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20 March 2011, Volume 31 Issue 2 Previous Issue    Next Issue

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ANNOUNCEMENT Acta mathematica scientia,Series B. 2011, 31 (2):  0-0.  DOI: 10.1016/S0252-9602(11)60236-1 Abstract ( 493 )   RICH HTML PDF (55KB) ( 646 )   Save A special issue of Acta Mathematica Scientia, to be published in 2011, will be dedicated to the 85th birthday of Peter D. Lax, who is one of the most prominent mathematicians of the past hundred years. Peter Lax has made important and seminal contributions in many areas of pure and applied mathematics, including  the theory of integrable systems and solitons, with applications to fluid dynamics and physics, scattering theory, and the theory of shock waves in hyperbolic conservation laws, with applications to gas dynamics. He also exerted a great influence in launching the field of scientific computation. Over the years, Peter Lax has been a great supporter of mathematics in China, having helped numerous Chinese mathematicians. We invite contributions to the special issue from students, postdocs and other colleagues and friends of Peter Lax. If you plan to contribute a paper, please inform the Standing Editors of the special issue, by March 31, 2011. Standing Editors: Gui-Qiang Chen, Constantine Dafermos, Xiaqi Ding, Tai-Ping Liu ~~Gui-Qiang Chen: chengq@maths.ox.ac.uk ~~Constantine Dafermos: Constantine_Dafermos@brown.edu ~~Xiaqi Ding: xqding@amt.ac.cn ~~Tai-Ping Liu: liu@math.stanford.edu Related Articles | Metrics

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ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES ZHOU Jia-Zu Acta mathematica scientia,Series B. 2011, 31 (2):  361-366.  DOI: 10.1016/S0252-9602(11)60237-3 Abstract ( 698 )   RICH HTML PDF (142KB) ( 1349 )   Save Let M be a compact convex hypersurface of class C2, which  is assumed to bound a nonempty convex body K in the Euclidean space Rn and H be the mean curvature of M. We obtain a lower bound of the total square of mean curvature ∫M H2dA. The bound is the Minkowski quermassintegral of the convex body K. The total square of mean curvature attains the lower bound when M is an (n-1)-sphere. References | Related Articles | Metrics

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A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS SHI Dong-Yang, REN Jin-Cheng, GONG Wei Acta mathematica scientia,Series B. 2011, 31 (2):  367-382.  DOI: 10.1016/S0252-9602(11)60238-5 Abstract ( 1004 )   RICH HTML PDF (574KB) ( 1756 )   Save In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis. References | Related Articles | Metrics

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ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM LIU Hong, SONG Yong-Zhong Acta mathematica scientia,Series B. 2011, 31 (2):  383-398.  DOI: 10.1016/S0252-9602(11)60239-7 Abstract ( 692 )   RICH HTML PDF (195KB) ( 1039 )   Save In this article, linear regular index 2 DAEs A(t)[D(t)x(t)]'+B(t)x(t)=q(t) are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular index 1DAEs are obtained by a regularization method. We study the behavior of the solution of the regularization system via asymptotic expansions. The error analysis between the solutions of the DAEs and its regularization system is given. References | Related Articles | Metrics

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DENSITY PROPERTIES OF MAPPING SPACES FOR OPERATOR SPACES DONG Zhe, JIANG Hai-Yi Acta mathematica scientia,Series B. 2011, 31 (2):  399-407.  DOI: 10.1016/S0252-9602(11)60240-3 Abstract ( 531 )   RICH HTML PDF (169KB) ( 1022 )   Save In this article, we give the sufficient and necessary conditions for which several important mapping  spaces are weak* dense in the corresponding completely bound mapping spaces. References | Related Articles | Metrics

