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LOCAL LIKELIHOOD METHOD IN THE PROBLEMS RELATED TO CHANGE POINTS

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Chinese Annals of Mathematics,Series B 1990年第3期11卷 363-375页

作者： KRISHNAIAH P.R. 缪柏其赵林城 Center for Multivariate Analysis University of Pittsburgh Department of Mathematics University of Science and Technology of China

In this paper, the so-called local likelihood method is suggested for solving thechange point problems when the data are distributed as multivariate normal. Thedetection procedures proposed not only provide strongly eonsistent estimates for thenumber and locations of the change points, but also simplify significantly thecomputation.

关键词： LOCAL simplify likelihood multivariate estimates 七无切二 verify underlying arise

On pattern formation in the Gray-Scott model

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Science China Mathematics 2007年第3期50卷 377-386页

作者： Rui PENG Ming-xin WANG Institute of Nonlinear Complex Systems China Three Gorges UniversityYichang 443002China Department of Mathematics Southeast UniversityNanjing 210018China

In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.

关键词： Gray-Scott model pattern formation a priori estimates existence.

DEGREE OF COPOSITIVE POLYNOMIAL APPROXIMATION

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Chinese Annals of Mathematics,Series B 1989年第3期10卷 409-415页

作者：余祥明 Department of Mathematics Nanjing University Nanjing Jiangsu China

Denoteby n（f） the degree of copositive approximation to f（x） by polynomials of degree≤n. For function f（x） ∈ Ck[-1, 1] which alternates in sign finitely many timesin [-1, 1], the author obtains the following J... 详细信息

关键词： finitely integer estimates polynomial signa inequality monotone indue verify 川七

本刊英文版Vol.39(2023),No.5论文摘要(英文)

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数学学报（中文版） 2023年第4期66卷 I0001-I0008页

Monge-Ampère Type Equations on Almost Hermitian Manifolds Jiao Gen ZHANG Abstract In this paper we consider the Monge-Ampere type equations on compact almost Hermitian manifolds.We derive C^(∞) a priori estimates under the existence of an admissible C-subsolution.Finally,we obtain an existence result if there exists an admissible supersolution.

关键词： admissible estimates priori

The Characteristics-mixed Finite Element Method for Enhanced Oil Recovery Simulation and Optimal Order L^2 Error Estimate

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Chinese Science Bulletin 1993年第21期38卷 1761-1766页

作者：袁益让 Department of Mathematics Shandong University Jinan 250100 PRC

This article discusses the enhanced oil recovery numerical simulation of the chemical flooding(such as surfactants, alcohol, polymers) composed of two-dimensional multicomponent, ultiphase and incompressible mixed fluids. After the oil field is waterflooded, there is still a large amount of crude oil left in the oil deposit. By adding certain chemical substances to the fluid injected, its driving capacity can be greatly increased. The mathematical model of two-dimensional enhanced oil recovery simulation can be described

关键词： enhanced oil recovery cross interference characteristics-mixed finite element method L^2 error estimates

CONVERGENCE OF LEGENDRE METHODS FOR NAVIER-STOKES EQUATIONS

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Journal of Computational Mathematics 1994年第4期12卷 298-311页

作者： CHEN, ZT E, WN LUOYANG EDUC INST LUO YANGPEOPLES R CHINA UNIV CALIF LOS ANGELES DEPT MATHLOS ANGELESCA 90024

This paper is concerned with spectral type of methods using Legendre polynomials. Both Galerkin and collocation approximations for the Navier-Stokes equations are considered and their rates of convergence are obtained. As a consequence, it is shown that these methods achieve spectral accuracy if the solutions to the Navier-Stokes equations are smooth.

关键词： Stokes Navier estimates incompressible discretization Philadelphia Heidelberg Berlin Chebyshev Burgers

DISTORTION THEOREM FOR BIHOLOMORPHIC MAPPINGS IN TRANSITIVE DOMAINS(Ⅱ)

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Chinese Annals of Mathematics,Series B 1992年第4期13卷 471-484页

作者：郑学安龚昇 Department of Mathematics Anhui University Hefei Anhui 230039 China. Department of Mathematics University of Science and Technology of China Hefei Anhui 230026 China.

Based on [1], this paper gives concrete estimates for distortion theorem for biholomorphic convex mappings in classical domains of types Ⅰ, Ⅱ, and Ⅲ including transitive domains which are holomorphically homeomorph... 详细信息

关键词： convex distortion estimates normalized invariant 二尹 kernel satisfy verify Domain

THE EXISTENCE OF CLOSE GEODESICS ON A COMPLETE RIEM ANNIAN MANIFOLD

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Chinese Annals of Mathematics,Series B 1989年第1期10卷 85-93页

作者：李江帆 Institute of Mathematics Fudan University Shanghai China

This paper studios the existence of closed geodesics in the homotopy class of a given closed curve. Let M be a complete Riemannian manifold without boundary, f∈C1（S1, M）. Look at S1 as [0, 2π]/{0, 2π}. The following results are proved:A. The initial value problem of heat equation ift=τ（fi）, f0=f always admits a global solution.B. （Existence of closed geodesics）. If there exists a compact set KM such that f（S1）∩K≠φ andE（f）≤（1/π）l（K）2,then there exists a closed geodesic homotopic to f. If then the closed geodesic is minimal.C. Some estimates about injective radius are obtained.Some example is found showing that the inequalities in B are sharp.

关键词： Riemannian manifold estimates sharp boundedness radius showing neighborhood progr inverse

ADMISSIBILITY OF QUADRATIC estimates OF ERROR VARIANCE IN LINEAR MODELS

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中国科学A辑(英文版) 1982年第2期 113-124页

作者：吴启光成平李国英 Institute of Systems Science Academia Sinica

Consider linear models Y=Xβ+ε=X（β1…,βp）′+（ε1…,ε?）′,where n≥p, X is known,ε1,…,εn are independent, Eεi=0,Eεi2=σ2,Eεi3=0, and Eεi4=3σ4,i=1,…,n,β∈Rp, 0<σ2<∞,Denote ?={Y’AY:A≥0}. For the los... 详细信息

Consider linear models Y=Xβ+ε=X（β1…,βp）′+（ε1…,ε?）′,where n≥p, X is known,ε1,…,εn are independent, Eεi=0,Eεi2=σ2,Eεi3=0, and Eεi4=3σ4,i=1,…,n,β∈Rp, 0estimates for σ2 when ε～N（0, σ2In） is derived.

关键词： admissible estimates ERROR lemma 二尹 satis uniformly inequality assumption verified