In order to improve the seismic performance of adjacent buildings,two types of tuned inerter damper(TID)damping systems for adjacent buildings are proposed,which are composed of springs,inerter devices and dampers in ...In order to improve the seismic performance of adjacent buildings,two types of tuned inerter damper(TID)damping systems for adjacent buildings are proposed,which are composed of springs,inerter devices and dampers in serial or in parallel.The dynamic equations of TID adjacent building damping systems were derived,and the H2 norm criterion was used to optimize and adjust them,so that the system had the optimum damping performance under white noise random excitation.Taking TID frequency ratio and damping ratio as optimization parameters,the optimum analytical solutions of the displacement frequency response of the undamped structure under white noise excitation were obtained.The results showed that compared with the classic TMD,TID could obtain a better damping effect in the adjacent buildings.Comparing the TIDs composed of serial or parallel,it was found that the parallel TIDs had more significant advantages in controlling the peak displacement frequency response,while the H2 norm of the displacement frequency response of the damping system under the coupling of serial TID was smaller.Taking the adjacent building composed of two ten-story frame structures as an example,the displacement and energy collection time history analysis of the adjacent building coupled with the optimum design parameter TIDs were carried out.It was found that TID had a better damping effect in the full-time range compared with the classic TMD.This paper also studied the potential power of TID in adjacent buildings,which can be converted into available power resources during earthquakes.展开更多
Due to the presence of turbid media, such as microdust and water vapor in the environment, outdoor pictures taken under hazy weather circumstances are typically degraded. To enhance the quality of such images, this wo...Due to the presence of turbid media, such as microdust and water vapor in the environment, outdoor pictures taken under hazy weather circumstances are typically degraded. To enhance the quality of such images, this work proposes a new hybrid λ2-λ0 penalty model for image dehazing. This model performs a weighted fusion of two distinct transmission maps, generated by imposing λ2 and λ0 norm penalties on the approximate regression coefficients of the transmission map. This approach effectively balances the sparsity and smoothness associated with the λ0 and λ2 norms, thereby optimizing the transmittance map. Specifically, when the λ2 norm is penalized in the model, an updated guided image is obtained after implementing λ0 penalty. The resulting optimization problem is effectively solved using the least square method and the alternating direction algorithm. The dehazing framework combines the advantages of λ2 and λ0 norms, enhancing sparse and smoothness, resulting in higher quality images with clearer details and preserved edges.展开更多
High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurat...High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.展开更多
The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversio...The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversion.To solve this problem,we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics.Moreover,the reconstruction of the sparse refl ection coeffi cient is implemented by the mixed L1_L2 norm algorithm,which converts the L0 norm problem into an L1 norm problem.Additionally,a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error.The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods.It not only has better denoising and smoothing eff ects but also improves the recognition accuracy of thin interbeds.The actual data application also shows that the new method can eff ectively expand the seismic frequency band and improve seismic data resolution,so the method is conducive to the identifi cation of thin interbeds for beach-bar sand reservoirs.展开更多
Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direc...Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients.This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes.Optimal error estimate in L2 norm is obtained for the schemes.Compared with the finite volume element method of the same convergence order,our method is more effective in terms of running time with the increasing of the computing scale.Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.展开更多
We obtain an upper bound for the average error of the quasi-Griinwald interpolation based on the zeros of Chebyshev polynomial of the second kind in the Wiener space.
