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20 July 2011, Volume 31 Issue 4 Previous Issue    Next Issue

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ON A BI-HARMONIC EQUATION INVOLVING CRITICAL EXPONENT: EXISTENCE AND MULTIPLICITY RESULTS Zakaria Boucheche, Ridha Yacoub, Hichem Chtioui Acta mathematica scientia,Series B. 2011, 31 (4):  1213-1244.  DOI: 10.1016/S0252-9602(11)60311-1 Abstract ( 587 )   RICH HTML PDF (337KB) ( 1058 )   Save In this paper,  we consider the problem of existence as well as multiplicity results for a bi-harmonic equation under the Navier boundary conditions: Δ2 u=K(x)up, u>0 in Ω, Δu= u=0 on ∂Ω, where Ω is a smooth domain in Rn, n≥5, and p+1 = 2n/n-4 is the critical Sobolev exponent. We obtain highlightly a new criterion of existence, which provides existence results for a dense subset of positive functions, and generalizes Bahri-Coron type criterion in dimension six. Our argument gives also estimates on the Morse index of the obtained solutions and extends some known results. Moreover, it provides, for generic K, Morse inequalities at infinity, which delivers  lower bounds for the number of solutions. As further applications of this  Morse theoretical approach, we prove more existence results. References | Related Articles | Metrics

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RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY WU Fu-Ke, HU Shi-Geng, MAO Xue-Rong Acta mathematica scientia,Series B. 2011, 31 (4):  1245-1258.  DOI: 10.1016/S0252-9602(11)60312-3 Abstract ( 744 )   RICH HTML PDF (200KB) ( 1358 )   Save This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with un-bounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations. References | Related Articles | Metrics

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THE POINTWISE ESTIMATES TO SOLUTIONS FOR 1-DIMENSIONAL LINEAR THERMO-VISCO-ELASTIC SYSTEM HAO Xin-Wen, PENG Shao-Yu Acta mathematica scientia,Series B. 2011, 31 (4):  1259-1271.  DOI: 10.1016/S0252-9602(11)60313-5 Abstract ( 697 )   RICH HTML PDF (185KB) ( 792 )   Save In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential sys- tem. The solutions of the system show some decay property due to the parabolicity. Based on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’principle is shown. References | Related Articles | Metrics

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QUASI-NEUTRAL LIMIT OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM YANG Xiu-Hui Acta mathematica scientia,Series B. 2011, 31 (4):  1272-1280.  DOI: 10.1016/S0252-9602(11)60314-7 Abstract ( 598 )   RICH HTML PDF (156KB) ( 897 )   Save This paper is concerned with the quasi-neutral limit of the bipolar Navier-Stokes-Poisson system. It is rigorously proved, by introducing the new modulated energy functional and using the refined energy analysis, that the strong solutions of the bipolar Navier-Stokes-Poisson system converge to the strong solution of the compressible Navier-Stokes equations as the Debye length goes to zero. Moreover, if we let the viscous coeffi-cients and the Debye length go to zero simultaneously, then we obtain the convergence of the strong solutions of bipolar Navier-Stokes-Poisson system to the strong solution of the compressible Euler equations. References | Related Articles | Metrics

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ON DIFFERENCE EQUATIONS RELATING TO GAMMA FUNCTION CHEN Zong-Xuan, HUANG Zhi-Bo, ZHANG Ran-Ran Acta mathematica scientia,Series B. 2011, 31 (4):  1281-1294.  DOI: 10.1016/S0252-9602(11)60315-9 Abstract ( 753 )   RICH HTML PDF (192KB) ( 901 )   Save We consider the existence, the growth, poles, zeros, fixed points and the Borel exceptional value of solutions for the following difference equations relating to Gamma function y(z + 1) − y(z) = R(z) and y(z + 1) = P(z)y(z). References | Related Articles | Metrics

