On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

A Hydroperoxide-Mediated Decarboxylation of α-Ketoacids Enables the Chemoselective Acylation of Amines

Strategies for the formation of amide bonds, that is, one of the most basic and important transformations in organic synthesis, have so far focused predominantly on dehydration reactions. Herein, we report and demonstrate the practical utility of a novel decarboxylative amidation of α-ketoacids by using inexpensive tert-butyl hydroperoxide (TBHP), which is characterized by high yields, a broad substrate scope, mild reaction conditions, and a unique chemoselectivity. These features enable the synthesis of peptides from amino acid derived α-ketoacids under preservation of the stereochemical information.     

一类函数方程的稳定性及微商配置解

本文对一类重要的函数方程建立解稳定性定理,提出微商配置解,证明了收敛性.     

非均匀加宽单模激光器的最佳透射率

给出四能级系统非均匀加宽单模激光器最佳透射率的表达式和分布曲线,并与均匀加宽单模激光器最佳透射率进行了比较.叙述了非均匀加宽单模激光器的特点.     

Dual Characterizations of Set Containments with Strict Convex Inequalities

Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated systems. The convex sets considered in this paper are the solution sets of an arbitrary number of convex inequalities, which can be either weak or strict inequalities. Particular cases of dual characterizations of set containments have played key roles in solving large scale knowledge-based data classification problems where they are used to describe the containments as inequality constraints in optimization problems. The idea of evenly convex set (intersection of open half spaces), which was introduced by W. Fenchel in 1952, is used to derive the dual conditions, characterizing the set containments.     

线性常微分方程的保线性变换及其应用

研究了线性常微分方程的保线性变换，得到任意两个二阶线性常微分方程等价的条件，并用于求解一类二阶线性变系数齐次常微分方程．对数学物理方法教学中怎样通过适当的变换把给定的二阶线性变系数齐次常微分方程化为可解的方程给出了合理解释。     

Diffraction by a wedge at skew incidence: integral representations of Cauchy-Carleman for the electromagnetic fields

An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given.     

一类非线性方程存在多个极限环的一个充分条件

关于方程(1)的极限环唯多性问题,不少人作了研究,[1]引进“n重互相包含”曲线类,,经[2]的改进获得较好的结果,但这类曲线要求的条件较多。本文不从[1]的观点出发,不包含[1]的全部条件,独立地用①11。’,LtnnoB变换折叠相平面,据轨线与折叠线交点的位置,对(1)的等价方程按线性方程积分,将积分的正负项作成比值进行比较,得出一组充分条件。