多工况多约束下离散变量桁架结构的拓扑优化设计

提出了一个多工况下受应力、位移约束的离散变量桁架结构的拓扑优化方法，给出了结构拓扑形式变更时的约束处理方法及杆件删除策略，使基结构设计空间的维数不断降低，达到最优拓扑，避免了奇异解的出现，在算例中指出了截面离散集和位移约束对最优拓扑的影响；算例给出了满意的拓扑优化解。     

Ideal Topology on Effect Algebras

The ideals of effect algebras induce a topology on effect algebras. The operations and of effect algebras are continuous with respect to this topology.     

Strong topologies on vector-valued function spaces

Let be a real Banach space and let E be an ideal of L ⁰ over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function , defined by , belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.     

On a nonlocal problem for semilinear differential equations with upper semicontinuous nonlinearities in general Banach spaces

Sufficient conditions on the existence of mild solutions for the following semilinear nonlocal evolution inclusion with upper semicontinuous nonlinearity: u^′(t)∈A(t)u(t)+F(t,u(t)), 0<t?d, u(0)=g(u), are given when g is completely continuous and Lipschitz continuous in general Banach spaces, respectively. An example concerning the partial differential equation is also presented.     

Feasibility-Solvability Theorem for a Generalized System

In this paper, we consider a generalized system in the framework of the formulation proposed by Blum and Oettli. The concepts of feasibility and strict feasibility are introduced for a generalized system and a feasibility-solvability theorem is obtained. This work was supported by the Foundation for Young Teacher in Sichuan University (07069), the National Natural Science Foundation of China (10826064, 10671135) and the Specialized Research Fund for the Doctoral Program of Higher Education (20060610005). The authors thank Professor L.D. Muu (Hanoi) and the referee for valuable comments and suggestions which lead to improvements of this paper.     

Monotonicity and best approximation in Orlicz-Sobolev spaces with the Luxemburg norm

Criteria for strict monotonicity, upper (lower) locally uniform monotonicity and uniform monotonicity of Orlicz-Sobolev spaces with the Luxemburg norm are given. Some applications to best approximation are presented.     

Dual characterization of properties of risk measures on Orlicz hearts

We extend earlier representation results for monetary risk measures on Orlicz hearts. Then we give general conditions for such risk measures to be Gateaux-differentiable, strictly monotone with respect to almost sure inequality, strictly convex modulo translation, strictly convex modulo comonotonicity, or monotone with respect to different stochastic orders. The theoretical results are used to analyze various specific examples of risk measures. We thank Andreas Hamel and Michael Kupper for fruitful discussions and helpful comments. P. Cheridito has been supported by NSF Grant DMS-0642361, a Rheinstein Award and a Peek Fellowship. T. Li has been supported by a Marshall Scholarship and a Merage Fellowship.     

Perturbed kernel approximation on homogeneous manifolds

Current methods for interpolation and approximation within a native space rely heavily on the strict positive-definiteness of the underlying kernels. If the domains of approximation are the unit spheres in euclidean spaces, then zonal kernels (kernels that are invariant under the orthogonal group action) are strongly favored. In the implementation of these methods to handle real world problems, however, some or all of the symmetries and positive-definiteness may be lost in digitalization due to small random errors that occur unpredictably during various stages of the execution. Perturbation analysis is therefore needed to address the stability problem encountered. In this paper we study two kinds of perturbations of positive-definite kernels: small random perturbations and perturbations by Dunkl's intertwining operators [C. Dunkl, Y. Xu, Orthogonal polynomials of several variables, Encyclopedia of Mathematics and Its Applications, vol. 81, Cambridge University Press, Cambridge, 2001]. We show that with some reasonable assumptions, a small random perturbation of a strictly positive-definite kernel can still provide vehicles for interpolation and enjoy the same error estimates. We examine the actions of the Dunkl intertwining operators on zonal (strictly) positive-definite kernels on spheres. We show that the resulted kernels are (strictly) positive-definite on spheres of lower dimensions.     

Portfolio selection under strict uncertainty: A multi-criteria methodology and its application to the Frankfurt and Vienna Stock Exchanges

In modern portfolio theory, it is common practice to first compute the risk-reward efficient frontier and then to support an individual investor in selecting a portfolio that meets his/her preferences for profitability and risk. Potential flaws include (a) the assumption that past data provide sufficient evidence for predicting the future performances of the securities under consideration and (b) the necessity to mathematically determine or approximate the investor’s utility function. In this paper, we propose a methodology whose initial phase filters portfolios that are inefficient from a historical perspective. While this is consistent with traditional approaches, the second phase differs from the standard approach as it uses a decision table constructed by considering multiple scenarios assuming strict uncertainty. The table cells measure consequences by a multi-criteria linear performance index of simulated future returns, which avoids difficulties with performance ratios. The real world applicability is illustrated through two studies based on data from the stock exchanges in Frankfurt and Vienna.