On p-ω-hyponormal operators

In what follows,H means a complex Hilbert space.Call an invertible operator T log-hyponormal if log(T*T)log(TT*). Let T=U|T| be the polar decomposition of T.     

SOME PROPERTIES OF SUPER-DECOMPOSABLE OPERATORS

In this paper,the following main resvlts have been proved:1.Let T∈B(X) be a super-decomposable operator,then for any hyperinvariant subspace Y of T,the operator T/Y is super-decomposable.2.The operator T∈B(X) is super-decomposable if and only if T/Y is super-decomposable for any hyperinvariant subspace Y of T.3. If T∈B(X) has on open spectral resolvent,then T is superdecomposable.     

《一条摄动定理》一文的补遗

In this paper, a simple proof of the following perturbation theorem is given:Suppose that i) T is a self-adjoint operator in the Hilbert space with discrete spectrum σ(T)={λ_n|n=1,2,…}, λ_1≤λ_2≤… and λ_n=cn~P(1+0(1/n)),c>0, p>0.ii) Let 0≤v<1. Let P be a linear operator such that thedomain of P contains the domain of T~v and PT~(-v) is bounded.iii) p(1-v)>1.Then T+P has Property S and T+P and T have an asymptotically common decomposition. Furthermore, if v≤1/2, T+P has the strong Property S.     

A NOTE ON NORMAL ELEMENTARY OPERATORS

Let(T_1,T_2)and (S_1~*,S_2~*) be double commuting subnormal operator pairs,X and K be bounded linear operators with T_1KS_1 T_2KS_2=0. Then (1)||T_1XS_1 T_2XS_2 K||≥||K||and (2)||T_1XS_1 T_2XS_2 K_1|_2~2=||T_1XS_1 T_2XS_2 ||_2~2 ||K||_2~2if K is Hilbert-Schmidt operator,Let T and S* be dominant operator and subnormal operator, respectively, and K is Hilbert-Schmidt operator, then (3)||TX-XS K||_2~2=||TX-XS||_2~2 ||K||_2~2if TK KS;and (4)||TXS-X K||_2~2=||TXS-X||_2~2 ||K||_2~2 if TKS=K. These generalize the results of (1)and (3).     

本性正规算子的Aluthge变换

设T∈B(H), T=U|T|是算子T的极分解, 则定义Tt=|T|tU|T|1-t和Tt(*)=|T*|tU|T*|1-t(其中0相似文献   

关于广义Aluthge变换的数值域的研究

设T∈B(H),T=U|T|是算子T的极分解,则定义T t=|T|tU|T|1-t和T t(*)=|T*|tU|T*|1-t(其中0＜t＜1)分别为算子的广义Aluthge变换和广义*-Aluthge变换.文章主要利用算子矩阵分块技巧,研究了三者之间的本性谱、数值域、本性数值域的关系,推广了吴培元的结果.     

有界线性算子广义Aluthge变换的谱分析

设T是复Hilbert空间中的有界线性算子,给出了T和它的广义Aluthge变换Δλ(T)=|T|λU|T|1-λ(0λ1)在点谱、剩余谱、连续谱、近似点谱和谱之间的关系.     

Decomposition in blocks at the level of wavelet coefficients and T（1 ） theorem on Hardy space

This paper deals with the estabhshment of T(1) theorem on Hardy space H^l under condition of weak regldarity. An operator or a function is identified on the basis of their wavelet coefficients which axe regrouped on some blocks. The actions of each block operator ( pseudo-annular operator) on each block function(atom) axe exactly analyzed to establish T( 1 ) theorem on Hardy space.     

Binding number,minimum degree and bipancyclism in bipartite graphs

Let G =(V_1,V_2,E) be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B(G),is defined to be n if G =K_n and min i∈{1,2}|N(S)|n min |N(S)|/|S|otherwise.We call G bipancyclic if it contains a cycle of every even length m for 4 ≤ m ≤ 2n.A theorem showed that if G is a balanced bipartite graph with 2n vertices,B(G) 3 / 2 and n 139,then G is bipancyclic.This paper generalizes the conclusion as follows:Let 0 c 3 / 2 and G be a 2-colmected balanced bipartite graph with 2n(n is large enough) vertices such that B(G) c and δ(G)(2-c)n/(3-c)+2/3.Then G is bipancyclic.     

