Second order mixed type duality in multiobjective programming problems

Second order mixed type dual is introduced for multiobjective programming problems. Results about weak duality, strong duality, and strict converse duality are established under generalized second order (F,ρ)-convexity assumptions. These results generalize the duality results recently given by Aghezzaf and Hachimi involving generalized first order (F,ρ)-convexity conditions.     

Almost automorphic solutions for abstract functional differential equations

For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations.     

A monotone iterative scheme for a nonlinear second order equation based on a generalized anti–maximum principle

In this paper, a generalized anti–maximum principle for the second order differential operator with potentials is proved. As an application, we will give a monotone iterative scheme for periodic solutions of nonlinear second order equations. Such a scheme involves the L^p norms of the growth, 1 ≤ p ≤ ∞, while the usual one is just the case p = ∞.     

On nash equilibrium solutions in nonzero-sum stochastic games with complete information

Two-person nonzero-sum stochastic games with complete information are considered. It is shown that it is sufficient to search the equilibrium solutions in a class of deterministic strategy pairs — the so-calledintimidation strategy pairs. Furthermore, properties of the set of all equilibrium losses of such strategy pairs are proved.     

一类泛函微分方程周期解的存在性与应用

本文给出了一类滞后型泛函微分方程有一个周期解的四个充分性定理，其结果明显地优于著名的Ｙｏｓｈｉｚａｗａ周期解定理，最后给出了应用实例。     

Asynchronous and corrected-asynchronous finite difference solutions of PDEs on MIMD multiprocessors

A major problem in achieving significant speed-up on parallel machines is the overhead involved with synchronizing the concurrent processes. Removing the synchronization constraint has the potential of speeding up the computation, while maintaining greater computation flexibility (e.g. differences in processors speed; differences in the data input to processors). We construct asynchronous (AS) finite difference schemes for the solution of PDEs by removing the synchronization constraint. We analyze the numerical properties of these schemes. Based on the analysis, we develop corrected-asynchronous (CA) finite difference schemes which are specifically constructed for an asynchronous processing. We present asynchronous (AS) and corrected-asynchronous (CA) finite difference schemes for the multi-dimensional heat equation. Although our discussion concentrates on the Euler scheme it should serve only as a sample, as it can be extended to other schemes and other PDEs.These schemes are implemented on the shared-memory multi-userSequent Balance machine. Numerical results for one and two dimensional problems are presented. It is shown experimentally that synchronization penalty can be about 50% of run time: in most cases, the asynchronous scheme runs twice as fast as the parallel synchronous scheme. In general, the efficiency of the parallel schemes increases with processor load, with the time-level, and with the problem dimension. The efficiency of the AS may reach 90% and over, but it provides accurate results only for steady-state values. The CA, on the other hand, is less efficient but provides more accurate results for intermediate (non steady-state) values. The results show the potential of developing asynchronous finite deference schemes for steady-state as well as non steadystate problems.This research was partially supported by a grant from The Basic Research Foundation administrated by The Israel Academy of Sciences and Humanities.A reduced version of the paper was presented at the 4th SIAM Conference on Parallel Processing for Scientific Computing, Dec. 11–13, 1989, Chicago, USA.The work by this author was supported by research grant 337 of the Israeli National Council for Research and Development in the years 1990–1991.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NASI-18107 while the author was in residence at the Institute for Computer Applications in Sciences and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665, USA.     

HOMOCLINIC SOLUTIONS FOR AUTONOMOUS DIFFERENTIAL EQUATIONS

ＨＯＭＯＣＬＩＮＩＣ　ＳＯＬＵＴＩＯＮＳ　ＦＯＲ　ＡＵＴＯＮＯＭＯＵＳ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳ￥ＺｅｎｇＷｅｉｙａｏ（曾唯尧）（ＨｕｎａｎＬｉｇｈｔＩｎｄｕｓｔｒｉａｌＣｏｌｌｅｇｅ）＆ＷａｎｇＸｕｅｘｉｎ（王学鑫）（Ｚｈｅｊｉ...     

变分方法与反向上下解

本文在非线性方程的下解不小于上解这一条件（即反向上下解条件）下研究了其解的存在性．我们证明了，如果非线性算子方程有变分结构，有一对反向上下解，对应的算子映某个锥入锥并且满足一定的辅助条件，那么这一方程在锥中至少有两个解．另外，本文还研究了反向上下解条件下非线性椭圆边值问题正解的存在性．     

一个反应扩散方程的门槛结果

本文讨论反应扩散方程Ｃａｕｃｈｙ问题解的整体存在性，渐近性质和Ｂｌｏｗｕｐ问题．其中或者１＜ｑ＜ｐ＜＋∞，ｎ＝２．得到门槛结果．     

指数型二分性与拟自治奇异摄动系统

通过对Ｋ．Ｊ．Ｐａｌｍｅｒ￣［４］中方法的改进，本文讨论了摄动系统有界解的存在性，得到了不同于［４］中的结果，并把改进了的方法运用到拟自治奇异摄动系统，得到了拟自治奇异摄动系统存在有界解的一个简洁的充分条件。本文的方法还提供了一个处理摄动项含小参数的方法。