A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In th...A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization （PSO）. The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.展开更多
In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and...In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.展开更多
Dual-polarization(dual-pol)radar variables provide information about the quantity,type,size,and water content of hydrometeors.Assimilating these dual-pol radar variables into numerical weather prediction models can en...Dual-polarization(dual-pol)radar variables provide information about the quantity,type,size,and water content of hydrometeors.Assimilating these dual-pol radar variables into numerical weather prediction models can enhance forecast accuracy.Observation operators are essential for radar data assimilation.This study focuses on applying a realistic dual-pol radar observation operator to more accurately calculate dual-pol radar variables.Previously reported dual-pol radar observation operators tended to overestimate radar variables near 0℃ in convective precipitation and simulate unrealistic dual-pol radar variables in subfreezing regions.To address this,the improved operator(KNU dual-pol radar observation operator;K-DROP)limits the distribution of mixed-phase hydrometeors,which have both solid and liquid properties,in areas with strong updrafts and downdrafts,improving the overestimation of radar variables near the melting layer.Additionally,by applying the observed snow axis ratio during winter to K-DROP,the issue of differential reflectivity(Z_(DR))being calculated as a constant value in subfreezing regions has been improved.By incorporating the observed maximum radius of hydrometeors into K-DROP,the overestimation of reflectivity(Z_(H))in subfreezing regions,the overestimation of Z_(DR)in warm regions,and the underestimation of specific differential phase(K_(DP))in subfreezing regions and overestimation in warm regions,are improved.Compared to previous operators,the enhanced version reported in the present work produces more realistic dual-pol radar variables.展开更多
Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted...Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).展开更多
Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the pr...Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the progression of the disease through susceptible,exposed,infected,and recovered populations.The focus is on simulating this model using the fractional Caputo derivative,allowing both qualitative and quantitative analyses of boundedness,positivity,and solution uniqueness.Fixed-point theory and Lipschitz conditions are employed to confirm the existence and uniqueness of solutions,while Lyapunov functions establish the global stability of both disease-free and endemic equilibria.The study further examines the role of the Caputo operator by solving the generalized power-law kernel via a two-step Lagrange polynomial method.This approach offers practical advantages in handling additional data points in integral forms,though Newton polynomial-based schemes are generally more accurate and can outperform Lagrange-based Adams-Bashforth methods.Graphical simulations validate the proposed numerical approach for different fractional orders(ν)and illustrate the influence of model parameters on disease dynamics.Results indicate that increasing the fractional order accelerates the decline of Lassa fever in both human and rodent populations.Moreover,fractional-order modeling provides more nuanced insights than traditional integer-order models,suggesting potential improvements for medical intervention strategies.The study demonstrates that carefully chosen fractional orders can optimize convergence and enhance the predictive capacity of Lassa fever models,offering a promising direction for future research in epidemiological modeling.展开更多
Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in oper...Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.展开更多
It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and t...It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.展开更多
In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the intera...In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws,we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.展开更多
Investigating the combined effects of mining damage and creep damage on slope stability is crucial,as it can comprehensively reveal the non-linear deformation characteristics of rock under their joint influence.This s...Investigating the combined effects of mining damage and creep damage on slope stability is crucial,as it can comprehensively reveal the non-linear deformation characteristics of rock under their joint influence.This study develops a fractional-order nonlinear creep constitutive model that incorporates the double damage effect and implements a non-linear creep subroutine for soft rock using the threedimensional finite difference method on the FLAC3D platform.Comparative analysis of the theoretical,numerical,and experimental results reveals that the fractional-order constitutive model,which incorporates the double damage effect,accurately reflects the distinct deformation stages of green mudstone during creep failure and effectively captures the non-linear deformation in the accelerated creep phase.The numerical results show a fitting accuracy exceeding 97%with the creep test curves,significantly outperforming the 61%accuracy of traditional creep models.展开更多
In this paper, Adomian decomposition method （ADM） with high accuracy and fast convergence is introduced to solve the fractional-order piecewise-linear （PWL） hyperchaotic system. Based on the obtained hyperchaotic ...In this paper, Adomian decomposition method （ADM） with high accuracy and fast convergence is introduced to solve the fractional-order piecewise-linear （PWL） hyperchaotic system. Based on the obtained hyperchaotic sequences, a novel color image encryption algorithm is proposed by employing a hybrid model of bidirectional circular permutation and DNA masking. In this scheme, the pixel positions of image are scrambled by circular permutation, and the pixel values are substituted by DNA sequence operations. In the DNA sequence operations, addition and substraction operations are performed according to traditional addition and subtraction in the binary, and two rounds of addition rules are used to encrypt the pixel values. The simulation results and security analysis show that the hyperchaotic map is suitable for image encryption, and the proposed encryption algorithm has good encryption effect and strong key sensitivity. It can resist brute-force attack, statistical attack, differential attack, known-plaintext, and chosen-plaintext attacks.展开更多
