A posteriori error estimator for eigenvalue problems by mixed finite element method

In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergence result of the eigenfunction approximation.Its efficiency and reliability are proved by both theoretical analysis and numerical experiments.     

Testing heteroscedasticity in nonparametric regression models based on residual analysis

The importance of detecting heteroscedasticity in regression analysis is widely recognized because efficient inference for the regression function requires that heteroscedasticity should be taken into account. In this paper, a simple test for heteroscedasticity is proposed in nonparametric regression based on residual analysis. Furthermore, some simulations with a comparison with Dette and Munk＇s method are conducted to evaluate the performance of the proposed test. The results demonstrate that the method in this paper performs quite satisfactorily and is much more powerful than Dette and Munk＇s method in some cases.     

本刊英文版2013年56卷第5期摘要(英文)

A posteriori error estimator for eigenvalue problems by mixed finite element method JIA ShangHui,CHEN HongTao & XIE HeHu Abstract In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergence result of the eigenfunction approximation.Its efficiency and reliability are proved by both theoretical analysis and numerical experiments.     

BAYESIAN ANALYSIS OF DATA WITH ONLY ONE FAILURE

The hearings of a certain type have their lives following a Weibull distribution. In a life test with 20 sets of bearings, only one set failed within the specified time, and none of the remainder failed even after the time of to estimate the reliabilWith a set of testing data like that in Table 1, it is required to estimate the reliability at the mission time, In this paper, we first use hierarchical Bayesian method of determine the prior distribution and the Bayesian estimates of various probabilities of failures, pi‘s, then use the method of least squares to estimate the parameters of the Weibull distribution and the reliability. Actual computation shows that the estimates so obtained are rather robust. And the results have been adopted for practical use.     

Exact Confidence Limits for the Parameter of an Exponential Distribution in the Accelerated Life Tests under Type-ⅠCensoring

Life data frequently arise in many reliability studies,such as accelerated life tests studies.This paper considers the part of life data where failure and censoring observations may exist.To develop statistical methods and theory for the analysis of these data,a new approach was proposed to obtain the exact lower and upper confidence limits for the mean life of the exponential distribution with Type-I censoring data.It is assumed that the acceleration factor is a random variable,and that the distribution of the acceleration factor is known from some empirical information or the meta analysis.A method for constructing the lower and upper confidence limits for the parameter based on an ordering relation among the sample space was proposed.Simulation studies and analyses of two examples suggest that the proposed method performed well.     

A Pole Assignment Design Method of Process Control System for Tubular Heat Exchanger

This paper has first studied the simplified model of tubular heat exchanger which is widely used in the industry and other field. On the basis of reference 2,a new pole assignment design method of process control system with derivative control action is found. For the above system, the method and the formation which calculate the feedback matrix K and gain matrix L is given,and the simulation of the system is made.     

THE HIERARCHICAL BAYESIAN ANALYSIS OF THE ZERO-FAILURE DATA

The life distribution of some type of engines is Weibull distribution (or normal distribution). We have done life tests censored at fixed times τ1…τ2 , totally 51 times. The result is all zero-failure! What we will do is to estimate the reliability R(τ) = P(T > τ) , here T is the life of this type of engines.This paper tries to seek the estimate failure probability pi = P(T ≤τ) by the hierarchical Bayesian analysis and reliability R(τ) by the least square method in two situations. The result shows, estimation of R(τ) is robust.     

简单半序约束下估计位置参数的一个非参方法

This paper deals with estimating parameters under simple order when samples come from location models. Based on the idea of Hodges and Lehmann estimator (H-L estimator), a new approach to estimate parameters is proposed, which is difference with the classical L1 isotonic regression and L2 isotonic regression. An algorithm to compute estimators is given. Simulations by the Monte-Carlo method is applied to compare the likelihood functions with respect to L1 estimators and weighted isotonic H-L estimators.     

基于NOD误差的非参数回归模型估计的渐近性质（英文）

In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.     

部分线性模型中的非参数部分的线性性检验

In this paper,we propose the test statistic to check whether the nonpara- metric function in partially linear models is linear or not.We estimate the nonpara- metric function in alternative by using the local linear method,and then estimate the parameters by the two stage method.The test statistic under the null hypothesis is calculated,and it is shown to be asymptotically normal.     

Generalized empirical likelihood inference in semiparametric regression model for longitudinal data

In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix. It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals.     

L1-Norm Estimation and Random Weighting Method in a Semiparametric Model

In this paper, the L_1-norm estimators and the random weighted statistic for a semiparametric regression model are constructed, the strong convergence rates of estimators are obtain under certain conditions, the strong efficiency of the random weighting method is shown. A simulation study is conducted to compare the L_1-norm estimator with the least square estimator in term of approximate accuracy, and simulation results are given for comparison between the random weighting method and normal approximation method.     

Burgers方程的带有限制算子的Chebyshev谱方法

In this paper, a restraint operator is used to improve the stability of the Chebyshev spectral method. The generalized stability of this new method is proved and the rate of convergence is analyzed. The numerical results show the advantage of the method.     

干酪根演变中热力学参数的优化模型及其识别

In this paper, a mathematical model with respect to the optimalidentification of the thermodynamic parameters is established. The identifiabitity of the dynamics problem is proved and necessary conditions of the optimality are given.     

A weak condition for secant method to solve systems of nonlinear equations

In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x0 is replaced by that with xl, the first approximation generated by the secant method with the initial data x-1 and x0. Under the bounded conditions of the divided difference, a convergence theorem is obtained and two examples to illustrate the weakness of convergence conditions are provided. Moreover, the secant method is applied to a system of nonlinear equations to demonstrate the viability and effectiveness of the results in the paper.     

A METHOD FOR SOLVING THE INVERSE SCATTERING PROBLEM FOR SHAPE AND IMPEDANCE

The inverse problem considered in this paper is to determine the shape and the impedance of an obstacle from a knowledge of the time-harmonic incident field and the phase and amplitude of the far field pattern of the scattered wave in two-dimension. Single-layer potential is used to approach the scattered waves. An approximation method is presented and the convergence of the proposed method is established. Numerical examples are given to show that this method is both accurate and easy to use.     

序约束下AR(p)-ARCH(q)模型参数的估计与检验

In this paper, we study a stationary AR(p)-ARCH(q) model with parameter vectors a and β. We propose a method for computing the maximum likelihood estimator (MLE) of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order: α1≥α2≥…≥αq, andβ1≥β2≥…βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio (LR) test statistic for the testing problem and derive its asymptotic null distribution.     

Gamma分布族中形状参数的一个新估计

In this paper, a new estimator of the shape parameter in the family of Gamma distribution is constructed by using the moment idea, and it is proved that this estimator is strongly consistent and asymptotically normal.     

A NEW NUMERICAL METHOD FOR TWO-PHASE IMMISCIBLE INCOMPRESSIBLE PROBLEM

Two-phase, immiscible, incompressible flow in porous media is governed by a system of nonlinear partial differential equations. In most practical applications convection physically dominates diffusion, and the object of this paper is to develop a finite difference method combined with the method of characteristics and the lumped mass method to treat the parabolic equation of the differential system. This method is shown satisfy the maximum principle and its error analysis is presented.     

Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems

For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper.