关于HSOLSSOM（2^nu^1）的谱

本文讨论型为２＾ｎｕ＾１的有对称正交侣的带洞自正交拉丁方（ＨＳＯＬＳＳＯＭ（２＾ｎｕ＾１））的谱。证明当ｎ≤９时,ＨＳＯＬＳＳＯＭ（２＾ｎｕ＾１）存在的充分必要条件是ｕ为偶数且ｎ≥３ｕ／２＋１;当ｎ≥２６３时,若ｕ为偶数且ｎ≥２（ｕ－２）,则ＨＳＯＬＳＳＯＭ（２＾ｎｕ＾１）存在。     

关于二元样条空间S3r^4（△＊）的维数

设△＊是任何三角剖分△的ＨＣＴ细分的三角剖分。本文建立了定义于△＊上的二元样条函数空间Ｓ３ｒ＾ｒ（△＊）的维数公式，我们的证明方法同时给出了Ｓ３ｒ＾４（△＊）的一组显示的基函数，并阐明基函数具有某种意义的局部最小支集。     

de Sitter空间中具平行平均曲率向量的完备类空子流形

本文证明了ｄｅＳｉｔｔｅｒ空间中具平行平均曲率向量的完备类空子流形在Ｈ２〉Ｃ时其第二基本形式模长平方是上有界的，从而推广了Ｕ－ＨａｎｇＫＩ＾（４）及Ｑ．Ｍ．Ｃｈｅｎｇ＾（３）中的结果。     

沿曲线的极大算子和Hilbert变换的L^p有界性

本文沿Ｒ＾ｎ中曲线的极大算子Ｍ和Ｈｉｌｂｅｒｔ变换Ｈ的Ｌ＾ｐ有界性。对一类凸曲线，证明了Ｍ和Ｈ都是Ｌ＾ｐ（Ｒ＾ｎ）上的有界算子，ｐ＞１／     

高维常平均曲率超曲面的数量曲率的空隙

本文证明了当高维球面中闭常平均曲率超曲面Ｍ＾ｎ的平均曲率│Ｈ│＜Ｃ（ｎ）时，若Ｍ的数量曲率Ｒ为常数，则Ｒ不属于［ａ（ｎ，Ｈ），ａ（ｎ，Ｈ）＋ｎ／４），其中ａ（ｎ，Ｈ）＝ｎ（ｎ－９／４）＋ｎ＾２（ｎ－２）／２（ｎ－１）Ｈ＾２－ｎ（ｎ－２）／２（ｎ－１）√ｎ＾２Ｈ＾４＋４（ｎ－１）Ｈ＾２。     

半整权模形式Fourier系数的两个注记

地于ｆ（ｚ）＝∑ａｎｅ（ｎｚ）∈Ｓｋ（Г０（Ｎ））Ｈ．Ｉｗａｎｉｅｃ＾［２］证明了ａｎ＜＜ｎ＾ｋ／２－２／７＋ε，其中ｎ为无平方因子正整数。在本文中我们将推广这个结果。     

Toeplitz算子空间的W—闭包

本文讨论了Ｔｏｅｐｌｉｔｚ算子空间的Ｗ－闭包，我们证明了Ｂｅｒｇｍａｎ空间Ｌ＾２ａ（Ｄ）上全体Ｔｏｅｐｌｉｔｚ算子的Ｗ闭包等于Ｂ（Ｌ＾２ａ（Ｄ）（定理１），另外，我们给出Ｃ＾ｍ（ｎ＞１）中单位球面Ｓ上的Ｈａｒｄｙ空间Ｈ＾２（Ｓ）上的Ｔｏｅｐｌｉｔｚ算子的一个有趣刻划（命题２）。     

关于S^＊p（β）及H^＊p（β）的不等式

设Ｓ＾＊ｐ（β）表示单位圆│Ｚ│〈１内的一族ｐ次对称，正则，单叶，β级星象函数，且Ｈ＾８ｐ（β）表示单位圆不０〈│ｚ│〈１内的一族ｐ次对称，正则，单叶，β级星象函数。本文得到的一些有关函数族Ｓ＾＊ｐ（β）及Ｈ＾＊ｐ（β）的不等式。这些结果都是精确的。     

二维全平面上具线性阻尼Navier—Stokes方程组解的有限维行为

西方考虑具线性阻尼Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组解的大时间性态。我们证明了当ｆ∈Ｈ＾１，ｆ「ｌｎｌｎ（ｅ＾ｅ＋｜ｘ｜）」＾１／２∈Ｌ＾２时上述 问题在Ｌ＾２中整体涓引子的存在性，给出了整体吸引子的Ｈａｕｓｄｏｒｆｆ及Ｆｒａｃｔａｌ维数的上界估计。     

De Sitter空间中具有常均曲率的类空超曲面（Ⅱ）

设Ｍ＾ｎ是Ｄｅ Ｓｉｔｔｅｒ空间Ｓ１＾ｎ＋１中具有常数平均曲率且第二基本形式长度的平方为常数的完备类空超曲面，若Ｓ≤２（ｎ－１）＾１／２，则Ｍ＾ｎ是等参超曲面。     

On the class of norm limits of nilpotents

It is known that every operator on a Hilbert space whose invariant subspace lattice is possibly is a norm-limit of a sequence of nilpotent operators. In this note we study properties of such approximating sequences.

