On the structure of a cone of normal unbounded completely positive maps

The paper suggests a constructive characterization of unbounded completely positive maps introduced earlier by Chebotarev for the theory of quantum dynamical semigroups. We prove that such cones are generated by a positive self-adjoint “reference” operator ΛεB(H) as follows: for any completely positive unbounded map Ф(·)εCPn*(F) these exists a completely positive normal bounded mapR(·)εCPn(H) such that ϕ(·)=ΛR(·)Λ. The class contains mappings that are unclosable sesquilinear forms. Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 194–205, February, 1999.     

循环群诸类问题探

主要探讨:(i)循环群的定义和性质;(ii)循环群及其子群特征;(iii)同构于Vn、(Z+0)及其推广.     

Affine Demazure modules and T-fixed point subschemes in the affine Grassmannian

Let G be a simple algebraic group defined over C and T be a maximal torus of G. For a dominant coweight λ of G, the T-fixed point subscheme of the Schubert variety in the affine Grassmannian GrG is a finite scheme. We prove that for all such λ if G is of type A or D and for many of them if G is of type E, there is a natural isomorphism between the dual of the level one affine Demazure module corresponding to λ and the ring of functions (twisted by certain line bundle on GrG) of . We use this fact to give a geometrical proof of the Frenkel-Kac-Segal isomorphism between basic representations of affine algebras of A,D,E type and lattice vertex algebras.     

THE ISOMETRIC EXTENSION OF AN INTO MAPPING FROM THE UNIT SPHERE S[e（Γ）] TO THE UNIT SPHERE S（E）

This is such a article to consider an ＂into＂ isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition （using the Krein-Milman property） under which an into-isometric mapping from the unit sphere of e（Γ） to the unit sphere of a normed space E can be linearly isometric extended.     

Additive maps preserving the ascent and descent of operators

Let and be the algebras of all bounded linear operators on infinite dimensional complex Banach spaces X and Y, respectively. We characterize additive maps from onto preserving different quantities such as the nullity, the defect, the ascent, and the descent of operators.     

On Extension of 1-Lipschitz Mappings between Two Unit Spheres of lp(Γ) Type Spaces (1

FANG Xi Nian 《数学研究与评论》2009,29(4)

基于旋转椭球体的等轴状场源体重力异常场模型构建方法

在中心埋藏浅、测量精度高的场合,采用球体作为有限大小、近于等轴状的场源体的模型进行重力异常正演会造成较大误差。提出一种基于旋转椭球体的等轴状场源体重力异常模型。通过改变长、短轴长度以匹配场源体形态,降低正演误差。在已有绕短轴旋转型旋转椭球体的引力位的基础上,推导旋转椭球体完整的重力异常基本表达式。将结果与球体重力异常比较,分析其间的特征差异,验证了结果的正确性。     

Three dimensional homogeneous Finsler manifolds

In this paper we study three dimensional homogeneous Finsler manifolds. We first obtain a complete list of the three‐dimensional homogeneous manifolds which admit invariant Finsler metrics. Then we consider invariant Randers metrics and present the classification of three dimensional homogeneous Randers spaces under isometrics.     

工作休假和休假中止的M/G/1排队模型的适定性

主要研究工作休假和休假中止的M/G/1排队系统,首先将对应于此系统的数学模型转化为抽象Cauchy问题,其次证明对应于此排队模型的主算子生成正压缩C0半群T(t),然后证明T(t)是局部等距的,最后证明此模型存在唯一的非负时间依赖解。     

图同构的必要条件

结合图对应的邻接矩阵,利用矩阵的秩和矩阵的合同关系,得到了图同构的一个必要条件;然后给出了图同构的一个理论判断的算法．