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01 May 1999, Volume 19 Issue 2 Previous Issue    Next Issue

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The bootstrap approximation of paremetric estimator in a semii parametric model under fixed desiqn Chen Minghua Acta mathematica scientia,Series A. 1999, 19 (2):  121-129.  Abstract ( 799 )   RICH HTML PDF (367KB) ( 699 )   Save We consider semiparametric regression model under fixed design yi = xiβ + g(ti) + ei,i=1,2,…,n. For the estimators β^n of β and σ^n2 of σ2, defined by using the least squares and usual nonparametric weighted method, we use the resampling method to establish the bootstrap statistic β^n* for β^n and σ^n*2 for σ^n2, and then prove that under the given original sample the asymptotic distributions of n1/2(β^n* -β^n) and n1/2(σ^n*2 -σ^n*2) are same as the ones of n1/2(β^n-β) and n1/2(σ^n2-σ2), respectively. References | Related Articles | Metrics

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An equivalent definition of box dimension and its application Wang Wanheng Acta mathematica scientia,Series A. 1999, 19 (2):  130-137.  Abstract ( 762 )   RICH HTML PDF (363KB) ( 936 )   Save In this paper we present a new definition of box dimension, which can be more easily testified compared with the existing definitions. On the basis of this result, we give its simple applications and an algorithm to compute box dimensions of fractal sets. References | Related Articles | Metrics

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Existence of muliple positive solution for Δ2 α=λμ+μ(N+4)/(N-4)+μf(x)   Guo Zhenhua, Deng Yinbin Acta mathematica scientia,Series A. 1999, 19 (2):  138-148.  Abstract ( 710 )   RICH HTML PDF (395KB) ( 914 )   Save In this paper, we discuss the existence and nonexistence of solutions for the problem Δ2u =λu + u(N+4)/(N-4)+μf(x), x∈Ω, u| Ω=Δu| Ω=0, N>4, where Ω is a bounded smoothness domain in RN,λ∈R\+1,μ≥0,f(x) is a given nonnegative function. Some interesting results have been obtained. References | Related Articles | Metrics

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A method from design to sampling Changxing Ma Acta mathematica scientia,Series A. 1999, 19 (2):  149-153.  Abstract ( 872 )   RICH HTML PDF (313KB) ( 902 )   Save Zhang and Wang (1996) gave uniform design sampling that developed uniform design to sampling. In this paper we give a general method from design to sampling, that may develop a set of points with fine uniformity to sampling in which all samples have the same fine uniformity. References | Related Articles | Metrics

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Finite w-algbras and transverse poisson structure Liu Zhaonan Acta mathematica scientia,Series A. 1999, 19 (2):  154-158.  Abstract ( 594 )   RICH HTML PDF (313KB) ( 691 )   Save In this paper, one show that finite W-algebras are so-called transverse poisson structure on semisimple Lie algebras. References | Related Articles | Metrics

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The existence and uniqueness of solution foor two-point boundary value problems in banach spaces Song Guangxing Acta mathematica scientia,Series A. 1999, 19 (2):  159-164.  Abstract ( 825 )   RICH HTML PDF (311KB) ( 719 )   Save By using partial order method, the existence and uniqueness theorem of solution for twopoint boundary value problem of second order ordinary differential equations in Banach spaces is obtained. References | Related Articles | Metrics

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Singular integral equations on the bounds for two classes of boundless regions Zhong Shouguo Wu Jianming Acta mathematica scientia,Series A. 1999, 19 (2):  165-171.  Abstract ( 746 )   RICH HTML PDF (349KB) ( 713 )   Save In this paper it is given that direct method of solution for general singular integral equations on the bounds for two classes of boundless regions, where coefficient and kernel density in equations fulfill certain analytic conditions on their boundless regions. References | Related Articles | Metrics

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The isometric approximation problem from infinite dimension L 1space into continuous function space Zhan Dapeng Acta mathematica scientia,Series A. 1999, 19 (2):  172-175.  Abstract ( 699 )   RICH HTML PDF (308KB) ( 822 )   Save This paper proves that the IAP on B(L1(Ω),C(k)) has a negative answer, where dim L1(Ω) is infinite and K is compact. References | Related Articles | Metrics

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Structure coefficient of the banach spaces Hu Changsong Acta mathematica scientia,Series A. 1999, 19 (2):  176-179.  Abstract ( 769 )   RICH HTML PDF (294KB) ( 671 )   Save        In this paper we given the structure coefficient of the Banach spaces. References | Related Articles | Metrics

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A decomposition method for soling a class of bilevel convex programming Wan Zhongping| Ji Changming Acta mathematica scientia,Series A. 1999, 19 (2):  180-186.  Abstract ( 802 )   RICH HTML PDF (328KB) ( 1089 )   Save The equivalence of a class of bilevel convex programming and the corresponding convex programming is researched. The duality and saddle-point of the convex programming is discussed.A decomposition method for solving the bilevel convex programming is grved. References | Related Articles | Metrics

