On reflexive and

On reflexive subobject lattices and reflexive endomorphism algebras

In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.

On Polar Cones and Differentiability in Reflexive Banach Spaces

Let $X$ be a  Banach  space, $Csubset X$  be  a  closed  convex  set  included  in  a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a  bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set  $C$,  so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

‎Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...

On bicyclic reflexive graphs

On Unicyclic Reflexive Graphs

If G is a simple graph (a non-oriented graph without loops or multiple edges), its (0, 1)-adjacency matrix A is symmetric and roots of the characteristic polynomial PG (λ) = det (λI −A) (the eigenvalues of G, making up its spectrum) are all real numbers, for which we assume their non-increasing order: λ1 ≥ λ2 ≥ · · · ≥ λn. In a connected graph for the largest eigenvalue λ1 (the index of the gra...