一般耦合Maxwell－SchrOdinger方程的Cauchy问题（1）

本文研究了一般耦合Ｍａｘｗｅｌｌ－Ｓｃｈｒｏｄｉｎｇｅｒ方程的Ｃａｕｃｈｙ问题，采用正则化方法，借助于推广的Ｈ．Ｐｅｃｈｅｒ引理及其它分析工具，在光滑解的框架下，建立了任意维空间中一般耦合Ｍａｘｗｅｌｌ－Ｓｃｈｒｏｄｉｎｇｅｒ方程的Ｃａｕｃｈｙ问题的局部适定性．     

具有Lipschitz连续系数的Kirchhoff方程

作者考虑了一个非局部项仅为Ｌｉｐｓｃｈｉｔｚ连续函数的非齐次Ｋｉｒｃｈｈｏｆ方程的Ｃａｕｃｈｙ问题．在初值和右端项“小”的条件下，我们获得了此问题整体解的存在唯一性．     

Banach空间中Cauchy问题解存在定理的注记

本文讨论Ｂａｎａｃｈ空间中的Ｃａｕｃｈｙ问题解的存在性定理。证明了Ｃａｕｃｈｙ方程右端函数ｆ（·）为ｋ－集压缩映象时，Ｃａｕｃｈｙ问题的解必存在，从而，将通常要求ｆ（·）满足Ｌｉｐ条件或绝对连续这两种条件统一起来，并加以推广。     

非局部非线性发展方程解的存在性与唯一性

本文利用Ｂａｎａｃｈ不动点定理证明一类非线性发展方程的非局部Ｃａｕｃｈｙ问题解的存在性与唯一性，及其对非局部拟线性抛物方程的应用。     

KdV—KSV方程的初值问题

本文证明了ＫｄＶ－ＫＳＶ方程的周期边值问题和Ｃａｕｃｈｙ问题广义解和古典解的整体存在性，正则性及唯一性。     

高阶KdV方程（组）Cauchy问题解的唯一性

本文在内，应用能量不等式方法，证明了一类更加广泛的高阶ＫｄＶ方程　及方程组　，Ｃａｕｃｈｙ问题解的唯一性和解对初值连续依赖性．     

一般非线性发展方程解的长时间行为

本文研究了一般形式的非线性发展方程Ｃａｕｃｈｙ问题的解关于时间的渐近性质．其结果覆盖并部分推广了导数非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程，Ｋｏｒｔｅｗｅｇ－ｄｅＶｒｉｅｓ方程和Ｂｅｎｊａｍｉｎ－Ｏｎｏ等方程的有关结果．     

四元数分析中的T算子与两类边值问题

本文研究四元数分析中的非齐次 Ｄｉｒａｃ方程．引入了这类方程的分布解即 Ｔ算子,证明了Ｔ算子的一些性质并考察了非齐次Ｄｉｒａｃ方程的Ｄｉｒｉｃｈｌｅｔ边值问题,并将结果推广到高阶非齐次Ｄｉｒａｃ方程及这种方程的一类边值问题的情况．     

一类波动方程组的初边值问题

本文主要讨论Ｒ＾ｎ中区域Ω上的广义ＢＢＭ方程组的初边值问题，通过引入强解的概念和应用不动点原理，得到了该问题强解之存在与唯一性。文中亦讨论了解的正则性。     

二阶偏微分方程的广义Cauchy问题

本文应用Ｇｒｅｅｎ公式求解偏微分方程的广义Ｃａｕｃｈｙ问题，得到了解的积分表达式。并将一般Ｃａｕｃｈｙ问题归结为广义Ｃａｕｃｈｙ问题的特例，从而用本方法统一处理了各类Ｃａｕｃｈｙ问题。     

On the Multiplicity Problem and the Isomorphism Problem for the Four Subspace Algebra

Let Λ be the four subspace algebra. We show that for any Λ-module M there exists an algorithm (up to the problem of finding roots of the so-called characteristic polynomial of M) with relatively low polynomial complexity of determining multiplicities of all direct summands of M. Moreover, we give a fully algorithmic criterion for deciding if two Λ-modules M and N are isomorphic.     

确定Sturm-Liouville问题中系数的反问题

讨论确定Sturm－Liouville问题中算子的系数α（x）或者q（x）的问题．在一定条件下,系数α（x）或者q（x）可由数据或者数据唯一确定,这里的u_j（x）满足而构成L²（0,1）的一个基,α和β为给定的实数.     

Modified Moment Problem in Complex Domains

We study the moment problem in a complex domain. The results obtained generalize and sharpen the well-known Kaz'min result. We also consider applications of these results to the Abel--Goncharov problem (the uniqueness and construction problem) and to the completeness problem for systems of analytic functions.     

Capacitated transportation problem with bounds on RIM conditions

Motivated by dead-mileage problem assessed in terms of running empty buses from various depots to starting points, we consider a class of the capacitated transportation problems with bounds on total availabilities at sources and total destination requirements. It is often difficult to solve such problems and the present paper establishes their equivalence with a balanced capacitated transportation problem which can be easily solved by existing methods. Sometimes, total flow in transportation problem is also specified by some external decision maker because of budget/political consideration and optimal solution of such problem is of practical interest to the decision maker and has motivated us to discuss such problem. Various situations arising in unbalanced capacitated transportation problems have been discussed in the present paper as a particular case of original problem. In addition, we have discussed paradoxical situation in a balanced capacitated transportation problem and have obtained the paradoxical solution by solving one of the unbalanced problems. Numerical illustrations are included in support of theory.     

The weighted Fermat-Torricelli problem on a surface and an “inverse” problem

We study the weighted Fermat-Torricelli (w.F-T) problem for geodesic triangles on a C² complete surface and on an Aleksandrov space of curvature bounded above by a real number K and solve an “inverse” problem on a C² complete surface. The solution of the w.F-T problem and the inverse w.F-T problem on a C² complete surface is based on the differentiation of the length of geodesics with respect to the arc length.     

Minimum power multicasting problem in wireless networks

In this paper we deal with the minimum power multicasting (MPM) problem in wireless ad-hoc networks. By using an appropriate choice of the decision variables and by exploiting the topological properties of the problem, we are able to define an original formulation based on a Set Covering model. Moreover, we propose for its solution two exact procedures that include a preprocessing technique that reduces the huge number of the model’s constraints. We also report some experimental results carried out on a set of randomly generated test problems.     

Interface Problems for Elliptic Systems

Interface problems for elliptic systems of second order partial differential equations are studied. The main result is that the solution in the neighborhood of the singular point can be divided into two parts one of which is a solution to the homogeneous system with constant coefficients, and the other one possesses higher regularity.     

下料问题的优化模型及其快速算法

结合生产实际中具体的下料问题,本文建立了该类问题的优化模型,并提出下料方式的遴选三准则,即高利用率优先准则,长度优先准则和时间优先准则.运用本文的算法对一维下料的利用率高达99.6%,机器时间4秒.对二维的利用率为98.9%,机器时间约7秒.