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25 April 2016, Volume 36 Issue 2 Previous Issue    Next Issue

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MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R2 Yujin GUO, Lu LU Acta mathematica scientia,Series B. 2016, 36 (2):  317-324.  DOI: 10.1016/S0252-9602(16)30001-7 Abstract ( 115 )   RICH HTML PDF   Save Starting with the many-body Schrödinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean-field regime, as the particle number N→∞ and however the scattering length κ→0. By fixing N|κ|, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R2. References | Related Articles | Metrics

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DIFFERENTIAL OPERATORS OF INFINITE ORDER IN THE SPACE OF RAPIDLY DECREASING SEQUENCES M. MALDONADO, J. PRADA, M. J. SENOSIAIN Acta mathematica scientia,Series B. 2016, 36 (2):  325-333.  DOI: 10.1016/S0252-9602(16)30002-9 Abstract ( 64 )   RICH HTML PDF   Save We consider the space of rapidly decreasing sequences s and the derivative operator D defined on it. The object of this article is to study the equivalence of a differential operator of infinite order; that is φ(D)=φkDk.φk constant numbers an a power of D. Dn, meaning, is there a isomorphism X (from s onto s) such that Xφ(D)=DnX?. We prove that if φ(D) is equivalent to Dn, then φ(D) is of finite order, in fact a polynomial of degree n. The question of the equivalence of two differential operators of finite order in the space s is addressed too and solved completely when n=1. References | Related Articles | Metrics

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A BINARY INFINITESIMAL FORM OF TEICHMÜLLER METRIC AND ANGLES IN AN ASYMPTOTIC TEICHMÜLLER SPACE Yan WU, Yi QI Acta mathematica scientia,Series B. 2016, 36 (2):  334-344.  DOI: 10.1016/S0252-9602(16)30003-0 Abstract ( 45 )   RICH HTML PDF   Save The geometry of Teichmüller metric in an asymptotic Teichmüller space is studied in this article. First, a binary infinitesimal form of Teichmüller metric on AT(X) is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmüller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained. References | Related Articles | Metrics

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FAST ALGORITHM FOR CALDERÓN-ZYGMUND OPERATORS: CONVERGENCE SPEED AND ROUGH KERNEL Qixiang YANG, Yong DING Acta mathematica scientia,Series B. 2016, 36 (2):  345-358.  DOI: 10.1016/S0252-9602(16)30004-2 Abstract ( 72 )   RICH HTML PDF   Save In this article, we consider a fast algorithm for first generation Calderón-Zygmund operators. First, we estimate the convergence speed of the relative approximation algorithm. Then, we establish the continuity on Besov spaces and Triebel-Lizorkin spaces for the operators with rough kernel. References | Related Articles | Metrics

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WEAK TYPE INEQUALITY FOR THE MAXIMAL OPERATOR OF WALSH-KACZMARZ-MARCINKIEWICZ MEANS Ushangi GOGINAVA, Károly NAGY Acta mathematica scientia,Series B. 2016, 36 (2):  359-370.  DOI: 10.1016/S0252-9602(16)30005-4 Abstract ( 64 )   RICH HTML PDF   Save The main aim of this article is to prove that the maximal operator σ*κ of the Marcinkiewicz-Fejér means of the two-dimensional Fourier series with respect to Walsh-Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3. References | Related Articles | Metrics

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ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM Zhong WANG, Shangbin CUI Acta mathematica scientia,Series B. 2016, 36 (2):  371-384.  DOI: 10.1016/S0252-9602(16)30006-6 Abstract ( 61 )   RICH HTML PDF   Save In this article, we consider the well-posedness of a coherently coupled Schrödinger system with four waves mixing in space dimension n≤4. The Cauchy problem for the cubic system is studied in L2 for n≤2 and in H1 for n≤4. We obtain two sharp conditions between global existence and blow up. References | Related Articles | Metrics

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A STABILIZED MIXED FINITE ELEMENT FORMULATION FOR THE NON-STATIONARY INCOMPRESSIBLE BOUSSINESQ EQUATIONS Zhendong LUO Acta mathematica scientia,Series B. 2016, 36 (2):  385-393.  DOI: 10.1016/S0252-9602(16)30007-8 Abstract ( 67 )   RICH HTML PDF   Save In this study, we employ mixed finite element (MFE) method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence, uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation. References | Related Articles | Metrics

