On the Pesin set of expansive geodesic flows in manifolds with no conjugate points

In this paper, we show that the Pesin set of an expansive geodesic flow in compact manifold with no conjugate points and bounded asymptote coincides a.e with an open and dense set of the unit tangent bundle. We also show that the set of hyperbolic periodic orbits is dense in the unit tangent bundle.     

Cookie-Cuter集的多重Fractal分解的Packing维数

直线上的Ｃｏｏｋｉｅ－Ｃｕｔｔｅｒ集是一个扩张动力系统的不变集，并且是一个Ｆｒａｃｔａｌ集合．本文得到Ｃｏｏｋｉｅ－Ｃｕｔｔｅｒ集的多重Ｆｒａｃｔａｌ分解的Ｐａｃｋｉｎｇ维数，从而证明其是Ｔａｙｌｏｒ意义下的Ｆｒａｃｔａｌ集合     

Finite termination of the proximal point algorithm in Banach spaces

In this paper, we show that the convex optimization problem can be solved by the proximal point algorithm in a finite number of steps under the assumption that the solution set is a set of weak sharp minima.     

Graphs with disjoint dominating and paired-dominating sets

A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains a perfect matching. In this paper, we show that no minimum degree is sufficient to guarantee the existence of a disjoint dominating set and a paired-dominating set. However, we prove that the vertex set of every cubic graph can be partitioned into a dominating set and a paired-dominating set.     

tvs锥度量空间上同胚映射的可扩性

设$f$是紧tvs锥度量空间上同胚映射. 本文证明了$f$是tvs锥可扩的当且仅当$f$有生成元. 进一步, 如果$f$是tvs锥可扩的,则具有收敛半轨的点集是可数集. 本文的这些结果改进了拓扑动力系统的一些可扩同胚定理, 将有助于研究tvs锥度量空间上同胚映射的动力性质.     

Density of the Extremal Solutions for a Class of Second Order Boundary Value Problem

In this paper, we prove a theorem on the existence of extremal solutions to a second-order differential inclusion with boundary conditions, governed by the subdifferential of a convex function. We also show that the extremal solutions set is dense in the solutions set of the original problem.     

锥连续锥拟凹多目标规划问题弱有效解集的连通性

本文讨论了锥连续锥拟凹向量函数的弱有效解集的连通性问题；证明了当可行集X为紧凸集，目标函数f在X上锥连续锥拟凹时，其弱有效解集是连通的，在一定的意义下，改进了文献[1] 中的结果。     

Existence of infinitely many homoclinic orbits to Aubry sets for positive definite Lagrangian systems

In this paper, we study the problem of homoclinic orbits to Aubry sets for time-periodic positive definite Lagrangian systems. We show that there are infinitely many homoclinic orbits to some Aubry set under the conditions that the associated Mather set is uniquely ergodic and the first relative homology group of the projection of this Aubry set is nonzero.     

Continuums of solutions for integral inclusions on the half line

In this paper we show that the solution set of certain Volterra inclusions on the half line is a continuum.     

BOOLEAN ALGEBRAS IN AST

In this paper we investigate Boolean algebras and their subalgebras in Alternative Set Theory (AST). We show that any two countable atomless Boolean algebras are isomorphic and we give an example of such a Boolean algebra. One other main result is, that there is an infinite Boolean algebra freely generated by a set. At the end of the paper we show that the sentence “There is no non-trivial free group which is a set” is consistent with AST.     

An existence result for farsighted stable sets of games in characteristic function form

In this paper we show that every finite-player game in characteristic function form (not necessarily with side payments) obeying an innocuous condition (that the set of individually rational pay-off vectors is bounded) possesses a farsighted von-Neumann–Morgenstern stable set.     

低复杂度序列的维数

本文研究符号空间中由零拓扑熵序列组成的集合.通过构造适当的自相似集,证明了该集合的盒维数为1,而Hausdorff维数为0.     

