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20 May 2013, Volume 33 Issue 3 Previous Issue    Next Issue

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DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS Jacek DZIOK|Ravinder Krishna RAINA|Janusz SOKóL Acta mathematica scientia,Series B. 2013, 33 (3):  609-620.  DOI: 10.1016/S0252-9602(13)60024-7 Abstract ( 301 )   RICH HTML PDF (241KB) ( 1097 )   Save This article presents some new results on the class SLM of functions that are analytic in the open unit disc U = {z : |z| < 1} satisfying the conditions that f(0) = 0, f′(0) = 1, and α （1 +zf´´(z)/f′(z)）+ (1 − α)zf′(z)/f(z) ∈p(U) for all z ∈ U, where α is a real number and p(z) =1 + τ 2z2/1 − τ z − τ 2z2 (z ∈ U). The number τ = (1 − √5)/2 is such that τ 2 = 1 + τ . The class SLM introduced by J. Dziok, R.K. Raina, and J. Sok´o l [3, Appl. Math. Comput. 218 (2011), 996-1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory. References | Related Articles | Metrics

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ON EQUITABLE VERTEX DISTINGUISHING EDGE COLORINGS OF TREES YAO Bing, CHEN Xiang-En, SHAN Song-Ling Acta mathematica scientia,Series B. 2013, 33 (3):  621-630.  DOI: 10.1016/S0252-9602(13)60025-9 Abstract ( 220 )   RICH HTML PDF (231KB) ( 486 )   Save It has been known that determining the exact value of vertex distinguishing edge index ′s(G) of a graph G is difficult, even for simple classes of graphs such as paths, cycles, bipartite complete graphs, complete, graphs, and graphs with maximum degree 2. Let nd(G) denote the number of vertices of degree d in G, and let  x ′es(G) be the equitable vertex distinguishing edge index of G. We show that a tree T holds n1(T)≤x  ′s(T) ≤ n1(T) + 1 and  x ′s(T) = x  ′es(T) if T satisfies one of the following conditions (i) n2(T) ≤ Α(T) or (ii) there exists a constant c with respect to 0 < c < 1 such that n2(T)≤ cn1(T) and ∑3≤d≤Δ(T) nd(T) ≤ (1 − c)n1(T) + 1. References | Related Articles | Metrics

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CONCENTRATION OF SOLUTIONS FOR THE MEAN CURVATURE PROBLEM Wael ABDELHEDI Acta mathematica scientia,Series B. 2013, 33 (3):  631-642.  DOI: 10.1016/S0252-9602(13)60026-0 Abstract ( 240 )   RICH HTML PDF (185KB) ( 878 )   Save We consider the problem of conformal metrics equivalent to the Euclidean met-ric, with zero scalar curvature and prescribed mean curvature on the boundary of the ball Bn , n≥4. By variational methods, we prove the existence of two peak solutions that concen-trate around a strict local maximum points of the mean curvature under certain conditions. References | Related Articles | Metrics

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GLOBAL SOLUTIONS AND FINITE TIME BLOW UP FOR DAMPED KLEIN-GORDON EQUATION XU Run-Zhang, DING Yun-Hua Acta mathematica scientia,Series B. 2013, 33 (3):  643-652.  DOI: 10.1016/S0252-9602(13)60027-2 Abstract ( 311 )   RICH HTML PDF (178KB) ( 1046 )   Save We study the Cauchy problem of strongly damped Klein-Gordon equation. Global existence and asymptotic behavior of solutions with initial data in the potential well are de-rived. Moreover, not only does finite time blow up with initial data in the unstable set is proved, but also blow up results with arbitrary positive initial energy are obtained. References | Related Articles | Metrics

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LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES Anna AVALLONE, Paolo VITOLO Acta mathematica scientia,Series B. 2013, 33 (3):  653-677.  DOI: 10.1016/S0252-9602(13)60028-4 Abstract ( 290 )   RICH HTML PDF (273KB) ( 875 )   Save Let L be a pseudo-D-lattice. We prove that the exhaustive lattice uniformities on L which makes the operations of L uniformly continuous form a Boolean algebra isomorphic to the centre of a suitable complete pseudo-D-lattice associated to L. As a consequence, we obtain decomposition theorems—such as Lebesgue and Hewitt–Yosida decompositions—and control theorems—such as Bartle–Dunford–Schwartz and Rybakov theorems—for modular measures on L. References | Related Articles | Metrics

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A NOTE ON GRADIENT BLOWUP RATE OF THE INHOMOGENEOUS HAMILTON-JACOBI EQUATIONS ZHANG Zheng-Ce, LI Zhen-Jie Acta mathematica scientia,Series B. 2013, 33 (3):  678-686.  DOI: 10.1016/S0252-9602(13)60029-6 Abstract ( 909 )   RICH HTML PDF (174KB) ( 897 )   Save The gradient blowup of the equation ut = Δu + a(x)|∇u|p + h(x), where p > 2,  is studied. It is shown that the gradient blowup rate will never match that of the self-similar variables. The exact blowup rate for radial solutions is established under the assumptions on the initial data so that the solution is monotonically increasing in time. References | Related Articles | Metrics

