In this paper,we study an integral system involving m equations■where ui>0 in R^(n),0<α<n,and pi>1(i=1,2,…,m).Based on the optimal integrability intervals,we estimate the decay rates of the positive sol...In this paper,we study an integral system involving m equations■where ui>0 in R^(n),0<α<n,and pi>1(i=1,2,…,m).Based on the optimal integrability intervals,we estimate the decay rates of the positive solutions of the system at infinity.But estimating these rates is difficult because the relation between pi(i=1,2,…,m)is uncertain.To overcome this difficulty,we obtain the asymptotic behavior of all cases by discussing them separately.In addition,we also get the radial symmetry of positive solutions under some integrability condition.展开更多
In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β...In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β dy for x ∈ R n,where G α（x） is the kernel of Bessel potential of order α,0 ≤β 〈 α 〈 n,1 〈 p,q 〈 n-β/β and 1/p ＋ 1 ＋ 1/q ＋ 1 〉 n-α ＋ β/n.We show that positive solution pairs（u,v） ∈ L p ＋1（R n） × L q ＋1（R n） are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.展开更多
We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone non...We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n＋α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system：This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate展开更多
In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes...In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes in an integral form which was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions of （0.1） are radially symmetric and decreasing with respect to some point under some general conditions of integrability. The results essentially improve and extend previously known results [4, 8].展开更多
In this paper, Liouville-type theorems of nonnegative solutions for some elliptic integral systems are considered. We use a new type of moving plane method introduced by Chen-Li-Ou. Our new ingredient is the use of St...In this paper, Liouville-type theorems of nonnegative solutions for some elliptic integral systems are considered. We use a new type of moving plane method introduced by Chen-Li-Ou. Our new ingredient is the use of Stein-Weiss inequality instead of Maximum Principle.展开更多
This article investigates the anti-disturbance and stabilization problems for the nonlinear uncertain permanent magnet synchronous motor(PMSM)with stator voltage saturation and unknown load.A smooth switching mechanis...This article investigates the anti-disturbance and stabilization problems for the nonlinear uncertain permanent magnet synchronous motor(PMSM)with stator voltage saturation and unknown load.A smooth switching mechanism is presented to structure the adaptive integral terminal sliding mode control(SMC)strategy.The control design consists of compensation control and nominal control,which improves the rapidity and accuracy of trajectory tracking.The smooth saturation model based on the error function is applied to approximate the voltage saturation phenomenon.Additionally,to deal with the adverse effects of various unknown disturbances,including model parameter uncertainties and unknown external load disturbances,an improved disturbance observer(DO)is proposed.This observer effectively suppresses the fluctuations caused by fixed gain during the starting period of the system.Finally,the experimental results under different conditions show that the proposed strategy has good tracking and disturbance suppression performances.展开更多
Integral reinforcement learning(IRL)is an effective tool for solving optimal control problems of nonlinear systems,and it has been widely utilized in optimal controller design for solving discrete-time nonlinearity.Ho...Integral reinforcement learning(IRL)is an effective tool for solving optimal control problems of nonlinear systems,and it has been widely utilized in optimal controller design for solving discrete-time nonlinearity.However,solving the Hamilton-Jacobi-Bellman(HJB)equations for nonlinear systems requires precise and complicated dynamics.Moreover,the research and application of IRL in continuous-time(CT)systems must be further improved.To develop the IRL of a CT nonlinear system,a data-based adaptive neural dynamic programming(ANDP)method is proposed to investigate the optimal control problem of uncertain CT multi-input systems such that the knowledge of the dynamics in the HJB equation is unnecessary.First,the multi-input model is approximated using a neural network(NN),which can be utilized to design an integral reinforcement signal.Subsequently,two criterion networks and one action network are constructed based on the integral reinforcement signal.A nonzero-sum Nash equilibrium can be reached by learning the optimal strategies of the multi-input model.In this scheme,the NN weights are constantly updated using an adaptive algorithm.The weight convergence and the system stability are analyzed in detail.The optimal control problem of a multi-input nonlinear CT system is effectively solved using the ANDP scheme,and the results are verified by a simulation study.展开更多
For any country,the availability of electricity is crucial to the development of the national economy and society.As a result,decision-makers and policy-makers can improve the sustainability and security of the energy...For any country,the availability of electricity is crucial to the development of the national economy and society.As a result,decision-makers and policy-makers can improve the sustainability and security of the energy supply by implementing a variety of actions by using the evaluation of these factors as an early warning system.This research aims to provide a multi-criterion decision-making(MCDM)method for assessing the sustainability and security of the electrical supply.The weights of criteria,which indicate their relative relevance in the assessment of the sustainability and security of the energy supply,the MCDM method allow users to express their opinions.To overcome the impact of uncertainty and vagueness of expert opinion,we explore the notion of picture fuzzy theory,which is a more efficient and dominant mathematical model.Recently,the theory of Aczel-Alsina