Authors:Hakho HONG; Teng WANG Pages: 1177 - 1208 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Hakho HONG, Teng WANG 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.

Authors:Mina DINARVAND Pages: 1209 - 1220 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Mina DINARVAND In this paper, we introduce a new geometric constant C N J ( 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.

Authors:Turdebek N. Bekjan Pages: 1221 - 1229 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Turdebek N. Bekjan 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.

Authors:Dongcheng YANG Pages: 1237 - 1261 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Dongcheng YANG 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.

Authors:Xiaoni CHI; Hongjin WEI; Zhongping WAN; Zhibin ZHU Pages: 1262 - 1280 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Xiaoni CHI, Hongjin WEI, Zhongping WAN, Zhibin ZHU 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.

Authors:Jianjun HUANG Pages: 1281 - 1294 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Jianjun HUANG Let u = u(t,x, p) satisfy the transport equation ∂ u ∂ t + P p 0 ∂ ∂ x = , where f=f(t, x,p) belongs to Lp ((0,T)× R 3 × R 3) for 1< p <∞ and ∂ ∂ t + P p 0 ∂ ∂ x is the relativistic-free transport operator from the relativistic Boltzmann equation. We show the regularity of ∫ R 3 u ( t , x , p ) d p 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.

Authors:Van Hien LE; Dinh Ke TRAN; Trong Kinh CHU Pages: 1295 - 1318 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Van Hien LE, Dinh Ke TRAN, Trong Kinh CHU 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.

Authors:Dehua QIU; Pingyan CHEN; Volodin ANDREI Pages: 1319 - 1330 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Dehua QIU, Pingyan CHEN, Volodin ANDREI In this paper, the complete moment convergence for L p -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.

Authors:Guangzhi DU; Liyun ZUO Pages: 1331 - 1347 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Guangzhi DU, Liyun ZUO 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.

Authors:Guoqing ZHANG; Weiguo ZHANG; Sanyang LIU Pages: 1348 - 1360 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Guoqing ZHANG, Weiguo ZHANG, Sanyang LIU In this paper, we consider a class of N-Laplacian equations involving critical growth { - Δ N u = λ u N - 2 u + f ( x , u ) , x ∈ Ω , u ∈ W 0 1 , N ( Ω ) , u ( x ) ≥ 0 , x ∈ Ω , where Ω is a bounded domain with smooth boundary in ℝ N (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, λ≠λℓ (ℓ = 2,3,ċċċ), and λℓ is the eigenvalues of the operator ( - Δ N , W 0 1 , N ( Ω ) ) , which is defined by the ℤ2-cohomological index.

Authors:Guangwu WANG; Boling GUO Pages: 1361 - 1372 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Guangwu WANG, Boling GUO 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.

Authors:Rui BU; Jiecheng CHEN; Guoen HU Pages: 1373 - 1384 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Rui BU, Jiecheng CHEN, Guoen HU Let α ∈ ( 0 , n - 1 2 ) and T α 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 T α.

Authors:Biao WANG Pages: 1385 - 1398 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Biao WANG 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.

Authors:Meng YANG Pages: 1399 - 1414 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Meng YANG We give heat kernel estimates on Julia sets J(fc ) for quadratic polynomials fc (z)= z 2 + 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.

Authors:Wei DAI; Zhao LIU Pages: 1415 - 1436 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Wei DAI, Zhao LIU In this paper, we are concerned with the following Hardy-Sobolev type system (0.1) { ( - Δ ) α 2 u ( x ) = υ q ( x ) y t 2 ( - Δ ) α 2 υ ( x ) = u p ( x ) y t 1 , x = ( y , z ) ∈ ( ℝ k \ { 0 } ) × ℝ n - k , where 0<α<n, 0<t 1,t 2 < min{α,k}, and 1 < p ≤ τ 1 : = n + α - 2 t 1 n - α , 1 < q ≤ τ 2 : = n + α - 2 t 2 n - α . . We first establish the equivalence of classical and weak solutions between PDE system (0.2) { u ( x ) = ∫ ℝ n G α ( x , ξ ) u p ( ξ ) η t 2 d ξ υ ( x ) = ∫ ℝ n G α ( x , ξ ) u p ( ξ ) η t 2 d ξ , where G α ( x , ξ ) = c n , α x - ξ n - α is the Green's function of ( - Δ ) 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 z 0 in ℝn-k. In the subcritical case PubDate: 2017-08-27T16:02:54Z DOI: 10.1016/s0252-9602(17)30082-6

Authors:Yamna BOUKHATEM; Benyattou BENABDERRAHMANE Pages: 1453 - 1471 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Yamna BOUKHATEM, Benyattou BENABDERRAHMANE 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.

