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25 December 2017, Volume 37 Issue 6 Previous Issue    Next Issue

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STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE: EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY Junfeng LIU, Ciprian A. TUDOR Acta mathematica scientia,Series B. 2017, 37 (6):  1545-1566.  DOI: 10.1016/S0252-9602(17)30091-7 Abstract ( 92 )   RICH HTML PDF   Save In this paper we study a fractional stochastic heat equation on Rd (d ≥ 1) with additive noise (∂/∂t)u(t, x)=D(α/δ)u(t, x) +b(u(t, x)) +?H(t, x) where D(α/δ) is a nonlocal fractional differential operator and ?H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d=1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus. References | Related Articles | Metrics

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DUALITY OF GENERALIZED DUNKL-LIPSCHITZ SPACES Samir KALLEL Acta mathematica scientia,Series B. 2017, 37 (6):  1567-1593.  DOI: 10.1016/S0252-9602(17)30092-9 Abstract ( 62 )   RICH HTML PDF   Save The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces ∧α,p,qk (R), α ∈ R and 1 ≤ p, q ≤ ∞, in the context of Dunkl harmonic analysis. References | Related Articles | Metrics

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DETERMINING THE DISCRIMINATING DOMAIN FOR HYBRID LINEAR DIFFERENTIAL GAME WITH TWO PLAYERS AND TWO TARGETS Yanli HAN, Yan GAO Acta mathematica scientia,Series B. 2017, 37 (6):  1594-1606.  DOI: 10.1016/S0252-9602(17)30093-0 Abstract ( 62 )   RICH HTML PDF   Save This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain. Secondly, in order to determine that a bounded polyhedron is a discriminating domain, we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points (extreme points) and the existing ones need to verify all points in the bounded polyhedron. References | Related Articles | Metrics

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DECAY RATE OF FOURIER TRANSFORMS OF SOME SELF-SIMILAR MEASURES Xiang GAO, Jihua MA Acta mathematica scientia,Series B. 2017, 37 (6):  1607-1618.  DOI: 10.1016/S0252-9602(17)30094-2 Abstract ( 70 )   RICH HTML PDF   Save This paper is concerned with the Diophantine properties of the sequence {ξθn}, where 1 ≤ ξ < θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μλ with λ=θ-1 as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak, who consider the case of Bernoulli convolutions. As an application, we prove that μλ almost every x is normal to any base b ≥ 2, which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem. References | Related Articles | Metrics

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A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES Zi WANG, Yuwen WANG Acta mathematica scientia,Series B. 2017, 37 (6):  1619-1631.  DOI: 10.1016/S0252-9602(17)30095-4 Abstract ( 97 )   RICH HTML PDF   Save In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in[12] where "the generalized Banach lemma" was used. By the method of the perturbation analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces. References | Related Articles | Metrics

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BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS Zhensheng GAO, Zhong TAN Acta mathematica scientia,Series B. 2017, 37 (6):  1632-1638.  DOI: 10.1016/S0252-9602(17)30096-6 Abstract ( 73 )   RICH HTML PDF   Save In this paper, we consider the short time classical solution to a simplified hydrodynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establish a criterion for possible breakdown of such solutions at a finite time. More precisely, if (u, d) is smooth up to time T provided that ∫0T║∇×u(t,·)║BMO(R3) + ║∇d(t,·)║L4(R3)8dt < ∞. References | Related Articles | Metrics

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A VARIATIONAL-HEMIVARIATIONAL INEQUALITY IN CONTACT PROBLEM FOR LOCKING MATERIALS AND NONMONOTONE SLIP DEPENDENT FRICTION Stanis ław MIGÓRSKI, Justyna OGORZA LY Acta mathematica scientia,Series B. 2017, 37 (6):  1639-1652.  DOI: 10.1016/S0252-9602(17)30097-8 Abstract ( 77 )   RICH HTML PDF   Save We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle. References | Related Articles | Metrics

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LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS Hua CHEN, Hongge CHEN, Yirui DUAN, Xin HU Acta mathematica scientia,Series B. 2017, 37 (6):  1653-1664.  DOI: 10.1016/S0252-9602(17)30098-X Abstract ( 67 )   RICH HTML PDF   Save Let Ω be a bounded open domain in Rn with smooth boundary ∂Ω, X=(X1, X2, …, Xm) be a system of real smooth vector fields defined on Ω and the boundary ∂Ω is non-characteristic for X. If X satisfies the Hörmander's condition, then the vector field is finitely degenerate and the sum of square operator △X=???20170608???Xj2 is a finitely degenerate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △X on Ω. References | Related Articles | Metrics

