Contingent epiderivatives and set-valued optimization

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions.     

THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

1IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblem,where"o(x)isnon-negativesmoothfunctionsatisfying"o.(0)=0,"o.(1)=1'Whenconsideringtheblow-upofsolution,thefollowingproblemarisenaturally:Doesblow-upoccur?Howdoesthesolutionapproachtheblow-uptime'!Andwilersisthehotspotlocated(blow-upset)?WelookattheheatequationwithanonlillearboundaryconditiollHerefiisaboundeddomaininR",p>1isarealnumber.IthasbeenknownforalongtimethattheDroblelil(1.1).(1.2)withAL(~,0)--'no(x)doesnothaveaglobals…     

关于多目标数学规划的最优性条件

本文讨论定义于Ｂａｎａｃｈ空间的多目标数学规划，得到一些ε－最优解和（弱）有效解的必要条件，充分条件和必要充分条件。     

Helmholtz potentiality conditions for systems of difference-differential equations

For operators corresponding to systems ofμth-order difference-differential equations of neutral type, necessary and sufficient conditions for potentiality with respect to the classical bilinear form are obtained. These results are applied to first-order quasilinear systems. Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 437–442, September, 1998. The author wishes to express his thanks to V. M. Savchin for fruitful discussions and useful remarks.     

Boundary control of a hyperbolic system with time lags

This paper considers an optimal boundary control problem fora hyperbolic system in which constant time lags appear in thestate equation and in the boundary condition simultaneously.Making use of Lion's scheme, necessary and sufficient conditionsof optimality for the Neumann problem are derived.     

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

蒿甲醚在模拟体内酸碱环境中的代谢动力学研究

 利用高效液相法对蒿甲醚进行了模拟体内酸碱环境的代谢动力学研究 ,测定了蒿甲醚及其代谢产物双氢青蒿素、蒿甲醚呋喃酯的代谢曲线。结果表明 ,蒿甲醚在模拟体内肠道和血液的弱碱性环境条件下半衰期为2 87 2min(计算值 ) ;在模拟体内胃液的酸性环境条件下半衰期为 74 6min ;在两种条件下的主要代谢产物均为双氢青蒿素和蒿甲醚呋喃酯。该方法克服了以往文献所报道方法的一些缺点 ,不仅简化了样品制备方法 ,也提高了检测结果的准确性。     

Fused silica capillary deactivation with D4 in the presence of oxygen

A new, simple procedure to deactivate fused silica capillaries without hydrothermal treatment is proposed. Based on high temperature reactions of octamethylcyclotetrasiloxane (D₄) in the presence of oxygen, this procedure results, upon coating with dimethylsilicone (SE-30), in columns which give almost symmetric peaks for as little as 150 pg of critical compounds, such as decylamine, thereby demonstrating very high inertness. A mechanism of the deactivation procedure, which, in contrast to previously developed procedures, is based on thermal reactions under aerobic conditions, is proposed.     

Selective cleavage of acetals with ZnBr2 in dichloromethane

A selective cleavage of acetals of 1,2- and 1,3-diols has been achieved under mild conditions using ZnBr₂ in dichloromethane at room temperature. Acetal types cleavable by this procedure include benzylidene, isopropylidene and cyclohexylidene acetals. This method is compatible with several other types of hydroxyl protecting groups such as Bn, Bz, TBDPS, TIPS and TBDMS.