Authors:Ruyun MA; Hongliang GAO Pages: 1472 - 1482 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Ruyun MA, Hongliang GAO We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian { - ( φ ( u ′ ) ) ′ = λ f ( u ) , x ∈ ( 0 , 1 ) , u ′ ( 0 ) = 0 = u ′ ( 1 ) , where λ is a positive parameter, φ ( s ) = s 1 - s 2 , f ∈ C 1 ( [ 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 ∈ C 2([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.

Authors:Tao HAO; Juan LI Pages: 1497 - 1518 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Tao HAO, Juan LI 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.

Authors:Zhijuan ZHANG; Xijun YU; Yanzhen CHANG Pages: 1519 - 1535 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Zhijuan ZHANG, Xijun YU, Yanzhen CHANG 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 L 2-norm for the solution and the flux are O(h 2 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.

Authors:Feng DU; Chuanxi WU; Guanghan LI; Changyu XIA Pages: 1536 - 1544 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Feng DU, Chuanxi WU, Guanghan LI, Changyu XIA 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.

Authors:Olivier GUIBÉ; Alip OROPEZA Pages: 889 - 910 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Olivier GUIBÉ, Alip OROPEZA In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type { - div ( B ( x , u ) ∇ u ) = f in Ω , u = 0 on Γ o B ( x , u ) ∇ u ⋅ n → + γ ( x ) h ( u ) = g on Γ 1 where f and g are the element of L 1 (Ω) and L 1 (Γ1), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique.

Authors:Alberto CABADA; Nikolay D. DIMITROV Pages: 911 - 926 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Alberto CABADA, Nikolay D. DIMITROV This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green's function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.

Authors:Qun LIU; Daqing JIANG; Ningzhong SHI; Tasawar HAYAT; Ahmed ALSAEDI Pages: 927 - 940 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Qun LIU, Daqing JIANG, Ningzhong SHI, Tasawar HAYAT, Ahmed ALSAEDI This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo.

Authors:Sun-Hye PARK Pages: 965 - 973 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Sun-Hye PARK In this paper, we consider a von Karman equation with infinite memory. For von Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for von Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history.

Authors:Anyin XIA; Mingshu FAN; Shan LI Pages: 974 - 984 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Anyin XIA, Mingshu FAN, Shan LI This paper deals with the singularity and global regularity for a class of nonlinear porous medium system with time-dependent coefficients under homogeneous Dirichlet boundary conditions. First, by comparison principle, some global regularity results are established. Secondly, using some differential inequality technique, we investigate the blow-up solution to the initial-boundary value problem. Furthermore, upper and lower bounds for the maximum blow-up time under some appropriate hypotheses are derived as long as blow-up occurs.

Authors:R. AGARWAL; S. HRISTOVA; P. KOPANOV; D. O'Regan Pages: 985 - 997 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): R. AGARWAL, S. HRISTOVA, P. KOPANOV, D. O'Regan Differential equations with impulses at random moments are set up and investigated. We study the case of Gamma distributed random moments of impulses. Several properties of solutions are studied based on properties of Gammma distributions. Some sufficient conditions for p-moment exponential stability of the solutions are given.

Authors:Xiaoxiao ZHENG; Yadong SHANG; Xiaoming PENG Pages: 998 - 1018 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Xiaoxiao ZHENG, Yadong SHANG, Xiaoming PENG This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations { i u t + u x x = u v + u 2 u , v t t - v x x = ( u 2 ) x x . First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].

