Hot dry rock(HDR)is rich in reserve,widely distributed,green,low-carbon,and has broad development potential and prospects.In this paper,a distributionally robust optimization(DRO)scheduling model for a regionally inte...Hot dry rock(HDR)is rich in reserve,widely distributed,green,low-carbon,and has broad development potential and prospects.In this paper,a distributionally robust optimization(DRO)scheduling model for a regionally integrated energy system(RIES)considering HDR co-generation is proposed.First,the HDR-enhanced geothermal system(HDR-EGS)is introduced into the RIES.HDR-EGS realizes the thermoelectric decoupling of combined heat and power(CHP)through coordinated operation with the regional power grid and the regional heat grid,which enhances the system wind power(WP)feed-in space.Secondly,peak-hour loads are shifted using price demand response guidance in the context of time-of-day pricing.Finally,the optimization objective is established to minimize the total cost in the RIES scheduling cycle and construct a DRO scheduling model for RIES with HDR-EGS.By simulating a real small-scale RIES,the results show that HDR-EGS can effectively promote WP consumption and reduce the operating cost of the system.展开更多
Various application domains require the integration of distributed real-time or near-real-time systems with non-real-time systems.Smart cities,smart homes,ambient intelligent systems,or network-centric defense systems...Various application domains require the integration of distributed real-time or near-real-time systems with non-real-time systems.Smart cities,smart homes,ambient intelligent systems,or network-centric defense systems are among these application domains.Data Distribution Service(DDS)is a communication mechanism based on Data-Centric Publish-Subscribe(DCPS)model.It is used for distributed systems with real-time operational constraints.Java Message Service(JMS)is a messaging standard for enterprise systems using Service Oriented Architecture(SOA)for non-real-time operations.JMS allows Java programs to exchange messages in a loosely coupled fashion.JMS also supports sending and receiving messages using a messaging queue and a publish-subscribe interface.In this article,we propose an architecture enabling the automated integration of distributed real-time and non-real-time systems.We test our proposed architecture using a distributed Command,Control,Communications,Computers,and Intelligence(C4I)system.The system has DDS-based real-time Combat Management System components deployed to naval warships,and SOA-based non-real-time Command and Control components used at headquarters.The proposed solution enables the exchange of data between these two systems efficiently.We compare the proposed solution with a similar study.Our solution is superior in terms of automation support,ease of implementation,scalability,and performance.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
A linear matrix inequality (LMI)-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system und...A linear matrix inequality (LMI)-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system under consideration may have mis- matching norm bounded uncertainties in the state matrix as well as the input matrix, A sufficient condition for the existence of a sliding surface is given to guarantee asymptotic stability of the full order slJdJng mode dynamics. An LMI characterization of the slid- ing surface is given, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Finally, a simulation is given to show the effectiveness of the proposed method.展开更多
I firmly believe that of systems engineering is the requirement-driven force for the progress ofsoftware engineering, artificial intelligence and electronic technologies. The development ofsoftware engineering, artifi...I firmly believe that of systems engineering is the requirement-driven force for the progress ofsoftware engineering, artificial intelligence and electronic technologies. The development ofsoftware engineering, artificial intelligence and electronic technologies is the technical supportfor the progress of systems engineering. INTEGRATION can be considered as "bridging" the ex-isting technologies and the People together into a coordinated SYSTEM.展开更多
A new method.for the construction of integrable Hamiltonian system is proposed.For a given Poisson manifold the present paper constructs new Poisson brackets on it by making use of the Dirac-Poisson structure[1],and ...A new method.for the construction of integrable Hamiltonian system is proposed.For a given Poisson manifold the present paper constructs new Poisson brackets on it by making use of the Dirac-Poisson structure[1],and obtains .further new integrable Hamiltonian systems The constructed Poisson bracket is usual non-linear, and this new method is also different from usual ones[2-4].Two examples are given.展开更多
