Dependently typed programming uses precise variants of data structures to ensure program correctness in an economical way, but designing reusable libraries for all possible variants of data structures is a difficult problem. The authors addressed the problem by extending McBride’s ornaments to a framework of ornaments and refinements to support a modular structure for dependently typed librarie...

We show the existence of an exponential attractor for non-autono-mous dynamical system with bounded delay. considered case strong dissipativity then prove that result remains weak dissipativity. conclude global and ensure boundedness its fractal dimension.

In (Golchin A. and Rezaei P., Subpullbacks and flatness properties of S-posets. Comm. Algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right -posets  over a pomonoid  that can be described by surjectivity of  corresponding to certain (sub)pullback diagrams and new properties such as  and  were discovered. In this article first of all we describe po-flatness propertie...

Abstract Various inequivalent notions of attraction for autonomous dynamical systems have been proposed, each them useful to understand specific aspects attraction. Milnor’s notion a measure attractor considers invariant sets with positive basin attraction, while Ilyashenko’s weaker statistical points that approach the set in terms averages. In this paper we propose generalisations these nonaut...