Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of...Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.展开更多
We use the Fokas method to analyze the derivative nonlinear Schrodinger (DNLS) equation iqt (x, t) = -qxx (x, t)+(rq^2)x on the interval [0, L]. Assuming that the solution q(x, t) exists, we show that it ca...We use the Fokas method to analyze the derivative nonlinear Schrodinger (DNLS) equation iqt (x, t) = -qxx (x, t)+(rq^2)x on the interval [0, L]. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit (x, t) dependence, and it has jumps across {ξ∈C|Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a(ξ), b(ξ)}, {A(ξ), B(ξ)}, and {A(ξ), B(ξ)}, which in turn are defined in terms of the initial data q0(x) = q(x, 0), the bound- ary data g0(t)= q(0, t), g1(t) = qx(0, t), and another boundary values f0(t) = q(L, t), f1(t) = qx(L, t). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.展开更多
Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of...Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.展开更多
Developing and optimizing fuzzy relation equations are of great relevance in system modeling,which involves analysis of numerous fuzzy rules.As each rule varies with respect to its level of influence,it is advocated t...Developing and optimizing fuzzy relation equations are of great relevance in system modeling,which involves analysis of numerous fuzzy rules.As each rule varies with respect to its level of influence,it is advocated that the performance of a fuzzy relation equation is strongly related to a subset of fuzzy rules obtained by removing those without significant relevance.In this study,we establish a novel framework of developing granular fuzzy relation equations that concerns the determination of an optimal subset of fuzzy rules.The subset of rules is selected by maximizing their performance of the obtained solutions.The originality of this study is conducted in the following ways.Starting with developing granular fuzzy relation equations,an interval-valued fuzzy relation is determined based on the selected subset of fuzzy rules(the subset of rules is transformed to interval-valued fuzzy sets and subsequently the interval-valued fuzzy sets are utilized to form interval-valued fuzzy relations),which can be used to represent the fuzzy relation of the entire rule base with high performance and efficiency.Then,the particle swarm optimization(PSO)is implemented to solve a multi-objective optimization problem,in which not only an optimal subset of rules is selected but also a parameterεfor specifying a level of information granularity is determined.A series of experimental studies are performed to verify the feasibility of this framework and quantify its performance.A visible improvement of particle swarm optimization(about 78.56%of the encoding mechanism of particle swarm optimization,or 90.42%of particle swarm optimization with an exploration operator)is gained over the method conducted without using the particle swarm optimization algorithm.展开更多
The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzz...The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.展开更多
This paper considers solving a multi-objective optimization problem with sup-T equation constraints A set covering-based technique for order of preference by similarity to the ideal solution is proposed for solving su...This paper considers solving a multi-objective optimization problem with sup-T equation constraints A set covering-based technique for order of preference by similarity to the ideal solution is proposed for solving such a problem. It is shown that a compromise solution of the sup-T equation constrained multi-objective optimization problem can be obtained by "solving an associated set covering problem. A surrogate heuristic is then applied to solve the resulting optimization problem. Numerical experiments on solving randomly generated multi-objective optimization problems with sup-T equation constraints are included. Our computational results confirm the efficiency of the proposed method and show its potential for solving large scale sup-T equation constrained multi-objective optimization problems.展开更多
In this paper an explicit finite-difference time-domain scheme for solving the Maxwell’s equations in non-staggered grids is presented.The proposed scheme for solving the Faraday’s and Amp`ere’s equations in a theo...In this paper an explicit finite-difference time-domain scheme for solving the Maxwell’s equations in non-staggered grids is presented.The proposed scheme for solving the Faraday’s and Amp`ere’s equations in a theoretical manner is aimed to preserve discrete zero-divergence for the electric and magnetic fields.The inherent local conservation laws in Maxwell’s equations are also preserved discretely all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta scheme.The remaining spatial derivative terms in the semi-discretized Faraday’s and Amp`ere’s equations are then discretized to provide an accurate mathematical dispersion relation equation that governs the numerical angular frequency and the wavenumbers in two space dimensions.To achieve the goal of getting the best dispersive characteristics,we propose a fourth-order accurate space centered scheme which minimizes the difference between the exact and numerical dispersion relation equations.Through the computational exercises,the proposed dual-preserving solver is computationally demonstrated to be efficient for use to predict the long-term accurate Maxwell’s solutions.展开更多
Kapur and Musser studied the theoretical basis for proof by consistency and ob-tained an inductive completeness result: p q if and only if p = q is true in everyinductive model. However, there is a loophole in their p...Kapur and Musser studied the theoretical basis for proof by consistency and ob-tained an inductive completeness result: p q if and only if p = q is true in everyinductive model. However, there is a loophole in their proof for the soundness part:p = q implies p = q is true in every inductive model. The aim of this paper is to give acorrect characterization of inductive soundness from an algebraic view by introducingstrong inductive models.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 11142014)the Scientific Research and Innovation Plan for College Graduates of Jiangsu Province,China (Grant No. CXLX12_0720)
文摘Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.
