中国科学院数学与系统科学研究院期刊网

Acta Mathematica Sinica, Chinese Series 2008 Vol.51

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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.   DOI: 10.12386/A2008sxxb0001
Abstract3522)      PDF(pc) (519KB)(840)       Save
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.
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Convergence of Implicit Iteration Process with Random Errors
Li Ping YANG; Gang HU
Acta Mathematica Sinica, Chinese Series    2008, 51 (1): 11-22.   DOI: 10.12386/A2008sxxb0002
Abstract2785)      PDF(pc) (452KB)(795)       Save
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.
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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.   DOI: 10.12386/A2008sxxb0003
Abstract3261)      PDF(pc) (377KB)(818)       Save
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.
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Norm Attainability of Generalized Derivations
Hong Ke DU; Yue Qing WANG; Qi
Acta Mathematica Sinica, Chinese Series    2008, 51 (1): 29-38.   DOI: 10.12386/A2008sxxb0004
Abstract2714)      PDF(pc) (340KB)(901)       Save
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.
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Twisted Self-Dual Hopf Algebra
Xiu Yan JIANG(1); Ling JIA(2)
Acta Mathematica Sinica, Chinese Series    2008, 51 (1): 39-44.   DOI: 10.12386/A2008sxxb0005
Abstract2761)      PDF(pc) (385KB)(827)       Save
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.
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Composition Operators Between Hardy Spaces on the Unit Ball
Luo LUO; Ji Huai SHI
Acta Mathematica Sinica, Chinese Series    2008, 51 (1): 45-50.   DOI: 10.12386/A2008sxxb0006
Abstract3251)      PDF(pc) (346KB)(819)       Save
We study the boundedness and compactness of the composition operators between Hardy spaces on the unit ball for the case q
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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.   DOI: 10.12386/A2008sxxb0007
Abstract3204)      PDF(pc) (421KB)(748)       Save
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.
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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.   DOI: 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).
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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.   DOI: 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.
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A Pair of Quasi-Biorthogonai Frame Wavelets
Zhi Hua ZHANG
Acta Mathematica Sinica, Chinese Series    2008, 51 (1): 81-90.   DOI: 10.12386/A2008sxxb0010
Abstract3019)      PDF(pc) (444KB)(869)       Save
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.
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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.   DOI: 10.12386/A2008sxxb0011
Abstract3670)      PDF(pc) (477KB)(781)       Save
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.
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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.   DOI: 10.12386/A2008sxxb0012
Abstract4326)      PDF(pc) (391KB)(825)       Save
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.
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Erection of Vámos Matroid
Hua MAO
Acta Mathematica Sinica, Chinese Series    2008, 51 (1): 109-114.   DOI: 10.12386/A2008sxxb0013
Abstract2500)      PDF(pc) (389KB)(719)       Save
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?".
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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.   DOI: 10.12386/A2008sxxb0014
Abstract2964)      PDF(pc) (471KB)(864)       Save
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.
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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.   DOI: 10.12386/A2008sxxb0015
Abstract2910)      PDF(pc) (337KB)(764)       Save
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.
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Jordan Semi-Triple Derivable Maps of Matrix Algebras
Wei DU; Jian Hua ZHANG
Acta Mathematica Sinica, Chinese Series    2008, 51 (1): 129-134.   DOI: 10.12386/A2008sxxb0016
Abstract3197)      PDF(pc) (351KB)(854)       Save
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))).
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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.   DOI: 10.12386/A2008sxxb0017
Abstract2962)      PDF(pc) (443KB)(805)       Save
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.
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Normal Familles and Shared Values of Meromorphic Functions
Qing De ZHANG; Chun Yan Qin
Acta Mathematica Sinica, Chinese Series    2008, 51 (1): 145-152.   DOI: 10.12386/A2008sxxb0018
Abstract3931)      PDF(pc) (356KB)(2951)       Save
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.
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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.   DOI: 10.12386/A2008sxxb0019
Abstract3980)      PDF(pc) (409KB)(780)       Save
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.
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On Uniform Concentration of Ground States of Nonlinear Schrdinger Equations
Ping Zheng ZHANG
Acta Mathematica Sinica, Chinese Series    2008, 51 (1): 165-170.   DOI: 10.12386/A2008sxxb0020
Abstract2967)      PDF(pc) (411KB)(738)       Save
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.