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THE RECURSION OPERATOR FOR A CONSTRAINED CKP HIERARCHY LI Chuan-Zhong, TIAN Ke-Lei, HE Jin-Song, CHENG Yi Acta mathematica scientia,Series B. 2011, 31 (4):  1295-1302.  DOI: 10.1016/S0252-9602(11)60316-0 Abstract ( 540 )   RICH HTML PDF (151KB) ( 799 )   Save This paper gives a recursion operator for a 1-constrained CKP hierarchy, and by the recursion operator it proves that the 1-constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition q = r. References | Related Articles | Metrics

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GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE LI Yong-Sheng, YANG Xin-Yu Acta mathematica scientia,Series B. 2011, 31 (4):  1303-1317.  DOI: 10.1016/S0252-9602(11)60317-2 Abstract ( 588 )   RICH HTML PDF (207KB) ( 946 )   Save The periodic initial value problem of a fifth-order shallow water equation ∂tu − ∂2x∂tu+ ∂3xu −∂5xu +3u∂xu −∂2xu ∂2xu -u∂3xu= 0 is shown to be globally well-posed in Sobolev spaces Hs(T) for s > 2/3 by I-method. For this equation lacks scaling invariance, we first reconsider the local result and pay special attention to the relationship between the lifespan of the local solution and the initial data, and then prove the almost conservation law, and finally obtain the global well-posedness by an iteration process. References | Related Articles | Metrics

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INVERSE COEFFICIENT PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES LIU Zhen-Hai, I.Szántò Acta mathematica scientia,Series B. 2011, 31 (4):  1318-1326.  DOI: 10.1016/S0252-9602(11)60318-4 Abstract ( 586 )   RICH HTML PDF (159KB) ( 957 )   Save This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gra-dient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained. References | Related Articles | Metrics

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EXAMPLES ON EXCEPTIONAL VALUES OF MEROMORPHIC FUNCTIONS PENG Yan-Hong, SUN Dao-Chun Acta mathematica scientia,Series B. 2011, 31 (4):  1327-1336.  DOI: 10.1016/S0252-9602(11)60319-6 Abstract ( 610 )   RICH HTML PDF (167KB) ( 1166 )   Save In this paper, by means of the definition of Borel exceptional value method, another exceptional value of meromorphic function which is a T exceptional value is defined by linking the concept of T direction. And we construct a meromorphic function with zero as Borel exceptional value, but not as T exceptional value; and another meromorphic function with zero as T exceptional value, but not as Borel exceptional value. References | Related Articles | Metrics

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THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS Mujeeb ur Rehman, Rahmat Ali Khan, Naseer Ahmad Asif Acta mathematica scientia,Series B. 2011, 31 (4):  1337-1346.  DOI: 10.1016/S0252-9602(11)60320-2 Abstract ( 673 )   RICH HTML PDF (179KB) ( 1494 )   Save In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type cDδ0+u(t) = f(t, u(t), cDσ0+u(t)), t ∈ [0, T], u(0) = ∂u(η), u(T) = βu(η), where 1 < δ < 2, 0 < σ < 1, α, β∈ R, η ∈ (0, T), αη(1 −β ) + (1 − α)(T − βη) ≠ 0 and cDδ0+, cDσ0+ are the Caputo fractional derivatives. We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results. Examples are also included to show the applicability of our results. References | Related Articles | Metrics

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COMPACT COMPOSITION OPERATORS ON GENERALIZED LIPSCHITZ SPACES DAI Ji-Neng, OUYANG Cai-Heng Acta mathematica scientia,Series B. 2011, 31 (4):  1347-1356.  DOI: 10.1016/S0252-9602(11)60321-4 Abstract ( 612 )   RICH HTML PDF (172KB) ( 954 )   Save In this paper, boundedness and compactness of the composition operator on the generalized Lipschitz spaces  ( > 1) of holomorphic functions in the unit disk are characterized. References | Related Articles | Metrics

