上三角无穷维Hamilton算子点谱的对称性

In this paper, by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H, a necessary and sufficient condition is obtained on the symmetry of σP（A） and σ1/P（-A^＊） with respect to the imaginary axis. Then the symmetry of the point spectrum of H is given, and several examples are presented to illustrate the results.     

板模型迁移算子的渐近点谱及其聚点(英文)

In this paper we investigate the asymptotic spectrum and accumulation of a transport operator A in slab geometry with continuous energy, anisotropic scattering and inhomogeneous medium. In L^p （1 ≤ p 〈 ＋∞） space we show a series of new results for the asymptotic point spectrum and accumulation of A.     

$(\omega')$性质及其摄动

In this note we define the property （ω′）, a variant of Weyl’s theorem, and establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for which property （ω′） holds by means of the variant of the essential approximate point spectrum σ1（·） and the spectrum defined in view of the property of consistency in Fredholm and index. In addition, the perturbation of property （ω′） is discussed.     

Tchebyshev Approximation by S~0_1(△) over Some Special Triangulations

The critical point set plays a central role in the theory of Tchebyshev approximation.Generally,in multivariate Tchebyshev approximation,it is not a trivial task to determine whether a set is critical or not.In this paper,we study the characterization of the critical point set of S 0 1(△) in geometry,where is restricted to some special triangulations(bitriangular,single road and star triangulations).Such geometrical characterization is convenient to use in the determination of a critical point set.     

一些特殊三角剖分上分片线性样条的最佳逼近问题

The critical point set plays a central role in the theory of Tchebyshev approximation.Generally,in multivariate Tchebyshev approximation,it is not a trivial task to determine whether a set is critical or not.In this paper,we study the characterization of the critical point set of S 0 1(△) in geometry,where is restricted to some special triangulations(bitriangular,single road and star triangulations).Such geometrical characterization is convenient to use in the determination of a critical point set.     

Tchebyshev Approximation by S01（△） over Some Special Triangulations

The critical point set plays a central role in the theory of Tchebyshev approximation.Generally,in multivariate Tchebyshev approximation,it is not a trivial task to determine whether a set is critical or not.In this paper,we study the characterization of the critical point set of S 0 1(△) in geometry,where is restricted to some special triangulations(bitriangular,single road and star triangulations).Such geometrical characterization is convenient to use in the determination of a critical point set.     

H^1-ESTIMATES OF LITTLEWOOD-PALEY AND LUSIN FUNCTIONS FOR JACOBI ANALYSIS

For a ≥β≥ -1/2 let △（x） = （2shx）^2α＋1 （2chx）2β＋1 denote the weight function on R＋ and L^1 （△） the space of integrable functions on R＋ with respect to △（x）dx, equipped with a convolution structure. For a suitable Ф ∈ L^1 （△）, we put Фt（x） = t^-1 △（x）^-1 △（x/t）Ф（x/t） for t 〉 0 and define the radial maximal operator MФ, as usual manner. We introduce a real Hardy space H^1 （△） as the set of all locally integrable functions f on R＋ whose radial maximal function MФ （f） belongs to L^1 （△）. In this paper we obtain a relation between H^1 （△） and H^1 （R）. Indeed, we characterize H^1 （△） in terms of weighted H^1 Hardy spaces on R via the Abel transform of f. As applications of H^1 （△） and its characterization, we shall consider （H^1 （△）,L^1 （△））-boundedness of some operators associated to the Poisson kernel for Jacobi analysis： the Poisson maximal operator Me, the Littlewood-Paley g-function and the Lusin area function S. They are bounded on L^p（△） for p 〉 1, but not true for p = 1. Instead, Mp, g and a modified Sa,r are bounded from H^1 （△） to L^1 （△）.     