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LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION Guangjun SHEN, Xiuwei YIN, Litan YAN Acta mathematica scientia,Series B. 2016, 36 (2):  394-408.  DOI: 10.1016/S0252-9602(16)30008-X Abstract ( 112 )   RICH HTML PDF   Save In this article, we study a least squares estimator (LSE) of θ for the Ornstein-Uhlenbeck process X0=0, dXt=θXtdt+dBta, b, t≥0 driven by weighted fractional Brownian motion Ba, b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s ∈[0, t]} as t tends to infinity. References | Related Articles | Metrics

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REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE Wenqiang ZHAO Acta mathematica scientia,Series B. 2016, 36 (2):  409-427.  DOI: 10.1016/S0252-9602(16)30009-1 Abstract ( 64 )   RICH HTML PDF   Save We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div(σ(x)∇u) and multiplicative noises. Under some mild conditions on the diffusion variable σ(x) and without any restriction on the upper growth p of nonlinearity, except that p>2, we show the existences of random attractor in D01, 2(DN, σ)∩ L?(DN)(?∈[2, 2p-2]) space, where DN is an arbitrary (bounded or unbounded) domain in RN, N≥2. For this purpose, some abstract results based on the omega-limit compactness are established. References | Related Articles | Metrics

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EXISTENCE, UNIQUENESS AND STABILITY OF RANDOM IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS A. Vinodkumar, K. Malar, M. Gowrisankar, P. Mohankumar Acta mathematica scientia,Series B. 2016, 36 (2):  428-442.  DOI: 10.1016/S0252-9602(16)30010-8 Abstract ( 113 )   RICH HTML PDF   Save In this article, we study the existence, uniqueness, stability through continuous dependence on initial conditions and Hyers-Ulam-Rassias stability results for random impulsive fractional differential systems by relaxing the linear growth conditions. Finally, we give examples to illustrate its applications. References | Related Articles | Metrics

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RECURRENCE FOR WEIGHTED TRANSLATIONS ON GROUPS Chung-Chuan CHEN Acta mathematica scientia,Series B. 2016, 36 (2):  443-452.  DOI: 10.1016/S0252-9602(16)30011-X Abstract ( 73 )   RICH HTML PDF   Save Let G be a locally compact group, and let 1≤p<∞. We characterize topologically multiply recurrent weighted translation operators on Lp(G) in terms of the Haar measure and the weight function. We also show that there do not exist any recurrent weighted translation operators on L∞(G). References | Related Articles | Metrics

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QUANTILE ESTIMATION WITH AUXILIARY INFORMATION UNDER POSITIVELY ASSOCIATED SAMPLES Yinghua LI, Yongsong QIN, Qingzhu LEI, Lifeng LI Acta mathematica scientia,Series B. 2016, 36 (2):  453-468.  DOI: 10.1016/S0252-9602(16)30012-1 Abstract ( 51 )   RICH HTML PDF   Save The empirical likelihood is used to propose a new class of quantile estimators in the presence of some auxiliary information under positively associated samples. It is shown that the proposed quantile estimators are asymptotically normally distributed with smaller asymptotic variances than those of the usual quantile estimators. References | Related Articles | Metrics

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SOME PROPERTIES OF OPERATOR-VALUED FRAMES Laura GAVRUTA, Pasc GAVRUTA Acta mathematica scientia,Series B. 2016, 36 (2):  469-476.  DOI: 10.1016/S0252-9602(16)30013-3 Abstract ( 101 )   RICH HTML PDF   Save Operator-valued frames (or g-frames) are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this article, we give a new formula for operator-valued frames for finite dimensional Hilbert spaces. As an application, we derive in a simple manner a recent result of A. Najati concerning the approximation of g-frames by Parseval ones. We obtain also some results concerning the best approximation of operator-valued frames by its alternate duals, with optimal estimates. References | Related Articles | Metrics