operations has attained a lot of attraction and has an extensive capability to acquire smooth approximated results during the aggregation process.However,Choquet integral operators are more flexible and are used to express correlation among different attributes.This article diagnoses an innovative theory of picture fuzzy set to derive robust mathematical methodologies of picture fuzzy Choquet Integral Aczel-Alsina aggregation operators.To prove the intensity and validity of invented approaches,some dominant properties and special cases are also discussed.An intelligent decision algorithm for the MCDM problem is designed to resolve complicated real-life applications under multiple conflicting criteria.Additionally,we discussed a numerical example to investigate a suitable electric transformer under consideration of different beneficial key criteria.A comparative study is established to capture the superiority and effectiveness of pioneered mathematical approaches with existing methodologies.展开更多
Since the first design of tactile sensors was proposed by Harmon in 1982,tactile sensors have evolved through four key phases:industrial applications(1980s,basic pressure detection),miniaturization via MEMS(1990s),fle...Since the first design of tactile sensors was proposed by Harmon in 1982,tactile sensors have evolved through four key phases:industrial applications(1980s,basic pressure detection),miniaturization via MEMS(1990s),flexible electronics(2010s,stretchable materials),and intelligent systems(2020s-present,AI-driven multimodal sensing).With the innovation of material,processing techniques,and multimodal fusion of stimuli,the application of tactile sensors has been continuously expanding to a diversity of areas,including but not limited to medical care,aerospace,sports and intelligent robots.Currently,researchers are dedicated to develop tactile sensors with emerging mechanisms and structures,pursuing high-sensitivity,high-resolution,and multimodal characteristics and further constructing tactile systems which imitate and approach the performance of human organs.However,challenges in the combination between the theoretical research and the practical applications are still significant.There is a lack of comprehensive understanding in the state of the art of such knowledge transferring from academic work to technical products.Scaled-up production of laboratory materials faces fatal challenges like high costs,small scale,and inconsistent quality.Ambient factors,such as temperature,humidity,and electromagnetic interference,also impair signal reliability.Moreover,tactile sensors must operate across a wide pressure range(0.1 k Pa to several or even dozens of MPa)to meet diverse application needs.Meanwhile,the existing algorithms,data models and sensing systems commonly reveal insufficient precision as well as undesired robustness in data processing,and there is a realistic gap between the designed and the demanded system response speed.In this review,oriented by the design requirements of intelligent tactile sensing systems,we summarize the common sensing mechanisms,inspired structures,key performance,and optimizing strategies,followed by a brief overview of the recent advances in the perspectives of system integration and algorithm implementation,and the possible roadmap of future development of tactile sensors,providing a forward-looking as well as critical discussions in the future industrial applications of flexible tactile sensors.展开更多
The fast-changing trajectory of energy systems toward renewables requires flexible,low-emission technologies that can buffer supply intermittently and offer large-scale energy storage systems.Moreso,hydrogen is increa...The fast-changing trajectory of energy systems toward renewables requires flexible,low-emission technologies that can buffer supply intermittently and offer large-scale energy storage systems.Moreso,hydrogen is increasingly viewed as a multi-scale flexibility resource capable of supporting deep decarbonization in renewable-dominated power systems,yet existing reviews often treat production,storage,and conversion technologies in isolation.Hydrogen offers the ability to convert,store and reconvert energy on various timescales.This review critically analyses the current literature of hydrogen production and storage in relation to power systems integration,synthesizing technical,economic and operational advances.The study synthesizes recent advances in electrolysis,particularly PEM and high-temperature SOEC systems,together with emerging PEC routes,biomass-to-hydrogen processes,and long-duration storage technologies.It considers,for storage,the performance and maturity of compressed gas,liquid hydrogen,metal and complex hydrides,liquid organic hydrogen carriers,and geological formations.Integration studies show that the value of hydrogen is enhanced as the share of renewables increases,providing seasonal storage,grid balancing,and sector coupling via power-to-hydrogen-to-power configurations.Yet technical,economic and other hurdles such as conversion losses,infrastructure requirements,and safety considerations are still holding back widespread implementation.The review also underlines the value of policy frameworks,such as country-level hydrogen strategies,carbon pricing,tax incentives,and harmonized safety standards to speed up adoption and reduce barriers to costs.The review synthesizes offer planners,operators,and policymakers a clear roadmap for aligning hydrogen deployment strategies with evolving technical requirements and high-renewable power-system conditions.By summarizing what is known and discussing opportunities for the future,this review is intended to be a roadmap towards maximizing hydrogen in reaching a flexible,resilient and carbon free power system.展开更多