Integral Theorems Based on a New Gradient Operator Derived from Biomembranes （Part I）： Fundamentals

A new gradient operator was derived in recent studies of topological structures and shape transitions in biomembranes. Because this operator has widespread potential uses in mechanics, physics, and biology, the operator‘s general mathematical characteristics should be investigated. This paper explores the integral characteristics of the operator. The second divergence and the differential properties of the operator are used to demonstrate new integral transformations for vector and scalar fields on curved surfaces, such as the second divergence theorem, the second gradient theorem, the second curl theorem, and the second circulation theorem. These new theorems provide a mathematical basis for the use of this operator in many disciplines.     

关于Fourier部分和算子范数上下界的新估值

研究Fourier算子Sn的范数‖Sn‖=1π∫π-π|sin2n 1/2t/2sint/2|dt.已知‖Sn‖具有表达式‖ Sn‖=4/π2 log n A n,其中A n表示与n相关且对n一致有界的数列.至今最好的估计是Rivlin给出的:‖Sn‖≤4/π2 log n 3,通过进一步精细的估计证明了4/π2 log n 1《‖Sn‖《4/π2 log n 2,从而给出了关于一致有界量An的上下界的一个新估计.     

一个人员指派问题(英文)

Let T be a set of personnel.Suppose that“≤”is a partial ordering relationon T(which expresses,for example,the seniority of the perssonnel)such that(T,≤)is a rooted tree.Let U be a subset of T.If U can be partitioned into groups eachconsisting of one leader,say t,and k ordinary members,say t_1,t_2,…,t_k,with theproperty that the leader must have higher seniority than the k ordinary members,     

New orthonormal and complete representation for complex scalar fields

The explicit common eigenvectors for complex scalar fields φ (x) and φ+ (x) are derived . They span an orthonormal and complete space. Based on this, the charge conjugate unitary operator and the operator which generates Bogolyubov pseudo-particles transformation can be neatly derived. It is emphasized that | ξ> is different from the direct product of two independent eigenvectors respectively belonging to two real scalar fields, and | ξ > is named the correlated eigenstates of φ( x) and φ+ (x).     

Study of operator reliability in nuclear power plants

The study of the reliability of operator's diagnosis and decision-making during abnormal events with HCR model has been introduced. A new approach has been proposed by the authors to deal with the classification of HIs. The modification of T0.5 by PSFs coefficients has been discussed. In addition, it is emphasized that T0. 5 and SD(σ) of response times can be used as a scale to predict and evaluate the reliability of crew/operator behavior. These processings provide improvement and refinement to HCR model and its practical application. The experiment for operator response time of Chinese NPP using a lull-scale simulator has proved the above-mentioned processings and presented the quantitative results of operator reliability in Chinese NPP.     

THE FREDHOLM THEOREM FOR SYSTEMS OF INTEGRO-FUNCTIONAL EQUATIONS

Some problems of hyperbolic systems of partial differential equations can be turned into systems of in-tegro-functional equations of the following form[1]here F(x) = (f_1(x),…,f_m(x))~T and H(x)=(h_1(x),…,t_m(x))~T both belong to (C~∞[-R,R])~m, are theunknown and know vector functions respectively; λis a parameter, 0相似文献   

THE CONTINUITY OF THE CARATHEODORY OPERATOR

Let X be a set of points on which a completely additive measure is given. Lot F(x.y) be a real-valued function which is defined for every point xeX and for every real number y and satisfies the Caratheodory conditions: F(x, y) is continuous in y for almost every x, and measurable in x for every y. It was proved by B. B. that the operator F defined by the equationis continuous in the space of the measurable functions on X. It was recently proved by M. A. that, if the given measure is continuous, the operator F, whenever it transforms the whole space If into Lq(1≤p,q<+∞) is continuous and baunded.     

