标度系统一致性矩阵容量的计算方法

本文研究正互反矩阵的变换性质 ,提出一种保持正互反矩阵一致性程度的等价分类 ,为计算各种标度系统下的一致矩阵容量提供了计算方法     

Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices

Let U_m be an m×m Haar unitary matrix and U_[m,n] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U_[m,n] as m/n→λ and n→∞. The rate function and the limit distribution are given explicitly. U_[m,n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.     

一个来自振动理论反问题的矩阵方程

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＲｎ×ｍｄｅｎｏｔｅｔｈｅｒｅａｌｎ×ｍｍａｔｒｉｘｓｐａｃｅ ,Ｒｎ×ｍｒ ｉｔｓｓｕｂｓｅｔｗｈｏｓｅｅｌｅｍｅｎｔｓｈａｖｅｒａｎｋｒ ,ＯＲｎ×ｎｔｈｅｓｅｔｏｆａｌｌｎ×ｎｏｒｔｈｏｇｏｎａｌｍａｔｒｉｃｅｓ,ＳＲｎ×ｎ(ＳＲｎ×ｎ≥ ,ＳＲｎ×ｎ>)ｔｈｅｓｅｔｏｆａｌｌｎ×ｎｒｅａｌｓｙｍｍｅｔｒｉｃ (ｓｙｍｍｅｔｒｉｃｐｏｓｉｔｉｖｅｓｅｍｉｄｅｆｉｎｉｔｅ ,ｐｏｓｉｔｉｖｅｄｅｆｉｎｉｔｅ)ｍａｔｒｉｃｅｓ.ＴｈｅｎｏｔａｔｉｏｎＡ>0 (≥ 0 ,<0 ,≤ 0 )ｍ…     

一类9n2次组合混合水平正交表的构造

本文利用正交表和投影矩阵的正交分解之间的关系,给出了一类9n2次组合混合水平正交表的构造方法,作为这种方法的应用,我们构造了一些新的具有较大非素数幂水平的144次混合水平正交表,并且这些正交表具有较高的饱和率.     

激光溅射Ni等离子体与气相CH3OH团簇的反应

用激光溅射 分子束技术研究了气相中Ni的等离子体与甲醇分子团簇的反应 .观察到Ni+ (CH3 OH) n、NiO+ (CH3 OH) n、H+ (CH3 OH) n、H3 O+ (CH3 OH) n 四个种类的团簇正离子和CH3 O-(CH3 OH) n(n≤ 2 5 )一种团簇负离子 .详细考察了激光烧蚀等离子体作用于脉冲分子束的不同位置时 ,对团簇产物种类和团簇尺寸大小的影响 .发现NiO+ (CH3 OH) n 是由Ni+ (CH3 OH) n 团簇内的脱甲烷反应生成的 ,而H+ (CH3 OH) n、H3 O+ (CH3 OH) n主要是激光等离子体中的电子与甲醇团簇碰撞电离产生的     

Local automorphisms of operator algebras on Banach spaces

In this paper we extend a result of Semrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms of matrix algebras for which we present a short proof. The need to get such a proof was formulated in Semrl's paper.

     

The solvability conditions for inverse eigenproblem of symmetric and anti‐persymmetric matrices and its approximation

The problem of generating a matrix A with specified eigen‐pair, where A is a symmetric and anti‐persymmetric matrix, is presented. An existence theorem is given and proved. A general expression of such a matrix is provided. We denote the set of such matrices by ??????_Eⁿ. The optimal approximation problem associated with ??????_Eⁿ is discussed, that is: to find the nearest matrix to a given matrix A* by A∈??????_Eⁿ. The existence and uniqueness of the optimal approximation problem is proved and the expression is provided for this nearest matrix. Copyright © 2002 John Wiley & Sons, Ltd.     

On perturbations of matrix pencils with real spectra, a revisit

This paper continues earlier studies by Bhatia and Li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra. A unifying framework for creating crucial perturbation equations is developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained.

     

Synthesis and characterization of isotopically enriched methylmercury (CH3201Hg+)

A simple procedure for the synthesis of an important standard, isotopically enriched methylmercury, which is not commercially available, has been established successfully. The isotopically enriched standard synthesized is utilized in conventional isotope dilution mass spectrometry (IDMS), as well as in speciated IDMS (SIDMS), for determination of the true concentration of methylmercury in environmental samples. The CH₃²⁰¹Hg⁺ standard has been synthesized from commercially available ²⁰¹HgO and tetramethyltin. The synthesis time required is 1 h at 60°C. The product is highly pure, yielding more than 90% as ²⁰¹Hg in CH₃²⁰¹Hg⁺. Hazardous dimethylmercury does not occur during this synthesis procedure. The product synthesized was analyzed using high‐performance liquid chromatography coupled with inductively coupled plasma mass spectrometry (ICP‐MS) and ICP‐MS alone in order to determine its concentration, isotopic composition and purity. The stability of the product was also evaluated for over 6 months and found to be stable at 4°C in the dark. The isotopically enriched methylmercury synthesized can be used in SIDMS and IDMS analyses as a standard. Copyright © 2003 John Wiley & Sons, Ltd.