局部对称黎曼流形中的极小子流形

In this paper, we discuss the compact minimal submanifolds in locally symmetric Riemannian manifolds. Two Pinching theorems are obtained and two corresponding results of Chern, S. S. and Yau S. T. are generalized.     

Submanifolds Of Maximal Nullity In Symmetric Spaces

A non-totally-geodesic submanifold of relative nullity n — 1 in a symmetric space M is a cylinder over one of the following submanifolds: a surface F ² of nullity 1 in a totally geodesic submanifold N³ ? M locally isometric to S ²(c) × ? or H ²(c) × ?; a submanifold F ^k+1 spanned by a totally geodesic submanifold F ^k(c) of constant curvature moving by a special curve in the isometry group of M; a submanifold F ^k+l of nullity k in a flat totally geodesic submanifold of M; a curve.     

On Minimal and Maximal Left Ideals in Ordered Semigroups*

The concept of maximal left ideals is introduced in ordered semigroups. Characterizatations of minimal left and maximal left ideals are given.     

紧黎曼对称空间到Grassmann流形的等变等距极小浸入

在本文中，我们利用李群及其表示理论作为主要工具，　讨论了紧黎曼对称空间到Ｇｒａｓｓｍａｎｎ　流形的等变等距极小浸入问题．     

Oscillatory Multipliers Related to the Wave Equation on Noncompact Symmetric Spaces

This paper is devoted to the study of a family of oscillatorymultipliers of the Laplace–Beltrami operator on symmetricspaces of the noncompact type. This family is related to theregularity (in space, for fixed time) of the solutions to thewave equation. Our method relies on estimates for the Poissonsemigroup in complex time, which were obtained in our previouspaper [6].     

Product Semigroups and Extrapolation Spaces

A new formulation of the theory of extrapolation spaces is used to recast a theorem on the resolvent of the sum of a generator of a semigroup and a Hille–Yosida operator and to prove a regularity result related to an abstract equation.     

乘积空间中非线性算子的极大极小不动点定理及迭代法*

本文研究了乘积空间中非线性算子的极大极小不动点和迭代法.作为我们结果的推论,一些耦合不动点定理被获得、它们推广了由郭大钧和Lankshmikantham获得的耦合不动点定理.(见Nonlinear Anal、11(1986),623-632)和由兰在[4]、[6]中获得的结果.     

Lévy–Khinchin Formula and Existence of Densities for Convolution Semigroups on Symmetric Spaces

We prove the existence of a smooth density for a convolution semigroup on a symmetric space and obtain its spherical representation.      

Schroedinger Flows on Compact Hermitian Symmetric Spaces and Related Problems

In this note,we prove that the Schroedinger flow of maps from a closed riemann surface into a compact irreducible Hermitian symmetic space admits a global weak solution.Also,we show the existence of weak solutions to the initial value problem of Heisenberg model with Lie algebra values,which is closely related to the Schroedinger flow on compact Hermitian symmetric spaces.     

Minimal Presentations and Efficiency of Semigroups

A finite semigroup S is said to be efficient if it can be defined by a presentation (A | R) with |R| -|A|=rank(H2(S)). In this paper we demonstrate certain infinite classes of both efficient and inefficient semigroups. Thus, finite abelian groups, dihedral groups D2n with n even, and finite rectangular bands are efficient semigroups. By way of contrast we show that finite zero semigroups and free semilattices are never efficient. These results are compared with some well-known results on the efficiency of groups.     

Constructing Almost Symmetric Numerical Semigroups from Irreducible Numerical Semigroups

Every almost symmetric numerical semigroup can be constructed by removing some minimal generators from an irreducible numerical semigroup with its same Frobenius number.     

Semigroups of Partial Isometries and Symmetric Operators

Let \({{\{ V(t) | \ t \in [0 , \infty) \}}}\) be a one-parameter strongly continuous semigroup of contractions on a separable Hilbert space and let V(?t) : = V*(t) for \({t \in [0, \infty)}\). It is shown that if V(t) is a partial isometry for all \({t \in [-t_0 , t_0], t_0 > 0}\), then the pointwise two-sided derivative of V(t) exists on a dense domain of vectors. This derivative B is necessarily a densely defined symmetric operator. This result can be viewed as a generalization of Stone’s theorem for one-parameter strongly continuous unitary groups, and is used to establish sufficient conditions for a self-adjoint operator on a Hilbert space \({\mathcal{K}}\) to have a symmetric restriction to a dense linear manifold of a closed subspace \({\mathcal H \subset \mathcal K}\). A large class of examples of such semigroups consisting of the compression of the unitary group generated by the operator of multiplication by the independent variable in \({\mathcal {K} := \oplus _{i=1} ^n L^2 (\mathbb {R})}\) to certain model subspaces of the Hardy space of n?compenent vector valued functions which are analytic in the upper half plane is presented.     

Recombination Semigroups on Measure Spaces

The dynamics of recombination in genetics leads to an interesting nonlinear differential equation, which has a natural generalization to a measure valued version. The latter can be solved explicitly under rather general circumstances. It admits a closed formula for the semigroup of nonlinear positive operators that emerges from the forward flow and is, in general, embedded in a multi-parameter semigroup.     

Banach空间中一类混合型非线性微分-积分方程的最大最小解的存在性

用单调迭代的方法和一些新的比较结果，研究了Banach空间中一类事型非线性微分－积分方程的最大最小解，我们用空间E的弱完备性和锥P的正规性（这时可推出P是正则的）来代替紧性条件。     

A Generalization of Symmetric Inverse Semigroups

The set of difunctional binary relations D_X plays a special role in representing inverse semigroups by binary relations. However, D_X is not an inverse semigroup either with the standard operation ∘, or with an alternative operation introduced in [6]. We introduce a new binary operation ⋄ on the set B_X of binary relations. We demonstrate that (D_X, ⋄) is an inverse semigroup, and the symmetric inverse semigroup (I_X, ∘) is a subsemigroup of (D_X,⋄).