Considering that the controller feedback gain and the observer gain are of additive norm-bounded variations, a design method of observer-based H-infinity output feedback controller for uncertain Delta operator systems...Considering that the controller feedback gain and the observer gain are of additive norm-bounded variations, a design method of observer-based H-infinity output feedback controller for uncertain Delta operator systems is proposed in this paper. A sufficient condition of such controllers is presented in linear matrix inequality （LMI） forms. A numerical example is then given to illustrate the effectiveness of this method, that is, the obtained controller guarantees the closed-loop system asymptotically stable and the expected H-infinity performance even if the controller feedback gain and the observer gain are varied.展开更多
By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x...By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.展开更多
The problem of H∞ filtering for polytopic Delta operator linear systems is investigated. An improved H∞ performance criterion is presented based on the bounded real lemma. Upon the improved performance criterion, a ...The problem of H∞ filtering for polytopic Delta operator linear systems is investigated. An improved H∞ performance criterion is presented based on the bounded real lemma. Upon the improved performance criterion, a sufficient condition for the existence of parameter-dependent H∞ filtering is derived in terms of linear matrix inequalities. The designed filter can be obtained from the solution of a convex optimization problem. The filter design makes full use of the parameter-dependent approach, which leads to a less conservative result than conventional design methods. A numerical example is given to illustrate the effectiveness of the proposed approach.展开更多
Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal ro...Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.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
On January 3,the United States launched a military operation against the sovereign nation of Venezuela.“capturing”its president,Nicolas Maduro.This event is far from a mere isolated"law enforcement operation&qu...On January 3,the United States launched a military operation against the sovereign nation of Venezuela.“capturing”its president,Nicolas Maduro.This event is far from a mere isolated"law enforcement operation";it represents a blatant challenge to the international legal system centered around the United Nations Charter and a thorough and dangerous trampling of the fundamental principles of intemmational relations.展开更多
In this paper, we first give the definition of possibly non-unital function system, which is a characterization of the self-adjoint subspace of the space of continuous functions on a compact Hausdorff space with the i...In this paper, we first give the definition of possibly non-unital function system, which is a characterization of the self-adjoint subspace of the space of continuous functions on a compact Hausdorff space with the induced order and norm structure. Similar to operator system case, we define the unitalization of a possibly non-unital function system. Then we construct two possibly non-unital operator system structures on a given possibly non-unital function system, which are the analogues of minimal and maximal operator spaces on a normed space. These two structures have many interesting relations with the minimal and maximal operator system structures on a given function system.展开更多
With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the it...With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.展开更多
The problem of observer-based adaptive sliding mode control of delta operator systems with time-varying delays subject to input nonlinearity is investigated. The slope parameters of this nonlinearity are unmeasured. A...The problem of observer-based adaptive sliding mode control of delta operator systems with time-varying delays subject to input nonlinearity is investigated. The slope parameters of this nonlinearity are unmeasured. A novel adaptive control law is established such that the sliding surface in the state-estimation space can be reached in a finite time. A delay-dependent sufficient condition for the asymptotic stability of both the error system and the sliding mode dynamics is derived via linear matrix inequality(LMI). Finally, a simulation example is presented to show the validity and advantage of the proposed method.展开更多
The main theme of this paper is to consider a notion of 'approximately unital operator systems' including both C*-algebras and unital operator systems.The goals are to prove a version of the Choi-Effros theore...The main theme of this paper is to consider a notion of 'approximately unital operator systems' including both C*-algebras and unital operator systems.The goals are to prove a version of the Choi-Effros theorem for these systems,to introduce a functorial process for forming an approximately unital operator systems from a given matrix ordered vector space with a proper approximate order unit,to study second duals of these objects and to prove that a C*-algebra can be characterized as an approximately unital operator system that is also an approximately unital matrix ordered *-algebra.展开更多
1.Urgent requirements for developing Feng Yun satellite observation operators In the past two decades,satellite measurements have been widely utilized for understanding and predicting weather and climate,and are now a...1.Urgent requirements for developing Feng Yun satellite observation operators In the past two decades,satellite measurements have been widely utilized for understanding and predicting weather and climate,and are now an essential component in global observing systems.展开更多
For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy princi...For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.展开更多
