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On solitary *** 2 A unified perturbation theory for higher-order waves

Acta Mechanica Sinica 2005年第6期21卷 515-530页

作者： Theodore Yaotsu Wu Xinlong Wang Wendong Qu California Institute of Technology Pasadena CA 91125 U.S.A. Fellow Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China State Key Laboratory of Modern Acoustics and Institute of Acoustics Nanjing University Nanjing 210093 China California Institute of Technology Pasadena CA 91125 U.S.A PIMCO Newport Beach CA 92660 U.S.A.

A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter family of solutions in exact form, with all the coefficients determined in rational numbers. Comparative studies are pursued to investigate the effects due to changes of base parameters on （i） the accuracy of the theoretically predicted wave properties and （ii） the rate of convergence of perturbation expansion. Two important results are found by comparisons between the theoretical predictions based on a set of parameters separately adopted for expansion in turn. First, the accuracy and the convergence of the perturbation expansions, appraised versus the exact solution provided by an earlier paper [1] as the standard reference, are found to depend, quite sensitively, on changes in base parameter. The resulting variations in the solution are physically displayed in various wave properties with differences found dependent on which property （e.g. the wave amplitude, speed, its profile, excess mass, momentum, and energy）, on what range in value of the base, and on the rank of the order n in the expansion being addressed. Secondly, regarding convergence, the present perturbation series is found definitely asymptotic in nature, with the relative error δ （n）（the relative mean-square difference between successive orders n of wave elevations） reaching a minimum, δm at a specific order, n = n both depending on the base adopted, e.g. nm,α= 11-12 based on parameter α （wave amplitude）, nm,δ = 15 on δ （amplitude-speed square ratio）, and nm.ε= 17 on ε （ wave number squared）. The asymptotic range is brought to completion by the highest order of n = 18 reached in this work.

关键词： Solitary waves on water Unified perturbation theory Base functions Base parameters asymptotic representation

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UNSTEADY INTERFACIAL WAVES DUE TO SINGULARITIES IN TWO SEMI-INFINITE INVISCID FLUIDS

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Journal of Hydrodynamics 2005年第6期17卷 730-736页

作者： LU Dong-qiang WEI Gang YOU Yun-xiang The State Key Laboratory of Ocean Engineering Shanghai Jiaotong University Shanghai 200030 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China School of Naval Architecture Ocean and Civil Engineering Shanghai Jiaotong University Shanghai200030 China

The generation of unsteady interfacial gravity waves by a singularity immersed in two semi-infinite fluids was analytically investigated in detail by the methods of integral transform and of stationary-phase analysis. The fluids were assumed to be initially stationary, immiscible, inviscid and incompressible. The disturbed flows, generated by an impulsive and oscillatory source/dipole immersed above or be neath the interface, were governed by the *** equations. The kinematic and dynamic boundary conditions on the interface were linearized for the small-amplitude waves. By means of the stationary phase analysis on the exact integral form solutions, the asymptotic representations for the interracial waves were derived for large time with a fixed distance to time ratio. The relation between a submerged singularity and a sur face pressure point was discussed. It is found that the local wavelength and the local wave period of the interracial waves are elongated in comparison with those of free-surface waves for a single fluid.

关键词： interfacial waves singularity two-fluid system asymptotic representation

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asymptotic Properties of Wavelet Estimators in Partially Linear Errors-in-variables Models with Long-memory Errors

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Acta Mathematicae Applicatae Sinica 2018年第1期34卷 77-96页

作者： Hong-chang HU Heng-jian CUI Kai-can LI School of Mathematics and Statistics Hubei Normal University Huangshi 435002 China School of Mathematical science Capital Normal University Beijing 100048 China

While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.

