中国科学院数学与系统科学研究院期刊网

15 July 2009, Volume 52 Issue 04
    

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  • Yong YAO Jia XU Chengdu Institute of Computer Applications,Chinese Academy of Sciences, Chengdu 610041,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 3-8. https://doi.org/10.12386/A2009sxxb0078
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    The real linear combination of power functions is called a generalized polynomial. In this paper,we prove that the Descartes' law of signs for generalized polynomials holds.That is to say the number of positive roots of a generalized polynomial is not more than the number of the sign changes of its coefficients.Then,using this law,we generalize the method of descent for proving the proposition of symmetric inequalities. Finally,the generalized method of descent is applied to the problems of power mean, which is more efficient and effective.
  • Wen Sheng WANG Department of Statistics,East China Normal University,Shanghai 200062,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 9-18. https://doi.org/10.12386/A2009sxxb0079
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    In this paper,by applying the Skorohod martingale embedding theorem,we prove a strong invariance principle for negatively associated Gaussian sequences under power decay rates.As consequences,we establish the law of the iterated logarithm and Chung-type law of the iterated logarithm for negatively associated Gaussian sequences.
  • Hong Chang HU School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 19-28. https://doi.org/10.12386/A2009sxxb0080
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    Consider the semiparametric regression model y_i=X_i~Tβ+g(t_i)+ε_i(i= 1,...,n),where random errors{ε_i,i=1,...,n}are stationary and long range dependence (LRD) stochastic processes,and Xi is a vector of random design points.Under this case,the wavelet estimators of both parameters and nonparameters are attained, and consistency and convergence rates in probability are investigated under some mild conditions.Our results generalize some corresponding results in the model with independent random errors.
  • De Hua QIU School of Mathematics and Computational Science,Guangdong University of Business Studies, Guangzhou 510320,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 29-38. https://doi.org/10.12386/A2009sxxb0081
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    General convergence rate theorems are obtained for weighted sums of arrays of Banach space valued random elements.These theorems extend and improve the related known works in the literature.
  • Fang Sheng QIAN School of Mathematical Sciences,Suzhou University,Suzhou 215006,P.R.China College of Mathematics and Information Science,Haerbin Teacher's Universty, Haerbin 150025,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 39-42. https://doi.org/10.12386/A2009sxxb0082
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    We obtain some group theoretic conditions for the existence of p-blocks with defect 0 in an extension group of a nilpotent group by an abelian group and in a p-nilpotent group.

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  • Yu Feng LU Jun YANG Department of Applied Mathematics,Dalian University of Technology, Dalian 116024,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 43-54. https://doi.org/10.12386/A2009sxxb0083
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    First,we prove the fact that the invariant Laplacian commutes with the Berezin transform on the weighted Bergman space A_α~2.Secondly,we consider the question for which square integral functions f and g on A_α~2 the densely defined products H_fH_g~* are bounded and give a sufficient condition.Furthermore,We will completely describe when Hankel products on A_α~2 are compact.We also obtain similar results for the mixed Haplitz products H_gT■ and T_fH_g~*,where f and g are square integrable on the unit disk and f is analytic.
  • Ling XIAO Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing 100190,P.R.China Fu Cai LI Department of Mathematics,Nanjing University,Nanjing 210093,P.R.China Shu WANG College of Applied Sciences,Beijing University of Technolog
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 55-68. https://doi.org/10.12386/A2009sxxb0084
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    The combined quasineutral and inviscid limit for the Vlasov-Maxwell-Fokker -Planck system is rigorously derived in this paper.It is shown that the renormalized solution of Vlasov-Maxwell-Fokker-Planck system converges to the strong solution of the so-called electron magnetohydrodynamics equations.The proof of convergence result relies on the weak convergence compactness method and the relative-entropy method.