Driven by the global energy transition and the urgent“dual carbon”goals,regional integrated energy system(RIES)planning is undergoing a paradigm shift from carbon reduction to negative carbon emissions.This paper pr...Driven by the global energy transition and the urgent“dual carbon”goals,regional integrated energy system(RIES)planning is undergoing a paradigm shift from carbon reduction to negative carbon emissions.This paper provides a comprehensive review of the theoretical frameworks and technical pathways for RIES planning from a carbon-centric perspective.A key contribution is the proposed Carbon-Energy-Economy(CEE)triple-dimensional governance framework,which endogenizes carbon factors into planning decisions through emission constraints,trading mechanisms,and capture technologies.We first analyze the fundamental characteristics of RIES and their critical role in achieving carbon neutrality,detailing advancements in multi-energy coupling models,energy router concepts,and standardized energy hub modeling.The paper further explores multi-energy flow analysis methods,and systematically compares the applicability and limitations of various planning algorithms,with emphasis on addressing uncertainties from renewable integration.Finally,we highlight the integration of artificial intelligence with traditional optimization methods,offering new pathways for intelligent,adaptive,and low-carbon RIES planning.This review underscores the transition towards data-physical fusion models,cooperative uncertainty optimization,multi-market planning,and innovative zero/negative-carbon technological routes.展开更多
As circuit feature sizes approach the nanoscale,traditional Copper(Cu)interconnects face significant hurdles posed by rising resistance-capacitance(RC)delay,electromigration,and high power dissipation.These limitation...As circuit feature sizes approach the nanoscale,traditional Copper(Cu)interconnects face significant hurdles posed by rising resistance-capacitance(RC)delay,electromigration,and high power dissipation.These limitations impose constraints on the scalability and reliability of future semiconductor technologies.Our paper describes the new Vertical multilayer Aluminium Boron Nitride Nanoribbon(AlBN)interconnect structure,integrated with Density functional theory(DFT)using first-principles calculations.This study explores AlBN-based nanostructures with doping of 1Cu,2Cu,1Fe(Iron),and 2Fe for the application of Very Large Scale Integration(VLSI)interconnects.The AlBN structure utilized the advantages of vertical multilayer interconnects to both reduce the RC delay while enhancing signal integrity.Key parameters like Fermi energy,bandgap,binding energy,conduction channels,quantum resistance,and RC delay were analyzed.Through modeling and large-scale simulation,the structural,electronic,and stability attributes of the AlBN interconnects are analyzed,and the results illustrate considerable improvements in signal propagation against Cu interconnect structures.These findings confirm the tunable,high-performance nature of AlBN-2Fe,making it a promising candidate for future high-speed,low-power VLSI interconnect technologies.We demonstrated an advanced energy-efficient interconnect that can be easily scaled for future nanoscale VLSI circuit design and gives rise to a next generation of viable interconnect technology for high-capacity,high-speed,reliable semiconductor technology.展开更多
This survey presents a comprehensive examination of sensor fusion research spanning four decades,tracing the methodological evolution,application domains,and alignment with classical hierarchical models.Building on th...This survey presents a comprehensive examination of sensor fusion research spanning four decades,tracing the methodological evolution,application domains,and alignment with classical hierarchical models.Building on this long-term trajectory,the foundational approaches such as probabilistic inference,early neural networks,rulebasedmethods,and feature-level fusion established the principles of uncertainty handling andmulti-sensor integration in the 1990s.The fusion methods of 2000s marked the consolidation of these ideas through advanced Kalman and particle filtering,Bayesian–Dempster–Shafer hybrids,distributed consensus algorithms,and machine learning ensembles for more robust and domain-specific implementations.From 2011 to 2020,the widespread adoption of deep learning transformed the field driving some major breakthroughs in the autonomous vehicles domain.A key contribution of this work is the assessment of contemporary methods against the JDL model,revealing gaps at higher levels-especially in situation and impact assessment.Contemporary methods offer only limited implementation of higher-level fusion.The survey also reviews the benchmark multi-sensor datasets,noting their role in advancing the field while identifying major shortcomings like the lack of domain diversity and hierarchical coverage.By synthesizing developments across decades and paradigms,this survey provides both a historical narrative and a forward-looking perspective.It highlights unresolved challenges in transparency,scalability,robustness,and trustworthiness,while identifying emerging paradigms such as neuromorphic fusion and explainable AI as promising directions.This paves the way forward for advancing sensor fusion towards transparent and adaptive next-generation autonomous systems.展开更多
The spatial organization of urban-rural systems is fundamentally shaped by the agglomeration and diffusion effects inherent in human-Earth processes,giving rise to distinct gradient-based and hierarchical structures.U...The spatial organization of urban-rural systems is fundamentally shaped by the agglomeration and diffusion effects inherent in human-Earth processes,giving rise to distinct gradient-based and hierarchical structures.Understanding the complexity of these interactions and their multidimensional drivers is essential for deciphering the mechanisms of integrated urban-rural development.Here,we apply a novel hierarchical spatial system framework based on the human-Earth system,combining social network analysis and multi-level modeling,to examine the evolution of the socio-spatial structure in the Beijing-Tianjin-Hebei region from 2000 to 2020.We developed a comprehensive evaluation system spanning economic,social,environmental,and infrastructural dimensions to characterize spatial patterns across multiple network levels,including city clusters,metropolitan areas,municipal-counties,towns,and villages.Our analysis reveals three key findings:First,the density of foundational network connections