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25 December 2016, Volume 36 Issue 6 Previous Issue    Next Issue

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GLOBAL SOLUTION TO 1D MODEL OF A COMPRESSIBLE VISCOUS MICROPOLAR HEAT-CONDUCTING FLUID WITH A FREE BOUNDARY Nermina MUJAKOVIC, Nelida CRNJARIC-ZIC Acta mathematica scientia,Series B. 2016, 36 (6):  1541-1576.  DOI: 10.1016/S0252-9602(16)30090-X Abstract ( 92 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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MONOTONICITY IN ORLICZ-LORENTZ SEQUENCE SPACES EQUIPPED WITH THE ORLICZ NORM Wanzhong GONG, Daoxiang ZHANG Acta mathematica scientia,Series B. 2016, 36 (6):  1577-1589.  DOI: 10.1016/S0252-9602(16)30091-1 Abstract ( 70 )   RICH HTML PDF   Save In Orlicz-Lorentz sequence space λ ?,ω° with the Orlicz norm, uniform monotonicity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in λ ?,ω° are discussed. References | Related Articles | Metrics

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LARGE TIME BEHAVIOR OF A THIRD GRADE FLUID SYSTEM Xiaojuan CHAI, Zhengzheng CHEN, Weisheng NIU Acta mathematica scientia,Series B. 2016, 36 (6):  1590-1608.  DOI: 10.1016/S0252-9602(16)30092-3 Abstract ( 112 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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RIGIDITY OF COMPACT SURFACES IN HOMOGENEOUS 3-MANIFOLDS WITH CONSTANT MEAN CURVATURE Jing WANG, Yinshan ZHANG Acta mathematica scientia,Series B. 2016, 36 (6):  1609-1618.  DOI: 10.1016/S0252-9602(16)30093-5 Abstract ( 96 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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A PROJECTION-TYPE ALGORITHM FOR SOLVING GENERALIZED MIXED VARIATIONAL INEQUALITIES Kai TU, Fuquan XIA Acta mathematica scientia,Series B. 2016, 36 (6):  1619-1630.  DOI: 10.1016/S0252-9602(16)30094-7 Abstract ( 139 )   RICH HTML PDF   Save 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→R∪{+∞} is a proper function. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported. References | Related Articles | Metrics

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A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS Bashir AHMAD, Sotiris K. NTOUYAS, Jessada TARIBOON Acta mathematica scientia,Series B. 2016, 36 (6):  1631-1640.  DOI: 10.1016/S0252-9602(16)30095-9 Abstract ( 118 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES Shisheng ZHANG, Lin WANG, Lijuan QIN, Zhaoli MA Acta mathematica scientia,Series B. 2016, 36 (6):  1641-1650.  DOI: 10.1016/S0252-9602(16)30096-0 Abstract ( 158 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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EXISTENCE OF WEAK SOLUTIONS FOR SOME SINGULAR PARABOLIC EQUATION Li XIA, Jingna LI, Qiang LIU Acta mathematica scientia,Series B. 2016, 36 (6):  1651-1661.  DOI: 10.1016/S0252-9602(16)30097-2 Abstract ( 104 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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WEIGHTED PSEUDO ALMOST-PERIODIC SOLUTIONS OF SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH MIXED DELAYS Mohammed Salah M'HAMDI, Chaouki AOUITI, Abderrahmane TOUATI, Adel M. ALIMI, Vaclav SNASEL Acta mathematica scientia,Series B. 2016, 36 (6):  1662-1682.  DOI: 10.1016/S0252-9602(16)30098-4 Abstract ( 124 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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ON GENERALIZED FEYNMAN-KAC TRANSFORMATION FOR MARKOV PROCESSES ASSOCIATED WITH SEMI-DIRICHLET FORMS Xinfang HAN, Li MA Acta mathematica scientia,Series B. 2016, 36 (6):  1683-1698.  DOI: 10.1016/S0252-9602(16)30099-6 Abstract ( 86 )   RICH HTML PDF   Save Suppose that X is a right process which is associated with a semi-Dirichlet form (ε, D(ε)) on L2(E; m). Let J be the jumping measure of (ε, D(ε)) satisfying J(E×E-d)<∞. Let u∈D(ε)b:=D(ε)∩L∞(E; m), we have the following Fukushima's decomposition ?(Xt)-?(X0)=Mtu+Ntu. Define Ptuf(x)=Ex[eNtuf(Xt)]. Let Qu(f, g)=ε(f, g)+ε(u, fg) for f, g∈D(ε)b. In the first part, under some assumptions we show that (Qu, D(ε)b) is lower semi-bounded if and only if there exists a constant α0≥0 such that ||Ptu||2≤eα0t for every t>0. If one of these assertions holds, then (Ptu)t≥0 is strongly continuous on L2(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 At and give two sufficient conditions for PtAf(x)=Ex[eAtf(Xt)] to be strongly continuous. References | Related Articles | Metrics

