数学物理学报(英文版)

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WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS

胡国恩, 朱月萍

数学物理学报(英文版). 2011 (3): 749-764. DOI: 10.1016/S0252-9602(11)60273-7

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In this paper, the authors consider the weighted estimates for the commutators of multilinear Calder\'on-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≤k≤m1/p_k, then for any weight w, the commutators of m-linear Calder\'on-Zygmund operator are bounded from L^p¹(Rⁿ, M_L_{(log L）^σw})×L^p²(Rⁿ, Mw)×…×L^pm(Rⁿ, Mw) to L^p(Rⁿ, w) with σ to be a constant depending only on p₁ and the order of commutator.

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HÖLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

步尚全

数学物理学报(英文版). 2011 (3): 765-777. DOI: 10.1016/S0252-9602(11)60274-9

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We study H\"older continuous solutions for the second order integro-differential equations with infinite delay (P₁): u''(t)+ cu'(t)+∫^t_-∞β (t-s)u'(s)ds+∫^t_-∞γ(t-s)u(s)ds =Au(t)-∫^t_-∞δ(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 ∈C^α (R，X) and β, γ, δ ∈L¹(R₊). Under suitable assumptions on the kernels β, γ and δ, we completely characterize the C^α-well-posedness of (P₁) by using operator-valued C^α-Fourier multipliers.

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

尹景学, 金春花, 杨莹

数学物理学报(英文版). 2011 (3): 778-790. DOI: 10.1016/S0252-9602(11)60275-0

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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.

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

Tsing-San Hsu, Huei-Lin Li

数学物理学报(英文版). 2011 (3): 791-804. DOI: 10.1016/S0252-9602(11)60276-2

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

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EQUIVARIANT HEAT INVARIANTS OF THE LAPLACIAN AND NONMININMAL OPERATORS DIFFERENTIAL FORMS

王勇

数学物理学报(英文版). 2011 (3): 805-814. DOI: 10.1016/S0252-9602(11)60277-4

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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 coefficients 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 equivariant Gilkey-Branson-Fulling formula.

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NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS

陈绍春, 郑艳君, 毛士鹏

数学物理学报(英文版). 2011 (3): 815-825. DOI: 10.1016/S0252-9602(11)60278-6

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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.

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

孙和军, 陈大广

数学物理学报(英文版). 2011 (3): 826-834. DOI: 10.1016/S0252-9602(11)60279-8

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In this paper, we investigate the Dirichlet eigenvalue problem of fourth-order weighted polynomial operator

Δ² u -a Δu +b u =Λρu, in Ω ( Rⁿ,
u|_∂Ω=∂u/∂ν|_∂Ω=0,
where the constants a, b ≥0. We obtain some estimates for the upper bounds of the (k+1)-th eigenvalue Λ_k+1in terms of the first k eigenvalues. Moreover, these results contain some results for the biharmonic operator.

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ON THE C. CHANG TYPE INEQUALITY OF ALGEBROID FUNCTIONS

孙道椿, 高宗升

数学物理学报(英文版). 2011 (3): 835-842. DOI: 10.1016/S0252-9602(11)60280-4

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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.

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MULTISCALE HOMOGENIZATION OF NONLINEAR HYPERBOLIC EQUATIONS WITH SEVERAL TIME SCALES

Jean Louis Woukeng, David Dongo

数学物理学报(英文版). 2011 (3): 843-856. DOI: 10.1016/S0252-9602(11)60281-6

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We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting. We obtain an accurate omogenization 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.

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

袁益让

数学物理学报(英文版). 2011 (3): 857-881. DOI: 10.1016/S0252-9602(11)60282-8

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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 arithmetic 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 difference operators and prior estimates, are adopted. The estimates in l ²norm 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.

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

张剑文

数学物理学报(英文版). 2011 (3): 882-896. DOI: 10.1016/S0252-9602(11)60283-X

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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.

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ACCURACY ENHANCEMENT FOR THE SIGNORINI PROBLEM WITH FINITE ELEMENT METHOD

李明霞, 陈竑焘, 毛士鹏

数学物理学报(英文版). 2011 (3): 897-908. DOI: 10.1016/S0252-9602(11)60284-1

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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.

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MULTIPLE SOLUTIONS FOR ASYMPTOTICALLY LINEAR ELLIPTIC EQUATIONS INVOLVING NATURAL GROWTH TERM

张贻民, 沈尧天

数学物理学报(英文版). 2011 (3): 909-924. DOI: 10.1016/S0252-9602(11)60285-3

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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)=∫₀^s 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.

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THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LÉVY JUMP

周国立, 侯振挺

数学物理学报(英文版). 2011 (3): 925-933. DOI: 10.1016/S0252-9602(11)60286-5

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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 Lévy process, and then show the exponential convergence of (p_t)_t≥0 to equilibrium uniform on any bounded subset in H.