In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smoo...In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.展开更多
Echo canceller generally needs a double-talk detector which is used to keep the adaptive filter from diverging in the appearance of near-end speech.In this paper we adopt a new double-talk detection algorithm based on...Echo canceller generally needs a double-talk detector which is used to keep the adaptive filter from diverging in the appearance of near-end speech.In this paper we adopt a new double-talk detection algorithm based on I_(2)norm to detect the existence of near-end speech in an acoustic echo canceller.We analyze this algorithm from the point of view of functional analysis and point out that the proposed double-talk detection algorithm has the same performance as the classic one in a finite Banach space.The remarkable feature of this algorithm is its higher accuracy and better computation complexity.The fine properties of this algorithm are confirmed by computer simulation and the application in a multimedia communication system.展开更多
Motion deblurring is a basic problem in the field of image processing and analysis. This paper proposes a new method of single image blind deblurring which can be significant to kernel estimation and non-blind deconvo...Motion deblurring is a basic problem in the field of image processing and analysis. This paper proposes a new method of single image blind deblurring which can be significant to kernel estimation and non-blind deconvolution. Experiments show that the details of the image destroy the structure of the kernel, especially when the blur kernel is large. So we extract the image structure with salient edges by the method based on RTV. In addition, the traditional method for motion blur kernel estimation based on sparse priors is conducive to gain a sparse blur kernel. But these priors do not ensure the continuity of blur kernel and sometimes induce noisy estimated results. Therefore we propose the kernel refinement method based on L0 to overcome the above shortcomings. In terms of non-blind deconvolution we adopt the L1/L2 regularization term. Compared with the traditional method, the method based on L1/L2 norm has better adaptability to image structure, and the constructed energy functional can better describe the sharp image. For this model, an effective algorithm is presented based on alternating minimization algorithm.展开更多
This paper introduces the algebraic property of bivariate orthonormal Jacobi polynomials into geometric approximation. Based on the latest results on the transformation formulae between bivariate Bernstein polynomials...This paper introduces the algebraic property of bivariate orthonormal Jacobi polynomials into geometric approximation. Based on the latest results on the transformation formulae between bivariate Bernstein polynomials and Jacobi polynomials, we naturally deduce a novel algorithm for multi-degree reduction of triangular B^zier surfaces. This algorithm possesses four characteristics： ability of error forecast, explicit expression, less time consumption, and best precision. That is, firstly, whether there exists a multi-degree reduced surface within a prescribed tolerance is judged beforehand; secondly, all the operations of multi-degree reduction are just to multiply the column vector generated by sorting the series of the control points of the original surface in lexicographic order by a matrix; thirdly, this matrix can be computed at one time and stored in an array before processing degree reduction; fourthly, the multi-degree reduced surface achieves an optimal approximation in the norm L2. Some numerical experiments are presented to validate the effectiveness of this algorithm, and to show that the algorithm is applicable to information processing of products in CAD system.展开更多
In the paper, we analyze the L2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L2 norm of the finite element solution is of second ...In the paper, we analyze the L2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L2 norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the finite element solution. The result holds for most of the popular lower order finite element methods in the literature including： the Powell-Sabin C1 -P2 macro element, the nonconforming Morley element, the C1 -Q2 macro element, the nonconforming rectangle Morley element, and the nonconforming incomplete biquadratic element. In addition, the result actually applies to the nonconforming Adini element, the nonconforming Fraeijs de Veubeke elements, and the nonconforming Wang- Xu element and the Wang-Shi-Xu element provided that the saturation condition holds for them. This result solves one long standing problem in the literature： can the L2 norm error estimate of lower order finite element methods of the fourth order problem be two order higher than the error estimate in the energy norm？展开更多
In this work,the Benjamin-Bona-Mahony-Burgers(BBMB)equation is solved using an improvised cubic B-spline collocation technique.This equation describes the propagation of small amplitude waves in a non-linear dispersiv...In this work,the Benjamin-Bona-Mahony-Burgers(BBMB)equation is solved using an improvised cubic B-spline collocation technique.This equation describes the propagation of small amplitude waves in a non-linear dispersive medium,in the modeling of unidirectional planar waves.Due to the higher smoothness and sparse nature of matrices corresponding to splines,cubic B-splines are chosen as the basis function in the collocation method.But,the optimal accuracy and order of convergence cannot be achieved using the standard B-spline collocation method.So to overcome this,improvised cubic B-splines are formed by making posteriori corrections to cubic B-spline interpolant and its higher-order derivatives.The Crank-Nicolson scheme is used to discretize the temporal domain along with the quasilinearization process to deal with the nonlinear terms.The spatial domain discretization is carried out using the improvised cubic B-spline collocation method(ICSCM).The stability analysis of the technique is performed using the von-Neumann scheme.Several test problems are solved numerically and obtained results are compared with the results available in the literature.The aim of the paper is to show that such improvised techniques which were earlier used to solve ODEs,can be applied to solve the BBMB equation also,with excellent accuracy in results.展开更多