  • Qiao Fen JIANG Huai Jie ZHONG School of Mathematics and Computer Science,Fujian Normal University, Fuzhou 350007,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 69-78. https://doi.org/10.12386/A2009sxxb0085
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    In this paper,a sufficient condition which makes the product of two semiregular operators be semi-regular is presented.We obtain the stablities of analytical core and quasi-nilpotent part of semi-regular operators under small communicative perturbations. We get that the generalized Kato spectrum and the semi-regular spectrum differ of at most countably many isolated points;By means of this result,we show the stablities of analytical core and quasi-nilpotent part on a component of the generalized Kato resolvent set of a bounded operator.
  • Mao Fa WANG Pei De LIU College of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 79-88. https://doi.org/10.12386/A2009sxxb0086
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    Let φ be a holomorphic mapping from the polydisk D~m into the polydisk Dn,or from the polydisk D~m into the unit ball Bn,and X an infinite dimensional complex Banach space.In this paper,we study the action of the associated composition operator C_φbetween vector-valued Hardy and Bergman spaces defined on D~n or B_n. Some sufficient and necessary conditions for such composition operators to be bounded are obtained.
  • Hao LIU Institute of Mathematics,College of Mathematics and Information Science, Henan University,Kaifeng 475001,P.R.China Jie HONG Department of Mathematics,Shaanxi University of Technology,Hanzhong 723001,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 89-98. https://doi.org/10.12386/A2009sxxb0087
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    This paper deals with homogeneous expansion of complete quasiconvex mappings on bounded convex Reinhardt domain D_p in C~n.Let f(z):D_p→C~n(p_j>2) be a normalized biholomorphic complete quasiconvex mapping and k be the natural number that satisfies k
  • Zhi Ming FENG Department of Mathematics,Leshan Teachers College,Leshan 614000,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 99-108. https://doi.org/10.12386/A2009sxxb0088
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    In this paper,by using representation theoretic method,the author gives series expression of weighted Bergman kernels of bounded domains in given conditions, and computes weighted Bergman kernel function on Cartan-Hartogs domains of the first type by using generalized Selberg integral formula.
  • Guang Qiang LAN School of Science,Beijing University of Chemical Technology,Beijing 100029,P.R.China School of Mathematical Sciences,Beijing Normal University,Beijing 100875,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 109-114. https://doi.org/10.12386/A2009sxxb0089
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    New sufficient conditions on the strong uniqueness and the non-explosion are derived for d dimensional stochastic differential equations on R~d(d≥2)with non-Lipschitzian and time dependent coefficients,which extend and improve Fang,Zhang's and Yamada,Watanabe's results,and the new conditions are sharp in a sense.
  • Cheng Jun GUO School of Applied Mathematics,Guangdong University of Technology, Guangzhou 510006,P.R.China Yuan Tong XU Department of Mathematics,Sun Yat-Sen University,Guangzhou 510275,P.R.China Zhi Ming GUO College of Mathematics and Information Science
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 115-128. https://doi.org/10.12386/A2009sxxb0090
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    By the critical theory and S~1-index theory,we obtain some new results of the existence and multiplicity of periodic solutions for a class of three-order neutral differential equations.
  • Hong Yue QUAN College of Mathematics and Computer Science, Hu'nan Normal University,Changsha 410081,P.R.China College of Mathematics and Computing Science,Changsha University of Science and Technology, Changsha 410076,P.R.China Guo Qiu WANG College of Mat
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 129-140. https://doi.org/10.12386/A2009sxxb0091
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    In order to overcome some of the shortcomings of 2-band wavelet and develop application of wavelet,we provide a general way for constructing symmetric orthogonal multi-band scaling function.The characterizations of scaling function and scaling sequence are considered.A scheme for constructing scaling sequence of shortest length with a given regularity order m is obtained lastly.
