Turnpike property for extremals of variational problems with vector-valued functions

In this paper we study the structure of extremals of variational problems with large enough , fixed end points and an integrand from a complete metric space of functions. We will establish the turnpike property for a generic integrand . Namely, we will show that for a generic integrand , any small and an extremal of the variational problem with large enough , fixed end points and the integrand , for each the set is equal to a set up to in the Hausdorff metric. Here is a compact set depending only on the integrand and are constants which depend only on and , .

     

Solutions for a class of optimal control problems with time delay,part 2

In this work, we analyze the structure of optimal solutions for a class of optimal control problems with time delay whose state is governed by a nonlinear autonomous Volterra integrodifferential equation. We establish that an almost optimal finite trajectory defined on an interval [0, ] is contained in a small neighborhood of the optimal steady state for all , where is a constant which depends on the neighborhood and does not depend on .The author thanks A. Leizarowitz for fruitful discussions.     

Infinite Matrix Rings on Spaces with Signed-Weakly Gliding Hump Property

Ｌｅｔωｂｅｔｈｅｓｐａｃｅｏｆａｌｌｓｃａｌａｒｖａｌｕｅｄｓｅｑｕｅｎｃｅｓ,ａｎｄ φｉｔｓｓｕｂｓｐａｃｅｗｉｔｈｏｎｌｙｆｉｎｉｔｅｌｙｍａｎｙｎｏｎ ｚｅｒｏｃｏｏｒｄｉｎａｔｅｓ.ＡｌｉｎｅａｒｓｕｂｓｐａｃｅＥｏｆωｉｓｃａｌｌｅｄａｓｅｑｕｅｎｃｅｓｐａｃｅ.　Ｗｅｓａｙｔｈａｔａｎｏｎ ｚｅｒｏｖｅｃｔｏｒｓｅｑｕｅｎｃｅ {ｚ(ｎ) }ｉｎωｉｓａｂｌｏｃｋｓｅｑｕｅｎｃｅｉｆｔｈｅｒｅｅｘｉｓｔｓａｓｔｒｉｃｔｌｙｉｎｃｒｅａｓｉｎｇｓｅｑｕｅｎｃｅｏｆｐｏｓｉｔｉｖｅｉｎｔｅｇｅｒ…     

锥方向高阶广义邻近导数及高阶Mond-Weir对偶(英文)

本文引入了集值映射的锥方向的高阶广义邻近导数.应用这种导数,构建了约束的集值优化问题的一种高阶Mond-Weir型对偶,并建立了相应的弱对偶,强对偶和逆对偶性,获得的结果推广了文献中的相应结论.     

Birkhoff’s conjecture and almost periodic motions on torusT 2

The relation between rotation number and almost periodic motion for almost allC ⁵ systems onT ² which have no critical points is established. The result that every solution of such systems is a Liapunov stable and almost periodic motion is proved. Project supported by the National Natural Science Foundation of China.     

Fuzzy Optimization Problems Based on Ordering Cones

The solution concepts of the fuzzy optimization problems using ordering cone (convex cone) are proposed in this paper. We introduce an equivalence relation to partition the set of all fuzzy numbers into the equivalence classes. We then prove that this set of equivalence classes turns into a real vector space under the settings of vector addition and scalar multiplication. The notions of ordering cone and partial ordering on a vector space are essentially equivalent. Therefore, the optimality notions in the set of equivalence classes (in fact, a real vector space) can be naturally elicited by using the similar concept of Pareto optimal solution in vector optimization problems. Given an optimization problem with fuzzy coefficients, we introduce its corresponding (usual) optimization problem. Finally, we prove that the optimal solutions of its corresponding optimization problem are the Pareto optimal solutions of the original optimization problem with fuzzy coefficients.     

A Solution Concept for Fuzzy Multiobjective Programming Problems Based on Convex Cones

A solution concept for fuzzy multiobjective programming problems based on ordering cones (convex cones) is proposed in this paper. The notions of ordering cones and partial orderings on a vector space are essentially equivalent. Therefore, the optimality notions in a real vector space can be elicited naturally by invoking a concept similar to that of the Pareto-optimal solution in vector optimization problems. We introduce a corresponding multiobjective programming problem and a weighting problem of the original fuzzy multiobjective programming problem using linear functionals so that the optimal solution of its corresponding weighting problem is also the Pareto-optimal solution of the original fuzzy multiobjective programming problem.     

On the generic nonexistence of rational geodesic foliations in the torus, Mather sets and Gromov hyperbolic spaces

Given a rational homology classh in a two dimensional torusT ², we show that the set of Riemannian metrics inT ² with no geodesic foliations having rotation numberh isC ^k dense for everyk N. We also show that, generically in theC ² topology, there are no geodesic foliations with rational rotation number. We apply these results and Mather's theory to show the following: let (M, g) be a compact, differentiable Riemannian manifold with nonpositive curvature, if (M, g) satisfies the shadowing property, then (M, g) has no flat, totally geodesic, immersed tori. In particular,M has rank one and the Pesin set of the geodesic flow has positive Lebesgue measure. Moreover, if (M, g) is analytic, the universal covering ofM is a Gromov hyperbolic space.Partially supported by CNPq-GMD, FAPERJ, and the University of Freiburg.     

秩约束下矩阵方程AX=B的反对称解及其最佳逼近

本文研究了秩约束下矩阵方程AX=B的反对称解问题.利用矩阵秩的方法,获得了矩阵方程AX=B有最大秩和最小秩解的充分必要条件以及定秩解的表达式,同时对于最小秩解的解集合,得到了最佳逼近解.     

Solutions of Fuzzy Multiobjective Programming Problems Based on the Concept of Scalarization

Scalarization of fuzzy multiobjective programming problems using the embedding theorem and the concept of convex cone (ordering cone) is proposed in this paper. Since the set of all fuzzy numbers can be embedded into a normed space, this motivation naturally inspires us to invoke the scalarization techniques in vector optimization problems to evaluate the a multiobjective programming problem. Two solution concepts are proposed in this paper by considering different convex cones.     

A bivariate optimal replacement policy for a system subject to a generalized failure and repair process

Traditionally, in the studies of the optimal maintenance policies for repairable systems, the nonhomogeneous Poisson process model, which corresponds to the minimal repair process, has been intensively applied. However, in many practical situations, the repair type is not necessarily minimal. In this article, a new repair process based on a new counting process model (so‐called the generalized Polya process) is introduced. Then, the issue of the optimal replacement problem is discussed. A bivariate preventive replacement policy is developed and the properties of the optimal policy are studied. Illustrative examples are also presented. In addition, a comparison with a conventional replacement policy is performed.     

Expansions of ordered fields without definable gaps

In this paper we are concerned with definably, with or without parameters, (Dedekind) complete expansions of ordered fields, i. e. those with no definable gaps. We present several axiomatizations, like being definably connected, in each of the two cases. As a corollary, when parameters are allowed, expansions of ordered fields are o‐minimal if and only if all their definable subsets are finite disjoint unions of definably connected (definable) subsets. We pay attention to how simply (in terms of the quantifier complexity and/or usage of parameters) a definable gap in an expansion is so. Next we prove that over parametrically definably complete expansions of ordered fields, all one‐to‐one definable (with parameters) continuous functions are monotone and open. Moreover, in both parameter and parameter‐free cases again, definably complete expansions of ordered fields satisfy definable versions of the Heine‐Borel and Extreme Value theorems and also Bounded Intersection Property for definable families of closed bounded subsets.