increased significantly,reflecting a trend toward spatial concentration driven by policy-led regional integration.Second,network structures at the city-cluster and metropolitan scales exhibited a pattern of“initial expansion followed by convergence”,accompanied by notable shifts in their spatial centers of gravity.In parallel,differentiated patterns of agglomeration and expansion were evident in the township-and village-level networks of Baoding,Tangshan,and Handan,while village-level networks in Anxin,Quyang,and other locations demonstrated distinct developmental trends.Third,community structures demonstrated strong functional homophily and interactive cohesion across multiple dimensions,with metropolitan and township communities undergoing restructuring that reflects a reconfiguration of cross-level influence and functional coupling.Spatially,the system manifests as a gradient structure of interwoven point,line,and area networks,establishing a mechanism for functional differentiation and transmission from rural to urban areas.This study provides theoretical foundations and methodological support for understanding the spatial organization logic of integrated urban-rural development,offering practical reference value for advancing regional coordination and rural revitalization in a scientifically informed manner.展开更多
Energy storage-equipped photovoltaic(PV-storage)systems can meet frequency regulation requirements under various operating conditions,and their coordinated support for grid frequency has become a future trend.To addre...Energy storage-equipped photovoltaic(PV-storage)systems can meet frequency regulation requirements under various operating conditions,and their coordinated support for grid frequency has become a future trend.To address frequency stability issues caused by low inertia and weak damping,this paper proposes a multi-timescale frequency regulation coordinated control strategy for PV-storage integrated systems.First,a self-synchronizing control strategy for grid-connected inverters is designed based on DC voltage dynamics,enabling active inertia support while transmitting frequency variation information.Next,an energy storage inertia support control strategy is developed to enhance the frequency nadir,and an active frequency support control strategy for PV system considering a frequency regulation deadband is proposed,where the deadband value is determined based on the power regulation margin of synchronous generators,allowing the PV-storage system to adaptively switch between inertia support and primary frequency regulation under different disturbance conditions.This approach ensures system frequency stability while fully leveraging the regulation capabilities of heterogeneous resources.Finally,the real-time digital simulation results of the PV-storage integrated system demonstrate that,compared to existing control methods,the proposed strategy effectively reduces the rate of change of frequency and improves the frequency nadir under various disturbance scenarios,verifying its effectiveness.展开更多
To enhance the low-carbon economic efficiency and increase the utilization of renewable energy within integrated energy systems(IES),this paper proposes a low-carbon dispatch model integrating power-to-gas(P2G),carbon...To enhance the low-carbon economic efficiency and increase the utilization of renewable energy within integrated energy systems(IES),this paper proposes a low-carbon dispatch model integrating power-to-gas(P2G),carbon capture and storage(CCS),hydrogen fuel cell(HFC),and combined heat and power(CHP).The P2G process is refined into a two-stage structure,and HFC is introduced to enhance hydrogen utilization.Together with CCS and CHP,these devices form a multi-energy conversion system coupling electricity,heat,cooling,and gas.A laddertype carbon trading approach is adopted to flexibly manage carbon output by leveraging marginal cost adjustments.To evaluate the resilience of the proposed low-carbon scheduling strategy involving multiple energy units under the variability of renewable energy,a two-level robust optimization framework is developed.This model captures the most adverse scenarios of wind and solar generation.The dispatch strategy is validated against these extreme conditions to demonstrate its flexibility and effectiveness.The problem is solved using the GUROBI optimization tool.Results from simulations indicate that themodel increases renewable energy integration by 39.1%,and achieves reductions of 15.96%in carbon emissions and 16.29%in operational expenditures.The results demonstrate that the strategy ensures both economic efficiency and environmental performance under uncertain conditions.Compared with existing studies that separately model two-stage P2G or CCS devices,this paper integrates HFC,CHP,and CCS into a unified dispatchable system,enabling refined hydrogen utilization and flexible carbon circulation.Furthermore,the introduction of a laddertype carbon pricing mechanism,combined with multi-energy storage participation in implicit demand response,creates a dynamic and cost-sensitive dispatch framework.These modeling strategies go beyond conventional linear IES formulations and provide more realistic system representations.The proposed approach not only deepens the coupling among electric,thermal,and gas systems,but also offers a feasible pathway for high-penetration renewable integration in low-carbon energy systems.展开更多
In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^...In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^(1-a_uθ)(x)/|x-y|^(n-a))dx,y∈ ?R_+~n,where n 2, 2-n < a < 1, κ, θ > 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system.展开更多
In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the unique...In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle.展开更多
Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. T...Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.展开更多
By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations ...By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results in this paper improve some known results.展开更多
基金supported by the NSFC(11871278)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX23-1669).
