关于双曲空间中n维Pedoe不等式及应用

本文应用距离几何的理论与方法,研究了双曲空间中n维单形的几何不等式问题,建立了双曲空间中涉及两个单形棱长的n维Pedoe不等式和彭-常不等式,由此获得双曲空间n维单形的一些新的不等式.     

高维Neuberg-Pedoe不等式的推广

对欧氏空间 En中的两个 n维单形 ,给出了著名的 Neuberg-Pedoe不等式的高维推广 ,从而推广和改进了已有一些文献中的结论 .     

On a Generalization of the Hermite Constant

We report some results on the theory of quasiperiodic sphere packings controlled by a finite group G in the n-dimensional Euclidean space, constructed by means of an higher dimensional Euclidean space which contains G-invariant lattices. A generalization of the Hermite constant is used to find upper bounds of the density.     

关于单形一个对偶式的商榷与两个新的对偶式

讨论了n维欧氏空间E^n中n维单形不等式的对偶式．利用距离几何理论与解析方法，建立了n维单形两个不等式的对偶式，指出了最近所建立的单形Finsler-Hadwiger不等式的A维对偶式是错误的．     

Laguerre minimal surfaces in ℝ3

Laguerre geometry of surfaces in R^3 is given in the book of Blaschke, and has been studied by Musso and Nicolodi, Palmer, Li and Wang and other authors. In this paper we study Laguerre minimal surface in 3-dimensional Euclidean space R^3. We show that any Laguerre minimal surface in R^3 can be constructed by using at most two holomorphic functions. We show also that any Laguerre minimal surface in R^3 with constant Laguerre curvature is Laguerre equivalent to a surface with vanishing mean curvature in the 3-dimensional degenerate space R0^3.     

关于n维单形的两个轨迹定理

在n维欧氏空间En中,应用向量方法,给出了关于n维单形的两个优美的轨迹定理.     

A Class of Schur Convex Functions and Several Geometric Inequalities

Schur convexity, Schur geometrical convexity and Schur harmonic convex-ity of a class of symmetric functions are investigated. As consequences some known inequalities are generalized. In addition, a cl...     

凸域上拟双曲测地线直径的Gehring-Hayman 恒等式

利用型函数和最大项m（σ）的几何意义研究全平面上Dirichlet级数的增长性,得到了Dirichlet级数增长性与系数、指数之间关系的四个结论,推广了以往研究增长性的相关结果.     

Strong Solutions and Pathwise Control for Non-Linear Stochastic system with Poisson Jumps in n-Dimensional Space

The existence of a pathwise unique strong solution for the stochastic differential equation (S. D. E. ) with Poisson jumps in n-dimensional space without continuity assumption on drift coefficient, which even can be greater than linear growth, and without Lipsehitz condition on diffusion coefficients is obtained. Then the existence of a p athwise stochastic optimal Bang-Bang control for a very much non-linear systemwith Poisson jumps in w-dimensional space is derived. The result is also applied to obtain a maximum likelihood estimate (MLE) of parameter for some continuous,S. D. E. with non-Lipschitz cefficients in n-dimensional space.     

球面空间单形的两个几何不等式（英文）

In this paper, by using the theory and method of distance geometry, we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length and volume of one simplex and the volume,height and(n-1)-dimensional volume of the side of another simplex in the n-dimensional spherical space. They are the extensions of the results [10] in the n-dimensional Euclidean geometry to the n-dimensional spherical space.     

The octahedron theorem in Minkowski three-space a metric vector space proof of Miquel's theorem in the Laguerre plane

As is well known [1, p.480], the cycles and spears of the real Laguerre plane can be represented by the points and null planes of three-dimensional Minkowski space. Miquel's theorem in the Laguerre plane can then be expressed as an intrinsically interesting Minkowski space theorem the octahedron theorem. We outline the correspondence between the two theorems, and then give a metric vector space proof of the octahedron theorem, thereby providing an alternate proof of Miquel's theorem. We then discuss the generalization of both theorems to more general spaces.     

Some constructions of divisible designs from Laguerre geometries

In the nineties, A.G. Spera introduced a construction principle for divisible designs. Using this method, we get series of divisible designs from finite Laguerre geometries. We show a close connection between some of these divisible designs and divisible designs whose construction was based on a conic in a plane of a three-dimensional projective space.     

Some Linear Functionals Having Classical Orthogonal Polynomials as Moments

In this paper, we deal with some linear functionals on the vector space of polynomials whose moments are, in certain normalization, classical orthogonal polynomials (Hermite, Laguerre and Gegenbauer). We show that these linear functionals are semiclassical of class, at most, three. We give the coefficients in the three-term recurrence relations that the corresponding monic orthogonal polynomial sequences satisfy.     

高维情形的Routh定理

本文研究了n维欧氏空间En中n维单形的体积有关问题.利用距离几何的理论与解析方法,建立了n维情形的Routh定理,作为其特例建立了n维情形的Ceva定理.     

Rigidity and stability of submanifolds with entropy close to one

Geometriae Dedicata - We show that an n-dimensional surface whose entropy is close to that of an n-dimensional plane is close in Hausdorff distance to some n-dimensional plane at every scale....     

再论Pedoe不等式的高维推广及应用

本文对欧氏空间E~n中的两个n维单形,给出了著名的Pedoe不等式的一个实质性推广,并讨论了它的应用.     

关于高维单形的两个性质

应用度量几何理论与解析方法,研究了n维欧氏空间En中n维单形的性质,将三角形内心与中线两个性质推广到n维单形,获得n维单形内心与中位面的两个性质.     

局部域上的Herz型Besov空间

令K为局部域,Kn为K上n维向量空间.本文讨论Herz型Besov空间Kaq,pBsβ(Kn)的某些性质.     

Picard-Zahlen komplexer Tori

We give explicit equations for the calculation of Chern classes of holomorphic line bundles on a complex torus X. As easy applications we deduce properties of the Picard numbers ρ(X) of n-dimensional tori, when the complex structure changes. The tori with ρ(X)≥k form a countable union of analytic subsets in a moduli space M; furthermore the set of tori with ρ(X)=k is empty or dense in M. For n-dimensional tori one has O≤ρ(X)≤n², but for n≥3 not all numbers 0≤k≤n² occur as Picard numbers. We conclude our considerations with a list of examples and with some remarks about this gap phenomenon in the distribution of Picard numbers of complex tori.