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NOTES ON THE SPECTRAL PROPERTIES OF THE WEIGHTED MEAN DIFFERENCE OPERATOR G(u, v;Δ) OVER THE SEQUENCE SPACE l1 Vatan KARAKAYA, Ezgi ERDOGAN Acta mathematica scientia,Series B. 2016, 36 (2):  477-486.  DOI: 10.1016/S0252-9602(16)30014-5 Abstract ( 81 )   RICH HTML PDF   Save In the study by Baliarsingh and Dutta[Internat. J.Anal., Vol.2014(2014), Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G(u, v;Δ) over the sequence space l1. The product operator G(u, v;Δ) over l1 is defined by (G(u, v;Δ) x)k=ukvi (xi-xi-1) with xk=0 for all k<0, where x=(xk)∈l1, and u and v are either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G(u, v;Δ) on the sequence space l1. References | Related Articles | Metrics

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CONVERGENCE OF INVARIANT MEASURES FOR MULTIVALUED STOCHASTIC DIFFERENTIAL EQUATIONS Yue GUAN, Hua ZHANG Acta mathematica scientia,Series B. 2016, 36 (2):  487-498.  DOI: 10.1016/S0252-9602(16)30015-7 Abstract ( 77 )   RICH HTML PDF   Save This article is concerned with the weak convergence of invariant measures associated with multivalued stochastic differential equations in the finite dimensional space. References | Related Articles | Metrics

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WEAK TIME-PERIODIC SOLUTIONS TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS Hong CAI, Zhong TAN Acta mathematica scientia,Series B. 2016, 36 (2):  499-513.  DOI: 10.1016/S0252-9602(16)30016-9 Abstract ( 71 )   RICH HTML PDF   Save The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from[3] in the following sense:we extend the class of pressure functions, that is, we consider lower exponent γ. References | Related Articles | Metrics

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GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LINEAR AND NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS Xiaobao ZHU Acta mathematica scientia,Series B. 2016, 36 (2):  514-526.  DOI: 10.1016/S0252-9602(16)30017-0 Abstract ( 130 )   RICH HTML PDF   Save In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations (Δ-∂/∂t)u(x, t)+q(x, t)u(x, t)=0 and nonlinear parabolic equations (Δ-∂/∂t)u(x, t)+h(x, t)up(x, t)=0(p>1) on Riemannian manifolds. As applications, we obtain some theorems of Liouville type for positive ancient solutions of such equations. Our results generalize that of Souplet-Zhang ([1], Bull. London Math. Soc. 38(2006), 1045-1053) and the author ([2], Nonlinear Anal. 74(2011), 5141-5146). References | Related Articles | Metrics

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INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRÉZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL Jing ZHANG, Shiwang MA Acta mathematica scientia,Series B. 2016, 36 (2):  527-536.  DOI: 10.1016/S0252-9602(16)30018-2 Abstract ( 77 )   RICH HTML PDF   Save In this article, we give a new proof on the existence of infinitely many sign-changing solutions for the following Brézis-Nirenberg problem with critical exponent and a Hardy potential -Δu-μu/|x|2=λu+|u|2*-2u in Ω, u=0 on ∂Ω, where Ω is a smooth open bounded domain of RN which contains the origin, 2*=2N/N-2 is the critical Sobolev exponent. More precisely, under the assumptions that N≥7, μ∈[0, μ-4), and μ=(N-2)2/4, we show that the problem admits infinitely many sign-changing solutions for each fixed λ>0. Our proof is based on a combination of invariant sets method and Ljusternik-Schnirelman theory. References | Related Articles | Metrics

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POSITIVE STEADY STATES AND DYNAMICS FOR A DIFFUSIVE PREDATOR-PREY SYSTEM WITH A DEGENERACY Lu YANG, Yimin ZHANG Acta mathematica scientia,Series B. 2016, 36 (2):  537-548.  DOI: 10.1016/S0252-9602(16)30019-4 Abstract ( 76 )   RICH HTML PDF   Save In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system. References | Related Articles | Metrics

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MULTIPLICITY OF SOLUTIONS FOR A QUASILINEAR ELLIPTIC EQUATION Ke WU, Xian WU Acta mathematica scientia,Series B. 2016, 36 (2):  549-559.  DOI: 10.1016/S0252-9602(16)30020-0 Abstract ( 69 )   RICH HTML PDF   Save We study a quasilinear elliptic equation with polynomial growth coefficients. The existence of infinitely many solutions is obtained by a dual method and a nonsmooth critical point theory. References | Related Articles | Metrics