文摘In this paper,we study an integral system involving m equations■where ui>0 in R^(n),0<α<n,and pi>1(i=1,2,…,m).Based on the optimal integrability intervals,we estimate the decay rates of the positive solutions of the system at infinity.But estimating these rates is difficult because the relation between pi(i=1,2,…,m)is uncertain.To overcome this difficulty,we obtain the asymptotic behavior of all cases by discussing them separately.In addition,we also get the radial symmetry of positive solutions under some integrability condition.
基金Chen research is supported by NSF of China (10961015)Yang research is supported by NSF of China (10961016)the GAN PO555 Program of Jiangxi
文摘In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β dy for x ∈ R n,where G α（x） is the kernel of Bessel potential of order α,0 ≤β 〈 α 〈 n,1 〈 p,q 〈 n-β/β and 1/p ＋ 1 ＋ 1/q ＋ 1 〉 n-α ＋ β/n.We show that positive solution pairs（u,v） ∈ L p ＋1（R n） × L q ＋1（R n） are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.
基金supported by NSF Grant DMS-0604638Li partially supported by NSF Grant DMS-0401174
文摘We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n＋α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system：This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate
基金Supported by National Natural Science Foundation of China-NSAF (10976026)
文摘In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes in an integral form which was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions of （0.1） are radially symmetric and decreasing with respect to some point under some general conditions of integrability. The results essentially improve and extend previously known results [4, 8].
文摘In this paper, Liouville-type theorems of nonnegative solutions for some elliptic integral systems are considered. We use a new type of moving plane method introduced by Chen-Li-Ou. Our new ingredient is the use of Stein-Weiss inequality instead of Maximum Principle.
基金supported by the National Natural Science Foundation under Grant 62273189the Shandong Province Natural Science Foundation under Grant ZR2021MF005Systems Science Plus Joint Research Program of Qingdao University under Grant XT2024201 of China supporting this research work.
文摘This article investigates the anti-disturbance and stabilization problems for the nonlinear uncertain permanent magnet synchronous motor(PMSM)with stator voltage saturation and unknown load.A smooth switching mechanism is presented to structure the adaptive integral terminal sliding mode control(SMC)strategy.The control design consists of compensation control and nominal control,which improves the rapidity and accuracy of trajectory tracking.The smooth saturation model based on the error function is applied to approximate the voltage saturation phenomenon.Additionally,to deal with the adverse effects of various unknown disturbances,including model parameter uncertainties and unknown external load disturbances,an improved disturbance observer(DO)is proposed.This observer effectively suppresses the fluctuations caused by fixed gain during the starting period of the system.Finally,the experimental results under different conditions show that the proposed strategy has good tracking and disturbance suppression performances.
文摘Integral reinforcement learning(IRL)is an effective tool for solving optimal control problems of nonlinear systems,and it has been widely utilized in optimal controller design for solving discrete-time nonlinearity.However,solving the Hamilton-Jacobi-Bellman(HJB)equations for nonlinear systems requires precise and complicated dynamics.Moreover,the research and application of IRL in continuous-time(CT)systems must be further improved.To develop the IRL of a CT nonlinear system,a data-based adaptive neural dynamic programming(ANDP)method is proposed to investigate the optimal control problem of uncertain CT multi-input systems such that the knowledge of the dynamics in the HJB equation is unnecessary.First,the multi-input model is approximated using a neural network(NN),which can be utilized to design an integral reinforcement signal.Subsequently,two criterion networks and one action network are constructed based on the integral reinforcement signal.A nonzero-sum Nash equilibrium can be reached by learning the optimal strategies of the multi-input model.In this scheme,the NN weights are constantly updated using an adaptive algorithm.The weight convergence and the system stability are analyzed in detail.The optimal control problem of a multi-input nonlinear CT system is effectively solved using the ANDP scheme,and the results are verified by a simulation study.
