04 December 2008, Volume 24 Issue 12

    

• Select all
  |

Articles
• Select
  Self-Dual Weak Hopf Algebras

  Munir AHMED, Fang LI

  Acta Mathematica Sinica. 2008, 24(12): 1935-1948. https://doi.org/10.1007/s10114-008-6592-7

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper,we define the notion of self-dual graded weak Hopf algebra and self-dual semilattice graded weak Hopf algebra.We give characterization of finite-dimensional such algebras when they are in structually simple forms in the sense of E.L.Green and E.N.Morcos.We also give the definition of self-dual weak Hopf quiver and apply these types of quivers to classify the finite-dimensional self-dual semilattice graded weak Hopf algebras.Finally,we prove partially the conjecture given by N.Andruskiewitsch and H.-J.Schneider in the case of finite-dimensional pointed semilattice graded weak Hopf algebra H when grH is self-dual.
• Select
  Self-intersecting Geodesics and Entropy of the Geodesic Flow

  Sigurd ANGENENT

  Acta Mathematica Sinica. 2008, 24(12): 1949-1952. https://doi.org/10.1007/s10114-008-6439-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Given a symmetric Finsler metric on T² whose geodesic flow has zero topological entropy,we show that the lift in the universal covering R2→T² of any closed geodesic on T² must be an embedded curve in R2.
• Select
  On the Stability of a Cubic Functional Equation

  Abbas NAJATI, Choonkil PARK

  Acta Mathematica Sinica. 2008, 24(12): 1953-1964. https://doi.org/10.1007/s10114-008-6560-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper,we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation
  2f(x+2y)+f(2x-y)=5f(x+y)+5f(x-y)+15f(y)
  in the spirit of Hyers,Ulam,Rassias and G?vruta.
• Select
  Some New Results on Transition Probability

  Yu Quan XIE

  Acta Mathematica Sinica. 2008, 24(12): 1965-1984. https://doi.org/10.1007/s10114-008-6054-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper,we study the basic properties of stationary transition probability of Markov processes on a general measurable space (E,E),such as the continuity,maximum probability,zero point,positive probability set,standardization,and obtain a series of important results such as Continuity Theorem,Representation Theorem,Lévy Theorem and so on.These results are very useful for us to study stationary tri-point transition probability on a general measurable space (E,E).Our main tools such as Egoroff's Theorem,Vitali-Hahn-Saks's Theorem and the theory of atomic set and well-posedness of measure are also very interesting and fashionable.
• Select
  Combinatorics on Words in Symbolic Dynamics: The Quadratic Map

  Wan Ji DAI, Kebo LÜ, Jun WANG

  Acta Mathematica Sinica. 2008, 24(12): 1985-1994. https://doi.org/10.1007/s10114-008-7490-8

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  This paper is contributed to the combinatorial properties of the MSS sequences,which are the periodic kneading words of quadratic maps defined on a interval.An explicit expression of adjacency relations on MSS sequences of given lengths is established.
• Select
  Brill-Noether Theory for Rank Two Vector Bundles Generated by Their Sections

  Jian Bo XIAO, Xiao Jiang TAN

  Acta Mathematica Sinica. 2008, 24(12): 1995-2010. https://doi.org/10.1007/s10114-008-7268-z

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We here study the Brill-Noether theory for rank two vector bundles generated by their sections.We generalize the vanishing theorem,the Clifford theorem and the existence theorem to such bundles.
• Select
  A Characterization of the Smallest Suzuki 2-Group

  Qin Hai ZANG

  Acta Mathematica Sinica. 2008, 24(12): 2011-2014. https://doi.org/10.1007/s10114-008-7135-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let G be a finite nonabelian group which has no abelian maximal subgroups and satisfies that any two non-commutative elements generate a maximal subgroup.Then G is isomorphic to the smallest Suzuki 2-group of order 64.
• Select
  A Note on the Browder’s and Weyl’s Theorem

  M. AMOUCH, H. ZGUITTI

  Acta Mathematica Sinica. 2008, 24(12): 2015-2020. https://doi.org/10.1007/s10114-008-6633-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let T be a Banach space operator,E(T) be the set of all isolated eigenvalues of T and π(T) be the set of all poles of T.In this work,we show that Browder's theorem for T is equivalent to the localized single-valued extension property at all complex numbers λ in the complement of the Weyl spectrum of T,and we give some characterization of Weyl's theorem for operator satisfying E(T)=π(T).An application is also given.
• Select
  Convex Mappings on Some Reinhardt Domains

