非完整约束奇异广义力学系统的Poincaré-Cartan积分

对受高阶微商非完整约束并用奇异Lagrange量描述的广义力学系 统，基于广义Apell-Четаев约束条件，并考虑到系统的内在约束，导出了该非完整 约 束奇异广义力学系统的广义Poincaré-Cartan积分不变量. 并证明了该不变量与非完整约束 奇异广义力学系统的广义正则方程等价.     

A transform method for linear evolution PDEs on a finite interval

We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series.     

线性均衡约束最优化的一个广义投影强次可行方向法

本文讨论带线性均衡约束最优化问题,首先利用摄动技术和一个互补函数将问题等价转化为一般约束最优化问题,然后结合广义投影技术和强次可行方向法思想,建立了问题的一个新算法.算法在迭代过程中保证搜索方向不为零,从而使得每次迭代只需计算一次广义投影.在适当的条件下,证明了算法的全局收敛性,并对算法进行了初步的数值试验.     

关于Banach空间中凸泛函的广义次梯度不等式

本文在前人^[1,2]的基础之上，以凸泛函的次梯度不等式为工具，将Jensen不等式推广到Banach空间中的凸泛函，导出了Banach空间中的Bochner积分型的广义Jensen不等式，给出其在Banach空间概率论中某些应用，从而推广了文献[3—6]的工作．     

On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.     

Harnack inequality for some classes of Markov processes

In this paper we establish a Harnack inequality for nonnegative harmonic functions of some classes of Markov processes with jumps. Mathematics Subject Classification (2000): Primary 60J45, 60J75, Secondary 60J25.This work was completed while the authors were in the Research in Pairs program at the Mathematisches Forschungsinstitut Oberwolfach. We thank the Institute for the hospitality.The research of this author is supported in part by NSF Grant DMS-9803240.The research of this author is supported in part by MZT grant 0037107 of the Republic of Croatia.     

Fractions continues de matrices,convergence et applications

The aim of this article is to give some property of continued fraction with matrices arguments, about their convergence and others applications. At the end of this work, we present a resolution of the Algebraic Riccati Equation by giving an explicit continued fraction development of its solution. This revised version was published online in August 2006 with corrections to the Cover Date.     

Delta and singular delta locus for one‐dimensional systems of conservation laws

This work gives a condition for existence of singular and delta shock wave solutions to Riemann problem for 2×2 systems of conservation laws. For a fixed left‐hand side value of Riemann data, the condition obtained in the paper describes a set of possible right‐hand side values. The procedure is similar to the standard one of finding the Hugoniot locus. Fluxes of the considered systems are globally Lipschitz with respect to one of the dependent variables. The association in a Colombeau‐type algebra is used as a solution concept. Copyright © 2004 John Wiley &Sons, Ltd.     

非饱和土本构关系的混合物理论(Ⅱ)--线性本构方程和场方程

通过对非饱和土非线性本构方程和场方程的线性化，推导出了非饱和土的线性本构方程和场方程，把线性方程表示为与Biot饱和多孔介质方程相似的形式；证明了Darcy定律对非饱和土的适用性；说明了Biot饱和多孔介质方程是这些线性方程的特征。所有这些都表明用混合理论处理非饱和土本构问题的正确性。     

Mean value in invexity analysis

In this paper, a generalization of the mean value theorem is considered in the case of functions defined on an invex set with respect to η (which is not necessarily connected).