How to calculate the highly oscillatory integrals is the bottleneck that restraints the research of light wave and electromagnetic wave＇s propagation and scattering. Levin method is a classical quadrature method for ...How to calculate the highly oscillatory integrals is the bottleneck that restraints the research of light wave and electromagnetic wave＇s propagation and scattering. Levin method is a classical quadrature method for this type of integrals. Unfortunately it is susceptible to the system of linear equations＇ ill-conditioned behavior. We bring forward a universal quadrature method in this paper, which adopts Chebyshev differential matrix to solve the ordinary differential equation （ODE）. This method can not only obtain the indefinite integral＇ function values directly, but also make the system of linear equations well-conditioned for general oscillatory integrals. Furthermore, even if the system of linear equations in our method is ill-conditioned, TSVD method can be adopted to solve them properly and eventually obtain accurate integral results, thus making a breakthrough in Levin method＇s susceptivity to the system of linear equations＇ ill-conditioned behavior.展开更多
In this paper,we prove two supercongruences conjectured by Z.-W.Sun via the Wilf-Zeilberger method.One of them is,for any prime p>3,4F3[7/6 1/2 1/2 1/2 1/6 1 1]-1/8]-1/2≡p(-2/p)+p^(3)/4(2/p)Ep-3 (mod p^(4))where(&...In this paper,we prove two supercongruences conjectured by Z.-W.Sun via the Wilf-Zeilberger method.One of them is,for any prime p>3,4F3[7/6 1/2 1/2 1/2 1/6 1 1]-1/8]-1/2≡p(-2/p)+p^(3)/4(2/p)Ep-3 (mod p^(4))where(·/p)stands for the Legendre symbol,and E_(n)is the n-th Euler number.展开更多
This work is concerned with the convergence and stability of the truncated EulerMaruyama(EM)method for super-linear stochastic differential delay equations(SDDEs)with time-variable delay and Poisson jumps.By construct...This work is concerned with the convergence and stability of the truncated EulerMaruyama(EM)method for super-linear stochastic differential delay equations(SDDEs)with time-variable delay and Poisson jumps.By constructing appropriate truncated functions to control the super-linear growth of the original coefficients,we present two types of the truncated EM method for such jump-diffusion SDDEs with time-variable delay,which is proposed to be approximated by the value taken at the nearest grid points on the left of the delayed argument.The first type is proved to have a strong convergence order which is arbitrarily close to 1/2 in mean-square sense,under the Khasminskii-type,global monotonicity with U function and polynomial growth conditions.The second type is convergent in q-th(q<2)moment under the local Lipschitz plus generalized Khasminskii-type conditions.In addition,we show that the partially truncated EM method preserves the mean-square and H∞stabilities of the true solutions.Lastly,we carry out some numerical experiments to support the theoretical results.展开更多
The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,etc.In this paper,the original truncated complex singular value decomposition problem is fo...The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,etc.In this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et al.is presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence rate.Numerical experiments are provided to illustrate the efficiency of the proposed method.Comparisons with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach.展开更多
Convergence of modified truncated Euler-Maruyama(MTEM)method for stochastic differential equations(SDEs)with(1/2+α)-Holder continuous diffusion coefficients are investigated in this paper.We prove that the MTEM metho...Convergence of modified truncated Euler-Maruyama(MTEM)method for stochastic differential equations(SDEs)with(1/2+α)-Holder continuous diffusion coefficients are investigated in this paper.We prove that the MTEM method for SDE converges to the exact solution in L9 sense under given conditions.Two examples are provided to support our conclusions.展开更多
In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz c...In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition.The order of convergence is obtained.Moreover,we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs.Numerical examples are provided to support our conclusions.展开更多
The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explici...The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.展开更多
In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for stud...In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear systems. The periodic solution of Duffing equation is calculated by means of our method.展开更多
Recently,the authors of[Commun.Theor.Phys.56(2011)397]made a number of useful observations on Exp-function method.In this study,we focus on another vital issue,namely,the misleading results of double Exp-function method.