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Hopf bifurcation in the multi-dimension biomathematics model under small perturbation Yuan Xiaofeng Guo Ruihai Wu Yunhua Acta mathematica scientia,Series A. 1999, 19 (2):  187-195.  Abstract ( 769 )   RICH HTML PDF (397KB) ( 780 )   Save The six-dimension biomathematics model is studied. Interactions among the microbes are considered and the model in [1] [2] is improved. The problems on center manifold and Hopf bifurcation a re discussed .The center manifold and the criterion quantity of Hopf bifurcation are computed by using symbolic software based on computer algebra. The numerical examples are given. The idea and method on Automated Theorem proving can be applied to various complex biodynamical systems. References | Related Articles | Metrics

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The alternating birection schemes and numerical analysis for three dimensional transport accumulation (oil and water) Yuan Yirang Acta mathematica scientia,Series A. 1999, 19 (2):  196-205.  Abstract ( 929 )   RICH HTML PDF (414KB) ( 770 )   Save The software for oilgas transport and accumulation is to describe the history of oilgas transport accumulation in basin evolution. It is of great value in rational evaluation of prospecting and defines oil deposit location. The mathematical model can be described as a coupled system of nonlinear partial differential equations with initialboundary value problems. This thesis, from actual conditions such as the effects of gravitation, buoyancy, capillary pressure and the three-dimensional characteristic of largescale scienceengineering computation, puts forward a kind of characteristic finite element alternatingdirection schemes, this is, by dividing it into three continuous one-dimensional problems. By making use tensor product algorithm、negative norm estimate and theory of prior estimates. Optimal order estimates in L2 norm are derived for the error in approximate solutions. References | Related Articles | Metrics

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Anomalous transport properities of plasmas Liu Chao Liu Zhenxing Acta mathematica scientia,Series A. 1999, 19 (2):  206-210.  Abstract ( 713 )   RICH HTML PDF (342KB) ( 1124 )   Save Anomalous transport phenomena are important processes in laboratory , astrophysics and space plasmas ．Using quasilinear theory this article has studied the anomalous transport properties of the collisionless magnetized plasmas and obtained the matrix formula of the Anomalous resistivity 、particle diffusion and heat diffusivity. Applying dimension method, the explicit relationships between Anomalous transport coefficients and background physical variables are made out. It is found that, Anomalous particle diffusion and heat diffusivity have the form of which agree with observations. References | Related Articles | Metrics

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Exponential stability of hopfield type stochastic delay neural netuworks Shen Yi, Liao Xiaoxin Acta mathematica scientia,Series A. 1999, 19 (2):  211-218.  Abstract ( 883 )   RICH HTML PDF (354KB) ( 736 )   Save In this paper the exponential stability in mean square and almost surely exponential stability are investigated for stochastic neural networks with delay of the form dx(t)=[-Ax(t)+Bσ(x(t-τ))]dt + f(t,x(t),x(t-τ))dw(t). For such neural networks, several sufficient conditions for the exponential stability are established by the Lyapunov function method together with martigale inequalities, The obtained results are dependent of the size of delay. Some stability criteria in the literature for the deterministic neural networks with delay x’(t) = -Ax(t)+ Bσ(x(t-τ)) and neural networks x’(t) = -Ax(t) + Bσ(x(t)) are included as special cases. References | Related Articles | Metrics

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On the stability of wavelet frames Sun Wenchang, Zhou Xingwei Acta mathematica scientia,Series A. 1999, 19 (2):  219-223.  Abstract ( 761 )   RICH HTML PDF (310KB) ( 886 )   Save  The theory of frames is very important for wavelet　analysis. For φ∈L2(R) and a>1, b>0, I.Daubechies gave a sufficient condition ensuring{aj/2}φ(aj x-kb):j,k∈Z to be a frame for L2(R).Recently, much effort has spent on the study of the stability of wavelet frames.In this paper, after obtaining a multivariate version of Kadec's 1/4-theorem, we study the stability of wavelet frames when　φ, {aj} and {k} have some perturbation simultaneously.In particular, we study the effect of the perturbation to {aj}. References | Related Articles | Metrics

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Non-self-adjoin and non-compact abstract boundary value problem Wu Kaisu| Yang Mingzhu( Acta mathematica scientia,Series A. 1999, 19 (2):  224-232.  Abstract ( 799 )   RICH HTML PDF (381KB) ( 893 )   Save In this paper, a nonself-adjoin and noncompact abstract boundary value problem is studied in Hilbert space X. We construct the sparting projection of space X with WienerHopf method and prove the solvability of abstract boundary problem. References | Related Articles | Metrics

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Invariant conic surface of fibonacci trace map Liu Qinghui Acta mathematica scientia,Series A. 1999, 19 (2):  233-240.  Abstract ( 741 )   RICH HTML PDF (372KB) ( 776 )   Save Appling the KAM theorem of reversible map in [1],we prove that in certain conditions,for reversible map on R3, there exists invariant conic surface near fixed point. We prove there exists this kind of invariant conic surface for Fibonacci map. References | Related Articles | Metrics