，由于复合材料和周期结构的材料系数ail（x）在局部区域内间断且跳跃性很大，加上区域内含有周期性洞穴或裂缝，且周期长度很小．一般而言，直接采用有限元方法进行数值模拟，其计算量大得惊人，甚至难以实现．文山针对这种特征，提出了一种可计算的双尺度渐近分析模式，本文在此基础上给出了相应的有限元算法，它包括：1．周期解在一个基本构造上的有限元计算；2．边界层的有限元计算．同时，给出了相应的误差分析．2．周期解的有限元计算首先考虑下列形式的边值问题；其中把，代E尸（on叫，iii（0关于E—（EI，ZZ…     

二阶非线性扰动差分方程解的渐近性质

将讨论的差分方程△（rm-1x0-1）＋qnxn=anf（xn）看成是其对应的齐次差分方程Δ（rn-1Δyn-1）＋qnyn=0的非线性扰动，其中f（x）为[0，∞）连续函数．设对应的齐次差分方程非振动，zn和yn为其主解和非主解．本文将运用压缩映象原理，获得方程存在渐近于其对应齐次方程主解的解的充分条件．并用方程的系数给出其渐近的精确表示．     

弱Hardy空间上的参数型Marcinkiewicz积分

证明了参数型Marcinkiewicz积分μΩ^p是（H^p,∞ , L^p,∞）（0〈p≤1）型的算子，这里Ω是满足Lipα条件的R^＊上的零次齐次函数．对于p=1，减弱了Ω的条件μΩ^p得到μΩ^p是（H^1,∞ , L^1,∞）型的．作为上述结果的推论，得到了μΩ^p是弱（1，1）型的算子．     

参数展开摄动法

本文提出一个参数展开摄动法,作为一个应用,讨论了非线性项上带有的参数不是很小时的一般Duffing方程的解。求得了解的渐近展开式。 本文还讨论了广义Duffing方程λ~2x+ex~3=O,这个方程不宜用寻常的摄动法求其渐近解,但用参数展开摄动法可以求其渐近解,文中构造了解的渐近形式,提出了二次近似与一次近似渐近解的稳定判据。     

关于多项式和的Waring问题（Ⅰ）

设ｆｋ（ｘ）为ｋ次整系数多项式，最高次项系数为正且ｆｋ（ｘ）－ｆｋ（０）没有固定因子．Ｒｋ（ｎ）记整数ｎ表为这样的一个二次、五个三次及一个ｋ次多项式和的表法数，ｕｋ（ｎ）记ｎ表为两个二次、三个三次及一个ｋ次多项式和的表法数．本文得到了当ｋ＝３、４、５时，Ｒｋ（ｎ）的渐近公式及当ｋ≥２时ｕｋ（ｎ）的渐近公式．     

ADIF迭代法及其有关问题

§1.引言 本文将考虑二维自共轭二阶椭圆型方程边值问题:其中Ω为有界开域;在闭域Ω上系数P,Q和f Lipschitz连续并有P,Q>0,(x,y)∈Ω。用有限差分法或有限元方法求其数值解,通常导致如下稀疏正定矩阵的线性代数方程组的求解问题:     

二阶非齐次线性微分方程的常数变易法

在数学后继课程的学习中,常遇到如下的定解问题：书中告诉我们可用参数（常数）变易法来解,但到底如何求得其解呢？好多同学都感到束手无策．翻阅同济大学犒等数学》教材,只有一阶非齐次线性微分方程的常数变易法,现来介绍二阶以上非齐次线性微分方程．设讨论的n阶非齐次线性微分方程为：其中及都是区间a＜x＜b上的连续函数．（1）对应的齐次线性方程为：我们知道：n阶齐次线性方程（2）一定存在n个线性无关的解．并且（2）的通解可表示为：其中Q,Q,…,C为任意常数,儿（X）,儿（X）,…,人（x）为（2）的一组线性无关解．方程（…     

含有广义p-Laplacian算子的非线性椭圆边值问题和m增生映射的值域北大核心CSCD

证明了m增生映射的一个值域扰动结论并用于讨论一类含有广义p-Laplacian算子的非线性椭圆边值问题在L^2（Ω）中解的存在性．探究了非线性椭圆边值问题的解与m增生映射零点的关系．构造了迭代序列用以弱收敛或强收敛到非线性椭圆边值问题的解．本文采用了构造新算子和拆分方程的技巧,推广和补充了以往的相关研究成果．     

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.     

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.