数学物理学报(英文版)

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THE IMPROVED RECONSTRUCTION METHOD FOR NONUNIFORM ATTENUATED SPECT DATA

沈正洁, 王金平

数学物理学报(英文版). 2015 (3): 527-538. DOI: 10.1016/S0252-9602(15)30001-1

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In this article, we study reconstruction of nonuniform attenuated SPECT data and present analytic reconstruction formulae which are similar to Novikov's inversion formula. Furthermore, we extend Natterer's results.

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THE BOUNDARY INTEGRAL METHOD FOR THE HELMHOLTZ EQUATION WITH CRACKS INSIDE A BOUNDED DOMAIN

郭军, 范丽丽, 严国政

数学物理学报(英文版). 2015 (3): 539-551. DOI: 10.1016/S0252-9602(15)30002-3

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We consider a kind of scattering problem by a crack Γ that is buried in a bounded domain D, and we put a point source inside the domain D. This leads to a mixed boundary value problem to the Helmholtz equation in the domain D with a crack Γ. Both sides of the crack Γ are given Dirichlet-impedance boundary conditions, and different boundary condition (Dirichlet, Neumann or Impedance boundary condition) is set on the boundary of D. Applying potential theory, the problem can be reformulated as a system of boundary integral equations. We establish the existence and uniqueness of the solution to the system by using the Fredholm theory.

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FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS

A. AGHAJANI, M. MURSALEEN, A. SHOLE HAGHIGHI

数学物理学报(英文版). 2015 (3): 552-566. DOI: 10.1016/S0252-9602(15)30003-5

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In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.

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HOMOGENIZATION FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES

冯斌华, 赵敦, 孙春友

数学物理学报(英文版). 2015 (3): 567-582. DOI: 10.1016/S0252-9602(15)30004-7

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We study the nonlinear Schrödinger equation with time-oscillating nonlinearity and dissipation originated from the recent studies of Bose-Einstein condensates and optical systems which reads iψ_t+Δψ +φ(ωt)|ψ|^αψ+iζ(ωt)ψ= 0.Under some conditions, we show that as ω→∞, the solution ψ_ω will locally converge to the solution of the averaged equation iψ_t+Δψ +φ₀|ψ|^αψ+iζ₀ψ= 0 with the same initial condition in L^q((0, T),B_r^s,2)for all admissible pairs (q, r), where T ∈ (0,T_max). We also show that if the dissipation coefficient ζ₀ large enough, then,ψ_ω is global if ω is sufficiently large and ψ_ω converges to ψ in L^q((0,∞),B_r^s,2), for all admissible pairs (q, r). In particular, our results hold for both subcritical and critical nonlinearities.

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SHADOWING, EXPANSIVENESS AND SPECIFICATION FOR C¹-CONSERVATIVE SYSTEMS

Mário BESSA, Manseob LEE, 文晓

数学物理学报(英文版). 2015 (3): 583-600. DOI: 10.1016/S0252-9602(15)30005-9

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We prove that a C¹-generic volume-preserving dynamical system (diffeomorphism or flow) has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in [10, 27],we prove that the C¹-robustness, within the volume-preserving context, of the expansiveness property and the weak specifica- tion property, imply that the dynamical system (diffeomorphism or flow) is Anosov.

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ON SOLVABILITY OF THE INTEGRODIFFERENTIAL HYPERBOLIC EQUATION WITH PURELY NONLOCAL CONDITIONS

Ahcene MERAD, Abdelfatah BOUZIANI, Cenap OZEL, Adem KILIÇMAN

数学物理学报(英文版). 2015 (3): 601-609. DOI: 10.1016/S0252-9602(15)30006-0

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In this study, we prove the existence, uniqueness, and continuous dependence upon the data of solution to integro-differential hyperbolic equation with purely nonlocal (integral) conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain the solution using a numerical technique (Stehfest algorithm) by inverting the Laplace transform.

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ASYMPTOTIC BEHAVIOR OF LINEAR ADVANCED DIFFERENTIAL EQUATIONS

Nguyen Tien DUNG

数学物理学报(英文版). 2015 (3): 610-618. DOI: 10.1016/S0252-9602(15)30007-2

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In this article, we consider a general class of linear advanced differential equations, and obtain explicitly sufficient conditions of convergence and exponential convergence to zero. A necessary condition is provided as well.

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STATIONARY DISTRIBUTION OF A STOCHASTIC SIR MODEL WITH SATURATED INCIDENCE AND ITS ASYMPTOTIC STABILITY

林玉国, 蒋达清, 靳曼莉

数学物理学报(英文版). 2015 (3): 619-629. DOI: 10.1016/S0252-9602(15)30008-4

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In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributions of the solution. We prove that the densities can converge in L¹ to an invariant density.

