15 January 2006, Volume 49 Issue 1

    

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  Existence of Solutions for Random Second-Order Multivalued Periodic Problems

  Guo Cheng LI, Shi Ji SONG, Che

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 1-6. https://doi.org/10.12386/A2006sxxb0001

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  In this paper, we study the existence of solutions for random second-order multivalued periodic problem, and prove the existence theorems under most common hypotheses for both the convex and nonconvex problems. An application to random periodic feedback control system is also considered.
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  The Characterization of Bounded Generalized Inverse Module Maps and Application

  Lun Chuan ZHANG

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 7-10. https://doi.org/10.12386/A2006sxxb0002

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  In this paper, we introduce the concept of "Bounded generalized inverse module maps" and give an equivalent characterization. As application, we obtain a factor decomposition theorem of certain important bounded module maps, such that the famous Douglas decomposition theorem on Hilbert space becomes a special case.
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  Hausdorff Centered Measure of Uniform 3-part Cantor Set

  Mei Feng DAI(1), Huo Jun RUAN(

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 11-18. https://doi.org/10.12386/A2006sxxb0003

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  The uniform 3-part Cantor set K(λ, 3) is a self-similar fractal set satisfying the open set condition. In this paper, the exact value of the s-dimensional Hausdorff centered measure of K(λ,3) is given by computing the upper spherical density of a probability measure μ at point x, where s = logλ1/3 is the Hausdorff dimension of K(λ,3).
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  A Note on p-ω-Hyponormal Operators

  Chang Sen YANG, Hai Ying LI

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 19-28. https://doi.org/10.12386/A2006sxxb0004

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  For 0
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  k-Space Property of S_ω×X and Related Results

  Shou LIN(1), Chuan LIU(2)

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 29-38. https://doi.org/10.12386/A2006sxxb0005

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  In this paper some functions of product and mapping properties of k-spaces with a point-countable k-network are discussed via special metric spaces Tω and Tω1. The relationships among the three classes of spaces, which are introduced respectively for solving the "the products of k-spaces question" posed by Michael in 1973, are analysed via Tω; on the other hand, some internal characterizations of closed images of locally separable metric spaces are studied via Tω1.
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  On Hardy-Type Integral Inqualities with Some Functions

  Yong HONG

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 39-44. https://doi.org/10.12386/A2006sxxb0006

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  By applying the way of weigh coefficient and Fubini theorem, we give some new Hardy-type integral inequalities with some functions.
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  Finitely Generated Lie Algebras of Operators

  Shan Li SUN,Peng CAO

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 45-50. https://doi.org/10.12386/A2006sxxb0007

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  Let A be an associative algebra, T1,... ,Tn EEEEE A. Write T = (T1,..., Tn), ε(T) denotes Lie algebra generated by T. It is shown that if ε(T) is a nilpotent Lie algebra, it is finite-dimensional. A sufficient and necessary condition for ε(T) to be a finite-dimensional nilpotent Lie algebra is given. If A is considered as a Banach algebra B(X) of all bounded linear operators on a Banach space X, it is proved that if the Lie algebra generated by quasinilpotent T1, T2 is finite-dimensional nilpotent Lie algebra, T1T2,T1 + T2 are also quasinilpotent; if the Lie algebra generated by non-zero compact operator T1 and non-scalar value operator T2 is finite-dimensional, T2 has nontrivial hyperinvariant subspace. This generalizes Lomonosov's theorem on invariant subspace of bounded linear operators.
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  Isometries and 2-Local Isometries on Cartan Bimodule Algebras in Hyperfinite Factors of Type Ⅱ_1

  Pei Sheng JI(1), Cui Ping WEI(

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 51-58. https://doi.org/10.12386/A2006sxxb0008

