Authors:Martin G. GRIGORYAN; Stepan SARGSYAN Pages: 293 - 300 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Martin G. GRIGORYAN, Stepan SARGSYAN In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems: for any ε ∈ (0,1), there exists a measurable set E ⊂ [0,1) of measure bigger than 1 — ε such that for any function f ∈ L1 [0,1), it is possible to find a function g ∈ L1 [0,1) coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing.

Authors:Yansheng ZHONG; Chunyou SUN Pages: 301 - 315 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Yansheng ZHONG, Chunyou SUN A new approach is established to show that the semigroup {S(t)} t ≥0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in Lq (Ω) (2 ≤ q < ∞) with respect to the initial value. As an application, this proves the upper-bound of fractal dimension for its global attractor in the corresponding space.

Authors:Jingjun GUO; Chujin LI Pages: 316 - 328 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Jingjun GUO, Chujin LI In this article, we study the existence of collision local time of two independent d-dimensional fractional Ornstein-Uhlenbeck processes X H 1 t and X˜ H 2 t , with different parameters H i ∈ (0,1),i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its' chaos expansion.

Authors:Alexander ALEKSANDROV; Elena ALEKSANDROVA; Alexey ZHABKO; Yangzhou CHEN Pages: 329 - 341 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Alexander ALEKSANDROV, Elena ALEKSANDROVA, Alexey ZHABKO, Yangzhou CHEN A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.

Authors:Kazuhide NAKAJO Pages: 342 - 354 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Kazuhide NAKAJO Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {A n}nɛN be a family of monotone and Lipschitz continuos mappings of C into E*. In this article, we consider the improved gradient method by the hybrid method in mathematical programming [10] for solving the variational inequality problem for {A n} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space.

Authors:Lishuang PAN; An WANG Pages: 355 - 367 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Lishuang PAN, An WANG We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains.

Authors:M. Syed ALI; J. YOGAMBIGAI; Jinde CAO Pages: 368 - 384 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): M. Syed ALI, J. YOGAMBIGAI, Jinde CAO In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities (LMIs). Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin's formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

Authors:Zaiyun ZHANG; Jianhua HUANG; Mingbao SUN Pages: 385 - 394 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Zaiyun ZHANG, Jianhua HUANG, Mingbao SUN In this article, we investigate the initial value problem(IVP) associated with the defocusing nonlinear wave equation on ℝ2 as follows: { ∂ t t u - Δ u = - u 3 , u ( 0 , x ) = u 0 ( x ) , ∂ t u ( 0 , x ) = u 1 ( x ) , where the initial data (u 0, u 1) ɛ H s(ℝ2) × Hs−1 (ℝ2). It is shown that the IVP is global well-posedness in Hs(ℝ2) × Hs−1(ℝ2) for any 1 > s > 2/5. The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].

Authors:Na BA; Jinjun DAI Pages: 405 - 424 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Na BA, Jinjun DAI We study the bound states to nonlinear Schrödinger equations with electro-magnetic fields i h ∂ ψ ∂ t = ( h i ∇ - A ( x ) ) 2 ψ + V ( x ) ψ - K ( x ) p - 1 ψ = 0 , on ℝ + × ℝ N . Let G ( x ) = [ V ( x ) ] p + 1 p - 1 - N 2 [ K ( x ) ] - 2 p - 1 and suppose that G(x) has k local minimum points. For h > 0 small, we find multi-bump bound states ψh(x,t) = e −lEt/h Uh(χ) with Uh concentrating at the local minimum points of G(x) simultaneously as h → 0. The potentials V(x) and K(x) are allowed to be either compactly supported or unbounded at infinity.

Authors:Shenlian LI; Xuejun ZHANG; Si XU Pages: 425 - 438 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Shenlian LI, Xuejun ZHANG, Si XU Let p > 0 and μ be a normal function on [0,1), v ( r ) = ( 1 - r 2 ) 1 + n p μ ( r ) for r ∈ [0,1). In this article, the bounded or compact weighted composition operator Tϕ,ψ from the μ-Bergman space A p (μ) to the normal weight Bloch type space βν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator is compact from A p(μ) to βν is given. At the same time, the authors give the briefly sufficient and necessary condition that is compact on βμ for a > 1.

