IDEAL STRUCTURE IN CENTAIN C^*-TENSOR PRODUCTS

This paper discusses the ideal structure in tensor product $A\bigotimes B$ of C^*-algebra A and B,and introduces the concept of property (I) and property (K) with respect to the problem.When A is an AF(or scattered) C^*-algebra,it is shown that for any C^*-algebra B,the ideals in $A\bigotimes B$ can be expressed by those of A and B.     

Representations of twisted Yangians associated with skew Young diagrams

Let $G_M$ be either the orthogonal group $O_M$ or the symplectic group $Sp_M$ over the complex field; in the latter case the non-negative integer $M$ has to be even. Classically, the irreducible polynomial representations of the group $G_M$ are labeled by partitions $\mu=(\mu_{1},\mu_{2},\,\ldots)$ such that $\mu^{\prime}_1+\mu^{\prime}_2\le M$ in the case $G_M=O_M$, or $2\mu^{\prime}_1\le M$ in the case $G_M=Sp_M$. Here $\mu^{\prime}=(\mu^{\prime}_{1},\mu^{\prime}_{2},\,\ldots)$ is the partition conjugate to $\mu$. Let $W_\mu$ be the irreducible polynomial representation of the group $G_M$ corresponding to $\mu$. Regard $G_N\times G_M$ as a subgroup of $G_{N+M}$. Then take any irreducible polynomial representation $W_\lambda$ of the group $G_{N+M}$. The vector space $W_{\lambda}(\mu)={\rm Hom}_{\,G_M}( W_\mu, W_\lambda)$ comes with a natural action of the group $G_N$. Put $n=\lambda_1-\mu_1+\lambda_2-\mu_2+\ldots\,$. In this article, for any standard Young tableau $\varOmega$ of skew shape $\lm$ we give a realization of $W_{\lambda}(\mu)$ as a subspace in the $n$-fold tensor product $(\mathbb{C}^N)^{\bigotimes n}$, compatible with the action of the group $G_N$. This subspace is determined as the image of a certain linear operator $F_\varOmega (M)$ on $(\mathbb{C}^N)^{\bigotimes n}$, given by an explicit formula. When $M=0$ and $W_{\lambda}(\mu)=W_\lambda$ is an irreducible representation of the group $G_N$, we recover the classical realization of $W_\lambda$ as a subspace in the space of all traceless tensors in $(\mathbb{C}^N)^{\bigotimes n}$. Then the operator $F_\varOmega\(0)$ may be regarded as the analogue for $G_N$ of the Young symmetrizer, corresponding to the standard tableau $\varOmega$ of shape $\lambda$. This symmetrizer is a certain linear operator on $\CNn$$(\mathbb{C}^N)^{\bigotimes n} $ with the image equivalent to the irreducible polynomial representation of the complex general linear group $GL_N$, corresponding to the partition $\lambda$. Even in the case $M=0$, our formula for the operator $F_\varOmega(M)$ is new. Our results are applications of the representation theory of the twisted Yangian, corresponding to the subgroup $G_N$ of $GL_N$. This twisted Yangian is a certain one-sided coideal subalgebra of the Yangian corresponding to $GL_N$. In particular, $F_\varOmega(M)$ is an intertwining operator between certain representations of the twisted Yangian in $(\mathbb{C}^N)^{\bigotimes n}$.     

INVARIANT SUBSPACES AND EIGEVALUES OF ELEMENTS IN C-ALGEBRAS

Let A be a C~*-algebra and x an element in A. the following invariant subspace problem is considered: Does there exist an irreducible representation π of A such that π(x) has a non-trivial invarint subspace? And a positive solution of the problem for finite separable matroid C~*-algebras is given. Also the eigenvalues Of elements in C~*-algebras is considered. Some versions of Fredholm Alternatives are given.     

CONVERGENCE OF AN ALTERNATING A-φ SCHEME FOR QUASI-MAGNETOSTATIC EDDY CURRENT PROBLEM

We propose in this paper an alternating A-$\phi$ method for the quasi-magnetostatic eddy current problem by means of finite element approximations. Bounds for continuous and discrete error in finite time are given. And it is verified that provided the time step $\tau$ is sufficiently small, the proposed algorithm yields for finite time $T$ an error of $O(h+\tau^{1/2})$ in the $L^2$-norm for the magnetic field $H(= \mu^{-1} \nabla \times A)$, where $h$ is the mesh size, $\mu$ the magnetic permeability.     

