‎Let Γa be a graph whose each vertex is colored either white or black‎. ‎If u is a black vertex of Γ such that exactly one neighbor‎ ‎v of u is white‎, ‎then u changes the color of v to black‎. ‎A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that‎ if initially the vertices in Z are colored black and the remaining vertices are colored white‎, ‎then Z changes the col...

Let Γ=(V,E) be a graph and ‎W_(‎a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),‎…‎ ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...

The new class of wrought γ-γ/ Co-base superalloys, which are based on Co-Al-W system,  was developed by conventional hot working routes with a high volume fraction of γ/ precipitates and good mechanical properties. The aim of the present study was to predict the flow stress and hot deformation modeling of a novel γ-γ/ Co-base superalloy. The hot compression test...

Background: Interferon gamma (IFN-γ), a cytokine produced by a variety of cells is involved in the immune response against M. tuberculosis. It activates the production of other cytokines and molecules that kill mycobacterium. IFN-γ also has diagnostic role in identification of active and latent tuberculosis. Objective: To determine the level of IFN-γ in the blood of TB patients. Methods: Ninety...

An interesting problem in statistical physics is the condensation of classical particles in droplets or clusters when the pair-interaction is given by a stable LennardJones-type potential. We study two aspects of this problem. We start by deriving a large deviations principle for the cluster size distribution for any inverse temperature β ∈ (0,∞) and particle density ρ ∈ (0, ρcp) in the thermod...

We consider a homogenization problem for the magnetic GinzburgLandau functional in domains with a large number of small holes. We establish a scaling relation between sizes of holes and the magnitude of the external magnetic field when the multiple vortices pinned by holes appear in nested subdomains and their homogenized density is described by a hierarchy of variational problems. This stands ...

In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure which can be characterised by random measures. Based on the Fitzpatrick function concept we reduce the study of the asymptotic behaviour of monotone operato...

The formation of microdomains, also called rafts, in biomembranes can be attributed to the surface tension of the membrane. In order to model this phenomenon, a model involving a coupling between the local composition and the local curvature was proposed by Seul and Andelman in 1995. In addition to the familiar Cahn-Hilliard/Modica-Mortola energy, there are additional ‘forces’ that prevent larg...

Since the motion of dislocations is regarded as the main cause of plastic deformation, a large literature is focused on the problem of deriving plasticity models from more fundamental dislocation models. The starting point of our derivation is a semi-discrete dislocation model. The main novelty of our approach is that we consider a nonlinear dislocation energy, whereas most mathematical and eng...

A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté et al. (2002), the case where external loads induce a density of bending moment that produces a Cosserat...