This paper investigates the distributed Controllability of nonlocal Rayleigh beam. The mathematical problem is formulated as an abstract di, erential equation. It is shown that a sequence of eigenfunction of nonlocal Rayleigh beam forms Riesz basis. Based on Riesz basis properties and theory of abstract di, erential equation, it is proved that a vibrating nonlocal Rayleigh beam is approximately controllable under suitable distributed control force while it is not exponentially stable.

Introduction: Recent reports have shown that rare fluctuations in cardiac cycles are ‘ forgotten’ quickly in healthy individuals and it is possible to quantify the “ memory length” of a physiological time-series using an inverse statistical approach. Methods: In the present study, we assessed the effect of aging on memory length in cardiac rhythm. Results: There was a longer memory length in cardiac time-series of elderly subjects in comparison with younger adults for both decelerating and accelerating rare fluctuations in cardiac rhythm. Conclusion: The increased memory length of the cardiac time-series in elderly subjects may indicate reduced Controllability of cardiovascular regulatory system.

In this paper we give a method to determine the Controllability of the time-varying systems. For this purpose, we define a problem in calculus of variations over state function, their derivatives and control function corresponding to original system. Discretizing the new problem, we reach to a finite dimensional linear programming problem. Finally we solve this LP and find that the system is controllable or not. Also we may obtain a pair of admissible control and state.