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    20 September 2014, Volume 34 Issue 5 Previous Issue    Next Issue
    Articles
    SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA
    WANG Bo, XIE Zi-Qing, ZHANG Zhi-Min
    Acta mathematica scientia,Series B. 2014, 34 (5):  1357-1376.  DOI: 10.1016/S0252-9602(14)60089-8
    Abstract ( 200 )   RICH HTML PDF (280KB) ( 494 )   Save

    In this paper, a unified model for time-dependentMaxwell equations in dispersive media is considered. The space-time DG method developed in[29] is applied to solve the un-derlying problem. Unconditional L2-stability and error estimate of order O(τ r+1 + hk+1/2) are obtained when polynomials of degree at most r and k are used for the temporal dis-cretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r + 1 in temporal variable t.

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    AN ADAPTIVE MEMBRANE ALGORITHM FOR SOLVING COMBINATORIAL OPTIMIZATION PROBLEMS
    HE Juan-Juan, XIAO Jian-Hua, SHAO Ze-Hui
    Acta mathematica scientia,Series B. 2014, 34 (5):  1377-1394.  DOI: 10.1016/S0252-9602(14)60090-4
    Abstract ( 181 )   RICH HTML PDF (364KB) ( 1323 )   Save

    Membrane algorithms (MAs), which inherit from P systems, constitute a new parallel and distribute framework for approximate computation. In the paper, a membrane algorithm is proposed with the improvement that the involved parameters can be adaptively chosen. In the algorithm, some membranes can evolve dynamically during the computing
    process to specify the values of the requested parameters. The new algorithm is tested on a well-known combinatorial optimization problem, the travelling salesman problem. The em-pirical evidence suggests that the proposed approach is efficient and reliable when dealing with 11 benchmark instances, particularly obtaining the best of the known solutions in eight instances. Compared with the genetic algorithm, simulated annealing algorithm, neural net-work and a fine-tuned non-adaptive membrane algorithm, our algorithm performs better than them. In practice, to design the airline network that minimize the total routing cost on the CAB data with twenty-five US cities, we can quickly obtain high quality solutions using our algorithm.

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    GENERAL DECAY OF A TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATIONS WITH BOUNDARY MEMORY CONDITION
    Sun Hye PARK
    Acta mathematica scientia,Series B. 2014, 34 (5):  1395-1403.  DOI: 10.1016/S0252-9602(14)60091-6
    Abstract ( 182 )   RICH HTML PDF (153KB) ( 1089 )   Save

    In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.

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    COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL
    Zagharide Zine EL ABIDINE
    Acta mathematica scientia,Series B. 2014, 34 (5):  1404-1416.  DOI: 10.1016/S0252-9602(14)60092-8
    Abstract ( 153 )   RICH HTML PDF (197KB) ( 1059 )   Save

    Let m be a positive integer and B be the unit ball of Rn (≥ 2). We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem
    (−Δ)mu = a1(x)uα1 + a2(x)uα2 , lim|x|→1u(x)/(1 − |x|)m−1 = 0,
    where α1α2 ∈(−1, 1) and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.

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    ON A NEW CLASS OF ANALYTIC FUNCTION DERIVED BY A FRACTIONAL DIFFERENTIAL OPERATOR
    Rabha W. IBRAHIM, Janusz SOK′O L
    Acta mathematica scientia,Series B. 2014, 34 (5):  1417-1426.  DOI: 10.1016/S0252-9602(14)60093-X
    Abstract ( 194 )   RICH HTML PDF (169KB) ( 1382 )   Save

    Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk (type fractional differential equation). The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.

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    ON GLOBAL STABILITY OF A NONRESIDENT COMPUTER VIRUS MODEL
    Yoshiaki MUROYA, Huaixing LI, Toshikazu KUNIYA
    Acta mathematica scientia,Series B. 2014, 34 (5):  1427-1445.  DOI: 10.1016/S0252-9602(14)60094-1
    Abstract ( 296 )   RICH HTML PDF (297KB) ( 1109 )   Save

    In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.

