Solution differentiability and continuation of Newton's method for variational inequality problems over polyhedral sets

In this paper, we derive some further differentiability properties of solutions to a parametric variational inequality problem defined over a polyhedral set. We discuss how these results can be used to establish the feasibility of continuation of Newton's method for solving the variational problem in question.This work was based on research supported by the National Science Foundation under Grant No. ECS-87-17968.     

On the existence of m-point boundary value problem at resonance for higher order differential equation

By means of Mawhin's continuation theorem, we study m-point boundary value problem at resonance in the following form:

     

高阶中立型时滞差分方程正解的存在性

考虑l＋1阶中立型差分方程在对f较弱的限制条件下，本文绘出了方程（*）当p≠-1时存在正解的充分条件以及当p=-1时存在有界正解的充分必要条件．     

On higher order gravities, their analogy to GR, and dimensional dependent version of Duff’s trace anomaly relation

An almost brief, though lengthy, review introduction about the long history of higher order gravities and their applications, as employed in the literature, is provided. We review the analogous procedure between higher order gravities and GR, as described in our previous works, in order to highlight/manipulate its important achievements. Amongst which are presentation of an easy classification of higher order Lagrangians and its employment as a criteria in order to distinguish correct metric theories of gravity. For example, it does not permit the inclusion of only one of the second order Lagrangians in isolation. But, it does allow the inclusion of the cosmological term. We also discuss on the compatibility of our procedure and the Mach idea. We derive a dimensional dependent version of Duff’s trace anomaly relation, which in four-dimension is the same as the usual Duff relation. The Lanczos Lagrangian satisfies this new constraint in any dimension. The square of the Weyl tensor identically satisfies it independent of dimension, however, this Lagrangian satisfies the previous relation only in three and four dimensions.     

Higher order optimality conditions for Henig efficient solutions in set-valued optimization

In this paper, higher order generalized contingent epiderivative and higher order generalized adjacent epiderivative of set-valued maps are introduced. Necessary and sufficient conditions for Henig efficient solutions to a constrained set-valued optimization problem are given by employing the higher order generalized epiderivatives.     

Computation of Green's function for radiative transfer

In an accompanying paper, we develop the computational expressions for the higher order perturbation of the radiative transfer equation, and present some numerical results for typical cases. In this article, we discuss a number of issues regarding the implementation of the HOP computation: obtaining the Green's function, its expansion as a double series of Legendre polynomials, and obtaining the adjoint radiance of more general sources such as those for the fluxes at arbitrary altitudes. Examples of Green's function and its expansion coefficients are presented.     

A modified Fritz John optimality criterion

A modified Fritz John optimality criterion is presented for a certain class of nonlinear programming problems.This research was partially supported by AFOSR Grant No. AF-AFOSR-78-3518.     

氢化物发生-无色散原子荧光光谱法测定高纯阴极铜中砷、锑、铋、硒和碲

研究了在氨性溶液中，以镧盐为载体，共沉淀富集高纯阴极铜中杂质As、Sb、Bi、Se、Te,使之与基本铜分离，用氢化物原子荧光光谱法测定。考察了测定的最佳条件、共存元素对测定的影响及方法的准确度和精密度。     

高维系统周期解的存在性与唯一性

本文首先利用一种新方法讨论高维系统解的一致有界性，一致最终有界性及非常稳定性问题，然后将所获结果应用于高维系统周期解的存在性与唯一性的研究。另外，本文还提出了“阶梯形系统”的概念，并对其建立了一种利用系统部分方程周期解存在性判定整个系统周期解存在性的方法。     

DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

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