文摘For any country,the availability of electricity is crucial to the development of the national economy and society.As a result,decision-makers and policy-makers can improve the sustainability and security of the energy supply by implementing a variety of actions by using the evaluation of these factors as an early warning system.This research aims to provide a multi-criterion decision-making(MCDM)method for assessing the sustainability and security of the electrical supply.The weights of criteria,which indicate their relative relevance in the assessment of the sustainability and security of the energy supply,the MCDM method allow users to express their opinions.To overcome the impact of uncertainty and vagueness of expert opinion,we explore the notion of picture fuzzy theory,which is a more efficient and dominant mathematical model.Recently,the theory of Aczel-Alsina operations has attained a lot of attraction and has an extensive capability to acquire smooth approximated results during the aggregation process.However,Choquet integral operators are more flexible and are used to express correlation among different attributes.This article diagnoses an innovative theory of picture fuzzy set to derive robust mathematical methodologies of picture fuzzy Choquet Integral Aczel-Alsina aggregation operators.To prove the intensity and validity of invented approaches,some dominant properties and special cases are also discussed.An intelligent decision algorithm for the MCDM problem is designed to resolve complicated real-life applications under multiple conflicting criteria.Additionally,we discussed a numerical example to investigate a suitable electric transformer under consideration of different beneficial key criteria.A comparative study is established to capture the superiority and effectiveness of pioneered mathematical approaches with existing methodologies.
基金the financial support of the National Natural Science Foundation of China(NO.52173028)。
文摘Since the first design of tactile sensors was proposed by Harmon in 1982,tactile sensors have evolved through four key phases:industrial applications(1980s,basic pressure detection),miniaturization via MEMS(1990s),flexible electronics(2010s,stretchable materials),and intelligent systems(2020s-present,AI-driven multimodal sensing).With the innovation of material,processing techniques,and multimodal fusion of stimuli,the application of tactile sensors has been continuously expanding to a diversity of areas,including but not limited to medical care,aerospace,sports and intelligent robots.Currently,researchers are dedicated to develop tactile sensors with emerging mechanisms and structures,pursuing high-sensitivity,high-resolution,and multimodal characteristics and further constructing tactile systems which imitate and approach the performance of human organs.However,challenges in the combination between the theoretical research and the practical applications are still significant.There is a lack of comprehensive understanding in the state of the art of such knowledge transferring from academic work to technical products.Scaled-up production of laboratory materials faces fatal challenges like high costs,small scale,and inconsistent quality.Ambient factors,such as temperature,humidity,and electromagnetic interference,also impair signal reliability.Moreover,tactile sensors must operate across a wide pressure range(0.1 k Pa to several or even dozens of MPa)to meet diverse application needs.Meanwhile,the existing algorithms,data models and sensing systems commonly reveal insufficient precision as well as undesired robustness in data processing,and there is a realistic gap between the designed and the demanded system response speed.In this review,oriented by the design requirements of intelligent tactile sensing systems,we summarize the common sensing mechanisms,inspired structures,key performance,and optimizing strategies,followed by a brief overview of the recent advances in the perspectives of system integration and algorithm implementation,and the possible roadmap of future development of tactile sensors,providing a forward-looking as well as critical discussions in the future industrial applications of flexible tactile sensors.
基金funding this research work through the project number(PSAU/2025/01/38318).
文摘The fast-changing trajectory of energy systems toward renewables requires flexible,low-emission technologies that can buffer supply intermittently and offer large-scale energy storage systems.Moreso,hydrogen is increasingly viewed as a multi-scale flexibility resource capable of supporting deep decarbonization in renewable-dominated power systems,yet existing reviews often treat production,storage,and conversion technologies in isolation.Hydrogen offers the ability to convert,store and reconvert energy on various timescales.This review critically analyses the current literature of hydrogen production and storage in relation to power systems integration,synthesizing technical,economic and operational advances.The study synthesizes recent advances in electrolysis,particularly PEM and high-temperature SOEC systems,together with emerging PEC routes,biomass-to-hydrogen processes,and long-duration storage technologies.It considers,for storage,the performance and maturity of compressed gas,liquid hydrogen,metal and complex hydrides,liquid organic hydrogen carriers,and geological formations.Integration studies show that the value of hydrogen is enhanced as the share of renewables increases,providing seasonal storage,grid balancing,and sector coupling via power-to-hydrogen-to-power configurations.Yet technical,economic and other hurdles such as conversion losses,infrastructure requirements,and safety considerations are still holding back widespread implementation.The review also underlines the value of policy frameworks,such as country-level hydrogen strategies,carbon pricing,tax incentives,and harmonized safety standards to speed up adoption and reduce barriers to costs.The review synthesizes offer planners,operators,and policymakers a clear roadmap for aligning hydrogen deployment strategies with evolving technical requirements and high-renewable power-system conditions.By summarizing what is known and discussing opportunities for the future,this review is intended to be a roadmap towards maximizing hydrogen in reaching a flexible,resilient and carbon free power system.
基金supported by the Natural Science Foundation of China(Grants U2166211)Zhejiang Provincial Natural Science Foundation of China(Grants LY24E070006 and LMS25E070002).