The mathematical system is formulated by four partial differential equations combined with initial- boundary value conditions to describe transient behavior of three-dimensional semiconductor device with heat conducti...The mathematical system is formulated by four partial differential equations combined with initial- boundary value conditions to describe transient behavior of three-dimensional semiconductor device with heat conduction. The first equation of an elliptic type is defined with respect to the electric potential, the successive two equations of convection dominated diffusion type are given to define the electron concentration and the hole concentration, and the fourth equation of heat conductor is for the temperature. The electric potential appears in the equations of electron concentration, hole concentration and the temperature in the formation of the intensity. A mass conservative numerical approximation of the electric potential is presented by using the mixed finite volume element, and the accuracy of computation of the electric intensity is improved one order. The method of characteristic fractional step difference is applied to discretize the other three equations, where the hyperbolic terms are approximated by a difference quotient in the characteristics and the diffusion terms are discretized by the method of fractional step difference. The computation of three-dimensional problem works efficiently by dividing it into three one-dimensional subproblems and every subproblem is solved by the method of speedup in parallel. Using a pair of different grids （coarse partition and refined partition）, piecewise threefold quadratic interpolation, variation theory, multiplicative commutation rule of differential operators, mathematical induction and priori estimates theory and special technique of differential equations, we derive an optimal second order estimate in L2-norm. This numerical method is valuable in the simulation of semiconductor device theoretically and actually, and gives a powerful tool to solve the international problem presented by J. Douglas, Jr.展开更多
The authors discuss problems of approximation to functions in L2(Rn) and operators fromL2(Rn1) to L2(Rn2) by Radial-Basis Functions. The results obtained solve the problem ofcapability of RBF neural networks, a basic ...The authors discuss problems of approximation to functions in L2(Rn) and operators fromL2(Rn1) to L2(Rn2) by Radial-Basis Functions. The results obtained solve the problem ofcapability of RBF neural networks, a basic problem in neural networks.展开更多
Currently,the three-dimensional distribution of interlayer is realized by stochastic modeling.Traditionally,the three-dimensional geological modeling controlled by sedimentary facies models is built on the basis of lo...Currently,the three-dimensional distribution of interlayer is realized by stochastic modeling.Traditionally,the three-dimensional geological modeling controlled by sedimentary facies models is built on the basis of logging interpretation parameters and geophysical information.Because of shallow gas-cap,the quality of three-dimensional seismic data vertical resolution in research area cannot meet the interlayer research that is below ten meters.Moreover,sedimentary facies cannot commendably reveal interlayer distribution and the well density is very sparse in research area.So,it is difficult for conventional technology to finely describe interlayers.In this document,it uses L1-L2 combined norm constrained inversion to enhance the recognition capability of interlayer in seismic profile and improve the signal to noise ratio,the wave group characteristics and the vertical resolution of three-dimensional data and classifies petrophysical facies of interlayer based on core,sedimentary facies and logging interpretation.The interlayer model which is based on seismic inversion model and petrophysical facies can precisely simulate the distribution of reservoir and interlayer.The results show that the simulation results of this new methodology are consistent with the dynamic production perfectly which provide a better basis for producing and mining remaining oil and a new interlayer modeling method for sparse well density.展开更多
The author provides a finer local as well as semilocM convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space （m ...The author provides a finer local as well as semilocM convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space （m ≥ 1 a natural number）.展开更多
We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respe...We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:展开更多
基金This research was funded by the Natural Science Research Project of Higher Education Institutions in Anhui Province(Grant No.2022AH040045)the Anhui Provincial Natural Science Foundation(Grant No.2008085QE245)the Project of Science and Technology Plan of Department of Housing and Urban-Rural Development of Anhui Province(Grant No.2021-YF22).
