具有渐近非负Ricci曲率和无穷远处二次曲率衰减的流形

本文首先给出了具有渐近非负Ricci曲率流形的体积比较定理.然后给出了流形在一定的曲率衰减的条件下为有限拓扑型的引理,最后利用Abresch-Gromoll估计,给出了具有渐近非负Ricci曲率和无穷远处二次曲率衰减的流形的有限拓扑型条件.     

非紧完备的K(a)hler流形上的嵌入问题

本文证明了任一n维的非紧完备,具有有限拓扑型的Kahler流形,若它的Ricci曲率为正的,有限的且陈氏示性数有限,则它双全纯等价于拟射影代数簇.     

非紧完备的Khler流形上的嵌入问题

本文证明了任一n维的非紧完备,具有有限拓扑型的Kahler流形,若它的Ricci曲率为正的,有限的且陈氏示性数有限,则它双全纯等价于拟射影代数簇.     

Excess函数的应用

在本文中，我们研究了曲率有下界的开流形的拓扑，并推广了文[7]中的结果，证明了截曲率有下界的开流形如果它的excess函数被它的临界半径的某个函数所界定时，它就具有有限拓扑型或者微分同胚于R^n．     

K(a)hler流形上的单值化定理

本文研究了完备非紧且Ricci曲率正有界的n维K(a)hler流形上的单值化问题,利用Sobolev不等式,L2估计和Bézout估计和Gauss-Bonnet积分方法,得到了一个单值化定理,推广了流形为有限拓扑型的结果.     

小Excess与开流形的拓扑

本文中，我们应用比较几何的方法研究开流形的Excess与其拓扑之间的关系，我们证明了对于一个曲率下有界的开流形，当它的Excess被临界半径的某个函数所界定时，它就有有限拓扑型或微分同胚于n维z欧氏空间。     

广义典型流形的实例构作

陈述了广义典型流形(或拓扑域流形)的概念,并构作了拓扑域流形的若干实例,丰富了这类流形的内容,也给今后研究和运用拓扑域流形提供一些参考.     

完备非紧具非负曲率流形之拓扑结构

本文给出完备非紧具非负曲率的Riemann流形具有限拓扑型的一个简单证明.     

流形的去核乘积

一个拓扑空间X的k重去核乘积,指的是把乘积空间X~k中全部形如(x,…,x)的点去掉后所得到的子空间.吴文俊在[1]中提出了有限可剖分空间的一个新拓扑不变量,其中包括该空间的去核乘积的伦型,即有限可剖分空间的k重去核乘积的伦型是原空间的拓扑不变量,而且一般非同伦不变.[1]还提出在流形的范畴中,这个新拓扑不变量是否有新的意义的问题.本文指出,对于某一类流形来说,它的k重去核乘积的上同调群、同调群以及同伦     

完备非紧具非负曲率流形之拓扑结构

本文给出完备非紧具非负曲率的Ｒｉｅｍａｎｎ流形具有限拓扑型的一个简单证明     

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.     

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.     

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.     

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.     

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.     

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.     

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).     

Dynamic hemivariational inequality modeling viscoelastic contact problem with normal damped response and friction

In this article we examine an evolution problem, which describes the dynamic contact of a viscoelastic body and a foundation. The contact is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form. First we derive a formulation of the model in the form of a multidimensional hemivariational inequality. Then we establish a priori estimates and we prove the existence of weak solutions by using a surjectivity result for pseudomonotone operators. Finally, we deliver conditions under which the solution of the hemivariational inequality is unique.     

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.     

基于跳扩散过程的可转换债券的定价

本文标的股票的方程采用跳扩散方程,首先规定一个跳跃的涨跌区间,这样就可以很快的找出跳跃点,我们根据跳跃点将股价聚类,然后把各个类看成是总体中抽取出来的一个样本,我们就可以估计出跳扩散方程中的所有参数.由于我们的标的股票的方程是含跳过程,因此无法找出完全保值的自融资策略,但我们可以根据风险最小化的原理给出可转换债券的价格,最后运用Monte Carlo模拟计算出了南京水运转债在0时刻的价格。