Riemann面到复Grassmann流形的调和映射的构造

设φ是从Ｒｉｅｍａｎｎ面Ｍ到复Ｇｒａｓｓｍａｎｎ流形Ｇｋ，ｎ的调和映射．本文证得φ的Ｇａｕｓｓ丛之间的基本关系式．利用它和约化定理，证明了若干构造定理和调和序列的基本不等式，推广了Ｗｏｏｄ，Ｒａｍａｎａｔｈａｎ，Ｕｄａｇａｗａ，Ｂｕｒｓｔａｌｌ及Ｗｏｌｆｓｏｎ的相应结果．通过把迷向调和映射的Ｇａｕｓｓ丛作正交和，给出了从２维拓扑球到Ｇｋ，ｎ（２≤ｋ＜ｎ）的具有一切迷向阶的调和映射的例子，它们的曲率和Ｋａｈｌｅｒ角均为常值．     

拟欧氏空间IR_n~(n 2)中类空曲面的Gaus映照

本文讨论拟欧氏空间ＩＲｎ＋２ｎ中的类空曲面，利用Ｇａｕｓ映照给出这类曲面的一般表示公式，从而推广了Ａｋｕｔａｇａｗａ和Ｎｉｓｈｉｋａｗａ的结果．     

关于从曲面到复Grassmann流形中的调和映射

本文讨论从曲面到复Ｇｒａｓｓｍａｎｎ流形Ｇｋ，Ｎ中的调和映射，给出了调和序列中的基本直射变换与 因子分解中的基本旗变换的关系，从而证明了有阶的调和映射与有限的调和映射是一致的．     

复射影空间的实2-调和超曲面

本文研究了复射影空间中的实２－调和超曲面和实极小超曲面之间的关系,推广了Ｌａｗｓｏｎ Ｈ．Ｂ和Ｋｏｎ Ｍ．关于实极小超曲面的Ｐｉｎｃｈｉｎｇ结果     

关于超曲面上测度的Fourier变换的零点

设Ｓ是Ｅｕｃｌｉｄ空间Ｒ￣ｎ（ｎ≥２）中一个紧闭光滑超曲面，它关于原点中心对称，其Ｇａｕｓｓ曲率处处非零。设ｄμ是Ｓ上一个光滑正测度，是其Ｆｏｕｒｉｅｒ变换。本文证明，的零点集是一个紧集与可列多个微分同胚于单位球面的超曲面之无交并．     

关于超曲面上测度的Fourier交换的零点

设Ｓ是Ｅｕｃｌｉｄ空间Ｒ＾ｎ（ｎ≥２）中一个紧闭光滑超曲面，它关于原点中心对称，其Ｇａｕｓｓ曲率处处非零，设ｄμ是Ｓ上一个光滑正测度，ｄμ是其Ｆｏｕｒｉｅｒ变换，本文证明，ｄμ的零点集是一个紧集与可列多个微分同胚于单位球面的超曲面之无交并。     

De Sitter空间中紧致类空超曲面的积分公式及其Goddard猜想的应用

本文对ｄｅＳｉｔｅｒ空间Ｓｎ＋１１（１）中紧致类空超曲面建立Ｍｉｎｋｏｗｓｋｉ型公式，并给出其到ｒ－次（ｒ＝１，２，…，ｎ－１）平均曲率为常数超曲面的应用．当ｒ＝１时，我们得到Ｍｏｎｔｉｅｌ的结果．     

曲面到U（N）中有限的调和映射

本文证明了如果ｓ是从曲面Ω到Ｕ（Ｎ）中有限的调和映射，则Ａｚ，Ａｚ－是幂零的，并给出其逆不成立的反例。     

CP~n中的弱等焦Hopf超曲面

本文研究了ＣＰｎ中的弱等焦Ｈｏｐｆ超曲面的分类，弱等焦超曲面首先是由滕楚莲与Ｔｈｏｒｂｅｒｇｓｓｏｎ在［１３］中引入的，设 Ｍ是 ＣＰｎ中的弱等焦 Ｈｏｐｆ超曲面，则 Ｍ的不同焦半径的个数是 ２，４或６；并且当 ｇ＝ ２或 ４时， Ｍ在 ＣＰｎ中是等参的；当 ｇ＝ ６时，ｎ＝ ３，Ｍ＝π－１（Ｍ）与 Ｓ７中的等参超曲面不Ｌｉｅ等价，此处π：Ｓ７→ＣＰ３是Ｈｏｐｆ纤维化．     

欧氏空间中具有共形Gauss映照的曲面

本文考虑欧氏空间中具有共形Ｇａｕｓｓ映照的曲面．从Ｇａｕｓｓ映照的观点给出了 ｖｅｒｏｎｅｓｅ曲面的一个新特征．     

Permissible growth rates for Birkhoff type universal harmonic functions

A harmonic function H on is said to be universal (in the sense of Birkhoff) if its set of translates is dense in the space of all harmonic functions on with the topology of local uniform convergence. The main theorem includes the result that such functions, H, can have any prescribed order and type. The growth result is compared with a similar known theorem for G.D. Birkhoff's universal holomorphic functions and contrasted with known growth theorems for MacLane-type universal harmonic and holomorphic functions.     

