Max—min神经网络的一种有效学习算法

本文在Ａ．Ｂｌａｎｃｏ等人的算法的基础上，提出了ｍａｘ－ｍｉｎ神经网络的一种改进了的反馈学习算法，严格证明了该算法的迭代收敛性，理论分析及实例计算结果均表明，本文算法具有算法简单，收敛速度快，输出误差小等显著特点。     

Periodic solutions for p-Laplacian neutral functional differential equation with multiple deviating arguments

By using the theory of coincidence degree, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with multiple deviating arguments, a new result on the existence of periodic solutions is obtained.     

Rational choice based on vague preferences

This paper studies vague preferences. In contrast to the concept of fuzzy preferences, the more general notion of vague preferences does not entail the assumption that the different degrees of preference are completely ordered. It is shown that the more general concept of a vague preference order arises very naturally in the context of aggregating a set of (exact) weak orders. Furthermore, necessary and sufficient conditions for the rationalizability of an exact choice function by means of a vague preference order are given. It turns out that in the general case these conditions are weaker than in the case where the degrees of preference are completely ordered. Consequently, there exist choice functions which are rationalizable by a general vague preference order but which are not rationalizable by a fuzzy preference order, or more generally by any vague preference order which induces a complete ranking of the degrees of preference. Examples of such choice functions are provided.This is a revised version of a discussion paper which was written at the University of Karlsruhe. I am grateful to Georg Bol and an anonymous referee for valuable comments. The research has been made possible by a fellowship of the DFG (Deutsche Forschungsgemeinschaft) which is also gratefully acknowledged.     

Ground state solution for differential equations with left and right fractional derivatives

In this work, we study the existence of positive solutions for a class of fractional differential equation given by (1) where . Using the mountain pass theorem and comparison argument, we prove that (1) at least has one nontrivial solution. Copyright © 2015 John Wiley & Sons, Ltd.     

Sobolev-Lorentz范数约束下的次临界型Adams不等式

本文在Sobolev-Lorentz空间W2L2,q(R4)的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp Moser-Trudinger and Adams ...     

一类连续变量脉冲中立型差分方程

研究具连续变量脉冲中立型时滞差分方程△[y(t)-p(t)y(t-τ)]+q(t)y(t-σ)=0,t≠tky(tk+)-y(tk)=bky(tk),k=1,2,…利用辅助方程,建立等价定理,得到了方程解振动的显式充分性条件.     

具有偏差变元的双曲型微分方程组解的振动性

本文获得了双曲型方程组在齐次Neumann,Dirichlet和Robin边值条件下,所有解振动的充分条件.     

具有时滞的非线性强迫微分方程振动的充分必要条件

对于一类特殊的具有时滞的二阶次线性强迫微分方程x"(t) +a (t)|x(τ(t))|γsgnx(τ(t)) =g(t)(0＜τ＜1),给出了它的所有解振动的一个充要条件.     

HOMOCLINIC ORBITS FOR LAGRANGIAN SYSTEMS

The existence of at least two homoclinic orbits for Lagrangian system (LS) is proved, wherethe Lagrangian L(t,x,y) =1/2∑aij(x)yiyj-V(t, x), in which the potential V(t,x) is globallysurperquadratic in x and T-periodic in t. The Concentration-Compactness Lemma and Mini-max argument are used to prove the existences.     

Triangular lattice Potts models

In this paper we study the 3-state Potts model on the triangular lattice which has two- and three-site interactions. Using a Peierls argument we obtain a rigorous bound on the transition temperature, thereby disproving a conjecture on the location of its critical point. Low-temperature series are generated and analyzed for three particular choices of the coupling constants; a phase diagram is then drawn on the basis of these considerations. Our analysis indicates that the antiferromagnetic transition and the transition along the coexistence line are of first order, implying the existence of a multicritical point in the ferromagnetic region. Relation of the triangularq-state Potts model with other lattice-statistical problems is also discussed. In particular, an Ashkin-Teller model and the hard-hexagon lattice gas solved by Baxter emerge as special cases in appropriate limits.Supported in part by NSF grant No. DMR 78-18808.