The time evolution operator (Schrödinger functional) of quantum field theory can be expressed in terms of first quantised particles moving on S1/Z2. We give a graphical derivation of this that generalises to second quantised string theory. Tduality then relates evolution through time t with evolution through 1/t and an interchange of string fields and backgrounds. Introduction In the mechanics ...

We re-analyze the issue of redshifts induced by a moving cosmic string by looking at moving sources and observers on a conical spacetime in a fully relativistic approach. By replacing the concept of a moving spacetime with the more clearly defined concept of moving sources and observers in the string spacetime, we show that there is no effect: the only redshift is a Doppler shift due to the mot...

In this paper, we study the stabilization of an axially moving viscoelastic beam with Logarithmic Source Terms. We obtain asymptotic stability result global solution, for certain class relaxation functions. The proofs is obtained by using multiplier technique. extend a recent in Kelleche and Tatar Khemmoudj \cite{l12}.

In this paper, the vibration suppression problem of an axially moving power transmission belt is investigated. The equations of motion of the moving belt is first derived by using Hamilton’s principle for systems with changing mass. The total mechanical energy of the belt system is considered as a Lyapunov function candidate. Using the Lyapunov second method, a nonlinear boundary control law th...

In this paper, based on the classical Fourth-Order Runge-Kutta method, the modified FourthOrder Runge-Kutta method is presented for solving nonlinear vibration of axially travelling string system, that is to solve time varying and nonlinear differential equations. The classical Fourth-Order Runge-Kutta method can only be used to solve first-order linear differential equations. Its main idea is ...