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A UNIFIED CLASS OF ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS J. Dziok Acta mathematica scientia,Series B. 2011, 31 (4):  1357-1366.  DOI: 10.1016/S0252-9602(11)60322-6 Abstract ( 630 )   RICH HTML PDF (153KB) ( 942 )   Save In this paper we introduce new classes of analytic functions with fixed argu-ment of coefficients defined by subordination. Coefficient estimates, distortion theorems, integral means inequalities, and the radii of convexity and starlikeness are investigated. Convolution properties are also pointed out. References | Related Articles | Metrics

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ON COMPACT COMPOSITION OPERATORS ON A CLASS OF HOLOMORPHIC FUNCTION SPACES OVER THE UNIT BALL IN Cn LONG Su-Juan Acta mathematica scientia,Series B. 2011, 31 (4):  1367-1376.  DOI: 10.1016/S0252-9602(11)60323-8 Abstract ( 538 )   RICH HTML PDF (173KB) ( 905 )   Save In this paper, a general function space X(Bn) over the unit ball in Cn with norm k · kX(Bn) is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a compact composition operator on X(Bn), related to works of [8] and [10]. References | Related Articles | Metrics

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SCHWARZ-PICK ESTIMATES FOR BOUNDED HOLOMORPHIC FUNCTIONS ON CLASSICAL DOMAINS LIU Xiang, CHEN Zhi-Hua Acta mathematica scientia,Series B. 2011, 31 (4):  1377-1382.  DOI: 10.1016/S0252-9602(11)60324-X Abstract ( 625 )   RICH HTML PDF (149KB) ( 1325 )   Save In this paper, Schwarz-Pick estimates for high order Fr´echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball. References | Related Articles | Metrics

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ESTIMATES ON EIGENVALUES FOR THE BIHARMONIC OPERATOR ON A BOUNDED DOMAIN IN Hn(−1) HUANG Guang-Yue, LI Xin-Xiao Acta mathematica scientia,Series B. 2011, 31 (4):  1383-1388.  DOI: 10.1016/S0252-9602(11)60325-1 Abstract ( 626 )   RICH HTML PDF (133KB) ( 1124 )   Save In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the (k + 1)th eigenvalue in terms of the first kth eigenvalues independent of the domains. References | Related Articles | Metrics

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DECAY ESTIMATES OF PLANAR STATIONARY WAVES FOR DAMED WAVE EQUATIONS WITH NONLINEAR CONVECTION IN#br# MULTI-DIMENSIONAL HALF SPACE FAN Li-Li, LIU Hong-Xia, YIN Hui Acta mathematica scientia,Series B. 2011, 31 (4):  1389-1410.  DOI: 10.1016/S0252-9602(11)60326-3 Abstract ( 848 )   RICH HTML PDF (263KB) ( 940 )   Save This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space Rn ? utt − Δu + ut + divf(u) = 0, t > 0, x = (x1, x′)∈ Rn+(:= R+ × Rn−1), u(0, x) = u0(x) → u+, as x1 →+∞, ut(0, x) = u1(x), u(t, 0, x′) = ub, x′ = (x2, x3, · · · , xn) ∈ Rn−1. (I) For the non-degenerate case f′1(u+) < 0, it was shown in [10] that the above initial-boundary value problem (I) admits a unique global solution u(t, x) which converges to the corresponding planar stationary wave Φ(x1) uniformly in x1 ∈R+ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u(t, x) for t →+∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f′1(ub) < 0. The main purpose of this paper devoted to discussing the case of f′1(ub) ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates. References | Related Articles | Metrics

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Cl -GV TRIVIALITY OF FUNCTION GERMS AND NEWTON POLYHEDRA LIU Heng-Xing, ZHANG Dun-Mu Acta mathematica scientia,Series B. 2011, 31 (4):  1411-1424.  DOI: 10.1016/S0252-9602(11)60327-5 Abstract ( 529 )   RICH HTML PDF (211KB) ( 879 )   Save Weprovideestimates onthedegreeof Cl -GV determinacy(G is oneofMather’s groups R or K ) of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to some Newton polyhedron. The result gives lan explicit order such that the Cl geometrical structure of a function germ is preserved l after higher order perturbations, which generalizes the result on Cl-G triviality of function germs given by M.A.S.Ruas. References | Related Articles | Metrics