To surmount the deficiency in studying the multiple equilibrium states in the atmosphere motion with highly truncated spectral method, the trigonometric functions for describing the proto-typical 500 hPa height fields...To surmount the deficiency in studying the multiple equilibrium states in the atmosphere motion with highly truncated spectral method, the trigonometric functions for describing the proto-typical 500 hPa height fields and the outgoing long wave radiation (OLR) fields are retrieved re-spectively for the northward bias and the southward bias years of the western Pacific subtropical high with corresponding observational data and the optimum subset retrieval method for four fac-tors. Then the evolution mechanism of the western Pacific subtropical high is studied by means of multiple equilibrium state theory. The results show that the cause of inducing the abnormal location of the western Pacific subtropical high is differences in the early external thermal forcing, which evoke different waveforms in atmosphere. If the early meridional and zonal external thermal forcing differences are stronger, there are wave-mean flow and wave-wave interactions between the response waveforms in atmosphere. In such a case, the western Pacific subtropical high shifts northward obviously. On the contrary, when the early meridional and zonal external thermal forcing differences are weaker, there is no wave-mean flow interaction between the response waveforms in atmosphere, and accordingly the position of the western Pacific subtropical high oscillates with the external thermal forcing oscillation, and is on the south of normal.展开更多
Orbital-free density functional theory(OFDFT)is a quantum mechanical method in which the energy of a material depends only on the electron density and ionic positions.We examine some popular algorithms for optimizing ...Orbital-free density functional theory(OFDFT)is a quantum mechanical method in which the energy of a material depends only on the electron density and ionic positions.We examine some popular algorithms for optimizing the electron density distribution in OFDFT,explaining their suitability,benchmarking their performance,and suggesting some improvements.We start by describing the constrained optimization problem that encompasses electron density optimization.Next,we discuss the line search(including Wolfe conditions)and the nonlinear conjugate gradient and truncated Newton algorithms,as implemented in our open source OFDFT code.We finally focus on preconditioners derived from OFDFT energy functionals.Newlyderived preconditioners are successful for simulation cells of all sizes without regions of low electron-density and for small simulation cells with such regions.展开更多
In a variety of modern applications there arises a need to tessellate the domain into representative regions,called Voronoi cells.A particular type of such tessellations,called centroidal Voronoi tessellations or CVTs...In a variety of modern applications there arises a need to tessellate the domain into representative regions,called Voronoi cells.A particular type of such tessellations,called centroidal Voronoi tessellations or CVTs,are in big demand due to their optimality properties important for many applications.The availability of fast and reliable algorithms for their construction is crucial for their successful use in practical settings.This paper introduces a new multigrid algorithm for constructing CVTs that is based on the MG/Opt algorithm that was originally designed to solve large nonlinear optimization problems.Uniform convergence of the new method and its speedup comparing to existing techniques are demonstrated for linear and nonlinear densities for several 1d and 2d problems,and O(k)complexity estimation is provided for a problem with k generators.展开更多
In this paper, under the Painleve-integrable condition, the auto-Biicklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various met...In this paper, under the Painleve-integrable condition, the auto-Biicklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method, truncated Painleve expansion method, extendedvariable-coefficient balancing-act method, and Lax pair. Additionally, the compatibility for the truncated Painleve expansion method and extended variable-coetfficient balancing-act method is testified.展开更多
In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dt C model, a stochastic volatility(SV) model assuming that the stock return has a doubly ...In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dt C model, a stochastic volatility(SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis for the parameters is made and Markov Chain Monte Carlo(MCMC) is used for computing the posterior estimates of the model parameters and forecasting in the empirical application of Shanghai Stock Exchange Composite Index(SSECI) with respect to the proposed SV-dt C model and two classic SV-N(SV model with Normal distribution)and SV-T(SV model with Student-t distribution) models. The empirical analysis shows that the proposed SV-dt C model has better performance by model checking, including independence test(Projection correlation test), Kolmogorov-Smirnov test(K-S test) and Q-Q plot. Additionally, deviance information criterion(DIC) also shows that the proposed model has a significant improvement in model fit over the others.展开更多
The maximum predicting error of the commonly used passive truncated mooring system method may reach 30%due to the difference of dynamic characteristics between the truncated and full-depth mooring line.In this paper,t...The maximum predicting error of the commonly used passive truncated mooring system method may reach 30%due to the difference of dynamic characteristics between the truncated and full-depth mooring line.In this paper,the experimental strategy called three-parameter(displacement,velocity and acceleration)active control method at the truncated point of mooring line is established to implement the synchronous equivalent of motion and force,and the realization of active truncated mooring system for model test is studied theoretically.The influences of threeparameter and one-parameter(displacement)active control strategies on the compensation effects are compared by numerical study.The results show that the established three-parameter active control method can feasibly realize the static and dynamic equivalent of truncated and full-depth mooring system,laying a good foundation for the following physical model test of active truncated mooring system.展开更多
文摘How to calculate the highly oscillatory integrals is the bottleneck that restraints the research of light wave and electromagnetic wave＇s propagation and scattering. Levin method is a classical quadrature method for this type of integrals. Unfortunately it is susceptible to the system of linear equations＇ ill-conditioned behavior. We bring forward a universal quadrature method in this paper, which adopts Chebyshev differential matrix to solve the ordinary differential equation （ODE）. This method can not only obtain the indefinite integral＇ function values directly, but also make the system of linear equations well-conditioned for general oscillatory integrals. Furthermore, even if the system of linear equations in our method is ill-conditioned, TSVD method can be adopted to solve them properly and eventually obtain accurate integral results, thus making a breakthrough in Levin method＇s susceptivity to the system of linear equations＇ ill-conditioned behavior.