The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(...The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.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
Since the voltage source converter based high voltage direct current(VSC-HVDC)systems owns the features of nonlinearity,strong coupling and multivariable,the classical proportional integral(PI)control is hard to obtai...Since the voltage source converter based high voltage direct current(VSC-HVDC)systems owns the features of nonlinearity,strong coupling and multivariable,the classical proportional integral(PI)control is hard to obtain content control effect.Hence,a new perturbation observer based fractional-order PID(PoFoPID)control strategy is designed in this paper for(VSC-HVDC)systems with offshore wind integration,which can efficiently boost the robustness and control performance of entire system.Particularly,it employs a fractional-order PID(FoPID)fra-mework for the sake of compensating the perturbation estimate,which dramatically boost the dynamical responds of the closed-loop system,and the cooperative beetle antennae search(CBAS)algorithm is adopted to quickly and effi-ciently search its best control parameters.Besides,CBAS algorithm is able to efficiently escape a local optimum because of a suitable trade-off between global exploration and local exploitation can be realized.At last,comprehensive case studies are carried out,namely,active and reactive power tracking,5-cycle line-line-line-ground(LLLG)fault,and offshore wind farm integration.Simulation results validate superiorities and effectiveness of PoFoPID control in com-parison of that of PID control and feedback linearization sliding-mode control(FLSMC),respectively.展开更多
In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval...In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.展开更多
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.展开更多
Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective to...Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.展开更多
In this paper,a fractional-order kinematic model is utilized to capture the size-dependent static bending and free vibration responses of piezoelectric nanobeams.The general nonlocal strains in the Euler-Bernoulli pie...In this paper,a fractional-order kinematic model is utilized to capture the size-dependent static bending and free vibration responses of piezoelectric nanobeams.The general nonlocal strains in the Euler-Bernoulli piezoelectric beam are defined by a frame-invariant and dimensionally consistent Riesz-Caputo fractional-order derivatives.The strain energy,the work done by external loads,and the kinetic energy based on the fractional-order kinematic model are derived and expressed in explicit forms.The boundary conditions for the nonlocal Euler-Bernoulli beam are derived through variational principles.Furthermore,a finite element model for the fractional-order system is developed in order to obtain the numerical solutions to the integro-differential equations.The effects of the fractional order and the vibration order on the static bending and vibration responses of the Euler-Bernoulli piezoelectric beams are investigated numerically.The results from the present model are validated against the existing results in the literature,and it is demonstrated that they are theoretically consistent.Although this fractional finite element method(FEM)is presented in the context of a one-dimensional(1D)beam,it can be extended to higher dimensional fractional-order boundary value problems.展开更多
The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated.The power-law memory of the system is characterized using the Caputo fractional derivativ...The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated.The power-law memory of the system is characterized using the Caputo fractional derivative operator.Additionally,time delays in the potential field force and coupling force transmission are both considered.Firstly,based on the delay decoupling formula,combined with statistical mean method and the fractional-order Shapiro–Loginov formula,the“statistic synchronization”among particles is obtained,revealing the statistical equivalence between the mean field behavior of the system and the behavior of individual particles.Due to the existence of the coupling delay,the impact of the coupling force on synchronization exhibits non-monotonic,which is different from the previous monotonic effects.Then,two kinds of theoretical expression of output amplitude gains G and G are derived by time-delay decoupling formula and small delay approximation theorem,respectively.Compared to G,G is an exact theoretical solution,which means that G is not only more accurate in the region of small delay,but also applies to the region of large delay.Finally,the study of the output amplitude gain G and its resonance behavior are explored.Due to the presence of the potential field delay,a new resonance phenomenon termed“periodic resonance”is discovered,which arises from the periodic matching between the potential field delay and the driving frequency.This resonance phenomenon is analyzed qualitatively and quantitatively,uncovering undiscovered characteristics in previous studies.展开更多
