The quasi-reversibility method to solve the Cauchy problems for parabolic equations

In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain of QT with strong restrictions to the measured boundary data. On the other hand, weakening the conditions on the measured data, then combining the duality method in optimization with the quasi-reversibility method, we solve the Cauchy problems for parabolic equations in the presence of noisy data. Using this method, we can get the proper regularization parameter ε that we need in the quasi-reversibility method and obtain the convergence rate of approximate solutions as the noise of amplitude δ tends to zero.     

鞍点问题迭代解法收敛因子估计

分析Ｂａｎｋ（１９９０年）的论文中的求解鞍点问题的迭代解法,得到一个改进的收敛因子估计。     

STABILITY OF DISPLACEMENT TO THE SECOND FUNDAMENTAL PROBLEM IN PLANE ELASTICITY

In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density happen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain （unit disk） and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained.     

三阶柯西差分方程在几类群上的解

在几类群上讨论了三阶柯西差分方程解的存在性问题,将二阶柯西差分方程的已有结论进一步推广到三阶的情况,并给出在不同群上的一般解.     

Existence of periodic solutions

An apparatus for proving existence theorems for periodic solutions of equations with discontinuous right-hand side and differential inclusions is developed. Translated fromMatematischeskie Zametki, Vol. 61, No. 5, pp. 769–784, May, 1997. Translated by V. N. Dubrovsky     

The Capacitated Team Orienteering Problem: A Bi-level Filter-and-Fan method

This paper focuses on vehicle routing problems with profits and addresses the so-called Capacitated Team Orienteering Problem. Given a set of customers with a priori known profits and demands, the objective is to find the subset of customers, for which the collected profit is maximized, and to determine the visiting sequence and assignment to vehicle routes assuming capacity and route duration restrictions. The proposed method adopts a hierarchical bi-level search framework that takes advantage of different search landscapes. At the upper level, the solution space is explored on the basis of the collected profit, using a Filter-and-Fan method and a combination of profit oriented neighborhoods, while at the lower level the routing of customers is optimized in terms of traveling distance via a Variable Neighborhood Descent method. Computational experiments on benchmark data sets illustrate the efficiency and effectiveness of the proposed approach. Compared to existing results, new upper bounds are produced with competitive computational times.     

扰动压缩条件的点列收敛性问题

研究完备度量空间X中满足ρ(xn,xn+1)≤Lρ(xn-1,xn)+εn的点列{xn}收敛性问题,其中L∈(0,1)为常数,εn非负是无穷小量称为扰动.文中的主要结论是:点列{xn}的收敛性由扰动εn决定,即当幂级数sum from n=1 to ∞εnxn的收敛半径R>1/L时,点列{xn}收敛.特别地,当R>1时,点列收敛;而R=1时,{xn}敛散性不能确定.     

Uniform approximations to Cauchy principal value integrals of oscillatory functions

This paper presents an interpolatory type integration rule for the numerical evaluation of Cauchy principal value integrals of oscillatory integrands , where -1<τ<1, for a given smooth function f(x). The proposed method is constructed by interpolating f(x) at practical Chebyshev points and subtracting out the singularity. A numerically stable procedure is obtained and the corresponding algorithm can be implemented by fast Fourier transform. The validity of the method has been demonstrated by several numerical experiments.