Authors:Dexing KONG; Qi LIU Pages: 745 - 755 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Dexing KONG, Qi LIU In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation ∂ 2 g i j ∂ t 2 + μ ( 1 + t ) λ ∂ g i j ∂ t = - 2 R i j , on Riemann surface. On the basis of the energy method, for 0 < λ ≤ 1, μ > λ + 1, we show that there exists a global solution gij to the hyperbolic geometry flow with time-dependent dissipation with asymptotic flat initial Riemann surfaces. Moreover, we prove that the scalar curvature R(t,x) of the solution metric gij remains uniformly bounded.

Authors:Xiaoli DING; Yaolin JIANG Pages: 756 - 768 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Xiaoli DING, Yaolin JIANG Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As far as we known, the nonnegativity of solutions of the nonlinear fractional differential-algebraic equations is still not studied. In this article, we investigate the nonnegativity of solutions of the equations. Firstly, we discuss the existence of nonnegative solutions of the equations, and then we show that the nonnegative solution can be approached by a monotone waveform relaxation sequence provided the initial iteration is chosen properly. The choice of initial iteration is critical and we give a method of finding it. Finally, we present an example to illustrate the efficiency of our method.

Authors:Xiaofei ZHANG; Jin LU; Xiaofei LI Pages: 769 - 777 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Xiaofei ZHANG, Jin LU, Xiaofei LI In this article, the sharp growth theorem for almost starlike mappings of complex order λ is given firstly. Secondly, distortion theorem along a unit direction is also established as the application of the growth theorem. In particular, using our results can reduce to some well-known results.

Authors:Jianlin ZHANG; Yuming QIN Pages: 778 - 790 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Jianlin ZHANG, Yuming QIN In this article, we establish exact solutions to the Cauchy problem for the 3D spherically symmetric incompressible Navier-Stokes equations and further study the existence and asymptotic behavior of solution.

Authors:Gholamreza ZAMANI ESKANDANI; Soheila AZARMI; Masoumeh RAEISI Pages: 791 - 804 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Gholamreza ZAMANI ESKANDANI, Soheila AZARMI, Masoumeh RAEISI In this article, we introduce and investigate the concept of multivalued hybrid mappings in CAT(0) spaces by using the concept of quasilinearization. Also, we present a new iterative algorithm involving products of Moreau-Yosida resolvents for finding a common element of the set of minimizers of a finite family of convex functions and a common fixed point of two multivalued hybrid mappings in CAT(0) spaces.

Authors:Huifang LIU; Zhiqiang MAO Pages: 819 - 828 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Huifang LIU, Zhiqiang MAO In this article, the existence of finite order entire solutions of nonlinear difference equations f n + P d ( z , f ) = p 1 e α 1 z + p 2 e α 2 z are studied, where n ≥ 2 is an integer, Pd(z, f) is a difference polynomial in f of degree d(≤ n − 2), p1, p2 are small meromorphic functions of ez , and α1, α2 are nonzero constants. Some necessary conditions are given to guarantee that the above equation has an entire solution of finite order. As its applications, we also find some type of nonlinear difference equations having no finite order entire solutions.

Authors:Qingzhai Fan; Xiaochun Fang Pages: 829 - 842 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Qingzhai Fan, Xiaochun Fang We introduce a special tracial Rokhlin property for unital C*-algebras. Let A be a unital tracial rank zero C*-algebra (or tracial rank no more than one C*-algebra). Suppose that α:G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C*-algebra. Then, the crossed product C*-algebra C*(G, A,α) has tracia rank zero (or has tracial rank no more than one). In fact, we get a more general results.

Authors:Yong LIN; Yiting WU Pages: 843 - 856 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Yong LIN, Yiting WU Let G=(V,E) be a locally finite connected weighted graph, and Δ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut=Δu + f(u) on G. The blow-up phenomenons for ut=Δu + f(u) are discussed in terms of two cases: (i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.

