Attractors of Weakly Asymptotically Compact Set-Valued Dynamical Systems

The existence of weak attractors is established for set-valued dynamical systems which are weakly asymptotically compact and weakly dissipative. Here weak properties mean with respect to at least one trajectory for each initial value. A condition ensuring the uniqueness of such weak attractors is given. The results are illustrated with an application involving a partial differential inclusion in bounded and unbounded domains. Mathematics Subject Classifications (2000) 34D45, 37B25, 37B75, 58C06.     

A Modified Relaxation Scheme for Mathematical Programs with Complementarity Constraints

In this paper, we consider a mathematical program with complementarity constraints. We present a modified relaxed program for this problem, which involves less constraints than the relaxation scheme studied by Scholtes (2000). We show that the linear independence constraint qualification holds for the new relaxed problem under some mild conditions. We also consider a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is C-stationary to the original problem under the MPEC linear independence constraint qualification and, if the Hessian matrices of the Lagrangian functions of the relaxed problems are uniformly bounded below on the corresponding tangent space, it is M-stationary. We also obtain some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices mentioned above are new and can be verified easily. This work was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports, and Culture of Japan. The authors are grateful to an anonymous referee for critical comments.     

Electron spin relaxation of radicals in weak magnetic fields

The review summarizes the results of studies on specific features of spin relaxation of radicals in liquids in weak magnetic fields. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1642–1654, October, 2006.     

BMO与弱核条件下的Calderón-Zygmund算子交换子的有界性

本文证明了BMO与弱核条件下Calderón-Zygmund奇异积分算子的交换子 [B,T]f=BTf-T(Bf)的L2有界性,这里B ∈BMO,T对增生的b1,b2,满足 T(b1)∈BMO,T*(b2)∈BMO,b2Tb1∈WBP．     

On n ‐contractive fuzzy logics

It is well known that MTL satisfies the finite embeddability property. Thus MTL is complete w. r. t. the class of all finite MTL‐chains. In order to reach a deeper understanding of the structure of this class, we consider the extensions of MTL by adding the generalized contraction since each finite MTL‐chain satisfies a form of this generalized contraction. Simultaneously, we also consider extensions of MTL by the generalized excluded middle laws introduced in [9] and the axiom of weak cancellation defined in [31]. The algebraic counterpart of these logics is studied characterizing the subdirectly irreducible, the semisimple, and the simple algebras. Finally, some important algebraic and logical properties of the considered logics are discussed: local finiteness, finite embeddability property, finite model property, decidability, and standard completeness. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Duality in nonlinear multiobjective programming using augmented Lagrangian functions

A vector-valued generalized Lagrangian is constructed for a nonlinear multiobjective programming problem. Using the Lagrangian, a multiobjective dual is considered. Without assuming differentiability, weak and strong duality theorems are established using Pareto efficiency.The research of the second author was partially supported a GTE/SLU grant while visiting St. Lawrence University in the summer of 1991.     

From two mesons and (V-A) weak currents to the standard model of quark and lepton interactions

This retrospective paper traces the conceptual evolution of two theories in which the author was involved—the two-meson theory (with H A Bethe) in 1947 and the universal (V-A) theory of weak interactions (with E C G Sudarshan) in 1957—into the present-day standard model of particle interactions. Part 1 is entitled ‘From the pion to QCD and pseudo-Goldstone bosons” and Part 2 “From the muon and neutrino to QFD and chiral anomalies’. Adapted from two lectures delivered at the University of Rochester in October, 1987.     

论平面上的可求长曲线

本文利用Hausdorff分数型导数与积分理论给出平面上可求长曲线的积分表 达式.     

C*-Algebras and Controlled Topology

We describe some aspects of the relationship between the controlled topology and C*-algebra approaches to the Novikov conjecture.     

不可分素C^k—代数与本原C^＊—代数的讨论

本文证明：若Ａ是不可分的素Ｃ＾＊－代数，且包含非０的Ｌｉｍｉｎａｌ遗传Ｃ＾＊－子代数，则Ａ是本原Ｃ＾＊－代数，本文还给出了Ｉ型Ｃ＾＊－代数为本原Ｃ＾＊－代数的充要条件。