Authors:Shulin LYU; Yang CHEN Pages: 439 - 462 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Shulin LYU, Yang CHEN We study the probability that all eigenvalues of the Laguerre unitary ensemble of n by n matrices are in (0, t), that is, the largest eigenvalue distribution. Associated with this probability, in the ladder operator approach for orthogonal polynomials, there are recurrence coefficients, namely, an (t) and αn (t) and βn , as well as three auxiliary quantities, denoted by rn (t), Rn (t), and ση (t). We establish the second order differential equations for both β n (t) and r n (t). By investigating the soft edge scaling limit when α = O(n) as n → ∞ or a is finite, we derive a Pu, the σ-form, and the asymptotic solution of the probability. In addition, we develop differential equations for orthogonal polynomials Pn(z) corresponding to the largest eigenvalue distribution of LUE and GUE with n finite or large. For large n, asymptotic formulas are given near the singular points of the ODE. Moreover, we are able to deduce a particular case of Chazy's equation for satisfying the σ-form of P IV or P V .

Authors:Na ZOU; Hong QIN Pages: 477 - 487 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Na ZOU, Hong QIN Doubling is a simple but powerful method of constructing two-level fractional factorial designs with high resolution. This article studies uniformity in terms of Lee discrepancy of double designs. We give some linkages between the uniformity of double design and the aberration case of the original one under different criteria. Furthermore, some analytic linkages between the generalized wordlength pattern of double design and that of the original one are firstly provided here, which extend the existing findings. The lower bound of Lee discrepancy for double designs is also given.

Authors:Xiaolong QIN; Sun Young CHO Pages: 488 - 502 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Xiaolong QIN, Sun Young CHO In this article, fixed points of generalized asymptotically quasi-ϕ-nonexpansive mappings and equilibrium problems are investigated based on a monotone projection algorithm. Strong convergence theorems are established without the aid of compactness in the framework of reflexive Banach spaces.

Authors:Mohamed AMOUCH; Youness FAOUZI Pages: 503 - 510 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Mohamed AMOUCH, Youness FAOUZI A Banach space operator satisfies generalized Rakocevic's property (gw) if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the spectrum of T. In this note, we characterize hypecyclic and supercyclic operators satisfying the property (gw).

Authors:Min DING; Shengbo GONG Pages: 511 - 526 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Min DING, Shengbo GONG We consider the vibration of elastic thin plates under certain reasonable assumptions. We derive the nonlinear equations for this model by the Hamilton Principle. Under the conditions on the hyperbolicity for the initial data, we establish the local time well-posedness for the initial and boundary value problem by Picard iteration scheme, and obtain the estimates for the solutions.

Authors:Heping LIU; Hongbo ZENG Pages: 527 - 538 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Heping LIU, Hongbo ZENG Let Δ be full Laplacian on H-type group G . Then for every compact set D ⊆ G , a local estimate of the Schrodinger maximal operator holds, that is, ∫ D sup 0 < t < 1 e i t Δ f ( x ) 2 d x ∼ < ‖ f ‖ H s 2 , s > 1 2 . We also show that the above inequality fails when s < 1/4.

Authors:Huan HAN; Huan-Song ZHOU Pages: 539 - 554 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Huan HAN, Huan-Song ZHOU The existence of a global minimizer for a variational problem arising in registration of diffusion tensor images is proved, which ensures that there is a regular spatial transformation for the registration of diffusion tensor images.

Authors:Lixia WANG; Shiwang MA; Na XU Pages: 555 - 572 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Lixia WANG, Shiwang MA, Na XU In this article, we study the following nonhomogeneous Schrodinger-Poisson equations { - Δ u + λ V ( x ) u + K ( x ) ϕ u = f ( x , u ) + g ( x ) , x ∈ R 3 , - Δ ϕ = K ( x ) u 2 , x ∈ R 3 , where λ > 0 is a parameter. Under some suitable assumptions on V, K, f and g, the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. In particular, the potential V is allowed to be sign-changing.

Authors:Haibo Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Haibo YU This article considers the global regularity to the initial-boundary value problem for the 2D incompressible MHD with mixed partial dissipation and magnetic diffusion. To overcome the difficulty caused by the vanishing viscosities, we first establish the elliptic system for U x and b y, which are estimated by ∇ × ux and ∇ × by , respectively. Then, we establish the global estimates for ∇ × u and ∇ × b.

Authors:Adela Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Adela CAPĂTĂ The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set.

Authors:Hui KAN; Xiaozhou YANG Pages: 1 - 25 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Hui KAN, Xiaozhou YANG In this paper, we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law { ∂ t u + ∂ x f ( u ) + ∂ y g ( u ) = 0 , u ( x , y , 0 ) = u 0 ( x , y ) . In which initial data can be unbounded. Although the existence and uniqueness of the weak entropy solution are obtained, little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation. So we construct such scheme in our paper and get some new results.

