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15 October 2004, Volume 20 Issue 5
    

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  • A Property of g-Expectation
    Long JIANG
    Acta Mathematica Sinica. 2004, 20(5): 769-778. https://doi.org/10.1007/s10114-004-0377-4
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    This paper proves that,under the hypothesis g(t,0,0)≡0 and some natural assumptions,the generator g of a backward stochastic differential equation can be uniquely determined by the corresponding g-expectations with all terminal conditions.The main result of this paper also confirms and extends Peng Shige's conjecture.
  • Littlewood-Paley and Pseudo-Differential Operators on Herz-type Spaces over Vilenkin Groups
    Yue Ping ZHU
    Acta Mathematica Sinica. 2004, 20(5): 779-784. https://doi.org/10.1007/s10114-004-0384-5
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    In this paper,we mainly investigate the boundedness of Littlewood-Paley functions and pseudo-differential operators on weighted Herz-type Hardy spaces over locally compact Vilenkin groups.
  • L2(Rn) Boundedness for the Commutators of Homogeneous Singular Integral Operators
    Guo En HU, Bo Lin MA
    Acta Mathematica Sinica. 2004, 20(5): 785-792. https://doi.org/10.1007/s10114-004-0335-1
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    The commutators of singular integral operators with homogeneous kernel are studied,where Ω is homogeneous of degree zero,and has mean value zero on the unit sphere.It is proved that Ω∈L(logL)k+1(Sn-1) is a sufficient condition such that the k-th order commutator is bounded on L2(Rn).
  • On the Self-adjointness of the Product Operators of Two mth-Order Differential Operators on [0, +∞)
    Jian Ye AN, Jiong SUN
    Acta Mathematica Sinica. 2004, 20(5): 793-802. https://doi.org/10.1007/s10114-004-0386-3
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    In the present paper,the self-adjointness of the product of two mth-order differential operators on [0,+∞) is studied.By means of the construction theory of self-adjoint operators and matrix computation,we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint,which extends the results in the second order case.
  • Upper Bounds for the Laplacian Graph Eigenvalues
    Jiong Sheng LI, Yong Liang PAN
    Acta Mathematica Sinica. 2004, 20(5): 803-806. https://doi.org/10.1007/s10114-004-0332-4
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    We first apply non-negative matrix theory to the matrix K=D+A,where D and A are the degree-diagonal and adjacency matrices of a graph G,respectively,to establish a relation on the largest Laplacian eigenvalue λ1(G) of G and the spectral radius ρ(K) of K.And then by using this relation we present two upper bounds for λ1(G) and determine the extrernal graphs which achieve the upper bounds.
  • Linear Maps Preserving Idempotence on Nest Algebras
    Jian Lian CUI, Jin Chuan HOU
    Acta Mathematica Sinica. 2004, 20(5): 807-820. https://doi.org/10.1007/s10114-004-0314-6
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    In this paper,we discuss the rank-1-preserving linear maps on nest algebras of Hilbert-space operators.We obtain several characterizations of such linear maps and apply them to show that a weakly continuous linear bijection on an atomic nest algebra is idempotent preserving if and only if it is a Jordan homomorphism,and in turn,if and only if it is an automorphism or an anti-automorphism.
  • Stability of C-regularized Semigroups
    Miao LI, Quan ZHENG
    Acta Mathematica Sinica. 2004, 20(5): 821-828. https://doi.org/10.1007/s10114-004-0349-8
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    Let Τ=(T(t))t≥0 to be a bounded C-regularized semigroup generated by A on a Banach space X and R(C) be dense in X.We show that if there is a dense subspace Y of X such that for every x∈Y,σu(A,Cx),the set of all points λ∈iR to which (λ-A)-1 Cx can not be extended holomorphically,is at most countable and σr(A)∩iR=ø,then Τ is stable.A stability result for the case of R(C) being non-dense is also given.Our results generalize the work on the stability of strongly continuous semigroups.
  • Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
    Hai Yun ZHOU
    Acta Mathematica Sinica. 2004, 20(5): 829-836. https://doi.org/10.1007/s10114-004-0347-x
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    In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces.The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.
  • On Pairs of Linear Equations in Three Prime Variables
    Hong Ze LI, Richard J. MCINTOSH
    Acta Mathematica Sinica. 2004, 20(5): 837-850. https://doi.org/10.1007/s10114-003-0302-2
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    In this paper,we consider the simultaneous representation of pairs of integers as linear combinations in three prime variables and obtain a related numerical bound.
  • An Application of Exponential Sum Estimates
    Yuan YI, Wen Peng ZHANG
    Acta Mathematica Sinica. 2004, 20(5): 851-858. https://doi.org/10.1007/s10114-004-0351-1
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    Let p be an odd prime and let δ be a fixed real number with 0<δ<2.For an integer a with 0<a<p,denote by ā the unique integer between 0 and p satisfying aā≡1 (mod p).Further,let {x} denote the fractional part of x.We derive an asymptotic formula for the number of pairs of integers (a,b) with .
  • A Decomposition Theorem for the Solutions to the Interface Problems of Quasi-Linear Elliptic Equations
    Lung An YING
    Acta Mathematica Sinica. 2004, 20(5): 859-868. https://doi.org/10.1007/s10114-004-0374-7
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    Interface problems for second order quasi-linear elliptic partial differential equations in a two-dimensional space are studied.We prove that each weak solution can be decomposed into two parts near singular points,one of which is a finite sum of functions of the form crα logm rφ(θ),where the coefficients c depend on the H1-norm of the solution,the C0,δ-norm of the solution,and the equation only;and the other one of which is a regular one,the norm of which is also estimated.
  • Almost Sure Central Limit Theorems for Heavily Trimmed Sums
    Fang WANG, Shi Hong CHENG
    Acta Mathematica Sinica. 2004, 20(5): 869-878. https://doi.org/10.1007/s10114-004-0342-2
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    We obtain an almost sure central limit theorem (ASCLT) for heavily trimmed sums.We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d.random variables with .
  • Wavelets and Wavelet Packets Related to a Class of Dilation Matrices
    Qiao Fang LIAN
    Acta Mathematica Sinica. 2004, 20(5): 879-892. https://doi.org/10.1007/s10114-004-0385-4
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    The construction of wavelets generated from an orthogonal multiresolution analysis can be reduced to the unitary extension of a matrix,which is not easy in most cases.Jia and Micchelli gave a solution to the problem in the case where the dilation matrix is 2I and the dimension does not exceed 3.In this paper,by the method of unitary extension of a matrix,we obtain the construction of wavelets and wavelet packets related to a class of dilation matrices.
  • Torsion Completeness of Sylow p-Groups in Semisimple Group Rings
    P. V. DANCHEV
    Acta Mathematica Sinica. 2004, 20(5): 893-898. https://doi.org/10.1007/s10114-003-0304-0
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    Let G be an abelian p-group and K be a field of the first kind with respect to p of charK≠p and of sp(K) =NorN∪ {0}.Then it is shown that the normed Sylow p-subgroup S(KG) is torsion complete if and only if G is bounded (Theorem 1).An analogous fact is proved for the case when K is of the second kind (Theorem 2).These completely settle a conjecture posed by us in Compt.Rend.Acad.Bulg.Sci.(1993) and are also a supplement to our result in the modular case published in Acta Math.Hungar.(1997).
  • Smooth Solution to the 1-Dimensional Spin Equations of Antiferromagnets
    Shi Jin DING, Bo Ling GUO
    Acta Mathematica Sinica. 2004, 20(5): 899-912. https://doi.org/10.1007/s10114-004-0346-y
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    In this paper,the global existence and uniqueness of a smooth solution to the periodic initial-value problem of the spin equations of antiferromagnets in 1 dimension are proved.
  • Frame Self-orthogonal Mendelsohn Triple Systems
    Yun Qing XU, Han Tao ZHANG
    Acta Mathematica Sinica. 2004, 20(5): 913-924. https://doi.org/10.1007/s10114-004-0370-y
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    A Mendelsohn triple system of order ν,MTS(ν) for short,is a pair (X,B) where X is a ν-set (of points) and B is a collection of cyclic triples on X such that every ordered pair of distinct points from X appears in exactly one cyclic triple of B.The cyclic triple (a,b,c) contains the ordered pairs (a,b),(b,c) and (c,a).An MTS(ν) corresponds to an idempotent semisymmetric Latin square (quasigroup) of order ν.An MTS(ν) is called frame self-orthogonal,FSOMTS for short,if its associated semisymmetric Latin square is frame self-orthogonal.It is known that an FSOMTS(1n) exists for all n≡1 (mod 3) except n=10 and for all n≥15,n≡0 (mod 3) with possible exception that n=18.In this paper,it is shown that (i) an FSOMTS(2n) exists if and only if n≡0,1 (mod 3) and n>5 with possible exceptions n∈{9,27,33,39};(ii) an FSOMTS(3n) exists if and only if n≥4,with possible exceptions that n∈{6,14,18,19}.
  • An Arc as the Inverse Limit of a Single Bonding Map of Type N on [0,1]
    Hong MO, Song Quan SHI, Fang Ping ZENG, Jie Hua MAI
    Acta Mathematica Sinica. 2004, 20(5): 925-932. https://doi.org/10.1007/s10114-004-0363-x
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    Let I=[0,1],c1,c2∈(0,1) with c1<c2 and f:I→I be a continuous map satisfying: are both strictly increasing and is strictly decreasing.Let A={x∈[0,c1]∣f(x)=x},a=maxA,a1 =max(A\{a}),and B={x∈[c2,1]∣f(x)=x},b=minB,b1 =min(B\{b}).Then the inverse limit (I,f) is an arc if and only if one of the following three conditions holds:

    (1) If c1<f (c1)≤c2 (resp.c1≤f (c2)<c2),then f has a single fixed point,a period two orbit,but no points of period greater than two or f has more than one fixed point but no points of other periods,furthermore,if A≠φ and B≠φ,then f (c2)>a (resp.f (c1)<b).

    (2) If f (c1)≤c1 (resp.f (c2)≥c2),then f has more than one fixed point,furthermore,if B≠φ and A\{a}≠φ,f (c2)≥a or if a1<f (c2)<a,f2 (c2)>f (c2),(resp.f has more than one fixed point,furthermore,if A≠φ and B\{b}≠φ,f (c1)≤b or if b<f (c2)<b1,f2 (c1)<f (c1)).

    (3) If f (c1)>c2 and f (c2)<c1,then f has a single fixed point,a single period two orbit lying in I\(u,v) but no points of period greater than two,where u,v∈[c1,c2] such that f (u)=c2 and f (v)=c1.

  • Non-linear Semigroup of a Class of Abstract Semilinear Functional Differential Equations with a Non-Dense Domain
    Mostafa ADIMY, Mostafa LAKLACH, Khalil EZZINBI
    Acta Mathematica Sinica. 2004, 20(5): 933-942. https://doi.org/10.1007/s10114-004-0341-3
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    In this work,we are concerned with a general class of abstract semilinear autonomous functional differential equations with a non-dense domain on a Banach space.Our objective is to study,using the Crandall-Liggett approach,the solutions as a semigroup of non-linear operators.
  • Order Environments of Topological Spaces
    J. H. LIANG, K. KEIMEL
    Acta Mathematica Sinica. 2004, 20(5): 943-948. https://doi.org/10.1007/s10114-004-0365-8
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    In this paper it is proved that a space may be realized as the set of the maximal elements in a continuous poset if and only if it is Tychonoff.
  • Summing Boolean Algebras
    Antonio AIZPURU, Antonio GUTIÉRREZ-DÁVILA
    Acta Mathematica Sinica. 2004, 20(5): 949-960. https://doi.org/10.1007/s10114-003-0306-y
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    In this paper we will study some families and subalgebras F of P (N) that let us characterize the unconditional convergence of series through the weak convergence of subseries F.As a consequence,we obtain a new version of the Orlicz-Pettis theorem,for Banach spaces.We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.
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