Semiclassical String Solutions on 1/2 BPS Geometries

We study semiclassical string solutions on the 1/2 BPS geometry of type IIB string theory characterized by concentric rings on the boundary plane. We consider both folded rotating strings carrying nonzero R-charge and circular pulsating strings. We find that unlike rotating strings, as far as circular pulsating strings are concerned, the dynamics remains qualitatively unchanged when the concentric rings replace AdS_5\times S^5. Using the gravity dual we have also studied the Wilson loop of the corresponding gauge theory. The result is qualitatively the same as that in AdS_5\times S^5 in the global coordinates where the corresponding gauge theory is defined on S^3\times R. We show that there is a correction to 1/L leading order behavior of the potential between external objects.Comment: 17 pages, latex file, v2: refs. adde

Domination Number of the Non-commuting Graph of Finite Groups

Let G be a non-abelian group. The non-commuting graph of group G, shown by ΓG, is a graph with the vertex set G \ Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are adjacent whenever ab ≠ ba. A set S ⊆ V(Γ) of vertices in a graph Γ is a dominating set if every vertex v ∈ V(Γ) is an element of S or adjacent to an element of S. The domination number of a graph Γ denoted by γ(Γ), is the minimum size of a dominating set of Γ. </p><p>Here, we study some properties of the non-commuting graph of some finite groups. In this paper, we show that \gamma(\Gamma_G)<\frac{|G|-|Z(G)|}{2}. Also we charactrize all of groups G of order n with t = ∣Z(G)∣, in which $\gamma(\Gamma_{G})+\gamma(\overline{\Gamma}_{G})\in \{n-t+1,n-t,n-t-1,n-t-2\}.

Evaluation of genetic diversity in barley (Hordeum vulgare L.) from Wollo high land areas using agromorphological traits and hordein

This study aimed to determine the genetic diversity and relationships among barley varieties (Hordeum vulgare L.) growing at Wollo Highland areas by using hordein and agro-morphological traits. Twenty (20) varieties were laid down in randomized complete block design (RCBD) design with three replications; they were planted by irrigation at Wollo University, Dessie Campus from January to May 2014. The genetic analysis using hordein was done in the laboratory of Ethiopian Biodiversity Institute (EBI) in July 2014. Ten (10) competitive random plants from the rows of the experimental plots were taken for recording their agromorphological characters. Electrophoretic separation of barley storage proteins or hordeins was done using acid polyacrylamide gel electrophoresis (A-PAGE). The traits: day of heading, day of maturity, grain yield (kg/ha), plant height, spike length, number of spiklet per spike, kernel number per spike, weight of seed per spike and biomass yield (g/plot) were highly significant for the diversity of barely, whereas thousand seed weight was less significant. The results reveal positive correlation between spike length and number of spiklet per spike (the highest correlations from the agro morphological traits); the next highly correlated traits were kernel weight per spike and thousand seed weight. The A-PAGE analysis showed limited variation among the analysed accessions. The Nei’s genetic distance for all varieties of barely varied from 0.0000 to 1.6094. It is found that the 20 genotypes of barely investigated in this research were having a gene diversity (h) of overall populations (0.138) using hordein. The cluster analysis grouped the 20 barely genotypes into three different clusters using agro-morphological traits and into four clusters using hordein. This indicates the presence of wide diversity among the tested genotypes. From cluster mean values of agro-morphological traits, genotypes in cluster III deserve consideration for directly developing high yielding barely varieties. The result of the principal components analysis revealed that the first three principal components having greater than 1 eigenvalue contributed 84.22% of the total variation. From this study, it can be concluded that the presence of high morphological variation indicated the potential of Wollo Highland areas in contributing to barley improvement and conservation activities of land areas.Key words: Acid polyacrylamide gel electrophoresis, agro-morphological traits, hordein, genetic distance, hordeum vulgare, variability