In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic so...In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.展开更多
In this paper, the sectorial oscillation of the solutions of higher order homo- geneous linear differential equationswith infinite order entire function coefficients is studied. Results are obtained to extend some res...In this paper, the sectorial oscillation of the solutions of higher order homo- geneous linear differential equationswith infinite order entire function coefficients is studied. Results are obtained to extend some results in [19] and [18].展开更多
This paper proposes a novel distributed optimization algorithm with fractional order dynamics to solve linear algebraic equations.Firstly,the authors proposed“Consensus+Projection”flow with fractional order dynamics...This paper proposes a novel distributed optimization algorithm with fractional order dynamics to solve linear algebraic equations.Firstly,the authors proposed“Consensus+Projection”flow with fractional order dynamics,which has more design freedom and the potential to obtain a better convergent performance than that of conventional first order algorithms.Moreover,the authors prove that the proposed algorithm is convergent under certain iteration order and step-size.Furthermore,the authors develop iteration order switching scheme with initial condition design to improve the convergence performance of the proposed algorithm.Finally,the authors illustrate the effectiveness of the proposed method with several numerical examples.展开更多
In this work,a novel gradient descent method based on event-triggered strategy has been proposed,which involves integer and fractional order iteration.Firstly,the convergence of integer order iterative optimization me...In this work,a novel gradient descent method based on event-triggered strategy has been proposed,which involves integer and fractional order iteration.Firstly,the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked.Based on this result,a fractional order iteration approach has been developed by modelling the system with fractional order dynamics.Secondly,to reduce the comsumption of computation,a feedback based event-triggered mechanism has been introduced to the gradient descent method.The convergence of this new event-triggered optimization algorithm is guaranteed by using a Lyapunov method,and Zeno behavior is proved to be avoided simultaneously.Lastly,the effectiveness and advantages of the proposed algorithms are verified by numerical simulations.展开更多
This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann con...This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.展开更多
基金This work is supported by the National Natural Science Foundation of China (No.10161006)the Natural Science Foundation of Jiangxi Province (No.0311043).
文摘In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.
基金supported by the NSF of Jiangxi Province(2010GZC0187)NSF of Educational Department of the Hubei Province(T201009,Q20112807)NFS of China(11201395)
文摘In this paper, the sectorial oscillation of the solutions of higher order homo- geneous linear differential equationswith infinite order entire function coefficients is studied. Results are obtained to extend some results in [19] and [18].
基金supported by the National Natural Science Foundation of China under Grant Nos.62103003,62073001,and 61973002the Anhui Provincial Key Research and Development Project under Grant2022i01020013+3 种基金the University Synergy Innovation Program of Anhui Province under Grant No.GXXT-2021-010the Anhui Provincial Natural Science Foundation under Grant No.2008085J32the National Postdoctoral Program for Innovative Talents under Grant No.BX20180346the General Financial Grant from the China Postdoctoral Science Foundation under Grant No.2019M660834。
文摘This paper proposes a novel distributed optimization algorithm with fractional order dynamics to solve linear algebraic equations.Firstly,the authors proposed“Consensus+Projection”flow with fractional order dynamics,which has more design freedom and the potential to obtain a better convergent performance than that of conventional first order algorithms.Moreover,the authors prove that the proposed algorithm is convergent under certain iteration order and step-size.Furthermore,the authors develop iteration order switching scheme with initial condition design to improve the convergence performance of the proposed algorithm.Finally,the authors illustrate the effectiveness of the proposed method with several numerical examples.
基金supported by the National Natural Science Foundation of China under Grant No.61973291。
文摘In this work,a novel gradient descent method based on event-triggered strategy has been proposed,which involves integer and fractional order iteration.Firstly,the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked.Based on this result,a fractional order iteration approach has been developed by modelling the system with fractional order dynamics.Secondly,to reduce the comsumption of computation,a feedback based event-triggered mechanism has been introduced to the gradient descent method.The convergence of this new event-triggered optimization algorithm is guaranteed by using a Lyapunov method,and Zeno behavior is proved to be avoided simultaneously.Lastly,the effectiveness and advantages of the proposed algorithms are verified by numerical simulations.
文摘This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.