Quasi-concave functions on meet-semilattices

This paper deals with maximization of set functions defined as minimum values of monotone linkage functions. In previous research, it has been shown that such a set function can be maximized by a greedy type algorithm over a family of all subsets of a finite set. In this paper, we extend this finding to meet-semilattices.We show that the class of functions defined as minimum values of monotone linkage functions coincides with the class of quasi-concave set functions. Quasi-concave functions determine a chain of upper level sets each of which is a meet-semilattice. This structure allows development of a polynomial algorithm that finds a minimal set on which the value of a quasi-concave function is maximum. One of the critical steps of this algorithm is a set closure. Some examples of closure computation, in particular, a closure operator for convex geometries, are considered.     

Dominating and total dominating partitions in cubic graphs

In this paper, we continue the study of domination and total domination in cubic graphs. It is known [Henning M.A., Southey J., A note on graphs with disjoint dominating and total dominating sets, Ars Combin., 2008, 89, 159–162] that every cubic graph has a dominating set and a total dominating set which are disjoint. In this paper we show that every connected cubic graph on nvertices has a total dominating set whose complement contains a dominating set such that the cardinality of the total dominating set is at most (n+2)/2, and this bound is essentially best possible.     

划分图上的正影响数

一个社会网络中通常包括具有正面影响和负面影响的两类人员,为了研究这个社会网络中人们之间相互影响的某些规律,引入了一个新的概念. 用划分图G=(V,E),V=V⁺ \cup V^-表示这样的一个社会网络,其中V⁺和V^- 分别表示正面人员的集合和负面人员的集合. 图G的一个点子集D\subseteq V^-被称为G的一个正影响集,若G的每个点的至少一半的邻点在D\cup V⁺中. G的所有正影响集的最小基数称为G的正影响数. 给出G的正影响数的几个下界并证明了这些界是紧的. 此外,还证明了求正影响数问题在二部图和弦图上都是NP-完全的.     

The nearest point problem in a polyhedral set and its extensions

In this paper we investigate the relationship between the nearest point problem in a polyhedral cone and the nearest point problem in a polyhedral set, and use this relationship to devise an effective method for solving the latter using an existing algorithm for the former. We then show that this approach can be employed to minimize any strictly convex quadratic function over a polyhedral set. Through a computational experiment we evaluate the effectiveness of this approach and show that for a collection of randomly generated instances this approach is more effective than other existing methods for solving these problems.     

Implications of the constant rank constraint qualification

This paper investigates properties of a parametric set defined by finitely many equality and inequality constraints under the constant rank constraint qualification (CRCQ). We show, under the CRCQ, that the indicator function of this set is prox-regular with compatible parametrization, that the set-valued map that assigns each parameter to the set defined by that parameter satisfies a continuity property similar to the Aubin property, and that the Euclidean projector onto this set is a piecewise smooth function. We also show in the absence of parameters that the CRCQ implies the Mangasarian-Fromovitz constraint qualification to hold in some alternative expression of the set.     

Existence and stability of minimax regret equilibria

In this paper, we study minimax regret equilibria. First, existence theorem of minimax regret equilibria is proved. Further, the generic stability of minimax regret equilibria is studied. We show that the set of minimax regret equilibria for most of problems (in sense of Baire category) is a singleton set.     

A Subspace of Hölder Space Consisting Only of Nonsmoothest Functions

In the first part of this paper, we give a complete answer to an old question of the geometric theory of Banach spaces; namely, we construct an infinite-dimensional closed subspace of Hölder space such that each function not identically zero is not smoother at each point than the nonsmoothest function in Hölder space. In the second part, using constructions from the first part, we show that the set of functions from Hölder space which are smoother on a set of positive measure than the nonsmoothest function is a set of first category in this space.     

Mixed uncertainty sets for robust combinatorial optimization

In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only recently it has been recognized that the process of building useful uncertainty sets is in itself a challenging task that requires mathematical support. In this paper, we propose an approach to go beyond the classic setting, by assuming multiple uncertainty sets to be prepared, each with a weight showing the degree of belief that the set is a “true” model of uncertainty. We consider theoretical aspects of this approach and show that it is as easy to model as the classic setting. In an extensive computational study using a shortest path problem based on real-world data, we auto-tune uncertainty sets to the available data, and show that with regard to out-of-sample performance, the combination of multiple sets can give better results than each set on its own.