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EXACT EVALUATIONS OF FINITE |TRIGONOMETRIC SUMS BY SAMPLING THEOREMS M.H. Annaby, R.M. Asharabi Acta mathematica scientia,Series B. 2011, 31 (2):  408-418.  DOI: 10.1016/S0252-9602(11)60241-5 Abstract ( 639 )   RICH HTML PDF (167KB) ( 1154 )   Save We use the sampling representations associated with Sturm-Liouville difference operators to derive generalized integral-valued trigonometric sums. This extends the known results where zeros of Chebyshev polynomials of the first kind are involved to the use of the eigenvalues of difference operators, which leads to new identities. In these identities Bernoulli's numbers play a role similar to that of Euler's in the old ones. Our technique differs from that of Byrne-Smith (1997) and Berndt-Yeap (2002). References | Related Articles | Metrics

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A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS SHI Jing-Tao, WU Zhen Acta mathematica scientia,Series B. 2011, 31 (2):  419-433.  DOI: 10.1016/S0252-9602(11)60242-7 Abstract ( 731 )   RICH HTML PDF (204KB) ( 1895 )   Save A stochastic maximum principle for the risk-sensitive optimal control problem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained. References | Related Articles | Metrics

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CYCLIC VECTORS AND CELLULAR INDECOMPOSABLE OPERATORS ON Qp SPACES YE Shan-Li, LOU Zeng-Jian Acta mathematica scientia,Series B. 2011, 31 (2):  434-440.  DOI: 10.1016/S0252-9602(11)60243-9 Abstract ( 582 )   RICH HTML PDF (162KB) ( 1085 )   Save We identify the functions whose polynomial multiples are weak* dense in Qp spaces and prove that if |f(z)|≥|g(z)| and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operator Mz on Qp spaces is cellular indecomposable. References | Related Articles | Metrics

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OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U6(2) ZHANG Liang-Cai, SHI Wu-Jie Acta mathematica scientia,Series B. 2011, 31 (2):  441-450.  DOI: 10.1016/S0252-9602(11)60244-0 Abstract ( 638 )   RICH HTML PDF (195KB) ( 1606 )   Save Let G be a finite group and π(G)={p1, p2, …, pk} be the set of the primes dividing the order of G. We define its prime graph Γ(G) as follows. The vertex set of this graph is π(G), and two distinct vertices p, q are joined by an edge if and only if pq ∈πe(G). In this case, we write p～q. For p ∈π(G),  put deg(p):=|{q ∈π(G) | p～q|, which is called the degree of p. We also define D(G):=(deg(p1), deg(p2), … , deg(pk)), where p1<p2<…<pk, which is called the degree pattern  of G.  We say a  group G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and  degree pattern as G. Specially, a 1-fold OD-characterizable  group is simply called an OD-characterizable group. Let L:=U6(2). In this article, we classify all finite groups with the same order and degree pattern as an almost simple groups related to L. In fact, we prove that L and  L.2 are OD-characterizable, L.3 is 3-fold OD-characterizable, and L.S3 is 5-fold OD-characterizable. References | Related Articles | Metrics

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A HEAT KERNEL VERSION OF HARDY'S THEOREM FOR THE LAGUERRE HYPERGROUP HUANG Ji-Zheng, LIU He-Ping Acta mathematica scientia,Series B. 2011, 31 (2):  451-458.  DOI: 10.1016/S0252-9602(11)60245-2 Abstract ( 514 )   RICH HTML PDF (162KB) ( 1517 )   Save In this article, we prove a heat kernel version of Hardy's theorem for the Laguerre hypergroup. References | Related Articles | Metrics

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POINCARÉSERIES AND AN APPLICATION TO WEYL ALGEBRAS WANG Zhi-Hua, WEI Jun-Chao, LI Li-Bin Acta mathematica scientia,Series B. 2011, 31 (2):  459-467.  DOI: 10.1016/S0252-9602(11)60246-4 Abstract ( 644 )   RICH HTML PDF (170KB) ( 1374 )   Save Let An be the n-th Weyl algebra over a field of characteristic 0 and M a finitely generated module over An. By further exploring the relationship between the Poincaré series and the dimension and the multiplicity of M, we are able to prove that the tensor product of two finitely generated modules over An has the multiplicity   equal to the  product of the multiplicities of both modules. It turns out that we can compute the dimensions and the multiplicities of some homogeneous subquotient modules of An. References | Related Articles | Metrics