  Yi HONG, Wen Ge CHEN

  Acta Mathematica Sinica. 2008, 24(12): 2021-2028. https://doi.org/10.1007/s10114-008-6521-9

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper,we consider the following Reinhardt domains.Let M=(M1,M2,...,Mn):[0,1]→[0,1]n be a C2-function and Mj(0)=0,Mj(1)=1,Mj">0,C_1jr^p_j-1<Mj' (r) <C_2jr^p_j-1r∈(0,1),pj>2,1≤j≤n,0<C1j<C2j be constants.Define
  
  Then DM⊂Cn is a convex Reinhardt domain.We give an extension theorem for a normalized biholomorphic convex mapping f:DM→Cn.
• Select
  Generalized Empirical Likelihood Inference in Semiparametric Regression Model for Longitudinal Data

  Gao Rong LI, Ping TIAN, Liu Gen XUE

  Acta Mathematica Sinica. 2008, 24(12): 2029-2040. https://doi.org/10.1007/s10114-008-6434-7

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper,we consider the semiparametric regression model for longitudinal data.Due to the correlation within groups,a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix.It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions,and hence it can be used to construct the confidence regions of the parameters.A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals.
• Select
  Additive Maps Between Standard Operator Algebras Compressing Certain Spectral Functions

  Jin Chuan HOU, Li HUANG

  Acta Mathematica Sinica. 2008, 24(12): 2041-2048. https://doi.org/10.1007/s10114-008-6428-5

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We characterize the surjective additive maps compressing the spectral function Δ(·) between standard operator algebras acting on complex Banach spaces,where Δ(·) stands for any one of nine spectral functions σ(·),σl(·),σr(·),σl(·) ∩ σr(·),∂σ(·),ησ(·),σap(·),σs(·),and σap(·) ∩ σs(·).
• Select
  Parabolic Littlewood-Paley g-Function with Rough Kernel

  Qing Ying XUE, Yong DING, KôzôYABUTA

  Acta Mathematica Sinica. 2008, 24(12): 2049-2060. https://doi.org/10.1007/s10114-008-6338-6

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this note,we give the L^p (1<p<∞) boundedness of the parabolic Littlewood-Paley g-function with rough kernel.
• Select
  A Maschke Type Theorem for Weak Hopf Algebras

  J. N. ALONSOÁLVAREZ, J. M. FERNÁNDEZ VILABOA, R. GONZÁLEZ RODRÍGUEZ, A. B. RODRÍGUEZ RAPOSO

  Acta Mathematica Sinica. 2008, 24(12): 2065-2080. https://doi.org/10.1007/s10114-008-6047-1

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper,we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral,thus extending the classical theory developed by Doi in the Hopf algebra setting.Also,from these results,we deduce a version of Maschke's Theorem for (H,B)-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.
• Select
  Superlinearly Convergent Affine Scaling Interior Trust-Region Method for Linear Constrained LC¹ Minimization

  De Tong ZHU

  Acta Mathematica Sinica. 2008, 24(12): 2081-2100. https://doi.org/10.1007/s10114-008-5444-9

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian.We propose and analyze a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian.The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints.The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required.Applications of the algorithm to some nonsmooth optimization problems are discussed.
• Select
  Completeness of the System {z^λn} in L²[B,α₀]

  Ju Hong NING, Guan Tie DENG

  Acta Mathematica Sinica. 2008, 24(12): 2101-2110. https://doi.org/10.1007/s10114-008-5317-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let B be an unbounded domain located outside an angle domain with vertex at the origin,Λ={λ_nn}(n=1,2,...) be a sequence of complex numbers satisfying sup | arg(λ_n)|<α<π/2 and denote by M(Λ)={z^λ,λ∈Λ} the corresponding system of functions z_λ(λ∈Λ).Let α₀(z) be a weight function defined on B.We obtain a completeness theorem for the system M(Λ) in the Hilbert space L²[B,α₀].