AN ITERATIVE PROCESS FOR FINDING APPROXIMATE SOLUTIONS TO NONLINEAR EQUATIONS OF STRONGLY ACCRETIVE OPERATORS

In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator frow X to X, or to the unique fixed point of T when T is a Lipschitzian and strictly pseudocontractive mapping from a nonempty closed convex subset K of X into itself. Our results are the extension and improvements of the earlier and recent results in this field.     

k-拟-*-A(ｎ)算子的性质(英文)

An operator T is called k-quasi-*-A（n） operator, if T^*k|T¹⁺ⁿ|^2/（1+n）T^k ≥T^*k|T^* |²T^k , k ∈ Z, which is a generalization of quasi-*-A（n） operator. In this paper we prove some properties of k-quasi-*-A（n） operator, such as, if T is a k-quasi-*-A（n） operator and N（T ）■N（T^* ）, then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A（n） operator and N（T ）■N（T ）, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.     

ITERATIVE APPROXIMATION OF FIXED POINTS FOR MULTIVALUED OPERATORS OF THE MONOTONE TYPE IN UNIFORMLY SMOOTH BANACH SPACES

In this paper, let K be a nonempty subset of a uniformly smooth Banach space X, and T:K→2~k be a multivalued operator of the monotone type. The iterative sequence which converges strongly to the unique fixed point of T is given. Our results are the extension and improvements of the results obtained previously by several authors including Dunn, Chidume, Deng and Ding.     

Existence and Uniqueness of Positive Solutions for a System of Multi-order Fractional Differential Equations

In this paper, we prove the existence and uniqueness of positive solutions for a system of multi-order fractional differential equations. The system is used to represent constitutive relation for viscoelastic model of fractional differential equa-tions. Our results are based on the fixed point theorems of increasing operator and the cone theory, some illustrative examples are also presented.     

Small Compact Perturbation of Operators in B∞（Ω）

Abstract： We consider an approximation problem related to strongly irreducible operators, that is, does the direct sum of a strongly irreducible operator in B∞（Ω） and certain operator have a small compact perturbation which is a strongly irreducible operator in B∞（Ω）？ In this paper, we prove that the direct sum of any strongly irreducible operator in B∞（Ω） and certain biquasitriangular operator have small compact perturbations which are strongly irreducible operators in B∞（Ω）.     

POSITIVE SOLUTIONS TO FOURTH-ORDER NEUMANN BOUNDARY VALUE PROBLEM

In this paper, we study a class of fourth-order Neumann boundary value problem (NBVP for short). By virtue of fixed point index and the spectral theory of linear operators, the existence of positive solutions is obtained under the assumption that the nonlinearity satisfies sublinear or superlinear conditions, which are relevant to the first eigenvalue of the corresponding linear operator.     

LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT

In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin‘s function corresponding to the Green‘s function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex.     

求解一类非线性规划的连续同伦方法(英文)

In this paper we present a homotopy continuation method for finding the Karush-Kuhn-Tucker point of a class of nonlinear non-convex programming problems. Two numerical examples are given to show that this method is effective. It should be pointed out that we extend the results of Lin et al. （see Appl. Math. Comput., 80（1996）, 209-224） to a broader class of non-convex programming problems.     

MODELING PHOTONIC CRYSTALS WITH COMPLEX UNIT CELLS BY DIRICHLET-TO-NEUMANN MAPS

For a photonic crystal （PhC） of finite size, it is important to calculate its transmission and reflection spectra. For two-dimensional （2-D） PhCs composed of a square lattice of circular cylinders, the problem can be solved by an efficient method based on the Dirichlet-to-Neumann （DtN） map of the unit cell and a marching scheme using a pair of operators. In this paper, the DtN operator marching method is extended to handle 2-D PhCs with complex unit cells and arbitrary lattice structures.     

COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space HP（Bn） to μ-Bloch space Bμ（Bn）. The conditions are some supremums concerned with ψ,φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.     

Reducibility for Schr¨odinger Operator with Finite Smooth and Time-Quasi-periodic Potential

In this paper, the author establishes a reduction theorem for linear Schr¨odinger equation with finite smooth and time-quasi-periodic potential subject to Dirichlet boundary condition by means of KAM(Kolmogorov-Arnold-Moser) technique. Moreover, it is proved that the corresponding Schr¨odinger operator possesses the property of pure point spectra and zero Lyapunov exponent.     

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.     

Boundedness of the commutator of Marcinkiewicz integral with rough variable kernel

In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space Lγ^2（R^n） to the Lebesgue space L^2（R^n）, which is a substantial improvement and extension of some known results.