The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system an...The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system and showed that the time evolution equations for n≤3 obtained by nonlinearizing the time parts of Lax systems for AKNS hierarchy are Liouville integrable under the constraint of the spatial part.展开更多
The modern history of management systems is almost the same as the history of modern management science. Implicit management systems have been in existence for many 100s of years. ISO has paid attention to the issue o...The modern history of management systems is almost the same as the history of modern management science. Implicit management systems have been in existence for many 100s of years. ISO has paid attention to the issue of the integrated management systems since the ISO 9000 family standards for quality management systems (QMS) and ISO 14000 series standards for environment management syste(EMS) were published. ISO/TAG(Technical Advisory Group)12 was formed by the ISO/TM(Technical Management Board) in early 1997 with the mandate to achieve greater compatibility between the relevant ISO/TC 176 and ISO/TC 207 standards in the field of management systems, auditing, terms and definitions. The report was submitted to TMB by TAG 12 in 1999.展开更多
Multi-criteria handoff algorithms have been playing a more important role than the traditional handoff algorithms.In order to balance the satisfaction of users and the efficiency of networks,it is necessary to develop...Multi-criteria handoff algorithms have been playing a more important role than the traditional handoff algorithms.In order to balance the satisfaction of users and the efficiency of networks,it is necessary to develop new technologies to improve the validity of handoff algorithms.Intelligent and optimized handoff algorithms in hybrid networks that integrate Ad hoc and mobile cellular systems are well-adaptive and robust.They are able to implement handoffs adaptively,according to specific multi-factors such as different Quality of Service(QoS)requirements,network states and mobile node conditions in the future hybrid networks.Therefore,these intelligent and optimized algorithms can make more effective handover decision,and accordingly improve the system’s performance.The future research will tackle intelligent or optimized vertical handoff algorithms for integrated Ad hoc and mobile cellular networks to improve their whole system performance.展开更多
The enhanced definition of Mechatronics involves the four underlying characteristics of integrated,unified,unique,and systematic approaches.In this realm,Mechatronics is not limited to electro-mechanical systems,in th...The enhanced definition of Mechatronics involves the four underlying characteristics of integrated,unified,unique,and systematic approaches.In this realm,Mechatronics is not limited to electro-mechanical systems,in the multi-physics sense,but involves other physical domains such as fluid and thermal.This paper summarizes the mechatronic approach to modeling.Linear graphs facilitate the development of state-space models of mechatronic systems,through this approach.The use of linear graphs in mechatronic modeling is outlined and an illustrative example of sound system modeling is given.Both time-domain and frequency-domain approaches are presented for the use of linear graphs.A mechatronic model of a multi-physics system may be simplified by converting all the physical domains into an equivalent single-domain system that is entirely in the output domain of the system.This approach of converting(transforming)physical domains is presented.An illustrative example of a pressure-controlled hydraulic actuator system that operates a mechanical load is given.展开更多
国际上先进的“人与系统整合”(Human Systems Integration,HSI)体系和应用案例表明,HSI是系统工程的重要组成部分,在系统工程早期考虑人与系统整合,有助于实现以人为中心的系统设计,在技术、经济、安全等方面实现硬件、软件和人之间的...国际上先进的“人与系统整合”(Human Systems Integration,HSI)体系和应用案例表明,HSI是系统工程的重要组成部分,在系统工程早期考虑人与系统整合,有助于实现以人为中心的系统设计,在技术、经济、安全等方面实现硬件、软件和人之间的合理平衡。基于核电厂复杂系统设计中存在的问题和未来以系统工程为基础的研发策略,本文提出了在核电厂建立人因系统工程(HSE)体系的建议,并对核电厂HSE所关注的领域、研究方向和需要解决的问题提出了作者观点,以期为核电厂HSE体系的建立提供一定思路。展开更多
We study the physical properties of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields. By using a combination of numerical analysis and analytical method, we obtain the surface energy and elementary e...We study the physical properties of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields. By using a combination of numerical analysis and analytical method, we obtain the surface energy and elementary excitations of the model. It shows that the contributions of the two boundary fields to the surface energy are additive. We also find that there exists a kind of excitations related to the boundary string.展开更多
