Let $G$ be a finite group. The main supergraph $mathcal{S}(G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o(x) mid o(y)$ or $o(y)mid o(x)$. In this paper, we will show that $Gcong L_{2}(q)$ if and only if $mathcal{S}(G)cong mathcal{S} (L_{2}(q))$, where $q$ is a prime power. This work implies that Thompsonchr('39')s problem holds for the simpl...

And what if the only reality in existence was virtual reality? The individual identity in virtual reality has always been studied with regards to individual identity in reality. Indeed, the individual in virtual reality is considered as a real individual to whom we removed fundamental features: spatial unity (Leibniz) and temporal identity or sameness (Ricoeur, 1990). In other words, a virtual ...

We say an algebraic object or property over a field k is arithmetic if it becomes trivial or vanishes after finite separable base extension. Since such objects or properties owe their existence to the presence of “arithmetic gaps” in k, i.e., the failure of k to be algebraically closed, we view them as responses to specific arithmetic properties of k, and we study them in order to gain insight ...

1. A function is arithmetic if it is defined on the positive integers. Those arithmetic functions which assume real values and satisfy f(ab)-f(a)+f(b) for mutually prime integers a, b are classically called additive. The following examples illustrate the interest of these functions, both for themselves and for their applications. An additive function is defined by its values on the prime powers...

Facing a second major event of computational linguistics in Prague in the history of Czech CL – the ACL Annual Meeting in June 2007 – we cannot leave the first such event – COLING 1982 – unmentioned. But alas – most unfortunately, we have to start with very sad news about the then President of the Congress, Professor Ján Horecký, who died on August 11th, 2006 in his hometown Stupava (near Brati...

A lot of decisions are made during boardroom meetings. After a discussion, the head of the board often asks for a quick poll. But what if you cannot join the meeting? So called boardroom voting schemes have been proposed to conduct the poll over the Internet and thereby enabling also those who are not present but available online to participant in the poll. But what if you are not available at ...

Assume that some businessmen wish to have a meeting. For this to occur, they usually have to meet somewhere. If they cannot meet physically, then they can take part in a video (or audio) conference to discuss whatever needs to be discussed. But what if their meeting is meant to be private? In this case they need a cryptographic protocol that allows them to exchange their ideas remotely, while k...

g-frames in hilbert spaces are a redundant set of operators which yield a repre-sentation for each vector in the space. in this paper we investigate the connection betweeng-frames, g-orthonormal bases and g-riesz bases. we show that a family of bounded opera-tors is a g-bessel sequences if and only if the gram matrix associated to its denes a boundedoperator.