## 2011年03期 (共 篇) 引用文章 全选

## TAUBERIAN THEOREMS FOR WEAK ALMOST CONVERGENT FUNCTIONS

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The almost convergent function which was introduced by Raimi [6] and dis- cussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences (see [5]). In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2+.

## A NEW ALGORITHM FOR COMPUTING LARGEST REAL PART EIGENVALUE OF MATRICES: COLLATZ PERRON-FROBERNIUS' APPROACH

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This paper describes a new method and algorithm for the numerical solution of eigenvalues with the largest real part of positive matrices. The method is based on a numerical implementation of Collatz's eigenvalue inclusion theorem for non-negative irre- ducible matrices. Eigenvalues are analyzed for the studies of the stability of linear systems. Finally, a numerical discussion is given to derive the required number of mathematical op- erations of the new algorithm. Comparisons between the new algorithm and several well known ones, such as Power, and QR methods, are discussed.

## ON THE EXCEPTIONAL FIELDS FOR A CLASS OF REAL QUADRATIC FIELDS

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In this paper, we give a lower bound exp(2.2×108) for those discriminants of real quadratic fields Q(√d) with d=N2-4 and h(d)=1.

## MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SUPERLINEAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE

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In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

## THE MAXIMUM AND MINIMUM DEGREES OF RANDOM BIPARTITE MULTIGRAPHS

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In this paper the authors generalize the classic random bipartite graph model, and define a model of the random bipartite multigraphs as follows: let m=m(n) be a positive integer-valued function on n and (n, m; {pk}) the probability space consisting of all the labeled bipartite multigraphs with two vertex sets A={a1,a2,...,an} and B= {b1, b2,..., bm}, in which the numbers taibj of the edges between any two vertices ai∈A and bj∈B are identically distributed independent random variables with distribution P{taibj}=k}=pk, k=0, 1, 2,..., where pk≥0 and ∑ pk=1. They obtain that Xc,d,A, the number of vertices in A with degree between c and d of Gn,m∈ (n, m;{Pk}) has asymptotically Poisson distribution, and answer the following two questions about the space (n,m; {pk}) with {pk} having geometric distribution, binomial distribution and Poisson distribution, respectively. Under which condition for {Pk} can there be a function D(n) such that almost every random multigraph Gnm∈ (n, m; {pk}) has maximum degree D(n) in A? under which condition for {pk} has almost every multigraph Gn,m∈ (n,m;{pk}) a unique vertex of maximum degree in A?

## NEW SYSTEMS OF GENERALIZED QUASI-VARIATIONAL INCLUSIONS IN FC-SPACES AND APPLICATIONS

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In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure. By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.

## MORITA CONTEXT OF WEAK HOPF ALGEBRAS

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Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra AH. We prove that the smash product A#H is an A-ring with a grouplike character, and give a criterion for A#H to be Frobenius over A. Using the theory of A-rings, we mainly construct a Morita context connecting the smash product A#H and the invariant subalgebra AH, which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery.

## A MULTIDIMENSIONAL CENTRAL LIMIT THEOREM WITH SPEED OF CONVERGENCE FOR AXIOM A DIFFEOMORPHISMS

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Let T: X→X be an Axiom A diffeomorphism, m the Gibbs state for a Holder continuous function g. Assume that f : X→Rd is a H(o)lder continuous function with ∫X fdm=0. If the components of f are cohomologously independent, then there exists with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ2. Moreover, there exists a real number A>0 such that, for any integer n≥1,Prokhorov metric.

## ON SYMMETRIC EXTENDED MS-ALGEBRAS WHOSE CONGRUENCES ARE PERMUTABLE

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Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained by Jie Fang on symmetric extended De Morgan algebras are generalized.

## THE SCHUR CONVEXITY OF GINI MEAN VALUES IN THE SENSE OF HARMONIC MEAN

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We prove that the Gini mean values S(a, b; x, y) are Schur harmonic convex with respect to (x, y) ∈(0, ∞)×(0, ∞) if and only if (a, b) ∈{(a, b) : a≥O, a≥b, a+b+1≥ 0}∪{(a, b) : b≥0, b≥a, a+b+1≥0}and Schur harmonic concave with respect to (x,y) ∈(0, ∞)×(0, ∞) if and only if (a,b) ∈{(a,b) :a≤0,b≤0,a+b+1≤0}.

## HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE

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Let Mn be an n-dimensional complete connected and oriented hypersurface in a hyperbolic space Hn+1(c) with non-zero constant mean curvature H and two distinct principal curvatures. In this paper, we show that (1) if the multiplicities of the two distinct principal curvatures are greater than 1, then Mn is isometric to the Riemannian product Sk(r)×Hn-k(-1/(r2+ρ2)), where r>0 and 1-c and one of the two distinct principal curvatures is simple, then Mn is isometric to the Riemannian product Sn-1(r)×H1(-1/(r2+ρ2)) or S1(r)×Hn-1(-1/(r2+ρ2)), r>0, if one of the following conditions is satisfied (i) S≤=(n-1)t22+c2t2-2 on Mn or (ii) S≥(n-1)t12+c2t1-2 on Mn or (iii) (n-1)t22+c2t22≤S≤(n-1)t12+c2t1-2 on Mn, where t1 and t2 are t2 are the positive real roots of (1.5).

## THE OPTIMAL STRATEGY FOR INSURANCE COMPANY UNDER THE INFLUENCE OF TERMINAL VALUE

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This paper considers a model of an insurance company which is allowed to invest a risky asset and to purchase proportional reinsurance. The objective is to find the policy which maximizes the expected total discounted dividend pay-out until the time of bankruptcy and the terminal value of the company under liquidity constraint. We find the solution of this problem via solving the problem with zero terminal value. We also analyze the influence of terminal value on the optimal policy.

## UNIQUENESS OF ENTIRE FUNCTIONS SHARING ONE VALUE

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We deal with the problem of entire functions sharing one value weakly. More- over, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].

## QUALITATIVE ANALYSIS OF HEPATITIS B VIRUS INFECTION MODEL WITH IMPULSIVE VACCINATION AND TIME DELAY

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According to the epidemic state, propagation mode and transformation be- tween HBV infection states, the Hepatitis B Virus (HBV) infection with impulsive vac- cination and time delay are modelled and analyzed. The control methods of impulsive vaccination and active therapy are adopted. By using comparative theorem of impulsive differential equation, the sufficient conditions that Hepatitis B Virus will be eliminated eventually or be persistent are derived.

## INCOMPRESSIBLE PAIRWISE INCOMPRESSIBLE SURFACES IN LINK COMPLEMENTS

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The central subject of studying in this paper is incompressible pairwise in- compressible surfaces in link complements. Let L be a non-split prime link and let F be an incompressible pairwise incompressible surface in S3-L. We discuss the properties that the surface F intersects with 2-spheres in S3-L. The intersection forms a topological graph consisting of a collection of circles and saddle-shaped discs. We introduce topological graphs and their moves (R-move and S2-move), and define the characteristic number of the topological graph for F ∩ S±2. The characteristic number is unchanged under the moves. In fact, the number is exactly the Euler Characteristic number of the surface when a graph satisfies some conditions. By these ways, we characterize the properties of incompressible pairwise incompressible surfaces in alternating (or almost alternating) link complements. We prove that the genus of the surface equals zero if the component number of F ∩ S±2. (or F ∩ S-2) is less than five and the graph is simple for alternating or almost alternating links, Furthermore, one can prove that the genus of the surface is zero if #( F)≤8.

## GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A NONLOCAL EVOLUTION p-LAPLACE SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

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In this paper, the authors discuss the global existence and blow-up of the solution to an evolution ρ-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.

## ENDPOINT ESTIMATES FOR FRACTIONAL INTEGRAL ASSOCIATED TO SCHRODINGER OPERATORS ON THE HEISENBERG GROUPS

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Let L=-ΔHn+V be the Schr(o)dinger operator on the Heisenberg groups Hn, where V is a nonnegative function satisfying the reverse H(o)lder inequality. In this article, the author obtains the BMOL and BLOL estimates of the fractional integrals associated to L.

## FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

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This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hansdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hansdorff dimension and capacity.

## EXISTENCE OF WEAK SOLUTIONS TO A DEGENERATE STEAD-STATE SEMICONDUCTOR EQUATIONS

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In this paper, we consider a degenerate steady-state drift-diffusion model for semiconductors. The pressure function used in this paper is (s)=sα(α>1). We present existence results for general nonlinear diffusivities for the degenerate Dirichlet-Neumann mixed boundary value problem.

## λ-STATISTICAL CONVERGENCE OF ORDER α

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In this paper, we introduce the concept of λ-statistical convergence of order α. Also some relations between the λ-statistical convergence of order α and strong (V, λ)- summability of order α are given.

## INTERFACE BEHAVIOR OF COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DISCONTINUOUS BOUNDARY CONDITIONS AND VACUM

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In this paper, we study a one-dimensional motion of viscous gas near vacuum. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier-Stokes equations, and the free boundaries are the interfaces separating the gas from vacuum, across which the density changes discontinuosly. Smoothness of the solutions and the uniqueness of the weak solutions are also discussed. The present paper extends results in Luo-Xin-Yang [12] to the jump boundary conditions case.

## THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LEVY JUMP

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In this article, we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Levy process, and then show the exponential convergence of (pt)t≥0 to equilibrium uniform on any bounded subset in H.

## MULTIPLE SOLUTIONS FOR ASYMPTOTICALLY LINEAR ELLIPTIC EQUATIONS INVOLVING NATURAL GROWTH TERM

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In this article, under some conditions on the behaviors of the perturbed function f(x, s) or its primitive F(x, s) = f03 f(x,t)dt near infinity and near zero, a class of asymptotically linear elliptic equations involving natural growth term is studied. By computing the critical group, the existence of three nontrivial solutions is proved.

## ACCURACY ENHANCEMENT FOR THE SIGNORINI PROBLEM WITH FINITE ELEMENT METHOD

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In this paper, we study the accuracy enhancement for the frictionless Signorini problem on a polygonal domain with linear finite elements. Numerical test is given to verify our result.

## THE INVISCID AND NON-RESISTIVE LIMIT IN THE CAUCHY PROBLEM FOR 3-D NONHOMOGENEOUS INCOMPRESSIBLE MAGNETO-HYDRODYNAMICS

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In this paper, the inviscid and non-resistive limit is justified for the local-in- time solutions to the equations of nonhomogeneous incompressible magneto-hydrodynamics (MHD) in R3. We prove that as the viscosity and resistivity go to zero, the solution of the Cauchy problem for the nonhomogeneous incompressible MHD system converges to the solution of the ideal MHD system. The convergence rate is also obtained simultaneously.

## THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

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Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. The upwind finite difference schemes applicable to parallel arith- metic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as change of variables, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order dif- ference operators and prior estimates, are adopted. The estimates in 12 norm are derived to determine the error in the approximate solution. This method was already applied to the numerical simulation of migration-accumulation of oil resources.

## MULTISCALE HOMOGENIZATION OF NONLINEAR HYPERBOLIC EQUATIONS WITH SEVERAL TIME SCALES

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We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting. We obtain an accurate homogenization result. We also show that as the nonlinear term depends on the microscopic time variable, the global homogenized problem thus obtained is a system consisting of two hyperbolic equations. It is also shown that in spite of the presence of several time scales, the global homogenized problem is not a reiterated one.

## ON THE C.CHANG TYPE INEQUALITY OF ALGEBROID FUNCTIONS

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In this paper, we investigate the growth relations between algebroid functions and their derivatives, and extend famous C. Chang inequality (see [1, 4]) of meromorphic functions to algebroid functions.

## ESTIMATES FOR EIGENVALUES OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR

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In this paper, we investigate the Dirichlet eigenvalue problem of fourth-order weuggted polynomial operator{△2u-a△u+bu=Apu,in Ω∈Rn,u∣aΩ=au/av∣aΩ=0 where the constants a, b≥0. We obtain some estimates for the upper bounds of the (k+1)-th eigenvalue Λk+1 in terms of the first k eigenvalues. Moreover, these results contain some results for the biharmonic operator.

## NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS

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In the use of finite element methods to the planar elasticity problems, one difficulty is to overcome locking when elasticity constant λ→∞. In the case of traction boundary condition, another difficulty is to make the discrete Korn's second inequality valid. In this paper, a triangular element is presented. We prove that this element is locking-free, the discrete Korn's second inequality holds and the convergence order is two.

## EQUIVARIANT HEAT INVARIANTS OF THE LAPLACIAN AND NONMININMAL OPERATORS ON DIFFERENTIAL FORMS

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In this paper, we compute the first two equivariant heat kernel coefficients of the Bochner Laplacian on differential forms. The first two equivariant heat kernel coeffi- cients of the Bochner Laplacian with torsion are also given. We also study the equivariant heat kernel coefficients of nonminimal operators on differential forms and get the equivari- ant Gilkey-Branson-Fulling formula.

## MULTIPLICITY OF POSITIVE SOLUTIONS FOR SINGULAR ELLIPTIC SYSTEMS WITH CRITICAL SOBOLEV-HARDY AND CONCAVE EXPONENTS

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In this paper, we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains. By means of variational methods, the multiplicity of positive solutions to this problem is obtained.

## CRITICAL EXPONENTS OF EVOLUTIONARY p-LAPLACIAN WITH INTERIOR AND BOUNDARY SOURCES

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This paper is concerned with the evolutionary p-Laplacian with interior and boundary sources. The critical exponents for the nonlinear sources are determined.

## H(O)LDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

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We study Holder continuous solutions for the second order integro-differential equations with infinite delay (P1): u″(t)+cu′(t)+∫-∞tβ(t-s)u′(s)ds+∫-∞tγ(t-s)u(s)ds= Au(t)-∫-∞tδ(t-s)Au(s)ds+f(t) on the line R, where 0<α<1, A is a closed operator in a complex Banach space X, c∈C is a constant, f∈Cα(R,X) and β,γ,δ∈L1(R+). Under suitable assumptions on the kernels β,γ and δ, we completely characterize the Cα- well-posedness of (P1) by using operator-valued Cα-Fourier multipliers.

## WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS

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In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators. By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p1∈(1, ∞), p2,...,p<,m>∈(1, ∞]) p ∈(0, ∞) with 1/p=∑1/pk, then for any weight w, the commutators of m-linear Calderón-Zygmund operator are bounded from Lp1 (Rn, M<,L(log L)σw>)×Lp2 (Rn, Mw)×...×Lpm (Rn, Mw) to Lp(Rn, w) with σ to be a constant depending only on p1 and the order of commutator.

## NORMAL STRUCTURE AND SOME GEOMETRIC PARAMETERS RELATED TO THE MODULUS OF U-CONVEXITY IN BANACH SPACES

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We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters UXα(ε) and βX(ε), both related to Gao's modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.

## MARKOV-MODULATED MEAN-VARIANCE PROBLEM FOR AN INSURER

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In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insurance company is modeled as a diffusion process whose diffusion and drift parameters switch over time according to the same Markov chain. We study the Markov-modulated mean-variance problem for the insurer and derive explicitly the closed form of the efficient strategy and efficient frontier. In the case of no regime switching, we can see that the efficient frontier in our paper coincides with that of [10] when there is no pure jump.

## SEVERAL WEAK-TYPE WEIGHTED INEQUALITIES IN ORLICZ MARTINGALE CLASSES

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The aim of this paper is to establish several necessary and sufficient conditions in order that the weighted inequality p(Mf>λ)Φ(λ)≤∫<,Ω>Ψ(C|f|)σdμ, λ>0 or ρ(Mf>λ)≤C∫<,Ω>Φ(Cλ-1|f|)σdμ, λ>0 holds for every uniformly integral martingale f=(fn), where M is the Doob's maximal operator, Φ, Ψ are both Φ-functions, and ρ, σ are weights.