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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.   DOI: 10.12386/A2008sxxb0021
Abstract3164)      PDF(pc) (417KB)(703)       Save
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.
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Well-Formed Normal Forms in Intermediate Logics
Heng ZHANG(1); Ming Yi ZHANG(2
Acta Mathematica Sinica, Chinese Series    2008, 51 (1): 181-190.   DOI: 10.12386/A2008sxxb0022
Abstract1874)      PDF(pc) (552KB)(727)       Save
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.
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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.   DOI: 10.12386/A2008sxxb0023
Abstract2325)      PDF(pc) (416KB)(695)       Save
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.
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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.   DOI: 10.12386/A2008sxxb0024
Abstract2693)      PDF(pc) (502KB)(621)       Save
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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On Hua's Five Prime Squares Theorem with One Prime in Arithmetic Progressions
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 209-218.   DOI: 10.12386/A2008sxxb0025
Abstract2514)      PDF(pc) (434KB)(334)       Save
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Jordan Isomorphisms on Nest Subalgebras of Factor von Neumann Algebras
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 219-224.   DOI: 10.12386/A2008sxxb0026
Abstract2569)      PDF(pc) (355KB)(191)       Save
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Characterization of Image Space of Gauss Wavelet Transform
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 225-234.   DOI: 10.12386/A2008sxxb0027
Abstract2653)      PDF(pc) (533KB)(203)       Save
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Several Classes of Upper Bounds for the Laplacian Spectral Radius of a Graph
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 235-240.   DOI: 10.12386/A2008sxxb0028
Abstract4171)      PDF(pc) (288KB)(205)       Save
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Hochschild (Co)-Homology Groups of Zn-Galois Coverings of Exterior Algebras in Two Variables
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 241-252.   DOI: 10.12386/A2008sxxb0029
Abstract2289)      PDF(pc) (511KB)(172)       Save
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Classifications of Ramification System for Symmetric Group
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 253-264.   DOI: 10.12386/A2008sxxb0030
Abstract2732)      PDF(pc) (549KB)(349)       Save
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The Endpoint Estimates for the Commutator of Marcinkiewicz Integral
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 265-274.   DOI: 10.12386/A2008sxxb0031
Abstract4063)      PDF(pc) (397KB)(200)       Save
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The Strong Law of Large Numbers of Negatively Associated Random Variables and Its Applications
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 275-280.   DOI: 10.12386/A2008sxxb0032
Abstract2376)      PDF(pc) (438KB)(197)       Save
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Complete Moment Convergence for Sequence of Identically Distributed ρ-Mixing Random Variables
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 281-290.   DOI: 10.12386/A2008sxxb0033
Abstract2657)      PDF(pc) (407KB)(195)       Save
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Localization and Asymptotic Behavior of Solutions to Degenerate Parabolic Equations with Variable Density and Absorption
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 291-298.   DOI: 10.12386/A2008sxxb0034
Abstract2531)      PDF(pc) (494KB)(184)       Save
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Exotic Options Pricing Formulae with Stochastic Interest Rates
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 299-310.   DOI: 10.12386/A2008sxxb0035
Abstract2431)      PDF(pc) (636KB)(215)       Save
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On the Computational Complexity of the Theory of Complete Binary Trees
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 311-318.   DOI: 10.12386/A2008sxxb0036
Abstract2767)      PDF(pc) (524KB)(171)       Save
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Growth Properties for a Class of Subharmonic Functions in Half Space
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 319-326.   DOI: 10.12386/A2008sxxb0037
Abstract2556)      PDF(pc) (408KB)(177)       Save
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Relations Between Strongly Minimal Sets in Models
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 327-334.   DOI: 10.12386/A2008sxxb0038
Abstract2261)      PDF(pc) (392KB)(175)       Save
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Hypercyclicity for Operator Matrices
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 335-342.   DOI: 10.12386/A2008sxxb0039
Abstract2410)      PDF(pc) (388KB)(215)       Save
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Drop Theorem and Drop Property in Topological Linear Spaces
Acta Mathematica Sinica, Chinese Series    2008, 51 (2): 343-350.   DOI: 10.12386/A2008sxxb0040
Abstract2307)      PDF(pc) (393KB)(303)       Save
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