Impact of Partial Separability on Large-Scale Optimization

ELSO is an environment for the solution oflarge-scale optimization problems. With ELSO the user is required to provide only code for the evaluation of a partially separable function. ELSO exploits the partialseparability structure of the function to computethe gradient efficiently using automatic differentiation.We demonstrate ELSO's efficiency by comparing thevarious options available in ELSO.Our conclusion is that the hybrid option in ELSOprovides performance comparable to the hand-coded option, while having the significantadvantage of not requiring a hand-coded gradient orthe sparsity pattern of the partially separable function.In our test problems, which have carefully coded gradients,the computing time for the hybrid AD option is within a factor of two of thehand-coded option.     

Concerning the multiplicators of Fourier series in the trigonometric system

In this paper we prove theorems on multiplicators of Fourier series inL _p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998.     

A Survey on Explicit Representation Formulae for Fundamental Solutions of Linear Partial Differential Operators

In the present article, we aim at treating the existence of fundamental solutions of linear partial differential operators with constant coefficients from the viewpoint of setting up explicit formulae yielding fundamental solutions.     

具连续分布滞量的非线性中立型抛物偏泛函微分方程的振动性

考虑一类具连续分布滞量的非线性中立型抛物偏泛函微分方程解的振动性,借助Green定理和时滞微分不等式获得了这类方程在Robin,Dirichlet边值条件下所有解振动的若干充分条件.     

Unified approach to photo-and electro-production of mesons with arbitrary spins

A new approach to identify the independent amplitudes along with their partial wave multipole expansions, for photo-and electro-production is suggested, which is generally applicable to mesons with arbitrary spin-parity. These amplitudes facilitate direct identification of different resonance contributions.      

确定线性偏微分方程组可积系统的对合特征集方法

基于Ritt-Wu特征集方法和Riquier-Janet理论,给出一种将线性微分方程组化成简单标准形式的有效算法．该算法通过消去冗余和添加可积条件获得线性微分方程组的完全可积系统(有形式幂级数解)或不相容判定．该算法不仅适用于常系数的线性偏微分方程组,而且对于变系数(以函数为系数)仍然有效．作者还给出了完全可积系统判定定理及其严格证明．     

Viscosity solutions of fully nonlinear parabolic systems

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128.     

非平稳NA序列部分和的精确渐近性

本文探讨了非平稳NA序列部分和的精确渐近性．以前的文献在讨论NA序列此类极限性质时都附加有强平稳条件的限制,这必然会给一些问题的研究带来不便．周知,非平稳NA序列在许多实际问题中是大量存在的,所以解除强平稳条件的束缚具有较大的理论和实际意义,这正是本文的目的之所在,同时本文也将已有的一些结果包含成为特殊情形．     

独立不同分布随机变盆序列的部分和的增量有多小

关于独立同分布随机变量部分和的增量有多小问题，目前已有了著名的结果.本文通过与独立同分布情形时完全不同的途径，讨论了独立不同分布情形时相应的问题.在矩母函数存在的条件下，获得了与同分布情形相近的结论.