By the best approximation theory, it is first proved that the SISO （single-input single-output） linear Takagi-Sugeno （TS） fuzzy systems can approximate an arbitrary polynomial which, according to Weierstrass appro...By the best approximation theory, it is first proved that the SISO （single-input single-output） linear Takagi-Sugeno （TS） fuzzy systems can approximate an arbitrary polynomial which, according to Weierstrass approximation theorem, can uniformly approximate any continuous functions on the compact domain. Then new sufficient conditions for general linear SISO TS fuzzy systems as universal approximators are obtained. Formulae are derived to calculate the number of input fuzzy sets to satisfy the given approximation accuracy. Then the presented result is compared with the existing literature＇s results. The comparison shows that the presented result needs less input fuzzy sets, which can simplify the design of the fuzzy system, and examples are given to show its effectiveness.展开更多
Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power sta...Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power stations).To solve the problem,we propose an energy harvesting based task scheduling and resource management framework to provide robust and low-cost edge computing services for smart grid.First,we formulate an energy consumption minimization problem with regard to task offloading,time switching,and resource allocation for mobile devices,which can be decoupled and transformed into a typical knapsack problem.Then,solutions are derived by two different algorithms.Furthermore,we deploy renewable energy and energy storage units at edge servers to tackle intermittency and instability problems.Finally,we design an energy management algorithm based on sampling average approximation for edge computing servers to derive the optimal charging/discharging strategies,number of energy storage units,and renewable energy utilization.The simulation results show the efficiency and superiority of our proposed framework.展开更多
Wigner-Ville distribution(WVD)is widely used in the field of signal processing due to its excellent time-frequency(TF)concentration.However,WVD is severely limited by the cross-term when working with multicomponent si...Wigner-Ville distribution(WVD)is widely used in the field of signal processing due to its excellent time-frequency(TF)concentration.However,WVD is severely limited by the cross-term when working with multicomponent signals.In this paper,we analyze the property differences between auto-term and cross-term in the one-dimensional sequence and the two-dimensional plane and approximate entropy and Rényi entropy are employed to describe them,respectively.Based on this information,we propose a new method to achieve adaptive cross-term removal by combining seeded region growing.Compared to other methods,the new method can achieve cross-term removal without decreasing the TF concentration of the auto-term.Simulation and experimental data processing results show that the method is adaptive and is not constrained by the type or distribution of signals.And it performs well in low signal-to-noise ratio environments.展开更多
This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV i...This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.展开更多
Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons.Previous ...Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons.Previous quantitative analyses often simplified the chorus dispersion relation by using the cold plasma assumption.However,the applicability of the cold plasma assumption is doubtful,especially during geomagnetic disturbances.We here present a systematic statistical analysis on the validity of the cold plasma dispersion relation of chorus waves based on observations from the Van Allen Probes over the period from 2012 to 2018.The statistical results show that the observed magnetic field intensities deviate substantially from those calculated from the cold plasma dispersion relation and that they become more pronounced with an increase in geomagnetic activity or a decrease in background plasma density.The region with large deviations is mainly concentrated in the nightside and expands in both the radial and azimuthal directions as the geomagnetic activity increases or the background plasma density decreases.In addition,the bounce-averaged electron scattering rates are computed by using the observed and cold plasma dispersion relation of chorus waves.Compared with usage of the cold plasma dispersion relation,usage of the observed dispersion relation considerably lowers the minimum resonant energy of electrons and lowers the scattering rates of electrons above tens of kiloelectronvolts but enhances those below.Furthermore,these differences are more pronounced with the enhancement of geomagnetic activity or the decrease in background plasma density.展开更多
In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional...LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.展开更多
Suppose thatλ_(1),λ_(2),λ_(3),λ_(4),λ_(5)are nonzero real numbers,not all of the same sign,andλ_(1)/λ_(2)is irrational and algebraic.Let V be a well-spaced sequence,δ>0.In this paper,it is proved that,for ...Suppose thatλ_(1),λ_(2),λ_(3),λ_(4),λ_(5)are nonzero real numbers,not all of the same sign,andλ_(1)/λ_(2)is irrational and algebraic.Let V be a well-spaced sequence,δ>0.In this paper,it is proved that,for anyε>0,the number of v∈V with v≤N such that the following inequality|λ_(1)p_(1)~2+λ_(2)p_(2)~2+λ_(3)p_(3)~4+λ_(4)p_(4)~4+λ_5p_5~4-v|<v^(-δ)has no solution in prime variables p_(1),p_(2),p_(3),p_(4),p_(5)does not exceed O(N^(29/32+2δ+ε)).展开更多