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COMPACT COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES ON BOUNDED SYMMETRIC DOMAINS LV Xiao-Fen, HU Zhang-Jian Acta mathematica scientia,Series B. 2011, 31 (2):  468-476.  DOI: 10.1016/S0252-9602(11)60247-6 Abstract ( 746 )   RICH HTML PDF (163KB) ( 1272 )   Save In this article, we borrow the idea of using Schur's test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetric domain Ω, and verify that Cφ is compact on Lqa(Ω, dvβ) if and only if K(φ(z), φ(z))/K(z, z)→0 as z→∂Ω under a mild condition, where K(z, w) is the Bergman kernel. References | Related Articles | Metrics

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COMMUTATORS OF BOCHNER-RIESZ OPERATORS FOR A CLASS OF RADIAL FUNCTIONS XIA Xia, LU Shan-Zhan Acta mathematica scientia,Series B. 2011, 31 (2):  477-482.  DOI: 10.1016/S0252-9602(11)60248-8 Abstract ( 618 )   RICH HTML PDF (147KB) ( 1196 )   Save In this article, we prove the boundedness of commutators generated by Bochner-Riesz operators below the critical index and BMO functions on the class of radial functions in Lp (Rn) with |1/p-1/2|<(1+2α)/(2n). References | Related Articles | Metrics

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OPTIMAL PORTFOLIO ON TRACKING THE EXPECTED WEALTH PROCESS WITH LIQUIDITY CONSTRAINTS LUO Kui, WANG Guang-Ming, HU Yi-Jun Acta mathematica scientia,Series B. 2011, 31 (2):  483-490.  DOI: 10.1016/S0252-9602(11)60249-X Abstract ( 673 )   RICH HTML PDF (161KB) ( 1508 )   Save In this article, the authors consider the optimal portfolio on tracking the expected wealth process with liquidity constraints. The constrained optimal portfolio is first formulated as minimizing the cumulate variance between the wealth process and the expected wealth process. Then, the dynamic programming methodology is applied to reduce the whole problem to solving the Hamilton-Jacobi-Bellman equation coupled with the liquidity constraint, and the method of Lagrange multiplier is applied to handle the constraint. Finally, a numerical method is proposed to solve the constrained HJB equation and the constrained optimal strategy. Especially, the explicit solution to this optimal problem is derived when there is no liquidity constraint. References | Related Articles | Metrics

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ON COMPACTNESS FOR ITERATED COMMUTATORS LIU Yong-Min, YU Yan-Yan Acta mathematica scientia,Series B. 2011, 31 (2):  491-500.  DOI: 10.1016/S0252-9602(11)60250-6 Abstract ( 712 )   RICH HTML PDF (180KB) ( 1019 )   Save The authors study  the iterated commutators on the weighted Bergman spaces A2(Φ), and  prove that Cn/h is compact on A2(Φ) if and only if  h ∈B0. References | Related Articles | Metrics

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ON SPACELIKE AUSTERE SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACE DONG Yu-Xin, HAN Ying-Bo Acta mathematica scientia,Series B. 2011, 31 (2):  501-511.  DOI: 10.1016/S0252-9602(11)60251-8 Abstract ( 631 )   RICH HTML PDF (174KB) ( 1113 )   Save In this article, we construct some spacelike austere submanifolds in pseduo-Euclidean spaces. We also get some indefinite special Lagrangian submanifolds by constructing twisted normal bundle of spacelike austere submanifolds in pseduo-Euclidean spaces. References | Related Articles | Metrics

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ON THE GLOBAL STABILITY CONJECTURE OF THE GENOTYPE SELECTION MODEL S.H. Saker Acta mathematica scientia,Series B. 2011, 31 (2):  512-528.  DOI: 10.1016/S0252-9602(11)60252-X Abstract ( 742 )   RICH HTML PDF (287KB) ( 908 )   Save In 1994, Grove, Kocic, Ladas, and Levin conjectured that the local stability and global stability conditions of the fixed point y =1/2 in the genotype selection model should be equivalent. In this article, we give an affirmative answer to this conjecture and prove that local stability implies global stability. Some illustrative examples are included to demonstrate the validity and applicability of the results. References | Related Articles | Metrics

