Robust linear optimization under general norms

We explicitly characterize the robust counterpart of a linear programming problem with uncertainty set described by an arbitrary norm. Our approach encompasses several approaches from the literature and provides guarantees for constraint violation under probabilistic models that allow arbitrary dependencies in the distribution of the uncertain coefficients.     

Modules over Operator Algebras and Its Module Maps

ＭｏｄｕｌｅｓｏｖｅｒＯｐｅｒａｔｏｒＡｌｇｅｂｒａｓａｎｄＩｔｓＭｏｄｕｌｅＭａｐｓＸｕＴｉａｎｚｈｏｕ（许天周）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ，２１００９３）ＡｂｓｔｒａｃｔＬｅ...     

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.     

Dual frames in connected with generalized sampling in shift-invariant spaces

The aim of this article is to derive stable generalized sampling in a shift-invariant space by using some special dual frames in L²(0,1). These sampling formulas involve samples of filtered versions of the functions in the shift-invariant space. The involved samples are expressed as the frame coefficients of an appropriate function in L²(0,1) with respect to some particular frame in L²(0,1). Since any shift-invariant space with stable generator is the image of L²(0,1) by means of a bounded invertible operator, our generalized sampling is derived from some dual frame expansions in L²(0,1).     

Urn模型的B网及其应用

Urn模型的离散概率分布被用于构造逼近格式,具有Bernstein多项式的许多特性。本文用B网技术对Urn模型概率分布给出新的解释,指出了Urn模型B网的诸多性质,导出分布函数曲线的导数公式,构造了Urn分布的对偶基及与此相关的拟插值算子。     

Dual Si-H effects in platinum-catalyzed silane reduction of carboxamides leading to a practical synthetic process of tertiary-amines involving self-encapsulation of the catalyst species into the insoluble silicone resin formed

Combination of commercially available platinum catalysts with siloxanes containing more than two Si-H groups is found to be an efficient catalyst system for the reduction of carboxamides to amines. In particular, facile removal of silicon and platinum residues from the product can be achieved by the use of polymethylhydrosiloxanes as reducing reagents.     

双波长分光光度法同时测定岩石矿物中的微量金和钯

本文提出以硫代米蚩酮为显色剂，用双波长分光光度法同时测定岩石矿物中的微量金和钯的方法，消除了测定金钯的相互干扰，该方法简便，快速，选择性好，用于矿石样品中金和钯的测定，结果满意。     

双功能催化剂体系作用下乙烯二聚和共聚合的研究

用乙烯为原料在双功能催化剂体系的作用下通过二聚和共聚合反应，直接合成线性低密度聚乙烯（ＬＬＤＰＥ）．所用二聚反应催化剂为钛酸正丁酯（Ｔｉ（ＯＢｕ）_４），共聚催化剂为ＴｉＣｌ_４／ＭｇＣｌ_２（ＺＭ－１催化剂）．研究了二聚反应动力学行为及影响双功能催化剂体系动力学过程的一些因素．结果表明利用这两种催化剂组成双功能催化剂体系能够很方便地制得密度范围在０．９０－０．９３，Ｅｔ／１０００Ｃ在１０－４０的ＬＬＤＰＥ．     

Chiral separation of the four stereoisomers of a novel antianginal agent using a dual cyclodextrin system in capillary electrophoresis

Reported here is an analytical method enabling the stereochemical resolution of a new antianginal compound possessing two stereogenic centers, leading to four stereoisomers. Only one of these isomers is currently under development as a novel antianginal agent and consequently, the other three isomers are considered as unwanted chiral impurities. Therefore, an enantioselective method is required in order to check its enantiomeric purity. This paper presents a method exploiting the high efficiency of capillary electrophoresis and the complexing properties of cyclodextrins to achieve the separation of the four stereoisomers of this weakly basic compound (pKa = 7.4). For this purpose, the combination of a neutral cyclodextrin, hydroxypropyl-gamma-cyclodextrin (HP-gamma-CD), and an anionic cyclodextrin, carboxymethyl-beta-cyclodextrin (CM-beta-CD), was added to the separation buffer running in an uncoated silica capillary. After selection of the suitable cyclodextrin system, satisfactorily separation conditions were as follows: 30 mM phosphate buffer (pH 6.4) containing 10 mM of HP-gamma-CD and 10 mM of CM-beta-CD, running voltage +30 kV. The resulting run time and resolutions were respectively about 17 min and between 1.95 and 2.84. Linearity curves (0.993 < r2 < 0.998) are also shown.