中国科学院数学与系统科学研究院期刊网

15 January 2008, Volume 51 Issue 1
    

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  • Isometries and Equivalences of Quantum Codes
    Tai Lin LIU(1); Qiao Yan WEN(2
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 1-10. https://doi.org/10.12386/A2008sxxb0001
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    Some results on the isometries and equivalences of quantum codes are pre- sented,one of which generalizes one of the results of Bogart et al.,by these results, we construct an isometry of quantum codes which is not an equivalent mapping but preserves the symplectic inner product,i.e.,a theorem of MacWilliams cannot be gen- eralized to the quantum codes.
  • Convergence of Implicit Iteration Process with Random Errors
    Li Ping YANG; Gang HU
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 11-22. https://doi.org/10.12386/A2008sxxb0002
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    In this paper,strong convergence theorems for approximation of common fixed points of a finite family of asymptotically demicontractive mappings are proved in an arbitrary Banach space using an implicit iteration scheme with random errors. Our results of this paper improve and extend the corresponding results.
  • Extension of Isometries Between Unit Spheres of Normed Space E and l~1(Γ)
    Xi Nian FANG(1); Jian Hua WANG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 23-28. https://doi.org/10.12386/A2008sxxb0003
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    We study the extension of isometries between the unit spheres of normed space E and l~1(F).We obtain that any surjective isometry between the unit spheres of normed space E and l~1(F)can be extended to be a linear isometry on the whole space E,and give an affirmative answer to the corresponding Tingley's problem.
  • Norm Attainability of Generalized Derivations
    Hong Ke DU; Yue Qing WANG; Qi
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 29-38. https://doi.org/10.12386/A2008sxxb0004
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    In this note,the norm attainability of elementary operators and generalized derivations is established.We prove that if an elementary operator and a generalized derivation defined on B(H)are norm-attinable,then the restrictions on the unitary group of B(H)of the elementary operator and the generalized derivation are also norm-attainable,respectively,where B(H)denotes the set of all bounded linear op- erators on a Hilbert space H.
  • Twisted Self-Dual Hopf Algebra
    Xiu Yan JIANG(1); Ling JIA(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 39-44. https://doi.org/10.12386/A2008sxxb0005
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    The main purpose of this paper is to construct a new Hopf algebra denoted by R(?)K#_σH arising from two important structures,crossed product algebra structure and twisted Smahs coprodcuct structure,and discuss under what condition it will be a self-dual Hopf algebra.We recover the results of[7]by trivializing the right coaction.
  • Composition Operators Between Hardy Spaces on the Unit Ball
    Luo LUO; Ji Huai SHI
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 45-50. https://doi.org/10.12386/A2008sxxb0006
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    We study the boundedness and compactness of the composition operators between Hardy spaces on the unit ball for the case q
  • Analytic Solutions for a Second-Order Iterative Functional Differential Equation near Resonance
    Tong Bo Liu(1); Jian Guo SI(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 51-60. https://doi.org/10.12386/A2008sxxb0007
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    In this paper,the second-order differential equation involving iterates of the unknown function x″(z)=G(z,x(z),x~2(z),...,x~m(z))is investigated in the com- plex field C for the existence of analytic solutions.By reducing the equation with the Schr(?)der transformation,x(z)=y(αy~(-1)(z)),to another functional differential equation without iteration of the unknown functionα~2y″(αz)y′(z)-αy′(αz)y″(z)= (y′(z))~3G(y(z),y(αz),...,y(α~mz)),we give the existence of its local invertible analytic solutions.We discuss not only thoseαgiven in Schr(?)der transformation in the hyper- bolic case 0<|α|<1 and resonance,i.e.,at a root of the unity,but also thoseαnear resonance(i.e.,near a root of the unity)under Brjuno condition.
  • Multiplications and Convolutions in Ultradifferentiable Function Spaces ε_* and D_*
    Guang WANG(1); Ai Zhi LI(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 61-68. https://doi.org/10.12386/A2008sxxb0008
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    In this paper,the multiplication and convolution of functions in theω- ultradifferentiable function spaces ε_*(R~N)andω-test function spaces D*(R~N)are dis- cussed,and it is obtained that D(R~N)is the multiplier space of D*(R~N),D(R~N)is the multiplier space of ε_*(R~N)in the sense of convolution,and the Parseval equation holds in the spaces of D*(R~N).
