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
The integrated nested Laplace approximation(INLA)algorithm provides a computationally efficient approach for approximate Bayesian inference,overcoming the limitations of traditional Markov chain Monte Carlo(MCMC)metho...The integrated nested Laplace approximation(INLA)algorithm provides a computationally efficient approach for approximate Bayesian inference,overcoming the limitations of traditional Markov chain Monte Carlo(MCMC)methods.This paper reviews INLA algorithm and provides a systematic review of six key books that explore the theoretical foundations,practical implementations,and diverse applications of INLA.These six books cover spatial and spatio-temporal modelling,general Bayesian inference,SPDE-based spatial analysis,geospatial health data,regression modelling,and dynamic time series.In addition,these books highlight the versatility of INLA method in handling complex models while maintaining high computational efficiency.This paper begins with an introduction to the INLA method and algorithm,followed by a systematic review of six key publications in the field.展开更多
Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular s...Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular set functions attracts much attention since the 1970s.A large body of work has been done using approximation algorithms.When the dimension of the independent variable of the set function changes from one tok,it is called ak-submodular set function.Thek-submodular set function,a generalization of the classical submodular set function,arises in diverse fields with varied applications.In many practical scenarios,quantifying the degree of closeness to submodularity becomes essential,leading to concepts such as approximately submodular set functions and the diminishing-return(DR) ratio.This paper investigates ak-dimensional set function under matroid constraints,which may lack full submodularity.Instead,we focus on an approximately non-ksubmodular set function characterized by its DR ratio.Employing a greedy algorithmic approach,we derive an approximation guarantee for this problem.Notably,when the DR ratio is set to one,our results align with existing findings in the literature.Experimental results demonstrate the superiority of our algorithm over the baselines.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approxima...To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approximates the densest k-subgraphs of the entire graph through four steps:partitioning the large-scale dynamic graph,constructing a partial set of the densest k-subgraphs,heuristically merging the subgraph sets,and finally extracting the densest k-subgraphs.This approach significantly reduces the computational time for large-scale dynamic graphs while simultaneously improving the quality of the resulting subgraphs.This algorithm is applicable to various definitions of“density”and can accommodate diverse requirements on the number of edges.When integrated with existing static densest subgraph detection algorithms,it achieves scalability and computational efficiency.Theoretical analysis demonstrates that the optimal density of the densest k-subgraphs extracted by the proposed algorithm reaches 0.9.To evaluate the performance of the algorithm,experiments were conducted on four billion-scale datasets:Friendster,Orkut,YouTube,and DBLP.The results indicate that the proposed algorithm outperforms static methods in both runtime efficiency and subgraph quality on large-scale dynamic graphs.展开更多
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
LetΨ={ψn}n≥1 be an iterated function system(IFS)on[0,1]with attractor J.Associated with each x∈J,there is a sequence{ωn(x)}n≥1 consisting of integers,called the digit sequence of x,such that■((1))We revisit the...LetΨ={ψn}n≥1 be an iterated function system(IFS)on[0,1]with attractor J.Associated with each x∈J,there is a sequence{ωn(x)}n≥1 consisting of integers,called the digit sequence of x,such that■((1))We revisit the Borel-Bernstein theorem in a d-decaying Gauss-like IFS,and completely characterize the metrical properties of the set■whereΦ:ℕ→ℝis a positive function.展开更多
State constraints in nonlinear systems are commonly pursued by resorting to barrier functions,which enforce constraints over the entire duration of system operation.We propose a universal intermittent state-constraine...State constraints in nonlinear systems are commonly pursued by resorting to barrier functions,which enforce constraints over the entire duration of system operation.We propose a universal intermittent state-constrained solution,which not only offers flexibility by activating constraints just during specific time periods of interest to the user,but also successfully accommodates different types of constraint boundaries.The innovative shifting functions are proposed to facilitate seamless transitions between constrained and unconstrained operational phases,resulting in more user-friendly design and implementation.By blending an improved shifting transformation into intermittent constraint design,we construct a universal barrier function upon the constrained states,with which our control strategy removes the limitations on constraint functions and completely obviates the feasibility conditions.Furthermore,a modified fuzzy approximator driven by the prediction error rather than the tracking error achieves decoupling of the control and estimation loops,which not only ensures the estimation performance,but also facilitates proof of stability.Finally,the effectiveness of the proposed scheme is assessed by numerical simulation.展开更多
Motivated by the recent experimental discovery of superconductivity in rhombohedral tetralayer graphene,we investigate the pairing mechanism arising from the density–density interactions within the random-phase appro...Motivated by the recent experimental discovery of superconductivity in rhombohedral tetralayer graphene,we investigate the pairing mechanism arising from the density–density interactions within the random-phase approximation.This approach successfully highlights the dominance of the chiral p-wave pairing between electrons with the same spin and valley index at low densities,while also predicting the superconducting range in agreement with experimental findings.Furthermore,we examine the characteristics of distinct superconducting regions:SC1 and SC2 exhibit chiral finite-momentum superconductivity with pronounced phase fluctuations,whereas SC4 displays zero-momentum spin-singlet superconductivity.展开更多
This paper presents a simplified design tool based on semi-analytical formulations to investigate the dynamic response of an immersed composite cylinder subjected to a far-field underwater explosion.The cylinder is si...This paper presents a simplified design tool based on semi-analytical formulations to investigate the dynamic response of an immersed composite cylinder subjected to a far-field underwater explosion.The cylinder is simply supported,fully submerged and filled with air inside.A classical shell theory using a Double Fourier series solution combined with the first-order Doubly Asymptotic Approximation(DAA1)formulation is adapted to model the fluid-structure interaction.An explicit non-standard finite difference scheme is applied to solve the coupled differential equations in time domain.The validity of DAA1 model is established by comparing the LS-DYNA/USA finite element results with existing experimental data from the literature.Then the proposed semi-analytical solutions are compared to the LS-DYNA/USA results,showing good correlation with a discrepancy of 7%for peak deflections and±9%for maximum stresses at the stand-off point for cylinders with relatively small length over radius ratios.Parametric studies examining the effect of different loading conditions,areal masses,and material configurations reveal that a large charge mass located far from the composite panel turns out to be more damaging than a small mass located nearby due to a broader pressure-time profile.Finally,the proposed model demonstrates a significant reduction in computation time,being approximately 30 times faster than its numerical counterpart,LS-DYNA/USA,making it a valuable tool for the preliminary design stages.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
Accurate satellite data assimilation under all-sky conditions requires enhanced parameterization of scattering properties for frozen hydrometeors in clouds.This study aims to develop a nonspherical scattering look-up ...Accurate satellite data assimilation under all-sky conditions requires enhanced parameterization of scattering properties for frozen hydrometeors in clouds.This study aims to develop a nonspherical scattering look-up table that contains the optical properties of five hydrometeor types—rain,cloud water,cloud ice,graupel,and snow—for the Advanced Radiative Transfer Modeling System(ARMS)at frequencies below 220 GHz.The discrete dipole approximation(DDA)method is employed to compute the single-scattering properties of solid cloud particles,modeling these particles as aggregated roughened bullet rosettes.The bulk optical properties of the cloud layer are derived by integrating the singlescattering properties with a modified Gamma size distribution,specifically for distributions with 18 effective radii.The bulk phase function is then projected onto a series of generalized spherical functions,applying the delta-M method for truncation.The results indicate that simulations using the newly developed nonspherical scattering look-up table exhibit significant consistency with observations under deep convection conditions.In contrast,assuming spherical solid cloud particles leads to excessive scattering at mid-frequency channels and insufficient scattering at high-frequency channels.This improvement in radiative transfer simulation accuracy for cloudy conditions will better support the assimilation of allsky microwave observations into numerical weather prediction models.·Frozen cloud particles were modeled as aggregates of bullet rosettes and the optical properties at microwave range were computed by DDA.·A complete process and technical details for constructing a look-up table of ARMS are provided.·The ARMS simulations generally show agreement with observations of MWTS and MWHS under typhoon conditions using the new look-up table.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
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 by the National Natural Science Foundation of China[grant number 12001266]the Humanities and Social Science Projects ofMinistry of Education of China[grant number 19YJCZH166]supported by the National Natural Science Foundation of China[grant numbers 12271168 and 12531013].
文摘The integrated nested Laplace approximation(INLA)algorithm provides a computationally efficient approach for approximate Bayesian inference,overcoming the limitations of traditional Markov chain Monte Carlo(MCMC)methods.This paper reviews INLA algorithm and provides a systematic review of six key books that explore the theoretical foundations,practical implementations,and diverse applications of INLA.These six books cover spatial and spatio-temporal modelling,general Bayesian inference,SPDE-based spatial analysis,geospatial health data,regression modelling,and dynamic time series.In addition,these books highlight the versatility of INLA method in handling complex models while maintaining high computational efficiency.This paper begins with an introduction to the INLA method and algorithm,followed by a systematic review of six key publications in the field.
基金Supported by the Natural Science Foundation of Shandong Province (No.ZR2023MA031)the Natural Science Foundation of China (No.12201619)。
文摘Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular set functions attracts much attention since the 1970s.A large body of work has been done using approximation algorithms.When the dimension of the independent variable of the set function changes from one tok,it is called ak-submodular set function.Thek-submodular set function,a generalization of the classical submodular set function,arises in diverse fields with varied applications.In many practical scenarios,quantifying the degree of closeness to submodularity becomes essential,leading to concepts such as approximately submodular set functions and the diminishing-return(DR) ratio.This paper investigates ak-dimensional set function under matroid constraints,which may lack full submodularity.Instead,we focus on an approximately non-ksubmodular set function characterized by its DR ratio.Employing a greedy algorithmic approach,we derive an approximation guarantee for this problem.Notably,when the DR ratio is set to one,our results align with existing findings in the literature.Experimental results demonstrate the superiority of our algorithm over the baselines.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金The National Natural Science Foundation of China(No.62172443).
文摘To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approximates the densest k-subgraphs of the entire graph through four steps:partitioning the large-scale dynamic graph,constructing a partial set of the densest k-subgraphs,heuristically merging the subgraph sets,and finally extracting the densest k-subgraphs.This approach significantly reduces the computational time for large-scale dynamic graphs while simultaneously improving the quality of the resulting subgraphs.This algorithm is applicable to various definitions of“density”and can accommodate diverse requirements on the number of edges.When integrated with existing static densest subgraph detection algorithms,it achieves scalability and computational efficiency.Theoretical analysis demonstrates that the optimal density of the densest k-subgraphs extracted by the proposed algorithm reaches 0.9.To evaluate the performance of the algorithm,experiments were conducted on four billion-scale datasets:Friendster,Orkut,YouTube,and DBLP.The results indicate that the proposed algorithm outperforms static methods in both runtime efficiency and subgraph quality on large-scale dynamic graphs.
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
基金supported by the Scientific Research Project of Colleges and Universities in Anhui Province(2024AH050016)supported by the NSFC(12171172).The third author was supported by the NSFC(12201476)the Fundamental Research Funds for the Central Universities.
文摘LetΨ={ψn}n≥1 be an iterated function system(IFS)on[0,1]with attractor J.Associated with each x∈J,there is a sequence{ωn(x)}n≥1 consisting of integers,called the digit sequence of x,such that■((1))We revisit the Borel-Bernstein theorem in a d-decaying Gauss-like IFS,and completely characterize the metrical properties of the set■whereΦ:ℕ→ℝis a positive function.
基金supported by the Fundamental Research Funds for the Central Universities(N2404005)the National Key Research and Development Program of China(2018YFA0702200)+2 种基金Liaoning Revitalization Talents Program(XLYC1801005)the National Natural Science Foundation of China(U23B20118)the Nature Science Foundation of Liaoning Province of China(2022JH25/10100008)。
文摘State constraints in nonlinear systems are commonly pursued by resorting to barrier functions,which enforce constraints over the entire duration of system operation.We propose a universal intermittent state-constrained solution,which not only offers flexibility by activating constraints just during specific time periods of interest to the user,but also successfully accommodates different types of constraint boundaries.The innovative shifting functions are proposed to facilitate seamless transitions between constrained and unconstrained operational phases,resulting in more user-friendly design and implementation.By blending an improved shifting transformation into intermittent constraint design,we construct a universal barrier function upon the constrained states,with which our control strategy removes the limitations on constraint functions and completely obviates the feasibility conditions.Furthermore,a modified fuzzy approximator driven by the prediction error rather than the tracking error achieves decoupling of the control and estimation loops,which not only ensures the estimation performance,but also facilitates proof of stability.Finally,the effectiveness of the proposed scheme is assessed by numerical simulation.
基金supported by the National Natural Science Foundation of China (Grant Nos.12447125,12234016,and 12174317)the New Cornerstone Science Foundation。
文摘Motivated by the recent experimental discovery of superconductivity in rhombohedral tetralayer graphene,we investigate the pairing mechanism arising from the density–density interactions within the random-phase approximation.This approach successfully highlights the dominance of the chiral p-wave pairing between electrons with the same spin and valley index at low densities,while also predicting the superconducting range in agreement with experimental findings.Furthermore,we examine the characteristics of distinct superconducting regions:SC1 and SC2 exhibit chiral finite-momentum superconductivity with pronounced phase fluctuations,whereas SC4 displays zero-momentum spin-singlet superconductivity.
基金supported by French Defense Innovation Agency(AID-DGA)(Grant No.ANR-21-ASM2-0002-02)in the framework of the Astrid Maturation SUCCESS+project,a collaborative French research project.
文摘This paper presents a simplified design tool based on semi-analytical formulations to investigate the dynamic response of an immersed composite cylinder subjected to a far-field underwater explosion.The cylinder is simply supported,fully submerged and filled with air inside.A classical shell theory using a Double Fourier series solution combined with the first-order Doubly Asymptotic Approximation(DAA1)formulation is adapted to model the fluid-structure interaction.An explicit non-standard finite difference scheme is applied to solve the coupled differential equations in time domain.The validity of DAA1 model is established by comparing the LS-DYNA/USA finite element results with existing experimental data from the literature.Then the proposed semi-analytical solutions are compared to the LS-DYNA/USA results,showing good correlation with a discrepancy of 7%for peak deflections and±9%for maximum stresses at the stand-off point for cylinders with relatively small length over radius ratios.Parametric studies examining the effect of different loading conditions,areal masses,and material configurations reveal that a large charge mass located far from the composite panel turns out to be more damaging than a small mass located nearby due to a broader pressure-time profile.Finally,the proposed model demonstrates a significant reduction in computation time,being approximately 30 times faster than its numerical counterpart,LS-DYNA/USA,making it a valuable tool for the preliminary design stages.
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.
基金supported by the National Key Research and Development Program of China(Grant No.2021YFB3900400)the National Natural Science Foundation of China(Grant Nos.U2142212 and 42361074)。
文摘Accurate satellite data assimilation under all-sky conditions requires enhanced parameterization of scattering properties for frozen hydrometeors in clouds.This study aims to develop a nonspherical scattering look-up table that contains the optical properties of five hydrometeor types—rain,cloud water,cloud ice,graupel,and snow—for the Advanced Radiative Transfer Modeling System(ARMS)at frequencies below 220 GHz.The discrete dipole approximation(DDA)method is employed to compute the single-scattering properties of solid cloud particles,modeling these particles as aggregated roughened bullet rosettes.The bulk optical properties of the cloud layer are derived by integrating the singlescattering properties with a modified Gamma size distribution,specifically for distributions with 18 effective radii.The bulk phase function is then projected onto a series of generalized spherical functions,applying the delta-M method for truncation.The results indicate that simulations using the newly developed nonspherical scattering look-up table exhibit significant consistency with observations under deep convection conditions.In contrast,assuming spherical solid cloud particles leads to excessive scattering at mid-frequency channels and insufficient scattering at high-frequency channels.This improvement in radiative transfer simulation accuracy for cloudy conditions will better support the assimilation of allsky microwave observations into numerical weather prediction models.·Frozen cloud particles were modeled as aggregates of bullet rosettes and the optical properties at microwave range were computed by DDA.·A complete process and technical details for constructing a look-up table of ARMS are provided.·The ARMS simulations generally show agreement with observations of MWTS and MWHS under typhoon conditions using the new look-up table.
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.