Improved genetic operator for genetic algorithm

The mutation operator has been seldom improved because ressearchers hardly suspect its ability to prevent genetic algorithm(GA) from converging prematurely.Due to its importance to GA,the authors of this paper study influence on the diversity of genes in the same locus,and point out that traditional mutation,to some extent,can result in premature convergence of genes(PCG) in the same locus.The above drawback of the traditional mutation operator causes the loss of critical alleles.Inspired by digital technique,we introduce two kinds of boolean operation into GA to develop a novel mutation operator and discuss its contribution of preventing the loss of critical alleles.The experimental results of function optimizatioin show that the improved mutation operator can effectively prevent premature convegence,and can provide a wide selection range of control parameters for GA.     

Simultaneous in-situ determination of U-Pb age and trace elements in zircon by LA-ICP-MS in 20 μm spot size

Simultaneous in-situ determination of U-Pb ages and 20 trace elements of three international zircon standards （91500, GJ1 and TEMORA 1） and one laboratory zircon standard （SK10-2） separated from Cenozoic fine-grained gabbro was carried out on quadrupole ICP-MS equipped with 193 nm excimer laser in 20 μm spot size. The weighted mean ^206Pb/^238U ages of 91500, GJ1 and TEMORA 1 are 1064.4±4.8 Ma （2σ）, 603.2±2.4 Ma （2σ） and 418.2±2.4 Ma （2σ）, respectively. The relative standard deviations （RSDs） of ^206Pb/^238U ages （2σ） are less than 2.2% for single measurements and 0.6% for weighted means. The obtained weighted mean ^206Pb/^238U ages of three standard zircons agree with the recommended values within 2σrerror. The weighted mean ^206Pb/^238U age of SK10-2 is 31.42=0.25 Ma （2σ） and the RSDs of ^206Pb/^238U ages （2σ） are between 2.4% and 5.7% for single measurements and less than 0.8% for weighted mean. The obtained weighted mean ^206Pb/^238U age is in good agreement with the age obtained by Yuan （2004）. Trace element concentrations of NIST612 and NIST614 obtained under the same LA-ICP-MS operating conditions agree with the recommended values within analytical error. The results indicate that it is possible to measure U-Pb age and trace elements simultaneously by LA-ICP-MS in a small spot size of 20μm.     

A Neurocomputing Model for Binary Coded Genetic Algorithm

A neurocomputing model for Genetic Algorithm (GA) to break the speed bottleneck of GA was proposed. With all genetic operations parallel implemented by NN-based sub-modules, the model integrates both the strongpoint of parallel GA (PGA) and those of hardware GA (HGA). Moreover a new crossover operator named universe crossover was also proposed to suit the NN-based realization.This model was tested with a benchmark function set, and the experimental results validated the potential of the neurocomputing model.The significance of this model means that HGA and PGA can be integrated and the inherent parallelism of GA can be explicitly and farthest realized, as a result, the optimization speed of GA will be accelerated by one or two magnitudes compered to the serial implementation with same speed hardware, and GA will be turned from an algorithm into a machine.     

EXTENDING POMPEIU OPERATOR AND THE COMPACTNESS OF SOLUTION SET FOR A CLASS OF HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS

This paper discusses chiefly the compactness of solution set of following equationswhere △ is the Laplacian in Sobolev's sense, a;(x),i= 0,1,…n, n≥ 3, are real square matrices of dimen-sion N×V , bounded and measurable in a bounded multiply connected domain Ω, the boundary S is as-sumed to be sufficiently smooth, u(x) is unknown vector, z = (x_1,x_2,…,x_n) Ω R~z,m≥1,|S_1|issuperficial measure of the unit sphere of R~Z, |i|=i_1+ i_2 +… + i., △~m=△(△~(m-1)). ,(Ω), ,(Ω), … denote the classes of vectors or matrices whose elements belong to L,(Ω),W,(Ω),…. A vector or a matrix is said to be continuous differentiable, bounded and measurable if so are its ele-