基金supported by grants from the National Science Foundation of China (10971031 11271079+2 种基金 11075055)Doctoral Programs Foundation of the Ministry of Education of Chinathe Shanghai Shuguang Tracking Project (08GG01)
文摘We use the Fokas method to analyze the derivative nonlinear Schrodinger (DNLS) equation iqt (x, t) = -qxx (x, t)+(rq^2)x on the interval [0, L]. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit (x, t) dependence, and it has jumps across {ξ∈C|Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a(ξ), b(ξ)}, {A(ξ), B(ξ)}, and {A(ξ), B(ξ)}, which in turn are defined in terms of the initial data q0(x) = q(x, 0), the bound- ary data g0(t)= q(0, t), g1(t) = qx(0, t), and another boundary values f0(t) = q(L, t), f1(t) = qx(L, t). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.
文摘Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.
基金supported by the National Natural Sci-ence Foundation of China(62006184,62076189,61873277).
文摘Developing and optimizing fuzzy relation equations are of great relevance in system modeling,which involves analysis of numerous fuzzy rules.As each rule varies with respect to its level of influence,it is advocated that the performance of a fuzzy relation equation is strongly related to a subset of fuzzy rules obtained by removing those without significant relevance.In this study,we establish a novel framework of developing granular fuzzy relation equations that concerns the determination of an optimal subset of fuzzy rules.The subset of rules is selected by maximizing their performance of the obtained solutions.The originality of this study is conducted in the following ways.Starting with developing granular fuzzy relation equations,an interval-valued fuzzy relation is determined based on the selected subset of fuzzy rules(the subset of rules is transformed to interval-valued fuzzy sets and subsequently the interval-valued fuzzy sets are utilized to form interval-valued fuzzy relations),which can be used to represent the fuzzy relation of the entire rule base with high performance and efficiency.Then,the particle swarm optimization(PSO)is implemented to solve a multi-objective optimization problem,in which not only an optimal subset of rules is selected but also a parameterεfor specifying a level of information granularity is determined.A series of experimental studies are performed to verify the feasibility of this framework and quantify its performance.A visible improvement of particle swarm optimization(about 78.56%of the encoding mechanism of particle swarm optimization,or 90.42%of particle swarm optimization with an exploration operator)is gained over the method conducted without using the particle swarm optimization algorithm.
基金This work was partially supported by the Natural Science Foundation of China (No. 611 74094) the Tianjin Natural Science Foundation of China (No. 13JCYBJC1 7400) the Program for New Century Excellent Talents in University of China (No. NCET-10-0506).
文摘The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.
文摘This paper considers solving a multi-objective optimization problem with sup-T equation constraints A set covering-based technique for order of preference by similarity to the ideal solution is proposed for solving such a problem. It is shown that a compromise solution of the sup-T equation constrained multi-objective optimization problem can be obtained by "solving an associated set covering problem. A surrogate heuristic is then applied to solve the resulting optimization problem. Numerical experiments on solving randomly generated multi-objective optimization problems with sup-T equation constraints are included. Our computational results confirm the efficiency of the proposed method and show its potential for solving large scale sup-T equation constrained multi-objective optimization problems.
基金supported by the National Science Council of the Republic of China under the Grants NSC96-2221-E-002-293-MY2,NSC96-2221-E-002-004,and CQSE97R0066-69.
文摘In this paper an explicit finite-difference time-domain scheme for solving the Maxwell’s equations in non-staggered grids is presented.The proposed scheme for solving the Faraday’s and Amp`ere’s equations in a theoretical manner is aimed to preserve discrete zero-divergence for the electric and magnetic fields.The inherent local conservation laws in Maxwell’s equations are also preserved discretely all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta scheme.The remaining spatial derivative terms in the semi-discretized Faraday’s and Amp`ere’s equations are then discretized to provide an accurate mathematical dispersion relation equation that governs the numerical angular frequency and the wavenumbers in two space dimensions.To achieve the goal of getting the best dispersive characteristics,we propose a fourth-order accurate space centered scheme which minimizes the difference between the exact and numerical dispersion relation equations.Through the computational exercises,the proposed dual-preserving solver is computationally demonstrated to be efficient for use to predict the long-term accurate Maxwell’s solutions.
文摘Kapur and Musser studied the theoretical basis for proof by consistency and ob-tained an inductive completeness result: p q if and only if p = q is true in everyinductive model. However, there is a loophole in their proof for the soundness part:p = q implies p = q is true in every inductive model. The aim of this paper is to give acorrect characterization of inductive soundness from an algebraic view by introducingstrong inductive models.