中国科学院数学与系统科学研究院期刊网

15 September 2009, Volume 52 Issue 05
    

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  • He Guo LIU Department of Mathematics,Hubei University,Wuhan 430062,P.R.China Yu Jie MA KLMM,Institute of Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 3-10. https://doi.org/10.12386/A2009sxxb0103
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    For a p-automorphism φ of an abelian p-group A with finite rank,an inequality on rank A,|φ| and rank C_A(φ) is obtained.The inequality is also generalized to the case for endormorphisms of some abelian groups.
  • Xi Wang CAO Department of Mathematical Sciences,Nanjing University of Aeronautics and Astronautics, Nanjing 210016,P.R.China State Key of Information Security,Beijing 100049,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 11-16. https://doi.org/10.12386/A2009sxxb0104
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    Any function which maps from a finite field to itself can be represented as a polynomial,and a permutation polynomial is in fact a one-to-one map from a finite field to itself.Hence the research on permutation polynomials has been an important subject for at least 140 years,especially from 70s of the last century for the necessary of the study of cryptography.In this paper,two kinds of permutation polynomials are provided,and the reversibility of the these polynomials is proved.Therefore,one can construct a security key exchange protocol from these functions.
  • Hong Ya GAO College of Mathematics and Computer Science,Hebei University,Baoding 071002,P.R.China Hebei Provincial Center of Mathematics,Shijiazhuang 050016,P.R.China Hai Hong LIU College of Mathematics and Computer Science,Hebei University,Baoding 071002
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 17-22. https://doi.org/10.12386/A2009sxxb0105
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    The definition of weakly(K_1,K_2(x))-quasiregular mappings is given,and then its higher integrability result is obtained by using the technique of isoperimetric inequality and weakly reverse Hlder inequality.The result is applied to the generalized solutions of Beltrami system with three characteristic matrices in high dimensional spaces.
  • Qiao Fang LIAN Department of Mathematics,Beijing Jiaotong University,Beijing 100044,P.R.China Yun Zhang LI College of Applied Sciences,Beijing University of Technology,Beijing 100124,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 23-30. https://doi.org/10.12386/A2009sxxb0106
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    Motivated by its application in signal denoising,image compression,etc., wavelet frames have interested many mathematicians.In this paper,we discuss the construction of wavelet frames via a frame multiresolution analysis(FMRA) associated with a dilation matrix of determinant±2.An explicit expression of FMRA frame wavelet is obtained.Some examples are also provided to illustrate the general theory.
  • Dong Xiang CHEN School of Mathematical Science,Beijing Normal University,Beijing 100875,P.R.China Department of Mathematics,Jiangxi Normal University,Nanchang 330022,P.R.China Xiao Li CHEN Department of Mathematical,Jiangxi Normal University,Nanchang 3300
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 31-42. https://doi.org/10.12386/A2009sxxb0107
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    This paper is devoted to studying the CBMO estimates for commutators of some kinds of sublinear operators with rough kernel on homogeneous Morrey-Herz spaces.Some known results are extended.
  • Zhen Gang ZHAO Department of Mathematics,Capital Normal University,Beijing 100037,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 43-50. https://doi.org/10.12386/A2009sxxb0108
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    We give the definition of double harmonic Bergman space and prove that its reproducing kernel has product property,we give a proof that the double harmonic Bergman projection is L~p-bounded.We solve the problem of duality spaces.
  • Yue Xiang HE Yue Shan WANG Department of Basic Science,Jiaozuo University,Jiaozuo 454003,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 51-60. https://doi.org/10.12386/A2009sxxb0109
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    We show that the commutator of Marcinkiewicz integralμΩis bounded from local Hardy spaces h~1(R~n) into spaces h_q~1(R~n) = h~1(R~n) + L~q(R~n)(q>1).Here the kernel is a homogeneous function of degree zero with cancellation property and satisfies the logarithmic type Lipschitz conditions.
  • Xiao Yi WANG Huashang College Guangdong University of Business Studies,Guangzhou 511300,P.R.China Ming Jun LI School of Mathematics and Computational Science,Xiangtan 411105,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 61-66. https://doi.org/10.12386/A2009sxxb0110
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    Model shift maps is a class of special chaotic maps on symbolic space and received much attention.In this paper,we proved that on one-sided symbolic space, model shift map is topologically conjugate with the traditional shift map.Also we found a kind of symbolic dynamical system with topological entropy log1.618,and it's chaos in the sense of Devaney.At last,we found a special map with the whole symbolic space as its minimal set and which is not chaos.
  • Man Zi HUANG College of Mathematics and Computer Science,Hu'nan Normal University, Changsha 410081,P.R.China Yu Ming CHU Department of Mathematics,Huzhou Teachers College,Huzhou 313000,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 67-74. https://doi.org/10.12386/A2009sxxb0111
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    Suppose that D■ R~n is a bounded domain,z_0∈D,c>0 and Fis the family of Apollonian inner geodesicsγ ■ D with end point z_0.In this paper,we prove that D is a John domain if ā_D(x_1,x_2)≤cj_D(x_1,x_2) for anyγ∈ΓF and all x_1,x_2∈γ, where ā_D(x_1,x_2) denotes the Apollonian inner metric between x_1 and x_2 in D,and j_D(x_1,x_2) = log(1 +(|x_1+x_2|)/(min_(j=1,2) d(x_j,D))).