A new type of symmetry,ren-symmetry,describing anyon physics and corresponding topological physics,is proposed.Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such...A new type of symmetry,ren-symmetry,describing anyon physics and corresponding topological physics,is proposed.Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as super-symmetric quantum mechanics,super-symmetric gravity,super-symmetric string theory,super-symmetric integrable systems and so on.Supersymmetry and Grassmann numbers are,in some sense,dual conceptions,and it turns out that these conceptions coincide for the ren situation,that is,a similar conception of ren-number(R-number)is devised for ren-symmetry.In particular,some basic results of the R-number and ren-symmetry are exposed which allow one to derive,in principle,some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems.Training examples of ren-integrable KdV-type systems and ren-symmetric KdV equations are explicitly given.展开更多
The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierar...The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
Wearable sensing systems,as a spearhead of artificial intelligence,are playing increasingly important roles in many fields especially health monitoring.In order to achieve a better wearable experience,rationally integ...Wearable sensing systems,as a spearhead of artificial intelligence,are playing increasingly important roles in many fields especially health monitoring.In order to achieve a better wearable experience,rationally integrating the two key components of sensing systems,that is,power supplies and sensors,has become a desperate requirement.However,limited by device designs and fabrication technologies,the current integrated sensing systems still face many great challenges,such as safety,miniaturization,mechanical stability,energyefficiency,sustainability,and comfortability.In this review,the key challenges and opportunities in the current development of integrated wearable sensing systems are summarized.By summarizing the typical configurations of diverse wearable power supplies,and recent advances concerning the integrated sensing systems driven by such power supplies,the representative integrated designs,and micro/nanofabrication technologies are highlighted.Lastly,some new directions and potential solutions aiming at the device-level integration designs are outlooked.展开更多
In this paper, we are concerned with the following Hardy-Sobolev type system{(-?)^(α/2) u(x) =v^q(x)/|y|^(t_2) (-?)α/2 v(x) =u^p(x)/|y|^(t_1),x =(y, z) ∈(R ~k\{0}) × R^(n-k),(0.1)where 0 < α < n, 0 <...In this paper, we are concerned with the following Hardy-Sobolev type system{(-?)^(α/2) u(x) =v^q(x)/|y|^(t_2) (-?)α/2 v(x) =u^p(x)/|y|^(t_1),x =(y, z) ∈(R ~k\{0}) × R^(n-k),(0.1)where 0 < α < n, 0 < t_1, t_2 < min{α, k}, and 1 < p ≤ τ_1 :=(n+α-2t_1)/( n-α), 1 < q ≤ τ_2 :=(n+α-2 t_2)/( n-α).We first establish the equivalence of classical and weak solutions between PDE system(0.1)and the following integral equations(IE) system{u(x) =∫_( R^n) G_α(x, ξ)v^q(ξ)/|η|t^2 dξ v(x) =∫_(R^n) G_α(x, ξ)(u^p(ξ))/|η|^(t_1) dξ,(0.2)where Gα(x, ξ) =(c n,α)/(|x-ξ|^(n-α))is the Green's function of(-?)^(α/2) in R^n. Then, by the method of moving planes in the integral forms, in the critical case p = τ_1 and q = τ_2, we prove that each pair of nonnegative solutions(u, v) of(0.1) is radially symmetric and monotone decreasing about the origin in R^k and some point z0 in R^(n-k). In the subcritical case (n-t_1)/(p+1)+(n-t_2)/(q+1)> n-α,1 < p ≤ τ_1 and 1 < q ≤ τ_2, we derive the nonexistence of nontrivial nonnegative solutions for(0.1).展开更多
This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric ...This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric functions have been presented.In virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,respectively.In addition,the solutions of these integrable systems have been discussed.展开更多
A random simulation method was used for treatment of systems of Volterra integral equations of the second kind. Firstly, a linear algebra system was obtained by discretization using quadrature formula. Secondly, this ...A random simulation method was used for treatment of systems of Volterra integral equations of the second kind. Firstly, a linear algebra system was obtained by discretization using quadrature formula. Secondly, this algebra system was solved by using relaxed Monte Carlo method with importance sampling and numerical approximation solutions of the integral equations system were achieved. It is theoretically proved that the validity of relaxed Monte Carlo method is based on importance sampling to solve the integral equations system. Finally, some numerical examples from literatures are given to show the efficiency of the method.展开更多
基金King Saud University for funding this research through the Researchers Supporting Program Number(RSPD2024R704),King Saud University,Riyadh,Saudi Arabia.