     

Strongly singular convolution operators on the Heisenberg group

We consider the mapping properties of a model class of strongly singular integral operators on the Heisenberg group ; these are convolution operators on whose kernels are too singular at the origin to be of Calderón-Zygmund type. This strong singularity is compensated for by introducing a suitably large oscillation.

Our results are obtained by utilizing the group Fourier transform and uniform asymptotic forms for Laguerre functions due to Erdélyi.

     

WEIERSTRASS REPRESENTATION FORSURFACES WITH PRESCRIBED NORMALGAUSS MAP AND GAUSS CURVATURE IN H~3

The author obtains a Weierstrass representation for surfaces with prescribed normal Gauss map and Gauss curvature in H3. A differential equation about the hyperbolic Gauss map is also obtained, which characterizes the relation among the hyperbolic Gauss map, the normal Gauss map and Gauss curvature. The author discusses the harmonicity of the normal Gauss map and the hyperbolic Gauss map from surface with constant Gauss curvature in H3 to S2 with certain altered conformal metric. Finally, the author considers the surface whose normal Gauss map is conformal and derives a completely nonlinear differential equation of second order which graph must satisfy.     

On various types of homogeneous Riemannian spaces with an isotropy group which decomposes

Homogeneous Riemannian spaces are considered whose isotropy group H decomposes into the direct product of irreducible subgroups and the identity operator acting in mutually orthogonal planes in the tangent space of a point M. We exclude the special cases when an irreducible subgroup in the decomposition of H is semisimple and acts on a plane whose dimension is a multiple of four. These spaces admit a rigid tensor structuref satisfying the conditionf ³ +f = 0.Translated from Matematicheskie Zametki, Vol. 5, No. 3, pp. 361–372, March, 1969.     

A class of semigroups having almost trivial multiplications

In this note we completely describe the structure of algebraic semigroups S with Sx=S or Sx degenerate and xS=S or xS degenerate for each x∈S. We then apply our results in characterizing the separately continuous multiplications on a topological space whose only self-maps are either surjective or have degenerate image. In particular, we find that any locally compact Hausdorff space with this property can admit only trivial separately continuous multiplications. Examples of spaces satisfying this property are certain continua discovered by H. Cook [1]. The authors are indebted to Karl H. Hofmann and James T. Rogers for conversations elucidating the topological implications of Theorem 1. The second author supported by NSF Grant GP28655     

3-一致超图的反馈数研究

超图H=(V,E)顶点集为V,边集为E.S■V是H的顶点子集,如果H/S不含有圈,则称S是H的点反馈数,记τc(H)是H的最小点反馈数.本文证明了:(i)如果H是线性3-一致超图,边数为m,则τc(H)≤m/3;(ii)如果H是3-一致超图,边数为m,则τc(H)≤m/2并且等式成立当且仅当H任何一个连通分支是孤立顶点或者长度为2的圈.A■V是H的边子集,如果H\A不含有圈,则称A是H的边反馈数,记τc′(H)是H的最小边反馈数.本文证明了如果H是含有p个连通分支的3-一致超图,则τc’(H)≤2m-n+p.     

A Liouville-type theorem on halfspaces for the Kohn Laplacian

Let be the Kohn Laplacian on the Heisenberg group and let be a halfspace of whose boundary is parallel to the center of . In this paper we prove that if is a non-negative -superharmonic function such that

then in .

     

One and two dimensional Cantor-Lebesgue type theorems

Let be any function which grows more slowly than exponentially in i.e., There is a double trigonometric series whose coefficients grow like and which is everywhere convergent in the square, restricted rectangular, and one-way iterative senses. Given any preassigned rate, there is a one dimensional trigonometric series whose coefficients grow at that rate, but which has an everywhere convergent partial sum subsequence. There is a one dimensional trigonometric series whose coefficients grow like and which has the everywhere convergent partial sum subsequence For any there is a one dimensional trigonometric series whose coefficients grow like and which has the everywhere convergent partial sum subsequence All these examples exhibit, in a sense, the worst possible behavior. If is increasing and has arbitrarily large gaps, there is a one dimensional trigonometric series with unbounded coefficients which has the everywhere convergent partial sum subsequence

     

The groups of quasiconformal homeomorphisms on Riemann surfaces

Suppose is a connected Riemann surface. Let denote the homeomorphism group of with the compact-open topology, and denote the subgroup of quasiconformal mappings of onto itself, and let and denote the identity components of and respectively. In this paper we show that the pair is an -manifold, and determine their topological types.

     

Maps preserving numerical ranges of operator products

Let be a complex Hilbert space, the algebra of all bounded linear operators on and the real linear space of all self-adjoint operators on . We characterize the surjective maps on or that preserve the numerical ranges of products or Jordan triple-products of operators.