Authors:Zhenhai LIU; Shengda ZENG Pages: 26 - 32 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Zhenhai LIU, Shengda ZENG In this paper, we consider a new differential variational inequality (DVI, for short) which is composed of an evolution equation and a variational inequality in infinite Banach spaces. This kind of problems may be regarded as a special feedback control problem. Based on the Browder's theorem and the optimal control theory, we show the existence of solutions to the mentioned problem.

Authors:Yuehua GE; Bo TAN Pages: 33 - 46 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Yuehua GE, Bo TAN Let m ≥ 1 be an integer, 1 < β ≤ m + 1. A sequence ɛ1 ɛ2 ɛ3 with ɛi ∈ {0,1, … m} is called a β-expansion of a real number x if x = ∑ i ∈ i β i . It is known that when the base β is smaller than the generalized golden ration, any number has uncountably many expansions, while when β is larger, there are numbers which has unique expansion. In this paper, we consider the bases such that there is some number whose unique expansion is purely periodic with the given smallest period. We prove that such bases form an open interval, moreover, any two such open intervals have inclusion relationship according to the Sharkovskii ordering between the given minimal periods. We remark that our result answers an open question posed by Baker, and the proof for the case m = 1 is due to Allouche, Clarke and Sidorov.

Authors:Dragos-Patru COVEI Pages: 47 - 57 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Dragos-Patru COVEI In this article, we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation technique. Our results complete and improve a work published recently by Zhang and Zhou (existence of entire positive k-convex radial solutions to Hessian equations and systems with weights. Applied Mathematics Letters, Volume 50, December 2015, Pages 48–55).

Authors:Changlin Xiang First page: 58 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Changlin Xiang This note is a continuation of the work [17]. We study the following quasilinear elliptic equations - Δ p u - μ x p u p - 2 u = Q ( x ) u N p N - p - 2 u , x ∈ ℝ N , where 1 < p < N,0 ≤ μ < ((N-p)/p)p and Q ɛ L∞ ℝ N . Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.

Authors:Zhigang PENG; Gangzhen ZHONG Pages: 69 - 78 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Zhigang PENG, Gangzhen ZHONG Let A be the space of functions analytic in the unit disk D={z: z < 1}. Let U denote the set of all functions f ɛ A satisfying the conditions f(0)=f′(0)−1=0 and f ′ ( z ) ( z f ( z ) ) 2 - 1 < 1 ( z < 1 ) . Also, let Ω denote the set of all functions f ɛ A satisfying the conditions f(0) = f′(0)-1 = 0 and z f ′ ( z ) - f ( z ) < 1 2 ( z < 1 ) . In this article, we discuss the properties of U and Ω.

Authors:Guowei LIU Pages: 79 - 96 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Guowei LIU This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension. First, the pointwise estimates of solutions are obtained, furthermore, we obtain the optimal Lp , 1 ≤ p ≤ + ∞, convergence rate of solutions for small initial data. Then we establish the local existence of solutions, the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data. Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.

Authors:Jun WANG; Zongxuan CHEN Pages: 97 - 107 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Jun WANG, Zongxuan CHEN In this paper, we mainly investigate the dynamical properties of entire solutions of complex differential equations. With some conditions on coefficients, we prove that the set of common limiting directions of Julia sets of solutions, their derivatives and their primitives must have a definite range of measure.

Authors:Jing CUI; Litan YAN Pages: 108 - 118 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Jing CUI, Litan YAN In this paper, we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H ɛ (½, 1) in a Hilbert space. We employ the α-norm in order to reflect the relationship between H and the fractional power α. Sufficient conditions are established by using stochastic analysis theory and operator theory. An example is provided to illustrate the effectiveness of the proposed result.

Authors:Mohammed D. KASSIM; Khaled M. FURATI; Nasser-eddine TATAR Pages: 119 - 130 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Mohammed D. KASSIM, Khaled M. FURATI, Nasser-eddine TATAR In this paper, we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the right hand side. A non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method. The range of blow up is found to depend only on the lower order derivative. This is in line with the well-known fact for an internally weakly damped wave equation that solutions will converge to solutions of the parabolic part.

Authors:Meili LIANG; Yingying HUO Pages: 131 - 138 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Meili LIANG, Yingying HUO The article investigates the growth of multiple Dirichlet series. The lower order and the linear order of n-tuple Dirichlet series in ℂ n are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained.

Authors:Mohamed BEN AYED; Habib FOURTI Pages: 139 - 173 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Mohamed BEN AYED, Habib FOURTI In this paper we prove an existence result for the nonlinear elliptic problem: Δu = K u 5, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain of ℝ3 and K is a positive function in Ω¯. Our method relies on studying its corresponding subcritical approximation problem and then using a topological argument.

