中国科学院数学与系统科学研究院期刊网
AMS

05 April 2007, Volume 23 Issue 4
    

  • Select all
    |
    Articles
  • A Representation of the Lorentz Spin Group and Its Application
    Qi Keng LU, Ke WU
    Acta Mathematica Sinica. 2007, 23(4): 577-598. https://doi.org/10.1007/s10114-007-0930-z
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    For an integer m≥4,we define a set of 2[m/2]×2[m/2] matrices γj(m),(j=0,1,...,m-1)which satisfy γj(m)γk(m)+γk(m)γj(m)=2ηjk(m)I[m/2],where (ηjk(m))0≤j,k< m-1 is a diagonal matrix,the first diagonal element of which is 1 and the others are -1,I[m/2] is a 2[m/2]×2[m/2] identity matrix with [m/2] being the integer part of m/2.For m=4 and 5,the representation H(m)of the Lorentz Spin group is known.For m≥6,we prove that
    (i)when m=2n,(n≥3),H(m)is the group generated by the set of matrices

    (ii)when m=2n+1,(n≥3),H(m)is generated by the set of matrices
    .
  • On the Relationship Between the Baum-Katz-Spitzer Complete Convergence Theorem and the Law of the Iterated Logarithm
    De Li LI, Andrew ROSALSKY, Andrei VOLODIN
    Acta Mathematica Sinica. 2007, 23(4): 599-612. https://doi.org/10.1007/s10114-005-0908-7
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    "For a sequence of i.i.d.Banach space-valued random variables {Xn;n≥1} and a sequence of positive constants {an;n≥1},the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm is investigated.Sets of conditions are provided under which
    (i) lim supn→∞‖Sn‖/an<∞ a.s.and
    for all ε>λ for some constantλ∈[0,∞) are equivalent;
    (ii) For all constants λ∈[0,∞),

