具有广义FGM相依结构的复合泊松过程的Esscher定价泛函

本文考虑索赔额与等待时间具有广义FGM相依结构的复合泊松过程,仿照文献[5]的方法,求出了其矩母函数的显式表达式,给出了其矩母函数的n阶导数的计算方法,并最终求出了其Esscher定价泛函．     

组合分布在求解直线上n步随机游动首次通过问题上的应用

基于组合过程模型给出其轨道对目标集的首次通过概率及首中点的分布函数 ,并由此给出直线上n步随机游动的首次通过概率及首中点分布函数的一类显式 .     

非负曲率流形的体积增长估计

本文利用非负曲率流形上的Busemann函数和穷竭函数的性质,得出了在某紧致子集外满足一定非负曲率条件的完备非紧的(复) n维K■hler流形的体积增长至少是n次的．推广了陈兵龙和朱熹平教授新近的一个结果．     

数列[(n!)~(1/n)/n]的单调有界性及其极限

数列nn !n 是严格单调递减的 ,且有 1e 相似文献   

(n+1)重周期和准周期Riemann边值问题

该文首先考虑了Rⁿ⁺¹维欧氏空间中(n+1)重周期正则函数和(n+1)重准周期正则函数的一些性质, 然后分别讨论了n+1重周期和准周期Riemann边值问题, 分别给出了两种边值问题 解的显式表达式和可解条件.     

K(n,-n,2n)方程的显式行波解及其动力学性质

利用动力系统分支理论和定性理论研究了K(n,-n,2n)方程的显式行波解.并借助于行波解动力学性质对这些解进行取舍,指出一些精确的显式解可能会给出一些错误的信息,即在求解精确的显式行波解前理解该行波解的动力学行为的必要性.文章最后通过数值模拟验证了相关的结论.     

四元数分析中正则函数与非齐次n阶程(e)nF/(e)(z)n=f的某些边值问题

主要讨论了四元数空间中正则函数与非齐次n阶方程(e)nw/(e)(z)n=f在超球上的Dirichlet问题和双圆柱上具有任意整数指标的Riemann-Hilbert问题,给出了可解条件和解的积分表示式.     

n阶常系数线性非齐次微分方程及欧拉方程的通解的一种显式表达式

§1引言对于形如y~((n))+p_1y~((n-1))+p_2y~((n-2))+…+p_(n-1)y＇+p_ny=f(x)的微分方程[其中P_i(i=1,2,…,n)为常数],若能求出其对应齐次方程的n个特征根,则很容易写出该齐次方程的通解Y(x)的显式表达式。     

n元随机变量联合分布的分解

定义和研究了函数Sum(n,t),并借助于此以模n剩余类环上函数的频谱理论为工具解决了n元随机变量联合分布的分解问题。     

求n元二次式极值的纯矩阵方法

极值问题是实际工作中经常遇到的问题。《n元二次式的极值问题》(赵祖舜,《数学通报》1992年第二期)一文,利用化二次型为标准形和配方,得到了判别n元二次式是否存在极值,和求出极值的一个方法。但按照该方法求一个n元二次式极值,要分四步来完成。本文目的是提出一个更     

只有一个B—函数的完备黎曼流形

讨论了只有一个Ｂｕｓｅｍａｎｎ函数的完备非紧黎曼流形的几何拓扑性质。     

关于H. Wu问题

著名几何学家Ｈ．Ｗｕ在「４」中提出这样的问题：若一完备非紧的黎曼流形仅有两个符号相反的Ｂｕｓｅｍａｎｎ函数,则该流形的结构如何？本文在流形具非负Ｒｉｃｃｉ曲率或截曲率具下界的情况下部分地解决了这一问题。同时还讨论了流形在具非负曲率条件下有关的一些性质。     

Busemann Functions and Barrier Functions

On a smooth, non-compact, complete, boundaryless, connected Riemannian manifold there are two kinds of functions: Busemann functions with respect to rays and barrier functions with respect to lines (if there exists at least one). In this paper we collect some known properties on Busemann functions and introduce some new fundamental properties on barrier functions. Based on these properties of barrier functions, we could define some relations on the set of lines and thus classify them. With the equivalence relation we introduced, we present a generalization of a rigidity conjecture.     