Authors:Yongting HUANG; Hongxia LIU Pages: 857 - 888 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Yongting HUANG, Hongxia LIU In this article, we are concerned with the nonlinear stability of the rarefaction wave for a one-dimensional macroscopic model derived from the Vlasov-Maxwell-Boltzmann system. The result shows that the large-time behavior of the solutions coincides with the one for both the Navier-Stokes-Poisson system and the Navier-Stokes system. Both the time-decay property of the rarefaction wave profile and the influence of the electromagnetic field play a key role in the analysis.

Authors:Shujun LIU; Fangqi CHEN; Zejun WANG Pages: 889 - 897 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Shujun LIU, Fangqi CHEN, Zejun WANG In this article, we give the existence of global L ∞ bounded entropy solutions to the Cauchy problem of a generalized n × n hyperbolic system of LeRoux type. The main difficulty lies in establishing some compactness estimates of the viscosity solutions because the system has been generalized from 2 × 2 to n × n and more linearly degenerate characteristic fields emerged, and the emergence of singularity in the region {v 1=0} is another difficulty. We obtain the existence of the global weak solutions using the compensated compactness method coupled with the construction of entropy-entropy flux and BV estimates on viscous solutions.

Authors:Shibin SU; Xiaokui ZHAO Pages: 898 - 914 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Shibin SU, Xiaokui ZHAO The initial boundary value problem of the one-dimensional magneto-hydrodynamics system, when the viscosity, thermal conductivity, and magnetic diffusion coefficients are general smooth functions of temperature, is considered in this article. A unique global classical solution is shown to exist uniquely and converge to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1.

Authors:Rui LI; Chong LAI; Yonghong WU Pages: 915 - 925 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Rui LI, Chong LAI, Yonghong WU The existence of global weak solutions for a generalized Benjamin-Bona-Mahony-Burgers equation is established in the space C ( [ 0 , ∞ ) × R ) ∩ L ∞ ( [ 0 , ∞ ) ; H 1 ( R ) ) under the condition that its initial value belongs to the space H1(R). A one-sided super bound estimate and a space-time higher-norm estimate on the first order derivatives of the solution with respect to the space variable are derived to prove the existence.

Authors:Ling LI; Hongyi LI; Di ZHAO Pages: 926 - 934 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Ling LI, Hongyi LI, Di ZHAO In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P ( D n , B N ) is C 1 + α at z 0 ∈ E r ⊂ ∂ D n with f(0)= 0 and f ( z 0 ) = w 0 ∈ ∂ B N for any n, N ≥ 1, then there exist a nonnegative vector λ f = ( λ 1 , 0 , … , λ r , 0 , … , 0 ) T ∈ R 2 n satisfying λ i ≥ 1 2 2 n - 1 for 1 ≤ i ≤ r such that ( D f ( z ′ 0 ) ) T w ′ 0 = diag ( λ f ) z ′ 0 , where z ′ 0 and w ′ 0 are real versions of z 0 and w 0, respectively.

Authors:Pengyan WANG; Yongzhong WANG Pages: 935 - 949 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Pengyan WANG, Yongzhong WANG In this article, we study positive solutions to the system { A α u ( x ) = C n , α P V ∫ R n a 1 ( x - y ) ( u ( x ) - u ( y ) ) x - y n + α d y = f ( u ( x ) , υ ( x ) ) , B β υ ( x ) = C n , β P V ∫ R n a 2 ( x - y ) ( υ ( x ) - υ ( y ) ) x - y n + β d y = g ( u ( x ) , υ ( x ) ) . To reach our aim, by using the method of moving planes, we prove a narrow region principle and a {decay at infinity} by the iteration method. On the basis of these results, we conclude radial symmetry and monotonicity of positive solutions for the problems involving the weighted fractional system on an unit ball and the whole space. Furthermore, non-existence of nonnegative solutions on a half space is given.

Authors:Fei SONG; Yi QI; Guangming HU Pages: 950 - 964 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Fei SONG, Yi QI, Guangming HU The eventually distance minimizing ray (EDM ray) in moduli spaces of the Riemann surfaces of analytic finite type with 3g + n − 3 > 0 is studied, which was introduced by Farb and Masur [5]. The asymptotic distance of EDM rays in a moduli space and the distance of end points of EDM rays in the boundary of the moduli space in the augmented moduli space are discussed in this article. A relation between the asymptotic distance of EDM rays and the distance of their end points is established. It is proved also that the distance of end points of two EDM rays is equal to that of end points of two Strebel rays in the Teichmüller space of a covering Riemann surface which are leftings of some representatives of the EDM rays. Meanwhile, simpler proofs for some known results are given.