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ON F-SENSITIVE PAIRS TAN Feng, ZHANG Rui-Feng Acta mathematica scientia,Series B. 2011, 31 (4):  1425-1435.  DOI: 10.1016/S0252-9602(11)60328-7 Abstract ( 455 )   RICH HTML PDF (195KB) ( 1113 )   Save In the present paper, we define sensitive pairs via Furstenberg families and discuss the relation of three definitions: sensitivity, F-sensitivity and F-sensitive pairs, see Theorem 1. For transitive systems, we give some su?cient conditions to ensure the existence of F-sensitive pairs. In particular, each non-minimal E system (M system, P sys- tem) has positive lower density (Fs, Fr resp.)-sensitive pairs almost everywhere. Moreover, each non-minimal M system is Fts-sensitive. Finally, by some examples we show that: (1) F-sensitivity can not imply the existence of F-sensitive pairs. That means there exists an F-sensitive system, which has no F-sensitive pairs. (2) There is no immediate relation be- tween the existence of sensitive pairs and Li-Yorke chaos, i.e., there exists a system (X,f) without Li-Yorke scrambled pairs, which has κB-sensitive pairs almost everywhere. (3) If the system (G,f) is sensitive, where G is a finite graph, then it has κB-sensitive pairs almost everywhere. References | Related Articles | Metrics

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GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS WU Shun-Tang Acta mathematica scientia,Series B. 2011, 31 (4):  1436-1448.  DOI: 10.1016/S0252-9602(11)60329-9 Abstract ( 627 )   RICH HTML PDF (182KB) ( 1563 )   Save The initial boundary value problem for a viscoelastic equation |ut|ρ utt -Δu-Δutt +∫t 0g(t-s)Δu(s)ds+|mut| ut = |u|p u in a bounded domain is considered, where ρ,m,p > 0 and g is a nonnegative and decaying function. The general uniform decay of solution energy is discussed under some conditions on the relaxation function g and the initial data by adopting the method of [14, 15, 19]. This work generalizes and improves earlier results in the literature. References | Related Articles | Metrics

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CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM XU Jian-Kai, TAN Zhong Acta mathematica scientia,Series B. 2011, 31 (4):  1449-1456.  DOI: 10.1016/S0252-9602(11)60330-5 Abstract ( 611 )   RICH HTML PDF (167KB) ( 879 )   Save In this paper, we consider the following integral system: ???u(x) = v (y) dy, ? n n-α R |x-y| (1.1) ??? up(y) ?v(x) = n-μdy, n R |x-y| where 0 < α, μ < n; p,q ≥ 1. Using the method of moving planes in an integral form which was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions of (0.1) are radially symmetric and decreasing with respect to some point under some general conditions of integrability. The results essentially improve and extend previously known results [4, 8]. References | Related Articles | Metrics

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DARBOUX TRANSFORMATION OF A NONLINEAR EVOLUTION EQUATION AND ITS EXPLICIT SOLUTIONS LI Wen-Min, HAN You-Qin, ZHOU Gao-Jun Acta mathematica scientia,Series B. 2011, 31 (4):  1457-1464.  DOI: 10.1016/S0252-9602(11)60331-7 Abstract ( 633 )   RICH HTML PDF (279KB) ( 1331 )   Save In this paper, we study a differential-difference equation associated with dis-crete 3 ×3 matrix spectral problem. Based on gauge transformation of the spectral problm, Darboux transformation of the differential-difference equation is given. In order to solve the differential-difference equation, a systematic algebraic algorithm is given. As an appli-cation, explicit soliton solutions of the differential-difference equation are given. References | Related Articles | Metrics

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CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE EQUENCES OF ORDER m Ivana Djolovi′c, Eberhard Malkowsky Acta mathematica scientia,Series B. 2011, 31 (4):  1465-1474.  DOI: 10.1016/S0252-9602(11)60332-9 Abstract ( 941 )   RICH HTML PDF (179KB) ( 1116 )   Save In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Baffsar ([17]) defined the Euler spaces of m-th order difference sequences er0( Δ（m）), erc(Δ（m） ) and er∞(Δ（m） ) and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that pur-pose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c0, c and l∞. The main tool for our characterizations is the Hausdorff measure of noncompactness. References | Related Articles | Metrics

