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25 October 2017, Volume 37 Issue 5 Previous Issue    Next Issue

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ZERO DISSIPATION LIMIT TO A RIEMANN SOLUTION FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS Hakho HONG, Teng WANG Acta mathematica scientia,Series B. 2017, 37 (5):  1177-1208.  DOI: 10.1016/S0252-9602(17)30067-X Abstract ( 80 )   RICH HTML PDF   Save For the general gas including ideal polytropic gas, we study the zero dissipation limit problem of the full 1-D compressible Navier-Stokes equations toward the superposition of contact discontinuity and two rarefaction waves. In the case of both smooth and Riemann initial data, we show that if the solutions to the corresponding Euler system consist of the composite wave of two rarefaction wave and contact discontinuity, then there exist solutions to Navier-Stokes equations which converge to the Riemman solutions away from the initial layer with a decay rate in any fixed time interval as the viscosity and the heat-conductivity coefficients tend to zero. The proof is based on scaling arguments, the construction of the approximate profiles and delicate energy estimates. Notice that we have no need to restrict the strengths of the contact discontinuity and rarefaction waves to be small. References | Related Articles | Metrics

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ON A GENERALIZED GEOMETRIC CONSTANT AND SUFFICIENT CONDITIONS FOR NORMAL STRUCTURE IN BANACH SPACES Mina DINARVAND Acta mathematica scientia,Series B. 2017, 37 (5):  1209-1220.  DOI: 10.1016/S0252-9602(17)30068-1 Abstract ( 61 )   RICH HTML PDF   Save In this paper,we introduce a new geometric constant CNJ(p)(a,X) of a Banach space X,which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant.Subsequently,we present several sufficient conditions for normal structure of a Banach space in terms of this new constant,the generalized James constant,the generalized García-Falset coefficient and the coefficient of weak orthogonality of Sims.Our main results of the paper generalize some known results in the recent literature. References | Related Articles | Metrics

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SZEGÖ TYPE FACTORIZATION OF HAAGERUP NONCOMMUTATIVE HARDY SPACES Turdebek N. BEKJAN Acta mathematica scientia,Series B. 2017, 37 (5):  1221-1229.  DOI: 10.1016/S0252-9602(17)30069-3 Abstract ( 51 )   RICH HTML PDF   Save Let M be a σ-finite von Neumann algebra equipped with a normal faithful state φ, and let A be a maximal subdiagonal algebra of M. We proved a Szegö type factorization theorem for the Haagerup noncommutative Hp-spaces. References | Related Articles | Metrics

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GENERALIZED RIEMANN INTEGRAL ON FRACTAL SETS Feng SU Acta mathematica scientia,Series B. 2017, 37 (5):  1230-1236.  DOI: 10.1016/S0252-9602(17)30070-X Abstract ( 119 )   RICH HTML PDF   Save The theory of integration to mathematical analysis is so important that many mathematicians continue to develop new theory to enlarge the class of integrable functions and simplify the Lebesgue theory integration. In this paper, by slight modifying the definition of the Henstock integral which was introduced by Jaroslav Kurzweil and Ralph Henstock, we present a new definition of integral on fractal sets. Furthermore, its integrability has been discussed, and the relationship between differentiation and integral is also established. As an example, the integral of Cantor function on Cantor set is calculated. References | Related Articles | Metrics

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THE VLASOV-MAXWELL-FOKKER-PLANCK SYSTEM WITH RELATIVISTIC TRANSPORT IN THE WHOLE SPACE Dongcheng YANG Acta mathematica scientia,Series B. 2017, 37 (5):  1237-1261.  DOI: 10.1016/S0252-9602(17)30071-1 Abstract ( 58 )   RICH HTML PDF   Save In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space. The global solutions to this system near the relativistic Maxwellian are constructed and the optimal time decay rate of global solutions are also obtained by an approach by combining the compensating function and energy method. References | Related Articles | Metrics

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SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH Xiaoni CHI, Hongjin WEI, Zhongping WAN, Zhibin ZHU Acta mathematica scientia,Series B. 2017, 37 (5):  1262-1280.  DOI: 10.1016/S0252-9602(17)30072-3 Abstract ( 89 )   RICH HTML PDF   Save In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming (CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone (SOC), we reformulate the CCP problem as the second-order cone problem (SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP. References | Related Articles | Metrics