关键词： partially linear errors-in-variables model nonlinear long dependent time series wavelet estimation asymptotic representation asymptotic distribution weak convergence rates

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SOME LARGE SAMPLE PROPERTIES OF AN ESTIMATOR OF THE HAZARD FUNCTION FROM RANDOMLY CENSORED DATA

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Acta Mathematica Scientia 1997年第2期17卷 230-240页

作者：王启华 Institute of Applied Mathematics Chinese Academy of Sciences Beijing 100080 China

In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptotic representation of lambda(n)(t) is also given, and the asymptotic representation is used to prove asymptotic normality of the hazard estimator.

关键词： weak convergence strong consistency asymptotic representation asymptotic normality

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FREE-SURFACE WAVES AND FAR WAKES GENERATED BY A FLOATING BODY IN A VISCOUS FLUID

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Journal of Hydrodynamics 2003年第4期15卷 10-16页

作者： Lu Dong-qiang Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China Dept. of Mech. Eng. Univ. of Hong Kong Hong Kong Hong Kong Inst. of Appl. Math. and Mech. Shanghai Univ. Shanghai 200072 China

The free-surface waves and the flow field due to a body moving on the surfaceof an incompressible viscous fluid of infinite depth were studied analytically. The floating bodywas modeled as a normal point pressure on the free surface. Based on the Oseen approximation forgoverning equations and the linearity assumption for boundary conditions, the exact solutions inintegral form for the free-surface elevation, the velocities and the pressure were given. Byemploying Lighthill's two-stage scheme, the asymptotic representations in far field for largeReynolds numbers were derived explicitly. The effect of viscosity on the wave profiles was expressedby an exponential decay factor, which removes the singular behavior predicted by the potentialtheory.

关键词： free-surface waves velocity distribution floating body viscosity asymptotic representation light-hill's two-stage scheme

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Fixed Design Nonparametric Regression with Truncated and Censored Data

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Acta Mathematicae Applicatae Sinica 2003年第2期19卷 229-238页

作者： Liu-quan SunAcademy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Abstract In this paper we consider a fixed design model in which the observations are subject to left truncation and right censoring. A generalized product-limit estimator for the conditional distribution at a given covariate value is proposed, and an almost sure asymptotic representation of this estimator is established. We also obtain the rate of uniform consistency, weak convergence and a modulus of continuity for this estimator. Applications include trimmed mean and quantile function *** applications demonstrate the usefulness of the new matrix products.

关键词： Keywords Nonparametric regression fixed design asymptotic representation truncated and censored data modulus of continuity

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Statistical Inference for Simple Tree Order in the Means of Stochastic Order on Stratified Contingency Tables

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Wuhan University Journal of Natural Sciences 2010年第2期15卷 93-98页

作者： YAN Guoyi1,2, CHEN Jingjing3 1.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China 2. School of Sciences, Wuhan Institute of Technology, Wuhan 430074, Hubei, China 3. School of Sciences, Wuhan University of Science and Technology, Wuhan 430081, Hubei, China School of Mathematics and Statistics Wuhan University Wuhan China School of Sciences Wuhan Institute of Technology Wuhan China School of Sciences Wuhan University of Science and Technology Wuhan China

In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula- tions are in simple tree order. We provide an asymptotic represen- tation of the order-restricted maximum likelihood estimate of the unknown parameters. The resulting estimators are proven to be ~n-consistent and asymptotically normal under appropriate conditions. A chi-squared test method is used for this hypothesis test problem. A real data set is applied to illustrate our theoretical result.

关键词： simple tree order chi-squared test asymptotic representation asymptotic distribution

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Estimation of Distribution Function Based on Presmoothed Relative-Risk Function

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Applied Mathematics 2022年第2期13卷 191-204页

作者： Abdurakhim Akhmedovich Abdushukurov Sukhrob Bakhodirovich Bozorov Dilshod Ravilovich Mansurov Moscow State University Tashkent Branch Tashkent Uzbekistan Guliston State University Gulistan Uzbekistan Navoi State Pedagogical Institute Navoi Uzbekistan

In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.

关键词： Random Censorship Product-Limit Relative Risk Presmoothed Proportional Hazards asymptotic representation Strong Consistency asymptotic Normality

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