The motion of stars in galaxies and the gravitational time dilatation

This article deals with the problem of the motion of stars in galaxies. By using the Newton's theory combined with a gravitational time dilatation for the weak gravitational field, it is possible to give a solution without using the dark matter

Time-dependent cosmological interpretation of quantum mechanics

The aim of this article is to define a time-dependent cosmological interpretation of quantum mechanics in the context of an infinite open FLRW universe. A time-dependent quantum state is defined for observers in similar observable universes by using the particle horizon. Then, we prove that the wave function collapse of this quantum state is avoided.Comment: 8 page

Stabilité des équations différentielles ordinaires

DE

Finite time stability conditions for non autonomous continuous systems

Finite time stability is defined for continuous non autonomous systems. Starting with a result from Haimo Haimo (1986) we then extend this result to n¡dimensional non autonomous systems through the use of smooth and nonsmooth Lyapunov functions as in Perruquetti and Drakunov (2000). One obtains two different sufficient conditions and a necessary one for finite time stability of continuous non autonomous systems

Finite-time output stabilization of the double integrator

International audienceThe problem of finite-time output stabilization of the double integrator is addressed applying the homogeneity approach. A homogeneous controller and a homogeneous observer are designed (for different degree of homogeneity) ensuring the finite-time stabilization. Their combination under mild conditions is shown to stay homogeneous and finite-time stable as well. The efficiency of the obtained solution is demonstrated in computer simulations

Preparation of future psychologists to aplication of unconvantational forms of studies in the process of the personality oriented studies in system eir defence

У статті обґрунтовується необхідність підготовки майбутніх психологів до застосування нетрадиційних форм навчання в процесі особистісно-орієнтованого навчання в системі післядипломної педагогічної освіти.In the article the necessity of training of future psychologists to use non-traditional forms of learning by student-centered learning in post-graduate teacher education

Global finite-time observers for non linear systems

International audienceA global finite-time observer is designed for nonlinear systems which are uniformly observable and globally Lipschitz. This result is based on a high-gain approach

A global high-gain finite-time observer

International audienceA global finite-time observer is designed for nonlinear systems which are uniformly observable and globally Lipschitz. This result is based on a high-gain approach combined with recent advances on finite-time stability using Lyapunov function and homogeneity concepts

Robust output feedback sampling control based on second order sliding mode

International audienceThis paper proposes a new second order sliding mode output feedback controller. This latter is developped in the case of finite sampling frequency and is using only output information in order to ensure desired trajectory tracking with high accuracy in a finite time in spite of uncertainties and perturbations. This new strategy is evaluated in simulations on an academic example

Unitary symmetries in wormhole geometry and its thermodynamics

From a geometric point of view, we show that the unitary symmetries $U(1)$ and $SU(2)$ stem fundamentally from Schwarzschild and Reissner-Nordstr\"om wormhole geometry through spacetime complexification. Then, we develop quantum tunneling which makes these wormholes traversable for particles. Finally, this leads to wormhole thermodynamics.Comment: 20 pages, revtex4, 1 figure, Published in European Physical Journal