I THE （μ＋ κ）oORBITS OF ESSENTIALLY NORMAL OPERATORS AND THEIR STRONG IRREDUCIBILITY

The authors characterize the (μ +κ)-orblts of a class essmntially normal operators and provethat some essentially normal operators with connected spectrum are strongly irreducible aftera small compact perturbation. This partially answers a question of Domigo A. Herrero.     

ON THE CLASSIFICATION OF AF-ALGEBRAS AND THEIR DIMENSION GROUPS （Ⅱ）

ＯＮＴＨＥＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＡＦ－ＡＬＧＥＢＲＡＳＡＮＤＴＨＥＩＲＤＩＭＥＮＳＩＯＮＧＲＯＵＰＳ（Ⅱ）￥ＨＵＡＮＧＺＨＡＯＢＯＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｉｓａｃｏｎｔｉｎｕａｔｉｏｎｏｆ［１］．Ｉｔｇｉｖｅｓｓｏｍｅａｐｐｌｉ...     

THE （u＋К）-ORBIT OF ESSENTIALLY NORMAL OPERATORS AND COMPACT PERTURBATIONS OF STRONGLY IRREDUCIBLE OPERATORS

Let Н be a complex,separable,infinite dimensional Hilbert space,T∈L(Н),(U+κ)(T) denotes the (U+κ)-orbit of T,i.e.,(U+κ)(T)={R^-1 TR:R is invertible and of the form unitary plus compact}.Let Ω be an analytic and simply connected Cauchy domain in C and n∈N,A（Ω,n）denotes the class of operators,each of which satisfies (i) T is essentially normal;(ii)σ(T)=Ω^-,ρF（T）∩σ（T）=Ω;（iii）ind(λ-T)=-n,nul(λ-T)=0,(λ∈Ω）。it is proved that given T1,T2∈A(Ω,n）and c>0,there exists a compact operator K with ||K||<ε such that T1+K∈(u+κ)(T2),this result generalizes a result of P.S.Guinand and L.Marcoux[6,15],Furthermore,the authors give a character of the norm closure of (u+κ)(T),and prove that for each T∈А(Ω,n）,there exists a compact (SI) perturbation of T whose norm can be arbitrarily small.     

DECOMPOSITION OF （1＋1）-DIMENTIONAL,（2W1）-DIMENTIONAL SOLITON EQUATIONS AND THEIR QUASI-PERIODIC SOLUTIONS

A new spectral problem is proposed, and nonlinear differential equations of the corresponding hierarchy are obtained. With the help of the nonlinearization appr...     

THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU（2,2）/S（U（2） × U（2））

Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.     

CONSERVATION LAWS FOR THE （1 ＋ 2）-DIMENSIONAL WAVE EQUATION IN BIOLOGICAL ENVIRONMENT＊

The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coef...     

THE ZEROS AND ORDER OF MEROMORPHIC SOLUTIONS OF f^（k）＋Bf=H（z）

1.IntroductionandResultsConsidernon-homogeneouslineardifferentialequationsoftheform1.Lameprovedin[7]TheoremA.LetB(z),PO(z),PI(z)*06epolynomialssuchthatdegB=n21,degPO=p<(n k)/kandH=PI(z)epo('),then(a)IfdegPI相似文献   

QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES B（Wpr（[0, 1）d）） AND B（Hpr（[0, 1]d））

We study the approximation of functions from anisotropic Sobolev classes B(W_p~r([0,1]~d)) and H¨older-Nikolskii classes B(W_p~r([0,1]~d)) in the L q([0,1] d) norm with q ≤ p in the quantum model of computation.We determine the quantum query complexity of this problem up to logarithmic factors.It shows that the quantum algorithms are significantly better than the classical deterministic or randomized algorithms.     