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    STARLIKENESS AND SUBORDINATION PROPERTIES OF A LINEAR OPERATOR
    Samaneh Gholizadeh HAMIDI, Suzeini Abdul HALIM, Janusz SOKóL
    Acta mathematica scientia,Series B. 2014, 34 (5):  1446-1460.  DOI: 10.1016/S0252-9602(14)60095-3
    Abstract ( 173 )   RICH HTML PDF (194KB) ( 950 )   Save

    In this paper, we introduce a new class of p-valent analytic functions defined by using a linear operator Lαk . For functions in this class Hαk (pλ; h) we estimate the coefficients. Furthermore, some subordination properties related to the operator Lαk are also derived.

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    SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS
    Manoj K. YADAV
    Acta mathematica scientia,Series B. 2014, 34 (5):  1461-1472.  DOI: 10.1016/S0252-9602(14)60096-5
    Abstract ( 143 )   RICH HTML PDF (189KB) ( 1084 )   Save

    In this article, we obtain explicit solutions of a linear PDE subject to a class of ra-dial square integrable functions with a monotonically increasing weight function |x|n−1eβ|x|2/2β ≥ 0, ∈ Rn. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in
    terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.

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    ON DISTRIBUTIONAL n-CHAOS
    TAN Feng, FU He-Man
    Acta mathematica scientia,Series B. 2014, 34 (5):  1473-1480.  DOI: 10.1016/S0252-9602(14)60097-7
    Abstract ( 248 )   RICH HTML PDF (180KB) ( 878 )   Save

    Let (X, f) be a topological dynamical system, where X is a nonempty compact and metrizable space with the metric d and f : XX is a continuous map. For any integer n ≥ 2, denote the product space by X(n) = X × · · · × X. We say a system (X, f) is generally distributionally n-chaotic if there exists a residual set DX(n) such that for any point x = (x1, · · · , xn) ∈ D,
    liminfk→∞#({i : 0 ≤ i k − 1,min{d(f i(xj), f i(xl)) : 1 ≤ j ≠ l ≤ n} < δ0})/k= 0
    for some real number δ0 > 0 and

    limsupfk→∞#({i : 0 ≤ i k − 1,max{d(f i(xj), f i(xl)) : 1 ≤ j ≠ l ≤ n} < δ0})/k= 1

    for any real number δ > 0, where #(·) means the cardinality of a set. In this paper, we show that for each integer n ≥ 2, there exists a system (Xσ) which satisfies the following conditions: (1) (Xσ) is transitive; (2) (Xσ) is generally distributionally n-chaotic, but has no distributionally (n + 1)-tuples; (3) the topological entropy of (Xσ) is zero and it has an
    IT-tuple.

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    ON SPECTRAL PROPERTIES OF A NEW OPERATOR OVER SEQUENCE SPACES c AND c0
    Ezgi ERDO GAN, Vatan KARAKAYA
    Acta mathematica scientia,Series B. 2014, 34 (5):  1481-1494.  DOI: 10.1016/S0252-9602(14)60098-9
    Abstract ( 194 )   RICH HTML PDF (196KB) ( 1283 )   Save

    In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces , c and c0 according to a new matrix operator W which is obtained by matrix product.

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    MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS
    SHANG Yue-Yun, WANG Li
    Acta mathematica scientia,Series B. 2014, 34 (5):  1495-1509.  DOI: 10.1016/S0252-9602(14)60099-0
    Abstract ( 162 )   RICH HTML PDF (219KB) ( 1455 )   Save
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    A POSTERIORI ERROR ESTIMATION OF THE NEW MIXED ELEMENT SCHEMES FOR SECOND ORDER ELLIPTIC PROBLEM ON ANISOTROPIC MESHES
    WANG Pei-Zhen, CHEN Shao-Chun
    Acta mathematica scientia,Series B. 2014, 34 (5):  1510-1518.  DOI: 10.1016/S0252-9602(14)60100-4
    Abstract ( 144 )   RICH HTML PDF (197KB) ( 1001 )   Save

    This paper presents a posteriori residual error estimator for the new mixed el-ement scheme for second order elliptic problem on anisotropic meshes. The reliability and efficiency of our estimator are established without any regularity assumption on the mesh. Key words error estimator; anisotropic meshes; new mixed element schemes

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    THE NON-CUTOFF BOLTZMANN EQUATION WITH POTENTIAL FORCE IN THE WHOLE SPACE
    LEI Yuan-Jie
    Acta mathematica scientia,Series B. 2014, 34 (5):  1519-1539.  DOI: 10.1016/S0252-9602(14)60101-6
    Abstract ( 267 )   RICH HTML PDF (250KB) ( 934 )   Save

    This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1–3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].