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A CHARACTERIZATION OF ORTHONORMAL WAVELET FAMILIES IN SOBOLEV SPACES LU Da-Yong, LI De-Feng Acta mathematica scientia,Series B. 2011, 31 (4):  1475-1488.  DOI: 10.1016/S0252-9602(11)60333-0 Abstract ( 512 )   RICH HTML PDF (188KB) ( 1211 )   Save In this paper, a characterization of orthonormal wavelet families in Sobolev spaces Hs(R) is established. References | Related Articles | Metrics

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THE HARDY TYPE INEQUALITY FOR THE MAXIMAL OPERATOR OF THE ONE-DIMENSIONAL DYADIC DERIVATIVE Ushangi Goginava Acta mathematica scientia,Series B. 2011, 31 (4):  1489-1493.  DOI: 10.1016/S0252-9602(11)60334-2 Abstract ( 579 )   RICH HTML PDF (133KB) ( 949 )   Save In this paper we prove that the maximal operator I* of dyadic derivative is not bounded from the Hardy space Hp [0, 1] to the Hardy space Hp [0, 1], when 0 < p  1. References | Related Articles | Metrics

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TRANSPORTATION INEQUALITIES FOR WEAKLY DEPENDENT SEQUENCES MA Yu-Tao Acta mathematica scientia,Series B. 2011, 31 (4):  1494-1502.  DOI: 10.1016/S0252-9602(11)60335-4 Abstract ( 555 )   RICH HTML PDF (173KB) ( 911 )   Save In [3], they gave necessary and sufficient condition for T1C and then as ap-plications T1C for weakly dependent sequences was established. In this note, based on Gozlan-L´eonard characterization for W1H-inequalities, we extends this result to W1H-inequalities. References | Related Articles | Metrics

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A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM SUN Mei-Na Acta mathematica scientia,Series B. 2011, 31 (4):  1503-1512.  DOI: 10.1016/S0252-9602(11)60336-6 Abstract ( 653 )   RICH HTML PDF (304KB) ( 928 )   Save In this note, we consider the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle when the vacuum is not involved. The solutions are obtained constructively and globally when the initial data consist of three pieces of constant states. Furthermore, it can be found that the Riemann solutions are stable with respect to such small perturbations of the initial data in this particular situation by investigating the limits of the solutions as the perturbed parameter " goes to zero. References | Related Articles | Metrics

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A NOTE ON GENERALIZED ABSOLUTE SUMMABILITY FACTORS FOR A TRIANGULAR MATRIX Ekrem Savas Acta mathematica scientia,Series B. 2011, 31 (4):  1513-1516.  DOI: 10.1016/S0252-9602(11)60337-8 Abstract ( 416 )   RICH HTML PDF (107KB) ( 812 )   Save In this paper, a general theorem on |A, δ|k-summability factors of infinite series is proved under different conditions. References | Related Articles | Metrics

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Lp CONTINUITY OF HÖRMANDER SYMBOL OPERATORS OpSm0,0 AND NUMERICAL ALGORITHM YANG Qi-Xiang Acta mathematica scientia,Series B. 2011, 31 (4):  1517-1534.  DOI: 10.1016/S0252-9602(11)60338-X Abstract ( 489 )   RICH HTML PDF (253KB) ( 854 )   Save If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for H¨ormander symbol operators OpSm0,0, which is different to the case Smρ,δ (0 ≤δ < ρ ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the Lp continuity of non infinite smooth operators OpSm0,0; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L2→L2 continuity for scale operators. By considering the influence region of scale operator, we get H1(= F0,21 ) → L1 continuity and L1 →BMO continuity. By interpolation theorem, we get also Lp(= F0,2p ) → Lp continuity for 1 < p < ∞. Our results are sharp for F0,2p →Lp continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces. References | Related Articles | Metrics

