SPHERICAL SIMPLICES AND THEIR POLARS

This article is about spherical simplices in the unit sphere.One of the purposes is to give a relation of dihedral anglesof a spherical simplex and its polar, and the other is to givetwo simple formulae of volumes of spherical simplices and theirpolars. We can calculate the volume of a spherical simplex andthe sum of volumes of it and its polar from these formulae forthe unit sphere in the odd- and even-dimensional Euclidean spaces,respectively.     

THE FOUR-DIMENSIONAL HYPERBOLIC SPHERICAL HARMONICS

In the four-dimensional hyperbolic space, we can derive Euler formula and establish the hyperbolic spherical polar coordinate and the hyperbolic spherical harmonics.     

ON THE GEOMETRY OF SPHERICAL VARIETIES

This is a survey article on the geometry of spherical varieties.     

復式乘積和球面乘積的關係

<正> 1.設X為一拓撲空間,以a_i表示X的n_i次同偷羣∏_(ni)(X)的一個元素.在球面乘積S~(n1)×…×S~(nr)中,最高次元的腔胞記為e~(n1+…+nr).在S~(n1)×…×S~(nr)中除去e~(n1+…+nr)而得一空間Y.設S~(nl)為nl次元球,為了印刷方便起見,把S~(nl)記作S(nl).在S(ni)中取一參考點x_i~o.設i_1相似文献   

齐性球对称分布的特征

设随机变量ｘ＝（ｘ１，…，ｘｎ）＇服从球对称分布，密度函数是ｃｎ［ｆ（ｘ＇ｘ）］＾ｇ（ｎ）。最后，将其中部分结果推广到多元球对称分布的情形。     

POINTWISE CONVERGENCE FOR EXPANSIONS IN SPHERICAL MONOGENICS

We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.     

球对称分布一些子类的特征函数

本文用统一的方法给出了对称Kotz型分布,多元PearsonⅡ分布和椭球logistic对称分布.我们的结果是Iyenger and Tong的结果的推广,另外我们得到了PearsonⅡ型的特征函数的另一种形式.同时,我们讨论了相关的问题.     

ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS

In this article,we study the first two eigenvalues of the higher order buckling problem on a domain in the unit sphere.We obtain an estimate on the second eigenvalue in terms of the first eigenvalue.In...     

BEST APPROXIMATION FOR WEIERSTRASS TRANSFORM CONNECTED WITH SPHERICAL MEAN OPERATOR

Using reproducing kernels for Hilbert spaces,we give best approximation for Weierstrass transform associated with spherical mean operator.Also,estimates of extremal functions are checked.