Category theory provides a more abstract and thus more general setting for considering the structure of mathematical objects. 2-dimensional quantum field theories arise in physics as objects that assign vector spaces to 1-manifolds and linear maps to 2-cobordisms. From a categorical perspective, we find that they are the same as commutative Frobenius algebras. Our main goal is to explain this e...

This paper is concerned with approximating the dominant left singular vector space of a real matrix A of arbitrary dimension, from block Krylov spaces generated by the matrix AAT and the block vector AX. Two classes of results are presented. First are bounds on the distance, in the two and Frobenius norms, between the Krylov space and the target space. The distance is expressed in terms of prin...

we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

let $fneq1,3$ be a positive integer‎. ‎we prove that there exists a numerical semigroup $s$ with embedding dimension three such that $f$ is the frobenius number of $s$‎. ‎we also show that‎ ‎the same fact holds for affine semigroups in higher dimensional monoids‎.