文摘Hot dry rock(HDR)is rich in reserve,widely distributed,green,low-carbon,and has broad development potential and prospects.In this paper,a distributionally robust optimization(DRO)scheduling model for a regionally integrated energy system(RIES)considering HDR co-generation is proposed.First,the HDR-enhanced geothermal system(HDR-EGS)is introduced into the RIES.HDR-EGS realizes the thermoelectric decoupling of combined heat and power(CHP)through coordinated operation with the regional power grid and the regional heat grid,which enhances the system wind power(WP)feed-in space.Secondly,peak-hour loads are shifted using price demand response guidance in the context of time-of-day pricing.Finally,the optimization objective is established to minimize the total cost in the RIES scheduling cycle and construct a DRO scheduling model for RIES with HDR-EGS.By simulating a real small-scale RIES,the results show that HDR-EGS can effectively promote WP consumption and reduce the operating cost of the system.
文摘Various application domains require the integration of distributed real-time or near-real-time systems with non-real-time systems.Smart cities,smart homes,ambient intelligent systems,or network-centric defense systems are among these application domains.Data Distribution Service(DDS)is a communication mechanism based on Data-Centric Publish-Subscribe(DCPS)model.It is used for distributed systems with real-time operational constraints.Java Message Service(JMS)is a messaging standard for enterprise systems using Service Oriented Architecture(SOA)for non-real-time operations.JMS allows Java programs to exchange messages in a loosely coupled fashion.JMS also supports sending and receiving messages using a messaging queue and a publish-subscribe interface.In this article,we propose an architecture enabling the automated integration of distributed real-time and non-real-time systems.We test our proposed architecture using a distributed Command,Control,Communications,Computers,and Intelligence(C4I)system.The system has DDS-based real-time Combat Management System components deployed to naval warships,and SOA-based non-real-time Command and Control components used at headquarters.The proposed solution enables the exchange of data between these two systems efficiently.We compare the proposed solution with a similar study.Our solution is superior in terms of automation support,ease of implementation,scalability,and performance.
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 in part by the National Basic Research Program of China(973 Program)(61334)
文摘A linear matrix inequality (LMI)-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system under consideration may have mis- matching norm bounded uncertainties in the state matrix as well as the input matrix, A sufficient condition for the existence of a sliding surface is given to guarantee asymptotic stability of the full order slJdJng mode dynamics. An LMI characterization of the slid- ing surface is given, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Finally, a simulation is given to show the effectiveness of the proposed method.
文摘I firmly believe that of systems engineering is the requirement-driven force for the progress ofsoftware engineering, artificial intelligence and electronic technologies. The development ofsoftware engineering, artificial intelligence and electronic technologies is the technical supportfor the progress of systems engineering. INTEGRATION can be considered as "bridging" the ex-isting technologies and the People together into a coordinated SYSTEM.
文摘A new method.for the construction of integrable Hamiltonian system is proposed.For a given Poisson manifold the present paper constructs new Poisson brackets on it by making use of the Dirac-Poisson structure[1],and obtains .further new integrable Hamiltonian systems The constructed Poisson bracket is usual non-linear, and this new method is also different from usual ones[2-4].Two examples are given.
文摘The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system and showed that the time evolution equations for n≤3 obtained by nonlinearizing the time parts of Lax systems for AKNS hierarchy are Liouville integrable under the constraint of the spatial part.