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VANISHING VISCOSITY FOR NON-ISENTROPIC GAS DYNAMICS WITH INTERACTING SHOCKS Xiaoding SHI, Yan YONG, Yinglong ZHANG Acta mathematica scientia,Series B. 2016, 36 (6):  1699-1720.  DOI: 10.1016/S0252-9602(16)30100-X Abstract ( 72 )   RICH HTML PDF   Save In this paper, we study the vanishing viscosity limit for non-isentropic gas dynamics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of shocks interacting at some positive time, we show that such solution is the vanishing viscosity limit of a family of smooth global solutions for a viscous system of conservation law. We remark that, after the interacting time, not only shocks but also contact discontinuity are generated. References | Related Articles | Metrics

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STABLE RECOVERY OF SIGNALS WITH THE HIGH ORDER D-RIP CONDITION Wengu CHEN, Yaling LI Acta mathematica scientia,Series B. 2016, 36 (6):  1721-1730.  DOI: 10.1016/S0252-9602(16)30101-1 Abstract ( 74 )   RICH HTML PDF   Save This paper establishes a high order condition on the restricted isometry property adapted to a frame D (D-RIP) for the signal recovery. It is shown that if the measurement matrix A satisfies the D-RIP condition δtk<√(t-1)/(t) for t>1, then all signals f which are sparse in terms of a tight frame D can be recovered stably or exactly via the l1-analysis model based on y=Af+z in l2 and Dantzig selector bounded noise setting. References | Related Articles | Metrics

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A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION Soumaya SÂANOUNI, Nihed TRABELSI Acta mathematica scientia,Series B. 2016, 36 (6):  1731-1746.  DOI: 10.1016/S0252-9602(16)30102-3 Abstract ( 106 )   RICH HTML PDF   Save We study the existence of positive solutions to a two-order semilinear elliptic problem with Dirichlet boundary condition     (Pλ)    -div(c(x)∇u)=λf(u) in Ω,             u=0 on ∂Ω, where Ω⊂Rn; n≥2 is a smooth bounded domain; f is a positive, increasing and convex source term and c(x) is a smooth bounded positive function on Ω. We also prove the existence of critical value and claim the uniqueness of extremal solutions. References | Related Articles | Metrics

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ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS Yong HE, Chunping ZHONG Acta mathematica scientia,Series B. 2016, 36 (6):  1747-1766.  DOI: 10.1016/S0252-9602(16)30103-5 Abstract ( 83 )   RICH HTML PDF   Save Let (M1,F1) and (M2,F2) be two strongly pseudoconvex complex Finsler manifolds. The doubly wraped product complex Finsler manifold (f2M1×f1M2, F) of (M1, F1) and (M2, F2) is the product manifold M1×M2 endowed with the warped product complex Finsler metric F2=f22F12+f12F22, where f1 and f2 are positive smooth functions on M1 and M2, respectively. In this paper, the most often used complex Finsler connections, holomorphic curvature, Ricci scalar curvature, and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components. Necessary and sufficient conditions for the DWP-complex Finsler manifold to be Kähler Finsler (resp., weakly Kähler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg) manifold are obtained, respectively. It is proved that if (M1, F1) and (M2, F2) are projectively flat, then the DWP-complex Finsler manifold is projectively flat if and only if f1 and f2 are positive constants. References | Related Articles | Metrics