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MULTIPLE SYMMETRIC RESULTS FOR A CLASS OF BIHARMONIC ELLIPTIC SYSTEMS WITH CRITICAL HOMOGENEOUS NONLINEARITY IN RN Zhiying DENG, Yisheng HUANG Acta mathematica scientia,Series B. 2017, 37 (6):  1665-1684.  DOI: 10.1016/S0252-9602(17)30099-1 Abstract ( 51 )   RICH HTML PDF   Save This paper is dedicated to studying the existence and multiplicity of symmetric solutions for a class of biharmonic elliptic systems with critical homogeneous nonlinearity in RN. By virtue of variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the parameters and the weighted functions. References | Related Articles | Metrics

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RICCATI-TYPE RESULT FOR MEROMORPHIC SOLUTIONS OF SYSTEMS OF COMPOSITE FUNCTIONAL EQUATIONS Lingyun GAO, Manli LIU Acta mathematica scientia,Series B. 2017, 37 (6):  1685-1694.  DOI: 10.1016/S0252-9602(17)30100-5 Abstract ( 71 )   RICH HTML PDF   Save By use of Nevanlinna value distribution theory, we will investigate the properties of meromorphic solutions of two types of systems of composite functional equations and obtain some results. One of the results we get is about both components of meromorphic solutions on the system of composite functional equations satisfying Riccati differential equation, the other one is property of meromorphic solutions of the other system of composite functional equations while restricting the growth. References | Related Articles | Metrics

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HYPONORMALITY OF BLOCK TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES Jongrak LEE Acta mathematica scientia,Series B. 2017, 37 (6):  1695-1704.  DOI: 10.1016/S0252-9602(17)30101-7 Abstract ( 75 )   RICH HTML PDF   Save In this paper we consider the block Toeplitz operators TΦ on the weighted Bergman space Aα2(D, Cn) and we give a necessary and sufficient condition for the hyponormality of block Toeplitz operators with symbol in the class of functions Φ=F + G* with matrix-valued polynomial functions F and G with degree 2. References | Related Articles | Metrics

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FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY Suiming SHANG, Yu TIAN, Yajing ZHANG Acta mathematica scientia,Series B. 2017, 37 (6):  1705-1726.  DOI: 10.1016/S0252-9602(17)30102-9 Abstract ( 73 )   RICH HTML PDF   Save In this paper, the stability and bifurcation behaviors of a predator-prey model with the piecewise constant arguments and time delay are investigated. Technical approach is fully based on Jury criterion and bifurcation theory. The interesting point is that the model will produce two different branches by limiting branch parameters of different intervals. Besides, image simulation is also given. References | Related Articles | Metrics

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ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION Iz-iddine EL-FASSI, Janusz BRZDȨK, Abdellatif CHAHBI, Samir KABBAJ Acta mathematica scientia,Series B. 2017, 37 (6):  1727-1739.  DOI: 10.1016/S0252-9602(17)30103-0 Abstract ( 99 )   RICH HTML PDF   Save We present results on approximate solutions to the biadditive equation f(x + y, z-w) + f(x-y, z + w)=2f(x, z)-2f(y, w) on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability. References | Related Articles | Metrics

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DISCONTINUOUS TRAVELING WAVE ENTROPY SOLUTIONS OF A MODIFIED ALLEN-CAHN MODEL Tianyuan XU, Chunhua JIN, Shanming JI Acta mathematica scientia,Series B. 2017, 37 (6):  1740-1760.  DOI: 10.1016/S0252-9602(17)30104-2 Abstract ( 63 )   RICH HTML PDF   Save This paper deals with the existence and the asymptotic behavior of discontinuous traveling wave entropy solutions for a modified Allen-Cahn model, in which, the usual Ficken-based model for phase transition is replaced with a more physical model with nonlinear diffusive flux. The discontinuous traveling waves correspond to the discontinuous phase transition phenomena. References | Related Articles | Metrics

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ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT Ap CLASS Dinghuai WANG, Jiang ZHOU, Wenyi CHEN Acta mathematica scientia,Series B. 2017, 37 (6):  1761-1774.  DOI: 10.1016/S0252-9602(17)30105-4 Abstract ( 89 )   RICH HTML PDF   Save This manuscript addresses Muckenhoupt Ap weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces Lp(ω) to weighted Morrey spaces Mqp(ω) for 1 < q < p < ∞. As a corollary, if M is (weak) bounded on Mqp (ω), then ω ∈ Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators T∈ on weighted Morrey spaces. Finally, we show that ω ∈ Ap if and only if ω ∈ BMOp'(ω) for 1 ≤ p < ∞ and 1/p + 1/p'=1. References | Related Articles | Metrics