文摘Driven by the global energy transition and the urgent“dual carbon”goals,regional integrated energy system(RIES)planning is undergoing a paradigm shift from carbon reduction to negative carbon emissions.This paper provides a comprehensive review of the theoretical frameworks and technical pathways for RIES planning from a carbon-centric perspective.A key contribution is the proposed Carbon-Energy-Economy(CEE)triple-dimensional governance framework,which endogenizes carbon factors into planning decisions through emission constraints,trading mechanisms,and capture technologies.We first analyze the fundamental characteristics of RIES and their critical role in achieving carbon neutrality,detailing advancements in multi-energy coupling models,energy router concepts,and standardized energy hub modeling.The paper further explores multi-energy flow analysis methods,and systematically compares the applicability and limitations of various planning algorithms,with emphasis on addressing uncertainties from renewable integration.Finally,we highlight the integration of artificial intelligence with traditional optimization methods,offering new pathways for intelligent,adaptive,and low-carbon RIES planning.This review underscores the transition towards data-physical fusion models,cooperative uncertainty optimization,multi-market planning,and innovative zero/negative-carbon technological routes.
文摘As circuit feature sizes approach the nanoscale,traditional Copper(Cu)interconnects face significant hurdles posed by rising resistance-capacitance(RC)delay,electromigration,and high power dissipation.These limitations impose constraints on the scalability and reliability of future semiconductor technologies.Our paper describes the new Vertical multilayer Aluminium Boron Nitride Nanoribbon(AlBN)interconnect structure,integrated with Density functional theory(DFT)using first-principles calculations.This study explores AlBN-based nanostructures with doping of 1Cu,2Cu,1Fe(Iron),and 2Fe for the application of Very Large Scale Integration(VLSI)interconnects.The AlBN structure utilized the advantages of vertical multilayer interconnects to both reduce the RC delay while enhancing signal integrity.Key parameters like Fermi energy,bandgap,binding energy,conduction channels,quantum resistance,and RC delay were analyzed.Through modeling and large-scale simulation,the structural,electronic,and stability attributes of the AlBN interconnects are analyzed,and the results illustrate considerable improvements in signal propagation against Cu interconnect structures.These findings confirm the tunable,high-performance nature of AlBN-2Fe,making it a promising candidate for future high-speed,low-power VLSI interconnect technologies.We demonstrated an advanced energy-efficient interconnect that can be easily scaled for future nanoscale VLSI circuit design and gives rise to a next generation of viable interconnect technology for high-capacity,high-speed,reliable semiconductor technology.
文摘This survey presents a comprehensive examination of sensor fusion research spanning four decades,tracing the methodological evolution,application domains,and alignment with classical hierarchical models.Building on this long-term trajectory,the foundational approaches such as probabilistic inference,early neural networks,rulebasedmethods,and feature-level fusion established the principles of uncertainty handling andmulti-sensor integration in the 1990s.The fusion methods of 2000s marked the consolidation of these ideas through advanced Kalman and particle filtering,Bayesian–Dempster–Shafer hybrids,distributed consensus algorithms,and machine learning ensembles for more robust and domain-specific implementations.From 2011 to 2020,the widespread adoption of deep learning transformed the field driving some major breakthroughs in the autonomous vehicles domain.A key contribution of this work is the assessment of contemporary methods against the JDL model,revealing gaps at higher levels-especially in situation and impact assessment.Contemporary methods offer only limited implementation of higher-level fusion.The survey also reviews the benchmark multi-sensor datasets,noting their role in advancing the field while identifying major shortcomings like the lack of domain diversity and hierarchical coverage.By synthesizing developments across decades and paradigms,this survey provides both a historical narrative and a forward-looking perspective.It highlights unresolved challenges in transparency,scalability,robustness,and trustworthiness,while identifying emerging paradigms such as neuromorphic fusion and explainable AI as promising directions.This paves the way forward for advancing sensor fusion towards transparent and adaptive next-generation autonomous systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.42293270,42530712)the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.42401334).
