‎Let $G$ be a finite non-abelian group with center $Z(G)$‎. ‎The non-commuting graph of $G$ is a simple undirected graph whose vertex set is $Gsetminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy ne yx$‎. ‎In this paper‎, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups‎..

let $g$ be a finite group and $pi_{e}(g)$ be the set of element orders of $g $. let $k in pi_{e}(g)$ and $s_{k}$ be the number of elements of order $k $ in $g$. set nse($g$):=${ s_{k} | k in pi_{e}(g)}$. in this paper, it is proved if $|g|=|$ pgl$_{2}(q)|$, where $q$ is odd prime power and nse$(g)= $nse$($pgl$_{2}(q))$, then $g cong $pgl$_

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

the non-commuting graph $nabla(g)$ of a non-abelian group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we 'll prove that if $g$ is a finite group with $nabla(g)congnabla(bs_{n})$, then $g cong bs_{n}$, where $bs_{n}$ is the symmetric group of degre...

The study of measurable and integrable selections from a correspondence (set-valued function) has been of interest for some time [e.g., see Aumann (1965), Hildenbrand (1974), etc.]. Here we take up the study of distributions of such selections. The motivation for doing this comes from Mathematical Economics [see Kannai (1970, section 7); the reader interested in the economic applications is ref...

When a non-interactive story is reread, the experience may change, even though the text remains the same. But what if the text is potentially different in each reading session, as is the case in an interactive story – how does rereading change in the context of interactive stories? In our earlier empirical studies of rereading we found that, surprisingly, readers of interactive stories reported...

We analyzed the effects of dopamine signaling on the temporal organization of rest and activity in Drosophila melanogaster. Locomotor behaviors were recorded using a video-monitoring system, and the amounts of movements were quantified by using an image processing program. We, first, confirmed that rest bout durations followed long-tailed (i.e., power-law) distributions, whereas activity bout d...

In standard arithmetic, if we, e.g., accidentally added a wrong number y to the preliminary result x, we can undo this operation by subtracting y from the result x+ y. A similar possibility to invert (undo) addition holds for intervals. In this paper, we show that if we add a single non-interval set, we lose invertibility. Thus, invertibility requirement leads to a new characterization of the c...

Perfectionists have excessively high standards and thus are prone to experience dissatisfaction and embarrassment. But what if they achieve perfection? The present study investigated in a sample of 194 university students how self-oriented and socially prescribed perfectionism predicted emotional reactions (satisfaction, dissatisfaction, pride, embarrassment) to imagined situations in which stu...