The interlace polynomial of a graph

Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial.It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers.     

弱广义向量拟似变分不等式解的存在性

研究拓扑向量空间上弱广义向量拟似变分不等式解的存在性问题.与Khaliq和Rashid等在单调或伪单调假设条件下,利用KKM定理证明解的存在性不同,在集值映射是非空凸值映射并且有开下截口的条件下,利用Fan-Browder不动点原理证明解的存在性.     

一种基于分段能量分析的桥式吊车镇定控制器设计方法

针对欠驱动桥式吊车系统,提出了一种基于分段能量分析的桥式吊车镇定控制器没计方法.具体而言,首先通过对系统特性进行分段分析构造出一个新的能量函数;随后,在其基础上设计了一种新型的能量控制器,并借助Lyapunov方法和LaSalle不变性原理证明了闭环系统的渐近稳定性.利用数值仿真与实际实验验证了所提出的控制算法具有良好的控制性能,对外界干扰具有较强的鲁捧性.此外,实验结果进一步表明:相比常规的能量控制方法与时间最优控制方法,该控制方法可降低驱动能耗,保征台车的快速精确定位,同时负载的摆角被抑制在更小的范围内,几乎无残余摆动.     

Leray-Schauder不动点定理的一个新证明

给出Leray-Schauder不动点定理的一个新证明.我们首先给出集值映射的焊接引理,利用集值映射的焊接引理和Kakutani不动点定理证明Leray-Schauder不动点定理,并证明Leray-Schauder不动点定理与Brouwer不动点定理等价.     

Minimal volume invariants,topological sphere theorems and biorthogonal curvature on 4‐manifolds

The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4‐manifolds. In addition, we provide topological sphere theorems for compact submanifolds of spheres and Euclidean spaces, provided that the full norm of the second fundamental form is suitably bounded.     

Generalization of the variational principle and the Hohenberg and Kohn theorems for excited states of Fermion systems

Through the entanglement of a collection of K non-interacting replicas of a system of N interacting Fermions, and making use of the properties of reduced density matrices the variational principle and the theorems of Hohenberg and Kohn are generalized to excited states. The generalization of the variational principle makes use of the natural orbitals of an N-particle density matrix describing the state of lowest energy of the entangled state. The extension of the theorems of Hohenberg and Kohn is based on the ground-state formulation of density functional theory but with a new interpretation of the concept of a ground state: It is the state of lowest energy of a system of KN Fermions that is described in terms of the excited states of the N-particle interacting system. This straightforward implementation of the line of reasoning of ground-state density functional theory to a new domain leads to a unique and logically valid extension of the theory to excited states that allows the systematic treatment of all states in the spectrum of the Hamiltonian of an interacting system.     

Distributions in fuzzy logic

Probability distributions associated with several ‘ply’-operators are discussed. These exact distributions are compared with relevant Gaussian approximations.     

A note on <Emphasis Type="Italic">q</Emphasis>-multiplicative functions

We prove the following statement. Let , and let . Suppose that, for all and , the sequence satisfies the relation

HOMOTOPY PERTURBATION SOLUTION AND PERIODICITY ANALYSIS OF NONLINEAR VIBRATION OF THIN RECTANGULAR FUNCTIONALLY GRADED PLATES

In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.     

一类非齐次A-调和方程组很弱解的性质

该文应用Hodge分解定理，得到了非齐次A—调和方程组-Di(A^ij(x,Du)) Difj(i(x)=0,j=1,…，m的很弱解是弱解，进一步，利用Morrey空间法与Campanato空间法以及齐次化方法，作者得出了该方程的很弱解是局部Hoelder连续的，并且得出了Hoelder连续指数μ与λ之间的多值函数关系式．