In this paper, we consider the designing of a new set of Uniquely Decodable Codes (UDC) for uncoded synchronous overloaded Code Division Multiple Access (CDMA) for the number of codes exceeding the assigned code length. For the construction, the proposed recursive method at iterationk generates a matrix that can be classified into k orthogonal subsets of different dimensions. Out of them, all b...

Data Envelopment Analysis (DEA) deals with evaluating a set of decision-making units (DMUs) based on nonparametric mathematical approaches. In classical DEA models, the given set of factors of DMUs is divided into two categories, inputs and outputs, while in some practical problems there are some measures whose membership to these categories is unclear. It means these factors treat different in...

A ring R is uniquely (nil) clean in case for any $a in R$ there exists a uniquely idempotent $ein R$ such that $a-e$ is invertible (nilpotent). Let $C =(A V W B)$ be the Morita Context ring. We determine conditions under which the rings $A,B$ are uniquely (nil) clean. Moreover we show that the center of a uniquely (nil) clean ring is uniquely (nil) clean.

let $g$ be a simple graph of order $n$ and size $m$.the edge covering of $g$ is a set of edges such that every vertex of $g$ is incident to at least one edge of the set. the edge cover polynomial of $g$ is the polynomial$e(g,x)=sum_{i=rho(g)}^{m} e(g,i) x^{i}$,where $e(g,i)$ is the number of edge coverings of $g$ of size $i$, and$rho(g)$ is the edge covering number of $g$. in this paper we stud...

Let $G$ be a simple graph of order $n$ and size $m$.The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$,where $e(G,i)$ is the number of edge coverings of $G$ of size $i$, and$rho(G)$ is the edge covering number of $G$. In this paper we stud...