The isolated invariant sets of a flow

Some definitions such as m-chain recurrent set, weakly gradient flow and generalized Morse decomposition for a flow defined on a topological space are introduced in this paper. Some conclusions, include the chain recurrent set contain the m-chain recurrent set; the m-chain recurrent set contain the non-wandering set, are proved. In some flows the non-wandering set is proper subset of the m-chain recurrent set; in the meantime the m-chain recurrent set is proper subset of the chain recurrent set. Moreover some criterions for the existence of trajectories joining singular points and a necessary and sufficient condition of the weakly gradient flow are also given here. At last the generalized Morse decomposition of the invariant set are discussed in the paper.     

Attractor, chain recurrent set and limit set of flow

The properties of attractor, chain recurrent set and limit set of the flow on a compact metric space are studied.     

Ergodic theorem for generalized long-range exclusion processes with positive recurrent transition probabilities

This paper is devoted to the ergodicity of generalized long-range exclusion processes with positive recurrent transition probabilities. The set of invariant probability measures and the corresponding domain of attraction for each invariant probability measure are described. This paper is partially supported the National Natural Science Foundation of China.     

广义多值直觉模糊软集及其在多属性决策中的应用

软集理论作为一种处理不确定问题的数学新工具弥补了传统模糊理论在参数工具上的不足。本文将广义模糊软集与多值直觉模糊集相结合,提出了广义多值直觉模糊软集的概念,给出了广义多值直觉模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,还将广义多值直觉模糊软集应用到多属性决策问题中去,给出相应的算法。并进行实例分析说明该决策方法的可行性和有效性。     

Existence and uniqueness of level sets for spiral crystal growth

We outline a new level set approach for spirals whose evolution follows the generalized curvature flow with a constant driving force. Our basic idea is that a spiral can be expressed as the intersection of an auxiliary surface and a Riemannian surface. Also we state and discuss the basic ideas for the uniqueness and existence of spiral motion using the level set approach. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Continued fractions,the group GL(2, ℤ), and Pisot numbers

The properties of continued fractions, generalized golden sections, and generalized Fibonacci and Lucas numbers are proved on the ground of the properties of subsemigroups of the group of invertible integer matrices. Some properties of special recurrent sequences are studied. A new proof of the Pisot-Vijayaraghavan theorem is given. Some connections between continued fractions and Pisot numbers are considered. Some unsolved problems are stated.     

An improved sectional-Anosov closing lemma

We prove that all nonwandering points of a sectional-Anosov flow on a compact 3-manifold can be approximated by periodic points or by points for which the omega-limit set is a singularity. This improves the closing lemma in Morales (Mich. Math. J. 56(1):29?C53, 2008). We also describe a sectional-Anosov flow for which the recurrent points are not dense in the nonwandering set.     

On generalized recurrent Riemannian manifolds

The object of the present paper is to study a type of Riemannian manifolds called generalized recurrent manifolds. We have constructed two concrete examples of such a manifold whose scalar curvature is non-zero non-constant. Some other properties have been considered. Among others it is shown that on a generalized recurrent manifold with constant scalar curvature, Weyl-semisymmetry and semisymmetry are equivalent. Sufficient condition for a generalized recurrent manifold to be a special quasi Einstein manifold is obtained.     

A new class of bilevel generalized mixed equilibrium problems in Banach spaces

A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.     

关于向量集值优化的Benson真有效性

对广义锥次数凸向量集值优化问题Benson真有效性解的标量化问题进行了研究,借助于一种新的择一性定理建立了广义锥次类凸向是集值优化问题Benson真有效解的Lagrange乘子型定理并讨论了乘子型对偶问题。     

一类多目标半无限分式规划的最优性条件

<正>0引言分式规划作为最优化的一个分支,近年来,获得了很大的发展,如,文[4]利用(F,α,ρ,d)-凸函数,文[5]利用半局部预不变凸函数等分别讨论了相应的分式规划问题等,这些成果极大地推动了分式规划的发展.     