  • Chun Mei DING Department of Mathematics,China Jiliang University,Hangzhou 310018,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 141-148. https://doi.org/10.12386/A2009sxxb0092
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    For multivariate Stancu polynomials,which are generalization of the Bernstein polynomials defined on the simplex,we define an appropriate K-functional and use it as a metric to estimate the order of approximation.Particulary,a strong type inverse inequality for the polynomials approximating the continuous functions is established.
  • Dong Sheng KANG Department of Mathematics,South-Central University for Nationalities,Wuhan 430074,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 149-158. https://doi.org/10.12386/A2009sxxb0093
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    Abstract LetΩR~N(N≥3)be a smooth bounded domain such that the different points a_i∈Ω,i=1,2,...,k,k≥2,1
  • Dong Ni TAN School of Mathematical Sciences,Nankai University,Tianjin 300071,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 159-162. https://doi.org/10.12386/A2009sxxb0094
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    We give a simple proof of the main result in[Hou Z.B.,Acta Mathematica Sinica,Chinese Series,2007,50(6):1435-1440]which shows that every isometry between unit sphere of AL~P-space can be extended to a linear isometry on AL~P-space.
  • Zhou Xin LI Yao Tian SHEN Yang Xin YAO Department of Mathematics,South China University of Technology,Guangzhou 510640,P.R.China E-mail:lizhouxin@tom.com;maytshen@scut.edu.cn;mayxyao@scut.edu.cn
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 163-176. https://doi.org/10.12386/A2009sxxb0095
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    We consider the existence and nonexistence of nontrivial solution for quasilinear elliptic equation under natural growth condition.In the previous works on such equation,one of the important assumptions is that the product of the natural growth term and the unknown function is not less than zero.We improve this condition,extend it to the minus part and get the boundary below which such equation has nontrivial solution.We prove the existence of the nontrivial solution via nonsmooth critical point theory.Moreover,we use the Pohozaev identity to prove that the equation does not have any solution when the product of the natural growth term and the unknown function is less than this boundary,which means that this boundary is the best one.
  • Jian Jun JIN Department of Mathematics,Suzhou University,Suzhou 215006,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 177-184. https://doi.org/10.12386/A2009sxxb0096
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    In this paper,we deal with a Hilbert-type series operator and obtain its norm.As applications,we give some generalizations of Hilbert-type inequalities with symmetric homogeneous kernel of-1-order,also consider some particular results.

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  • Fei HE School of Mathematical Sciences,Suzhou University,Suzhou 215006,P.R.China School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.China Rui Xia DONG School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.Chi
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 185-190. https://doi.org/10.12386/A2009sxxb0097
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    In bornological linear spaces,drop theorem is established and Mackey drop property is introduced.And we give the streaming sequence characterizations of the Mackey drop property. We also investigate the relationship between the Mackey drop property and the problem concerning some class of functions attaining the extreme values.
  • Yuan LI College of Mathematics and Information Science,Shaanxi Normal University, Xi'an 710062,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 191-198. https://doi.org/10.12386/A2009sxxb0098
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    We study the necessary and sufficient conditions for the invertibility and Moore-Penrose invertibility of anti-commutator pq+qp when p and q are projections in a C~*-algebra.The relations between the invertibility and Moore-Penrose invertibility of pq-qp and pq+qp are described.
  • Bin ZHAO Shao Hui LIANG College of Mathematics and Information Science,Shaanxi Normal University, Xi'an 710062,P.R.China
    Acta Mathematica Sinica, Chinese Series. 2009, (04): 199-210. https://doi.org/10.12386/A2009sxxb0099
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    In this paper,firstly,the definition of double quantale module is introduced, based on which,we prove that the category of double quantale modules is a pointed and connected category.Also,we study the equalizer,the coequalizer,the product, the collective pullback in the category of double quantale modules.Secondly,we give the structure of the limit of this category,so it is complete.At last,we talk about some properties of the inverse systems of the category of double quantale modules,we construct the inverse limit of the category of double quantale modules.Introducing the definition of a mapping between two inverse systems,we get the limit mapping in the category of double quantale modules.