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AVERAGE REGULARITY OF THE SOLUTION TO AN EQUATION WITH THE RELATIVISTIC-FREE TRANSPORT OPERATOR Jianjun HUANG, Zhenglu JIANG Acta mathematica scientia,Series B. 2017, 37 (5):  1281-1294.  DOI: 10.1016/S0252-9602(17)30073-5 Abstract ( 60 )   RICH HTML PDF   Save Let u=u (t,x,p) satisfy the transport equation =f,where f=f (t,x,p) belongs to Lp ((0,T)×R3×R3) for 1 < p < ∞ and  is the relativisticfree transport operator from the relativistic Boltzmann equation.We show the regularity of ∫R3 u(t,x,p) dp using the same method as given by Golse,Lions,Perthame and Sentis.This average regularity is considered in terms of fractional Sobolev spaces and it is very useful for the study of the existence of the solution to the Cauchy problem on the relativistic Boltzmann equation. References | Related Articles | Metrics

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GLOBALLY ATTRACTING SOLUTIONS TO IMPULSIVE FRACTIONAL DIFFERENTIAL INCLUSIONS OF SOBOLEV TYPE Van Hien LE, Dinh Ke TRAN, Trong Kinh CHU Acta mathematica scientia,Series B. 2017, 37 (5):  1295-1318.  DOI: 10.1016/S0252-9602(17)30074-7 Abstract ( 69 )   RICH HTML PDF   Save We study a generalized Cauchy problem associated with a class of impulsive fractional differential inclusions of Sobolev type in Banach spaces. Our aim is to prove the existence of a compact set of globally attracting solutions to the problem in question. An application to fractional partial differential equations subject to impulsive effects is given to illustrate our results. References | Related Articles | Metrics

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COMPLETE MOMENT CONVERGENCE FOR LP-MIXINGALES Dehua QIU, Pingyan CHEN, Volodin ANDREI Acta mathematica scientia,Series B. 2017, 37 (5):  1319-1330.  DOI: 10.1016/S0252-9602(17)30075-9 Abstract ( 63 )   RICH HTML PDF   Save In this paper, the complete moment convergence for Lp-mixingales are studied. Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued Lp-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature. References | Related Articles | Metrics

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LOCAL AND PARALLEL FINITE ELEMENT METHOD FOR THE MIXED NAVIER-STOKES/DARCY MODEL WITH BEAVERS-JOSEPH INTERFACE CONDITIONS Guangzhi DU, Liyun ZUO Acta mathematica scientia,Series B. 2017, 37 (5):  1331-1347.  DOI: 10.1016/S0252-9602(17)30076-0 Abstract ( 70 )   RICH HTML PDF   Save In this paper, we consider the mixed Navier-Stokes/Darcy model with Beavers-Joseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed and analyzed. Optimal errors are obtained and numerical experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithm. References | Related Articles | Metrics

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EXISTENCE RESULT FOR A CLASS OF N-LAPLACIAN EQUATIONS INVOLVING CRITICAL GROWTH Guoqing ZHANG, Weiguo ZHANG, Sanyang LIU Acta mathematica scientia,Series B. 2017, 37 (5):  1348-1360.  DOI: 10.1016/S0252-9602(17)30077-2 Abstract ( 51 )   RICH HTML PDF   Save In this paper,we consider a class of N-Laplacian equations involving critical growth where Ω is a bounded domain with smooth boundary in RN (N > 2),f (x,u) is of critical growth.Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti,we prove the existence of a nontrivial solution for any λ > λ1,λl=λl(l=2,3,…),and λl is the eigenvalues of the operator (-△N,W01,N(Ω)), which is defined by the Z2-cohomological index. References | Related Articles | Metrics

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EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION TO THE INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ MODELIN 2-DIMENSION Guangwu WANG, Boling GUO Acta mathematica scientia,Series B. 2017, 37 (5):  1361-1372.  DOI: 10.1016/S0252-9602(17)30078-4 Abstract ( 57 )   RICH HTML PDF   Save In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy. The main techniques is the Faedo-Galerkin approximation and weak compactness theory. References | Related Articles | Metrics