Authors:Shaojun TANG; Lan ZHANG Pages: 973 - 1000 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Shaojun TANG, Lan ZHANG We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small. The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.

Authors:Yonghui ZHOU; Yunrui YANG; Kepan LIU Pages: 1001 - 1024 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Yonghui ZHOU, Yunrui YANG, Kepan LIU This article is concerned with a population dynamic model with delay and quiescent stage. By using the weighted-energy method combining continuation method, the exponential stability of traveling waves of the model under non-quasi-monotonicity conditions is established. Particularly, the requirement for initial perturbation is weaker and it is uniformly bounded only at x = +∞ but may not be vanishing.

Authors:Azer KHANMAMEDOV; Sema YAYLA Pages: 1025 - 1042 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Azer KHANMAMEDOV, Sema YAYLA We investigate the initial-value problem for the semilinear plate equation containing localized strong damping, localized weak damping and nonlocal nonlinearity. We prove that if nonnegative damping coefficients are strictly positive almost everywhere in the exterior of some ball and the sum of these coefficients is positive a.e. in R n , then the semigroup generated by the considered problem possesses a global attractor in H 2 ( R n ) × L 2 ( R n ) . We also establish the boundedness of this attractor in H 3 ( R n ) × H 2 ( R n ) .

Authors:K. Divya JOSEPH; P.A. DINESH Pages: 1043 - 1056 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): K. Divya JOSEPH, P.A. DINESH This article is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain x > 0, t > 0. The number of boundary conditions, to be prescribed at the boundary x = 0, depends on the number of characteristics entering the domain. Because our system is nonlinear, the characteristic speeds depends on the unknown and the direction of the characteristics curves are known apriori. As it is well known, the boundary condition has to be understood in a generalised way. One of the standard way is using vanishing viscosity method. We use this method to construct solution for a particular class of initial and boundary data, namely the initial and boundary datas that lie on the level sets of one of the Riemann invariants.

Authors:Weifeng JIANG; Kaitai LI Pages: 1057 - 1104 Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Weifeng JIANG, Kaitai LI In this article, we investigate three-dimensional solution with helical symmetry in a gap between two concentric rotating cylinders, inside is a helicoidal surface (screw propeller) while outside is a cylindrical surface. Establish the partial differential equations and its variational formulation satisfied by a helical solution in a helical coordinate system using tensor analysis method, we provide a computational method for the power and propulsion of the screw. The existence and uniqueness of weak helical solutions are proved.

Authors:Janusz BRZDEK; Krzysztof CIEPLIŃSKI Pages: 377 - 390 Abstract: Publication date: March 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 2 Author(s): Janusz BRZDEK, Krzysztof CIEPLIŃSKI The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability results concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.

Authors:Huifang JIA; Gongbao LI Pages: 391 - 418 Abstract: Publication date: March 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 2 Author(s): Huifang JIA, Gongbao LI In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrödinger-Kirchhoff type - ∈ p M ( ∈ p - N ∫ R N ∇ u p ) Δ p u + V ( x ) u p - 2 u = f ( u ) in R N , where Δp is the p-Laplacian operator, 1 < p < N, M: R + → R + and V: R N → R + are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik-Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.

Authors:Huijuan SONG; Jingxue YIN; Zejia WANG Pages: 419 - 428 Abstract: Publication date: March 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 2 Author(s): Huijuan SONG, Jingxue YIN, Zejia WANG In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system - div ( h 1 ( x ) ∇ u p - 2 ∇ u ) = d ( x ) u r - 2 u + G u ( x , u , υ ) - div ( h 2 ( x ) ∇ υ q - 2 ∇ υ ) = f ( x ) υ s - 2 υ + G υ ( x , u , υ ) u = υ = 0 in Ω in Ω on ∂ Ω where Ω is a bounded domain in R N with smooth boundary ∂Ω, N≥2, 1 < r < p < ∞, 1 < s < q < ∞; h1(x) and h2(x) are allowed to have “essential” zeroes at some points in Ω ; d ( x ) u r - 2 u and f ( x ) υ s - 2 υ are small sources with Gu(x,u,v), Gv(x,u,v) being their high-order perturbations with respect to (u,v) near the origin, respectively.