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    EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX l p(Γ)(p >|1) SPACES
    YI Ji-Jin, WANG Rui-Dong, WANG Xiao-Xiao
    Acta mathematica scientia,Series B. 2014, 34 (5):  1540-1550.  DOI: 10.1016/S0252-9602(14)60102-8
    Abstract ( 137 )   RICH HTML PDF (184KB) ( 1212 )   Save

    In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces l p(Γ) and l p(Δ)(p > 1). We first derive the representation of isometries between the unit spheres of complex Banach spaces l p(Γ) and l p(Δ). Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces l p(Γ)and l p(Δ) can be extended to be a linear isometry on the whole space.

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    PERSISTENCE AND EXTINCTION OF A STOCHASTIC LOGISTIC MODEL WITH DELAYS AND IMPULSIVE PERTURBATION
    LU Chun, DING Xiao-Hua
    Acta mathematica scientia,Series B. 2014, 34 (5):  1551-1570.  DOI: 10.1016/S0252-9602(14)60103-X
    Abstract ( 166 )   RICH HTML PDF (316KB) ( 595 )   Save

    A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Furthermore, the theoretical analysis results are also
    derivated with the help of numerical simulations.

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    THE FEKETE-SZEGÖ|PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION
    Bogumi la KOWALCZYK, Adam LECKO
    Acta mathematica scientia,Series B. 2014, 34 (5):  1571-1583.  DOI: 10.1016/S0252-9602(14)60104-1
    Abstract ( 154 )   RICH HTML PDF (184KB) ( 790 )   Save

    An analytic function f in the unit disk D := {z ∈C : |z| < 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1 −z)2, D, if there exists δ ∈(−π/2, π/2) such that Re{e(1 − z)2f′(z)> 0, D. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szeg¨o problem is studied.

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    NONCOMMUTATIVE ORLICZ-HARDY SPACES
    Abdugheni ABDUREXIT, Turdebek N. BEKJAN
    Acta mathematica scientia,Series B. 2014, 34 (5):  1584-1592.  DOI: 10.1016/S0252-9602(14)60105-3
    Abstract ( 183 )   RICH HTML PDF (180KB) ( 429 )   Save

    Let (Φ, Ψ) be a pair of complementary N-functions and HΦ(A) and H Ψ(A) be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg¨o and innerouter type factorization theorems of Hp(A) to this case.

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    APPROXIMATION BY WALSH-KACZMARZ-FEJÉR MEANS ON THE HARDY SPACE
    George TEPHNADZE
    Acta mathematica scientia,Series B. 2014, 34 (5):  1593-1602.  DOI: 10.1016/S0252-9602(14)60106-5
    Abstract ( 158 )   RICH HTML PDF (181KB) ( 794 )   Save

    The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej´er means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0 < p ≤ 1/2.

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    CRITICAL EXPONENTS AND CRITICAL DIMENSIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH SINGULAR COEFFICIENTS
    WANG Li, WANG Ji-Xiu
    Acta mathematica scientia,Series B. 2014, 34 (5):  1603-1618.  DOI: 10.1016/S0252-9602(14)60107-7
    Abstract ( 159 )   RICH HTML PDF (233KB) ( 1049 )   Save

    Let B1 ⊂ RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical Sobolev exponent and singular coefficients:
    {−div(|∇u|p−2u) = |x|s|u|p*(s)−2uλ|x|t|u|p−2u, x B1,
    u|B1 = 0,
    where t, s > −p, 2 ≤ p < N, p*(s) = (N+s)p/Np and λ is a real parameter. We show particularly that the above problem exists infinitely many radial solutions if the space dimension N >p(p − 1)t + p(p2 p + 1) and λ ∈ (0, λ1,t), where λ1, t is the first eigenvalue of −Δp with the Dirichlet boundary condition. Meanwhile, the nonexistence of sign-changing radial solutions is proved if the space dimension N ≤(ps+p)min{1, p+t/p+s }+p2/p−(p−1)min{1, p+t/p+s } and λ > 0 is small.