This paper presents a systematic study on the modeling and stability analysis of fractional-order cascaded RLC networks with time delays.A generalized model of an n-stage cascaded RLC network with time delays is devel...This paper presents a systematic study on the modeling and stability analysis of fractional-order cascaded RLC networks with time delays.A generalized model of an n-stage cascaded RLC network with time delays is developed using the Caputo fractional derivative.The corresponding fractional-order differential equations are derived for both single-stage(n=1)and two-stage(n=2)configurations.The transcendental characteristic equation of the system is obtained via Laplace transform.By applying the Matignon stability criterion,asymptotic stability conditions are established for systems with and without time delays.It is shown that stability in the delay-free case depends mainly on the fractional orderα,whereas in the presence of time delays,stability is independent ofαand instead governed by the delay parameter τ.Notably,the critical delay threshold τ_(max) for system stability is derived analytically.A detailed numerical study(Table Ⅰ)further elucidates the effects of key parameters,including the resistance R,inductance L,capacitance C,fractional orderα,and time delayτon the stability behavior.This study provides a theoretical basis and practical design guidelines for tuning parameters to ensure stability in fractional-order circuits with time delays.展开更多
Breast cancer’s heterogeneous progression demands innovative tools for accurate prediction.We present a hybrid framework that integrates machine learning(ML)and fractional-order dynamics to predict tumor growth acros...Breast cancer’s heterogeneous progression demands innovative tools for accurate prediction.We present a hybrid framework that integrates machine learning(ML)and fractional-order dynamics to predict tumor growth across diagnostic and temporal scales.On the Wisconsin Diagnostic Breast Cancer dataset,seven ML algorithms were evaluated,with deep neural networks(DNNs)achieving the highest accuracy(97.72%).Key morphological features(area,radius,texture,and concavity)were identified as top malignancy predictors,aligning with clinical intuition.Beyond static classification,we developed a fractional-order dynamical model using Caputo derivatives to capture memory-driven tumor progression.The model revealed clinically interpretable patterns:lower fractional orders correlated with prolonged aggressive growth,while higher orders indicated rapid stabilization,mimicking indolent subtypes.Theoretical analyses were rigorously proven,and numerical simulations closely fit clinical data.The framework’s clinical utility is demonstrated through an interactive graphics user interface(GUI)that integrates real-time risk assessment with growth trajectory simulations.展开更多
基金supported by the National Natural Science Foundation of China (10872030)
文摘A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization （PSO）. The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.
文摘In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.
基金supported by the National Research Foundation(NRF)funded by the Korean government(MSIT)(Grant Nos.2022R1A2C1012361,2022R1A6A3A 13073165 and RS-2025-02242970).
文摘Dual-polarization(dual-pol)radar variables provide information about the quantity,type,size,and water content of hydrometeors.Assimilating these dual-pol radar variables into numerical weather prediction models can enhance forecast accuracy.Observation operators are essential for radar data assimilation.This study focuses on applying a realistic dual-pol radar observation operator to more accurately calculate dual-pol radar variables.Previously reported dual-pol radar observation operators tended to overestimate radar variables near 0℃ in convective precipitation and simulate unrealistic dual-pol radar variables in subfreezing regions.To address this,the improved operator(KNU dual-pol radar observation operator;K-DROP)limits the distribution of mixed-phase hydrometeors,which have both solid and liquid properties,in areas with strong updrafts and downdrafts,improving the overestimation of radar variables near the melting layer.Additionally,by applying the observed snow axis ratio during winter to K-DROP,the issue of differential reflectivity(Z_(DR))being calculated as a constant value in subfreezing regions has been improved.By incorporating the observed maximum radius of hydrometeors into K-DROP,the overestimation of reflectivity(Z_(H))in subfreezing regions,the overestimation of Z_(DR)in warm regions,and the underestimation of specific differential phase(K_(DP))in subfreezing regions and overestimation in warm regions,are improved.Compared to previous operators,the enhanced version reported in the present work produces more realistic dual-pol radar variables.
基金supported by the Zhejiang Province Natural Science Foundation of China(LY23A010003).
文摘Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).
文摘Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the progression of the disease through susceptible,exposed,infected,and recovered populations.The focus is on simulating this model using the fractional Caputo derivative,allowing both qualitative and quantitative analyses of boundedness,positivity,and solution uniqueness.Fixed-point theory and Lipschitz conditions are employed to confirm the existence and uniqueness of solutions,while Lyapunov functions establish the global stability of both disease-free and endemic equilibria.The study further examines the role of the Caputo operator by solving the generalized power-law kernel via a two-step Lagrange polynomial method.This approach offers practical advantages in handling additional data points in integral forms,though Newton polynomial-based schemes are generally more accurate and can outperform Lagrange-based Adams-Bashforth methods.Graphical simulations validate the proposed numerical approach for different fractional orders(ν)and illustrate the influence of model parameters on disease dynamics.Results indicate that increasing the fractional order accelerates the decline of Lassa fever in both human and rodent populations.Moreover,fractional-order modeling provides more nuanced insights than traditional integer-order models,suggesting potential improvements for medical intervention strategies.The study demonstrates that carefully chosen fractional orders can optimize convergence and enhance the predictive capacity of Lassa fever models,offering a promising direction for future research in epidemiological modeling.