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RANDOM ATTRACTORS FOR A STOCHASTIC HYDRODYNAMICAL EQUATION IN HEISENBERG PARAMAGNET GUO Bai-Ling, GUO Chun-Xiao, PU Xua-Ke Acta mathematica scientia,Series B. 2011, 31 (2):  529-540.  DOI: 10.1016/S0252-9602(11)60253-1 Abstract ( 557 )   RICH HTML PDF (184KB) ( 1091 )   Save This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in H1. References | Related Articles | Metrics

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EXPRESSION OF MEROMORPHIC SOLUTIONS OF SYSTEMS OF ALGEBRAIC DIFFERENTIAL EQUATIONS WITH EXPONENTIAL GAO Ling-Yun Acta mathematica scientia,Series B. 2011, 31 (2):  541-548.  DOI: 10.1016/S0252-9602(11)60254-3 Abstract ( 584 )   RICH HTML PDF (148KB) ( 1064 )   Save Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results. References | Related Articles | Metrics

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A DEGENERACY THEOREM FOR MEROMORPHIC MAPPINGS WITH TRUNCATED MULTIPLICITIES YAN Qi-Ming, CHEN Zhi-Hua Acta mathematica scientia,Series B. 2011, 31 (2):  549-560.  DOI: 10.1016/S0252-9602(11)60255-5 Abstract ( 625 )   RICH HTML PDF (190KB) ( 1069 )   Save In this article, we prove a degeneracy theorem for three linearly non-degenerate meromorphic mappings from Cn into PN(C), sharing 2N+2 hyperplanes in general position, counted with multiplicities truncated by 2. References | Related Articles | Metrics

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AN IMPROVEMENT OF THE OCTONIONIC TAYLOR TYPE THEOREM LIAO Jian-Quan, LI Xing-Min Acta mathematica scientia,Series B. 2011, 31 (2):  561-566.  DOI: 10.1016/S0252-9602(11)60256-7 Abstract ( 557 )   RICH HTML PDF (146KB) ( 1051 )   Save We prove that  the octonionic polynomials V kl1 …lkare independent of the associative orders   k. This improves the octonionic Taylor type theorem. References | Related Articles | Metrics

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RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID\\ WITH MULTIPLICATIVE NOISE ZHAO Cai-De, LI Yong-Sheng, ZHOU Sheng-Fan Acta mathematica scientia,Series B. 2011, 31 (2):  567-575.  DOI: 10.1016/S0252-9602(11)60257-9 Abstract ( 613 )   RICH HTML PDF (168KB) ( 1360 )   Save This article proves that the random dynamical system generated by a two-dimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space. References | Related Articles | Metrics

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ON A CLASS OF KÖTHE SEQUENCE SPACES WITH NORMAL STRUCTURE B.Zlatanov Acta mathematica scientia,Series B. 2011, 31 (2):  576-590.  Abstract ( 595 )   RICH HTML PDF (205KB) ( 945 )   Save In this note, we investigate the generalized modulus of convexity δ(λ) and the generalized modulus smoothness ρ(λ). We obtain  some estimates of these moduli for X=lp. We obtain inequalities between WCS coefficient of a K\"othe sequence space X and δX(λ). We show that, for a wide class of K\"othe sequence spaces X, if for some ε ∈(0, 9/10] holds δX(ε)>1/3(1-√3/2)ε, then X has normal structure. References | Related Articles | Metrics

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ON THE REGULARITY CRITERIA OF THE 3D NAVIER-STOKES EQUATIONS IN CRITICAL SPACES DONG Bai-Qing, Sadek Gala, CHEN Zhi-Min Acta mathematica scientia,Series B. 2011, 31 (2):  591-600.  DOI: 10.1016/S0252-9602(11)60259-2 Abstract ( 766 )   RICH HTML PDF (173KB) ( 1579 )   Save Regularity criteria of Leray-Hopf weak solutions to the three-dimensional  Navier-Stokes equations  in some critical spaces such as  Lorentz space, Morrey space and multiplier space are derived in terms of two partial derivatives, ∂1u1, ∂2u2, of  velocity fields. References | Related Articles | Metrics