A new proof of the rigidity problem

In this short note we give a new proof of the boundary rigidity problem in a Euclidean setting proved by Croke. Our method is based on the differentiability of Busemann functions and the characteristic of Euclidean metric on Riemannian manifolds without conjugate points.

     

Metric projections versus non-positive curvature

In this paper two metric properties on geodesic length spaces are introduced by means of the metric projection, studying their validity on Alexandrov and Busemann NPC spaces. In particular, we prove that both properties characterize the non-positivity of the sectional curvature on Riemannian manifolds. Further results are also established on reversible/non-reversible Finsler–Minkowski spaces.     

Geometry of manifolds with densities

We study the geometry of complete Riemannian manifolds endowed with a weighted measure, where the weight function is of quadratic growth. Assuming the associated Bakry–Émery curvature is bounded from below, we derive a new Laplacian comparison theorem and establish various sharp volume upper and lower bounds. We also obtain some splitting type results by analyzing the Busemann functions. In particular, we show that a complete manifold with nonnegative Bakry–Émery curvature must split off a line if it is not connected at infinity and its weighted volume entropy is of maximal value among linear growth weight functions.     

Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below: I

We investigate the finiteness structure of a complete non-compact n-dimensional Riemannian manifold M whose radial curvature at a base point of M is bounded from below by that of a non-compact von Mangoldt surface of revolution with its total curvature greater than π. We show, as our main theorem, that all Busemann functions on M are exhaustions, and that there exists a compact subset of M such that the compact set contains all critical points for any Busemann function on M. As corollaries by the main theorem, M has finite topological type, and the isometry group of M is compact.     

Minimal rays on closed surfaces

Given an arbitrary Riemannian metric on a closed surface, we consider length-minimizing geodesics in the universal cover. Morse and Hedlund proved that such minimal geodesics lie in bounded distance of geodesics of a Riemannian metric of constant curvature. Knieper asked when two minimal geodesics in bounded distance of a single constant-curvature geodesic can intersect. In this paper we prove an asymptotic property of minimal rays, showing in particular that intersecting minimal geodesics as above can only occur as heteroclinic connections between pairs of homotopic closed minimal geodesics. A further application characterizes the boundary at infinity of the universal cover defined by Busemann functions. A third application shows that flat strips in the universal cover of a nonpositively curved surface are foliated by lifts of closed geodesics of a single homotopy class.     

On tori without conjugate points

Summary In this paper we consider Riemannian metrics without conjugate points on an n-torus. Recent work of J. Heber established that the gradient vector fields of Busemann functions on the universal cover of such a manifold induce a natural foliation (akin to the weak stable foliation for a Riemannian manifold with negative sectional curvature) on the unit tangent bundle. The main result in the paper is that the metric is flat if this foliation is Lipschitz. We also prove that this foliation is Lipschitz if and only if the metric has bounded asymptotes. This confirms a conjecture of E. Hopf in this case.Oblatum 22-IX-1993 & 25-IV-1994Supported in part by NSF grant #DMS90-01707 and #DMS85-05550 while at MSRISupported by an NSF Postdoctoral Fellowship     

Geodesic rays,Busemann functions and monotone twist maps

We study the action-minimizing half-orbits of an area-preserving monotone twist map of an annulus. We show that these so-called rays are always asymptotic to action-minimizing orbits. In the spirit of Aubry-Mather theory which analyses the set of action-minimizing orbits we investigate existence and properties of rays. By analogy with the geometry of the geodesics on a Riemannian 2-torus we define a Busemann function for every ray. We use this concept to prove that the minimal average action A() is differentiable at irrational rotation numbers while it is generically non-differentiable at rational rotation numbers (cf. also [18]). As an application of our results in the geometric framework we prove that a Riemannian 2-torus which has the same marked length spectrum as a flat 2-torus is actually isometric to this flat torus.