基金Supported by the National Natural Science Foundation of China(Grant No.12001288)。
文摘In this paper,we prove two supercongruences conjectured by Z.-W.Sun via the Wilf-Zeilberger method.One of them is,for any prime p>3,4F3[7/6 1/2 1/2 1/2 1/6 1 1]-1/8]-1/2≡p(-2/p)+p^(3)/4(2/p)Ep-3 (mod p^(4))where(·/p)stands for the Legendre symbol,and E_(n)is the n-th Euler number.
基金the National Natural Science Foundation of China(62273003,12271003)the Open Project of Anhui Province Center for International Research of Intelligent Control of High-end Equipment(IRICHE-01)+4 种基金the Natural Science Foundation of Universities in Anhui Province(2022AH050993)the Startup Foundation for Introduction Talent of AHPU(2021YQQ058)the Royal Society(WM160014,Royal Society Wolfson Research Merit Award)the Royal Society and the Newton Fund(NA160317,Royal Society-Newton Advanced Fellowship)the Royal Society of Edinburgh(RSE1832)for their financial support.
文摘This work is concerned with the convergence and stability of the truncated EulerMaruyama(EM)method for super-linear stochastic differential delay equations(SDDEs)with time-variable delay and Poisson jumps.By constructing appropriate truncated functions to control the super-linear growth of the original coefficients,we present two types of the truncated EM method for such jump-diffusion SDDEs with time-variable delay,which is proposed to be approximated by the value taken at the nearest grid points on the left of the delayed argument.The first type is proved to have a strong convergence order which is arbitrarily close to 1/2 in mean-square sense,under the Khasminskii-type,global monotonicity with U function and polynomial growth conditions.The second type is convergent in q-th(q<2)moment under the local Lipschitz plus generalized Khasminskii-type conditions.In addition,we show that the partially truncated EM method preserves the mean-square and H∞stabilities of the true solutions.Lastly,we carry out some numerical experiments to support the theoretical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.12261026,11961012,12201149)by the Natural Science Foundation of Guangxi Province(Grant Nos.2016GXNSFAA380074,2023GXNSFAA026067)+4 种基金by the Innovation Project of GUET Graduate Education(Grant No.2022YXW01)by the GUET Graduate Innovation Project(Grant No.2022YCXS142)by the Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(Grant Nos.YQ23103,YQ21103,YQ22106)by the Special Fund for Science and Technological Bases and Talents of Guangxi(Grant No.2021AC06001)by the Guizhou Science and Technology Program of Projects(Grant No.ZK2021G339)。
文摘The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,etc.In this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et al.is presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence rate.Numerical experiments are provided to illustrate the efficiency of the proposed method.Comparisons with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach.
基金supported by the Natural Science Foundation of Beijing Municipality(Grant No.1192013).
文摘Convergence of modified truncated Euler-Maruyama(MTEM)method for stochastic differential equations(SDEs)with(1/2+α)-Holder continuous diffusion coefficients are investigated in this paper.We prove that the MTEM method for SDE converges to the exact solution in L9 sense under given conditions.Two examples are provided to support our conclusions.
基金This work is supported by the National Natural Science Foundation of China(No.11671113)the National Postdoctoral Program for Innovative Talents(No.BX20180347).
文摘In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition.The order of convergence is obtained.Moreover,we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs.Numerical examples are provided to support our conclusions.
基金Supported by the National Natural Science Foundation of Zhejiang Province under Grant No.LZ15A050001the National Natural Science Foundation of China under Grant No.11675146
文摘The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.
文摘In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear systems. The periodic solution of Duffing equation is calculated by means of our method.
文摘Recently,the authors of[Commun.Theor.Phys.56(2011)397]made a number of useful observations on Exp-function method.In this study,we focus on another vital issue,namely,the misleading results of double Exp-function method.
基金This work was supported by the National Key Program for Developing Basic Research (Grant No. 1998040900) and the National Natural Science Foundation of China (Grant No. D49965001).