Authors:Jing FU; Daqing JIANG; Ningzhong SHI; Tasawar HAYAT; Ahmed ALSAEDI Pages: 429 - 440 Abstract: Publication date: March 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 2 Author(s): Jing FU, Daqing JIANG, Ningzhong SHI, Tasawar HAYAT, Ahmed ALSAEDI This article addresses a stochastic ratio-dependent predator-prey system with Leslie-Gower and Holling type II schemes. Firstly, the existence of the global positive solution is shown by the comparison theorem of stochastic differential equations. Secondly, in the case of persistence, we prove that there exists a ergodic stationary distribution. Finally, numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings.

Authors:Mingquan WEI; Dunyan YAN Pages: 441 - 449 Abstract: Publication date: March 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 2 Author(s): Mingquan WEI, Dunyan YAN In this article, we obtain the sharp bounds from L P ( G n ) to the space wL P ( G n ) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from L P ( G n ) to the space L PI ( G n ) are obtained.

Authors:Huoyuan DUAN; Junhua MA Pages: 450 - 470 Abstract: Publication date: March 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 2 Author(s): Huoyuan DUAN, Junhua MA On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming (bi)linear macroelements or (bi)quadratic elements, and the rotation by conforming (bi)linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Jasbir Singh MANHAS, Ruhan ZHAO We characterize boundedness and compactness of products of differentiation operators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Shinji ADACHI, Masataka SHIBATA, Tatsuya WATANABE In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE analysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified Schrödinger equations.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Xiao ZHANG, Guoxing JI In this paper, we present some necessary and sufficient conditions for the existence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB=C=BXA in the setting of bounded linear operators on a Hilbert space. Moreover, we obtain the general forms of solutions, hermitian solutions and positive solutions to the system above.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Peide LIU, Maofa WANG In this article, by extending classical Dellacherie's theorem on stochastic sequences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis inequality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier's inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Mahmood POURGHOLAMHOSSEIN, Mohammad ROUZBEHANI, Massoud AMINI In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Nihed TRABELSI The existence of singular limit solutions are investigated by establishing a new Liouville type theorem for nonlinear elliptic system with sub-quadratic convection term and by using the nonlinear domain decomposition method.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Ozge AKCAY The aim of this paper is to construct the integral representation of the solution of Sturm-Liouville equation with eigenparameter-dependent discontinuity conditions at an interior point of the finite interval. Moreover, we examine the properties of the kernel function of this integral representation and obtain the partial differential equation provided by this kernel function.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Ping LI, Congbian MA, Youliang HOU Let O ( P τ L ) be the oscillation of the Possion semigroup associated with the parabolic Hermite operator L = ∂ t - Δ + x 2 . We show that O ( P τ L ) is bounded from L p ( R n + 1 ) into itself for 1 < p < ∞, bounded from L 1 ( R n + 1 ) into weak- L 1 ( R n + 1 ) and bounded from L c ∞ ( R n + 1 ) into BMO ( R n + 1 ) . In the case p =∞ we show that the range of the image of the operator O ( P τ L ) is strictly smaller than the range of a general singular operator.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Salah BOULAARAS, Mohammed Said TOUATI BRAHIM, Smail BOUZENADA, Abderrahmane ZARAI In this paper, a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are proved by using the Euler time scheme combined with Galerkin spatial method. Furthermore, an asymptotic behavior in Sobolev norm is deduced using Benssoussan-Lions' algorithm. Finally, the results of some numerical experiments are presented to support the theory.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Nihal Yilmaz ÖZGÜR, Nihal TAŞ Recently, the notion of an S-metric space is defined and extensively studied as a generalization of a metric space. In this paper, we define the notion of the S ∞-space and prove its completeness. We obtain a new generalization of the classical “Picard Theorem”.