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Tests for nonparametric parts on partially linear single index models

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Science china mathematics 2007年第3期50卷 439-449页

作者： Ri-quan ZHANG department of Statistics, east china normal university, shanghai 200062, china department of mathematics, Shanxi Datong university, Datong 037009, china department of Statistics East China Normal University Shanghai 200062China

Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.

关键词： local linear method partially linear single index models generalized likelihood ratio test Wilks phenomenon χ 2-distribution 62G10 62G20

Periodic Solutions of Schrdinger Flow from S^3 to S^2

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Chinese Annals of mathematics,Series B 2006年第4期27卷 401-410页

作者： Hao YIN department of mathematics East-China Normal University Shanghai 200062 China.

This paper deals with the periodic solutions of Schrǒdinger flow from S^3 to S^2. It is shown that the periodic solution is related to the variation of some functional and there exist S^1-invariant critical points to... 详细信息

关键词： Schrǒdinger flow Periodic solution Variational method

Method of sequential mesh on Koopman-Darmois distributions

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Science china mathematics 2010年第4期53卷 917-926页

作者： LI Yan & PU XiaoLong School of Finance and Statistics,east china normal university,shanghai 200241,china 1. School of Finance and Statistics East China Normal University Shanghai 200241 China

For costly and/or destructive tests,the sequential method with a proper maximum sample size is *** on Koopman-Darmois distributions,this paper proposes the method of sequential mesh,which has an acceptable maximum sample *** comparison with the popular truncated sequential probability ratio test,our method has the advantage of a smaller maximum sample size and is especially applicable for costly and/or destructive tests.

关键词： method of sequential mesh sequential probability ratio test (SPRT) Koopman-Darmois distributions maximum sample size

The　θ－Methods　in　Numerical　Solution　of　Systems　of　Differential　Equations　with　Two　Delay　Terms

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Journal of Systems Engineering and Electronics 1994年第3期5卷 32-40页

作者： Tian Hongjiong & Kuang Jiaoxun (department of mathematics, shanghai normal university, shanghai 200234, china) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤*** aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.

关键词： Delay differential equations Numerical solution θ-methods Asymptotic stability Schur polynomial.

HOMOCLINIC BIFURCATION WITH CODIMENSION 3

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Chinese Annals of mathematics,Series B 1994年第2期15卷 205-216页

作者： ZHU DEMING(department of Matehematics,east china normal university, shanghai 200062, china) E china normal UNIV DEPT MATHSHANGHAI 200062PEOPLES R CHINA

First it is proved that both the integral of the divergence and the Melnikov function are invariants of the C2 transformation. Then, the problem of the planar homoclinic bifurcation with codimension 3 is considered. It is proved that, in a small neighborhood of the origin in the parameter space of a Cr (r≥5) system, there exist exactly two Cr-1 semi- stable- limit- cycle branching surfaces, and their common boundary is a unique Cr-1 three-multiple- limit-cycle branching curve. The bifurcation pictures and the asymptotic expansions of the bifurcation functions are given. The stability criterion for the homoclinic loop is also obtained when the integral of the divergence is zero. The proof of the auxiliary theorems will be presented in [16].

关键词： Homoclinic bifurcation Codimension Semi-stable-limit-cycle branch Three- multiple-limit- cycle branch.

FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS

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Acta Mathematica Scientia 2007年第3期27卷 635-644页

作者：余宏旺汪志鸣 department of mathematics East China Normal University

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.

关键词： Multirate sampled-data control systems quantization Schur stable uniformly ultimately bounded

Note on families of semistable curves over P^1 with 4 singular fibers whose Jacobian are non-compact

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Science china mathematics 2010年第7期53卷 1710-1713页

作者： YU Fei 1, 2 1 Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, china 2 department of mathematics, east china normal university, shanghai 200062, china Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China department of mathematics East China Normal University Shanghai China

Let f : S → P 1 be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4 of them have non-compact Jacobian, then g = 2.

关键词： singular fiber adjoint linear system non-compact Jacobian

JACOBI SPECTRAL APPROXIMATIONS TO DIFFERENTIALEQUATIONS ON THE HALF LINE

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Journal of Computational mathematics 2000年第1期18卷 95-112页

作者： Ben-yu Guo(department of mathematics, shanghai normal university, shanghai 200234, china)(COM2MAC, Pohang university of Science and Technology, Pohang, Korea) 上海师范大学上海 200234

Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Alg... 详细信息

关键词： Jacobi spectral approximations differential equations on the half line stability and convergence

ON THE SPLITTINGS FOR RECTANGULAR SYSTEMS

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Journal of Computational mathematics 1995年第4期13卷 337-342页

作者： H.J. Tian(department of mathematics, shanghai normal university, shanghai, china) shanghai normal UNIV DEPT MATHSHANGHAIPEOPLES R CHINA

Recently, M. Hanke and M. Neumann([4]) have derived a necessary and sufficient condition on a splitting of A = U-V, which leads to a fixed point system, such that the iterative sequence converges to the least squares solution of minimum a-norm of the system Ax = b. In this paper, we give a necessary and sufficient condition on the splitting such that the iterative sequence converges to the weighted Moore-Penrose solution of the system Ax = b for every to is an element of C-n and every b is an element of C-m. We also provide a necessary and sufficient condition such that the iterative sequence is convergent for every to x(0) is an element of C-n.

关键词： AR Math ON THE SPLITTINGS FOR RECTANGULAR SYSTEMS