The neighbourhood polynomial G , is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph. In other word $N(G,x)=sum_{Uin N(G)} x^{|U|}$, where N(G) is neighbourhood complex of a graph, whose vertices are the vertices of the graph and faces are subsets of vertices that have a common neighbour. In this paper we compute this polynomial for some na...

Given a set S of n points in three dimensions, we study the maximum numbers of quadrics spanned by subsets of points in S in several ways. Among various results we prove that the number of empty circular cylinders is between Ω(n) and O(n) while we have a tight bound Θ(n) for empty ellipsoids. We also take interest in pairs of empty homothetic ellipsoids, with application to the number of combin...

The term “plea bargaining”has become a label often used to describe a series of disparate mechanisms to investigate,prosecute,and adjudicate criminal liability. For some,plea bargaining is the indispensable tool to address criminal conduct,while for others it has become a symbol of coercion and injustice. The purpose of this Article will be to distinguish the very different mechanisms that are ...

Different attempts have been made to answer Reich's question why the majority of those who are hungry don't steal and why the majority of those who are exploited don't strike. The two most influential approaches have been the ideological one and the gunman theory. The gunman theory seems to have the upper hand in that it not only explains many cases of successful oppression by a minority of a m...

in this paper, we introduce and study the concepts of $mathcal{i}_2$-convergence, $mathcal{i}_2^{*}$-convergence for double sequences of fuzzy real numbers, where $mathcal{i}_2$ denotes the ideal of subsets of $mathbb n times mathbb n$. also, we study some properties and relations of them.

let $g$ be an infinite group and $nin {3‎, ‎6}cup{2^k| kin mathbb{n}}$‎. ‎in this paper‎, ‎we prove that $g$ is an $n$-kappe group if and only if for any two infinite subsets $x$ and $y$ of $g$‎, ‎there exist $xin x$ and $yin y$ such that $[x^n‎, ‎y‎, ‎y]=1$‎.

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In this paper we introduce some ideal convergent double interval valued numbers sequence spaces defined by Orlicz function and study different properties of these spaces. We also establish some inclusion relations among them.