In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems （...In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems （DDEs）, As a concrete example, new families of exact solutions to the （2＋1）-dimensional Toda lattice system are obtained by the extended projective approach.展开更多
The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on...The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.展开更多
The effectiveness of evaluating an investment project based on predicting cash flows depends on the uncertainty of its future cash flows. The remoter the cash flows are, the higher the uncertainty is. Because of this,...The effectiveness of evaluating an investment project based on predicting cash flows depends on the uncertainty of its future cash flows. The remoter the cash flows are, the higher the uncertainty is. Because of this, this paper suggests to discount cash flows by applying risky index of time （RIT）. Thus, the discount rate used to discount the distant cash flows is higher that the discount rate used to discount the near cash flows. By this systematic method, the risk caused by the uncertainty of future cash flows can be hedged in making investment decision. To a certain degree, this approach is reasonable in evaluating investment alternatives under uncertainty. Furthermore, the paper puts forward a practical approach on determining RIT in practice.展开更多
With the aid of an improved projective approach and a linear variable separation method, new types of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function s...With the aid of an improved projective approach and a linear variable separation method, new types of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （2＋1）-dimensional Korteweg-de Vries system are derived. Usually, in terms of solitary wave solutions and rational function solutions, one can find some important localized excitations. However, based on the derived periodic wave solution in this paper, we find that some novel and significant localized coherent excitations such as dromions, peakons, stochastic fractal patterns, regular fractal patterns, chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications.展开更多
With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the（2＋1）-dimensional generalized Breor-Kaup（GB...With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the（2＋1）-dimensional generalized Breor-Kaup（GBK） system is derived.Based on the derived solitary wave solution,some chaotic behaviors of the GBK system are investigated.展开更多
By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solut...By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated.展开更多
For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exa...For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the （2＋l）-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.展开更多
The paper studies on case-based reasoning of uncertain product attributes in configuration design of a product family. Interval numbers characterize uncertain product attributes. By interpolating a number of certain v...The paper studies on case-based reasoning of uncertain product attributes in configuration design of a product family. Interval numbers characterize uncertain product attributes. By interpolating a number of certain values randomly to replace interval numbers and making projection pursuit analysis on source cases and target cases of expanded numbers, we can get a projection value in the optimal projection direction. Based on projection value, we can construct a case retrieval model of projection pursuit that can handle coexisting certain and uncertain product attributes. The application examples of chainsaw configuration design show that case retrieval is highly sensitive to reliable results.展开更多
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang LishuiThe authors are in debt to Profs. J.F. Zhang, Z.M. Sheng, and L.Q. Chen, Drs. Z.Y. Ma and W.H. Huang for their helpful suggestions and fruitful discussions, and express their sincere thanks to Prof. S.Y. Lou for his useful references.University under Grant No. KZ05010
文摘In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems （DDEs）, As a concrete example, new families of exact solutions to the （2＋1）-dimensional Toda lattice system are obtained by the extended projective approach.
基金supported by the National Natural Science Foundation of China(62176218,62176027)the Fundamental Research Funds for the Central Universities(XDJK2020TY003)the Funds for Chongqing Talent Plan(cstc2024ycjh-bgzxm0082)。
文摘The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.
文摘The effectiveness of evaluating an investment project based on predicting cash flows depends on the uncertainty of its future cash flows. The remoter the cash flows are, the higher the uncertainty is. Because of this, this paper suggests to discount cash flows by applying risky index of time （RIT）. Thus, the discount rate used to discount the distant cash flows is higher that the discount rate used to discount the near cash flows. By this systematic method, the risk caused by the uncertainty of future cash flows can be hedged in making investment decision. To a certain degree, this approach is reasonable in evaluating investment alternatives under uncertainty. Furthermore, the paper puts forward a practical approach on determining RIT in practice.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, the Foundation of New Century ＂151 Talent Engineering＂ of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05005 The authors are in debt to Profs. J.P. Fang, C.Z. Xu, and J.F. Zhang, and Drs. H.P. Zhu, Z.Y. Ma, and W.H. Huang for their fruitful discussions.
文摘With the aid of an improved projective approach and a linear variable separation method, new types of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （2＋1）-dimensional Korteweg-de Vries system are derived. Usually, in terms of solitary wave solutions and rational function solutions, one can find some important localized excitations. However, based on the derived periodic wave solution in this paper, we find that some novel and significant localized coherent excitations such as dromions, peakons, stochastic fractal patterns, regular fractal patterns, chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant Nos. Y6100257,Y6090545,and Y6110140)the Scientific Research Fund of Zhejiang Provincial Education Department,China (Grant No. Z201120169)
文摘With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the（2＋1）-dimensional generalized Breor-Kaup（GBK） system is derived.Based on the derived solitary wave solution,some chaotic behaviors of the GBK system are investigated.
基金Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y606252 and Y604106)the Scientific Research Fund of the Education Department of Zhejiang Province of China (Grant No. 200805981)the Natural Science Foundation of Zhejiang Lishui University (Grant No. KZ09005)
文摘By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272071, the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, and the Key Academic Discipline of Zhejiang Province under Grant No. 200412.The authors are in debt to Prof. J.F. Zhang and Dr. W.H. Huang for their helpful suggestions and fruitful discussions.
文摘For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the （2＋l）-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.
文摘The paper studies on case-based reasoning of uncertain product attributes in configuration design of a product family. Interval numbers characterize uncertain product attributes. By interpolating a number of certain values randomly to replace interval numbers and making projection pursuit analysis on source cases and target cases of expanded numbers, we can get a projection value in the optimal projection direction. Based on projection value, we can construct a case retrieval model of projection pursuit that can handle coexisting certain and uncertain product attributes. The application examples of chainsaw configuration design show that case retrieval is highly sensitive to reliable results.
