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 fa...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.展开更多
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 ...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.展开更多
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 asymptot...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.展开更多
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 ...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.展开更多
The surface waves generated by unsteady concentrated disturbances in an initially quiescent fluid of infinite depth with an inertial surface are analytically investigated for two- and three-dimensional cases. The flui...The surface waves generated by unsteady concentrated disturbances in an initially quiescent fluid of infinite depth with an inertial surface are analytically investigated for two- and three-dimensional cases. The fluid is assumed to be inviscid, incompressible and homogenous. The inertial surface represents the effect of a thin uniform distribution of non-interacting floating matter. Four types of unsteady concentrated disturbances and two kinds of initial values are considered, namely an instantaneous/oscillating mass source immersed in the fluid, an instantaneous/oscillating impulse on the surface, an initial impulse on the surface of the fluid, and an initial displacement of the surface. The linearized initial-boundary-value problem is formulated within the framework of potential flow. The solutions in integral form for the surface elevation are obtained by means of a joint Laplace-Fourier transform. The asymptotic representations of the wave motion for large time with a fixed distance- to-time ratio are derived by using the method of stationary phase. The effect of the presence of an inertial surface on the wave motion is analyzed. It is found that the wavelengths of the transient dispersive waves increase while those of the steady-state progressive waves decrease. All the wave amplitudes decrease in comparison with those of conventional free-surface waves. The explicit expressions for the freesurface gravity waves can readily be recovered by the present results as the inertial surface disappears.展开更多
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 condit...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.展开更多
In this paper,we focus on the problem of nonparametric quantile regression with left-truncated and right-censored data.Based on Nadaraya-Watson(NW)Kernel smoother and the technique of local linear(LL)smoother,we const...In this paper,we focus on the problem of nonparametric quantile regression with left-truncated and right-censored data.Based on Nadaraya-Watson(NW)Kernel smoother and the technique of local linear(LL)smoother,we construct the NW and LL estimators of the conditional quantile.Under strong mixing assumptions,we establish asymptotic representation and asymptotic normality of the estimators.Finite sample behavior of the estimators is investigated via simulation,and a real data example is used to illustrate the application of the proposed methods.展开更多
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 t...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.展开更多
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 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 I.aplace 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.展开更多
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 c...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 estimators.These applications demonstrate the usefulness of the new matrix products.展开更多
基金The project partly supported by the National Natural Science Foundation of China(19925414,10474045)
文摘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.
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China (10771163)
文摘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.
基金the National Natural Science Foundation of China(10602032)the Shanghai Rising-Star Program(07QA14022)the Shanghai Leading Academic Discipline Project(Y0103)
文摘The surface waves generated by unsteady concentrated disturbances in an initially quiescent fluid of infinite depth with an inertial surface are analytically investigated for two- and three-dimensional cases. The fluid is assumed to be inviscid, incompressible and homogenous. The inertial surface represents the effect of a thin uniform distribution of non-interacting floating matter. Four types of unsteady concentrated disturbances and two kinds of initial values are considered, namely an instantaneous/oscillating mass source immersed in the fluid, an instantaneous/oscillating impulse on the surface, an initial impulse on the surface of the fluid, and an initial displacement of the surface. The linearized initial-boundary-value problem is formulated within the framework of potential flow. The solutions in integral form for the surface elevation are obtained by means of a joint Laplace-Fourier transform. The asymptotic representations of the wave motion for large time with a fixed distance- to-time ratio are derived by using the method of stationary phase. The effect of the presence of an inertial surface on the wave motion is analyzed. It is found that the wavelengths of the transient dispersive waves increase while those of the steady-state progressive waves decrease. All the wave amplitudes decrease in comparison with those of conventional free-surface waves. The explicit expressions for the freesurface gravity waves can readily be recovered by the present results as the inertial surface disappears.
基金Supported by the National Natural Science Foundation of China(No.11471105,11471223)Scientific Research Item of Education Office,Hubei(No.D20172501)
文摘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.
基金supported by the National Natural Science Foundation of China(12071348)the Key Scientific Research Foundation of Henan Educational Committee(24A110001)Key Laboratory of Intelligent Computing and Applications(Ministry of Education),Tongji University,China.
文摘In this paper,we focus on the problem of nonparametric quantile regression with left-truncated and right-censored data.Based on Nadaraya-Watson(NW)Kernel smoother and the technique of local linear(LL)smoother,we construct the NW and LL estimators of the conditional quantile.Under strong mixing assumptions,we establish asymptotic representation and asymptotic normality of the estimators.Finite sample behavior of the estimators is investigated via simulation,and a real data example is used to illustrate the application of the proposed methods.
文摘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.
文摘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 I.aplace 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.
基金Partially supported by the National Natural Science Foundation of China (No.10071092).
文摘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 estimators.These applications demonstrate the usefulness of the new matrix products.