文摘The spatial organization of urban-rural systems is fundamentally shaped by the agglomeration and diffusion effects inherent in human-Earth processes,giving rise to distinct gradient-based and hierarchical structures.Understanding the complexity of these interactions and their multidimensional drivers is essential for deciphering the mechanisms of integrated urban-rural development.Here,we apply a novel hierarchical spatial system framework based on the human-Earth system,combining social network analysis and multi-level modeling,to examine the evolution of the socio-spatial structure in the Beijing-Tianjin-Hebei region from 2000 to 2020.We developed a comprehensive evaluation system spanning economic,social,environmental,and infrastructural dimensions to characterize spatial patterns across multiple network levels,including city clusters,metropolitan areas,municipal-counties,towns,and villages.Our analysis reveals three key findings:First,the density of foundational network connections increased significantly,reflecting a trend toward spatial concentration driven by policy-led regional integration.Second,network structures at the city-cluster and metropolitan scales exhibited a pattern of“initial expansion followed by convergence”,accompanied by notable shifts in their spatial centers of gravity.In parallel,differentiated patterns of agglomeration and expansion were evident in the township-and village-level networks of Baoding,Tangshan,and Handan,while village-level networks in Anxin,Quyang,and other locations demonstrated distinct developmental trends.Third,community structures demonstrated strong functional homophily and interactive cohesion across multiple dimensions,with metropolitan and township communities undergoing restructuring that reflects a reconfiguration of cross-level influence and functional coupling.Spatially,the system manifests as a gradient structure of interwoven point,line,and area networks,establishing a mechanism for functional differentiation and transmission from rural to urban areas.This study provides theoretical foundations and methodological support for understanding the spatial organization logic of integrated urban-rural development,offering practical reference value for advancing regional coordination and rural revitalization in a scientifically informed manner.
基金supported by the State Grid Corporation of China under Grant for Science and Technology Projects(No.SGNXJYOOZWJS2500029).
文摘Energy storage-equipped photovoltaic(PV-storage)systems can meet frequency regulation requirements under various operating conditions,and their coordinated support for grid frequency has become a future trend.To address frequency stability issues caused by low inertia and weak damping,this paper proposes a multi-timescale frequency regulation coordinated control strategy for PV-storage integrated systems.First,a self-synchronizing control strategy for grid-connected inverters is designed based on DC voltage dynamics,enabling active inertia support while transmitting frequency variation information.Next,an energy storage inertia support control strategy is developed to enhance the frequency nadir,and an active frequency support control strategy for PV system considering a frequency regulation deadband is proposed,where the deadband value is determined based on the power regulation margin of synchronous generators,allowing the PV-storage system to adaptively switch between inertia support and primary frequency regulation under different disturbance conditions.This approach ensures system frequency stability while fully leveraging the regulation capabilities of heterogeneous resources.Finally,the real-time digital simulation results of the PV-storage integrated system demonstrate that,compared to existing control methods,the proposed strategy effectively reduces the rate of change of frequency and improves the frequency nadir under various disturbance scenarios,verifying its effectiveness.
基金supported by the Key Project of Shanghai(Project Number A1-0224-25-002-02-040,Municipal Key Course—Heat Transfer)funded by the National Natural Science Foundation of China(Grant No.52077137).
文摘To enhance the low-carbon economic efficiency and increase the utilization of renewable energy within integrated energy systems(IES),this paper proposes a low-carbon dispatch model integrating power-to-gas(P2G),carbon capture and storage(CCS),hydrogen fuel cell(HFC),and combined heat and power(CHP).The P2G process is refined into a two-stage structure,and HFC is introduced to enhance hydrogen utilization.Together with CCS and CHP,these devices form a multi-energy conversion system coupling electricity,heat,cooling,and gas.A laddertype carbon trading approach is adopted to flexibly manage carbon output by leveraging marginal cost adjustments.To evaluate the resilience of the proposed low-carbon scheduling strategy involving multiple energy units under the variability of renewable energy,a two-level robust optimization framework is developed.This model captures the most adverse scenarios of wind and solar generation.The dispatch strategy is validated against these extreme conditions to demonstrate its flexibility and effectiveness.The problem is solved using the GUROBI optimization tool.Results from simulations indicate that themodel increases renewable energy integration by 39.1%,and achieves reductions of 15.96%in carbon emissions and 16.29%in operational expenditures.The results demonstrate that the strategy ensures both economic efficiency and environmental performance under uncertain conditions.Compared with existing studies that separately model two-stage P2G or CCS devices,this paper integrates HFC,CHP,and CCS into a unified dispatchable system,enabling refined hydrogen utilization and flexible carbon circulation.Furthermore,the introduction of a laddertype carbon pricing mechanism,combined with multi-energy storage participation in implicit demand response,creates a dynamic and cost-sensitive dispatch framework.These modeling strategies go beyond conventional linear IES formulations and provide more realistic system representations.The proposed approach not only deepens the coupling among electric,thermal,and gas systems,but also offers a feasible pathway for high-penetration renewable integration in low-carbon energy systems.
基金supported by National Natural Science Foundation of China (Grant No. 11571268)Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2017JQ1022)the Fundamental Research Funds for the Central Universities (Grant No. GK201802015)
文摘In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^(1-a_uθ)(x)/|x-y|^(n-a))dx,y∈ ?R_+~n,where n 2, 2-n < a < 1, κ, θ > 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system.
文摘In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle.
文摘Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.
基金SuppoSed by the NSF of Anhui Provincial Education Depaxtment(KJ2012A265,KJ2012B187)
文摘By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results in this paper improve some known results.