This paper utilizes a switched systems approach to deal with the problem of fault detectio for uncertain delta operator networked control system with packet dropouts and timevarying delays.Uncertainties exist in the m...This paper utilizes a switched systems approach to deal with the problem of fault detectio for uncertain delta operator networked control system with packet dropouts and timevarying delays.Uncertainties exist in the matrices of the systems and are norm-bounded time-varying.Two parts of packet dropouts are considered in this paper:From sensors to controllers,and from controllers to actuators.Two independent Bernoulli distributed white sequences are introduced to account for packet dropouts.Then an FD filter is designed under an arbitrary switching law.Furthermore,the sufficient conditions for the NCSs under consideration that are exponentially stable in the mean-square sense and satisfy H∞performance are obtained in terms of linear matrix inequalitie,multiple Lyapunov function and average dwell-tim approach.The explicit expression of the desired filter parameters is given.Finally,a numerical example verifies the effectiveness of the proposed method.展开更多
The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this ...The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].展开更多
This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block ...This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.展开更多
The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified...The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.展开更多
In this paper, we first introduce a new class of generalized accretive operators named （H,η）-accretive in Banach space. By studying the properties of （H,η）-accretive, we extend the concept of resolvent operators...In this paper, we first introduce a new class of generalized accretive operators named （H,η）-accretive in Banach space. By studying the properties of （H,η）-accretive, we extend the concept of resolvent operators associated with m-accretive operators to the new （H,η）-accretive operators. In terms of the new resolvent operator technique, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.展开更多
The authors study the existence of solutions for the nonlinear elliptic system {-Mλ＋,（D2u）=f（u,v）in Ω,-Mλ＋,（D2u）=g（u,v）inΩ,u≥0,v≥0 inΩ,u=v=0 on Ω, where Ω is a bounded convex domain in RN, N ≥ 2. I...The authors study the existence of solutions for the nonlinear elliptic system {-Mλ＋,（D2u）=f（u,v）in Ω,-Mλ＋,（D2u）=g（u,v）inΩ,u≥0,v≥0 inΩ,u=v=0 on Ω, where Ω is a bounded convex domain in RN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution （u, v）.展开更多
Compared with the Hamiltonian mechanics and the Lagrangian mechanics,the Birkhoffian mechanics is more general.The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators,which are prop...Compared with the Hamiltonian mechanics and the Lagrangian mechanics,the Birkhoffian mechanics is more general.The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators,which are proposed recently.Therefore,differential equations of motion within generalized fractional operators are established.Then,in order to find the solutions to the differential equations,Noether symmetry,conserved quantity,perturbation to Noether symmetry and adiabatic invariant are investigated.In the end,two applications are given to illustrate the methods and results.展开更多
The＇entanglement capacity of general two-qubit unitary operators is studied when auxiliary systems are allowed, and the analytical results based on linear entropy when input states are disentangled are given. From th...The＇entanglement capacity of general two-qubit unitary operators is studied when auxiliary systems are allowed, and the analytical results based on linear entropy when input states are disentangled are given. From the results the condition for perfect entangler, α1 = α2 = π/4, is obtained. Contrary to the case without auxiliary system, the parameter α3 may play active role to the entanglement capacity when auxiliary systems are allowed.展开更多
基金supported by the Natural Science Foundation of Fujian Province (No.2008J04016)the Fujian Education Bureau Foundation (No.JA07075)
文摘Considering that the controller feedback gain and the observer gain are of additive norm-bounded variations, a design method of observer-based H-infinity output feedback controller for uncertain Delta operator systems is proposed in this paper. A sufficient condition of such controllers is presented in linear matrix inequality （LMI） forms. A numerical example is then given to illustrate the effectiveness of this method, that is, the obtained controller guarantees the closed-loop system asymptotically stable and the expected H-infinity performance even if the controller feedback gain and the observer gain are varied.
基金Supported by the Scientific Research Foundation of Henan Provincial Education Com mittee(1999110018)
文摘By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.
文摘The problem of H∞ filtering for polytopic Delta operator linear systems is investigated. An improved H∞ performance criterion is presented based on the bounded real lemma. Upon the improved performance criterion, a sufficient condition for the existence of parameter-dependent H∞ filtering is derived in terms of linear matrix inequalities. The designed filter can be obtained from the solution of a convex optimization problem. The filter design makes full use of the parameter-dependent approach, which leads to a less conservative result than conventional design methods. A numerical example is given to illustrate the effectiveness of the proposed approach.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.42005003 and 41475094)。
文摘Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.
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.
文摘On January 3,the United States launched a military operation against the sovereign nation of Venezuela.“capturing”its president,Nicolas Maduro.This event is far from a mere isolated"law enforcement operation";it represents a blatant challenge to the international legal system centered around the United Nations Charter and a thorough and dangerous trampling of the fundamental principles of intemmational relations.
文摘In this paper, we first give the definition of possibly non-unital function system, which is a characterization of the self-adjoint subspace of the space of continuous functions on a compact Hausdorff space with the induced order and norm structure. Similar to operator system case, we define the unitalization of a possibly non-unital function system. Then we construct two possibly non-unital operator system structures on a given possibly non-unital function system, which are the analogues of minimal and maximal operator spaces on a normed space. These two structures have many interesting relations with the minimal and maximal operator system structures on a given function system.
文摘With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.