  • Long Guang HUANG School of Science,Jimei University,Xiamen 361021,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 75-80. https://doi.org/10.12386/A2009sxxb0112
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    The relationships between vector equilibrium problem and its dual problem for several kinds of generalized convex and generalized monotone mappings are dealt with.With the fixed point theorem of set-valued mapping,the existence conditions of solutions for vector equilibrium problem are presented.Moreover,a sufficient and necessary condition for vector equilibrium problem with a constraint qualification is shown.
  • Yong Liang HUO College of Mathematical and Statistics,Chongqing University of Arts and Sciences, Yongchuan 402160,P.R.China San Yang LIU Department of Applied Mathematics,Xidian University,Xi'an 710071,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 81-88. https://doi.org/10.12386/A2009sxxb0113
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    The continuity properties of optimal solution sets in parametric programming problems are discussed.Relying on the theory of set-valued analysis,we have obtained corresponding stability results of the optimal solution sets of stochastic programming when the random variable parameter is convergence in distribution,convergence in probability and almost everywhere convergence,respectively.
  • Xie Ping DING College of Mathematics and Software Science,Sichuan Normal University, Chengdu 610066,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 89-100. https://doi.org/10.12386/A2009sxxb0114
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    The notions of C_i(x)-FC-diagonally quasiconvex,Ci(x)-FC-quasiconvex and C_i(x)-FC-quasiconvex-like for set-valued mappings are introduced in FC-spaces without any convexity structure.By applying these notions and a maximal element theorem for a family of set-valued mappings on product FC-space due to author, some new existence theorems of solutions for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces.These results improve and generalize some recent known results in literature to noncompaet FC-spaces.
  • Jun Ru SI Hangzhou Dianzi University,Hangzhou 310018,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 101-110. https://doi.org/10.12386/A2009sxxb0115
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    We discuss the p-Koszul property for finitely generated modules over a noetherian semiperfect algebra and the so-called quasi-p-Koszul module is introduced. Let M be a quasi-p-Koszul module.By giving a second grading on the Koszul dual E(M),the structure of E(M) is discussed.We conclude that E(M) has the second grading concentrating in one degree.More precisely,we show that E~(ev)(M) is generated in degree 0 as a graded E~(ev)(A)-module.Under certain condition,the category of quasi-p-Koszul modules is extension-closed.
  • Lei WANG Zhi Ming JIN College of Science,National University of Defense Technology,Changsha 410073,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 111-126. https://doi.org/10.12386/A2009sxxb0116
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    Game option is an American-type option in essence,it was introduced by Kifer in 2000.In contrast to American option,it gives both writer and holder the right to exercise the option for their claims before expiring date.In this paper,we consider the problem of hedging Game Contingent Claims(GCC) in two cases.For the case that portfolio is unconstrained,we give a single arbitrage-free price P_0.whereas for the constrained case,the price is replaced by an arbitrage-free interval[h_(low),h_(up)]. Finally,for a special type of game option,we provide explicit expressions of the price and optimal portfolio for the writer and buyer.
  • Ling LU College of Mathematics and Information Science,Shaanxi Normal University, Xi'an 710062,P.R.China Section of Military Operation Research,Xi'an Military Academy,Xi'an 710108,P.R.China Huai Xin CAO Zheng Li CHEN Jun Cheng YIN College of Mathematics a
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 127-130. https://doi.org/10.12386/A2009sxxb0117
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    A series of properties of morphisms,monomorphisms and states on an effect algebra are discussed,and characterizations of morphisms and monomorphisms are given.It is proved that ifφ:E→F is additive,then it is morphism if and only ifφ(a') =(φ(a))'(■a∈E);and it is a monomorphism if and only if it is anti-order preserving,i.e.,φ(a)≤φ(b) implies a≤b.Finally,it is shown that if(P,≤) is a partially ordered set with the minimal and maxmual elements 0 and 1,respectively, and ifφis a family of mappings from P into[0,1]satisfying some conditions,then there exists a partial binary operation⊕in P such that(P,0,1,⊕) becomes an effect algebra withφas an order-determining state system.
  • Pin Ling WANG School of Mathematica and Information,Shanghai Lixin University of Commerce, Shanghai 201620,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 131-138. https://doi.org/10.12386/A2009sxxb0118
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    In this paper,it be proved:(1) Let f is a transcendental entire function, and have only zeros of order at least k+2,let E = {λ_n}_(n=1)~∞be an infinite point set in ■ with |λ_(n+1)/λ_n| > q > 1.Then f~(k) assumes all values w∈C,except possibly zero, infinitely often in C \ E.(2) Suppose that the complex sequence(a_n) and the positive sequence(P_n) satisfy for all n, Then if f is a transcendental entire function,and has only zeros of order at least k+2, the equation f~(k) = b must have infinitely many solutions outside the union of the discs B(a_n,p_n),for any b≠0.Hereβ> 1 and B(a_n,p_n) = {z:|z - a_n| < P_n}.
