关于多项式映射自同构恒等集的一个注记

本文给出了判定一个仿射代数集是否是一个自同构恒等集的充分条件.作为一个推论,我们给出了Mckay-Wang的一个问题的一个新证明.我们也给出了一些具体的例子来说明主要的定理.     

求解整数规划的单参数填充函数

本文给出了一个新的求解离散全局最优化问题的单参数填充函数,并给出了一个新的算法,同时给出了对几个测试问题的数据计算结果.     

截断切割问题的参数规划模型

对一个截断切割问题,本文给出了一个参数网络规划模型,总结了[3]中的解法,并给出了一个实例.     

从等周不等式谈Green公式的一个应用

Green公式给出了平面图形面积与曲线积分的关系,利用这种关系给出了平面曲线等周不等式的一个简捷证明,并给出了平面图形面积的一个近似计算公式以及两个教学计算实例.     

混合质点系的一类几何恒等式及其应用

首先给出了混合质点系的概念,然后又给出了关于混合质点系的一类几何恒等式,并且给出了一个有趣的应用.     

一个追逐问题的数学模型和matlab仿真

就两人绕正三角形的追逐问题建立起了两个数学模型:一个充分应用运动的周期性首先给出了两人共边的充要条件,然后直接给出在一个周期内两人共边的次数及起止时刻;另一个则利用初等数论的方法给出了两人共边的另一个充要条件.利用matlab长于计算和强大的绘图功能,分别给出了求解两个模型的matlab程序,通过动画仿真演示两个绕正三角形的追逐模型,并给出了二者同边的时间起止点和同边的次数.     

Choi不等式的一些研究和应用

1974年,Man-DuenChoi结合正定线性算子定义,给出了矩阵分析学中的一个重要不等式,这个不等式是Fiedler不等式的推广,利用一些正定矩阵的性质,给出Choi不等式的一个新的推到方法,并且用该不等式给出了Fiedler不等式的一个新证明.     

格矩阵的行列式与伴随矩阵

研究了格矩阵的行列式与伴随矩阵,给出了它们的一些代数性质,同时给出了由一个格矩阵构造一个传递矩阵的方法.     

基于矩阵初等变换的n元函数极值的快速判别法

给出了 n元函数极值的一个充分条件 ,并结合矩阵的初等变换建立了 n元函数极值的一种快速判别法 ,最后给出了一个例子     

缓增分布表示的一个直接证明（英文）

先给出了Schwartz空间的标准半范数族的一个等价的范数族,然后给出了缓增分布表示的一个直接证明.     

Well-posedness and blow-up for a modified two-component Camassa–Holm equation

In this article, we consider a newly modified two-component Camassa–Holm equation. First, we establish the local well-posedness result, then we present a precise blow-up scenario. Afterwards, we derive a new conservation law, by which and the precise blow-up scenario we prove three blow-up results and a blow-up rate estimate result.     

Expanding topological space,study and applications

In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to any fractal family of topological spaces is expanding. In particular, we prove that the more a topological space expands, the finer the topology of its indexed states is. Using multi-homeomorphisms over associated coproduct topological spaces, we define a locally expandable topological space and we prove that a locally expandable topological space has a topological expansion. Specifically, we prove that the fractal manifold is locally expandable and has a topological expansion.     

Optimal control of nonlinear evolution inclusions

In this paper, we study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control that illustrates the applicability of our results.This research was supported by NSF Grant No. DMS-88-02688.     

A conjecture on bipartite graphical regular representations

In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR.First, we find a natural obstruction that prevents a finite group from admitting a bipartite GRR. Then we give a complete classification of the finite groups satisfying this natural obstruction and hence not admitting a bipartite GRR. Based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite GRR.Next, we prove the existence of bipartite DRRs for most of the finite groups not admitting a bipartite GRR found in this paper. Actually, we prove a much stronger result: we give an asymptotic enumeration of the bipartite DRRs over these groups. Again, based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite DRR.     

Forecasting the integration of immigrants

In this research, we develop and introduce a theoretical and mathematical forecasting framework of immigrant integration using immigrant density as a single driver. First, we introduce the integration concepts we aim at forecasting. Thereafter, we introduce a theoretical and mathematical model of the relationship between integration and immigrant density. Based on this model, we develop a methodological forecasting framework. We test the framework using immigrant integration data from Spain. We produce the forecasts, and conduct the proper evaluation of them. Finally, we conclude with a brief discussion of the wider implications of our results.     

Asymptotic behaviour of a closed‐loop thermosyphon with linear friction and viscoelastic binary fluid

Viscoelastic fluids represent a major challenge both from an engineering and from a mathematical point of view. Recently, we have shown that viscoelasticity induces chaos in closed‐loop thermosyphons even when we consider binary fluids, this is, when we consider a solute in the fluid, as water and antifreezes, for example. In this work, we consider a linear friction law, and we show that in this case with the addition of a solute to the fluid we can prove, under some conditions, chaotic asymptotic behavior for suitable geometry of the circuit and heat flux or ambient temperature functions.     

Nonlinear elliptic differential equations with multivalued nonlinearities

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).     

A kinetic formulation for a model coupling free surface and pressurised flows in closed pipes

The aim of this paper is to present a kinetic formulation of a model for the coupling of transient free surface and pressurised flows. Firstly, we revisit the system of Saint-Venant equations for free surface flow: we state some properties of Saint-Venant equations, we propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises (in some general case) an energy and preserves the still water steady state. Secondly, we propose a model for pressurised flows in a Saint-Venant-like conservative formulation. We then propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises in any case an energy and preserves the still water steady state. Finally, we propose a dual model that couples these two types of flow.     

Properties of the Michaelis-Menten mechanism in phase space

We study the two-dimensional reduction of the Michaelis-Menten reaction of enzyme kinetics. First, we prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Second, we determine the concavity of all solutions in the first quadrant. Third, we establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we determine the asymptotic behaviour of the slow manifold at infinity. To this end, we show that the slow manifold can be constructed as a centre manifold for a fixed point at infinity.     

Some results concerning the state of bending for transversely isotropic plates

In this paper, we present a series of basic theorems for transversely isotropic plates characterized by a state of bending. More precisely, we show a reciprocal theorem and a uniqueness result without positive definiteness assumptions on the elastic coefficients. Moreover, we establish some variational and minimum principles. Finally, we give a Galerkin representation of the solution. Copyright © 2009 John Wiley & Sons, Ltd.