The aim of this paper is to extend the classical Larson-Sweedler theorem, namely that a k-bialgebra has non-singular integral (and in particular Frobenius) if and only it finite dimensional Hopf algebra, ‘many-object’ setting categories. To end, we provide new characterizations Frobenius V-categories develop theory for V-categories. Our results apply algebras any braided monoidal category as sp...

We review the basic theory of super G-spaces. We prove a theorem relating the action of a super Harish-Chandra pair (G0, g) on a supermanifold to the action of the corresponding super Lie group G. The theorem was stated in [DM99] without proof. The proof given here does not use Frobenius theorem but relies on Koszul realization of the structure sheaf of a super Lie group (see [Kosz83]). We prov...

A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...

In this paper, we study the thermodynamic phase transition in one dimensional systems with short range interaction. We begin by reviewing some famous non-existence result, such as Landau’s argument and van Hove’s theorem. And we point out that the PerronFrobenius theorem is generally used to determine whether there is phase transition in such kind of system. Then several examples that Perron-Fr...

INTRODUCTION The Cohomological Field Theory was propose by Kontsevich and Manin [5] for description of Gromov-Witten Classes. They prove that Cohomological Field Theory is equivalent to Formal Frobenius manifold. Formal Frobenius manifold is defined by a formal series F , satisfying to associative equations. In points of convergence the series F defines a Frobenius algebras. The set of these po...

We introduce a relative notion of the ’big images and preimages’-property for random topological Markov chains. This then implies that a relative version of the Ruelle-Perron-Frobenius theorem holds with respect to summable and locally Hölder continuous potentials.

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...