文摘In order to improve the seismic performance of adjacent buildings,two types of tuned inerter damper(TID)damping systems for adjacent buildings are proposed,which are composed of springs,inerter devices and dampers in serial or in parallel.The dynamic equations of TID adjacent building damping systems were derived,and the H2 norm criterion was used to optimize and adjust them,so that the system had the optimum damping performance under white noise random excitation.Taking TID frequency ratio and damping ratio as optimization parameters,the optimum analytical solutions of the displacement frequency response of the undamped structure under white noise excitation were obtained.The results showed that compared with the classic TMD,TID could obtain a better damping effect in the adjacent buildings.Comparing the TIDs composed of serial or parallel,it was found that the parallel TIDs had more significant advantages in controlling the peak displacement frequency response,while the H2 norm of the displacement frequency response of the damping system under the coupling of serial TID was smaller.Taking the adjacent building composed of two ten-story frame structures as an example,the displacement and energy collection time history analysis of the adjacent building coupled with the optimum design parameter TIDs were carried out.It was found that TID had a better damping effect in the full-time range compared with the classic TMD.This paper also studied the potential power of TID in adjacent buildings,which can be converted into available power resources during earthquakes.
文摘Due to the presence of turbid media, such as microdust and water vapor in the environment, outdoor pictures taken under hazy weather circumstances are typically degraded. To enhance the quality of such images, this work proposes a new hybrid λ2-λ0 penalty model for image dehazing. This model performs a weighted fusion of two distinct transmission maps, generated by imposing λ2 and λ0 norm penalties on the approximate regression coefficients of the transmission map. This approach effectively balances the sparsity and smoothness associated with the λ0 and λ2 norms, thereby optimizing the transmittance map. Specifically, when the λ2 norm is penalized in the model, an updated guided image is obtained after implementing λ0 penalty. The resulting optimization problem is effectively solved using the least square method and the alternating direction algorithm. The dehazing framework combines the advantages of λ2 and λ0 norms, enhancing sparse and smoothness, resulting in higher quality images with clearer details and preserved edges.
基金supported in part by the National Natural Science Foundation of China(61702475,61772493,61902370,62002337)in part by the Natural Science Foundation of Chongqing,China(cstc2019jcyj-msxmX0578,cstc2019jcyjjqX0013)+1 种基金in part by the Chinese Academy of Sciences“Light of West China”Program,in part by the Pioneer Hundred Talents Program of Chinese Academy of Sciencesby Technology Innovation and Application Development Project of Chongqing,China(cstc2019jscx-fxydX0027)。
文摘High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.
基金National Science and Technology Major Project(No.2016ZX05006-002 and 2017ZX05072-001).
文摘The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversion.To solve this problem,we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics.Moreover,the reconstruction of the sparse refl ection coeffi cient is implemented by the mixed L1_L2 norm algorithm,which converts the L0 norm problem into an L1 norm problem.Additionally,a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error.The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods.It not only has better denoising and smoothing eff ects but also improves the recognition accuracy of thin interbeds.The actual data application also shows that the new method can eff ectively expand the seismic frequency band and improve seismic data resolution,so the method is conducive to the identifi cation of thin interbeds for beach-bar sand reservoirs.
基金supported by the National Natural Science Foundation of China grants No.11971241.
文摘Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients.This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes.Optimal error estimate in L2 norm is obtained for the schemes.Compared with the finite volume element method of the same convergence order,our method is more effective in terms of running time with the increasing of the computing scale.Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.
基金Foundation item： Supported bv the National Natural Science Foundation of China（10471010）
文摘We obtain an upper bound for the average error of the quasi-Griinwald interpolation based on the zeros of Chebyshev polynomial of the second kind in the Wiener space.