  • Shu Dong LIU School of Mathematical Sciences,Qufu Normal University,Qufu 273165,P.R.China Xiao Chun FANG Department of Mathematics,Tongji University,Shanghai 200092,P.R.China Chang Cuo WEI Department of Mathematics,Ocean University of China,Qingdao 266071
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 139-144. https://doi.org/10.12386/A2009sxxb0119
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    We discuss isomorphism of hereditary C*-subalgebras of Cuntz algebra.We give all the hereditary C*-subalgebras of Cuntz algebra(matrix algebras over Cuntz algebra) up to isomorphism,and hence completely solve the isomorphism problem of hereditary C*-subalgebras of Cuntz algebra.Hereditary C*-subalgebras of certain purely infinite simple C*-algebras are also discussed.
  • Fang Gui WANG You Hua CHEN College of Mathematics and Software Science,Sichuan Normal University, Chengdu 610068,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 145-150. https://doi.org/10.12386/A2009sxxb0120
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    In this paper,we introduce the concepts of an integral element and the integral closure for modules,and discuss the integrally closed properties of submodules. It is proved that R is a Prüfer domain if and only if every torsion-free R-module is integrally closed,if and only if,for any R-module M,submodules of M are integrally closed in M.Moreover,we obtain that prime submodules of integrally closed R-modules are also integrally closed.
  • Zhen Xia GAO College of Mathematics and Information Science,Shaanxi Normal University, Xi'an 710062,P.R.China Shaanxi Shenmu Middle School,Shenmu 719300,P.R.China Huai Xin CAO College of Mathematics and Information Science,Shaanxi Normal University, Xi'an
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 151-158. https://doi.org/10.12386/A2009sxxb0121
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    We first give the definitions of φ-Ψ-approximate algebra homomorphism,η-approximate algebra homomorphism and the stability of approximate algebra homomorphism. Then we study the relations of algebra homomorphism,Jordan mapping and Jordan homomorphism.Finally,the stability of approximate algebra homomorphisms is solved.
  • Rong HU Department of Mathematics,Chengdu University of Information Technology, Chengdu 610000,P.R.China Ya Ping FANG Nan Jing HUANG Department of Mathematics,Sichuan University,Chengdu,Sichuan 610064,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 159-170. https://doi.org/10.12386/A2009sxxb0122
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    This paper deals with set optimization with weighted criteria.Some properties of optimal solutions for set optimization with weighted criteria are investigated. The concepts of(K,W)-regularity and(K,W)-semicompactness are introduced.Some optimality conditions for set optimization with weighted criteria are derived under (K,W)-regularity and(K,W)-semicompactness conditions.Finally,we discuss optimality conditions via directional derivatives.
  • Wei HE Department of Mathematics,Southeast University,Nanjing 210096,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 171-182. https://doi.org/10.12386/A2009sxxb0123
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    This paper deals mainly with composition operators on the Fock type space H_f over C~n.It generalizes the results in the one variable case and the results on the classical Fock space.Using the so-called normalization techniques,we characterize the bounded and compact composition operators on the space H_f and on its special form F_Ψ.We then focus on translation operators on the space F_s(0 < s≤1),and give a complete description of the finite dimensional translation invariant subspaces.We also compute the joint spectrum and joint essential spectrum of a tuple of translation operators on the space F_1.
  • Chuan Ju WU Departmemt of Information and Computation Science,Wuhan University of Science and Technology,Wuhan 430081,P.R.China Lu Qin LIU College of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 183-190. https://doi.org/10.12386/A2009sxxb0124
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    The paper determines the Hausdorff dimensions of the image,graph,inverse image and level sets of multi-self-similar Hunt processes on R_+~d through the multidimensional Lamperti representation.
  • Li Zhen CHEN School of Mathematical Sciences,Xiamen University,Xiamen 361005,P.R.China Jian WANG School of Mathematics and Computer Science,Fujian Normal University, Fuzhou 350007,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 191-196. https://doi.org/10.12386/A2009sxxb0125
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    In this paper,we study the Tingley's problem on the Co-sum of strictly convex normed spaces,and obtain an affirmative answer to the problem.
  • Yong Zhong HU Department of Mathematics Foshan University,Foshan 528000,P.R.China Ping Zhi YUAN Department of Mathematics Zhongshan University,Guangzhou 510275,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 197-202. https://doi.org/10.12386/A2009sxxb0126
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    Let a,b and c be fixed coprime positive integers.In this paper we prove that if a~2 + b~2 = c~3 and b is an odd prime power,then the diophantine equation a~x + b~y = c~z has unique positive integer solution(x,y,z) =(2,2,3).

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  • Xiao Hui YANG Deng Feng LI Institute of Applied Mathematics,He'nan University,Kaifeng 475004,P.R.China College of Mathematics and Information Sciences,He'nan University, Kaifeng 475004,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (05): 203-210. https://doi.org/10.12386/A2009sxxb0127
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    Some new equalities and inequalities for G-frames and their dual frames are estabished in this paper.Moreover,it is shown that these results extend and improve the existing results.