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MATRIX PRODUCT CODES WITH ROSENBLOOM-TSFASMAN METRIC CHEN Bo-Cong, LIN Li-Ren, LIU Hong-Wei Acta mathematica scientia,Series B. 2013, 33 (3):  687-700.  DOI: 10.1016/S0252-9602(13)60030-2 Abstract ( 264 )   RICH HTML PDF (189KB) ( 1055 )   Save In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom-Tsfasman distances of the matrix product codes are obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given. References | Related Articles | Metrics

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INTRINSIC EQUATIONS FOR A GENERALIZED RELAXED ELASTIC LINE ON AN ORIENTED SURFACE IN THE GALILEAN SPACE Tevfik SAHIN Acta mathematica scientia,Series B. 2013, 33 (3):  701-711.  DOI: 10.1016/S0252-9602(13)60031-4 Abstract ( 353 )   RICH HTML PDF (202KB) ( 1350 )   Save In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G3. References | Related Articles | Metrics

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EXISTENCE OF SOLUTIONS OF NONLINEAR FRACTIONAL PANTOGRAPH EQUATIONS K. BALACHANDRAN, S. KIRUTHIKA, J. J. TRUJILLO Acta mathematica scientia,Series B. 2013, 33 (3):  712-720.  DOI: 10.1016/S0252-9602(13)60032-6 Abstract ( 364 )   RICH HTML PDF (154KB) ( 1708 )   Save This article deals with the existence of solutions of nonlinear fractional panto-graph equations. Such model can be considered suitable to be applied when the corresponding process occurs through strongly anomalous media. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the main result obtained in this article. References | Related Articles | Metrics

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TRAJECTORY ATTRACTORS FOR NONCLASSICAL DIFFUSION EQUATIONS WITH FADING MEMORY WANG Yong-Hai, WANG Ling-Zhi Acta mathematica scientia,Series B. 2013, 33 (3):  721-737.  DOI: 10.1016/S0252-9602(13)60033-8 Abstract ( 315 )   RICH HTML PDF (220KB) ( 834 )   Save In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Miranville [7, 8], in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory. References | Related Articles | Metrics

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e-FILTERS OF MS-ALGEBRAS M. Sambasiva RAO Acta mathematica scientia,Series B. 2013, 33 (3):  738-746.  DOI: 10.1016/S0252-9602(13)60034-X Abstract ( 244 )   RICH HTML PDF (160KB) ( 1470 )   Save The notion of e-filters is introduced in an MS-algebra and characterized. The concept of D-filters is introduced and a set of equivalent conditions under which every D-filter is an e-filter are given. The properties of the space of all prime e-filters of an MS-algebra are observed. The concept of D-prime filters is introduced and then a set of equivalent conditions are derived for a prime e-filter to become a D-prime filter in topological terms. References | Related Articles | Metrics

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EXACT NULL CONTROLLABILITY OF NON-AUTONOMOUS FUNCTIONAL EVOLUTION SYSTEMS WITH NONLOCAL CONDITIONS FU Xian-Long, ZHANG Yu Acta mathematica scientia,Series B. 2013, 33 (3):  747-757.  DOI: 10.1016/S0252-9602(13)60035-1 Abstract ( 285 )   RICH HTML PDF (178KB) ( 1135 )   Save In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condi-tion or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is also provided to show an application of the obtained result. References | Related Articles | Metrics

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EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL´S INEQUALITY IN BANACH SPACES Dimplekumar N. CHALISHAJAR, K. KARTHIKEYAN Acta mathematica scientia,Series B. 2013, 33 (3):  758-772.  DOI: 10.1016/S0252-9602(13)60036-3 Abstract ( 439 )   RICH HTML PDF (205KB) ( 1630 )   Save We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ (n−1, n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder´s inequality, a suitable singular Gronwall´s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results. References | Related Articles | Metrics

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ZEROS AND FIXED POINTS OF DIFFERENCE OPERATORS OF MEROMORPHIC FUNCTIONS CUI Wei-Wei, YANG Lian-Zhong Acta mathematica scientia,Series B. 2013, 33 (3):  773-780.  DOI: 10.1016/S0252-9602(13)60037-5 Abstract ( 376 )   RICH HTML PDF (154KB) ( 1143 )   Save Let f be a transcendental meromorphic function and Δf(z) = f(z + 1) − f(z). A number of results are proved concerning the existences of zeros and fixed points of Δf(z) and Δf(z)/f(z) when f(z) is of order σ(f)=1. Examples show that some of the results are sharp. References | Related Articles | Metrics