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COMPACTNESS FOR THE COMMUTATOR OF BOCHNER-RIESZ OPERATOR Rui BU, Jiecheng CHEN, Guoen HU Acta mathematica scientia,Series B. 2017, 37 (5):  1373-1384.  DOI: 10.1016/S0252-9602(17)30079-6 Abstract ( 43 )   RICH HTML PDF   Save Let α ∈ (0,(n-1)/2) and Tα be the Bochner-Riesz operator of order α.In this paper,for n=2 and n ≥ 3,the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO (Rn) function and Tα. References | Related Articles | Metrics

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POSITIVE STEADY STATES OF A DIFFUSIVE PREDATOR-PREY SYSTEM WITH PREDATOR CANNIBALISM Biao WANG Acta mathematica scientia,Series B. 2017, 37 (5):  1385-1398.  DOI: 10.1016/S0252-9602(17)30080-2 Abstract ( 64 )   RICH HTML PDF   Save The purpose of this paper is to investigate positive steady states of a diffusive predator-prey system with predator cannibalism under homogeneous Neumann boundary conditions. With the help of implicit function theorem and energy integral method, non-existence of non-constant positive steady states of the system is obtained, whereas coexistence of non-constant positive steady states is derived from topological degree theory. The results indicate that if dispersal rate of the predator or prey is sufficiently large, there is no non-constant positive steady states. However, under some appropriate hypotheses, if the dispersal rate of the predator is larger than some positive constant, for certain ranges of dispersal rates of the prey, there exists at least one non-constant positive steady state. References | Related Articles | Metrics

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HEAT KERNEL ESTIMATES ON JULIA SETS Meng YANG Acta mathematica scientia,Series B. 2017, 37 (5):  1399-1414.  DOI: 10.1016/S0252-9602(17)30081-4 Abstract ( 49 )   RICH HTML PDF   Save We give heat kernel estimates on Julia sets J (fc) for quadratic polynomials fc (z)=z2+c for c in the main cardioid or the ±(1)/k-bulbs where k ≥ 2.First we use external ray parametrization to construct a regular,strongly local and conservative Dirichlet form on Julia set.Then we show that this Dirichlet form is a resistance form and the corresponding resistance metric induces the same topology as Euclidean metric.Finally,we give heat kernel estimates under the resistance metric. References | Related Articles | Metrics

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CLASSIFICATION OF POSITIVE SOLUTIONS TO A SYSTEM OF HARDY-SOBOLEV TYPE EQUATIONS Wei DAI, Zhao LIU Acta mathematica scientia,Series B. 2017, 37 (5):  1415-1436.  DOI: 10.1016/S0252-9602(17)30082-6 Abstract ( 58 )   RICH HTML PDF   Save In this paper,we are concerned with the following Hardy-Sobolev type system where 0 < α < n,0 < t1,t2 < min{α,k},and 1 < p ≤ τ1:=(n+α-2t1)/n-α,1 < q ≤ τ2:=(n+α-α2t2)/n-α. We first establish the equivalence of classical and weak solutions between PDE system (0.1) and the following integral equations (IE) system where Gα(x,ξ)=(cn,α)/|x-ξ|n-α is the Green's function of (-△)（α）/2 in Rn.Then,by the method of moving planes in the integral forms,in the critical case p=τ1 and q=τ2,we prove that each pair of nonnegative solutions (u,v) of (0.1) is radially symmetric and monotone decreasing about the origin in Rk and some point z0 in Rn-k.In the subcritical case （n-t1）/p+1 + （n-t2）/q+1 > n-α, 1 < p ≤ τ1 and 1 < q ≤ τ2,we derive the nonexistence of nontrivial nonnegative solutions for (0.1) References | Related Articles | Metrics

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LEFT-RIGHT BROWDER LINEAR RELATIONS AND RIESZ PERTURBATIONS Teresa ÁLVAREZ Acta mathematica scientia,Series B. 2017, 37 (5):  1437-1452.  DOI: 10.1016/S0252-9602(17)30083-8 Abstract ( 58 )   RICH HTML PDF   Save A closed linear relation T in a Banach space X is called left (resp. right) Fredholm if it is upper (resp. lower) semiFredholm and its range (resp. null space) is topologically complemented in X. We say that T is left (resp. right) Browder if it is left (resp. right) Fredholm and has a finite ascent (resp. descent). In this paper, we analyze the stability of the left (resp. right) Fredholm and the left (resp. right) Browder linear relations under commuting Riesz operator perturbations. Recent results of Zivkovic et al. to the case of bounded operators are covered. References | Related Articles | Metrics

