数形结合(待续)

数形结合（待续）晨旭（接上期）例１０（１９９０年理科）设函数ｙ＝ａｒｃｔｇｘ的图象沿ｘ轴正方向平移２个单位所得到的图象是Ｃ，又设图象Ｃ＇与Ｃ关于原点对称，那么Ｃ＇的对应函数分析：与图象Ｃ对应的函数是Ｃ＇与Ｃ关于原点对称，所以，与Ｃ’对应的函数应解选（...     

具p-Laplacian算子型奇异边值问题多重正解

本文讨论了一类具ｐ－Ｌａｐｌａｃｉａｎ算子型奇异边值问题（φｐ（ｘ＇））＇＋ａ（ｔ）ｆ（ｘ（ｔ））＝０,ｘ（０）－βｘ（０′）＝ ０,ｘ（１）＋ δｘ′（１）＝０多重正解的存在性,其中φｐ（ｘ）＝｜ｘ｜ｐ－２ｘ,ｐ＞１ 通过使用不动点指数定理, 在适当的条件下,建立了这类边值问题存在多重正解的充分条件．这些结果能被用来研究椭圆边值问 题多重径向对称解的存在性．     

一个高阶边值问题

本文考虑如下高阶多点边值问题：ｘ（ｎ）＝ｆ（ｔ，ｘ，ｘ＇，…，ｘ（ｘ－１），ｘ（０）＝ｘ（ξ）＝（１）＝ｘ＇（ξ）＝…＝ｘ（ｎ－３）（ξ）＝０，其中ξ∈（０，１）．对于ｆ有非线性增长的情况，利用基于度理论的不动点定理，建立了某些存在唯一性定理．     

多总体球性检验的似然比准则的非零渐近分布

多总体球性检验的似然比准则的非零渐近分布龚力强（华南建设学院西院广州５１０４０５）关键词：多总体球性；似然比检验；渐近分布ＡＭＳ（１９９１）主日分类：６２Ｅ２０．设ｘ。１，ｘ。。，…，ｘ；《１＝１，２，…，ｚ；Ｎ；＞户）为从卢维正态总体Ｎｐ（８，工）...     

强迫二阶非线性泛函微分方程解的振动性与渐近性

本文讨论强迫二阶非线性泛函微分方程（ａ（ｔ）ｘ＇（ｔ））＇＋ｐ（ｔ）ｆ（ｘ（ｔ），ｘ（ｑ（ｔ）））＝ｒ（ｔ）解的振动性与渐近性。所得结论改进和推广了已知的一些结果。     

一类二阶非线性微分方程的求积问题

讨论了二阶非线性微分方程ｙ″＋ｐ（ｘ）ｙ′＋Ｗ＇（ｙ）／Ｗ（ｙ）ｙ＇＾２＝Ｑ（ｘ）１／Ｗ（ｙ）Ｆ［ｘ，（ｙ＇Ｗ（ｙ）＾ａ］的可积性问题，提供了可积的一些充分条件，在Ｆ为某些特殊类型时，给出能解公式。     

一类微分差分方程的周期解

本文研究微分差分方程ｘ＇（ｔ）＝－ｆ（ｘ（ｔ），ｘ（ｔ－τ１））－ｆ（ｘ（ｔ），ｘ（ｔ－τ２））－．．．－ｆ（ｘ（ｔ），ｘ（ｔ－τｎ））非平凡周期解的存在性问题，得到了一些判别准则，推广和改进了文［１－４］的工作。     

Banach空间微分包含解的存在性和延拓定理

研究一类微分包含９集值微分方程）ｘ＇（ｔ）∈Ｆ（ｔ，ｚ），ｘ（ｔ０）＝ｘ０解的存在性，证明了解的存在和延拓定理。     

6p阶可解对称图的分类

设ｘ是简单无向图，Ｇ是Ａｕｔ（Ｘ）的一个于群，Ｘ称为Ｇ－对称的，如果Ｇ在ｘ的１－孤（即两相邻顶点构成的有序偶）集合上的作用是传递的；ｘ称为对称图，如果Ｘ是Ａｕｔ（ｘ）－对称的；ｘ称为可解对称的，如果Ａｕｔ（Ｘ）包含可解子群Ｇ，使Ｘ是Ｇ－对称的．本文给出了具有６Ｐ个顶点的可解对称图的一个分类，这里ｐ≥５是素数．     

