We study the canonical weak distributive law $\delta$ of powerset monad over semimodule for a certain class semirings containing, in particular, positive semifields. For this subclass we characterise as convex closure free set. Using abstract theory laws, compose and monads via $\delta$, obtaining subsets semimodule.

Paredaens and Van Gucht proved that the at relational algebra has the same expressive power as the nested relational algebra as far as queries over at relations and with at results are concerned We provide a new very direct proof of this fact using a simulation technique Our technique is also applied to partially answer a question posed by Suciu and Paredaens regarding the complexity of evaluat...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

Monads are used for various applications in computer science, and well-known is e.g. the interpretation of morphisms in the Kleisli category of the term monad as variable substitutions assigning variables to terms. An application building upon this observation is the equivalence between most general unifiers and co-equalizers in this category [13]. In this paper we will use monads with addition...

This work is motivated by knowledge discovery in attributed graphs. Our approach consists in extending the methodology of frequent closed pattern mining, as developed in Formal Concept Analysis (FCA), to the case where the objects in which attribute patterns may occur are the vertices of a graph, typically representing a social network. For that purpose we extend the framework of abstract conce...

We consider the structure of JordanH-pseudoalgebras which are linearly finitely generated over a Hopf algebra H . There are two cases under consideration: H = U(h) and H = U(h)#C[Γ], where h is a finite-dimensional Lie algebra over C, Γ is an arbitrary group acting on U(h) by automorphisms. We construct an analogue of the Tits–Kantor–Koecher construction for finite Jordan pseudoalgebras and des...

in this paper, we determine the structure of the space of multipliers of the range of a composition operator cφ that induces by the conditional expectation between two lp() spaces.

We introduce and study three notions of typeness for automata on infinite words. For an acceptance-condition class γ (that is, γ is weak, Büchi, co-Büchi, Rabin, or Streett), deterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same deterministic structure, nondeterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same structure, and γ...