In this paper, the improved Jacobian elliptic function expansion approach is extended and applied to constructing discrete solutions of the semi-discrete coupled modified Korteweg de Vries （mKdV） equations with the ...In this paper, the improved Jacobian elliptic function expansion approach is extended and applied to constructing discrete solutions of the semi-discrete coupled modified Korteweg de Vries （mKdV） equations with the aid of the symbolic computation system Maple. Some new discrete Jacobian doubly periodic solutions are obtained. When the modulus m →1, these doubly periodic solutions degenerate into the corresponding solitary wave solutions, including kink-type, bell-type and other types of excitations.展开更多
Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other ...Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.展开更多
A direct way to construct integrable couplings for discrete systems is presented by use of two semi-direct sum Lie algebras. As their applications, the discrete integrable couplings associated with modified Korteweg-d...A direct way to construct integrable couplings for discrete systems is presented by use of two semi-direct sum Lie algebras. As their applications, the discrete integrable couplings associated with modified Korteweg-de Vries （m-KdV） lattice and two hierarchies of discrete soliton equations are developed. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards the complete classification of integrable couplings.展开更多
Numerical diffusion and oscillatory behavior characteristics are averted applying numerical solutions of advection-diffusion equation are themselves immensely sophisticated. In this paper, two numerical methods have b...Numerical diffusion and oscillatory behavior characteristics are averted applying numerical solutions of advection-diffusion equation are themselves immensely sophisticated. In this paper, two numerical methods have been used to solve the advection diffusion equation. We use an explicit finite difference scheme for the advection diffusion equation and semi-discretization on the spatial variable for advection-diffusion equation yields a system of ordinary differential equations solved by Euler’s method. Numerical assessment has been executed with specified initial and boundary conditions, for which the exact solution is known. We compare the solutions of the advection diffusion equation as well as error analysis for both schemes.展开更多
This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that...This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.展开更多
Continuum-based discrete element method(CDEM)is an explicit numerical method used for simulation of progressive failure of geological body.To improve the efficiency of contact detection and simplify the calculation st...Continuum-based discrete element method(CDEM)is an explicit numerical method used for simulation of progressive failure of geological body.To improve the efficiency of contact detection and simplify the calculation steps for contact forces,semi-spring and semi-edge are introduced in calculation.Semispring is derived from block vertex,and formed by indenting the block vertex into each face(24semisprings for a hexahedral element).The formation process of semi-edge is the same as that of semi-spring(24semi-edges for a hexahedral element).Based on the semi-springs and semi-edges,a new type of combined contact model is presented.According to this model,six contact types could be reduced to two,i.e.the semi-spring target face contact and semi-edge target edge contact.By the combined model,the contact force could be calculated directly(the information of contact type is not necessary),and the failure judgment could be executed in a straightforward way(each semi-spring and semi-edge own their characteristic areas).The algorithm has been successfully programmed in C++program.Some simple numerical cases are presented to show the validity and accuracy of this model.Finally,the failure mode,sliding distance and critical friction angle of Jiweishan landslide are studied with the combined model.展开更多
Aiming at the problems of convergence-slow and convergence-free of Discrete Particle Swarm Optimization Algorithm(DPSO) in solving large scale or complicated discrete problem, this article proposes Intuitionistic Fuzz...Aiming at the problems of convergence-slow and convergence-free of Discrete Particle Swarm Optimization Algorithm(DPSO) in solving large scale or complicated discrete problem, this article proposes Intuitionistic Fuzzy Entropy of Discrete Particle Swarm Optimization(IFDPSO) and makes it applied to Dynamic Weapon Target Assignment(WTA). First, the strategy of choosing intuitionistic fuzzy parameters of particle swarm is defined, making intuitionistic fuzzy entropy as a basic parameter for measure and velocity mutation. Second, through analyzing the defects of DPSO, an adjusting parameter for balancing two cognition, velocity mutation mechanism and position mutation strategy are designed, and then two sets of improved and derivative algorithms for IFDPSO are put forward, which ensures the IFDPSO possibly search as much as possible sub-optimal positions and its neighborhood and the algorithm ability of searching global optimal value in solving large scale 0-1 knapsack problem is intensified. Third, focusing on the problem of WTA, some parameters including dynamic parameter for shifting firepower and constraints are designed to solve the problems of weapon target assignment. In addition, WTA Optimization Model with time and resource constraints is finally set up, which also intensifies the algorithm ability of searching global and local best value in the solution of WTA problem. Finally, the superiority of IFDPSO is proved by several simulation experiments. Particularly, IFDPSO, IFDPSO1~IFDPSO3 are respectively effective in solving large scale, medium scale or strict constraint problems such as 0-1 knapsack problem and WTA problem.展开更多
