Stimulated by a remark of J. L. Doob at the beginning of Appendix I to Kai Lai Chung’s English translation “Limit Distributions for Sums of Independent Variables” of the Russian classic by B. V. Gnedenko and A. N. Kolmogorov [5] we highlight the somewhat nonprobabilistic importance of characteristic functions and their positive definiteness property in a pedagogical attempt to introduce the not...

Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the short-pulse equation and holds both on an infinite line and in a periodic domain. Numerical illustrations of the finite-time wave breaking are given in a periodic ...

We present a photonic wave packet construction which is immune against the decoherence effects induced by the action of the Lorentz group. The amplitudes of a pure quantum state representing the wave packet remain invariant irrespective of the reference frame into which the wave packet has been transformed. Transmitted information is encoded in the helicity degrees of freedom of two correlated ...

A time-dependent wave packet method has been employed to calculate the state-to-state reaction probability for the H1H2O~0,0,0!→H2~v1 , j1!1OH~v2 , j2! reaction for J50 and initial nonrotating H2O on the modified Schatz–Elgersman potential energy surface in full six dimensions ~6D!. Starting from a wave packet for an atom–triatom asymptotic state in atom–triatom Jacobi coordinates, we transfer ...

The spreading of quantum mechanical wave packets are studied in two cases. Firstly we look at the time behavior of the packet width of a free particle confined in the observable Universe. Secondly, by imposing the conservation of the time average of the packet width of a particle driven by a harmonic oscillator potential, we find a zero-point energy which frequency is the de Broglie frequency. ...

The current paper investigates the influence of packet losses in network control systems (NCS’s) using the model predictive control (MPC) strategy. The study focuses on two main network packet losses due to sensor to controller and controller to actuator along the communication paths. A new Markov-based method is employed to recursively estimate the probability of time delay in controller to ac...