文摘To surmount the deficiency in studying the multiple equilibrium states in the atmosphere motion with highly truncated spectral method, the trigonometric functions for describing the proto-typical 500 hPa height fields and the outgoing long wave radiation (OLR) fields are retrieved re-spectively for the northward bias and the southward bias years of the western Pacific subtropical high with corresponding observational data and the optimum subset retrieval method for four fac-tors. Then the evolution mechanism of the western Pacific subtropical high is studied by means of multiple equilibrium state theory. The results show that the cause of inducing the abnormal location of the western Pacific subtropical high is differences in the early external thermal forcing, which evoke different waveforms in atmosphere. If the early meridional and zonal external thermal forcing differences are stronger, there are wave-mean flow and wave-wave interactions between the response waveforms in atmosphere. In such a case, the western Pacific subtropical high shifts northward obviously. On the contrary, when the early meridional and zonal external thermal forcing differences are weaker, there is no wave-mean flow interaction between the response waveforms in atmosphere, and accordingly the position of the western Pacific subtropical high oscillates with the external thermal forcing oscillation, and is on the south of normal.
基金We would like to thank the National Defense Science and Engineering Graduate Fellowship program(L.H.)and the National Science Foundation(E.A.C.)for funding.
文摘Orbital-free density functional theory(OFDFT)is a quantum mechanical method in which the energy of a material depends only on the electron density and ionic positions.We examine some popular algorithms for optimizing the electron density distribution in OFDFT,explaining their suitability,benchmarking their performance,and suggesting some improvements.We start by describing the constrained optimization problem that encompasses electron density optimization.Next,we discuss the line search(including Wolfe conditions)and the nonlinear conjugate gradient and truncated Newton algorithms,as implemented in our open source OFDFT code.We finally focus on preconditioners derived from OFDFT energy functionals.Newlyderived preconditioners are successful for simulation cells of all sizes without regions of low electron-density and for small simulation cells with such regions.
基金supported by the U.S.Department of Energy under Award DE-SC-0001691support from the ORAU Ralph E.Powe Junior Faculty Enhancement Award and from the National Science Foundation under the grants DMS-1056821 and DMS-0915013.
文摘In a variety of modern applications there arises a need to tessellate the domain into representative regions,called Voronoi cells.A particular type of such tessellations,called centroidal Voronoi tessellations or CVTs,are in big demand due to their optimality properties important for many applications.The availability of fast and reliable algorithms for their construction is crucial for their successful use in practical settings.This paper introduces a new multigrid algorithm for constructing CVTs that is based on the MG/Opt algorithm that was originally designed to solve large nonlinear optimization problems.Uniform convergence of the new method and its speedup comparing to existing techniques are demonstrated for linear and nonlinear densities for several 1d and 2d problems,and O(k)complexity estimation is provided for a problem with k generators.
基金supported by the Key Project of the Ministry of Education under Grant No.106033Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024+2 种基金Ministry of Education,National Natural Science Foundation of China under Grant Nos.60372095 and 60772023Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronautics,and National Basic Research Program of China (973 Program) under Grant No.2005CB321901
文摘In this paper, under the Painleve-integrable condition, the auto-Biicklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method, truncated Painleve expansion method, extendedvariable-coefficient balancing-act method, and Lax pair. Additionally, the compatibility for the truncated Painleve expansion method and extended variable-coetfficient balancing-act method is testified.
基金supported by the Open Fund of State Key Laboratory of New Metal Materials,Beijing University of Science and Technology (No.2022Z-18)。
文摘In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dt C model, a stochastic volatility(SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis for the parameters is made and Markov Chain Monte Carlo(MCMC) is used for computing the posterior estimates of the model parameters and forecasting in the empirical application of Shanghai Stock Exchange Composite Index(SSECI) with respect to the proposed SV-dt C model and two classic SV-N(SV model with Normal distribution)and SV-T(SV model with Student-t distribution) models. The empirical analysis shows that the proposed SV-dt C model has better performance by model checking, including independence test(Projection correlation test), Kolmogorov-Smirnov test(K-S test) and Q-Q plot. Additionally, deviance information criterion(DIC) also shows that the proposed model has a significant improvement in model fit over the others.
基金financially supported by the National Natural Science Foundation of China(Grant No.51979030)the Natural Science Foundation of Liaoning Province(Grant No.2021-KF-16-01)the Fundamental Research Funds for the Central Universities。
文摘The maximum predicting error of the commonly used passive truncated mooring system method may reach 30%due to the difference of dynamic characteristics between the truncated and full-depth mooring line.In this paper,the experimental strategy called three-parameter(displacement,velocity and acceleration)active control method at the truncated point of mooring line is established to implement the synchronous equivalent of motion and force,and the realization of active truncated mooring system for model test is studied theoretically.The influences of threeparameter and one-parameter(displacement)active control strategies on the compensation effects are compared by numerical study.The results show that the established three-parameter active control method can feasibly realize the static and dynamic equivalent of truncated and full-depth mooring system,laying a good foundation for the following physical model test of active truncated mooring system.