Semi-implicit direct kinetics(SIDK)is an innovative method for the temporal discretization of neutronic equations proposed by J.Banfield.The key approximation of the SIDK method is to substitute a timeaveraged quantit...Semi-implicit direct kinetics(SIDK)is an innovative method for the temporal discretization of neutronic equations proposed by J.Banfield.The key approximation of the SIDK method is to substitute a timeaveraged quantity for the fission source term in the delayed neutron differential equations.Hence,these equations are decoupled from prompt neutron equations and an explicit analytical representation of precursor groups is obtained,which leads to a significant reduction in computational cost.As the fission source is not known in a time step,the original study suggested using a constant quantity pertaining to the previous time step for this purpose,and a reduction in the size of the time step was proposed to lessen the imposed errors.However,this remedy notably diminishes the main advantage of the SIDK method.We discerned that if the original method is properly introduced into the algorithm of the point-implicit solver along with some modifications,the mentioned drawbacks will be mitigated adequately.To test this idea,a novel multigroup,multi-dimensional diffusion code using the finitevolume method and a point-implicit solver is developed which works in both transient and steady states.In addition to the SIDK,two other kinetic methods,i.e.,direct kinetics and higher-order backward discretization,are programmed into the diffusion code for comparison with the proposed model.The final code is tested at different conditions of two well-known transient benchmark problems.Results indicate that while the accuracy of the improved SIDK is closely comparable with the best available kinetic methods,it reduces the total time required for computation by up to 24%.展开更多
Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-compos...Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-composition theorems of standard martingale theory tosemi - order fuzzy supermaringales and submartingales.The structure of semi - order fuzzy supermaringales andsubmartingales and the conditions of that they has Doobdecomposition (resp. Riesz decomposition) are discussedin detail.展开更多
The article gives a semi-discrete method for solving high-dimension wave equationBy the method, high-dimension wave equation is converted by, means of diseretizationinto I-D wave equation system which is well-posed. T...The article gives a semi-discrete method for solving high-dimension wave equationBy the method, high-dimension wave equation is converted by, means of diseretizationinto I-D wave equation system which is well-posed. The convergence of the semidijcrete method is given. The numerical calculating resulis show that the speed of convergence is high.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10272071） and the Natural Science Foundation of Zhejiang Lishui University of China （Grant Nos KZ05004 and KY06024）.
文摘In this paper, the improved Jacobian elliptic function expansion approach is extended and applied to constructing discrete solutions of the semi-discrete coupled modified Korteweg de Vries （mKdV） equations with the aid of the symbolic computation system Maple. Some new discrete Jacobian doubly periodic solutions are obtained. When the modulus m →1, these doubly periodic solutions degenerate into the corresponding solitary wave solutions, including kink-type, bell-type and other types of excitations.
文摘Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.
文摘A direct way to construct integrable couplings for discrete systems is presented by use of two semi-direct sum Lie algebras. As their applications, the discrete integrable couplings associated with modified Korteweg-de Vries （m-KdV） lattice and two hierarchies of discrete soliton equations are developed. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards the complete classification of integrable couplings.
文摘Numerical diffusion and oscillatory behavior characteristics are averted applying numerical solutions of advection-diffusion equation are themselves immensely sophisticated. In this paper, two numerical methods have been used to solve the advection diffusion equation. We use an explicit finite difference scheme for the advection diffusion equation and semi-discretization on the spatial variable for advection-diffusion equation yields a system of ordinary differential equations solved by Euler’s method. Numerical assessment has been executed with specified initial and boundary conditions, for which the exact solution is known. We compare the solutions of the advection diffusion equation as well as error analysis for both schemes.
文摘This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.