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PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS Chaojun WANG, Yanyan CUI, Hao LIU Acta mathematica scientia,Series B. 2016, 36 (6):  1767-1779.  DOI: 10.1016/S0252-9602(16)30104-7 Abstract ( 66 )   RICH HTML PDF   Save In this paper, we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve the properties of SΩ*(β, A, B), almost starlike mapping of complex order λ on Ωn,p2,…,pn. Sequentially, we get that the modified Roper-Suffridge operators preserve spirallikeness of type β and order α, strongly pirallikeness of type β and order α, almost starlikeness of order α on Ωn,p2,…,pn. The conclusions provide a new approach to construct these biholomorphic mappings which have special geometric properties in several complex variables. References | Related Articles | Metrics

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EXISTENCE AND UNIQUENESS OF NON-TRIVIAL SOLUTION OF PARABOLIC p-LAPLACIAN-LIKE DIFFERENTIAL EQUATION WITH MIXED BOUNDARIES Li WEI, Rui CHEN, Ravi P. AGARWAL, Patricia YJ WONG Acta mathematica scientia,Series B. 2016, 36 (6):  1780-1792.  DOI: 10.1016/S0252-9602(16)30105-9 Abstract ( 77 )   RICH HTML PDF   Save One parabolic p-Laplacian-like differential equation with mixed boundaries is studied in this paper, where the item ((∂u)/(∂t)) in the corresponding studies is replaced by α(((∂u)/(∂t))), which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2(0, T; L2(Ω)) is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work. References | Related Articles | Metrics

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MULTIPLICITY RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN Yongqiang XU, Zhong TAN, Daoheng SUN Acta mathematica scientia,Series B. 2016, 36 (6):  1793-1803.  DOI: 10.1016/S0252-9602(16)30106-0 Abstract ( 93 )   RICH HTML PDF   Save In this paper, we consider a class of superlinear elliptic problems involving fractional Laplacian (-Δ)s/2u=λf(u) in a bounded smooth domain with zero Dirichlet boundary condition. We use the method on harmonic extension to study the dependence of the number of sign-changing solutions on the parameter λ. References | Related Articles | Metrics

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SHARP ESTIMATES OF ALL HOMOGENEOUS EXPANSIONS FOR A SUBCLASS OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α IN SEVERAL COMPLEX VARIABLES Xiaosong LIU, Taishun LIU Acta mathematica scientia,Series B. 2016, 36 (6):  1804-1818.  DOI: 10.1016/S0252-9602(16)30107-2 Abstract ( 91 )   RICH HTML PDF   Save In this article, first, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of type B and order α on the unit ball in complex Banach spaces are given. Second, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cn are also established. In particular, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings (include quasi-convex mappings of type A and quasi-convex mappings of type B) in several complex variables are get accordingly. Our results state that a weak version of the Bieberbach conjecture for quasi-convex mappings of type B and order α in several complex variables is proved, and the derived conclusions are the generalization of the classical results in one complex variable. References | Related Articles | Metrics

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THREE SOLUTIONS FOR A FRACTIONAL ELLIPTIC PROBLEMS WITH CRITICAL AND SUPERCRITICAL GROWTH Jinguo ZHANG, Xiaochun LIU Acta mathematica scientia,Series B. 2016, 36 (6):  1819-1831.  DOI: 10.1016/S0252-9602(16)30108-4 Abstract ( 94 )   RICH HTML PDF   Save In this paper, we deal with the existence and multiplicity of solutions to the fractional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we prove that our problem has at least three solutions. References | Related Articles | Metrics

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NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS Shuo SONG, Qionghui ZHANG, Na ZOU, Hong QIN Acta mathematica scientia,Series B. 2016, 36 (6):  1832-1840.  DOI: 10.1016/S0252-9602(16)30109-6 Abstract ( 73 )   RICH HTML PDF   Save The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies. References | Related Articles | Metrics