中国科学院数学与系统科学研究院期刊网

15 January 2012, Volume 55 Issue 1
    

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  • Mu ZHAO, Bai Cheng CHEN, Yong ZHOU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 1-16. https://doi.org/10.12386/A2012sxxb0001
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Generalized estimating equations method as a powerful method for estimating parameters, is wildly used in many fields, such as biostatistics, econometrics and medical insurance, and so on. For longitudinal data, We should take account into within-subject correlation structure in order to improve efficiency of a estimator. It is often useful to suppose that there is a parametric assumption within-subject correlation in longitudinal data analysis. But unreasonable assumptions made on within-subject correlation structure can result in inefficient estimation for parameters or even result in misspecification. For the generalized estimating equations with longitudinal data, we propose the extended GMM methods and extended EL methods and construct the large sample properties for our estimators. One of the proposed EL methods which is called block empirical likelihood is robust because of avoiding any assumptions on withinsubject correlation structure. We also provide two simulation examples to illustrate the finite properties for our estimators.  
  • Rui Feng ZHANG, Bian Min KOU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 17-26. https://doi.org/10.12386/A2012sxxb0002
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    We study a nonlinear Schrödinger equation modeling light waves propagating in a photorefractive crystal. We first construct the global weak attractor for this system. And then by exact analysis of the energy equation, we show that the global weak attractor is actually the global strong attractor. Further, we give the upper bound of the fractal and Hausdorff dimensions of the global attractor.  
  • Jian Fei WANG, Tai Shun LIU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 27-40. https://doi.org/10.12386/A2012sxxb0003
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    In this paper, various subfamilies Hk(RI(m,n))of holomorphic mappings defined in the first classical domain RI(m,n)are introduced. When k tends to +∞, this family reduces to the class of locally biholomorphic mappings on RI(m,n). We establish the Bonk distortion theorems for Hk(RI(m,n)). In particular, when k = 1 and k → +∞, the theorems reduce to that of Fitzgerald and Gong, respectively. When m = n = 1, this distortion theorem coincides with Liu and Minda as the unit disk case. As applications of the Bonk distortion theorems, various estimates of Bloch constants for these subfamilies of holomorphic mappings on RI(m,n)are obtained. We not only give all Bloch estimates of holomorphic mappings between 1 < k < +∞ defined in RI(m,n), but also extend our early Bloch constant estimates of the unit ball to the classical domain of the first type RI(m,n).  
  • Yue Di ZENG, Jian Long CHEN
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 41-54. https://doi.org/10.12386/A2012sxxb0004
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    In this paper, let C be a class of right R-modules closed under isomorphisms and direct summands. The relations between left(right)C-dimensions and left exact functors are considered for an(injectively)coresolving class C or a(projectively)resolving class C. In view of those, there are some applications.  
  • Jing Xian SUN, Xi An XU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 55-64. https://doi.org/10.12386/A2012sxxb0005
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    In this paper, firstly some existence results for unbounded connected component of solutions set of some nonlinear operator equations with parameter be obtained by using the global bifurcation theories, and then some existence results for positive solutions of a non-positone operator equation be obtained by using the positive connected property of the operator. The main results can be applied to various of differential boundary value problems to obtain the existence results for positive solutions without the assumption that the nonlinear terms are positone.  
  • Fang Gui WANG
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 65-76. https://doi.org/10.12386/A2012sxxb0006
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    A domain R is called ω-coherent if every finite type ideal is of finitely presented type. In this paper we show that ω-coherent domains are υ-coherent and if(RDTF,M)is a Milnor square, then for the case that F is the quotient field of D, R is ω-coherent if and only if D and T are ω-coherent and TM is a valuation domain; and for the case that F is not the quotient field of D, R is ω-coherent if and only if D is a field, [F:D] < ∞, M is a finite type ideal of R, T is ω-coherent and RM is coherent.  
  • Zheng Zheng CHEN, Wei An LIU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 77-90. https://doi.org/10.12386/A2012sxxb0007
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    We study the existence of solutions for the fully nonlinear elliptic system 

