Cn中多圆柱体的Riemann-Hilbert边值问题

本文研究了利用Poission核求解C^N（1≤n≤2）中单位多圆柱体上Riemann-Hilbert边值问题．同时，给出了其解的表达式和可解条件，并将原来求解空间从解析函数空间推广到亚纯函数空间．     

Zeros of univariate interval polynomials

Polynomials with perturbed coefficients, which can be regarded as interval polynomials, are very common in the area of scientific computing due to floating point operations in a computer environment. In this paper, the zeros of interval polynomials are investigated. We show that, for a degree n interval polynomial, the number of interval zeros is at most n and the number of complex block zeros is exactly n if multiplicities are counted. The boundaries of complex block zeros on a complex plane are analyzed. Numeric algorithms to bound interval zeros and complex block zeros are presented.     

A note on optimality conditions for the Euclidean. Multifacility location problem

Thekey problem of the Euclidean multifacility location (EMFL) problem is to decide whether a givendead point is optimal. If it is not optimal, we wish to compute a descent direction. This paper extends the optimality conditions of Calamai and Conn and Overton to the case when the rows of the active constraints matrix are linearly dependent. We show that linear dependence occurs wheneverG, the graph of the coinciding facilities, has a cycle. In this case the key problem is formulated as a linear least squares problem with bounds on the Euclidean norms of certain subvectors.     

On dispersive properties of discrete 2D Schrödinger and Klein-Gordon equations

We derive the long-time asymptotics for solutions of the discrete 2D Schrödinger and Klein-Gordon equations.     

Existence Theorems of Quasivariational Inclusion Problems with Applications to Bilevel Problems and Mathematical Programs with Equilibrium Constraint

In this paper, we establish existence theorems of quasivariational inclusion problems; from them, we establish existence theorems of mathematical programs with quasivariational inclusion constraint, bilevel problems, mathematical programs with equilibrium constraint and semi-infinite problems. This research was supported by the National Science Council of the Republic of China. The authors express their gradtitude to the referees for valuable suggestions.     

Self-Affine Sets and Graph-Directed Systems

   Abstract. A self-affine set in R ⁿ is a compact set T with A(T)= ∪ _{d∈ D} (T+d) where A is an expanding n× n matrix with integer entries and D ={d ₁ , d ₂ ,···, d _N } ⊂ Z ⁿ is an N -digit set. For the case N = | det(A)| the set T has been studied in great detail in the context of self-affine tiles. Our main interest in this paper is to consider the case N > | det(A)| , but the theorems and proofs apply to all the N . The self-affine sets arise naturally in fractal geometry and, moreover, they are the support of the scaling functions in wavelet theory. The main difficulty in studying such sets is that the pieces T+d, d∈ D, overlap and it is harder to trace the iteration. For this we construct a new graph-directed system to determine whether such a set T will have a nonvoid interior, and to use the system to calculate the dimension of T or its boundary (if T ^o ≠  ). By using this setup we also show that the Lebesgue measure of such T is a rational number, in contrast to the case where, for a self-affine tile, it is an integer.     

ILL-POSEDNESS FOR THE NONLINEAR DAVEY-STEWARTSON EQUATION

The nonlinear D-S equations on R^d, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space H^s whenever the exponent s is lower than that predicted by scaling or Galilean invariance, or when the regularity is too low to support distributional solutions. Authors analyze a class of solutions for which the zero-dispersion limit provides good approximations.     

抛物方程时间周期问题的有限元多格子动力学迭代

本文我们研究线性周期抛物方程的有限元多格子动力学迭代.多格子动力学迭代又称多重网格波形松弛,它是在函数空间中的一种迭代过程.对于由加速技术得到的多格子动力学迭代算子,我们通过计算周期函数的Fourier系数给出了新的谱表达式.从这些有用的表达式出发,我们推导了时间连续和离散格式的迭代收敛条件.数值实验进一步验证了本文的理论结果.     

计算最小奇异组的一个精化调和 Lanczos双对角化方法

在很多实际应用中需要计算大规模矩阵的若干个最小奇异组.调和投影方法是计算内部特征对的常用方法,其原理可用于求解大规模奇异值分解问题.本文证明了,当投影空间足够好时,该方法得到的近似奇异值收敛,但近似奇异向量可能收敛很慢甚至不收敛.根据第二作者近年来提出的精化投影方法的原理,本文提出一种精化的调和Lanczos双对角化方法,证明了它的收敛性.然后将该方法与Sorensen提出的隐式重新启动技术相结合,开发出隐式重新启动的调和Lanczos双对角化算法(IRHLB)和隐式重新启动的精化调和Lanczos双对角化算法(IRRHLB).位移的合理选取是算法成功的关键之一,本文对精化算法提出了一种新的位移策略,称之为"精化调和位移".理论分析表明,精化调和位移比IRHLB中所用的调和位移要好,且可以廉价可靠地计算出来.数值实验表明,IRRHLB比IRHLB要显著优越,而且比目前常用的隐式重新启动的Lanczos双对角化方法(IRLB)和精化算法IRRLB更有效.