非对称条件下的Chover重对数律

（Ｘｉ，ｉ＝１，２，．．．）是ｉ，ｉ，ｄ ｒｖ序列，Ｘ１的分布函数为Ｆ（ｘ），Ｆ（ｘ）是对称的特征指数为α的稳定分布时，Ｊ．Ｃｈｏｖｅｒ（１９６６）建立了一个部分和的重对数律，本文将Ｃｈｏｖｅｒ重对数律推广到一般非对称稳定条下。     

Compact Operators on Homogeneous Banach Spaces of Distributions on Locally Compact Abelian Groups

In this paper, two theorems about the compactness of almost invariant operators on homogeneous Banach spaces of distributions (in the sense of Feichtinger [11]) defined on a locally compact abelian group are proved. Our theorems generalize the corresponding results of K. de Leeuw [3] and Tewari and Madan [18] for operators on homogeneous Banach spaces on the circle group and Segal algebras on a compact abelian groups, respectively.AMS Subject Classification 2000: 43A85, 47B07.     

A CLASS OF HOMOGENEOUS SEMISIMPLE SPACES

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒａ１１ｔｅｎｓｏｒｆｉｅｌｄＩｏｎａｓｍｏｏｔｈｍａｎｉｆｏｌｄＭ．Ｔｈｅｎａｔｕｒａｌｇｅｎｅｒａｌｉｚａｔｉｏｎｏｆｔｈｅｃｏｍｐｌｅｘｓｔｒｕｃｔｕｒｅａｎｄｐａｒａｃｏｍｐｌｅｘｓｔｒｕｃｔｕ...     

Multi-vector Spherical Monogenics, Spherical Means and Distributions in Clifford Analysis

New higher-dimensional distributions have been introduced in the framework of Clifford analysis in previous papers by Brackx, Delanghe and Sommen. Those distributions were defined using spherical co-ordinates, the ＂finite part＂ distribution Fp x＋^μ on the real line and the generalized spherical means involving vector-valued spherical monogenics. In this paper, we make a second generalization, leading to new families of distributions, based on the generalized spherical means involving a multivector-valued spherical monogenic. At the same time, as a result of our attempt at keeping the paper self-contained, it offers an overview of the results found so far.     

一类广义齐次Moran集的Hausdorff维数

本文构造了一类具有类似高维Moran结构的集合,给出一些充分条件来计算其Hausdorff维数.     

Joint extensions in families of contractive commuting operator tuples

In this paper we systematically study extension questions in families of commuting operator tuples that are associated with the unit ball in Cd.     

Old and New on the Laplace-Beltrami Derivative

The (strong) Laplace-Beltrami derivative and related operators appear quite frequently in many problems involving Fourier series, spherical harmonics, approximation of functions and smoothness. This article intends to provide an overview with updates on such operators. While most of the results concerning the Laplace-Beltrami derivative found in the literature are stated in the three-dimensional setting, our approach includes higher-dimensional spheres. We present proofs for results which are labeled as known but are just mentioned elsewhere. Spherical moduli of smoothness and decay rates for eigenvalues of integral operators are also among the covered topics.     

A generalization of 2-homogeneous continua being locally connected

An elementary proof is given that if each pair of points of a homogeneous metric continuum can be mapped by a homeomorphism into an arbitrarily small connected set, then the continuum is locally connected.

     

Extendibility of homogeneous polynomials on Banach spaces

We study the -homogeneous polynomials on a Banach space that can be extended to any space containing . We show that there is an upper bound on the norm of the extension. We construct a predual for the space of all extendible -homogeneous polynomials on and we characterize the extendible 2-homogeneous polynomials on when is a Hilbert space, an -space or an -space.

     

Spherical functions and immanants

Let λ be an irreducible character of S_n corresponding to the partition (r,s) of n. Let A be a positive semidefinite Hermitian n × n matrix. Let d_λ(A) and per(A) be the immanants corresponding to λ and to the trivial character of S_n, respectively. A proof of the inequality dλ(A)≤λ(id)per(A) is given.     

球面闭曲线和Jacobi定理

回答了W.Fenchel所提出的一个问题.给出球面闭曲线的一个整体性质,并用以推广关于空间闭曲线的Jacobi定理.