This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are ...The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are computationally expensive and scarce.We propose a novel hyper-gradient type method with a warm-start strategy to address this challenge.Particularly,we first use a Taylor expansion-based approach to obtain a good initial point.Then we apply a hyper-gradient descent method with an ex-plicit approximate hyper-gradient.We establish the convergence results of our algorithm theoretically.Furthermore,when the follower employs the least squares loss function,our method is shown to reach an e-stationary point by solving quadratic subproblems.Numerical experiments show our algorithms are empirically orders of magnitude faster than the state-of-the-art.展开更多
In this work,we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution.As our first contr...In this work,we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution.As our first contribution,we establish non-negativity,boundedness of some solution components,existence globally in time,and uniqueness on a time interval[0,T]for an arbitrary T>0 for the time-continuous problem which extends known results of Kirschner’s model in the literature.As our second analytical result,we establish different equilibrium states and examine their stability properties in the time-continuous setting or discuss some numerical tools to evaluate this question.Our third contribution is the formulation of a non-standard finite-difference method which preserves non-negativity,boundedness of some time-discrete solution components,equilibria,and their stabilities.As our final theoretical result,we prove linear convergence of our non-standard finite-difference-formulation towards the time-continuous solution.Conclusively,we present numerical examples to illustrate our theoretical findings.展开更多
With the growing demand for compute-intensive applications such as artificial intelligence(AI)and video processing,traditional reconfigurable array processors fail to meet the requirements of high-performance computin...With the growing demand for compute-intensive applications such as artificial intelligence(AI)and video processing,traditional reconfigurable array processors fail to meet the requirements of high-performance computing and related domains,primarily due to their high power consumption and low energy efficiency.To address this limitation,this paper proposes an accuracy-adaptive approxi-mate reconfigurable array architecture featuring preset dual thresholds and support for four computa-tional accuracy levels,enabling flexible adaptation to diverse application needs.The architecture in-tegrates a self-adaptive mechanism that dynamically adjusts computational precision based on real-time error threshold feedback.To evaluate the proposed architecture,the you only look once version 5(YOLOv5)deep neural network algorithm is parallelized and deployed on the approximate recon-figurable array.Experimental results demonstrate that the architecture achieves an 18.93%reduc-tion in power consumption compared with conventional reconfigurable structures operating in full-pre-cision mode.Additionally,the design exhibits superior energy efficiency and reduced computational resource utilization,thereby significantly enhancing the overall performance and applicability of reconfigurable array processors in power-sensitive scenarios.展开更多
In recent years,variable-order fractional partial differential equations have attracted growing interest due to their enhanced ability tomodel complex physical phenomena withmemory and spatial heterogeneity.However,ex...In recent years,variable-order fractional partial differential equations have attracted growing interest due to their enhanced ability tomodel complex physical phenomena withmemory and spatial heterogeneity.However,existing numerical methods often struggle with the computational challenges posed by such equations,especially in nonlinear,multi-term formulations.This study introduces two hybrid numerical methods—the Linear-Sine and Cosine(L1-CAS)and fast-CAS schemes—for solving linear and nonlinear multi-term Caputo variable-order(CVO)fractional partial differential equations.These methods combine CAS wavelet-based spatial discretization with L1 and fast algorithms in the time domain.A key feature of the approach is its ability to efficiently handle fully coupled spacetime variable-order derivatives and nonlinearities through a second-order interpolation technique.In addition,we derive CAS wavelet operational matrices for variable-order integration and for boundary value problems,forming the foundation of the spatial discretization.Numerical experiments confirm the accuracy,stability,and computational efficiency of the proposed methods.展开更多
We consider the diffusion asymptotics of a coupled model arising in radiative transfer in a unit ball inℝ3 with one-speed velocity.The model consists of a steady kinetic equation satisfied by the specific intensity of...We consider the diffusion asymptotics of a coupled model arising in radiative transfer in a unit ball inℝ3 with one-speed velocity.The model consists of a steady kinetic equation satisfied by the specific intensity of radiation coupled with a nonhomogeneous elliptic equation satisfied by the material temperature.For the O(ϵ)boundary data of the intensity of the radiation and the suitable small boundary data of the temperature,we prove the existence,uniqueness and the nonequilibrium diffusion limit of solutions to the boundary value problem for the coupled model.展开更多
