Electrostatic Storage Ring

In the trial \cite{BNL} of measuring the proton electric moment, storage rings with electrostatic lattice have been considered. Here an overview is given about the main parameters regarding such a kind of focusing. Beyond confirming all the issues regarding this subject, a non-null element $M_{31}$ is introduced in all the $3\times 3$ matrices which deal with the vector $(x,x',\Delta p/p)$ and its role is discussed.Comment: 7 page

An Investigation on the Basic Conceptual Foundations of Quantum Mechanics by Using the Clifford Algebra

We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the and Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. We give proof of the quantum like Heisenberg uncertainty relations, the phenomenon of quantum Mach Zender interference as well as quantum collapse in some cases of physical interest We also discuss the problem of time evolution of quantum systems as well as the changes in space location. We also give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR . By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that are interpreted as logical statements, following the basic von Neumann results. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic.Comment: forthcoming papers; http://www.m-hikari.com/astp/forth/index.htm

Integration of partially integrable equations

Most evolution equations %or wave equations are partially integrable and, in order to explicitly integrate all possible cases, there exist several methods of complex analysis, but none is optimal. The theory of Nevanlinna and Wiman-Valiron on the growth of the meromorphic solutions gives predictions and bounds, but it is not constructive and restricted to meromorphic solutions. The Painleve' approach via the a priori singularities of the solutions gives no bounds but it is often (not always) constructive. It seems that an adequate combination of the two methods could yield much more output in terms of explicit (i.e. closed form) analytic solutions. We review this question, mainly taking as an example the chaotic equation of Kuramoto and Sivashinsky nu u''' + b u'' + mu u' + u^2/2 +A=0, nu nonzero, with nu,b,mu,A constants.Comment: 12 p, WASCOM XIII (Acireale, 19-25 June 2005

Analytic solitary waves of nonintegrable equations

Even if it is nonintegrable, a differential equation may nevertheless admit particular solutions which are globally analytic. On the example of the dynamical system of Kuramoto and Sivashinsky, which is generically chaotic and presents a high physical interest, we review various methods, all based on the structure of singularities, allowing us to characterize the analytic solution which depends on the largest possible number of constants of integration.Comment: LaTex 2e. To appear, Physica