**ON THE STUDY OF THE WAVE EQUATION SET ON A SINGULAR CYLINDRICAL DOMAIN**

CHAOUCHI BELGACEM

In this work we give new regularity results of solution for the linear wave equation set in a nonsmooth cylindrical domain. Di§erent types of initial and boundary conditions are imposed on the boundary of the singular domain. Our study is performed in some particular anisotropic Hölder spaces.

Presenter: Chaouchi Belgacem

**A DITOPOLOGICAL FUZZY STRUCTURAL VIEW OF HUTTON SPACES**

FİLİZ YILDIZ

The notion of texture was introduced by L. M. Brown as a point-based set- ting for the study of complement-free mathematical concepts, besides crisp sets, fuzzy sets, L-valued sets and intuitionistic sets.

Following that, it was shown that the ditopological texture spaces do indeed provide a unified setting for the study of topologies on Hutton algebras (fuzzy lattices) on the one hand, and of bitopological and topological spaces on the other. In this talk we will be especially interested in the generalization of the notion of Hutton texture to include the non-complemented case and the notion of Hutton space to Hutton dispace by not postulating an order-reversing involution and replacing the topology with a ditopology. Thus, many of the point-free concepts defined in the category of ditopological texture spaces will go over to the category whose objects are Hutton dispaces via some equivalence functors.

Presenter: Filiz Yıldız

**NEIMARK-SACKER BIFURCATION ANALYSIS IN A DISCRETE BACTERIA POPULATION MODEL**

G.KAYA AND S. KARTAL

In this paper, a differential equation with piecewise constant arguments model that describes a population density of a bacteria species in a microcosm is considered. From the discretization process of a differential equation with piecewise constant arguments, we obtain two dimensional discrete dynamical system. By using the center manifold theorem and bifurcation theory, it is shown that the discrete dy- namical system undergoes Neimark-Sacker bifurcation. The bifurcation diagrams, phase portraits and Lyapunov exponents are obtained for the discrete model.

Presenter: Güven Kaya

**AN IMPROVED HARDY-SOBOLEV INEQUALITY WITH SINGULAR WEIGHT AT THE BOUNDARY**

B. ABDELLAOUI, K. BIROUD, J. DAVILA, AND F. MAHMOUDI

Let Ω ⊂ RN be a bounded regular domain of RN and 1 < p < ∞. The paper is divided in two main parts. In the first part we prove the following improved Hardy Inequality for convex domains. (FORMULAS). The optimality of the exponent of the logarithmic term is also proved.

Presenter: Biroud Kheireddine

**COMPARABLE GRAPHS OF SUBMODULES**

ALİ ÖZTÜRK

Let R be an associative ring with identity and M be a right R-module. We define the comparable graph c(M) of M with all non-trivial submodules of M as vertices and two distinct vertices A,B are adjacent if and only if A<B or B<A. In this paper, we investigate the connectivity, completeness, girth, domination number, cut edges and bipartite of c(M). Moreover, we give connections between the graph-theoretic properties of c(M) and algebraic properties of M.

Presenter: Ali Öztürk