A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay result...A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.展开更多
Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressiv...Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.展开更多
Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressiv...Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.展开更多
Computer-aided experimental technique was used to study the Stokes deconvolution of X-ray diffraction profile. Considerable difference can be found between the Fourier coefficients obtained from the deconvolutions of ...Computer-aided experimental technique was used to study the Stokes deconvolution of X-ray diffraction profile. Considerable difference can be found between the Fourier coefficients obtained from the deconvolutions of singlet and doublet experimental profiles. Nevertheless, the resultant physical profiles corresponding to singlet and doublet profiles are identical. An approach is proposed to refine the Fourier coefficients, and the refined Fourier coefficients coincide well with that obtained from the deconvolution of singlet experimental profile.展开更多
In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems： for any ε∈ （0, 1）, there exists a measurable set E C [0, 1） of measure bigger than 1 - s such that ...In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems： for any ε∈ （0, 1）, there exists a measurable set E C [0, 1） of measure bigger than 1 - s such that for any function f ∈ LI[0, 1）, it is possible to find a function g ∈ L^1 [0, 1） coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing.展开更多
In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered...In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.展开更多
This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-sco...This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.展开更多
The aim of this work is to construct a new quadrature formula for Fourier Chebyshev coef ficients based on the divided differences of the integrand at points 1, 1 and the zeros of the n th Chebyshev polynomial o...The aim of this work is to construct a new quadrature formula for Fourier Chebyshev coef ficients based on the divided differences of the integrand at points 1, 1 and the zeros of the n th Chebyshev polynomial of the second kind. The interesting thing is that this quadrature rule is closely related to the well known Gauss Turn quadrature formula and similar to a recent result of Micchelli and Sharma, extending a particular case due to Micchelli and Rivlin.展开更多
The consideration of the time-varying covariate and time-varying coefficient effect in survival models are plausible and robust techniques. Such kind of analysis can be carried out with a general class of semiparametr...The consideration of the time-varying covariate and time-varying coefficient effect in survival models are plausible and robust techniques. Such kind of analysis can be carried out with a general class of semiparametric transformation models. The aim of this article is to develop modified estimating equations under semiparametric transformation models of survival time with time-varying coefficient effect and time-varying continuous covariates. For this, it is important to organize the data in a counting process style and transform the time with standard transformation classes which shall be applied in this article. In the situation when the effect of coefficient and covariates change over time, the widely used maximum likelihood estimation method becomes more complex and burdensome in estimating consistent estimates. To overcome this problem, alternatively, the modified estimating equations were applied to estimate the unknown parameters and unspecified monotone transformation functions. The estimating equations were modified to incorporate the time-varying effect in both coefficient and covariates. The performance of the proposed methods is tested through a simulation study. To sum up the study, the effect of possibly time-varying covariates and time-varying coefficients was evaluated in some special cases of semiparametric transformation models. Finally, the results have shown that the role of the time-varying covariate in the semiparametric transformation models was plausible and credible.展开更多
The recent boom of mass media communication (such as social media and mobiles) has boosted more applications of automatic facial expression recognition (FER). Thus, human facial expressions have to be encoded and reco...The recent boom of mass media communication (such as social media and mobiles) has boosted more applications of automatic facial expression recognition (FER). Thus, human facial expressions have to be encoded and recognized through digital devices. However, this process has to be done under recurrent problems of image illumination changes and partial occlusions. Therefore, in this paper, we propose a fully automated FER system based on Local Fourier Coefficients and Facial Fourier Descriptors. The combined power of appearance and geometric features is used for describing the specific facial regions of eyes-eyebrows, nose and mouth. All based on the attributes of the Fourier Transform and Support Vector Machines. Hence, our proposal overcomes FER problems such as illumination changes, partial occlusion, image rotation, redundancy and dimensionality reduction. Several tests were performed in order to demonstrate the efficiency of our proposal, which were evaluated using three standard databases: CK+, MUG and TFEID. In addition, evaluation results showed that the average recognition rate of each database reaches higher performance than most of the state-of-the-art techniques surveyed in this paper.展开更多
The order of magnitude of multiple Fourier coefficients of complex valued functions of generalized bounded variations like （∧^1,.. .,∧^N）BV^（p） and r-BV, over [0,2π]^ N, are estimated.
