This article introduces the current situation of the smart then describes the relationship of meter reliability characteristics meter＇s reliability and the failure mechanisms at first, and combined with its Bathtub C...This article introduces the current situation of the smart then describes the relationship of meter reliability characteristics meter＇s reliability and the failure mechanisms at first, and combined with its Bathtub Curve. It also introduces both the feasible failure tree model for meter lifecycle prediction based on actual experiences and meter reliability prediction methodology by SN 29500 norms based on this model. This article also brings forward that it is necessary that the ＂Learning Factor＂ shall be adopted in meter reliability prediction for new materials, new process, and customized parts by referring to GJB/Z299C. Thereafter, this article also tries to apply IEC 62059 and JB/T 50070 to introduce the feasible method for the lifecycle prediction result verification by accelerated lifecycle test. Furthermore, the article also explores ways to increase the firmware reliability in smart meter.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
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 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
In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coef...In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.展开更多
In this paper,our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients.When the diff...In this paper,our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients.When the diffusion coefficient is polynomially growing or linearly growing,the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval[0.T],respectively.In both situations,the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required.Two examples are provided to illustrate the theory.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
文摘This article introduces the current situation of the smart then describes the relationship of meter reliability characteristics meter＇s reliability and the failure mechanisms at first, and combined with its Bathtub Curve. It also introduces both the feasible failure tree model for meter lifecycle prediction based on actual experiences and meter reliability prediction methodology by SN 29500 norms based on this model. This article also brings forward that it is necessary that the ＂Learning Factor＂ shall be adopted in meter reliability prediction for new materials, new process, and customized parts by referring to GJB/Z299C. Thereafter, this article also tries to apply IEC 62059 and JB/T 50070 to introduce the feasible method for the lifecycle prediction result verification by accelerated lifecycle test. Furthermore, the article also explores ways to increase the firmware reliability in smart meter.
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.
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 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supported by the National Natural Science Foundation of China(Nos.11671113,12071101).
文摘In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.
文摘In this paper,our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients.When the diffusion coefficient is polynomially growing or linearly growing,the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval[0.T],respectively.In both situations,the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required.Two examples are provided to illustrate the theory.
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.
