On minimal coverings of groups by proper normalizers

For a finite group $G$, a {\it normalizer covering} of $G$ is a set of proper normalizers of some subgroups of $G$ whose union is $G$. First we give a necessary and sufficient condition for a group having a {\it normalizer covering}. Also, we find some properties of $p$-groups ($p$ a prime) having a normalizer covering. For a group $G$ with a normalizer covering, we define $\sigma_n(G)$ the minimum cardinality amongst all the normalizer coverings of $G$. In this article, we show that if $G$ is a $p$-group with a normalizer covering, then $\sigma_n(G)=p+1$ or 5. Finally, for any prime $p$ and positive integer $k$, we construct a solvable group $G$ with $\sigma_n(G)=p^k+1$

Adaptation of theatrical elements of nezami ganjawi: a case study on the ballad of khosrow and shirin

Nezami was one of the most skilled writers of Persian poems and ballads, not only he had his own signature style but the impact of his style is evident on the works of poets not contemporary to him. Nezami had sufficient knowledge about the popular sciences of his time (literary sciences, astronomy, Islamic sciences and the Arabic language), and his vast knowledge is evident in his body of work. He could be considered as a master playwright, because his masterpiece “The Ballad of Khosrow and Shirin” is amongst the best plays ever written, thus every adaptation of this masterpiece might result in an original and good quality creation. This paper tends to analyze some theatrical adaptations of the mentioned ballad, in order to examine their types of approach to this invaluable play.Keywords: Ganjawi, theatrical elements, Khosrow and Shirin, adaptatio

Double Relaxation via AdS/CFT

We exploit the AdS/CFT correspondence to investigate thermalization in an N=2 strongly coupled gauge theory including massless fundamental matter (quark). More precisely, we consider the response of a zero temperature state of the gauge theory under variation of an external electric field leading to a time-dependent current. The holographic dual of the above set-up is given by introducing a time-dependent electric field on the probe D7-brane embedded in an AdS_5 X S^5 background. In the dual gravity theory, due to a time-dependent electric field an apparent horizon forms on the brane which, according to AdS/CFT dictionary, is the counterpart of the thermalization process in the gauge theory. We classify different functions for time-dependent electric field and study their effect on the apparent horizon formation. In the case of pulse functions where the electric field varies from zero to zero, apart from non-equilibrium phase, we observe that two apparent horizons form on the brane. On the gauge theory side, it means that the state of the gauge theory experiences two different temperatures during the time evolution.Comment: 28 pages, 13 figures, published versio