We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-or...We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.展开更多
Quantitative inversion of fracture weakness plays an important role in fracture prediction.Considering reservoirs with a set of vertical fractures as horizontal transversely isotropic media,the logarithmic normalized ...Quantitative inversion of fracture weakness plays an important role in fracture prediction.Considering reservoirs with a set of vertical fractures as horizontal transversely isotropic media,the logarithmic normalized azimuthal elastic impedance(EI)is rewritten in terms of Fourier coefficients(FCs),the 90°ambiguity in the azimuth estimation of the symmetry axis is resolved by judging the sign of the second FC,and we choose the FCs with the highest sensitivity to fracture weakness and present a feasible inversion workflow for fracture weakness,which involves:(1)the inversion for azimuthal EI datasets from observed azimuthal angle gathers;(2)the prediction for the second FCs and azimuth of the symmetry axis from the estimated azimuthal EI datasets;and(3)the estimation of fracture weakness combining the extracted second FCs and azimuth of the symmetry axis iteratively,which is constrained utilizing the Cauchy sparse regularization and the low-frequency regularization in a Bayesian framework.Tests on synthetic and field data demonstrate that the 90°ambiguity in the azimuth estimation of the symmetry axis has been removed,and reliable fracture weakness can be obtained when the estimated azimuth of the symmetry axis deviates less than 30°,which can guide the prediction of fractured reservoirs.展开更多
In order to reduce the storage amount for the sparse coefficient matrix in pre-corrected fast Fourier transform （P-FFT） or fitting the Green function fast Fourier transform （FG-FFT）, the real coefficients are solv...In order to reduce the storage amount for the sparse coefficient matrix in pre-corrected fast Fourier transform （P-FFT） or fitting the Green function fast Fourier transform （FG-FFT）, the real coefficients are solved by improving the solution method of the coefficient equations. The novel method in both P-FFT and FG-FFT for the electric field integral equation （EFIE） is employed. With the proposed method, the storage amount for the sparse coefficient matrix can be reduced to the same level as that in the adaptive integral method （AIM） or the integral equation fast Fourier transform （IE-FFT）. Meanwhile, the new algorithms do not increase the number of the FFTs used in a matrix-vector product, and maintain almost the same level of accuracy as the original versions. Besides, in respect of the time cost in each iteration, the new algorithms have also the same level as AIM （or IE- FFF）. The numerical examples demonstrate the advantages of the proposed method.展开更多
Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying...Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying the linear load is generalized,and then it is expanded into the corresponding Fourier series.With the obtained summation results of the infinite series,it is found that they are related to Bernoulli num-bers and π. The recurrent formula of Bernoulli numbers is presented. The relationships among the coefficients of the beam,Bernoulli numbers and Euler numbers are found,and the relative mathematical formulas are presented.展开更多
In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial deriv...In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.展开更多
文摘A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.
文摘Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.
文摘Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.
文摘Computer-aided experimental technique was used to study the Stokes deconvolution of X-ray diffraction profile. Considerable difference can be found between the Fourier coefficients obtained from the deconvolutions of singlet and doublet experimental profiles. Nevertheless, the resultant physical profiles corresponding to singlet and doublet profiles are identical. An approach is proposed to refine the Fourier coefficients, and the refined Fourier coefficients coincide well with that obtained from the deconvolution of singlet experimental profile.
基金supported by State Committee Science MES RA,in frame of the research project N SCS 13-1A313
文摘In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems： for any ε∈ （0, 1）, there exists a measurable set E C [0, 1） of measure bigger than 1 - s such that for any function f ∈ LI[0, 1）, it is possible to find a function g ∈ L^1 [0, 1） coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing.
文摘In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.
基金supported by the Fundamental Research Funds for the Central Universities (QN0914)
文摘This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.
文摘The aim of this work is to construct a new quadrature formula for Fourier Chebyshev coef ficients based on the divided differences of the integrand at points 1, 1 and the zeros of the n th Chebyshev polynomial of the second kind. The interesting thing is that this quadrature rule is closely related to the well known Gauss Turn quadrature formula and similar to a recent result of Micchelli and Sharma, extending a particular case due to Micchelli and Rivlin.
文摘The consideration of the time-varying covariate and time-varying coefficient effect in survival models are plausible and robust techniques. Such kind of analysis can be carried out with a general class of semiparametric transformation models. The aim of this article is to develop modified estimating equations under semiparametric transformation models of survival time with time-varying coefficient effect and time-varying continuous covariates. For this, it is important to organize the data in a counting process style and transform the time with standard transformation classes which shall be applied in this article. In the situation when the effect of coefficient and covariates change over time, the widely used maximum likelihood estimation method becomes more complex and burdensome in estimating consistent estimates. To overcome this problem, alternatively, the modified estimating equations were applied to estimate the unknown parameters and unspecified monotone transformation functions. The estimating equations were modified to incorporate the time-varying effect in both coefficient and covariates. The performance of the proposed methods is tested through a simulation study. To sum up the study, the effect of possibly time-varying covariates and time-varying coefficients was evaluated in some special cases of semiparametric transformation models. Finally, the results have shown that the role of the time-varying covariate in the semiparametric transformation models was plausible and credible.