基金supported by the National Natural Science Foundation of China(Grant No.52475543)Natural Science Foundation of Henan(Grant No.252300421101)+1 种基金Henan Province University Science and Technology Innovation Talent Support Plan(Grant No.24HASTIT048)Science and Technology Innovation Team Project of Zhengzhou University of Light Industry(Grant No.23XNKJTD0101).
文摘Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.
基金supported by the NSFC(12301115)the Natural Science Foundation of Huzhou(2023YZ11,2024YZ37)the second author was supported by the NSFC(12071437).
文摘It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.
基金supported by the National Natural Science Foundation of China(61303211)Zhejiang Provincial Natural Science Foundation of China(LY17F030003,LY15F030009)
文摘In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws,we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.
基金support from the National Natural Science Foundation of China(No.52308316)the Scientific Research Foundation of Weifang University(Grant No.2024BS42)+2 种基金China Postdoctoral Science Foundation(No.2022M721885)the Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province(No.ZJRMG-2022-01)supported by Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(NO.SKLGME023017).
文摘Investigating the combined effects of mining damage and creep damage on slope stability is crucial,as it can comprehensively reveal the non-linear deformation characteristics of rock under their joint influence.This study develops a fractional-order nonlinear creep constitutive model that incorporates the double damage effect and implements a non-linear creep subroutine for soft rock using the threedimensional finite difference method on the FLAC3D platform.Comparative analysis of the theoretical,numerical,and experimental results reveals that the fractional-order constitutive model,which incorporates the double damage effect,accurately reflects the distinct deformation stages of green mudstone during creep failure and effectively captures the non-linear deformation in the accelerated creep phase.The numerical results show a fitting accuracy exceeding 97%with the creep test curves,significantly outperforming the 61%accuracy of traditional creep models.
基金supported by the National Natural Science Foundation of China(Grant Nos.61161006 and 61573383)
文摘In this paper, Adomian decomposition method （ADM） with high accuracy and fast convergence is introduced to solve the fractional-order piecewise-linear （PWL） hyperchaotic system. Based on the obtained hyperchaotic sequences, a novel color image encryption algorithm is proposed by employing a hybrid model of bidirectional circular permutation and DNA masking. In this scheme, the pixel positions of image are scrambled by circular permutation, and the pixel values are substituted by DNA sequence operations. In the DNA sequence operations, addition and substraction operations are performed according to traditional addition and subtraction in the binary, and two rounds of addition rules are used to encrypt the pixel values. The simulation results and security analysis show that the hyperchaotic map is suitable for image encryption, and the proposed encryption algorithm has good encryption effect and strong key sensitivity. It can resist brute-force attack, statistical attack, differential attack, known-plaintext, and chosen-plaintext attacks.
基金Supported by Sichuan Science and Technology Program (No.2022ZYD0010)。
文摘The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.
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the National Natural Science Foundation of China(51807085).
文摘Since the voltage source converter based high voltage direct current(VSC-HVDC)systems owns the features of nonlinearity,strong coupling and multivariable,the classical proportional integral(PI)control is hard to obtain content control effect.Hence,a new perturbation observer based fractional-order PID(PoFoPID)control strategy is designed in this paper for(VSC-HVDC)systems with offshore wind integration,which can efficiently boost the robustness and control performance of entire system.Particularly,it employs a fractional-order PID(FoPID)fra-mework for the sake of compensating the perturbation estimate,which dramatically boost the dynamical responds of the closed-loop system,and the cooperative beetle antennae search(CBAS)algorithm is adopted to quickly and effi-ciently search its best control parameters.Besides,CBAS algorithm is able to efficiently escape a local optimum because of a suitable trade-off between global exploration and local exploitation can be realized.At last,comprehensive case studies are carried out,namely,active and reactive power tracking,5-cycle line-line-line-ground(LLLG)fault,and offshore wind farm integration.Simulation results validate superiorities and effectiveness of PoFoPID control in com-parison of that of PID control and feedback linearization sliding-mode control(FLSMC),respectively.
基金Supported by NSFC (No.12361027)NSF of Inner Mongolia (No.2018MS01021)+1 种基金NSF of Shandong Province (No.ZR2020QA009)Science and Technology Innovation Program for Higher Education Institutions of Shanxi Province (No.2024L533)。
文摘In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.
