Independent sets of some graphs associated to commutative rings

Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is independent set of $G$, if no two vertices of $S$ are adjacent. The independence number $\alpha(G)$ is the size of a maximum independent set in the graph. %An independent set with cardinality Let $R$ be a commutative ring with nonzero identity and $I$ an ideal of $R$. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is an undirected graph whose vertices are the nonzero zero-divisors of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = 0$. Also the ideal-based zero-divisor graph of $R$, denoted by $\Gamma_I(R)$, is the graph which vertices are the set {x\in R\backslash I | xy\in I \quad for some \quad y\in R\backslash I\} and two distinct vertices $x$ and $y$ are adjacent if and only if $xy \in I$. In this paper we study the independent sets and the independence number of $\Gamma(R)$ and $\Gamma_I(R)$.Comment: 27 pages. 22 figure

Hemiconvulsion-Hemiplegia-Epilepsy Syndrome

ObjectiveHemiconvulsion-Hemiplegia-Epilepsy syndrome (HHE) is an initial phase of unilateral or predominantly unilateral convulsive seizures usually of long duration, with a second phase of hemiplegia (usually permanent), immediately following the hemiconvulsions;and then a third stage, characterized by the appearance of partial epileptic seizures. The causes of the initial convulsions in HHE syndrome are multiple but in many patients no cause in obvious. Neuroimaging studies demonstrate an acquired atrophy, that often is preceded by swelling and edema of the hemisphere. Here we report a case of 18 monthold boy, with an initial phase of repeated episodes of partial  seizures, followed by hemiparesis and epileptic seizures, with one episode of generalized convulsive status epilepticus . Minor head trauma was the trigger factor of the initial attack. Brain neuroimaging showed generalized atrophy , that was more prominent in the left hemisphere.

Formation of Nanocrystalline Solid Solution in Al-Fe-V-Si Alloys by Mechanical Alloying

In this study, the microstructural evolution of Al-Fe-V-Si alloy prepared by mechanical alloying starting from elemental powders was studied. X-ray diffraction results showed that by increasing the milling time, peak shifting and peak broadening of Al reflections occur due to dissolution of alloying elements and grain refinement, respectively. Reduction of Al lattice parameter by increasing the milling time indicates that an Al based solid solutions formed during mechanical alloying and solute concentration increased by increasing the milling time. After 60 h of milling, the microstructure consisted of a nanocrystalline Al solid solutions with a grain size of 19 nm and an internal strain of 0.55 in which Si phase was dispersed. In contrast to previous studies on rapidly solidified Al-Fe-V-Si alloys, there is no formation of trace of Al12(Fe,V)3Si or other intermetallic compounds in the as-milled condition. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3509

Determinants of Transport Mode Choice in the Austrian Province of Vorarlberg

Almost all countries have policies to reduce the usage of private car and to raise the usage of public transport by reducing the distance of travel, increasing density, increasing the access to public transport and so on. All of these developments are effective strategies for reducing car dependency. The factors which determine travel behavior of people are relatively broad. Besides the factors such as urban form and transport infrastructure, one important factor is the personal attribute which has a strong effect on the modal choice. By better understanding of this fact, the settlement development and transport planning can be integrated in a more sustainable way. This paper addresses the influence of socio-demographic and geographic factors on the selection of mode choice in the Austrian province of Vorarlberg. We used the mobility survey “Österreich unterwegs” from 2014 and applied bivariate and multinomial logit model in order to quantify the influence of factors on mode selection. Result show that the household size, age, gender, income and motivation of travel have a significant effect on the modal choice

Centrosymmetric graphs and a lower bound for graph energy of fullerenes

The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs

Balaban Index of an Infinite Class of Dendrimers

The Balaban index of a graph G is the first simple index of very low degeneracy. It is defined as the sum of topological distances from a given atom to any other atoms in a molecule. In this paper the Balaban index of an infinite family of dendrimers is computed. The result can be of interest in molecular data mining, particularly in searching the uniqueness of tested (hyper-branched) molecular graphs