FNCMA

Title:

Open problems in fractional differential equations theory and partial answers

Abstract

Of concern is a generalization of the telegraph problem to the fractional case in presence of a viscoelastic term. We study the well-posedness and the stability of the system. In particular, we want to shed some light on whether lower-order fractional derivatives and viscoelastic terms may dissipate the energy of the system or not. We recall that this is the case in the integer-order case, that is for the well-known telegraaph equation. In fact one of these two terms is enough to drive the system to equilibrium at a certain specific rate. In the fractional case, some basic rules are no-longer valid and therefore the situation is more delicate. We prove Mittag-leffter stability under certain smallness conditions on the relaxtion function.

Titre :

Méthodes de points intérieurs pour la programmation linéaire basées sur des récentes directions de descente

Résumé

On s’intéresse à la résolution des programmes linéaires par des méthodes de points intérieurs du type primal-dual de trajectoire centrale. Ces approches sont basées sur des différentes récentes directions de descente. Ces dernières permettent d’une part, de maintenir les itérations des algorithmes primaux-duaux au voisinage de la trajectoire centrale ce qui résout alors le problème de faisabilité. D’autre part, elles offrent des résultats importants concernant la complexité polynomiale et jouent un rôle crucial dans l’amélioration du comportement numérique des algorithmes en question.

Title :

Quantum deformations and recent development of Hom-type algebras.

Abstract :

A quantum deformation or q-deformation consists of replacing usual derivation by a sigma-derivation in algebras of vector fields. The main example is given by Jackson derivative and lead for example to q-deformation of sl_2, Witt algebra, Virasoro algebra and also Heisenberg algebras (oscillator algebras). The description of the new structures gave rise to a structure generalizing Lie algebras, called Hom-Lie algebras or quasi-Lie algebras studied first by Larsson and Silvestrov. Since then various classical algebraic structures and properties were extended to the Hom-type setting. The main feature is that the classical identities are twisted by homomorphisms.

The purpose of my talk is to give an overview of recent developments and provide some key constructions and examples on Hom-algebras and BiHom-algebras.

Title:

The impact of time-varying delay to stabilize solutions of the plate equation with weak-viscoelasticity in Rⁿ

Abstract

We consider a dynamical system with delay described by a differential equation with partial derivatives of hyperbolic type and delay with respect to a time variable. We establish a k(t)-stability of weak solution under suitable initial conditions in Rⁿ , n>4, by introducing an appropriate Lyapunov functions.

For more details see  https://uploads.strikinglycdn.com/files/ce031c13-7590-4c92-aa32-2206e9380a8d/Abstract.pdf?id=3723184