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  Let M be a hyperfinite factor of type Ⅱ1, D is a Cartan masa of M, T be a Cartan subalgebas of M with diagonal D which generates M. If Φ: T →T be an σ-weakly continuous (Banach) isometry, then Φ can be extended a isometry on M.If a map Φ: T→T satisfies that for every pair a, b ∈ T, there is a oooooooooo-weakly continuous isometry Φa,b on T such that Φa,b(a) = Φ(a), Φ>a,b(b) = Φ(b), then Φ is a linear isometry.
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  Hochschild Cohomological Groups of Dual Extensions

  Yun Ge XU, Xiang Yong ZENG

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 59-68. https://doi.org/10.12386/A2006sxxb0009

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  The formulae on the dimensions of Hochschild cohomological groups of dual extensions of hereditary algebras and a class of l-hereditary algebras are obtained ex-
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  About the Commutant of Cowen-Douglas Operators

  Yong Fei JIN, Zong Yao WANG

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 69-76. https://doi.org/10.12386/A2006sxxb0010

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  Let H be a complex seperable Hilbert space and L(H) denote the collection of bounded linear operators on H. In this paper, we first show that the quotient algebra (?)'(T)/rad(?)'(T) is not always commutative for each T ∈ Bn(Ω). Then after giving a sufficient condition for (?)'(T)/rad.(?)'(T) to be commutative, we show that the set of ,Bbn(Ω) operators A, with (?)'(A)/rad(?)'(A) commutative, is dense in Bn(Ω). Similar results are also established for Bmn(Ω) operators.
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  On the Mean Value of the Smarandache Power Function

  Zhe Feng XU

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 77-80. https://doi.org/10.12386/A2006sxxb0011

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  Given an positive integer n, we define the Smarandache power functions SP(n) as follows: SP(n) = min{m : n|mm, m ∈ N}. In this paper, we study the mean value distribution property of SP(n), and obtain a sharper asymptotic formula for the mean value of the Smarandache power function.
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  On Maximal Subfactors

  Li Guang WANG, Xiu Juan MA

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 81-86. https://doi.org/10.12386/A2006sxxb0012

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  If N is a factor of type Ⅱ1 and G is a finite group with a properly outer action a on N, then N is a maximal subfactor in N (?)α G when G is of prime order. Conversely, suppose that N (?) M is an inclusion of factors of type Ⅱ1 and M (?) M1 is the basic construction for N (?) M. If [M :N]= p is a prime number, N'∩M= CI, N'∩ M1 is abelian and N (?)M is of depth 2, then N is a maximal subfactor of M.
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  Solvability of a Third Order Nonlocal Boundary Value Problem at Resonance

  Zeng Ji DU(1), Xiao Jie LIN(2)

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 87-94. https://doi.org/10.12386/A2006sxxb0013

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  In this paper, we consider a third order nonlocal boundary value problem x'"(t) = f(t,x(t),x'(t),x"(t)), t ∈ (0,1), x(0) = 0, x"(0) = 0, z'(1) =(?)x'(s)dg(s), where f : [0,1] x R3 →R is a continuous function, g : [0,1]→[0,∞) is a nonde-creasing function with g(0) = 0. Under the resonance condition g(1) = 1, an existence result is given by using the coincidence degree theory.
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  Two Generalizations on a Problem of Lehmer

  Hua Ning LIU, Wei Peng ZHANG

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 95-104. https://doi.org/10.12386/A2006sxxb0014

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  Let p>2 be a prime, c be an integer with (c,p)=1. For each integer a with 1≤a≤p-1, there exists one and only one b with 1≤b≤p-1 such that ab ≡ c mod p. Professor Lehmer asked us to find the number of cases in which a and b are of opposite parity. In this paper, we give two generalizations on this problem, and obtain two interesting hybrid mean value formulae.
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  On Hardy-Littlewood Inverse Theorem in Bergman Spaces B_q~p (01)

  Fu Chong XING

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 105-114. https://doi.org/10.12386/A2006sxxb0015

