M. Habibi — Page 3 | Searcharxiv

arXiv2011

Packing of elastic wires in spherical cavities

We investigate the morphologies and maximum packing density of thin wires packed into spherical cavities. Using simulations and experiments, we find that ordered as well as disordered structures emerge, depending on the amount of internal torsion. We find that the highest packing densities are achieved in low torsion packings for large systems, but in high torsion packings for small systems. An analysis of both situations is given in terms of energetics and comparison is made to analytical models of DNA packing in viral capsids.

cond-mat.soft↗

arXiv2010

A note on co-maximal graph of non-commutative rings

Let $R$ be a ring with unity. The graph $Γ(R)$ is a graph with vertices as elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if $Ra+Rb=R$. Let $Γ_2(R)$ is the subgraph of $Γ(R)$ induced by the non-unit elements. H.R. Maimani et al. [H.R. Maimani et al., Comaximal graph of commutative rings, J. Algebra $319$ $(2008)$ $1801$-$1808$] proved that: ``If $R$ is a commutative ring with unity and the graph $Γ_2(R)\backslash J(R)$ is $n$-partite, then the number of maximal ideals of $R$ is at most $n$." The proof of this result is not correct. In this paper we present a correct proof for this result. Also we generalize some results given in the aforementioned paper for the non-commutative rings.

math.RA↗