大学生数学建模竞赛的独特魅力

大学生数学建模竞赛之所以在我国蓬勃发展 ,原因在于大学生数学建模竞赛是一项具有挑战性的开放的应用数学及计算机技术解决实际问题的综合性活动 ,有利于我们急需的创造性人才的培养 ,符合以人为本的社会发展理念 .     

On The Existence Of A Measurable Optimal Coupling Of Probability Kernels

In this paper, an existence theorem for a measurable optimal coupling of probability kernels on a σ-compact complete separable metric measurable space is obtained     

A Further Characterization Of Ellipsoids

In this note we extend a characterization of ellipsoids given in [6, Theorem 3.1.2.7], which is related to the classical characterization of ellipsoids as the only ovaloids with constant r-th affine mean curvature.     

Limit Cycle Bifurcations Of A Kind Of Lienard System With A Hypobolic Saddle And A Nilpotent Cusp

This paper gives a general theorem on the number of limit cycles of a near Hamiltonian system with a heteroclinic loop passing through a hyperbolic saddle and a nilpotent cusp. Then we study a kind of Lienard systems of type (n,4) for 3<=n<=27 and obtain the lower bound of the maximal number of limit cycles for this kind of system.     

Note On The Utility Of A Theorem Of Leindler–Meir–Totik

Our purpose is to generalize and to extend a theorem of S. Sharma and S. K. Varma [15] concerning the order of approximation by Abel means in the Lipschitz norm. The proof is basically based on a simple extension of a general theorem of L. Leindler, A. Meir and V. Totik [6] related to approximation by finite summability methods. This revised version was published online in June 2006 with corrections to the Cover Date.     

Existence And Uniqueness Of A Traveling Wave Front Of A Model Equation In Synaptically Coupled Neuronal Networks

Consider the model equation in synaptically coupled neuronal networks@u@t+ m(u − n)= ( − au) Z 10(c) ZRK(x − y)H uy, t −1c|x − y| − dydc+ ( − bu) Z 10( ) ZRW(x − y)H(u(y, t − ) − )dyd.In this model equation, u = u(x, t) stands for the membrane potential of a neuron at position x andtime t. The kernel functions K 0 and W 0 represent synaptic couplings between neurons insynaptically coupled neuronal networks. The Heaviside step function H = H(u − ) represents thegain function and it is defined by H(u − ) = 0 for all u < , H(0) = 12 and H(u − ) = 1 for allu > . The functions and represent probability density functions. The function f(u) m(u − n)represents the sodium current, where m > 0 is a positive constant and n is a real constant. Theconstants a 0, b 0, 0, 0 and > 0 represent biological mechanisms. This model equationis motivated by previous models in synaptically coupled neuronal networks.We will couple together intermediate value theorem, mean value theorem and many techniquesin dynamical systems to prove the existence and uniqueness of a traveling wave front of this modelequation. One of the most interesting and difficult parts is the proof of the existence and uniquenessof the wave speed. We will introduce several auxiliary functions and speed index functions to provethe existence and uniqueness of the front and the wave speed.     

Adjacent Extreme Points Of A Transportation Polytope

The adjacent extreme points of a Transportation Polytope are characterized by the circuit s contained in the support of its vertices. This result generalizes the Balinski and Russakoff [4] result on the Assignment Polytope     

关于任意随机适应序列部分和的一类局部极限定理

研究任意随机适应序列部分和的一类局部极限定理,推广了最近发表的几个结果．     

一类非定常对流占优扩散问题差分-流线扩散法的后处理

讨论了一类非定常对流占优扩散方程的差分-流线扩散格式(FDSD),利用插值后处理技术,提高了特殊网格下该FDSD格式在双线性元空间的精度,从而按L∞(L2(Ω) 模达到最优．     

Control And Synchronization Of Julia Sets Generated By A Class Of Complex Time-delay Rational Map

In this paper, a class of complex time-delay rational map is studied by analyzing the fractal and dynamical properties of its corresponding Julia sets (CTRM-Julia sets for short). By utilizing these given properties, a hybrid control method which contains both state feedback and parameters perturbation is applied to achieve the boundary control of CTRM-Julia set. Moreover, the synchronization of two different CTRM-Julia sets is also investigated by using coupling method. The synchronization index method is applied to demonstrate the relationship between the degree of synchronization and the coupling strength. Numerical examples are given to verify the effectiveness of control and synchronization methods.     

A Measure Of Asymmetry For Positive Semidefinite Matrices

It is known that a continuous map is the gradient of a convex function if and only if it is cyclically monotone. Also, a differentiable map F is the gradient of a function if and only if the matrices F ′(x) are symmetric for all x in the domain. Based on this connection between symmetry and monotonicity, we define a measure of asymmetry for positive semidefinite matrices.     

A Class Of Counterexamples Concerning an Open Problem

Kenneth R. Davidson raised ten open problems in the book Nest Algebras. One of theseopen problems isProblem 7 If K（交集）AlgL is weak^* dense in AlgL, where K is the set of all compact operators in B(H）,is L completely distributive? In this note, we prove that there is a reflexive subspace lattice L on some Hilbert space, which satisfies the following conditions: (a)F(AlgL) is dense in AlgL in the ultrastrong operator topology, where F(AlgL) is the set of all finite rank operators in AlgL; (b) L isn‘t a completely distributive lattice. The subspace lattices that satisfy the above conditions form a large class of lattices. As a special case of the result, it easy to see that the answer to Problem 7 is negative.