    where Ω⊂Rn, n ≥ 2 is a smooth bounded domain, -Mλ,∧+ is the Pucci operator with parameters 0 < λ ≤ Λ. Firstly, we show that the system has a bounded nonnegative solution if Fi, i=1,2 are uniformly bounded functions. Secondly, we prove that the system has a maximal nonnegative solution and a minimal nonnegative solution by using the method of super-subsolution combining with a fixed point theorem of increasing operator if {f1,f2}is quasi-increasing and the system has a supersolution and a subsolution. If {f1,f2} is either quasi-decreasing or blended quasi-monotony, the existence of a non-negative solution is presented by the Schauder fixed point theorem. For some particular type of Fi, the existence of positive solutions for the system is also obtained. We finally give some examples as application.  
  • Xiao Hong CAO, Qiao Ling XIN
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 91-100. https://doi.org/10.12386/A2012sxxb0008
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    A Hilbert space operator TB(H)may be said to be “consistent in invertibility” provided that for each SB(H), TS and ST are either both or neither invertible. The induced spectrum contributes the stability of generalized property(ω), for a bounded operator T acting on a Hilbert space, under perturbations by finite rank operators, by nilpotent operators and quisi-nilpotent operators commuting with T. The stability of generalized property(ω)of the operators which are the products of finitely normal operators are considered.  
  • Bin XU, Rong YUAN
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 101-110. https://doi.org/10.12386/A2012sxxb0009
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    We discuss the existence of positive almost periodic solutions for some neutral integral equation, by constructing a new fixed point theorem in the cone. Some new results are obtained.  
  • Yi Chao CHEN
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 111-116. https://doi.org/10.12386/A2012sxxb0010
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    Gross, Klein and Rieper(1993)obtained the genus distri- butions of necklaces. Chen, Liu and Wang(2006), and Yang, Liu(2007), calculated total embedding distributions of necklaces, they obtained recurrence relations and ex- plicit formula, respectively. In this paper, we get a simpler explicit formula for the total embedding distributions of necklaces.  
  • Yun Qiang YIN, Jian Ming ZHAN
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 117-130. https://doi.org/10.12386/A2012sxxb0011
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    This paper applies the concept of fuzzy soft sets to polygroup theory. The notions of(∈γ, ∈γ∨)-fuzzy soft polygroups and normal(∈γ, ∈γ∨)-fuzzy soft polygroups over a polygroup are introduced and their basic properties are investigated.  
  • Hai Li YUAN, Yi Jun HU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 131-140. https://doi.org/10.12386/A2012sxxb0012
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    We consider the dual risk model with interest and a constant dividend barrier. First, the integral-differential equation satisfied by the expected discounted dividend payments is given, and the closed form for the expected discounted dividend payments is provided in the case where profits follow an exponential distribution. Second, the integral-differential equation satisfied by the moments of the discounted dividend payments is given, and the closed form for the moments of the discounted dividend payments is also obtained in the case where profits follow an exponential distribution. Finally, we provide the numerical results for the expected discounted dividend payments in the case of exponential distribution.  
  • Yin Ying KONG
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 141-148. https://doi.org/10.12386/A2012sxxb0013
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    By using a Type-function of the infinite order, the growth and the distribution of values of the Laplace-Stieltjes transforms convergent in the right half-plane are investigated. Some results similar to the Dirichlet series are obtained.  
  • Xin An HAO, Li Shan LIU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 149-160. https://doi.org/10.12386/A2012sxxb0014
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    We study the existence of monotone positive solutions for the semipositone right focal boundary value problems 
     
    where λ > 0 is a parameter, n ≥ 3, 1 < k ≤ n-1 is fixed, f may change sign for 0 < t < 1 and we allow f is both semipositone and lower unbounded. Without making any monotone type assumption, the existence results of at least one and two monotone positive solutions are obtained by means of the fixed point theorems in cones.  
  • Ke LIU, Xiang REN
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 161-168. https://doi.org/10.12386/A2012sxxb0015
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    Let {Xi}i=1 be i.i.d random sequence with common distribution F(x)which belongs to one of the domains of attraction of D(Gγ),(γ∈R). The large quantile of F(x)is estimated under some conditions as the smoothing parameter is fixed, and the asymptotic distribution is obtained. And lead to asymptotic confidence interval.  
  • He Yan JIN, Yong Hua MAO
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 169-178. https://doi.org/10.12386/A2012sxxb0016
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    We will apply analytic methods to give the variational formula of the optimal constants in the Lp-Poincaré inequalities on the half line with finite measure and Dirichlet boundary condition. Moreover, by using iterating methods and the variational formula, we can get the explicit estimation of the optimal constants.  
  • Cun Ji YANG, Yu Hua LI
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 179-186. https://doi.org/10.12386/A2012sxxb0017
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    We discuss the boundedness of Fatou components of transcendental entire function with certain gaps. We prove that every component of its Fatou set is bounded.  
  • Jin Ke HAI, Zheng Xing LI
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 187-192. https://doi.org/10.12386/A2012sxxb0018
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    Mazur conjectured that the normalizer property holds for finite groups with abelian Sylow 2-subgroups. Let G be a finite group and let N be a normal subgroup of G such that Z(G/N)has only trivial units. In this paper, a connection is established between the automorphisms of G induced by units in Z(G/N)and Coleman automorphisms of N. Based on this connection, we confirm that if G is a finite group with abelian Sylow 2-subgroups and Z(G/F*(G))has only trivial units then Mazur's conjecture holds for G.