文摘In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.
基金Supported by the the National High Technology Development of China(863-306-ZT05)
文摘Echo canceller generally needs a double-talk detector which is used to keep the adaptive filter from diverging in the appearance of near-end speech.In this paper we adopt a new double-talk detection algorithm based on I_(2)norm to detect the existence of near-end speech in an acoustic echo canceller.We analyze this algorithm from the point of view of functional analysis and point out that the proposed double-talk detection algorithm has the same performance as the classic one in a finite Banach space.The remarkable feature of this algorithm is its higher accuracy and better computation complexity.The fine properties of this algorithm are confirmed by computer simulation and the application in a multimedia communication system.
基金Partially Supported by National Natural Science Foundation of China(No.61173102)
文摘Motion deblurring is a basic problem in the field of image processing and analysis. This paper proposes a new method of single image blind deblurring which can be significant to kernel estimation and non-blind deconvolution. Experiments show that the details of the image destroy the structure of the kernel, especially when the blur kernel is large. So we extract the image structure with salient edges by the method based on RTV. In addition, the traditional method for motion blur kernel estimation based on sparse priors is conducive to gain a sparse blur kernel. But these priors do not ensure the continuity of blur kernel and sometimes induce noisy estimated results. Therefore we propose the kernel refinement method based on L0 to overcome the above shortcomings. In terms of non-blind deconvolution we adopt the L1/L2 regularization term. Compared with the traditional method, the method based on L1/L2 norm has better adaptability to image structure, and the constructed energy functional can better describe the sharp image. For this model, an effective algorithm is presented based on alternating minimization algorithm.
基金Supported by the National Grand Fundamental Research 973 Program of China (Grant No. 2004CB719400)the National Natural Science Foun-dation of China (Grant Nos. 60673031 and 60333010)the National Natural Science Foundation for Innovative Research Groups (Grant No. 60021201)
文摘This paper introduces the algebraic property of bivariate orthonormal Jacobi polynomials into geometric approximation. Based on the latest results on the transformation formulae between bivariate Bernstein polynomials and Jacobi polynomials, we naturally deduce a novel algorithm for multi-degree reduction of triangular B^zier surfaces. This algorithm possesses four characteristics： ability of error forecast, explicit expression, less time consumption, and best precision. That is, firstly, whether there exists a multi-degree reduced surface within a prescribed tolerance is judged beforehand; secondly, all the operations of multi-degree reduction are just to multiply the column vector generated by sorting the series of the control points of the original surface in lexicographic order by a matrix; thirdly, this matrix can be computed at one time and stored in an array before processing degree reduction; fourthly, the multi-degree reduced surface achieves an optimal approximation in the norm L2. Some numerical experiments are presented to validate the effectiveness of this algorithm, and to show that the algorithm is applicable to information processing of products in CAD system.
文摘In the paper, we analyze the L2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L2 norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the finite element solution. The result holds for most of the popular lower order finite element methods in the literature including： the Powell-Sabin C1 -P2 macro element, the nonconforming Morley element, the C1 -Q2 macro element, the nonconforming rectangle Morley element, and the nonconforming incomplete biquadratic element. In addition, the result actually applies to the nonconforming Adini element, the nonconforming Fraeijs de Veubeke elements, and the nonconforming Wang- Xu element and the Wang-Shi-Xu element provided that the saturation condition holds for them. This result solves one long standing problem in the literature： can the L2 norm error estimate of lower order finite element methods of the fourth order problem be two order higher than the error estimate in the energy norm？
基金Ms.Shallu is thankful to CSIR New Delhi for providing finan-cial assistance in the form of JRF with File No.09/797(0016)/2018-EMR-I.