  • A New Proof for a Bandt-Wang Theorem
    Qian Yun TONG(1); Jun LUO(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 69-80. https://doi.org/10.12386/A2008sxxb0009
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    We discuss the boundary structure of lattice self-affine Tiles,and obtain a sufficient condition for the boundary of a plane lattice self-affine Tile to be a simple closed curve.And as a particular application of this condition,we will provide a new proof for a Bandt-Wang theorem.
  • A Pair of Quasi-Biorthogonai Frame Wavelets
    Zhi Hua ZHANG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 81-90. https://doi.org/10.12386/A2008sxxb0010
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    For a pair of dual frame multiresolution analyses,we construct a pair of dual frame wavelets and a pair of quasi-biorthogonal frame wavelets with the help of filter banks.Furthermore,we show necessary and sufficient conditions satisfied by filter bands of a pair of dual frame wavelets and a pair of quasi-biorthogonal frame wavelets.
  • Interpolation and Approximation by Neural Networks in Distance Space
    Fei Long CAO; Yong Quan ZHANG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 91-98. https://doi.org/10.12386/A2008sxxb0011
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    There have been many studies on interpolation by neural networks in Eu- clidean spaces.However,there are plentiful concrete problems which must be measured by using non-Euclidean metrics.This paper deals with the interpolation and approx- imation of neural networks in general non-Euclidean spaces.That is,first construct interpolation networks in general spaces,and then construct approximate interpolation networks,finally,study the approximation of continuous functional with approximating network.
  • Strong Convergence Theorem for Asymptotically Nonexpansive Mappings with Errors in Banach Spaces
    Liang Cai ZHAO; Shi Sheng ZHAN
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 99-108. https://doi.org/10.12386/A2008sxxb0012
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    Let E be a real Banach space with a uniformly Gteaux differentiable norm, D be a nonempty closed convex subset of E and T:D→D be an asymptotically nonexpansive mapping with a squence{k_n}[1,∞,k_n→1.It is shown that under some suitable conditions,the sequence with errors{x_n}defined by(1.3)and(1.5) converges strongly to some fixed points of T.The results presented in this paper also extend and improve some recent results.
  • Erection of Vámos Matroid
    Hua MAO
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 109-114. https://doi.org/10.12386/A2008sxxb0013
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    Using the relation between a matroid and its erections,especially the relation dealing with a special map f,this paper makes a concrete analysis of the concrete conditions for the erection of Vámos matroid.Afterwards,it obtains that except for the trivial case,Vámos matroid has no erections,thereby answering an open problem raised by Welsh"Does the Vámos matroid have an erection?".
  • A Global Curvature Pinching Result of the First Eigenvalue of Laplacian
    Pei He WANG(1); Chun Li SHEN(2
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 115-122. https://doi.org/10.12386/A2008sxxb0014
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    The lower bound of the first eigenvalue of Laplacian on closed manifolds is always a very interesting problem.We study this subject in this paper under the assumption of small global curvature pinching.Finally,we derive a lower bound of the first eigenvalue of Laplacian according to the geometry of the manifolds.
  • Strong Convergence of Modified Ishikawa Iteration for Asymptotically Nonexpansive Mappings
    Li Juan ZHANG; Jun Min CHEN
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 123-128. https://doi.org/10.12386/A2008sxxb0015
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    We introduce the modified Ishikawa iteration for asymptotically nonexpan- sive mappings by the CQ method,and prove the strong convergence theorems of the modified Ishikawa iteration process.These results extend and improve the correspond- ing ones now existing.
  • Jordan Semi-Triple Derivable Maps of Matrix Algebras
    Wei DU; Jian Hua ZHANG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 129-134. https://doi.org/10.12386/A2008sxxb0016
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    Let R be a 2-torsion free commutative ring with unity,and M_n(R)(n≥2) be the algebra of all n×n matrices over R.In this paper we prove that every mapΦ:M_n(R)→M_n(R)satisfyingΦ(ABA)=Φ(A)BA+AΦ(B)A+ABΦ(A)for all A,B∈M_n(R)is of the form:There exist T∈M_n(R)and an additive derivationφof R such thatΦ(A)=AT-TA+A_φfor all A=(a_(ij))∈M_n(R),where A_φ=(φ(a_(ij))).