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Zhiqiang GAO Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z . Denote by Z_n(z) the number of particles in the n-th generation in the model for each z ∈ Z . We derive the exact convergence rate in the local limit theorem for Z_n(z) assuming a condition like “ E N ( log N ) 1 + λ < ∞ ” for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): M. PIRHAJI, M. ZANGIABADI, H. MANSOURI In this paper, a corrector-predictor interior-point algorithm is proposed for symmetric optimization. The algorithm approximates the central path by an ellipse, follows the ellipsoidal approximation of the central-path step by step and generates a sequence of iterates in a wide neighborhood of the central-path. Using the machinery of Euclidean Jordan algebra and the commutative class of search directions, the convergence analysis of the algorithm is shown and it is proved that the algorithm has the complexity bound O ( r L ) for the well-known Nesterov-Todd search direction and O(rL) for the xs and sx search directions.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Fethi BEN BELGACEM In this paper, we introduce and study a method for the numerical solution of the elliptic Monge-Ampère equation with Dirichlet boundary conditions. We formulate the Monge-Ampère equation as an optimization problem. The latter involves a Poisson Problem which is solved by the finite element Galerkin method and the minimum is computed by the conjugate gradient algorithm. We also present some numerical experiments.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Amin ESFAHANI In this article, we establish the existence of a sign-changing solution and two sign-constant solutions for nonlinear nonlocal problem involving the BO-ZK operator on bounded domain. Our main tool is constrained minimization on appropriate Nehari manifolds.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Yue-Loong CHANG, Meng-Rong LI, C. Jack YUE, Yong-Shiuan LEE, Tsung-Jui CHIANG-LIN In this article, we work with the ordinary equation u ″ - n - q - 1 u ( n ) q = 0 and learn some interesting phenomena concerning the blow-up and the blow-up rate of solution to the equation.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Mohammad ZAREBNIA, Reza PARVAZ, Amir SABOOR BAGHERZADEH In this paper, we study an efficient asymptotically correction of a-posteriori error estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. The deviation of the error for Volterra integro-differential equations by using the defect correction principle is defined. Also, it is shown that for m degree piecewise polynomial collocation method, our method provides O ( h m + 1 ) as the order of the deviation of the error. The theoretical behavior is tested on examples and it is shown that the numerical results confirm the theoretical part.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): R. ABOULAICH, B. ACHCHAB, A. DAROUICHI In the present work, we investigate the inverse problem of reconstructing the parameter of an integro-differential parabolic equation, which comes from pollution problems in porous media, when the final observation is given. We use the optimal control framework to establish both the existence and necessary condition of the minimizer for the cost functional. Furthermore, we prove the stability and the local uniqueness of the minimizer. Some numerical results will be presented and discussed.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Yi QIN, Yanren HOU Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Wenlong SUN, Yeping LI This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated processes, to prove the existence of pullback exponential attractors and global pullback attractors and show that they both with finite fractal dimension. Further, we give the relationship between global pullback attractors and pullback exponential attractors.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Bochra NEFZI, Kamel BRAHIM, Ahmed FITOUHI The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Kamel MEZLINI, Néji BETTAIBI In this paper, we present an explicit realization of q-deformed Calogero-Vasiliev algebra whose generators are first-order q-difference operators related to the generalized discrete q-Hermite I polynomials recently introduced in [14]. Furthermore, we construct the wave functions and we determine the q-coherent states.

Abstract: Publication date: July 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 4 Author(s): Maofa WANG, Xingxing YAO, Fangwen DENG In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.

Authors:Xin Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Xin XU We are concerned with the zero dielectric constant limit for the full electro-magneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and ill-prepared initial data. The explicit convergence rate is also obtained by a elaborate energy estimate. Moreover, we show that for the well-prepared initial data, there is no initial layer, and the electric field always converges strongly to the limit function. While for the ill-prepared data case, there will be an initial layer near t=0. The strong convergence results only hold outside the initial layer.

Authors:Peng SUN Abstract: Publication date: May 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 3 Author(s): Peng SUN We prove a generalized Gauss-Kuzmin-Lévy theorem for the generalized Gauss transformation T p ( x ) = { p x } . In addition, we give an estimate for the constant that appears in the theorem.