塌陷型极值拟共形映射的性质

证明了如果f~μ是单位圆△上塌陷型极值拟共形映射,则存在与f~μ等价的极值拟共形映射f~(?)以及单位圆的子区域G,使得面(z)=0,(?)z∈G.     

EXTENSION OF MULTIPLIERS AND INJECTIVE HILBERT MODULES

The author studies the problem whether a multiplier of a hereditary C^*-subalgebra B of a C^*-algebra A can be extended to a multiplier of A. One related problem is the Hahn-Banach extension theorem for Hilbert modules over C^*-algebras. It is shown that every self-dual Hilbert module over W^*-algebra or an injective C^*-algebra is injective.     

Cn中单位球上$mu$-Bloch函数的等价刻画

设$\mu$是$[0,1)$上的正规函数, 给出了${\bf C}^{\it n}$中单位球$B$上$\mu$-Bloch空间$\beta_{\mu}$中函数的几种刻画. 证明了下列条件是等价的: (1) $f\in \beta_{\mu}$; \ (2) $f\in H(B)$且函数$\mu(|z|)(1-|z|^{2})^{\gamma-1}R^{\alpha,\gamma}f(z)$ 在$B$上有界; (3) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{1}-1}\frac{\partial^{M_{1}} f}{\partial z^{m}}(z)}$ 在$B$上有界, 其中$|m|=M_{1}$; (4) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{2}-1}R^{(M_{2})}f(z)}$ 在$B$上有界.     

多复变μ-Bloch空间上Gleason问题的可解性

设B和U~n分别表示C~n中单位球和多圆柱,并设μ是[0,1]上一个正规函数.对任意给定的b∈B,证明了Gleason问题(B,b,β_μ)是可解的,同时也证明了Gleason问题(U~n,0,β_μ)也是可解的.     

ON COHOMOLOGY OF INFINITESIMAL NEIGHBOURHOODS OF COMPLEX MANIFOLDS

In this paper,we introduce the concept of the(k,l)-th C~∞ infinitesimal neighbour-hoods of complex manifold M and difine defferential modules _(M,k-p,l-q)~(p,q) and _(M,k,l)~r forthe(k,l)-th C~∞ infinitesimal neighbourhoods.We prove some isomorphism theorems ofcohomology and hyper cohomology concerning _(M,k-p)~p and _(M,k-p)~,as followsH~p(M,_(M,k-r)~r)≈H_~p(M,_(M,k-r,l-*)~(r,*),H~p(M,_(M,k,l)~*)≈H_(DR)~p(M,C)and for hyper cohomologyH~p(M,_(M,k-*)~*≈H~p(M,C),H~p(M,_(M,k-*)~*)≈H~p(M,O_M).     

Hypercube and Tetrahedron Algebra

Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.     

On Numerical Solution of Quasilinear Boundary Value Problems with Two Small Parameters

We consider the singular perturbation problem $$-\varepsilon^2u"+\mu b(x,u)u'+c(x,u)=0,u(0),u(1)$$ given with two small parameters $\varepsilon$ and $\mu$ , $\mu =\varepsilon^{1+p},p>0$. The problem is solved numerically by using finite difference schemes on the mesh which is dense in the boundary layers. The convergence uniform in $\varepsilon$ is proved in the discrete $L^1$ norm. Some convergence results are given in the maximum norm as well.     

非双倍测度下的Marcinkiewicz积分的加权估计

Let μ be a nonnegative Radon measure on R d which satisfies the growth condition μ(B(x,r)) ≤ C0rn for all x ∈Rd and r >0,where C0 is a fixed constant and 0相似文献   

线性约束下Hermite-广义反Hamilton矩阵的最佳逼近问题

本文利用对称向量与反对称向量的特征性质,给出了约束矩阵集合非空的充分必要条件及矩阵的一般表达式.运用空间分解理论和闭凸集上的逼近理论,得到了任一n阶复矩阵在约束矩阵集合中的惟一最佳逼近解.     