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  In this paper, we study the Hardy-Littlewood inverse theorem about rotation modulus of continuity in Bergman spaces Bqp(0 < p < 1,q > 1). In an ordinary condition, we obtain a result as in Hp (0 < p < 1) spaces.
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  Generalized Power Comparability for Exchange Ideals

  Huan Yin CHEN

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 111-118. https://doi.org/10.12386/A2006sxxb0016

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  In this paper, we introduce a new class of partially power comparability and get a number of necessary and sufficient conditions for an exchange ideal to be a generalized cu-ideal. These results extend the corresponding theorems for exchange generalized cu-rings.
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  On Sums of Five Squares with a Fixed Numbes of Prime Factors

  Xian Meng MENG

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 119-128. https://doi.org/10.12386/A2006sxxb0017

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  Let N≡ 5 (mod 24) be a sufficiently large positive integer. Assume GRH (the generalized Riemann hypothesis), then the equation N = n_1~2+ n_2~2+…+ n_2~5 has solutions, where ni, i = 1,2,..., 5 has a fixed number of prime factors. Puthermore, an asymptotic formula for the number of solutions is obtained.
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  The Ternary Goldbach Problem in Arithmetic Progression (Ⅱ)

  Zhen CUI

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 129-138. https://doi.org/10.12386/A2006sxxb0018

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  In this article, we prove that the ternary Goladbach problem in arithmetic progression can be solved for almost all large positive moduli, where the moduli can be as large as AT1/6-ε.
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  Existence of Positive Fixed Points for a Convex Operators with Applications

  Zeng Qin ZHAO

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 139-144. https://doi.org/10.12386/A2006sxxb0019

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  Some existence results of positive fixed points for a convex operators is given by means of fixed point theorem of cone expansion and compression, then they are used to superlinear Hammerstein integral equations.
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  Empirical Likelihood Inference in Nonlinear Semiparametric EV Models with Validation Data

  Liu Gen XUE

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 145-154. https://doi.org/10.12386/A2006sxxb0020

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  Consider the nonlinear semiparametric model with errors in covariables, we construct three empirical log-likelihood ratio statistics for the unknown parameter with the help of validation data. It is shown that the proposed statistics have the asymptotic chi-square distribution, and hence the confidence regions of the parameter can be constructed accordingly. In addition, the least squares estimator of unknown parameter is constructed, and its asymptotic behaviors are proved. A simulation study is carried out to compare the proposed methods with the least-squares method in terms of the confidence regions and its coverage probabilities.
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  Law of the Iterated Logarithm for ρ-Mixing Sequences

  Guang Hui CAI

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 155-160. https://doi.org/10.12386/A2006sxxb0021

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  Let {Xi,i≥1} be ρ-mixing sequences with identical distributions, and these distributions belong to domain of normal attraction with non-degenerate stable distribution. With probability one, we have limsupn→∞ . And we get several equivaent conditions, which not only generalize the obtained results equivalent to ρ- mixing sequences, but also improve them.
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  The Existence of Positive Solution for the One-Dimensional p-Laplacian

  Ming XIONG, Shao Rong WANG

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 161-168. https://doi.org/10.12386/A2006sxxb0022

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  Some results of existence of positive solutions for the singular boundary value problems have been given, where the function f(t,x) may be singular at t = 0,1.
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  Edge-Negative Association in Random Spanning Forests and Connected Subgraphs on Connected Finite Graphs

  Xian Yuan WU

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 169-176. https://doi.org/10.12386/A2006sxxb0023

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  Let G be a connected finite graph. We consider three types of probability measures on Q, the set of subgraphs of G, which govern a random spanning tree, a random spanning forest, and a random connected subgraph respectively. Basing on the edge-negative association in uniform spanning tree , we construct a family of random spanning forests and random connected subgraphs on G which are edge-negative associated. Finally, we prove the edge-negative association property for uniform spanning forest in a special case of G.
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  Uniform Dimension of N-Parameter d-Dimensional Generalized α-Stable Process