基金supported by the National Natural Science Foundation of China under Grant Nos.U1404610,61473115,61374077 and 61203047Fundamental Research Project under Grant Nos.142300410293,142102210564 in the Science and Technology Department of Henan provincethe Science and Technology Research Key Project under Grant No.14A413001 in the Education Department of Henan Province
文摘The problem of observer-based adaptive sliding mode control of delta operator systems with time-varying delays subject to input nonlinearity is investigated. The slope parameters of this nonlinearity are unmeasured. A novel adaptive control law is established such that the sliding surface in the state-estimation space can be reached in a finite time. A delay-dependent sufficient condition for the asymptotic stability of both the error system and the sliding mode dynamics is derived via linear matrix inequality(LMI). Finally, a simulation example is presented to show the validity and advantage of the proposed method.
文摘The main theme of this paper is to consider a notion of 'approximately unital operator systems' including both C*-algebras and unital operator systems.The goals are to prove a version of the Choi-Effros theorem for these systems,to introduce a functorial process for forming an approximately unital operator systems from a given matrix ordered vector space with a proper approximate order unit,to study second duals of these objects and to prove that a C*-algebra can be characterized as an approximately unital operator system that is also an approximately unital matrix ordered *-algebra.
基金the support of the National Key Research and Development Program of China “Development of Meteorological Satellite Remote Sensing Technology and Platform for Global Monitoring, Assessments and Applications under the funding code of 2018YFC1506500”
文摘1.Urgent requirements for developing Feng Yun satellite observation operators In the past two decades,satellite measurements have been widely utilized for understanding and predicting weather and climate,and are now an essential component in global observing systems.
基金Supported by the National Natural Science Foundation of China under Grant No. 10962004the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20070126002+1 种基金the Natural Science Foundation of Inner Mongolia under Grant No. 20080404MS0104the Research Foundation for Talented Scholars of Inner Mongolia University under Grant No. 207066
文摘For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.
基金supported by the National Natural Science Foundation of China under Grant No.61471323。
文摘This paper utilizes a switched systems approach to deal with the problem of fault detectio for uncertain delta operator networked control system with packet dropouts and timevarying delays.Uncertainties exist in the matrices of the systems and are norm-bounded time-varying.Two parts of packet dropouts are considered in this paper:From sensors to controllers,and from controllers to actuators.Two independent Bernoulli distributed white sequences are introduced to account for packet dropouts.Then an FD filter is designed under an arbitrary switching law.Furthermore,the sufficient conditions for the NCSs under consideration that are exponentially stable in the mean-square sense and satisfy H∞performance are obtained in terms of linear matrix inequalitie,multiple Lyapunov function and average dwell-tim approach.The explicit expression of the desired filter parameters is given.Finally,a numerical example verifies the effectiveness of the proposed method.
基金Supported by National Natural Science Foundation of China
文摘The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10962004 and 11061019)the Doctoral Foundation of Inner Mongolia(Grant Nos.2009BS0101 and 2010MS0110)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20070126002)the Chunhui Program of the Ministry of Education of China(Grant No.Z2009-1-01010)
文摘This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.
基金supported by the National Natural Science Foundation of China (Grant No. 10962004)the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 20080404MS0104)
文摘The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.
文摘In this paper, we first introduce a new class of generalized accretive operators named （H,η）-accretive in Banach space. By studying the properties of （H,η）-accretive, we extend the concept of resolvent operators associated with m-accretive operators to the new （H,η）-accretive operators. In terms of the new resolvent operator technique, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.
基金supported by National Natural Sciences Foundations of China (10571175,10631030)
文摘The authors study the existence of solutions for the nonlinear elliptic system {-Mλ＋,（D2u）=f（u,v）in Ω,-Mλ＋,（D2u）=g（u,v）inΩ,u≥0,v≥0 inΩ,u=v=0 on Ω, where Ω is a bounded convex domain in RN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution （u, v）.
基金This work was supported by the National Natural Science Foun-dation of China(Grants 11802193 and 11972241)the Natural Sci-ence Foundation of Jiangsu Province(Grant BK20191454)the Young Scientific and Technological Talents Promotion Project of Suzhou Association for Science and Technology.
文摘Compared with the Hamiltonian mechanics and the Lagrangian mechanics,the Birkhoffian mechanics is more general.The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators,which are proposed recently.Therefore,differential equations of motion within generalized fractional operators are established.Then,in order to find the solutions to the differential equations,Noether symmetry,conserved quantity,perturbation to Noether symmetry and adiabatic invariant are investigated.In the end,two applications are given to illustrate the methods and results.
基金The project supported by National Natural Science Foundation of China under Grant No. 60433050
文摘The＇entanglement capacity of general two-qubit unitary operators is studied when auxiliary systems are allowed, and the analytical results based on linear entropy when input states are disentangled are given. From the results the condition for perfect entangler, α1 = α2 = π/4, is obtained. Contrary to the case without auxiliary system, the parameter α3 may play active role to the entanglement capacity when auxiliary systems are allowed.