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NASH EQUILIBRIA WITHOUT CONTINUITY OF THE CHOICE RULES José C.R. Alcantud Acta mathematica scientia,Series B. 2011, 31 (4):  1535-1540.  DOI: 10.1016/S0252-9602(11)60339-1 Abstract ( 513 )   RICH HTML PDF (144KB) ( 972 )   Save The proposal in Alcantud and Al´os-Ferrer [1], where players that express their tastes according to choice rules facing a competitive situation, is further exploited here. We prove that, under lack of continuity of the choice rules it is also possible to ensure the existence of equilibrium. We shall appeal to general situations that are fulfilled by well-established models, where players have non-transitive preferences of various types. References | Related Articles | Metrics

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SOME RESULTS ON PRODUCT COMPLEX FINSLER MANIFOLDS WU Zhi-Cheng, ZHONG Chun-Ping Acta mathematica scientia,Series B. 2011, 31 (4):  1541-1552.  DOI: 10.1016/S0252-9602(11)60340-8 Abstract ( 537 )   RICH HTML PDF (183KB) ( 893 )   Save Let (M, F) be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds (M1, F1) and (M2, F2). In this paper, we obtain the relationship between the Chern Finsler connection coefficients Γi;k associated to F and the Chern Finsler connection coefficients ˜ Γa;c,˜ Γα;γ associated to F1, F2, respectively. As applications we prove that, if both (M1, F1) and (M2, F2) are strongly Kähler Finsler (complex Berwald, or locally complex Minkowski, respectively) manifolds, so does (M, F). Furthermore, we prove that the holomorphic curvature KF = 0 if and only if KF1 = 0 and KF2 = 0. References | Related Articles | Metrics

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A FIXED POINT APPROACH TO THE STABILITY OF A GENERALIZED APOLLONIUS TYPE QUADRATIC FUNCTIONAL EQUATION WANG Zhi-Hua Acta mathematica scientia,Series B. 2011, 31 (4):  1553-1560.  DOI: 10.1016/S0252-9602(11)60341-X Abstract ( 703 )   RICH HTML PDF (148KB) ( 996 )   Save Using the fixed point method, this article proves the Hyers-Ulam-Rassias sta-bility of a generalized Apollonius type quadratic functional equation in Banach spaces. The conditions of these results are demonstrated by the quadratic functional equation of Apollonius type. References | Related Articles | Metrics

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AMBARZUMYAN’S THEOREM WITH EIGENPARAMETER IN THE BOUNDARY CONDITIONS YANG Chuan-Fu, YANG Xiao-Ping Acta mathematica scientia,Series B. 2011, 31 (4):  1561-1568.  DOI: 10.1016/S0252-9602(11)60342-1 Abstract ( 664 )   RICH HTML PDF (156KB) ( 1050 )   Save In this paper, the classical Ambarzumyan’s theorem for the regular Sturm-Liouville problem is extended to the case in which the boundary conditions are eigenpa-rameter dependent. Specifically, we show that if the spectrum of the operator −D2+q with eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero. References | Related Articles | Metrics

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NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH#br# STRUM-LIOUVILLE BOUNDARY CONDITIONS ZHAO Zeng-Qin Acta mathematica scientia,Series B. 2011, 31 (4):  1569-1582.  DOI: 10.1016/S0252-9602(11)60343-3 Abstract ( 712 )   RICH HTML PDF (193KB) ( 980 )   Save This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C2n−2[0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C2n−1[0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems. References | Related Articles | Metrics

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IMPROVED GAGLIARDO-NIRENBERG INEQUALITIES ON HEISENBERG TYPE GROUPS LUO Guang-Zhou Acta mathematica scientia,Series B. 2011, 31 (4):  1583-1590.  DOI: 10.1016/S0252-9602(11)60344-5 Abstract ( 581 )   RICH HTML PDF (164KB) ( 1446 )   Save Motivated by the idea of M. Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds, we prove an analogous result for Kohn’s sub-Laplacian on the Heisenberg type groups. The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type. References | Related Articles | Metrics