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ON UNIQUENESS FOR ALGEBROID FUNCTIONS OF FINITE ORDER

张平原, 扈培础

数学物理学报(英文版). 2015 (3): 630-638. DOI: 10.1016/S0252-9602(15)30009-6

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Guided by Lo.Yang's method, we concern the question that how algebroid functions are determined by their multiple values and deficient values and we prove an at most 3v-valued theorem for algebroid functions. The results are complemented by an example for completeness.

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EIGENFUNCTION EXPANSION FOR STURM-LIOUVILLE PROBLEMS WITH TRANSMISSION CONDITIONS AT ONE INTERIOR POINT

Oktay Sh. MUKHTAROV, Kadriye AYDEMIR

数学物理学报(英文版). 2015 (3): 639-649. DOI: 10.1016/S0252-9602(15)30010-2

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The purpose of this article is to extend some spectral properties of regular Sturm-Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with eigenparameter-dependent boundary conditions and two supplementary transmission conditions. We construct the resolvent operator and Green's function and prove theorems about expansions in terms of eigenfunctions in modified Hilbert space L₂[a, b].

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ON GLOBAL BEHAVIOR OF WEAK SOLUTIONS OF COMPRESSIBLE FLOWS OF NEMATIC LIQUID CRYSTALS

王伟伟

数学物理学报(英文版). 2015 (3): 650-672. DOI: 10.1016/S0252-9602(15)30011-4

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In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces. By adapting the arguments for the compressible Navier--Stokes equations, and carefully analyzing the direction field of liquid crystals in the equations of angular momentum, we show the existence of bounded absorbing sets, global bounded trajectories, and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ >5/3.

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CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE

吴昭君, 陈生安, 陈裕先

数学物理学报(英文版). 2015 (3): 673-680. DOI: 10.1016/S0252-9602(15)30012-6

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In this article, some facts of the value distribution theory for meromorphic functions with maximal deficiency sum in the plane will be considered in the punctured plane, and also the relationship between the deficiency of meromorphic function in the punctured plane and that of their derivatives is studied.

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THE PROBLEM FOR THE SUPERSONIC PLANE FLOW PAST A CURVED WEDGE

王丽

数学物理学报(英文版). 2015 (3): 681-689. DOI: 10.1016/S0252-9602(15)30013-8

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The problem for the supersonic plane flow described by TSD equation past a curved wedge is considered. For a given curved wedge, we will determine the corresponding shock and the solution behind the shock. Moreover, under suitable assumptions, we obtain the global existence and uniqueness for the above mentioned problem.

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ON THE HYERS-ULAM STABILITY OF AN EQUATION CHARACTERIZING MULTI-QUADRATIC MAPPINGS

Krzysztof CIEPLINSKI, Angelika SUROWCZYK

数学物理学报(英文版). 2015 (3): 690-702. DOI: 10.1016/S0252-9602(15)30014-X

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In this article, we prove, both in complete non-Archimedean normed spaces and in 2-Banach spaces, the generalized Hyers-Ulam stability of an equation characterizing multi-quadratic mappings. Our results generalize some known outcomes.

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ON ORDER AND TYPE OF MULTIPLE DIRICHLET SERIES

Meili LIANG

数学物理学报(英文版). 2015 (3): 703-708. DOI: 10.1016/S0252-9602(15)30015-1

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This article investigates the growth of multiple Dirichlet series. The order and the type of n-tuple Dirichlet series in Cⁿ are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained, which generalize some results about simple Dirichlet series of Lindelof and Pringsheim.

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EQUIVALENCE OF THREE DIFFERENT KINDS OF OPTIMAL CONTROL PROBLEMS FOR STOKES EQUATIONS

何培杰, 闫奇姝

数学物理学报(英文版). 2015 (3): 709-718. DOI: 10.1016/S0252-9602(15)30016-3

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This article presents an equivalence theorem for three different kinds of optimal control problems, which are optimal target control problems, optimal norm control problems, and optimal time control problems. Controlled systems in this study are internally controlled Stokes equations.

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INCOMPRESSIBLE LIMIT OF THE NON-ISENTROPIC MAGNETOHYDRODYNAMIC EQUATIONS IN BOUNDED DOMAINS

王术, 徐自立

数学物理学报(英文版). 2015 (3): 719-745. DOI: 10.1016/S0252-9602(15)30017-5

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The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condition for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.

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ASYMPTOTIC BEHAVIOR OF THE STOKES APPROXIMATION EQUATIONS FOR COMPRESSIBLE FLOWS IN R³

吴云顺, 谭忠

数学物理学报(英文版). 2015 (3): 746-760. DOI: 10.1016/S0252-9602(15)30018-7

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We consider the Stokes approximation equations for compressible flows in R³. The global unique solution and optimal convergence rates are obtained by pure energy method provided the initial perturbation around a constant state is small. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. As an immediate byproduct, the usual L^p-L²(1≤ p≤ 2) type of the optimal decay rate follow without requiring that the L^p norm of initial data is small.

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