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LARGE TIME BEHAVIOR OF SOLUTIONS TO THE PERTURBED HASEGAWA-MIMA EQUATION Lijuan WANG Acta mathematica scientia,Series B. 2017, 37 (6):  1775-1790.  DOI: 10.1016/S0252-9602(17)30106-6 Abstract ( 54 )   RICH HTML PDF   Save The large time behavior of solutions to the two-dimensional perturbed HasegawaMima equation with large initial data is studied in this paper. Based on the time-frequency decomposition and the method of Green function, we not only obtain the optimal decay rate but also establish the pointwise estimate of global classical solutions. References | Related Articles | Metrics

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THE EQUIVALENT CHARACTERIZATION OF F(p, q, s) SPACE ON BOUNDED SYMMETRIC DOMAINS OF Cn Shenlian LI, Xuejun ZHANG, Si XU Acta mathematica scientia,Series B. 2017, 37 (6):  1791-1802.  DOI: 10.1016/S0252-9602(17)30107-8 Abstract ( 59 )   RICH HTML PDF   Save Let Ω be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F(p,q,s) on Ω. Characterizing functions in the F(p,q,s) space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F(p,q,s) space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F(p,q,s) space and Bloch type space on Ω too. References | Related Articles | Metrics

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SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS FOR THE NON-NEWTONIAN FILTRATION EQUATIONS WITH NONLINEAR SOURCES AND A TIME-VARYING DELAY Fanchao KONG, Zhiguo LUO Acta mathematica scientia,Series B. 2017, 37 (6):  1803-1816.  DOI: 10.1016/S0252-9602(17)30108-X Abstract ( 46 )   RICH HTML PDF   Save This paper is concerned with the non-Newtonian filtration equations with nonlinear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results. References | Related Articles | Metrics

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THE GENERALIZED ROPER-SUFFRIDGE OPERATOR ON THE UNIT BALL IN COMPLEX BANACH AND HILBERT SPACES Yanyan CUI, Chaojun WANG, Hao LIU Acta mathematica scientia,Series B. 2017, 37 (6):  1817-1829.  DOI: 10.1016/S0252-9602(17)30109-1 Abstract ( 62 )   RICH HTML PDF   Save In this paper, we extend the Roper-Suffridge extension operator in complex Banach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit ball in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spirallike mappings in several complex variables. References | Related Articles | Metrics

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PROPERTIES OF DIFFERENCE PAINLEVÉ IV EQUATIONS Shuangting LAN, Zongxuan CHEN Acta mathematica scientia,Series B. 2017, 37 (6):  1830-1840.  DOI: 10.1016/S0252-9602(17)30110-8 Abstract ( 50 )   RICH HTML PDF   Save In this paper, we investigate difference Painlevé IV equations, and obtain some results on Nevanlinna exceptional values of transcendental meromorphic solutions w(z) with finite order, their differences △w(z)=w(z + 1)-w(z) and divided differences ((△w(z))/(w(z))). References | Related Articles | Metrics

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UNIFORM HÖLDER ESTIMATES FOR A TYPE OF NONLINEAR ELLIPTIC EQUATIONS WITH RAPIDLY OSCILLATORY COEFFICIENTS Rong DONG, Dongsheng LI Acta mathematica scientia,Series B. 2017, 37 (6):  1841-1860.  DOI: 10.1016/S0252-9602(17)30111-X Abstract ( 67 )   RICH HTML PDF   Save In this paper, a type of nonlinear elliptic equations with rapidly oscillatory coefficients is investigated. By compactness methods, we show uniform Hölder estimates of solutions in a C1 bounded domain. References | Related Articles | Metrics

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THE INTEGRATION OF ALGEBROIDAL FUNCTIONS Daochun SUN, Yingying HUO, Yinying KONG, Fujie CHAI Acta mathematica scientia,Series B. 2017, 37 (6):  1861-1869.  DOI: 10.1016/S0252-9602(17)30112-1 Abstract ( 53 )   RICH HTML PDF   Save In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros. References | Related Articles | Metrics

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EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRÖDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS Quanqing LI, Xian WU Acta mathematica scientia,Series B. 2017, 37 (6):  1870-1880.  DOI: 10.1016/S0252-9602(17)30113-3 Abstract ( 55 )   RICH HTML PDF   Save In this paper, we study the following generalized quasilinear Schrödinger equations with critical or supercritical growths -div(g2(u)∇u) + g(u)g'(u)|∇u|2 + V (x)u=f(x, u) + λ|u|p-2u, x ∈ RN, where λ > 0, N ≥ 3, g:R → R+ is a C1 even function, g(0)=1, g'(s) ≥ 0 for all s ≥ 0,???20170623???((g(s))/(|s|α-1)):=β > 0 for some α ≥ 1 and (α-1)g(s) > g'(s)s for all s > 0 and p ≥ α2*. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ > 0 using a change of variables and variational method. References | Related Articles | Metrics