In this paper, using the theory of Pell equation, the authors discuss the integrity of certain series related to generalized Lucas numbers. Under some conditions, the integrity of certain series involving generalized ...In this paper, using the theory of Pell equation, the authors discuss the integrity of certain series related to generalized Lucas numbers. Under some conditions, the integrity of certain series involving generalized Lucas numbers is completely solved.展开更多
The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity mode...The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.展开更多
This paper deals with the global practical tracking problem by output-feedback for a class of uncertain cascade systems with zero-dynamics and unmeasured states dependent growth.The systems investigated are substantia...This paper deals with the global practical tracking problem by output-feedback for a class of uncertain cascade systems with zero-dynamics and unmeasured states dependent growth.The systems investigated are substantially different from the closely related works,and have zero-dynamics,unknown growth rate,and unknown time-varying control coefficients.This makes the problem much more difficult to solve.Motivated by the authors' recent works,this paper proposes a new adaptive control scheme to achieve the global practical tracking.It is shown that the designed controller guarantees that the state of the resulting closed-loop system is globally bounded and the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time.This is achieved by combining the methods of universal control and dead zone with backstepping technique,and using the framework of performance analysis in the closely related works.A numerical example demonstrates the effectiveness of the theoretical results.展开更多
文摘In this paper, using the theory of Pell equation, the authors discuss the integrity of certain series related to generalized Lucas numbers. Under some conditions, the integrity of certain series involving generalized Lucas numbers is completely solved.
基金Project supported by the Natural Science Foundation(No. DMS 04-07866)the "Research Team on Complex Systems" of Chinese Academy of Sciences.
文摘The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.
基金supported by the National Natural Science Foundation of China under Grant Nos.61325016,61273084,61233014,and 61304013the Natural Science Foundation for Distinguished Young Scholar of Shandong Province of China under Grant No.JQ200919+1 种基金the Independent Innovation Foundation of Shandong University under Grant No.2012JC014the Doctoral Foundation of Jinan University under Grant No.XBS1413
文摘This paper deals with the global practical tracking problem by output-feedback for a class of uncertain cascade systems with zero-dynamics and unmeasured states dependent growth.The systems investigated are substantially different from the closely related works,and have zero-dynamics,unknown growth rate,and unknown time-varying control coefficients.This makes the problem much more difficult to solve.Motivated by the authors' recent works,this paper proposes a new adaptive control scheme to achieve the global practical tracking.It is shown that the designed controller guarantees that the state of the resulting closed-loop system is globally bounded and the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time.This is achieved by combining the methods of universal control and dead zone with backstepping technique,and using the framework of performance analysis in the closely related works.A numerical example demonstrates the effectiveness of the theoretical results.