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    ON POSITIVE G-SYMMETRIC SOLUTIONS OF A WEIGHTED QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL HARDY-SOBOLEV EXPONENT
    DENG Zhi-Ying, HUANG Yi-Sheng
    Acta mathematica scientia,Series B. 2014, 34 (5):  1619-1633.  DOI: 10.1016/S0252-9602(14)60108-9
    Abstract ( 145 )   RICH HTML PDF (239KB) ( 1117 )   Save

    In this paper, we are concerned with a weighted quasilinear elliptic equation involving critical Hardy–Sobolev exponent in a bounded G-symmetric domain. By using the symmetric criticality principle of Palais and variational method, we establish several existence and multiplicity results of positive G-symmetric solutions under certain appropriate
    hypotheses on the potential and the nonlinearity.

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    ON THE ALMOST EVERYWHERE CONVERGENCE FOR ARBITRARY STOCHASTIC SEQUENCE
    YANG Wei-Guo, TAO Lin-Lian, CHENG Xiao-Jun
    Acta mathematica scientia,Series B. 2014, 34 (5):  1634-1642.  DOI: 10.1016/S0252-9602(14)60109-0
    Abstract ( 148 )   RICH HTML PDF (154KB) ( 397 )   Save

    The purpose of this paper is to establish a class of strong limit theorems for arbitrary stochastic sequences. As corollaries, we generalize some known results.

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    COMMON FIXED POINT THEOREMS FOR THREE MAPS IN DISCONTINUOUS Gb-METRIC SPACES
    Jamal Rezaei ROSHAN, Nabiollah SHOBKOLAEI, Shaban SEDGHI, Vahid PARVANEH, Stojan RADENOVI′C
    Acta mathematica scientia,Series B. 2014, 34 (5):  1643-1654.  DOI: 10.1016/S0252-9602(14)60110-7
    Abstract ( 203 )   RICH HTML PDF (164KB) ( 1632 )   Save

    In [Aghajani A, Abbas M, Roshan JR. Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces. Filomat, 2013, in press], using the concepts of G-metric and b-metric Aghajani et al. defined a new type of metric which is called generalized b-metric or Gb-metric. In this paper, we prove a common fixed point theorem for three mappings in Gb-metric space which is not continuous. An example is presented to verify the effectiveness and applicability of our main result.

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    BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS
    M. GüRDAL, M.T. GARAYEV, S. SALTAN
    Acta mathematica scientia,Series B. 2014, 34 (5):  1655-1660.  DOI: 10.1016/S0252-9602(14)60111-9
    Abstract ( 147 )   RICH HTML PDF (156KB) ( 955 )   Save

    We investigate a basisity problem in the space ?pA(D) and in its invariant sub-spaces. Namely, let W denote a unilateral weighted shift operator acting in the space ?pA(D) , 1 ≤ p < ∞, by Wzn = λnzn+1, n ≥0, with respect to the standard basis
    {zn }n≥0 . Applying the so-called “discrete Duhamel product” technique, it is proven that for any integer k ≥ 1 the sequence {(wi+nk)−1(W | Ei)knfn≥0 is a basic sequence in Ei := span {zi+n : n ≥0 } equivalent to the basis {zi+n }n≥0 if and only if f(i)≠0. We also investigate a Banach algebra structure for the subspaces Ei, i ≥0.

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    BEST PROXIMITY POINT THEOREMS FOR SINGLE- AND SET-VALUED NON-SELF MAPPINGS
    Moosa GABELEH
    Acta mathematica scientia,Series B. 2014, 34 (5):  1661-1669.  DOI: 10.1016/S0252-9602(14)60112-0
    Abstract ( 191 )   RICH HTML PDF (143KB) ( 1534 )   Save

    We study the existence of best proximity points for single-valued non-self map-pings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results.

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    NON-CONFLICTING ORDERING CONES AND VECTOR OPTIMIZATION IN INDUCTIVE LIMITS
    QIU Jing-Hui
    Acta mathematica scientia,Series B. 2014, 34 (5):  1670-1676.  DOI: 10.1016/S0252-9602(14)60113-2
    Abstract ( 148 )   RICH HTML PDF (148KB) ( 458 )   Save

    Let (Eξ) = ind(Enξn) be an inductive limit of a sequence (Enξn)nN of locally convex spaces and let every step (Enξn) be endowed with a partial order by a pointed convex (solid) cone Sn. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence (Sn)nN of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.

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