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SOME REMARKS ON (L)-GREEN’S RELATIONS AND STRONGLY RPP SEMIGROUPS DU Lan, GUO Yu-Qi, K.P. Shum Acta mathematica scientia,Series B. 2011, 31 (4):  1591-1599.  DOI: 10.1016/S0252-9602(11)60345-7 Abstract ( 512 )   RICH HTML PDF (156KB) ( 972 )   Save In order to study rpp semigroups, in particular, some special cases, several facts on (l)-Green’s relations and strongly rpp semigroups are given as some remarks. References | Related Articles | Metrics

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LOCAL AUTOMORPHISMS OF SEMISIMPLE ALGEBRAS AND GROUP ALGEBRAS WANG Deng-Yin, GUAN Qi, ZHANG Dong-Ju Acta mathematica scientia,Series B. 2011, 31 (4):  1600-1612.  DOI: 10.1016/S0252-9602(11)60346-9 Abstract ( 486 )   RICH HTML PDF (204KB) ( 836 )   Save Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F-algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, FK the group algebra of K over F, then all local automorphisms of FK are also characterized. References | Related Articles | Metrics

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DE MORGAN ALGEBRAS WITH DOUBLE DEMI-PSEUDOCOMPLEMENTATION FANG Jie, WANG Lei-Bo Acta mathematica scientia,Series B. 2011, 31 (4):  1613-1623.  DOI: 10.1016/S0252-9602(11)60347-0 Abstract ( 463 )   RICH HTML PDF (174KB) ( 1061 )   Save The variety ddpM of de Morgan algebras with double demi-pseudocomplem-entation consists of those algebras (L;∧,∨,? ,* ,+ , 0, 1) of type (2, 2, 1, 1, 1, 0, 0) where (L; ∧,∨,? , 0, 1) is a de Morgan algebra, (L;∧,∨, *,+ , 0, 1) is a double demi-p-lattice and the operations x → x?, x → x* and x → x+ are linked by the identities x*? = x?*, x+? = x?+ and x*+ = x+*. In this paper, we characterize congruences on a ddpM-algebra, and give a description of the subdirectly irreducible algebras. References | Related Articles | Metrics

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SCHWARZ-PICK ESTIMATES FOR PARTIAL DERIVATIVES OF ARBITARY ORDER OF BOUNDED HOLOMORPHIC FUNCTIONS#br# IN THE UNIT BALL OF Cn DAI Shao-Yu, CHEN Huai-Hui Acta mathematica scientia,Series B. 2011, 31 (4):  1624-1632.  DOI: 10.1016/S0252-9602(11)60348-2 Abstract ( 477 )   RICH HTML PDF (159KB) ( 883 )   Save This paper gives a Schwarz-Pick estimate for bounded holomorphic functions in the unit ball of Cn. References | Related Articles | Metrics

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ON THE STABILITY OF FUSION FRAMES (FRAMES OF SUBSPACES) Mohammad Sadegh Asgari Acta mathematica scientia,Series B. 2011, 31 (4):  1633-1642.  DOI: 10.1016/S0252-9602(11)60349-4 Abstract ( 593 )   RICH HTML PDF (170KB) ( 1061 )   Save A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame (frame of subspaces) is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3(iii)] with extra information about the bounds. References | Related Articles | Metrics

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SOME INEQUALITIES OF HERMITE–HADAMARD TYPE FOR s-CONVEX FUNCTIONS Mohammad W. Alomari, Maslina Darus, Uˇgur S. Kirmaci Acta mathematica scientia,Series B. 2011, 31 (4):  1643-1652.  DOI: 10.1016/S0252-9602(11)60350-0 Abstract ( 506 )   RICH HTML PDF (156KB) ( 1977 )   Save In this paper several inequalities of the left-hand side of Hermite-Hadamard’s inequality are obtained for s-convex functions. References | Related Articles | Metrics