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

郭真华, 贺文

数学物理学报(英文版). 2011 (3): 934-952. DOI: 10.1016/S0252-9602(11)60287-7

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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.

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λ-STATISTICAL CONVERGENCE OF ORDER α

R.Colak, C. A. Bektas

数学物理学报(英文版). 2011 (3): 953-959. DOI: 10.1016/S0252-9602(11)60288-9

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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 αand strong ( V, λ}-summability of order α are given.

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

吴斌

数学物理学报(英文版). 2011 (3): 960-968. DOI: 10.1016/S0252-9602(11)60289-0

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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 φ(s)=s^α~(α>1). We present existence results for general nonlinear diffusivities for the degenerate Dirichlet-Neumann mixed boundary value problem.

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FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

陈振龙

数学物理学报(英文版). 2011 (3): 969-992. DOI: 10.1016/S0252-9602(11)60290-7

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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 Hausdorff dimensions of non-polar sets by constructing a
Cantor-type set to connect its Hausdorff dimension and capacity.

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

江寅生

数学物理学报(英文版). 2011 (3): 993-1000. DOI: 10.1016/S0252-9602(11)60291-9

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Let L=-Δ_Hⁿ+V be the Schr"odinger operator on the Heisenberg groups Hⁿ, where V is a nonnegative function satisfying the reverse H\"older inequality. In this article, the author obtains the BMO_L and BLO_L estimates of the fractional integrals associated to L.

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

吴学凇, 高文杰, 曹建文

数学物理学报(英文版). 2011 (3): 1001-1010. DOI: 10.1016/S0252-9602(11)60292-0

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In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-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.

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INCOMPRESSIBLE PAIRWISE INCOMPRESSIBLE SURFACES IN LINK COMPLEMENTS

韩友发

数学物理学报(英文版). 2011 (3): 1011-1019. DOI: 10.1016/S0252-9602(11)60293-2

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The central subject of studying in this paper is incompressible pairwise incompressible 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∩S²_±. 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∩S²₊ (or F∩S²_-) 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.

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

乔梅红, 齐欢, 陈迎春

数学物理学报(英文版). 2011 (3): 1020-1034. DOI: 10.1016/S0252-9602(11)60294-4

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According to the epidemic state, propagation mode and transformation between HBV infection states, the Hepatitis B Virus (HBV) infection with impulsive vaccination 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.

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NORMAL STRUCTURE AND SOME GEOMETRIC PARAMETERS RELATED TO THE MODULUS OFU-CONVEXITY IN BANACH SPACES

Ji Gao, Satit Saejung

数学物理学报(英文版). 2011 (3): 1035-1040. DOI: 10.1016/S0252-9602(11)60295-6

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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
U^a_X(ε) and β_X(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.

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SEVERAL WEAK-TYPE WEIGHTED INEQUALITIES IN ORLICZ MARTINGALE CLASSES

陈伟, 刘培德

数学物理学报(英文版). 2011 (3): 1041-1050. DOI: 10.1016/S0252-9602(11)60296-8

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The aim of this paper is to establish several necessary and sufficient conditions in order that the weighted inequality

ρ(Mf>λΦ(λ)≤C∫_Ωψ(C|f|)σdu, ∨λ>0

or

ρ(Mf>λΦ(λ)≤C∫_ΩΦ(Cλ^-1|f|)σdu, ∨λ>0

holds for every uniformly integral martingale f=(f_n), where M is the Doob's maximal operator, ψ, ψ are both Φ-functions, and ρ, σ are weights.

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MARKOV-MODULATED MEAN-VARIANCE PROBLEM FOR AN INSURER

王伟, 毕俊娜

数学物理学报(英文版). 2011 (3): 1051-1061. DOI: 10.1016/S0252-9602(11)60297-X

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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.

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UNIQUENESS OF ENTIRE FUNCTIONS SHARING ONE VALUE

林秀清, 林伟川

数学物理学报(英文版). 2011 (3): 1062-1076. DOI: 10.1016/S0252-9602(11)60298-1

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We deal with the problem of entire functions sharing one value weakly. Moreover, 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].

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

刘伟, 袁海丽, 胡亦钧

数学物理学报(英文版). 2011 (3): 1077-1090. DOI: 10.1016/S0252-9602(11)60299-3

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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.