基金the National Basic Research Program of the Ministry of Science and Technology of China (Grant No. 2010CB731506)the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2012BAK10B01)the Youth Science Fund of National Natural Science Foundation of China (Grant No. 11302230)
文摘Continuum-based discrete element method(CDEM)is an explicit numerical method used for simulation of progressive failure of geological body.To improve the efficiency of contact detection and simplify the calculation steps for contact forces,semi-spring and semi-edge are introduced in calculation.Semispring is derived from block vertex,and formed by indenting the block vertex into each face(24semisprings for a hexahedral element).The formation process of semi-edge is the same as that of semi-spring(24semi-edges for a hexahedral element).Based on the semi-springs and semi-edges,a new type of combined contact model is presented.According to this model,six contact types could be reduced to two,i.e.the semi-spring target face contact and semi-edge target edge contact.By the combined model,the contact force could be calculated directly(the information of contact type is not necessary),and the failure judgment could be executed in a straightforward way(each semi-spring and semi-edge own their characteristic areas).The algorithm has been successfully programmed in C++program.Some simple numerical cases are presented to show the validity and accuracy of this model.Finally,the failure mode,sliding distance and critical friction angle of Jiweishan landslide are studied with the combined model.
基金supported by The National Natural Science Foundation of China under Grant Nos.61402517, 61573375The Foundation of State Key Laboratory of Astronautic Dynamics of China under Grant No. 2016ADL-DW0302+2 种基金The Postdoctoral Science Foundation of China under Grant Nos. 2013M542331, 2015M572778The Natural Science Foundation of Shaanxi Province of China under Grant No. 2013JQ8035The Aviation Science Foundation of China under Grant No. 20151996015
文摘Aiming at the problems of convergence-slow and convergence-free of Discrete Particle Swarm Optimization Algorithm(DPSO) in solving large scale or complicated discrete problem, this article proposes Intuitionistic Fuzzy Entropy of Discrete Particle Swarm Optimization(IFDPSO) and makes it applied to Dynamic Weapon Target Assignment(WTA). First, the strategy of choosing intuitionistic fuzzy parameters of particle swarm is defined, making intuitionistic fuzzy entropy as a basic parameter for measure and velocity mutation. Second, through analyzing the defects of DPSO, an adjusting parameter for balancing two cognition, velocity mutation mechanism and position mutation strategy are designed, and then two sets of improved and derivative algorithms for IFDPSO are put forward, which ensures the IFDPSO possibly search as much as possible sub-optimal positions and its neighborhood and the algorithm ability of searching global optimal value in solving large scale 0-1 knapsack problem is intensified. Third, focusing on the problem of WTA, some parameters including dynamic parameter for shifting firepower and constraints are designed to solve the problems of weapon target assignment. In addition, WTA Optimization Model with time and resource constraints is finally set up, which also intensifies the algorithm ability of searching global and local best value in the solution of WTA problem. Finally, the superiority of IFDPSO is proved by several simulation experiments. Particularly, IFDPSO, IFDPSO1~IFDPSO3 are respectively effective in solving large scale, medium scale or strict constraint problems such as 0-1 knapsack problem and WTA problem.
文摘Semi-implicit direct kinetics(SIDK)is an innovative method for the temporal discretization of neutronic equations proposed by J.Banfield.The key approximation of the SIDK method is to substitute a timeaveraged quantity for the fission source term in the delayed neutron differential equations.Hence,these equations are decoupled from prompt neutron equations and an explicit analytical representation of precursor groups is obtained,which leads to a significant reduction in computational cost.As the fission source is not known in a time step,the original study suggested using a constant quantity pertaining to the previous time step for this purpose,and a reduction in the size of the time step was proposed to lessen the imposed errors.However,this remedy notably diminishes the main advantage of the SIDK method.We discerned that if the original method is properly introduced into the algorithm of the point-implicit solver along with some modifications,the mentioned drawbacks will be mitigated adequately.To test this idea,a novel multigroup,multi-dimensional diffusion code using the finitevolume method and a point-implicit solver is developed which works in both transient and steady states.In addition to the SIDK,two other kinetic methods,i.e.,direct kinetics and higher-order backward discretization,are programmed into the diffusion code for comparison with the proposed model.The final code is tested at different conditions of two well-known transient benchmark problems.Results indicate that while the accuracy of the improved SIDK is closely comparable with the best available kinetic methods,it reduces the total time required for computation by up to 24%.
文摘Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-composition theorems of standard martingale theory tosemi - order fuzzy supermaringales and submartingales.The structure of semi - order fuzzy supermaringales andsubmartingales and the conditions of that they has Doobdecomposition (resp. Riesz decomposition) are discussedin detail.
文摘The article gives a semi-discrete method for solving high-dimension wave equationBy the method, high-dimension wave equation is converted by, means of diseretizationinto I-D wave equation system which is well-posed. The convergence of the semidijcrete method is given. The numerical calculating resulis show that the speed of convergence is high.