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DISCRETE GALERKIN METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS P. MOKHTARY Acta mathematica scientia,Series B. 2016, 36 (2):  560-578.  DOI: 10.1016/S0252-9602(16)30021-2 Abstract ( 133 )   RICH HTML PDF   Save In this article, we develop a fully Discrete Galerkin(DG) method for solving initial value fractional integro-differential equations(FIDEs). We consider Generalized Jacobi polynomials(GJPs) with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. The fractional derivatives are used in the Caputo sense. The numerical solvability of algebraic system obtained from implementation of proposed method for a special case of FIDEs is investigated. We also provide a suitable convergence analysis to approximate solutions under a more general regularity assumption on the exact solution. Numerical results are presented to demonstrate the effectiveness of the proposed method. References | Related Articles | Metrics

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TOPOLOGICAL ENTROPY OF PERIODIC COVEN CELLULAR AUTOMATA Weibin LIU, Jihua MA Acta mathematica scientia,Series B. 2016, 36 (2):  579-592.  DOI: 10.1016/S0252-9602(16)30022-4 Abstract ( 55 )   RICH HTML PDF   Save We investigate topological entropy of periodic Coven cellular automatas; that is, the maps FB:{0, 1}Z→{0, 1}Z defined by FB(x)i=xi+(xi+j+bj) (mod 2), where B=b1b2…br∈{0, 1}r(r≥2), is a periodic word. In particular, we prove that if the minimal period of B is greater than r/2, the topological entropy is log 2. References | Related Articles | Metrics

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ON APPROXIMATELY (p, q)-WRIGHT AFFINE FUNCTIONS AND INNER PRODUCT SPACES Anna BAHYRYCZ, Magdalena PISZCZEK Acta mathematica scientia,Series B. 2016, 36 (2):  593-601.  DOI: 10.1016/S0252-9602(16)30023-6 Abstract ( 99 )   RICH HTML PDF   Save We prove, using the fixed point approach, some results on hyperstability (in normed spaces) of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces. References | Related Articles | Metrics

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GENERAL SPLIT FEASIBILITY PROBLEMS FOR TWO FAMILIES OF NONEXPANSIVE MAPPINGS IN HILBERT SPACES Jinfang TANG, Shih-sen CHANG, Min LIU Acta mathematica scientia,Series B. 2016, 36 (2):  602-613.  DOI: 10.1016/S0252-9602(16)30024-8 Abstract ( 97 )   RICH HTML PDF   Save The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results. References | Related Articles | Metrics

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FREDHOLM OPERATORS ON THE SPACE OF BOUNDED SEQUENCES Egor A. ALEKHNO Acta mathematica scientia,Series B. 2016, 36 (2):  614-634.  DOI: 10.1016/S0252-9602(16)30025-X Abstract ( 50 )   RICH HTML PDF   Save Necessary and sufficient conditions are studied that a bounded operator Tx=(x1*x, x2*x, …) on the space l∞, where xn*∈l∞*, is lower or upper semi-Fredholm; in partic-ular, topological properties of the set {x1*, x2*, …} are investigated. Various estimates of the defect d(T)=codim R(T), where R(T) is the range of T, are given. The case of xn*=dnxtn*, where dn∈R and xtn*≥0 are extreme points of the unit ball Bl∞*, that is, tn ∈βN, is considered. In terms of the sequence {tn}, the conditions of the closedness of the range R(T) are given and the value d(T) is calculated. For example, the condition {n:0<|dn|<δ}=Ø for some δ is sufficient and if for large n points tn are isolated elements of the sequence {tn}, then it is also necessary for the closedness of R(T) (tn0 is isolated if there is a neighborhood U of tn0 satisfying tn∉U for all n≠n0). If {n:|dn|<δ}=Ø, then d(T) is equal to the defect δ{tn} of {tn}. It is shown that if d(T)=∞ and R(T) is closed, then there exists a sequence {An} of pairwise disjoint subsets of N satisfying χAn∉R(T). References | Related Articles | Metrics