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HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE

苏变萍, 舒世昌, Yi Annie Han

数学物理学报(英文版). 2011 (3): 1091-1102. DOI: 10.1016/S0252-9602(11)60300-7

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Let Mⁿbe 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 S^k(r)×H^^n-k(-1/(r^2+ρ²)), where r>0 and 1<k<n-1; (2) if H²>-c and one of the two distinct principal curvatures is simple, then Mⁿis 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+c²t^-2₂ on Mⁿ or (ii) S≥(n-1)t²₁+c²t^-2₁ on Mⁿor (iii) (n-1)t²₂+c²t^-2₂≤S≤ (n-1)t²₁+c²t^-2₁ on Mⁿ, where t₁ and t₂ are the positive real roots of (1.5).

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

夏卫锋, 褚玉明

数学物理学报(英文版). 2011 (3): 1103-1112. DOI: 10.1016/S0252-9602(11)60301-9

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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≥0, 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}.

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ON SYMMETRIC EXTENDED MS-ALGEBRAS WHOSE CONGRUENCES ARE PERMUTABLE

罗从文

数学物理学报(英文版). 2011 (3): 1113-1122. DOI: 10.1016/S0252-9602(11)60302-0

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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.

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

夏红强, 檀大耀

数学物理学报(英文版). 2011 (3): 1123-1132. DOI: 10.1016/S0252-9602(11)60303-2

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Let T: X→ X be an Axiom A diffeomorphism, m the Gibbs state for a H\"older continuous function g. Assume that f: X→ R^d is a H\"older
continuous function with ∫_Xf dm=0. If the components of f are cohomologously independent, then there exists a positive definite
symmetric matrix σ²:=σ²(f) such that S_n^f/n converges in distribution 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,

∏(m_*{1/√n S_n^f), N(0, σ²))≤A /√n,
where m_*(1/√n S_n^f) denotes the distribution of 1/√n S_n^f with respect to m, and ∏ is the Prokhorov metric.

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MORITA CONTEXT OF WEAK HOPF ALGEBRAS

侯波, 张子龙, 蔡炳苓, 李燕

数学物理学报(英文版). 2011 (3): 1133-1141. DOI: 10.1016/S0252-9602(11)60304-4

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Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra A^H. 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 <A^H, A#H, A,A, τ, μ connecting the smash product A#H and the invariant subalgebra A^H, which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery.

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

丁协平

数学物理学报(英文版). 2011 (3): 1142-1154. DOI: 10.1016/S0252-9602(11)60305-6

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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.

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THE MAXIMUM AND MINIMUM DEGREES OF RANDOM BIPARTITE MULTIGRAPHS

陈爱莲, 张福基, 李皓

数学物理学报(英文版). 2011 (3): 1155-1166. DOI: 10.1016/S0252-9602(11)60306-8

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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 G(n, m; {p_k}) the probability space consisting of all the labeled bipartite multigraphs with two vertex sets A = {a₁, a₂, · · · , a_n} and B ={b₁, b₂, · · · , b_m}, in which the numbers tai,bj of the edges between any two vertices ai 2 A and bj 2 B are identically distributed independent random variables with distribution

P{t_ai,_bj= k} = p_k, k = 0, 1, 2, · · · ,
where p_k ≥ 0 and ∑^∞ _k=0 p_k = 1. They obtain that Xc,d,A, the number of vertices in A with degree between c and d of G_n,m ∈G(n, m; {p_k}) has asymptotically Poisson distribution, and answer the following two questions about the space G(n, m; {p_k}) with {p_k} having geometric distribution, binomial distribution and Poisson distribution, respectively. Under which condition for {p_k} can there be a function D(n) such that almost every random multigraph G_n,m ∈ G(n, m; {p_k}) has maximum degree D(n) in A? under which condition for {p_k} has almost every multigraph G_n,m ∈ G(n, m; {p_k}) a unique vertex of maximum degree in A?

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

郭大钧

数学物理学报(英文版). 2011 (3): 1167-1178. DOI: 10.1016/S0252-9602(11)60307-X

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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.

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ON THE EXCEPTIONAL FIELDS FOR A CLASS OF REAL QUADRATIC FIELDS

刘丽, 陆洪文

数学物理学报(英文版). 2011 (3): 1179-1188. DOI: 10.1016/S0252-9602(11)60308-1

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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.

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A NEW ALGORITHM FOR COMPUTING LARGEST REAL PART EIGENVALUE OF MATRICES: COLLATZ &|PERRON-FROBERNIUS&rsquo|APPROACH

Tedja Santanoe Oepomo

数学物理学报(英文版). 2011 (3): 1189-1202. DOI: 10.1016/S0252-9602(11)60309-3

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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.

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TAUBERIAN THEOREMS FOR WEAK ALMOST CONVERGENT FUNCTIONS

Meng-Kuang Kuo

数学物理学报(英文版). 2011 (3): 1203-1212. DOI: 10.1016/S0252-9602(11)60310-X

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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⁺.

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