文摘The recent boom of mass media communication (such as social media and mobiles) has boosted more applications of automatic facial expression recognition (FER). Thus, human facial expressions have to be encoded and recognized through digital devices. However, this process has to be done under recurrent problems of image illumination changes and partial occlusions. Therefore, in this paper, we propose a fully automated FER system based on Local Fourier Coefficients and Facial Fourier Descriptors. The combined power of appearance and geometric features is used for describing the specific facial regions of eyes-eyebrows, nose and mouth. All based on the attributes of the Fourier Transform and Support Vector Machines. Hence, our proposal overcomes FER problems such as illumination changes, partial occlusion, image rotation, redundancy and dimensionality reduction. Several tests were performed in order to demonstrate the efficiency of our proposal, which were evaluated using three standard databases: CK+, MUG and TFEID. In addition, evaluation results showed that the average recognition rate of each database reaches higher performance than most of the state-of-the-art techniques surveyed in this paper.
文摘The order of magnitude of multiple Fourier coefficients of complex valued functions of generalized bounded variations like （∧^1,.. .,∧^N）BV^（p） and r-BV, over [0,2π]^ N, are estimated.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11571366 and 11501570the Open Foundation of State Key Laboratory of High Performance Computing of China+1 种基金the Research Fund of National University of Defense Technology under Grant No JC15-02-02the Fund from HPCL
文摘We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.
基金the sponsorship of the National Natural Science Foundation of China(41674130)National Grand Project for Science and Technology(2016ZX05002-005)for funding this research.
文摘Quantitative inversion of fracture weakness plays an important role in fracture prediction.Considering reservoirs with a set of vertical fractures as horizontal transversely isotropic media,the logarithmic normalized azimuthal elastic impedance(EI)is rewritten in terms of Fourier coefficients(FCs),the 90°ambiguity in the azimuth estimation of the symmetry axis is resolved by judging the sign of the second FC,and we choose the FCs with the highest sensitivity to fracture weakness and present a feasible inversion workflow for fracture weakness,which involves:(1)the inversion for azimuthal EI datasets from observed azimuthal angle gathers;(2)the prediction for the second FCs and azimuth of the symmetry axis from the estimated azimuthal EI datasets;and(3)the estimation of fracture weakness combining the extracted second FCs and azimuth of the symmetry axis iteratively,which is constrained utilizing the Cauchy sparse regularization and the low-frequency regularization in a Bayesian framework.Tests on synthetic and field data demonstrate that the 90°ambiguity in the azimuth estimation of the symmetry axis has been removed,and reliable fracture weakness can be obtained when the estimated azimuth of the symmetry axis deviates less than 30°,which can guide the prediction of fractured reservoirs.
基金The National Basic Research Program of China(973Program)(No.2013CB329002)
文摘In order to reduce the storage amount for the sparse coefficient matrix in pre-corrected fast Fourier transform （P-FFT） or fitting the Green function fast Fourier transform （FG-FFT）, the real coefficients are solved by improving the solution method of the coefficient equations. The novel method in both P-FFT and FG-FFT for the electric field integral equation （EFIE） is employed. With the proposed method, the storage amount for the sparse coefficient matrix can be reduced to the same level as that in the adaptive integral method （AIM） or the integral equation fast Fourier transform （IE-FFT）. Meanwhile, the new algorithms do not increase the number of the FFTs used in a matrix-vector product, and maintain almost the same level of accuracy as the original versions. Besides, in respect of the time cost in each iteration, the new algorithms have also the same level as AIM （or IE- FFF）. The numerical examples demonstrate the advantages of the proposed method.
基金Supported by the National Natural Science Foundation of China(51276017)
文摘Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying the linear load is generalized,and then it is expanded into the corresponding Fourier series.With the obtained summation results of the infinite series,it is found that they are related to Bernoulli num-bers and π. The recurrent formula of Bernoulli numbers is presented. The relationships among the coefficients of the beam,Bernoulli numbers and Euler numbers are found,and the relative mathematical formulas are presented.
文摘In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.
