We study the category of wheeled PROPs using tools from Invariant Theory. A typical example a PROP is mixed tensor algebra V=T(V)⊗T(V⋆), where T(V) on an n-dimensional vector space over field K characteristic 0. First we classify all ideals initial object Z in PROPs. show that non-degenerate sub-wheeled V are exactly subalgebras form VG G closed, reductive subgroup general linear group GL(V). W...

This paper is a contribution to a new direction in descriptive set theory that is being extensively pursued over the last decade or so. It deals with the development of the theory of definable actions of Polish groups, the structure and classification of their orbit spaces, and the closely related study of definable equivalence relations. This study is motivated by basic foundational questions,...

In this paper, we introduce the notions of asymptotical strong σ 2 σ2 -equivalence, -statistical equivalence, lacunary -equivalence and equivalence in Wijsman sense for double set sequences. Also, investigate some relations between these new notions.

In this paper, we aim to overcome three major shortcomings of the FDH (Free Disposal Hull) directional distance function through developing two new, named Linear and Fractional CDFDH, complete FDH measures of efficiency. To accomplish this, we integrate the concepts of similarity and FDH directional distance function. We prove that the proposed measures are translation invariant and unit invari...