    and
    are equivalent.In general,no geometric conditions are imposed on the underlying Banach space.Corollaries are presented and new results are obtained even in the case of real-valued random variables.
  • Dimensional Properties of Fractional Brownian Motion
    Dong Sheng WU, Yi Min XIAO
    Acta Mathematica Sinica. 2007, 23(4): 613-622. https://doi.org/10.1007/s10114-005-0928-3
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let Bα={Bα(t),t∈RN} be an (N,d)-fractional Brownian motion with Hurst index α∈(0,1).By applying the strong local nondeterminism of Bα,we prove certain forms of uniform Hausdorff dimension results for the images of Bα when N>αd.Our results extend those of Kaufman for one-dimensional Brownian motion.
  • Poisson Equation on Some Complete Noncompact Manifolds
    Xu Qian FAN
    Acta Mathematica Sinica. 2007, 23(4): 623-638. https://doi.org/10.1007/s10114-005-0922-9
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We study the Poisson equation on some complete noncompact manifolds with asymptotically nonnegative curvature.We will also study the limiting behavior of the nonhomogeneous heat equation on some complete noncompact manifolds with nonnegative curvature.
  • Poisson Equation on Some Compl
    Xu Qian FAN
    Acta Mathematica Sinica. 2007, 23(4): 623-638. https://doi.org/10.1007/s10114-005-0922-9
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We study the Poisson equation
  • The Fibered Isomorphism Conjecture for Complex Manifolds
    S. K. ROUSHON
    Acta Mathematica Sinica. 2007, 23(4): 639-658. https://doi.org/10.1007/s10114-005-0759-2
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones,corresponding to the stable topological pseudoisotopy functor,is true for the fundamental groups of a class of complex manifolds.A consequence of this result is that the Whitehead group,reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free.We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.
  • The Order of Hypersubstitutions of Type(2, 2)
    Thawhat CHANGPHAS, Klaus DENECKE
    Acta Mathematica Sinica. 2007, 23(4): 659-670. https://doi.org/10.1007/s10114-005-0778-z
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Hypersubstitutions are mappings which map operation symbols to terms of the corresponding arities.They were introduced as a way of making precise the concept of a hyperidentity and generalizations to M-hyperidentities.A variety in which every identity is satisfied as a hyperidentity is called solid.If every identity is an M-hyperidentity for a subset M of the set of all hypersubstitutions,the variety is called M-solid.There is a Galois connection between monoids of hypersubstitutions and sublattices of the lattice of all varieties of algebras of a given type.Therefore,it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of M-solid varieties.In this paper,we study the order of each hypersubstitution of type (2,2),i.e.,the order of the cyclic subsemigroup generated by that hypersubstitution of the monoid of all hypersubstitutions of type (2,2).The main result is that the order is 1,2,3,4 or infinite.
  • Non-Linear Approximation of Functions with Mixed Smoothness by Sets of Finite Pseudo-Dimension
    Guang Gui CHEN, Gen Sun FANG, Yuan Long RUAN
    Acta Mathematica Sinica. 2007, 23(4): 671-676. https://doi.org/10.1007/s10114-005-0921-x
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper,the non-linear approximation on the class of multivariate functions with bounded mixed derivatives is investigated,and the asymptotic degree of the non-linear width on this class is determined.
  • The Minimax Equality; Sufficient and Necessary Conditions
    Anton STEFANESCU
    Acta Mathematica Sinica. 2007, 23(4): 677-684. https://doi.org/10.1007/s10114-005-0836-6
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The paper produces new versions of the minimax theorem based on original conditions.Moreover,we investigate not only the sufficiency,but also the necessity of such conditions.The proofs are very simple and preclude any topological technique.
  • Parameter Estimates in Random Intercept Mixed Effects Model for Repeated Measures
    Yan SUN, Gen Xiang CHAI
    Acta Mathematica Sinica. 2007, 23(4): 685-696. https://doi.org/10.1007/s10114-005-0793-0
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this article the following random intercept mixed effects model will be considered: yij=vi+xijTβ+εij,i=1,…,m;j=1,2,…,ni,where {vi} are i.i.d.random effects with mean α and finite variance σv2;{εij}are i.i.d.random errors with finite variance σε2.Here we will estimate α,σv2,σε2,β and study their large sample properties,such as strong consistency,strong convergence rates and asymptotic normality.
  • The Mehler Formula for the Generalized Clifford-Hermite Polynomials
    F. BRACKX, N. DE SCHEPPER, K. I. KOU, F. SOMMEN
    Acta Mathematica Sinica. 2007, 23(4): 697-704. https://doi.org/10.1007/s10114-005-0754-7
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The Mehler formula for the Hermite polynomials allows for an integral representation of the one-dimensional Fractional Fourier transform.In this paper,we introduce a multi-dimensional Fractional Fourier transform in the framework of Clifford analysis.By showing that it coincides with the classical tensorial approach we are able to prove Mehler's formula for the generalized Clifford-Hermite polynomials of Clifford analysis.
  • A Construction of Multiresolution Analysis on Interval
    Di Rong CHEN, Dao Hong XIANG
    Acta Mathematica Sinica. 2007, 23(4): 705-710. https://doi.org/10.1007/s10114-005-0772-5
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We present a concrete method of constructing multiresolution analysis on interval.The method generalizes the corresponding results of Cohen,Daubechies and Vial [Appl.Comput.Harmonic Anal.,1(1993),54-81].By the use of the subdivision operator,the expressions of the constructed functions are more compact.Furthermore,the method reveals more clearly some properties of multiresolution analysis with certain approximation order.
  • On the Multiplicity of a C∞-differentiable Function-germ
    Xu XU
    Acta Mathematica Sinica. 2007, 23(4): 711-714. https://doi.org/10.1007/s10114-005-0786-z
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Risler & Trotman in 1997 proved that the multiplicity of an analytic function germ is left-right lipschitz invariant,which provided a partial answer to Zariski conjecture.In this note,based on the recent work of Comte,Milman & Trotman,we generalize the work of them to prove that the multiplicity of a C∞-differentiable function germ is also left-right lipschitz invariant.
  • Oscillation of Second Order Nonlinear Delay Damped Difference Equations
    S. H. SAKER, B. G. ZHANG
    Acta Mathematica Sinica. 2007, 23(4): 715-722. https://doi.org/10.1007/s10114-005-0792-1
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Some new oscillation criteria for nonlinear delay difference equation with damping
    △2xn+pn△xn+F(n,xn-r,△xn-σ)=0,n=0,1,2,…,(*)
    are given.Our results partially solve the open problem posed in[Math.Bohemica,125(2000),421-430].Also,we will establish some new oscillation criteria for special cases of(*),which improve some of the well-known results in the literature.
  • On the Block Independence in G-Inverse and Reflexive Inner Inverse of A Partitioned Matrix
    Yong Hui LIU, Mu Sheng WEI
    Acta Mathematica Sinica. 2007, 23(4): 723-730. https://doi.org/10.1007/s10114-005-0787-y
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    By applying the multiple quotient singular value decomposition QQQQQ-SVD,we study the block independence in g-inverse and reflexive inner inverse of 2×2 partitioned matrices,and prove a conjecture in [YijuWang,SIAM J.Matrix Anal.Appl.,19(2),407-415(1998)].
  • Finite p-Groups Whose Abelian Subgroups Have a Trivial Intersection
    Shi Rong LI, Xiu Yun GUO
    Acta Mathematica Sinica. 2007, 23(4): 731-734. https://doi.org/10.1007/s10114-005-0795-y
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    A subgroup H of a finite group G is called a TI-subgroup if H∩Hx=1 or H for all x∈G.In this paper,a complete classification for finite p-groups,in which all abelian subgroups are TI-subgroups,is given.
  • Global Poincaré Inequalities on the Heisenberg Group and Applications
    Yu Xin DONG, Guo Zhen LU, Li Jing SUN
    Acta Mathematica Sinica. 2007, 23(4): 735-744. https://doi.org/10.1007/s10114-005-0874-0
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let f be in the localized nonisotropic Sobolev space Wlocl,p(Hn) on the n-dimensional Heisenberg group Hn=Cn×R,where 1≤p﹤Q and Q=2n+2 is the homogeneous dimension of Hn.Suppose that the subelliptic gradient is gloablly Lp integrable,i.e.,∫Hn|▽Hnf|pdu is finite.We prove a Poincaré inequality for f on the entire space Hn.Using this inequality we prove that the function f subtracting a certain constant is in the nonisotropic Sobolev space formed by the completion of C0∞(Hn) under the norm of