LIE SYMMETRY ANALYSIS AND PAINLEVE ANALYSIS OF THE NEW （2＋1）-DIMENSIONAL KdV EQUATION

Lie point symmetries associated with the new （2＋1）-dimensional KdV equation ut ＋ 3uxuy ＋ uxxy = 0 are investigated. Some similarity reductions are derived by solving the corresponding characteristic equations. Painlevé analysis for this equation is also presented and the soliton solution is obtained directly from the Bǎcklund transformation.     

THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND （ws）-COMPACT OPERATORS

Abstract The main purpose of this article is to prove a collection of new nxea point theorems for （ws）-compact and so-called 1-set weakly contractive operators under Leray- Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for （ws）-compact （in particular nonexpansive） self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.     

梯形映射族周期轨道的计算

运用符号动力学理论,研究一种特殊的一维分段线性映射族"梯形映射族"周期轨道的计算方法,确定其周期轨道的参数范围,给出了奇的最大周期序列对应参数的精确范围,以及偶的最大周期序列参数的近似范围.该方法可应用于更一般的单峰系统.     

参数化测度与一类算子的表示问题

本文利用参数化测试研究一类算子的表示问题，得到了所谓的参数化的Ｒｉｅｚｅ表示定理。     

有限域上随机变量联合分布及二阶矩的分解与应用

本文给出了有限域上随机变量联合概率和二阶矩的分解公式，给出了有限域上随机变量相互独立的谱刻划，应用上述结果，建立了在进行频次分析时，对有限域上随机向量构造的Χ平方统计量与该随机向量坐标函数的非零线性组合的Χ平方统计量之间的内在联系，给出了有限域上相关免疫函数谱特征的新证明，建立了有限域上多输出函数的差分分布与其广义Chrestenson循环谱之间的内在联系，建立了多输出函数的平衡性其差分分布之间的内在联系。     

弱型及加权弱拟(1,1)型算子的有界性

在这篇文章中 ,我们介绍了拟 (1 ,1 )型算子T ,给出了它的弱有界性和加权弱有界性     

伪抛物型复方程的Riemann─Hilbert初边值问题的可解性及其近似解的误差估计

本文使用参数开拓法证明了非线性伪抛物型复方程在多连通区域上的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ初边值问题的可解性，并对近似解作出了误差估计。     

两类新的广义Ball曲线曲面的求值算法及其应用

本文研究两类新的广义Ball曲线曲面的求值算法及其应用.其一是把Bezier曲线曲面的求值转换到这两类曲线曲面的求值,大大加快了计算速度.其二是给出Bezier曲线与这两类广义Ball曲线的统一表示,并利用这种表示给出它们之间相互转换的递归算法.     

THE EXISTENCE AND UNIQUENESS OF SOLUTION FOR A CLASS OF STOCHASTIC FUNCTIONAL EQUAFIONS ON S.P.SPACE

We staxt in discussing a class of more general functional equations in tliis paper, andthe maill ainl is to establish the existence and uniquenes8 of solution of a class of stochasticfunctioual equations on stochastic processes space (called "S.P space" for sllort). The11 usingthe resuIt to son1e specia1 kil1ds ofordillary differential equation, stochastic differential (integral)equation (called "S.D.E." or "S.I.E." fOr short), a series of corollaries l1ave been derived. Someof then1 can b…     

THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))

Let G = SU(2,2), K = S(U(2)×U(2)), and for l∈Z, let {τl}l∈z be a onedimensional K-type and let El be the line bundle over G/K associated to τl. It is shown that the τl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.     

OPERATOR AND MATRIX REPRESENTATION FOR THE GENERALIZED INVERSE A_(T,S)~(2)

. IntroductionIn this paper we adopt the same notations on generalized inverses of matrices andprojectors as those in [1].Several rePresentations for the generalized inverses of matrices, for example, those forthe Moors-Penrose inverse A and the Drazin inverse A(d), have led to[1--4]:where k = index (A).In order to study the matrix form of the above-mentioned operator represelltations,we denote linear operators by A, B,' ', and their matrices by the corresponding A, B,' '.All of the li…