Large deviation principles for the Hopfield model and the Kac-Hopfield model

Summary We study the Kac version of the Hopfield model and prove a Lebowitz-Penrose theorem for the distribution of the overlap parameters. At the same time, we prove a large deviation principle for the standard Hopfield model with infinitely many patterns.Work partially supported by the Commission of the European Communities under contract No. SC1-CT91-0695     

Initial value problem for mixed-type differential equations

The initial value problem is discussed for a class of linear functional differential equations of mixed type and various criteria on existence and uniqueness are obtained.     

一种全场三维共焦检测的新方法

提出了一种利用微光学阵更合成器件实现全场三维面形并行检测、记录的共焦方法。此方法的关键是，在共焦系统中引入一一微光学耻列合成器件来产生一点光源阵列，实现了对同一一剖面同时并行检测，并首次采用了ＣＣＤ面阵像元取代上孔光阑直接截取三维信息光强。本文讨论了该方法的三信息检测原理，响应关系，给出了初步的实验结果和三维重构图。     

H.26L性能分析与算法优化

在相同的码率控制策略的最优参数配置下，对H．26L，MPGE－4 ASP校验模型系统进行计算机仿真，实验表明，对于CIF和QCIF格式的图像，在压缩效率上H．26L要高于MPGE－4 ASP。相同峰值信噪比条件下，H．26L目标码率约为MPEG－4 ASP的1／3－1／5，然而H．26L的运算复杂也远高于MPEG－4 ASP。本文采用整像素和亚像素运动估值的快速算法，使运算复杂度的约降低到原来的1／3。     

Exponential sums and singular hypersurfaces

We give upper bounds for the absolute value of exponential sums in several variables attached to certain polynomials with coefficients in a finite field. This bounds are given in terms of invariants of the singularities of the projective hypersurface defined by its highest degree form. For exponential sums attached to the reduction modulo a power of a large prime of a polynomial f with integer coefficients and veryfying a certain condition on the singularities of its highest degree form, we give a bound in terms of the dimension of the Jacobian quotient . Received: 3 November 1997     

Thirteen ways to estimate global error

Summary Various techniques that have been proposed for estimating the accumulated discretization error in the numerical solution of differential equations, particularly ordinary differential equations, are classified, described, and compared. For most of the schemes either an outline of an error analysis is given which explains why the scheme works or a weakness of the scheme is illustrated.This research is partially supported by NSF Grant No. MCS-8107046     

An algorithm for a class of nonlinear fractional problems using ranking of the vertices

In this note we consider an algorithm for quasiconcave nonlinear fractional programming problems, based on ranking the vertices of a linear fractional programming problem and techniques from global optimization.