    We will also prove that the best constants and extremals for such Poincaré inequalities on Hn are the same as those for Sobolev inequalities on Hn.Using the results of Jerison and Lee on the sharp constant and extremals for L2 to L2q/q-2 Sobolev inequality on the Heisenberg group,we thus arrive at the explicit best constant for the aforementioned Poincaré inequality on Hn when P=2.We also derive the lower bound of the best constants for local Poincaré inequalities over metric balls on the Heisenberg group Hn.
  • A Lower Bound for the Differences of Powers of Linear Operators
    J. MALINEN, O. NEVANLINNA, V. TURUNEN, Z. YUAN
    Acta Mathematica Sinica. 2007, 23(4): 745-748. https://doi.org/10.1007/s10114-005-0765-4
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let T be a bounded linear operator in a Banach space,with σ(T)={1}.In 1983,Esterle-Berkani's conjecture was proposed for the decay of differences (I-T)Tn as follows: Either
    lim infn→∞(n +1)‖(I-T)Tn‖≥1/e
    or T=I.We prove this claim and discuss some of its consequences.
  • Positive Steady States of a Prey-predator Model with Diffusion and Non-monotone Conversion Rate
    Rui PENG, Ming Xin WANG, Wen Yan CHEN
    Acta Mathematica Sinica. 2007, 23(4): 749-760. https://doi.org/10.1007/s10114-005-0789-9
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper,we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition.We obtain some results of the existence and non-existence of positive steady states.The stability and uniqueness of positive steady states are also discussed.
  • Convergence of the Vlasov-Poisson-Boltzmann System to the Incompressible Euler Equations
    Ling HSIAO, Fu Cai LI, Shu WANG
    Acta Mathematica Sinica. 2007, 23(4): 761-768. https://doi.org/10.1007/s10114-005-0774-3
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper we establish the convergence of the Vlasov-Poisson-Boltzmann system to the incompressible Euler equations in the so-called quasi-neutral regime.The convergence is rigorously proved for time intervals on which the smooth solution of the Euler equations of the incompressible fluid exists.The proof relies on the relative-entropy method.
Journal Online
Links More
Wechat