FINITE DIFFERENCE METHOD AND ITS CONVERGENT ERROR ANALYSES FOR THERMISTOR PROBLEM

The therm istor problem is an initial-boundary value problem ofcoupled nonlineardif- ferentialequations.The nonlinear PDEs consist of a heat equation w ith the Joule heating as a source and a currentconservation equation w ith tem perature-dependentelectricalconductivity. This problem has im portant applications in industry.In this paper,A new finite difference schem e is proposed on nonuniform rectangularpartition forthe therm istor problem .In thetheo- reticalanalyses,the second-order error estim ates are obtained for electricalpotentialin discrete L2 and H1 norm s,and for the tem perature in L2 norm .In order to getthese second-order error estim ates,the Joule heating source is used in a changed equivalentform .

Monopulse instantaneous 3D imaging for wideband radar system

To avoid the complicated motion compensation in interferometric inverse synthetic aperture(InISAR)and achieve realtime three-dimensional(3 D)imaging,a novel approach for 3 D imaging of the target only using a single echo is presented.This method is based on an isolated scatterer model assumption,thus the scatterers in the beam can be extracted individually.The radial range of each scatterer is estimated by the maximal likelihood estimation.Then,the horizontal and vertical wave path difference is derived by using the phase comparison technology for each scatterer,respectively.Finally,by utilizing the relationship among the 3 D coordinates,the radial range,the horizontal and vertical wave path difference,the 3 D image of the target can be reconstructed.The reconstructed image is free from the limitation in InISAR that the image plane depends on the target's own motions and on its relative position with respect to the radar.Furthermore,a phase ambiguity resolution method is adopted to ensure the success of the 3 D imaging when phase ambiguity occurs.It can be noted that the proposed phase ambiguity resolution method only uses one antenna pair and does not require a priori knowledge,whereas the existing phase ambiguity methods may require two or more antenna pairs or a priori knowledge for phase unwarping.To evaluate the performance of the proposed method,the theoretical analyses on estimation accuracy are presented and the simulations in various scenarios are also carried out.

Reduced-order extrapolation spectral-finite difference scheme based on POD method and error estimation for three-dimensional parabolic equation

In this study, a classical spectral-finite difference scheme （SFDS） for the three-dimensional （3D） parabolic equation is reduced by using proper orthogonal decomposition （POD） and singular value decomposition （SVD）. First, the 3D parabolic equation is discretized in spatial variables by using spectral collocation method and the discrete scheme is transformed into matrix formulation by tensor product. Second~ the classical SFDS is obtained by difference discretization in time-direction. The ensemble of data are comprised with the first few transient solutions of the classical SFDS for the 3D parabolic equation and the POD bases of ensemble of data are generated by using POD technique and SVD. The unknown quantities of the classical SFDS are replaced with the linear combination of POD bases and a reduced- order extrapolation SFDS with lower dimensions and sufficiently high accuracy for the 3D parabolic equation is established. Third, the error estimates between the classical SFDS solutions and the reduced-order extrapolation SFDS solutions and the implementation for solving the reduced-order extrapolation SFDS are provided. Finally, a numerical example shows that the errors of numerical computations are consistent with the theoretical results. Moreover, it is shown that the reduced-order extrapolation SFDS is effective and feasible to find the numerical solutions for the 3D parabolic equation.

Physical background on estimating bvalue

The G R relation lg N=a-bM( 1954)is an empirical formula used widely in the seismicity research. But the linearity of b curves has great difference in different time and space domains. An interested question in this paper is that in how large a space time strength domain the b value has certain physical connotation. This study told us that we can get optimal statistical results of b value in those space time domains which can develop correspondent strong shocks with magnitude interval( M S≥8.5, 8.0≤ M S<8.5, 7.0≤ M S<8.0). Thus, the possible seismogenic areas in which strong shocks with different magnitude intervals develop can be inferred in different regions of the mainland of China. Finally, some new problems are proposed, such as the delimitation of seismic province, the seismicity parameter determination in seismic hazard analysis and in earthquake predictions by using b value.

The effects of additive outliers in INAR(1) process and robust estimation

In this paper, methods based on ranks and signs for estimating the parameters of thefirst-order integer-valued autoregressive model in the presence of additive outliers are proposed. In particular, we use the robust sample autocorrelations based on ranks and signsto obtain estimators for the parameters of the Poisson INAR(1) process. The effects ofadditive outliers on the estimates of parameters of integer-valued time series are examined. Some numerical results of the estimators are presented with a discussion of theobtained results. The proposed methods are applied to a dataset concerning the numberof different IP addresses accessing the server of the pages of the Department of Statistics of the University of Würzburg. The results presented here give motivation to use themethodology in practical situations in which Poisson INAR(1) process contains additiveoutliers.