广义模糊粗糙集的不确定性度量

研究广义模糊粗糙集的不确定性问题,利用一种新的信息熵定义模糊粗糙集的模糊性度量,并给出这种度量的性质,证明当且仅当A是经典可定义集合时其模糊粗糙集的模糊性度量FR(A)等于0。     

On intersections of abelian and nilpotent subgroups in finite groups. I

We consider Pontryagin’s generalized nonstationary example with identical dynamic and inertial capabilities of the players under phase constraints on the evader’s states. The boundary of the phase constraints is not a “death line” for the evader. The set of admissible controls is a ball centered at the origin, and the terminal sets are the origin. We obtain sufficient conditions for a multiple capture of one evader by a group of pursuers in the case when some functions corresponding to the initial data and to the parameters of the game are recurrent.     

Topology vs generalized rough sets

This paper investigates the relationship between topology and generalized rough sets induced by binary relations. Some known results regarding the relation based rough sets are reviewed, and some new results are given. Particularly, the relationship between different topologies corresponding to the same rough set model is examined. These generalized rough sets are induced by inverse serial relations, reflexive relations and pre-order relations, respectively. We point that inverse serial relations are weakest relations which can induce topological spaces, and that different relation based generalized rough set models will induce different topological spaces. We proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology.     

基于模糊博弈视角的企业联盟“双循环”合作对策研究

企业合作在“双循环”新发展格局下呈现出更多的模糊特征,能否形成稳定的模糊合作格局及持续合作的收益再分配策略成为合作联盟的关注点。将广义模糊超量博弈和模糊凸博弈及其广义解集应用到“双循环”新发展格局下企业联盟合作与收益再分配中,提出最大广义模糊超量博弈模型及其广义模糊谈判集,并基于最大广义模糊超量博弈均衡性的视角,对模糊凸博弈下广义模糊谈判集与核心的等价性质进行论证。研究结果不仅满足了“双循环”新发展格局下合作企业以部分资源参与合作的意愿,及企业联盟模糊凸合作博弈下再分配方案等价性证明需求,而且实现了保留部分收益用于联盟再发展的策略。     

Semicontinuity of the solution set to a parametric generalized strong vector equilibrium problem

This paper deals with the stability for a parametric generalized strong vector equilibrium problem. Under new assumptions, which do not contain any information about the solution set and monotonicity, we establish the lower semicontinuity and upper semicontinuity of the solution set to a parametric generalized strong vector equilibrium problem by using a scalarization method and a density result. These results are improve the corresponding ones in recent literature. Some examples are given to illustrate our results.     

Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency

In this paper, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Here, a generalized Stampacchia vector variational inequality is formulated as a tool to characterize quasi- or weak quasi-efficient points. By using two new classes of generalized convexity functions, under suitable constraint qualifications, the equivalence between Kuhn–Tucker vector critical points, solutions to the multiobjective problem and solutions to the generalized Stampacchia vector variational inequality in both weak and strong forms will be proved.     

Transient Bernoulli flow in multi-port fluid devices with arbitrary geometry

We present a method for the solution of transient flow in a multi-port fluid device with arbitrary geometry. The method is applicable to fluid devices where the fluid motion is primarily inviscid throughout the volume, but locally near a device port some accommodation to viscous flow is introduced. The internal flow is characterized by an array of purely geometrical factors between ports, essentially a set of generalized impedances; the state variables elicited are the average volume flow rates through the device ports. The method creates a set of coupled non-linear time-dependent ordinary differential equations. The solution to this set of equations is much faster, typically by orders of magnitude, than a single run of a transient CFD model. We demonstrate our method with a simple example; we show that the results of the method agree well with a full CFD calculation.     

Sectional-Anosov flows on certain compact 3-manifolds

A sectional-Anosov flow is a flow for which the maximal invariant set is sectional-hyperbolic. A generalized 3-handlebody is a compact manifold which is built from a 3-disc attaching 0, 1, 2 and 3-handles at its boundary, one at a time, by attaching maps. We prove that there exist a class of orientable generalized 3-handlebodies supporting sectional-Anosov flows, moreover this class of manifolds is strictly large than the previous one studied in [14].     

A class of convolution integral equations involving a generalized polynomial set

The aim of this paper is to derive a solution of a certain class of convolution integral equation of Fredholm type whose kernel involves a generalized polynomial set. Our main result is believed to be general and unified in nature. A number of (known or new) results follow as special cases, simply by specializing the coefficients and parameters involved in the generalized polynomial set. For the sake of illustration, some special cases are mentioned briefly.