文摘The modern history of management systems is almost the same as the history of modern management science. Implicit management systems have been in existence for many 100s of years. ISO has paid attention to the issue of the integrated management systems since the ISO 9000 family standards for quality management systems (QMS) and ISO 14000 series standards for environment management syste(EMS) were published. ISO/TAG(Technical Advisory Group)12 was formed by the ISO/TM(Technical Management Board) in early 1997 with the mandate to achieve greater compatibility between the relevant ISO/TC 176 and ISO/TC 207 standards in the field of management systems, auditing, terms and definitions. The report was submitted to TMB by TAG 12 in 1999.
基金This work was funded by the High- tech Research and Development Program of China (863 Program) under Grant 2006AA01Z208.
文摘Multi-criteria handoff algorithms have been playing a more important role than the traditional handoff algorithms.In order to balance the satisfaction of users and the efficiency of networks,it is necessary to develop new technologies to improve the validity of handoff algorithms.Intelligent and optimized handoff algorithms in hybrid networks that integrate Ad hoc and mobile cellular systems are well-adaptive and robust.They are able to implement handoffs adaptively,according to specific multi-factors such as different Quality of Service(QoS)requirements,network states and mobile node conditions in the future hybrid networks.Therefore,these intelligent and optimized algorithms can make more effective handover decision,and accordingly improve the system’s performance.The future research will tackle intelligent or optimized vertical handoff algorithms for integrated Ad hoc and mobile cellular networks to improve their whole system performance.
基金supported by research grants from the Natural Sciences and Engineering Research Council(NSERC)of Canada
文摘The enhanced definition of Mechatronics involves the four underlying characteristics of integrated,unified,unique,and systematic approaches.In this realm,Mechatronics is not limited to electro-mechanical systems,in the multi-physics sense,but involves other physical domains such as fluid and thermal.This paper summarizes the mechatronic approach to modeling.Linear graphs facilitate the development of state-space models of mechatronic systems,through this approach.The use of linear graphs in mechatronic modeling is outlined and an illustrative example of sound system modeling is given.Both time-domain and frequency-domain approaches are presented for the use of linear graphs.A mechatronic model of a multi-physics system may be simplified by converting all the physical domains into an equivalent single-domain system that is entirely in the output domain of the system.This approach of converting(transforming)physical domains is presented.An illustrative example of a pressure-controlled hydraulic actuator system that operates a mechanical load is given.
文摘国际上先进的“人与系统整合”(Human Systems Integration,HSI)体系和应用案例表明,HSI是系统工程的重要组成部分,在系统工程早期考虑人与系统整合,有助于实现以人为中心的系统设计,在技术、经济、安全等方面实现硬件、软件和人之间的合理平衡。基于核电厂复杂系统设计中存在的问题和未来以系统工程为基础的研发策略,本文提出了在核电厂建立人因系统工程(HSE)体系的建议,并对核电厂HSE所关注的领域、研究方向和需要解决的问题提出了作者观点,以期为核电厂HSE体系的建立提供一定思路。
基金financial supports from the National Key R&D Program of China (Grant No.2021YFA1402104)the National Natural Science Foundation of China (Grant Nos.12074410,12047502,12147160,11934015,11975183,and 11947301)+3 种基金Major Basic Research Program of Natural Science of Shaanxi Province,China (Grant Nos.2021JCW-19 and 2017ZDJC-32)Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No.XDB33000000)Double First-Class University Construction Project of Northwest Universitythe fellowship of China Postdoctoral Science Foundation (Grant Nos.2020M680724 and 2022M712580)。
文摘We study the physical properties of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields. By using a combination of numerical analysis and analytical method, we obtain the surface energy and elementary excitations of the model. It shows that the contributions of the two boundary fields to the surface energy are additive. We also find that there exists a kind of excitations related to the boundary string.
