Generalization of Ulam stability problem for Euler-Lagrange quadratic mappings

In 1968 S.M. Ulam proposed the problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?” In 1978 P.M. Gruber proposed the Ulam type problem: “Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this object by objects, satisfying the property exactly?” In this paper we solve the generalized Ulam stability problem for non-linear Euler-Lagrange quadratic mappings satisfying approximately a mean equation and an Euler-Lagrange type functional equations in quasi-Banach spaces and p-Banach spaces.     

The generalized Hyers-Ulam-Rassias stability of a cubic functional equation

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability for a cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x).     

再论一类二次系统的无界双中心周期环域的POincare分支

本文再一次讨论了具有双曲线与赤道弧为边界的双中心周期环域的二次系统的Poincare分支，并构造出了此系统出现极限环的(0，3)分布或出现一个三重极限环的具体例子．     

Some Global Optimization Problems on Stiefel Manifolds

Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers, and some global optimization methods were considered and tested on Stiefel manifolds. In the paper, test functions are given with known global optimum points and their optimal function values. A restriction, which leads to a discretization of the problem is suggested, which results in a problem equivalent to the well-known assignment problem.     

A Rigorous Lower Bound for the Optimal Value of Convex Optimization Problems

In this paper, we consider the computation of a rigorous lower error bound for the optimal value of convex optimization problems. A discussion of large-scale problems, degenerate problems, and quadratic programming problems is included. It is allowed that parameters, whichdefine the convex constraints and the convex objective functions, may be uncertain and may vary between given lower and upper bounds. The error bound is verified for the family of convex optimization problems which correspond to these uncertainties. It can be used to perform a rigorous sensitivity analysis in convex programming, provided the width of the uncertainties is not too large. Branch and bound algorithms can be made reliable by using such rigorous lower bounds.     

Characteristic Elements of Unimodular -lattices

Characteristic elements have been useful in the classification of unimodular lattices over the integers. This article gives an explicit formula for characteristic elements of a lattice in terms of a basis for the lattice and the dual of that basis.     

Approximation of the Quadratic Set Covering problem

We study in this article the polynomial approximation properties of the Quadratic Set Covering problem. This problem, which arises in many applications, is a natural generalization of the usual Set Covering problem. We show that this problem is very hard to approximate in the general case, and even in classical subcases (when the size of each set or when the frequency of each element is bounded by a constant). Then we focus on the convex case and give both positive and negative approximation results. Finally, we tackle the unweighted version of this problem.     

进化规划动态寻优机理分析

为了从整体上揭示进化规划 ( EP)算法的内在运行机制 ,探寻算法的动态寻优机理 ,本文从种群角度出发 ,建立了一种种群动态寻优微分方程模型 ,并对该模型进行了理论分析 .数值模拟结果说明了所建模型的正确性 ,并得出了一些有意义的结论     

A new approach for data editing and imputation

The editing-and-imputation problem concerns the question of finding errors in a record which does not satisfy a set of consistency rules. Once some potential errors have been localizated, it is also necessary to impute new values to the associated fields. The output dataset should consist of valid records and preserve similar statistical properties as the input dataset. Most of this work is usually done manually by statistical agencies, thus consuming a great deal of human resources. This paper presents a mathematical programming model to optimally solve the problem on surveys with categorical values and particular edits. We also describe a heuristic approach to deal with the more complex surveys. The heuristic procedure follows a combination of the widely-accepted hot-deck donor scheme and the multivariate regression analysis. It has been implemented in a graphical user interface running on standard personal computers, and has been tested on real-world surveys. This paper demonstrates the satisfactory performance of our automatic procedure.