Authors:Yin LI; Ruiying WEI; Zhengan YAO Pages: 174 - 186 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Yin LI, Ruiying WEI, Zhengan YAO In this paper, we study a nematic liquid crystals system in three-dimensional whole space ℝ3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L 1ℝ3 additionally.

Authors:Lingyun GAO Pages: 187 - 194 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Lingyun GAO In this paper, we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations, and obtain some interesting results. It extends some results concerning complex differential (difference) equations to the systems of differential-difference equations.

Authors:Juan J. NIETO; Bessem SAMET Pages: 195 - 204 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Juan J. NIETO, Bessem SAMET In this paper, we study the existence of solutions to an implicit functional equation involving a fractional integral with respect to a certain function, which generalizes the Riemann-Liouville fractional integral and the Hadamard fractional integral. We establish an existence result to such kind of equations using a generalized version of Darbo's theorem associated to a certain measure of noncompactness. Some examples are presented.

Authors:Liang WU; Yiming DING Pages: 205 - 222 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Liang WU, Yiming DING It is proposed a class of statistical estimators Ĥ = (Ĥ 1, … Ĥ) for the Hurst parameters H =(H 1, …, Hd ) of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are asymptotically normal. These estimators can be used to detect self-similarity and long-range dependence in multi-dimensional signals, which is important in texture classification and improvement of diffusion tensor imaging (DTI) of nuclear magnetic resonance (NMR). Some fractional Brownian sheets will be simulated and the simulated data are used to validate these estimators. We find that when Hi ≥ ½, the estimators are accurate, and when Hi < ½, there are some bias.

Authors:Qing YANG; Jiayan ZHU; Zhengbang LI Pages: 223 - 234 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Qing YANG, Jiayan ZHU, Zhengbang LI We propose the maximin efficiency robust test (MERT) for multiple nuisance parameters based on theories about the maximin efficiency robust test for only one nuisance parameter and investigate some theoretical properties about this robust test. We explore some theoretical properties about the power of the MERT for multiple nuisance parameters in a specified scenario intuitively further more. We also propose a meaningful example from statistical genetic field to which the MERT for multiple nuisance parameters can be well applied. Extensive simulation studies are conducted to testify the robustness of the MERT for multiple nuisance parameters.

Authors:Heping MA; Biu LIU Pages: 235 - 258 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Heping MA, Biu LIU In the present paper, with the help of the resolvent operator and some analytic methods, the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay. As an application, we also give one example to demonstrate our results.

Authors:Yirang YUAN; Qing YANG; Changfeng LI; Tongjun SUN Pages: 259 - 279 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Yirang YUAN, Qing YANG, Changfeng LI, Tongjun SUN Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L 2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.

Authors:Adam NOWAK; Krzysztof STEMPAK Pages: 280 - 292 Abstract: Publication date: January 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 1 Author(s): Adam NOWAK, Krzysztof STEMPAK We study potential operators and, more generally, Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian. We characterize those 1 ≤ p,q ≤ ∞, for which the potential operators are Lp – Lq bounded. This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions. We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers.

Authors:Nermina MUJAKOVIĆ; Nelida ČRNJARIĆ-ŽIC Pages: 1541 - 1576 Abstract: Publication date: November 2016 Source:Acta Mathematica Scientia, Volume 36, Issue 6 Author(s): Nermina MUJAKOVIĆ, Nelida ČRNJARIĆ-ŽIC In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.

Authors:Wanzhong GONG; Daoxiang ZHANG Pages: 1577 - 1589 Abstract: Publication date: November 2016 Source:Acta Mathematica Scientia, Volume 36, Issue 6 Author(s): Wanzhong GONG, Daoxiang ZHANG In Orlicz-Lorentz sequence space λ°ϕ, w with the Orlicz norm, uniform monotonic ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in λ°ϕ, w are discussed.

Authors:Xiaojuan CHAI; Zhengzheng CHEN; Weisheng NIU Pages: 1590 - 1608 Abstract: Publication date: November 2016 Source:Acta Mathematica Scientia, Volume 36, Issue 6 Author(s): Xiaojuan CHAI, Zhengzheng CHEN, Weisheng NIU We consider the large time behavior of a non-autonomous third grade fluid system, which could be viewed as a perturbation of the classical Navier-Stokes system. Under proper assumptions, we firstly prove that the family of processes generated by the problem admits a uniform attractor in the natural phase space. Then we prove the upper-semicontinuity of the uniform attractor when the perturbation tends to zero.