  Zhen Long CHEN(1), San Yang LI

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 177-186. https://doi.org/10.12386/A2006sxxb0024

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  The problem of the uniform dimensions for image sets and graph sets of N-parameter d-dimensional generalized a-stable process, which may not possess the uniform stochastic Holder condition, is investigated. The uniform Hausdorff dimension and the uniform Packing dimension for image sets of N-parameter d-dimensional generalized a-stable process are obtained, and the upper bounds of the uniform Hausdorff dimension and the uniform Packing dimension for graph sets are also given, the results contain the results of multi-parameter stable processes and generalized Brownian sheet.
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  Existence of Positive Solutions for BVP of Nonlinear Functional Difference Equation with p-Laplacian Operator

  Pei Xuan WENG, Zhi Hao GUO

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 187-194. https://doi.org/10.12386/A2006sxxb0025

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  The existence of positive solutions for boundary value problem of a nonlinear functional difference equation with p-Laplacian operator is investigated, where Φp(u) = |u|p-2u, p > 1, (?)(0) = 0, C+ = {(?) :(?) C, (?)(k)≥ 0, k ∈ [-(?),0]}. Sufficent conditions are obtained for the existence of at least one positive solution and two positive solutions.
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  On Sums of Nine Almost Equal Prime Cubes

  Guang Shi Lv

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 195-204. https://doi.org/10.12386/A2006sxxb0026

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  In this paper we enrich Hua's result by proving that each sufficiently large odd integer N can be written as N = p_1~3 +…+ p_9~3,with |Pj - 3((N/9)~(1/2))|≤U = N1/3-2/555+ε, where Pj are primes. This result is obtained by an iterative method and a hybrid estimate for Dirichlet polynomial.
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  Estimates of Maximal Divisor of k-th Power

  De Yu ZHANG(1), Wen GUang ZHAI

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 205-214. https://doi.org/10.12386/A2006sxxb0027

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  In this paper, we study the sum Tk,v(x, y) := ∑x
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  The Category of Modules over a Triangular Matrix Ring of Order n and Its Homological Characterizations

  Mei Hua SHI(1), Fang LI(2)

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 215-224. https://doi.org/10.12386/A2006sxxb0028

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  Firstly, we introduce the concept of triangular matrix ring of order n. Then, it is shown that the category mod Гn of finitely generated modules over a triangular matrix algebra Гn of order n is equivalent to the category Г(?)n. Moreover, we give the Jacobson radical of Гn, indecomposable projective objects in the category Гn(?) and the global dimension of Гn.
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  Asymptotics of the General Fifth Painlevé Equation

  Hui Zeng QIN, Ni Na SHANG

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 225-230. https://doi.org/10.12386/A2006sxxb0029

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  The asymptotic solution and connection formulae of Painleve equation are researched via a more direct method in this paper. The concrete method is: (1) To get the numerical solution first, then fit the oscillating asymptotic solution with the method of least squares; (2) According to the expression form of the oscillating asymptotic solution, the solution which depends on the relation between parameters is determined by means of harmonic balance method, that is, connection formulae. Use this kind of method to the general fifth Painleve equation, and let the parameters α,β,γ and δ satisfy some conditions. We find out the oscillating asymptotic solution and the connection formulae.
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  Universal Graded Lie Superalgebras

  Jie TONG(1), Yong Zheng ZHANG(

  Acta Mathematica Sinica, Chinese Series. 2006, 49(1): 231-240. https://doi.org/10.12386/A2006sxxb0030

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  For a given negatively graded Lie superalgebra K-, the universal graded Lie superalgrbras U of type K- is defined and its existence is proved. By posing additional conditions on K-, other types of universal graded Lie superalgebras are defined and discussed. The concept of universal graded Lie superalgebras leads naturally to the graded Cartan type Lie superalgebras, and it is proved that the graded Cartan type Lie superalgerbras K(m,n,ωA),S(m,n) and H(m,n) can be characterized as certain universal graded Lie superalgebras.