Authors:Inomjon GANIEV; Farrukh MUKHAMEDOV Pages: 1019 - 1032 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Inomjon GANIEV, Farrukh MUKHAMEDOV In this paper we prove the existence of conditional expectations in the noncommutative L p (M,Φ)-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative L p (M,Φ)-spaces.

Authors:Jae-Myoung KIM Pages: 1033 - 1047 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Jae-Myoung KIM We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are Hölder continuous near boundary provided that the scaled mixed Lp,q x,t -norm of the velocity vector field with 3/p+2q ≤ 2, 2 < q < ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution u ɛ Lp,q x,t with 1 ≤ 3 p + 2 p ≤ 3 2 , 3 < p < ∞ , the Hausdorff dimension of its singular set is no greater than max {p,q} ( 3 p + 2 p - 1 ) .

Authors:Paweł SZAFRANIEC Pages: 1048 - 1060 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Paweł SZAFRANIEC In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.

Authors:Minjie JIANG; Wei YAN; Yimin ZHANG Pages: 1061 - 1082 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Minjie JIANG, Wei YAN, Yimin ZHANG This current paper is devoted to the Cauchy problem for higher order dispersive equation u t + ∂ x 2 n + 1 u = ∂ x ( u ∂ x n u ) + ∂ x n - 1 ( u x 2 ) , n ≥ 2 , n ∈ N + . By using Besov-type spaces, we prove that the associated problem is locally well-posed in H ( - n 2 + 3 4 , - 1 2 n ) ( R ) . The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H ( s , a ) ( R ) with s < - n 2 + 3 4 and all a ∈ R .

Authors:Wei DING; Yueping ZHU Pages: 1083 - 1104 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Wei DING, Yueping ZHU In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces F ˙ p α , q ( ω ; R n 1 × R n 2 ) based on the Frazier and Jawerth' method in [11]. This space was firstly introduced in [18]. Then we establish its dual space and get that ( F ˙ p α , q ) * = CMO p - α , q ' for 0 < p ≤ 1.

Authors:Yunxia WEI; Yanping CHEN Pages: 1105 - 1114 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Yunxia WEI, Yanping CHEN This paper is concerned with obtaining theapproximate solution for Volterra-Hammerstein integral equation with a regular kernel. We choose the Gauss points associated with the Legendre weight function ω(x)=1 as the collocation points. The Legendre collocation discretization is proposed for Volterra-Hammerstein integral equation. We provide an error analysis which justifies that the errors of approximate solution decay exponentially in L2 norm and L∞ norm. We give two numerical examples in order to illustrate the validity of the proposed Legendre spectral collocation method.

Authors:Feng CHENG; Wei-Xi LI; Chao-Jiang XU Pages: 1115 - 1132 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Feng CHENG, Wei-Xi LI, Chao-Jiang XU In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L 2-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.

Authors:Tadeusz ANTCZAK Pages: 1133 - 1150 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Tadeusz ANTCZAK In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval-objective function are convex.

Authors:Chuanzhong LI Pages: 1151 - 1161 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Chuanzhong LI In this paper, we construct a new integrable equation called Möbius-Toda equation which is a generalization of q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the Möbius-Toda equation and a whole integrable Möbius-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the Möbius-Toda hierarchy are given and this leads to the existence of the tau function.

Authors:Qun HE; Fanqi ZENG; Daxiao ZENG Pages: 1162 - 1172 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Qun HE, Fanqi ZENG, Daxiao ZENG In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound estimates for the first eigenvalue of the mean Laplacian on Berwald manifolds, which generalize some results in Riemannian geometry.

Authors:Boling GUO; Xiaoyu XI Pages: 573 - 583 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Boling GUO, Xiaoyu XI In this article, we are concerned with the global weak solutions to the 1D compressible viscous hydrodynamic equations with dispersion correction δ2 ρ((φ(ρ))xxφ′(ρ)x with φ(ρ)=ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial conditions. The diffusion term ɛuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in [ 1 ] ( α = 1 2 ) to 0 < α ≤ 1. In addition, we perform the limit ɛ→ 0 with respect to 0 < α ≤ ½.

