Generalized nonlinear Schrödinger equation with time-dependent dissipation

The generalized nonlinear Schrödinger equation with time-dependent dissipation [1] is considered using decomposition [2].     

Variational inequalities for monotone operators in nonreflexive Banach spaces

The purpose of this paper is to study the existence problem of solutions and perturbation problem for some kind of variational inequalities with monotone operators in nonreflexive Banach spaces, and to obtain some results.     

Partial Orderings in the Category of Matrices over the Quaternion Field

ＰａｒｔｉａｌＯｒｄｅｒｉｎｇｓｉｎｔｈｅＣａｔｅｇｏｒｙｏｆＭａｔｒｉｃｅｓｏｖｅｒｔｈｅＱｕａｔｅｒｎｉｏｎＦｉｅｌｄＺｈｕａｎｇＷａｊｉｎ（庄瓦金）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈａｎｇＮｏｒｍａｌＣｏｌｌｅｇｅ，Ｆｕｊｉ...     

关于二次规划问题分段线性同伦算法的改进

本文利用Ｃｈｏｌｅｓｋｙ分解，Ｇａｕｓｓ消去等技术和定义适当的同伦映射，将关于二次规划问题的分段线性同伦算法加以改进，改进后的算法，对于严格凸二次规划来说，计算效率与Ｇｏｌｄｆａｒｂ－Ｉｄｎａｎｉ的对偶法相当。     

A variational approach to a micro-structured theory of solid-fluid mixtures

Summary In this paper, we present a micro-structured model for describing global deformations of heterogeneous mixtures. In particular, for a saturated solid-fluid mixture, we regard the solid volume fraction as a microstructural parameter so as to enlarge the space of admissible deformations with respect to the classical theory of mixtures. According to the variational approach, the governing equations are obtained as the stationarity of a suitable action functional. The micro-structured model is then forced to establish a second-gradient mixture theory, by introducing among the considered state parameters a suitable internal constraint. Finally, we determine under which (integrability) conditions the additional balance laws, typically employed to close the theory of porous media endowed with the volume fraction, can fit the variational framework. The authors wish to thank Prof. Francesco dell'Isola from University of Rome La Sapienza for his constructive criticism about the variational approach to continuum mechanics and the interpretation of the volume-fraction balance law.     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

Porosity of ill-posed problems

We prove that in several classes of optimization problems, including the setting of smooth variational principles, the complement of the set of well-posed problems is -porous.

     

跳过程的主特征值

本文给出了一般跳过程主特征值下界的一个变分公式．对于马氏链,所设条件常满足;所得估计在轻微条件下可达到精确．从这个意义上讲,所得到的公式是彻底的．     

Decomposition of search for -structures in DAGs

We show that the problem of searching for v-structures in a directed acyclic graph can be decomposed into searches in its decomposed subgraphs. This result simplifies the search for v-structures and the recovery of local causal relationships.     

On a Sobolev-type inequality related to the weighted p-Laplace operator

In this paper we deal with some Sobolev-type inequalities with weights that were proved by Maz'ya in [V.G. Maz'ja, Sobolev Spaces, Springer-Verlag, Berlin, 1980] and by Caffarelli, Kohn and Nirenberg in [L. Caffarelli, R. Kohn, L. Nirenberg, First order interpolation inequalities with weight, Compos. Math. 53 (1984) 259-275]. For integers 1?k?N denote points ξ∈RN=Rk×RN−k as pairs (x,y). Let p∈(1,N), q∈(p,p^∗] and assume . Then there exists c>0 such that