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INCOMPRESSIBLE LIMIT OF A COMPRESSIBLE LIQUID CRYSTALS SYSTEM HAO Yi-Hang, LIU Xian-Gao Acta mathematica scientia,Series B. 2013, 33 (3):  781-796.  DOI: 10.1016/S0252-9602(13)60038-7 Abstract ( 264 )   RICH HTML PDF (226KB) ( 536 )   Save This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space RN and a bounded domain of RN with Dirichlet boundary conditions. Here we set the number of dimension N = 2 or 3. References | Related Articles | Metrics

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ON THE mth ORDER DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS Metin BASARIR, Emrah Evren KARA Acta mathematica scientia,Series B. 2013, 33 (3):  797-813.  DOI: 10.1016/S0252-9602(13)60039-9 Abstract ( 315 )   RICH HTML PDF (244KB) ( 1016 )   Save In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space ?(u, v, p; Δ(m)), which consist of the sequences whose generalized weighted Δ(m)-difference means are in the linear space ?(p) defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from ?(u, v, p,Δ(m)) to ?∞, c, and c0. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space ?p(u, v, Δ(m)) (1≤p < 1). References | Related Articles | Metrics

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THE GROWTH ORDER OF SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS GAO Ling-Yun Acta mathematica scientia,Series B. 2013, 33 (3):  814-820.  DOI: 10.1016/S0252-9602(13)60040-5 Abstract ( 293 )   RICH HTML PDF (149KB) ( 639 )   Save Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equations, and extend some results of the growth order of solutions of systems of differential equations to systems of difference equat References | Related Articles | Metrics

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SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM ZHOU Shou-Ming, MU Chun-Lai, WANG Liang-Zhan Acta mathematica scientia,Series B. 2013, 33 (3):  821-829.  DOI: 10.1016/S0252-9602(13)60041-7 Abstract ( 334 )   RICH HTML PDF (169KB) ( 874 )   Save In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation. References | Related Articles | Metrics

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STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE Mohamed JLELI Acta mathematica scientia,Series B. 2013, 33 (3):  830-838.  DOI: 10.1016/S0252-9602(13)60042-9 Abstract ( 261 )   RICH HTML PDF (162KB) ( 1000 )   Save In this article, by solving a nonlinear differential equation, we prove the existence of a one parameter family of constant mean curvature hypersurfaces in the hyperbolic space with two ends. Then, we study the stability of these hypersurfaces. References | Related Articles | Metrics

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EXPLICIT ERROR ESTIMATE FOR THE NONCONFORMING WILSON´S ELEMENT ZHAO Ji-Kun, CHEN Shao-Chun Acta mathematica scientia,Series B. 2013, 33 (3):  839-846.  DOI: 10.1016/S0252-9602(13)60043-0 Abstract ( 280 )   RICH HTML PDF (225KB) ( 825 )   Save In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for theWilson´s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds. References | Related Articles | Metrics

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NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS LI Nan, WANG Chang-You Acta mathematica scientia,Series B. 2013, 33 (3):  847-854.  DOI: 10.1016/S0252-9602(13)60044-2 Abstract ( 635 )   RICH HTML PDF (151KB) ( 1224 )   Save In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results. References | Related Articles | Metrics

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PARAMETER IDENTIFICATION IN FRACTIONAL DIFFERENTIAL EQUATIONS LI Jing, GUO Bo-Ling Acta mathematica scientia,Series B. 2013, 33 (3):  855-864.  DOI: 10.1016/S0252-9602(13)60045-4 Abstract ( 261 )   RICH HTML PDF (168KB) ( 1375 )   Save References | Related Articles | Metrics

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ENERGY DISSIPATION FOR WEAK SOLUTIONS OF INCOMPRESSIBLE MHD EQUATIONS GAO Zhen-Sheng, TAN Zhong, WU Guo-Chun Acta mathematica scientia,Series B. 2013, 33 (3):  865-871.  DOI: 10.1016/S0252-9602(13)60046-6 Abstract ( 290 )   RICH HTML PDF (155KB) ( 1071 )   Save In this article, we mainly study the local equation of energy for weak solutions of 3D MHD equations. We define a dissipation term D(u,B) that stems from an eventual lack of smoothness in the solution, and then obtain a local equation of energy for weak solutions of 3D MHD equations. Finally, we consider the 2D case at the end of this article. References | Related Articles | Metrics

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REGULARITY PROPERTY OF SOLUTION TO TWO-PARAMETER STOCHASTIC VOLTERRA EQUATION WITH NON-LIPSCHITZ COEFFICIENTS JIANG Guo, WANG Xiang-Jun Acta mathematica scientia,Series B. 2013, 33 (3):  872-882.  DOI: 10.1016/S0252-9602(13)60047-8 Abstract ( 223 )   RICH HTML PDF (177KB) ( 852 )   Save This article proves the existence and uniqueness of solution to two-parameter stochastic Volterra equation with non-Lipschitz coefficients and driven by Brownian sheet, where the main tool is Bihari’s inequality in the plane. Moreover, we also discuss the time regularity property of the solution by Kolmogorov´s continuity criterion. References | Related Articles | Metrics