Recently braid group cryptosystems have been invented these are the AAG and KLCHKP cryptosystems. We present an algebraic key establisment protocol based on the difficulty of solving equations over algebraic structures. In (our group theoretic illustration of) our protocol its security is based...

The purpose of this paper is to distinguish, as much as possible, the concept of s-convexity from the concept of convexity and the concept of s-convexity in the first sense from the concept of s-convexity in the second sense. In this respect, the present work further develops a previous study by...

The paper gives the systematic analysis of singularities of transition processes in general dynamical systems. Dynamical systems depending on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters of the...

Based on the design of proportional and derivative (PD) observers, a new parameterization of all observers for descriptor systems is developed. Without using any additional transformations, the present observer parameterization is convenient and efficient to be performed. The connections between...

For solving the estimation problem for linear multivariable systems with measurement noises, a descriptor system approach is proposed. An augmented descriptor system is constructed and a new observer design technique, that is PID technique, is then developed. The existence condition of the PID...

In odd dimension space, under a microlocal geometric condition, we give the rate of decay of the local energy for solutions of the wave equation on exterior domain, with localized nonlinear damping.En dimension impaire d'espace, on détermine sous une condition géométrique microlocale, le taux...

In this paper, we show that any proof of the Collatz 3 + 1 Conjecture must have an infinite number of lines. Therefore, no formal proof is possible. We also discuss whether the proof strategy in this paper has any promise for proving that the Riemann Hypothesis is also unprovable