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A COUPLED CONTINUOUS-DISCONTINUOUS FEM APPROACH FOR CONVECTION DIFFUSION EQUATIONS ZHU Peng, XIE Zi-Qing, ZHOU Shu-Zi Acta mathematica scientia,Series B. 2011, 31 (2):  601-612.  DOI: 10.1016/S0252-9602(11)60260-9 Abstract ( 709 )   RICH HTML PDF (201KB) ( 1216 )   Save In this article, we introduce a coupled approach of local discontinuous Galerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. The discontinuous Galerkin method is adopted in the subdomain where the solution varies rapidly, while the standard finite element method is used in the other subdomain due to its lower computational cost. The stability and a priori error estimate are established. We prove that the coupled method has O((ε1/2}+h1/2)hk) convergence rate in an associated norm, where ε is the diffusion coefficient, h is the mesh size and k is the degree of polynomial. The numerical results verify our theoretical results. Moreover, 2k-order superconvergence of the numerical traces at the nodes, and the optimal convergence of the errors under L2 norm are observed numerically on the uniform mesh. The numerical results also indicate that the coupled method has the same convergence order and almost the same errors as the purely LDG method. References | Related Articles | Metrics

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FORCED OSCILLATION OF SECOND ORDER DIFFERENTIAL EQUATIONS WITH MIXED NONLINEARITIES Taher S.Hassan, Lynn Erbe, Allan Peterson Acta mathematica scientia,Series B. 2011, 31 (2):  613-626.  DOI: 10.1016/S0252-9602(11)60261-0 Abstract ( 652 )   RICH HTML PDF (196KB) ( 2141 )   Save This article is concerned with the oscillation of the forced second order differential equation with mixed nonlinearities (a(t)( x´(t)γ)´+p0(t) xγ( g0(t))+∑i=1npi(t)l x(gi(t))|αi sgn x (gi(t)) =e(t), where γ is a quotient of odd positive integers, αi>0, i=1, 2, …, n, a, e, and pi ∈C([ 0, ∞) , {R}, α(t) >0, gi: R→R are positive continuous functions on R with limt→∞gi(t)=∞, i=0, 1, …, n. Our results generalize and improve the results in a recent article by Sun and Wong [29]. References | Related Articles | Metrics

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ON PROPERTIES OF DIFFERENCE POLYNOMIALS CHEN Zong-Xuan, HUANG Zhi-Bo, ZHENG Xiu-Min Acta mathematica scientia,Series B. 2011, 31 (2):  627-633.  DOI: 10.1016/S0252-9602(11)60262-2 Abstract ( 676 )   RICH HTML PDF (145KB) ( 1425 )   Save We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f(z)f(z+c). References | Related Articles | Metrics

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MINIMUM CONGESTION SPANNING TREES IN BIPARTITE AND RANDOM GRAPHS M.I.Ostrovskii Acta mathematica scientia,Series B. 2011, 31 (2):  634-640.  DOI: 10.1016/S0252-9602(11)60263-4 Abstract ( 539 )   RICH HTML PDF (156KB) ( 1093 )   Save The first problem considered in this article reads: is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs? It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n3/2. References | Related Articles | Metrics

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WEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES WANG Mao-Fa Acta mathematica scientia,Series B. 2011, 31 (2):  641-651.  DOI: 10.1016/S0252-9602(11)60264-6 Abstract ( 775 )   RICH HTML PDF (175KB) ( 1667 )   Save In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show  that these vector-valued Dirichlet spaces are ifferent counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces. References | Related Articles | Metrics

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A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM WAN Zhong-Ping, WANG Guang-Min, LV Yi-Bing Acta mathematica scientia,Series B. 2011, 31 (2):  652-660.  DOI: 10.1016/S0252-9602(11)60265-8 Abstract ( 530 )   RICH HTML PDF (153KB) ( 1416 )   Save The penalty function method, presented many years ago, is an important numerical method for the mathematical programming  problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty function approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach. References | Related Articles | Metrics