We prove that the post-Newtonian time-dependent metric of the self-gravitating and collapsing infinitely-thin spherical shell does satisfy Einstein field equations to the corresponding order.Meanwhile, the leading-ord...We prove that the post-Newtonian time-dependent metric of the self-gravitating and collapsing infinitely-thin spherical shell does satisfy Einstein field equations to the corresponding order.Meanwhile, the leading-order components of the thin spherical shell's energy-momentum tensor are recovered.展开更多
Engineering tests can yield inaccurate data due to instrument errors,human factors,and environmental interference,introducing uncertainty in numerical model updating.This study employs the probability-box(p-box)method...Engineering tests can yield inaccurate data due to instrument errors,human factors,and environmental interference,introducing uncertainty in numerical model updating.This study employs the probability-box(p-box)method for representing observational uncertainty and develops a two-step approximate Bayesian computation(ABC)framework using time-series data.Within the ABC framework,Euclidean and Bhattacharyya distances are employed as uncertainty quantification metrics to delineate approximate likelihood functions in the initial and subsequent steps,respectively.A novel variational Bayesian Monte Carlo method is introduced to efficiently apply the ABC framework amidst observational uncertainty,resulting in rapid convergence and accurate parameter estimation with minimal iterations.The efficacy of the proposed updating strategy is validated by its application to a shear frame model excited by seismic wave and an aviation pump force sensor for thermal output analysis.The results affirm the efficiency,robustness,and practical applicability of the proposed method.展开更多
In the present paper,we obtain the converse results of approximation of a newly introduced genuine Bernstein-Durrmeyer operators in movable interval.We also get the moments properties of an auxiliary operator which ha...In the present paper,we obtain the converse results of approximation of a newly introduced genuine Bernstein-Durrmeyer operators in movable interval.We also get the moments properties of an auxiliary operator which has its own independent values.The moments of the auxiliary operators play important roles in establishing the main result(Theorem 4).展开更多
Let M_(n,p)=(X_(i,k))_(n×p)be an n×p random matrix whose p columns X^((1)),...,X^((p))are an n-dimensional i.i.d.random sample of size p from 1-dependent Gaussian populations.Instead of investigating the spe...Let M_(n,p)=(X_(i,k))_(n×p)be an n×p random matrix whose p columns X^((1)),...,X^((p))are an n-dimensional i.i.d.random sample of size p from 1-dependent Gaussian populations.Instead of investigating the special case where p and n are comparable,we consider a much more general case in which log n=o(p^(1/3)).We prove that the maximum interpoint distance Mn=max{|X_(i)-X_(j)|;1≤i<j≤n}converges to an extreme-value distribution,where X_(i)and X_(j)denote the i-th and j-th row of M_(n,p),respectively.The proofs are completed by using the Chen-Stein Poisson approximation method and the moderation deviation principle.展开更多
This work presents an adaptive tracking guidance method for robotic fishes. The scheme enables robots to suppress external interference and eliminate motion jitter. An adaptive integral surge line-of-sight guidance ru...This work presents an adaptive tracking guidance method for robotic fishes. The scheme enables robots to suppress external interference and eliminate motion jitter. An adaptive integral surge line-of-sight guidance rule is designed to eliminate dynamics interference and sideslip issues. Limited-time yaw and surge speed observers are reported to fit disturbance variables in the model. The approximation values can compensate for the system's control input and improve the robots' tracking accuracy.Moreover, this work develops a terminal sliding mode controller and third-order differential processor to determine the rotational torque and reduce the robots' run jitter. Then, Lyapunov's theory proves the uniform ultimate boundedness of the proposed method. Simulation and physical experiments confirm that the technology improves the tracking error convergence speed and stability of robotic fishes.展开更多
文摘By the best approximation theory, it is first proved that the SISO （single-input single-output） linear Takagi-Sugeno （TS） fuzzy systems can approximate an arbitrary polynomial which, according to Weierstrass approximation theorem, can uniformly approximate any continuous functions on the compact domain. Then new sufficient conditions for general linear SISO TS fuzzy systems as universal approximators are obtained. Formulae are derived to calculate the number of input fuzzy sets to satisfy the given approximation accuracy. Then the presented result is compared with the existing literature＇s results. The comparison shows that the presented result needs less input fuzzy sets, which can simplify the design of the fuzzy system, and examples are given to show its effectiveness.
基金supported in part by the National Natural Science Foundation of China under Grant No.61473066in part by the Natural Science Foundation of Hebei Province under Grant No.F2021501020+2 种基金in part by the S&T Program of Qinhuangdao under Grant No.202401A195in part by the Science Research Project of Hebei Education Department under Grant No.QN2025008in part by the Innovation Capability Improvement Plan Project of Hebei Province under Grant No.22567637H
文摘Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power stations).To solve the problem,we propose an energy harvesting based task scheduling and resource management framework to provide robust and low-cost edge computing services for smart grid.First,we formulate an energy consumption minimization problem with regard to task offloading,time switching,and resource allocation for mobile devices,which can be decoupled and transformed into a typical knapsack problem.Then,solutions are derived by two different algorithms.Furthermore,we deploy renewable energy and energy storage units at edge servers to tackle intermittency and instability problems.Finally,we design an energy management algorithm based on sampling average approximation for edge computing servers to derive the optimal charging/discharging strategies,number of energy storage units,and renewable energy utilization.The simulation results show the efficiency and superiority of our proposed framework.
基金Supported by the National Natural Science Foundation of China(62201171).
文摘Wigner-Ville distribution(WVD)is widely used in the field of signal processing due to its excellent time-frequency(TF)concentration.However,WVD is severely limited by the cross-term when working with multicomponent signals.In this paper,we analyze the property differences between auto-term and cross-term in the one-dimensional sequence and the two-dimensional plane and approximate entropy and Rényi entropy are employed to describe them,respectively.Based on this information,we propose a new method to achieve adaptive cross-term removal by combining seeded region growing.Compared to other methods,the new method can achieve cross-term removal without decreasing the TF concentration of the auto-term.Simulation and experimental data processing results show that the method is adaptive and is not constrained by the type or distribution of signals.And it performs well in low signal-to-noise ratio environments.
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-RP23066).
文摘This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.
基金supported by the National Natural Science Foundation of China (NSFC) through Grant Number 42074193
文摘Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons.Previous quantitative analyses often simplified the chorus dispersion relation by using the cold plasma assumption.However,the applicability of the cold plasma assumption is doubtful,especially during geomagnetic disturbances.We here present a systematic statistical analysis on the validity of the cold plasma dispersion relation of chorus waves based on observations from the Van Allen Probes over the period from 2012 to 2018.The statistical results show that the observed magnetic field intensities deviate substantially from those calculated from the cold plasma dispersion relation and that they become more pronounced with an increase in geomagnetic activity or a decrease in background plasma density.The region with large deviations is mainly concentrated in the nightside and expands in both the radial and azimuthal directions as the geomagnetic activity increases or the background plasma density decreases.In addition,the bounce-averaged electron scattering rates are computed by using the observed and cold plasma dispersion relation of chorus waves.Compared with usage of the cold plasma dispersion relation,usage of the observed dispersion relation considerably lowers the minimum resonant energy of electrons and lowers the scattering rates of electrons above tens of kiloelectronvolts but enhances those below.Furthermore,these differences are more pronounced with the enhancement of geomagnetic activity or the decrease in background plasma density.
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
文摘LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.
基金Supported by NSFC(Nos.12301006,12471009,12071238,11901566,12001047,11971476)Beijing Natural Science Foundation(No.1242003)。
文摘Suppose thatλ_(1),λ_(2),λ_(3),λ_(4),λ_(5)are nonzero real numbers,not all of the same sign,andλ_(1)/λ_(2)is irrational and algebraic.Let V be a well-spaced sequence,δ>0.In this paper,it is proved that,for anyε>0,the number of v∈V with v≤N such that the following inequality|λ_(1)p_(1)~2+λ_(2)p_(2)~2+λ_(3)p_(3)~4+λ_(4)p_(4)~4+λ_5p_5~4-v|<v^(-δ)has no solution in prime variables p_(1),p_(2),p_(3),p_(4),p_(5)does not exceed O(N^(29/32+2δ+ε)).
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
文摘The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are computationally expensive and scarce.We propose a novel hyper-gradient type method with a warm-start strategy to address this challenge.Particularly,we first use a Taylor expansion-based approach to obtain a good initial point.Then we apply a hyper-gradient descent method with an ex-plicit approximate hyper-gradient.We establish the convergence results of our algorithm theoretically.Furthermore,when the follower employs the least squares loss function,our method is shown to reach an e-stationary point by solving quadratic subproblems.Numerical experiments show our algorithms are empirically orders of magnitude faster than the state-of-the-art.
文摘In this work,we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution.As our first contribution,we establish non-negativity,boundedness of some solution components,existence globally in time,and uniqueness on a time interval[0,T]for an arbitrary T>0 for the time-continuous problem which extends known results of Kirschner’s model in the literature.As our second analytical result,we establish different equilibrium states and examine their stability properties in the time-continuous setting or discuss some numerical tools to evaluate this question.Our third contribution is the formulation of a non-standard finite-difference method which preserves non-negativity,boundedness of some time-discrete solution components,equilibria,and their stabilities.As our final theoretical result,we prove linear convergence of our non-standard finite-difference-formulation towards the time-continuous solution.Conclusively,we present numerical examples to illustrate our theoretical findings.
基金Supported by the National Science and Technology Major Project(No.2022ZD0119001)the National Natural Science Foundation of China(No.61834005,61802304)the Key R&D Program Projects in Shaanxi Province(No.2024GX-YBXM-100).
文摘With the growing demand for compute-intensive applications such as artificial intelligence(AI)and video processing,traditional reconfigurable array processors fail to meet the requirements of high-performance computing and related domains,primarily due to their high power consumption and low energy efficiency.To address this limitation,this paper proposes an accuracy-adaptive approxi-mate reconfigurable array architecture featuring preset dual thresholds and support for four computa-tional accuracy levels,enabling flexible adaptation to diverse application needs.The architecture in-tegrates a self-adaptive mechanism that dynamically adjusts computational precision based on real-time error threshold feedback.To evaluate the proposed architecture,the you only look once version 5(YOLOv5)deep neural network algorithm is parallelized and deployed on the approximate recon-figurable array.Experimental results demonstrate that the architecture achieves an 18.93%reduc-tion in power consumption compared with conventional reconfigurable structures operating in full-pre-cision mode.Additionally,the design exhibits superior energy efficiency and reduced computational resource utilization,thereby significantly enhancing the overall performance and applicability of reconfigurable array processors in power-sensitive scenarios.
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korean government(MSIT)(NRF-2021R1A2C1011817)the BK21 Program(Next Generation Education Program for Mathematical Sciences,4299990414089)funded by the Ministry of Education(MOE,Republic of Korea).
文摘In recent years,variable-order fractional partial differential equations have attracted growing interest due to their enhanced ability tomodel complex physical phenomena withmemory and spatial heterogeneity.However,existing numerical methods often struggle with the computational challenges posed by such equations,especially in nonlinear,multi-term formulations.This study introduces two hybrid numerical methods—the Linear-Sine and Cosine(L1-CAS)and fast-CAS schemes—for solving linear and nonlinear multi-term Caputo variable-order(CVO)fractional partial differential equations.These methods combine CAS wavelet-based spatial discretization with L1 and fast algorithms in the time domain.A key feature of the approach is its ability to efficiently handle fully coupled spacetime variable-order derivatives and nonlinearities through a second-order interpolation technique.In addition,we derive CAS wavelet operational matrices for variable-order integration and for boundary value problems,forming the foundation of the spatial discretization.Numerical experiments confirm the accuracy,stability,and computational efficiency of the proposed methods.
基金Zhang’s research was supported by the NSFC(12271423,12071044)the Fundamental Research Funds for the Central Universities(xzy012022005)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(23JSY026).
文摘We consider the diffusion asymptotics of a coupled model arising in radiative transfer in a unit ball inℝ3 with one-speed velocity.The model consists of a steady kinetic equation satisfied by the specific intensity of radiation coupled with a nonhomogeneous elliptic equation satisfied by the material temperature.For the O(ϵ)boundary data of the intensity of the radiation and the suitable small boundary data of the temperature,we prove the existence,uniqueness and the nonequilibrium diffusion limit of solutions to the boundary value problem for the coupled model.
基金supported in part by the National Natural Science Foundation of China under Grant No. 11973025the Program for New Century Excellent Talents in University under Grant No. NCET-10-0702。
文摘We prove that the post-Newtonian time-dependent metric of the self-gravitating and collapsing infinitely-thin spherical shell does satisfy Einstein field equations to the corresponding order.Meanwhile, the leading-order components of the thin spherical shell's energy-momentum tensor are recovered.
基金supported by the National Natural Science Foundation of China(Grant No.U23B20105).
文摘Engineering tests can yield inaccurate data due to instrument errors,human factors,and environmental interference,introducing uncertainty in numerical model updating.This study employs the probability-box(p-box)method for representing observational uncertainty and develops a two-step approximate Bayesian computation(ABC)framework using time-series data.Within the ABC framework,Euclidean and Bhattacharyya distances are employed as uncertainty quantification metrics to delineate approximate likelihood functions in the initial and subsequent steps,respectively.A novel variational Bayesian Monte Carlo method is introduced to efficiently apply the ABC framework amidst observational uncertainty,resulting in rapid convergence and accurate parameter estimation with minimal iterations.The efficacy of the proposed updating strategy is validated by its application to a shear frame model excited by seismic wave and an aviation pump force sensor for thermal output analysis.The results affirm the efficiency,robustness,and practical applicability of the proposed method.
文摘In the present paper,we obtain the converse results of approximation of a newly introduced genuine Bernstein-Durrmeyer operators in movable interval.We also get the moments properties of an auxiliary operator which has its own independent values.The moments of the auxiliary operators play important roles in establishing the main result(Theorem 4).
基金Supported by the National Natural Science Foundation of China(Grant Nos.1177117812171198)+2 种基金the Science and Technology Development Program of Jilin Province(Grant No.20210101467JC)the Technology Program of Jilin Educational Department During the“14th Five-Year”Plan Period(Grant No.JJKH20241239KJ)the Fundamental Research Funds for the Central Universities.
文摘Let M_(n,p)=(X_(i,k))_(n×p)be an n×p random matrix whose p columns X^((1)),...,X^((p))are an n-dimensional i.i.d.random sample of size p from 1-dependent Gaussian populations.Instead of investigating the special case where p and n are comparable,we consider a much more general case in which log n=o(p^(1/3)).We prove that the maximum interpoint distance Mn=max{|X_(i)-X_(j)|;1≤i<j≤n}converges to an extreme-value distribution,where X_(i)and X_(j)denote the i-th and j-th row of M_(n,p),respectively.The proofs are completed by using the Chen-Stein Poisson approximation method and the moderation deviation principle.
基金supported in part by the National Natural Science Foundation of China(62303117,T2325018,92367109)the Xiangjiang Scholar Program(XJ2023018)+2 种基金the Key Laboratory of System Control and Information Processing(Scip20240108)the Aeronautical Science Foundation of China(20230001144001)Fujian Provincial Natural Science Foundation(2024J01130098)
文摘This work presents an adaptive tracking guidance method for robotic fishes. The scheme enables robots to suppress external interference and eliminate motion jitter. An adaptive integral surge line-of-sight guidance rule is designed to eliminate dynamics interference and sideslip issues. Limited-time yaw and surge speed observers are reported to fit disturbance variables in the model. The approximation values can compensate for the system's control input and improve the robots' tracking accuracy.Moreover, this work develops a terminal sliding mode controller and third-order differential processor to determine the rotational torque and reduce the robots' run jitter. Then, Lyapunov's theory proves the uniform ultimate boundedness of the proposed method. Simulation and physical experiments confirm that the technology improves the tracking error convergence speed and stability of robotic fishes.
