Continuity of Multilinear Operators in Weighted Herz Spaces with Extreme Exponents

Continuity is obtained of some multilinear operators related to certain integral operators for the weighted Herz spaces with extreme exponents. The operators include the Littlewood–Paley and Marcinkiewicz operators.     

Three types of maximally entangled states for a two-particle system

Foratwo-particle(spin1/2)systemthespinstateisdescribedusingavectorinafour-dimensionalHilbertspace.Inangularmomentumcouplingtheory[1],theangularmomentumuncouplingandcouplingrepresentationsareusuallyadopted.WhilethesimultaneouseigenstatesoftheCSCO(s1z,s2z),12,12,12and12,arechosenasthebasisofangularmomentumuncouplingscheme,thesimultaneouseigenstatesoftheCSCO(2,zSS),,SM(12=+Sss),arechosenasthebasisofangularmomentumcouplingscheme,1212100,2轾=-臌1212110,2轾=+臌121211,1,1.=-=Thefo…     

WKB Wave Function of the General Time-Dependent Quadratic Hamiltonian System

We derived the WKB wave function for the general time-dependent quadratic Hamiltonian system using a unitary transformation method. We applied our research to sinusodially drived Caldirola–Kanai oscillator and confirmed that the time evolution of our approximated WKB wave function is similar to that of the exact one. This wave function can be used to analyze the interference between the probability amplitudes contributed by the area of overlap in phase space of quantum states.     

Partially isometric dilations of noncommuting -tuples of operators

Given a row contraction of operators on a Hilbert space and a family of projections on the space that stabilizes the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries that satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in our analysis is a connection with directed graphs. We use a Wold decomposition for partial isometries to describe the models for these dilations, and we discuss how the basic properties of a dilation depend on the row contraction.

     

链环的trip矩阵

ZULLI L首先构造了一个用于计算纽结Kauffman尖括号多项式的模2矩阵,纽结的trip矩阵.为了构造链环的trip矩阵,引入了一个带标识的穿有m个孔的圆盘来取代纽结情形下的圆盘,其中m为链环的分支数.主要结果为:定理若状态S是从状态AA…A经过i1,i2,…,ip位置上的标记替换(A换成B)而得的状态.设Ts是将trip矩阵T的左上角的n×n子块中ai1i1,ai2i2,…,aipip之值进行替换(0→1或1→0)所得的矩阵,则#(L|S)=n+m-秩(Ts).因此计算链环Kauffman尖括号多项式就归结为计算一组模2矩阵的秩.     

The mesa problem for Neumann boundary value problem

In this paper, we study the singular limit of the Porous Medium equation u_t=Δu^m+g(x,u), as m→∞, in a bounded domain with Neumann boundary condition.     

CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS

In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).     

张量对称类上诱导线性算子的数值半径

设V是一个n维线性空间,V_x~m(G)为V上的张量对称类.A为V的线性算子T的矩阵,K(A)为V_x~m(G)上的诱导线性算子K(T)的矩阵.本文从K(A)的数值半径Υ(K(A))和可分数值半径Υ_x(K(A))定义出发,研究了Υ(K(A))、Υ_x(K(A))与范数||A||_p(1≤p≤2)、广义矩阵函数d_x~G(A)的关系,得到了它们之间的两个不等式.     

一类矩阵多项式的秩特征

给出了一类矩阵多项式的秩特征定理及它的多种证法.     

Enclosure results for quasilinear systems of variational inequalities

In this paper we consider systems of quasilinear elliptic variational inequalities, and prove the existence of minimal and maximal (in the set theoretical sense) solutions within some ordered interval of an appropriately defined pair of sub- and supersolutions. We show that the notion of sub- and supersolutions of variational inequalities introduced here is consistent with the usual notion of sub-supersolutions for (variational) equations. For weakly coupled quasimonotone systems of variational inequalities the existence of smallest and greatest solutions is proved.