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FRACTIONAL ORDER BOUNDARY |VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL Hussein A.H.Salem Acta mathematica scientia,Series B. 2011, 31 (2):  661-672.  DOI: 10.1016/S0252-9602(11)60266-X Abstract ( 645 )   RICH HTML PDF (184KB) ( 1893 )   Save In this article, we  investigate the existence of Pseudo solutions for some  fractional order  boundary value problem  with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function.  To  encompass the full scope of this article, we give an example illustrating the main result. References | Related Articles | Metrics

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THE BANACH ALGEBRAS GENERATED BY OPERATORS WITH ONE-POINT SPECTRUM H.Seferoglu, N.Simsek Acta mathematica scientia,Series B. 2011, 31 (2):  673-680.  DOI: 10.1016/S0252-9602(11)60267-1 Abstract ( 588 )   RICH HTML PDF (163KB) ( 930 )   Save In this article, we present some results related to the structure of Banach algebras generated by operators with one-point spectrum. References | Related Articles | Metrics

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GLOBAL EXISTENCE AND NONEXISTENCE FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX CHEN Bo-Tao, MI Yong-Sheng, MU Chun-Lai Acta mathematica scientia,Series B. 2011, 31 (2):  681-693.  DOI: 10.1016/S0252-9602(11)60268-3 Abstract ( 909 )   RICH HTML PDF (192KB) ( 1134 )   Save This article deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve and the critical Fujita curve for the problem. Especially for the blow-up case, it is rather technical. It comes from the construction of the so-called Zel'dovich-Kompaneetz-Barenblatt profile. References | Related Articles | Metrics

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ON MULTIPLICATION AND COMULTIPLICATION MODULES H. Ansari-Toroghy, F. Farshadifar Acta mathematica scientia,Series B. 2011, 31 (2):  694-700.  DOI: 10.1016/S0252-9602(11)60269-5 Abstract ( 718 )   RICH HTML PDF (137KB) ( 2536 )   Save This article deals with some results concerning multiplication and comultiplication modules over a commutative ring. References | Related Articles | Metrics

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ON THE BRAIDED STRUCTURES OF RADFORD'S BIPRODUCT MA Tian-Shui, LI Hai-Ying, ZHAO Wen-Zheng Acta mathematica scientia,Series B. 2011, 31 (2):  701-715.  DOI: 10.1016/S0252-9602(11)60270-1 Abstract ( 597 )   RICH HTML PDF (177KB) ( 1287 )   Save We obtain the necessary and sufficient conditions for Radford's biproduct to be a braided Hopf algebra. As an application, a nontrivial example is given. References | Related Articles | Metrics

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VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES Eknarin Jankaew, Somyot Plubtieng, Anutep Tepphun Acta mathematica scientia,Series B. 2011, 31 (2):  716-726.  DOI: 10.1016/S0252-9602(11)60271-3 Abstract ( 657 )   RICH HTML PDF (162KB) ( 1115 )   Save In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces.  We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi [T. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 (1997), 71-83], and Yao and Chen[Y. Yao, R. Chen, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces,Nonlinear Analysis 67(2007), 1758-1763]. References | Related Articles | Metrics

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PARTIAL COMPACTNESS FOR LANDAU-LIFSHITZ MAXWELL EQUATION IN TWO-DIMENSION KOU Yan-Lei, DING Shi-Jin Acta mathematica scientia,Series B. 2011, 31 (2):  727-748.  DOI: 10.1016/S0252-9602(11)60272-5 Abstract ( 756 )   RICH HTML PDF (256KB) ( 989 )   Save We study the partial regularity of weak solutions to the 2-dimensional Landau-Lifshitz equations coupled with time dependent Maxwell equations by Ginzburg-Landau type approximation. Outside an energy concentration set of locally finite 2-dimensional parabolic Hausdorff measure, we prove the uniform local C∞ bounds for the approaching solutions and then extract a subsequence converging to a global weak solution of the Landau-Lifshitz-Maxwell equations which are smooth away from finitely many points. References | Related Articles | Metrics