  • Optimal Approximation Order for q-Stancu Operators Defined on a Simplex
    Feng Jun LI; Zong Ben XU; Kai
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 135-144. https://doi.org/10.12386/A2008sxxb0017
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    In this paper,a kind of multivariate linear operators,q-Stancu operators, are defined on a simplex,which generalize the famous Bernstein operators and Stancu operators.By establishing the upper and lower bound estimations of approximation order,the optimal approximation order(saturation order)and the characteristics of these operators approximating the continuous functions are characterized.Moreover, the saturation class of approximation is confirmed.
  • Normal Familles and Shared Values of Meromorphic Functions
    Qing De ZHANG; Chun Yan Qin
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 145-152. https://doi.org/10.12386/A2008sxxb0018
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    On the basis of fundamental Nevanlinna theory the problem of normality of meromorphic functions that share three finite complex values with their k-th derivatives (k is any positive integer)is discussed and some examples are provided to show the result is sharp.
  • On Global Solutions for the Competitor-Competitor-Mutualist Model with Cross-Diffusion
    Sheng Mao FU(1); Hai Yan GAO(2
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 153-164. https://doi.org/10.12386/A2008sxxb0019
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    Using the energy estimates and bootstrap arguments,the global existence of classical solutions for the competitor-competitor-mutualist model with cross-diffusion is proved when the space dimensions is at most 5.Under certain conditions of the coefficients of the reaction functions,the convergence of the solutions is established for the system by Lyapunov functions.
  • On Uniform Concentration of Ground States of Nonlinear Schrdinger Equations
    Ping Zheng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 165-170. https://doi.org/10.12386/A2008sxxb0020
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    This paper deals with a class of nonlinear Schrdinger equations-ε~2△v+ V(x)v=K(x)v~p,x∈R~N,v∈W~(1,2)(R~N),v(x)>0,with potential V(x)having a positive lower bound or vanishing at infinity,respectively.By the strong maximum principle we show that the ground states concentrate uniformly in smallε>0.
  • The Riemann-Hilbert Problems for Some Classes of Hyperbolic Equations in Commutative Quaternion Space
    Pi Wen YANG(1); Shuo YANG(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 171-180. https://doi.org/10.12386/A2008sxxb0021
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    We study the Riemann-Hilbert boundary value problems for some classes of hyperbolic equations in commutative quaternion algebra space with basis elements 1,i,j,k satisfying the relationship i~2=j~2=-1,ij=ji=k,and obtain the general solutions and the solvable conditions of the problems respectively in different cases.
  • Well-Formed Normal Forms in Intermediate Logics
    Heng ZHANG(1); Ming Yi ZHANG(2
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 181-190. https://doi.org/10.12386/A2008sxxb0022
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    We introduce a concept of well-formed normal forms in intermediate logics, and put forward a general method to investigate them.By applying this method,we show that HT is the weakest intermediate logic with general implicational normal form and that CPL is the only intermediate logic with restricted implicational normal form.
  • A Characterization of First Order Lattice-Valued Logic with the Lattice Being Finite Complemented and Having a Strong Character Formula
    Xue TONG(1); Rong Fang BIE(2);
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 191-196. https://doi.org/10.12386/A2008sxxb0023
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    This paper gives a characterization of first order lattice-valued logic with the lattice being finite,inverse and having a strong character formula,that is,if L is a regular logical system stronger than L_1 and L has compactness property and LS property,then L～L_1.
  • Some Limiting Results for Sequences of Random Vectors with Operator Stable Law
    Ping Yan CHEN(1); Xiang Dong L
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 197-208. https://doi.org/10.12386/A2008sxxb0024
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    For sequences of R~d-valued random vectors with operator stable distribu- tion(without Gaussian component)with an exponent A,an invertible linear operator, this paper obtians the limiting results for the partial sums and weighted sums(inculd- ing some classical summable methods,such as Cesàro's method,delayed sum,Euler's method,Borel's method and geometrical weighted sum,etc.)via integer test.As appli- cations,we obtain Chover-type laws of iterated logarithm for them under the spectral decomposition of A,which is related to the eigenvalues of A.
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