基金Supported by NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
文摘Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.
文摘Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.
基金Project supported by the National Natural Science Foundation of China(No.12172169)。
文摘In this paper,a fractional-order kinematic model is utilized to capture the size-dependent static bending and free vibration responses of piezoelectric nanobeams.The general nonlocal strains in the Euler-Bernoulli piezoelectric beam are defined by a frame-invariant and dimensionally consistent Riesz-Caputo fractional-order derivatives.The strain energy,the work done by external loads,and the kinetic energy based on the fractional-order kinematic model are derived and expressed in explicit forms.The boundary conditions for the nonlocal Euler-Bernoulli beam are derived through variational principles.Furthermore,a finite element model for the fractional-order system is developed in order to obtain the numerical solutions to the integro-differential equations.The effects of the fractional order and the vibration order on the static bending and vibration responses of the Euler-Bernoulli piezoelectric beams are investigated numerically.The results from the present model are validated against the existing results in the literature,and it is demonstrated that they are theoretically consistent.Although this fractional finite element method(FEM)is presented in the context of a one-dimensional(1D)beam,it can be extended to higher dimensional fractional-order boundary value problems.
基金supported by the Natural Science Foundation of Sichuan Province,China(Youth Science Foundation)(Grant No.2022NSFSC1952).
文摘The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated.The power-law memory of the system is characterized using the Caputo fractional derivative operator.Additionally,time delays in the potential field force and coupling force transmission are both considered.Firstly,based on the delay decoupling formula,combined with statistical mean method and the fractional-order Shapiro–Loginov formula,the“statistic synchronization”among particles is obtained,revealing the statistical equivalence between the mean field behavior of the system and the behavior of individual particles.Due to the existence of the coupling delay,the impact of the coupling force on synchronization exhibits non-monotonic,which is different from the previous monotonic effects.Then,two kinds of theoretical expression of output amplitude gains G and G are derived by time-delay decoupling formula and small delay approximation theorem,respectively.Compared to G,G is an exact theoretical solution,which means that G is not only more accurate in the region of small delay,but also applies to the region of large delay.Finally,the study of the output amplitude gain G and its resonance behavior are explored.Due to the presence of the potential field delay,a new resonance phenomenon termed“periodic resonance”is discovered,which arises from the periodic matching between the potential field delay and the driving frequency.This resonance phenomenon is analyzed qualitatively and quantitatively,uncovering undiscovered characteristics in previous studies.
基金supported by the National Natural Science Foundation of China(No.12371180)。
文摘This paper presents a systematic study on the modeling and stability analysis of fractional-order cascaded RLC networks with time delays.A generalized model of an n-stage cascaded RLC network with time delays is developed using the Caputo fractional derivative.The corresponding fractional-order differential equations are derived for both single-stage(n=1)and two-stage(n=2)configurations.The transcendental characteristic equation of the system is obtained via Laplace transform.By applying the Matignon stability criterion,asymptotic stability conditions are established for systems with and without time delays.It is shown that stability in the delay-free case depends mainly on the fractional orderα,whereas in the presence of time delays,stability is independent ofαand instead governed by the delay parameter τ.Notably,the critical delay threshold τ_(max) for system stability is derived analytically.A detailed numerical study(Table Ⅰ)further elucidates the effects of key parameters,including the resistance R,inductance L,capacitance C,fractional orderα,and time delayτon the stability behavior.This study provides a theoretical basis and practical design guidelines for tuning parameters to ensure stability in fractional-order circuits with time delays.
文摘Breast cancer’s heterogeneous progression demands innovative tools for accurate prediction.We present a hybrid framework that integrates machine learning(ML)and fractional-order dynamics to predict tumor growth across diagnostic and temporal scales.On the Wisconsin Diagnostic Breast Cancer dataset,seven ML algorithms were evaluated,with deep neural networks(DNNs)achieving the highest accuracy(97.72%).Key morphological features(area,radius,texture,and concavity)were identified as top malignancy predictors,aligning with clinical intuition.Beyond static classification,we developed a fractional-order dynamical model using Caputo derivatives to capture memory-driven tumor progression.The model revealed clinically interpretable patterns:lower fractional orders correlated with prolonged aggressive growth,while higher orders indicated rapid stabilization,mimicking indolent subtypes.Theoretical analyses were rigorously proven,and numerical simulations closely fit clinical data.The framework’s clinical utility is demonstrated through an interactive graphics user interface(GUI)that integrates real-time risk assessment with growth trajectory simulations.