基金sponsored by the National Natural Science Foundation of China(Nos.12235007,11975131)。
文摘A new type of symmetry,ren-symmetry,describing anyon physics and corresponding topological physics,is proposed.Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as super-symmetric quantum mechanics,super-symmetric gravity,super-symmetric string theory,super-symmetric integrable systems and so on.Supersymmetry and Grassmann numbers are,in some sense,dual conceptions,and it turns out that these conceptions coincide for the ren situation,that is,a similar conception of ren-number(R-number)is devised for ren-symmetry.In particular,some basic results of the R-number and ren-symmetry are exposed which allow one to derive,in principle,some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems.Training examples of ren-integrable KdV-type systems and ren-symmetric KdV equations are explicitly given.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147 and 11071159)the Natural Science Foundation of Shanghai,China (Grant No.09ZR1410800)+2 种基金the Science Foundation of the Key Laboratory of Mathematics Mechanization,China (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project,China (Grant No.J50101)the Key Disciplines of Shanghai Municipality of China (Grant No.S30104)
文摘The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
基金GRF,Hong Kong,Grant/Award Number:CityU 11305218Natural Science Foundation of Guangdong Province,Grant/Award Number:2019A1515011819Songshan Lake Materials Laboratory grant,Grant/Award Number:Y8D1041Z111。
文摘Wearable sensing systems,as a spearhead of artificial intelligence,are playing increasingly important roles in many fields especially health monitoring.In order to achieve a better wearable experience,rationally integrating the two key components of sensing systems,that is,power supplies and sensors,has become a desperate requirement.However,limited by device designs and fabrication technologies,the current integrated sensing systems still face many great challenges,such as safety,miniaturization,mechanical stability,energyefficiency,sustainability,and comfortability.In this review,the key challenges and opportunities in the current development of integrated wearable sensing systems are summarized.By summarizing the typical configurations of diverse wearable power supplies,and recent advances concerning the integrated sensing systems driven by such power supplies,the representative integrated designs,and micro/nanofabrication technologies are highlighted.Lastly,some new directions and potential solutions aiming at the device-level integration designs are outlooked.
基金supported by the NNSF of China(11371056)partly supported by the NNSF of China(11501021)+1 种基金the China Postdoctoral Science Foundation(2013M540057)partly supported by Scientific Research Fund of Jiangxi Provincial Education Department(GJJ160797)
文摘In this paper, we are concerned with the following Hardy-Sobolev type system{(-?)^(α/2) u(x) =v^q(x)/|y|^(t_2) (-?)α/2 v(x) =u^p(x)/|y|^(t_1),x =(y, z) ∈(R ~k\{0}) × R^(n-k),(0.1)where 0 < α < n, 0 < t_1, t_2 < min{α, k}, and 1 < p ≤ τ_1 :=(n+α-2t_1)/( n-α), 1 < q ≤ τ_2 :=(n+α-2 t_2)/( n-α).We first establish the equivalence of classical and weak solutions between PDE system(0.1)and the following integral equations(IE) system{u(x) =∫_( R^n) G_α(x, ξ)v^q(ξ)/|η|t^2 dξ v(x) =∫_(R^n) G_α(x, ξ)(u^p(ξ))/|η|^(t_1) dξ,(0.2)where Gα(x, ξ) =(c n,α)/(|x-ξ|^(n-α))is the Green's function of(-?)^(α/2) in R^n. Then, by the method of moving planes in the integral forms, in the critical case p = τ_1 and q = τ_2, we prove that each pair of nonnegative solutions(u, v) of(0.1) is radially symmetric and monotone decreasing about the origin in R^k and some point z0 in R^(n-k). In the subcritical case (n-t_1)/(p+1)+(n-t_2)/(q+1)> n-α,1 < p ≤ τ_1 and 1 < q ≤ τ_2, we derive the nonexistence of nontrivial nonnegative solutions for(0.1).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11965014 and 12061051)the National Science Foundation of Qinghai Province,China(Grant No.2021-ZJ-708)。
文摘This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric functions have been presented.In virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,respectively.In addition,the solutions of these integrable systems have been discussed.
文摘A random simulation method was used for treatment of systems of Volterra integral equations of the second kind. Firstly, a linear algebra system was obtained by discretization using quadrature formula. Secondly, this algebra system was solved by using relaxed Monte Carlo method with importance sampling and numerical approximation solutions of the integral equations system were achieved. It is theoretically proved that the validity of relaxed Monte Carlo method is based on importance sampling to solve the integral equations system. Finally, some numerical examples from literatures are given to show the efficiency of the method.