The Largest Accelerators and Colliders of Their Time

The Study Group for a GeV-scale Proton Synchrotron was launched in 1952 at CERN. Initially, an up-scaled version of the 3 GeV Cosmotron was considered but soon a new design based on the newly discovered alternating-gradient principle and promising a proton energy of 30 GeV was adopted by the CERN Council in the same year. In order to limit cost the energy was subsequently limited to 25 GeV and the project led by J.B. Adams was approved in 1953. The final parameters were fixed in 1954 and construction started in 1955. The CPS [1] became operational towards the end of 1959 reaching an energy of 28 GeV [2, 3]. It has turned out to be an extremely versatile facility [4] (Table 10.1).

Evolution of non-stationary processes and some maximum entropy principles

This paper studies, by using the speed-gradient principle, the evolution of non-stationary processes in the context of maximization of Varma, weighted Rényi, weighted Varma and Rényi-Tsallis of order α entropies.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.