We construct a compact convex generating set $$\mathcal {C}_n$$ of the moduli closed connected projective special real manifolds fixed dimension n. show that manifold corresponds to an inner point if and only it has regular boundary behaviour. Our results can be used describe deformations 5d supergravity theories with complete scalar geometries.

a set $wsubseteq v(g)$ is called a resolving set for $g$, if for each two distinct vertices $u,vin v(g)$ there exists $win w$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. the minimum cardinality of a resolving set for $g$ is called the metric dimension of $g$, and denoted by $dim(g)$. in this paper, it is proved that in a connected graph $...

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

the noncommuting graph $nabla (g)$ of a group $g$ is asimple graph whose vertex set is the set of noncentral elements of$g$ and the edges of which are the ones connecting twononcommuting elements. we determine here, up to isomorphism, thestructure of any finite nonabeilan group $g$ whose noncommutinggraph is a split graph, that is, a graph whose vertex set can bepartitioned into two sets such t...