Volume of unit ball in an n-dimensional normed space and its asymptotic properties

Let Bp^n={x∈R^b｜‖x‖p≤1} be the unit ball of p norm in the n-dimensional normed space εp＆n.The formula for the volume of Bp^n was obtained and its asymptotic properties were found out as n→∞and p→∞.

Solutions of Laplace Equation in n-Dimensional Spaces

The solutions of the Laplace equation in n-dimensional space are studied. The angular eigenfunctions have the form of associated Jacob/polynomials. The radial solution of the Helmholtz equation is derived.

使用UB-tree索引时态XML

如何在XML文档中表达时间相关的数据,跟踪历史信息和恢复文档在以前任意时刻的状态的问题,在最近的研究中受到不少的关注。许多文献提出了各种不同的模型。我们将这一类的问题归为索引时态XML文档的问题。本文将时态XML文档转换到n维空间的节点和直线,使用UB-tree对这些n维空间的节点和直线进行索引,并针对时态查询提出了新的查询算法。通过实验证明,这样的索引比之前针对时态模型提出的索引具有更好的性能。

关于单形稳定性的几何不等式的改进

利用距离几何论和几何不等式理论,研究了在En中,n维单形的几何不等式的稳定性,证明了n维单形宽度的Sallee-Alexander不等式和张-杨不等式的推广形式,并给出了n维单形几何不等式的稳定性版本.

Decay of a Mass-Less Field Far from Horizon of a Black Hole

Far from the horizon of a black hole of even space dimension n, a mass-less field decays as t1-2t-n in the time, where 1 is a harmonic mode of the sphere.

Unified Treatment of Screening Coulomb and Anharmonic Oscillator Potentials in Arbitrary Dimensions

A mapping is obtained relating radial screened Coulomb systems with low screening parameters to radial anharmonic oscillators in N-dimensional space. Using the formalism of supersymmetric quantum mechanics, it is shown that exact solutions of these potentials exist when the parameters satisfy certain constraints.

一类n-维单个守恒律的黎曼问题(英文)

借助于广义平面波解,解析地求解了一类n-维的单个守恒律的黎曼问题,所获得的解展示了两种不同的几何结构,包括一个中心疏散波和一个激波.

Explicit constants for Hardy’s inequality with power weight on n-dimensional product spaces

In this paper, Hardy operator H on n-dimensional product spaces G = (0, ∞)n and its adjoint operator H* are investigated. We use novel methods to obtain two main results. One is that we characterize the sufficient and necessary conditions for the operators H and H* being bounded from Lp(G, xα) to Lq(G, xβ), and the bounds of the operators H and H* are explicitly worked out. The other is that when 1 < p = q < +∞, norms of the operators H and H* are obtained.

Endpoint estimates for n-dimensional Hardy operators and their commutators

In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.

Commutators of n-dimensional rough Hardy operators

In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.

Best constants for Hausdorf operators on n-dimensional product spaces

In this paper, we study certain Hausdorff operators in the high-dimensional product spaces. We obtain their power weighted boundedness from Lp to Lq and characterize the necessary and sufficient conditions for their boundedness on the power weighted Lp spaces. Moreover, in the case p = q, we obtain the sharp bound constants.

Schur Convexity for Two Classes of Symmetric Functions and Their Applications

respectively, where r = 1, 2, … , n, and il, i2, … , is are positive integers. In this paper, the Schur convexity of Fn（X, r） and Gn（x, r） are discussed. As applications, by a bijective transformation of independent variable for a Schur convex function, the authors obtain Schur convexity for some other symmetric functions, which subsumes the main results in recent literature; and by use of the theory of majorization establish some inequalities. In particular, the authors derive from the results of this paper the Weierstrass inequalities and the Ky Fan＇s inequality, and give a generalization of Safta＇s conjecture in the n-dimensional space and others.

Hochschild cohomology of Beilinson algebra of exterior algebra

Let An be the Beilinson algebra of exterior algebra of an n-dimensional vector space, which is derived equivalent to the endomorphism algebra Endox （T） of a tilting complex T = II^ni=0^Ox （i） of coherent COx-modules over a projective scheme X = P^nk. In this paper we first construct a minimal projective bimodule resolution of An, and then apply it to calculate k-dimensions of the Hochsehild cohomology groups of An in terms of parallel paths. Finally, we give an explicit description of the cup product and obtain a Gabriel presentation of Hochschild cohomology ring of An. As a consequence, we provide a class of algebras of finite global dimension whose Hochschild cohomology rings have non-trivial multiplicative structures.

Kinematic Formulas of Total Mean Curvatures for Hypersurfaces

kinematic Euclidean By using the moving frame method, the authors obtain a kind of asymmetric formulas for the total mean curvatures of hypersurfaces in the n-dimensional space

Orientable Small Covers over a Product Space

A small cover is a closed manifold M^n with a locally standard （Z2）^n-action such that its orbit space is a simple convex polytope P^n. Let A^n denote an n-simplex and P（m） an m-gon. This paper gives formulas for calculating the number of D-J equivalent classes and equivariant homeomorphism classes of orientable small covers over the product space △^n1 × △^n2 × P（m）, where n1 is odd.