THE STRUCTURE OF UNIT GRUOP OF F3nT39F_{3n} T_{39}

Let $RG$ be the gruop ring of the group $G$ over ring $R$ and $U(RG)$ be its unitgroup. In this paper, we obtain the structure of unit group of $F_{3n} T_{39}$

The hyper-Wiener index of the generalized hierarchical product of graphs

AbstractThe hyper Wiener index of the connected graph G is WW(G)=12∑{u,v}⊆V(G)(d(u,v)+d(u,v)2), where d(u,v) is the distance between the vertices u and v of G. In this paper we compute the hyper-Wiener index of the generalized hierarchical product of two graphs and give some applications of this operation

A CHARACTERIZATION OF PSL(4,p) BY SOME CHARACTER DEGREE

‎Let G be a finite group and cd(G) be the set of irreducible character degree of G‎. ‎In this paper we prove that if  p is a prime number‎, ‎then the simple group PSL(4,p) is uniquely determined by its order and some its character degrees‎.

On the Narumi-Katayama Index of Composite Graphs

The Narumi-Katayama index of a graph G, denoted by N K(G), is equal to the product of degrees of vertices of G. In this paper we investigate its behavior under several binary operations on graphs. We present explicit formulas for its values for composite graphs in terms of its values for operands and some auxiliary invariants. We demonstrate applications of our results to several chemically relevant classes of graphs and show how the Narumi-Katayama index can be used as a measure of graph irregularity. (doi: 10.5562/cca2329

Computing the Szeged Index of Two Type Dendrimer Nanostars

In this paper we compute the szeged index of the first and second type of dendrimer nanostar

Deep Sketch-Photo Face Recognition Assisted by Facial Attributes

In this paper, we present a deep coupled framework to address the problem of matching sketch image against a gallery of mugshots. Face sketches have the essential in- formation about the spatial topology and geometric details of faces while missing some important facial attributes such as ethnicity, hair, eye, and skin color. We propose a cou- pled deep neural network architecture which utilizes facial attributes in order to improve the sketch-photo recognition performance. The proposed Attribute-Assisted Deep Con- volutional Neural Network (AADCNN) method exploits the facial attributes and leverages the loss functions from the facial attributes identification and face verification tasks in order to learn rich discriminative features in a common em- bedding subspace. The facial attribute identification task increases the inter-personal variations by pushing apart the embedded features extracted from individuals with differ- ent facial attributes, while the verification task reduces the intra-personal variations by pulling together all the fea- tures that are related to one person. The learned discrim- inative features can be well generalized to new identities not seen in the training data. The proposed architecture is able to make full use of the sketch and complementary fa- cial attribute information to train a deep model compared to the conventional sketch-photo recognition methods. Exten- sive experiments are performed on composite (E-PRIP) and semi-forensic (IIIT-D semi-forensic) datasets. The results show the superiority of our method compared to the state- of-the-art models in sketch-photo recognition algorithm

A CHARACTERIZATION OF U4(2) BY NSE

‎Let $G$ be a finite group and $\omega(G)$ be the set of element orders of $G$‎. ‎Let $k\in\omega(G)$ and $m_k$ be the number of elements of order $k$ in $G$‎. ‎Let $nse(G)=\{m_k|k\in \omega(G)\}$‎. ‎The aim of this paper is to prove that‎, ‎if $G$ is a finite group such that nse($G$)=nse($U_4(2)$)‎, ‎then $G\cong U_4(2)$