文摘In this work,the Benjamin-Bona-Mahony-Burgers(BBMB)equation is solved using an improvised cubic B-spline collocation technique.This equation describes the propagation of small amplitude waves in a non-linear dispersive medium,in the modeling of unidirectional planar waves.Due to the higher smoothness and sparse nature of matrices corresponding to splines,cubic B-splines are chosen as the basis function in the collocation method.But,the optimal accuracy and order of convergence cannot be achieved using the standard B-spline collocation method.So to overcome this,improvised cubic B-splines are formed by making posteriori corrections to cubic B-spline interpolant and its higher-order derivatives.The Crank-Nicolson scheme is used to discretize the temporal domain along with the quasilinearization process to deal with the nonlinear terms.The spatial domain discretization is carried out using the improvised cubic B-spline collocation method(ICSCM).The stability analysis of the technique is performed using the von-Neumann scheme.Several test problems are solved numerically and obtained results are compared with the results available in the literature.The aim of the paper is to show that such improvised techniques which were earlier used to solve ODEs,can be applied to solve the BBMB equation also,with excellent accuracy in results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11101124 and 11271231)the National Tackling Key Problems Program for Science and Technology(Grant No.20050200069)the Doctorate Foundation of the Ministry of Education of China(Grant No.20030422047)
文摘The mathematical system is formulated by four partial differential equations combined with initial- boundary value conditions to describe transient behavior of three-dimensional semiconductor device with heat conduction. The first equation of an elliptic type is defined with respect to the electric potential, the successive two equations of convection dominated diffusion type are given to define the electron concentration and the hole concentration, and the fourth equation of heat conductor is for the temperature. The electric potential appears in the equations of electron concentration, hole concentration and the temperature in the formation of the intensity. A mass conservative numerical approximation of the electric potential is presented by using the mixed finite volume element, and the accuracy of computation of the electric intensity is improved one order. The method of characteristic fractional step difference is applied to discretize the other three equations, where the hyperbolic terms are approximated by a difference quotient in the characteristics and the diffusion terms are discretized by the method of fractional step difference. The computation of three-dimensional problem works efficiently by dividing it into three one-dimensional subproblems and every subproblem is solved by the method of speedup in parallel. Using a pair of different grids （coarse partition and refined partition）, piecewise threefold quadratic interpolation, variation theory, multiplicative commutation rule of differential operators, mathematical induction and priori estimates theory and special technique of differential equations, we derive an optimal second order estimate in L2-norm. This numerical method is valuable in the simulation of semiconductor device theoretically and actually, and gives a powerful tool to solve the international problem presented by J. Douglas, Jr.
基金Project supported by the National Natural Science Foundation of Chin
文摘The authors discuss problems of approximation to functions in L2(Rn) and operators fromL2(Rn1) to L2(Rn2) by Radial-Basis Functions. The results obtained solve the problem ofcapability of RBF neural networks, a basic problem in neural networks.
文摘Currently,the three-dimensional distribution of interlayer is realized by stochastic modeling.Traditionally,the three-dimensional geological modeling controlled by sedimentary facies models is built on the basis of logging interpretation parameters and geophysical information.Because of shallow gas-cap,the quality of three-dimensional seismic data vertical resolution in research area cannot meet the interlayer research that is below ten meters.Moreover,sedimentary facies cannot commendably reveal interlayer distribution and the well density is very sparse in research area.So,it is difficult for conventional technology to finely describe interlayers.In this document,it uses L1-L2 combined norm constrained inversion to enhance the recognition capability of interlayer in seismic profile and improve the signal to noise ratio,the wave group characteristics and the vertical resolution of three-dimensional data and classifies petrophysical facies of interlayer based on core,sedimentary facies and logging interpretation.The interlayer model which is based on seismic inversion model and petrophysical facies can precisely simulate the distribution of reservoir and interlayer.The results show that the simulation results of this new methodology are consistent with the dynamic production perfectly which provide a better basis for producing and mining remaining oil and a new interlayer modeling method for sparse well density.
文摘The author provides a finer local as well as semilocM convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space （m ≥ 1 a natural number）.
文摘We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:
