Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures

This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in (relatively) hyperbolic groups". We study there the existential theory of torsion free hyperbolic and relatively hyperbolic groups, in particular those with virtually abelian parabolic subgroups. We show that the satisfiability of systems of equations and inequations is decidable in these groups. In the second part, called "Finding relative hyperbolic structures", we provide a general algorithm that recognizes the class of groups that are hyperbolic relative to abelian subgroups.Comment: Two independant parts 23p + 9p, revised. To appear separately in Israel J. Math, and Bull. London Math. Soc. respectivel

Some integral inequalities on time scales

In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.Comment: 8 page

Accidental parabolics and relatively hyperbolic groups

By constructing, in the relative case, objects analoguous to Rips and Sela's canonical representatives, we prove that the set of images by morphisms without accidental parabolic, of a finitely presented group in a relatively hyperbolic group, is finite, up to conjugacy.Comment: Revision, 24 pages, 4 figure

Relative hyperbolicity of hyperbolic-by-cyclic groups

Let $G$ be a torsion-free hyperbolic group and $\alpha$ an automorphism of $G$. We show that there exists a canonical collection of subgroups that are polynomially growing under $\alpha$, and that the mapping torus of $G$ by $\alpha$ is hyperbolic relative to the suspensions of the maximal polynomially growing subgroups under $\alpha$.Comment: 17 pages, 1 figur

Λ\Lambda CDM jerk parameter in symmetric teleparallel cosmology

In this paper, we have examined the recently proposed modified symmetric teleparallel gravity, in which gravitational Lagrangian is given by an arbitrary function of non-metricity scalar $Q$. We have considered the $\Lambda$CDM jerk parameter to express the Hubble rate. Moreover, we have used 57 points of Hubble $H\left( z\right)$ and 1048 points of Pantheon datasets to constraint our model parameters by means of the Markov Chain Monte Carlo analysis. The mean values and the best fit obtained give consistent Hubble rate and deceleration parameter compared to the observation values. In order to study the current accelerated expansion scenario of the Universe with the presence of the cosmological fluid as a perfect fluid, we have considered two forms of teleparallel gravity. We have studied the obtained field equations with the proposed forms of $f(Q)$ models, specifically, linear $f\left( Q\right) =\alpha Q+\beta$ and non-linear $f\left( Q\right) =Q+mQ^{n}$ models. Next, we have discussed the physical behavior of cosmological parameters such as energy density, pressure, EoS parameter, and deceleration parameter for both model. To ensure the validity of our proposed cosmological models, we have checked all energy conditions. The properties of these parameters confirm that our models describe the current acceleration of the expansion of the Universe. This result is also corroborated by the energy conditions criteria. the Finally, the EoS parameter for both models indicates that the cosmological fluid behaves like a quintessence dark energy model.Comment: 12 pages, 10 figure

Parabolic groups acting on one-dimensional compact spaces

Given a class of compact spaces, we ask which groups can be maximal parabolic subgroups of a relatively hyperbolic group whose boundary is in the class. We investigate the class of 1-dimensional connected boundaries. We get that any non-torsion infinite f.g. group is a maximal parabolic subgroup of some relatively hyperbolic group with connected one-dimensional boundary without global cut point. For boundaries homeomorphic to a Sierpinski carpet or a 2-sphere, the only maximal parabolic subgroups allowed are virtual surface groups (hyperbolic, or virtually $\mathbb{Z} + \mathbb{Z}$).Comment: 10 pages. Added a precision on local connectedness for Lemma 2.3, thanks to B. Bowditc

Kabylie : Géographie

« KABYLIE » (E.B.) La Kabylie, principale région berbérophone d’Algérie, occupe une place très particulière dans l’ensemble du monde berbère contemporain ; cette situation justifie une attention particulière, avec un dossier considérable qui rassemble 18 notices – et qui bien sûr est loin d’être exhaustif ! Le poids démographique de la Kabylie, son rôle dans l’histoire récente de l’Algérie, l’importance et le dynamisme de ses élites de tous types, son rôle décisif dans l’émergence de la consc..

Typologie et dynamique des chênaies vertes en Algérie

Le chêne vert figure parmi les essences forestières les plus importantes de la région méditerranéenne. L'état actuel de ses peuplements en Algérie, la régression de son aire, son importance écologique et la nécessité, dans le contexte mondial actuel, de promouvoir la conservation de la biodiversité et le développement durable des écosystèmes sont autant d'éléments qui nous ont amenés à envisager l'élaboration d'une typologie des chênaies vertes en Algérie, qui constituerait la première étape préalable à toute stratégie de gestion. L'importance du territoire étudié, a permis d'analyser et d'évaluer, à différentes échelles, la diversité de la chênaie verte en relation avec celle des milieux climatique et édaphique, et d'appréhender les conséquences d'un dérèglement fonctionnel sur les caractéristiques biologiques et phytogéographiques des phytocénoses (communautés végétales) ainsi que sur les propriétés trophiques (nutritives) et hydriques du sol

Kabylie : Géographie

« KABYLIE » (E.B.) La Kabylie, principale région berbérophone d’Algérie, occupe une place très particulière dans l’ensemble du monde berbère contemporain ; cette situation justifie une attention particulière, avec un dossier considérable qui rassemble 18 notices – et qui bien sûr est loin d’être exhaustif ! Le poids démographique de la Kabylie, son rôle dans l’histoire récente de l’Algérie, l’importance et le dynamisme de ses élites de tous types, son rôle décisif dans l’émergence de la consc..

No-splitting property and boundaries of random groups

We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.Comment: 20 page