COMPLETELY POSITIVE MAPS AND $*$-OMORPHISM OF $\[{C^*}\]$-ALGEBRAS

Let $A$, $B$ be unital $\[{C^*}\]$-algebras. $\[{\chi _A} = \{ \varphi |\varphi \]$ are all completely postive linear maps from $\[{M_n}(C)\]$ to $A$ with $\[\left\| {a(\varphi )} \right\| \le 1\]$ $}$. $\[(a(\varphi ) = \left( {\begin{array}{*{20}{c}} {\varphi ({e_{11}})}& \cdots &{\varphi ({e_{1n}})}\{}& \cdots &{}\{\varphi ({e_{n1}})}& \cdots &{\varphi ({e_{nn}})} \end{array}} \right),\]$ where $\[\{ {e_{ij}}\} \]$ is the matrix unit of $\[{M_n}(C)\]$. Let $\[\alpha \]$ be the natural action of $\[SU(n)\]$ on $\[{M_n}(C)\]$ For $\[n \ge 3\]$, if $\[\Phi \]$ is an $\[\alpha \]$-invariant affine isomorphism between $\[{\chi _A}\]$ and $\[{\chi _B}\]$, $\[\Phi (0) = 0\]$, then $A$ and $B$ are $\[^*\]$-isomorphic In this paper a counter example is given for the case $\[n = 2\]$.     

GIRSANOV＇S THEOREM ON ABSTRACT WIENER SPACES

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形式三角矩阵环的PS性质和CESS性质

设$R$是环. 称右$R$-模$M$是PS-模,如果$M$具有投射的socle. 称$R$是PS-环,如果$R_R$是PS-模. 称$M$是CESS-模,如果$M$的任意具有基本socle的子模是$M$的某个直和因子的基本子模.本文给出了形式三角矩阵环 $T=\left( \begin{array}{cc} A & 0 \\     

An $L_1$ Minimization Problem by Generalized Rational Functions

Let $P,Q \subset L_1(X,\Sigma,\mu)$ and $q(x)>0$ a. e. in $X$ for all $q\in Q$. Define $R=\{p/q:p\in P,q\in Q\}$. In this paper we discuss an $L_1$ minimization problem of a nonnegative function $E(z,x)$, i.e. we wish to find a minimum of the functional $\phi(r)=\int _X qE(r,x)d\mu$ form $r=p/q\in R$. For such a problem we have established the complete characterizations of its minimum and of uniqueness of its minimum, when both $P,Q$ are arbitrary convex subsets.     

一类缺项算子矩阵的四类点谱的扰动

有界线性算子的点谱可进一步细分为4类,分别为$\sigma_{p1}$, $\sigma_{p2}$, $\sigma_{p3}$ 和$\sigma_{p4}$.设 $H, K$为无穷维可分的Hilbert空间,用$M_C$表示$2\times 2$上三角算子矩阵$\left(\begin{array}{cc} A & C \\ 0 & B \\ \end{array} \right)$,对于给定的 $A\in B(H),~B\in B(K)$,描述了集合$\bigcap\limits_{C\in B(K,H)}\sigma_{p1}(M_C)$, $\bigcap\limits_{C\in B(K,H)}\sigma_{p2}(M_C)$, $\bigcap\limits_{C\in B(K,H)}\sigma_{p3}(M_C)$和$\bigcap\limits_{C\in B(K,H)}\sigma_{p4}(M_C)$.     

Morgan-Scott型剖分上的样条空间的奇异性

Multivariate spline function is an important research object and tool in Computational Geometry. The singularity of multivariate spline spaces is a difficult problem that is ineritable in the research of the structure of multivariate spline spaces. The aim of this paper is to reveal the geometric significance of the singularity of bivariate spline space over Morgan-Scott type triangulation by using some new concepts proposed by the first author such as characteristic ratio, characteristic mapping of lines （or ponits）, and characteristic number of algebraic curve. With these concepts and the relevant results, a polished necessary and sufficient conditions for the singularity of spline space S u＋1^u （△MS^u） are geometrically given for any smoothness u by recursion. Moreover, the famous Pascal＇s theorem is generalized to algebraic plane curves of degree n≥3.     

拟线性双曲组在半有界初始轴上的柯西问题整体经典解的渐近性态

In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.