M. Mirzavaziri
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Mashhad, Iran
[ 1 ] - Characterization of Lie higher Derivations on $C^{*}$-algebras
Let $mathcal{A}$ be a $C^*$-algebra and $Z(mathcal{A})$ the center of $mathcal{A}$. A sequence ${L_{n}}_{n=0}^{infty}$ of linear mappings on $mathcal{A}$ with $L_{0}=I$, where $I$ is the identity mapping on $mathcal{A}$, is called a Lie higher derivation if $L_{n}[x,y]=sum_{i+j=n} [L_{i}x,L_{j}y]$ for all $x,y in mathcal{A}$ and all $ngeqslant0$. We show that ${L_{n}}_{n...
[ 2 ] - Product of derivations on C$^*$-algebras
Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...
[ 3 ] - Uniquely Remotal Sets in $c_0$-sums and $ell^infty$-sums of Fuzzy Normed Spaces
Let $(X, N)$ be a fuzzy normed space and $A$ be a fuzzy boundedsubset of $X$. We define fuzzy $ell^infty$-sums and fuzzy $c_0$-sums offuzzy normed spaces. Then we will show that in these spaces, all fuzzyuniquely remotal sets are singletons.
[ 4 ] - THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G
To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the ...
[ 5 ] - The application and development of graph theory through the space syntax method: The implementation of analytical practical model in architecture
Abstract Over the last few decades, different mathematical methods have been used to design and analyze architectural spaces. Meanwhile, the graph theory provides an abstract model to study the spatial configuration, so that a simple and flexible mathematical framework is obtained to analyze the spatial topological features and their relationship with social and functional concepts in architec...