Authors:Dongyang SHI; Xin LIAO; Lele WANG Pages: 584 - 592 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Dongyang SHI, Xin LIAO, Lele WANG In this article, a nonconforming quadrilateral element (named modified quasi-Wilson element) is applied to solve the nonlinear schrödinger equation (NLSE). On the basis of a special character of this element, that is, its consistency error is of order O(h 3) for broken H 1-norm on arbitrary quadrilateral meshes, which is two order higher than its interpolation error, the optimal order error estimate and superclose property are obtained. Moreover, the global superconvergence result is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.

Authors:Ruirui YANG; Wei ZHANG; Xiangqing LIU Pages: 593 - 606 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Ruirui YANG, Wei ZHANG, Xiangqing LIU In this article, by using the method of invariant sets of descending flow, we obtain the existence of sign-changing solutions of p-biharmonic equations with Hardy potential in ℝN.

Authors:Miaokun WANG; Yuming CHU Pages: 607 - 622 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Miaokun WANG, Yuming CHU In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.

Authors:Nguyen Van THIN Pages: 623 - 656 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Nguyen Van THIN In 1996, C. C. Yang and P. C. Hu [8] showed that: Let f be a transcendental meromorphic function on the complex plane, and a ≠ 0 be a complex number; then assume that n ≥ 2, n 1, …,n k are nonnegative integers such that n 1 + ⋯ + n k ≥ 1 ; thus f n ( f ′ ) n 1 ⋯ ( f ( k ) ) n k − a has infinitely zeros. The aim of this article is to study the value distribution of differential polynomial, which is an extension of the result of Yang and Hu for small function and all zeros of f having multiplicity at least k ≥ 2. Namely, we prove that f n ( f ′ ) n 1 ⋯ ( f ( k ) ) n k − a ( z ) has infinitely zeros, where f is a transcendental meromorphic function on the complex plane whose all zeros have multiplicity at least k ≥ 2, and a(z) ≡ 0 is a small function of f and n ≥ 2, n 1,…,n k are nonnegative integers satisfying n 1+…+ n k ≥ 1. Using it, we establish some normality criterias for a family of meromorphic functions under a condition where differential polynomials generated by the members of the family share a holomorphic function with zero points. The results of this article are supplement of some problems studied by J. Yunbo and G. Zongsheng [6], and extension of some problems studied X. Wu and Y. Xu [10]. The main result of this article also leads to a counterexample to the converse of Bloch's principle.

Authors:Chunlei HE; Shoujun HUANG; Xiaomin XING Pages: 657 - 667 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Chunlei HE, Shoujun HUANG, Xiaomin XING This article concerns the self-similar solutions to the hyperbolic mean curvature flow (HMCF) for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.

Authors:Tianjiao XUE; Runling AN; Jinchuan HOU Pages: 668 - 678 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Tianjiao XUE, Runling AN, Jinchuan HOU Let A be a unital algebra and M be a unital A -bimodule. A linear map δ: A → M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ ( A ) ∘ B + A ∘ δ ( B ) = δ ( A ∘ B ) for any A , B ∈ A with A ○ B= P, here A ○ B = AB + BA is the usual Jordan product. In this article, we show that if A = A lg N is a Hilbert space nest algebra and M = B ( H ) , or A = M = B ( X ) , then, a linear map δ : A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B ( X ) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.

Authors:Feng Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Feng SU 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.

Authors:Teresa Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Teresa ÁLVAREZ 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.

Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Ágota P. HORVÁTH 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.

Authors:Fei HOU Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Fei HOU This paper is a continue work of [4,5]. In the previous two papers, we studied the Cauchy problem of the multi-dimensional compressible Euler equations with time-depending damping term - μ ( 1 + t ) λ ρ u , where λ≥0 and μ > 0 are constants. We have showed that, for all λ≥0 and μ>0, the smooth solution to the Cauchy problem exists globally or blows up in finite time. In the present paper, instead of the Cauchy problem we consider the initial-boundary value problem in the half space ℝd + with space dimension d = 2,3. With the help of the special structure of the equations and the fluid vorticity, we overcome the difficulty arisen from the boundary effect. We prove that there exists a global smooth solution for 0 ≤ λ <1 when the initial data is close to its equilibrium state. In addition, exponential decay of the fluid vorticity will also be established.