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GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS Yamna BOUKHATEM, Benyattou BENABDERRAHMANE Acta mathematica scientia,Series B. 2017, 37 (5):  1453-1471.  DOI: 10.1016/S0252-9602(17)30084-X Abstract ( 65 )   RICH HTML PDF   Save A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered. Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g. References | Related Articles | Metrics

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MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF SEMIPOSITONE NEUMANN PROBLEMS WITH SINGULAR φ-LAPLACIAN Ruyun MA, Hongliang GAO Acta mathematica scientia,Series B. 2017, 37 (5):  1472-1482.  DOI: 10.1016/S0252-9602(17)30085-1 Abstract ( 62 )   RICH HTML PDF   Save We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian where λ is a positive parameter,φ(s)=(s)/√1-s2,f ∈ C1([0,∞),R),f'(u)> 0 for u > 0,and for some 0 < β < θ such that f(u)< 0 for u ∈[0,β)(semipositone) and f(u)> 0 for u > β. Under some suitable assumptions,we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique.Further,if f ∈ C2([0,β)∪(β,∞),R), f"(u) ≥ 0 for u ∈[0,β) and f"(u) ≤ 0 for u ∈(β,∞),then there exist exactly 2n+1 positive solutions for some interval of λ,which is dependent on n and θ.Moreover,We also give some examples to apply our results. References | Related Articles | Metrics

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THE ENERGY FUNCTION WITH RESPECT TO THE ZEROS OF THE EXCEPTIONAL HERMITE POLYNOMIALS Agota P. HORVATH Acta mathematica scientia,Series B. 2017, 37 (5):  1483-1496.  DOI: 10.1016/S0252-9602(17)30086-3 Abstract ( 39 )   RICH HTML PDF   Save We examine the energy function with respect to the zeros of exceptional Hermite polynomials. The localization of the eigenvalues of the Hessian is given in the general case. In some special arrangements we have a more precise result on the behavior of the energy function. Finally we investigate the energy function with respect to the regular zeros of the exceptional Hermite polynomials. References | Related Articles | Metrics

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BSDES IN GAMES, COUPLED WITH THE VALUE FUNCTIONS. ASSOCIATED NONLOCAL BELLMAN-ISAACS EQUATIONS Tao HAO, Juan LI Acta mathematica scientia,Series B. 2017, 37 (5):  1497-1518.  DOI: 10.1016/S0252-9602(17)30087-5 Abstract ( 61 )   RICH HTML PDF   Save We establish a new type of backward stochastic differential equations (BSDEs) connected with stochastic differential games (SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs) equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair (W,U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs' condition. References | Related Articles | Metrics

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LOCAL DISCONTINUOUS GALERKIN METHOD FOR ELLIPTIC INTERFACE PROBLEMS Zhijuan ZHANG, Xijun YU, Yanzhen CHANG Acta mathematica scientia,Series B. 2017, 37 (5):  1519-1535.  DOI: 10.1016/S0252-9602(17)30088-7 Abstract ( 55 )   RICH HTML PDF   Save In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional domains. The interface may be arbitrary smooth curves. It is shown that the error estimates in L2-norm for the solution and the flux are O (h2|logh|) and O (h|logh|1/2),respectively.In numerical experiments,the successive substitution iterative methods are used to solve the LDG schemes.Numerical results verify the efficiency and accuracy of the method. References | Related Articles | Metrics

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UNIVERSAL INEQUALITIES FOR A HORIZONTAL LAPLACIAN VERSION OF THE CLAMPED PLATE PROBLEM ON CARNOT GROUP Feng DU, Chuanxi WU, Guanghan LI, Changyu XIA Acta mathematica scientia,Series B. 2017, 37 (5):  1536-1544.  DOI: 10.1016/S0252-9602(17)30089-9 Abstract ( 80 )   RICH HTML PDF   Save In this paper, we investigate a horizontal Laplacian version of the clamped plate problem on Carnot groups and obtain some universal inequalities. Furthermore, for the lower order eigenvalues of this eigenvalue problem on carnot groups, we also give some universal inequalities. References | Related Articles | Metrics