Mutlhews-Sumner定理的证明

本文证明了：若Ｇ是２连通无爪图且δ（Ｇ）≥ｎ－２３，则Ｇ是Ｈａｍｉｌｔｏｎ图     

Growth estimates of conjugate harmonic polynomials in domains of the complex plane

For an arbitrary Jordan domain G one establishes an estimate of the norm of the operator of harmonic conjugation in spaces of harmonic polynomials of degree at most n, n=1, 2,....Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 772–777, June, 1990.     

关于简单MCD图

设G是阶为n的简单图，若G中没有两个等长圈且具有最大可能的边数，则称G为简单MCD图。本文通过引进路分解概念给出了两个关于图中圈数的结果并应用它们证明了下述定理：若G是简单MCD图，则G不是2连通可平面图且对所有整数n，除七个例外，G不是阶为n的含有同胚于K4的2连通图。     

應用正二次微分形式的理論於映照半徑之乘積

<正> §1.設G是z平面上的一個區域,a_1,a_2,…,a_n是G中的n個不同的有限點.G_1,…,G_n是G中的一組不相重叠的單連區域,a_ν∈G_ν(ν=1,2,…,n).又設x_1,x_2,…,x_n是一組正數.設R(a_ν,G_ν)是區域G_ν在a_ν的映照半徑,則R(a_ν,G_ν)≤≤4|a_ν—a_ν′|,(ν’≠ν).因此,當n>1時G_1,G_2,…,G_n儘管變動,     

Gelfand-Kirillov dimensions of the ℤ2-graded oscillator representations of \mathfrak{s}\mathfrak{l}(n)

We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl(n,F)-modules that appeared in the Z²-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand-Kirillov dimension. They contain weight modules with unbounded weight multiplicities and completely pointed modules.     

n-connectedness in pure 2-complexes

A graph is a 1-dimensional simplicial complex. In this work we study an interpretation of “n-connectedness” for 2-dimensional simplicial complexes. We prove a 2-dimensional analogue of a theorem by Whitney for graphs: Theorem (A Whitney type theorem for pure 2-complexes).Let G be a pure 2-complex with no end-triangles. Then G is n-connected if and only if the valence of e is at least n for every interior edge e of G, and there does not exist a juncture set J of less than n edges of G. Examples ofn-connected pure 2-complexes are then given, and some consequences are proved.     

Almansi decomposition for Dunkl operators

Let Ωbe a G-invariant convex domain in RN including 0, where G is a Coxeter group associated with reduced root system R. We consider functions f defined in Ωwhich are Dunkl polyharmonic, i.e. (△h)nf =0 for some integer n. Here △h=∑j=1N Dj2 is the Dunkl Laplacian, and Dj is the Dunkl operator attached to the Coxeter group G, where kv is a multiplicity function on R and σv is the reflection with respect to the root v. We prove that any Dunkl polyharmonic function f has a decomposition of the form f(x)=f0(x) |x|2f1(x) … |x|2(n-1)fn-1(x),(?)x∈Ω, where fj are Dunkl harmonic functions, i.e. △hfj = 0. This generalizes the classical Almansi theorem for polyharmonic functions as well as the Fischer decomposition.     

On an analogue of the runge theorem for harmonic differential forms

A variant of the classical theorem of Runge is established for harmonic differenrial forms on an open subset of ℝⁿ. It generalizes the case of analytic functions for n=2. Harmonic forms with point singularities are introduced, and a theorem of displacement of poles is proved. An integral representation analogous to the Cauchy formula is constructed. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 109–117.     

调和分析与信道编解码研究——献给陆善镇教授75华诞

信道编码是通信系统的关键技术之一,其传统的理论工具是代数和有限域GF（p）.本文在有噪信道的信道编码数学模型基础上,介绍基于调和分析的新型信道编码理论,分别应用调和分析的重要工具压缩感知与Walsh-Hadamard变换实现信道编解码和信道编码盲识别.本文综述基于调和分析的信道编码的一些基本结果并介绍最新进展,主要包括：Gilbert-Varshamov界、l1解码、RIP（restricted isometry property）条件和Walsh-Hadamard变换等.