Authors:Jing WANG; Yinshan ZHANG Pages: 1609 - 1618 Abstract: Publication date: November 2016 Source:Acta Mathematica Scientia, Volume 36, Issue 6 Author(s): Jing WANG, Yinshan ZHANG In this paper, we establish a rigidity theorem for compact constant mean curvature surfaces of the Berger sphere in terms of the surfaces' geometric invariants. This extends the previous similar result on compact minimal surfaces of the Berger sphere.

Authors:Kai TU; Fuquan XIA Pages: 1619 - 1630 Abstract: Publication date: November 2016 Source:Acta Mathematica Scientia, Volume 36, Issue 6 Author(s): Kai TU, Fuquan XIA We propose a projection-type algorithm for generalized mixed variational inequality problem in Euclidean space ℝn. We establish the convergence theorem for the proposed algorithm, provided the multi-valued mapping is continuous and f-pseudomonotone with nonempty compact convex values on dom(f), where f: ℝn → ℝU{+∞} is a proper function. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported.

Authors:Bashir AHMAD; Sotiris K. NTOUYAS; Jessada TARIBOON Pages: 1631 - 1640 Abstract: Publication date: November 2016 Source:Acta Mathematica Scientia, Volume 36, Issue 6 Author(s): Bashir AHMAD, Sotiris K. NTOUYAS, Jessada TARIBOON In this paper, we discuss the existence of solutions for a nonlocal hybrid boundary value problem of Caputo fractional integro-differential equations. Our main result is based on a hybrid fixed point theorem for a sum of three operators due to Dhage, and is well illustrated with the aid of an example.

Authors:Shih-sen CHANG; Lin WANG; Lijuan QIN; Zhaoli MA Pages: 1641 - 1650 Abstract: Publication date: November 2016 Source:Acta Mathematica Scientia, Volume 36, Issue 6 Author(s): Shih-sen CHANG, Lin WANG, Lijuan QIN, Zhaoli MA The purpose of this paper is to introduce and study the split equality variational inclusion problems in the setting of Banach spaces. For solving this kind of problems, some new iterative algorithms are proposed. Under suitable conditions, some strong convergence theorems for the sequences generated by the proposed algorithm are proved. As applications, we shall utilize the results presented in the paper to study the split equality feasibility problems in Banach spaces and the split equality equilibrium problem in Banach spaces. The results presented in the paper are new.

Authors:Li XIA; Jingna LI; Qiang LIU Pages: 1651 - 1661 Abstract: Publication date: November 2016 Source:Acta Mathematica Scientia, Volume 36, Issue 6 Author(s): Li XIA, Jingna LI, Qiang LIU In this paper, we are concerned with a singular parabolic equation subject to Dirichlet boundary condition and initial condition. Under different assumptions on μ, ν and ψ, some existence results are obtained by applying parabolic regularization method and the sub-super solutions method.

Authors:Mohammed Salah M'HAMDI; Chaouki AOUITI; Abderrahmane TOUATI; Adel M. ALIMI; Vaclav SNASEL Pages: 1662 - 1682 Abstract: Publication date: November 2016 Source:Acta Mathematica Scientia, Volume 36, Issue 6 Author(s): Mohammed Salah M'HAMDI, Chaouki AOUITI, Abderrahmane TOUATI, Adel M. ALIMI, Vaclav SNASEL In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays. Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper complement the previously known ones. Finally, an illustrative example is given to demonstrate the effectiveness of our results.

Authors:Xinfang HAN; Li MA Pages: 1683 - 1698 Abstract: Publication date: November 2016 Source:Acta Mathematica Scientia, Volume 36, Issue 6 Author(s): Xinfang HAN, Li MA Suppose that X is a right process which is associated with a semi-Dirichlet form (ɛ, D(ɛ)) on L 2 (E; m). Let J be the jumping measure of (ɛ, D(ɛ)) satisfying J(E × E − d) < ro. Let u G D(ɛ) b : = D(ɛ) ∩ L ∞ (E; m), we have the following Fukushima's decomposition ũ (X t ) − ũ (X o) = Mu t + Nu t . Define Pu t f (x) = Ex[eNu t f (Xt )]. Let Q u (f, g) = ɛ (f, g) + ɛ (u, fg) for f, g ∈ D(ɛ)b. In the first part, under some assumptions we show that (Qu , D(ɛ) b ) is lower semi-bounded if and only if there exists a constant α o ≥ 0 such that P t u 2 ≤ eα ot for every t > 0. If one of these assertions holds, then (P t u ) t≥ o is strongly continuous on L 2(E; m). If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J(E × E − d) < ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of A t and give two sufficient conditions for P t A f (x) = Ex [eA t f (Xt)] to be strongly continuous.