We develop a theory of sets with distributive products (called shelves and multi-shelves) and of their homology. We relate the shelf homology to the rack and quandle homology. 1. Binary distributive operations Let X be a set. Binary operations ? : X ×X → X with composition x ?1 ?2y = (x ?1 y) ?2 y and the identity x ? y = x form a monoid, M(X). A collection of operations ?i, i ∈ I is called mut...

In this paper the authors have studied the Glivenko congruence R in a 0-distributive nearlattice S defined by " () R b a ≡ if and only if 0 = ∧ x a is equivalent to 0 = ∧ x b for each S x ∈ ". They have shown that the quotient nearlattice R S is weakly complemented. Moreover, R S is distributive if and only if S is 0-distributive. They also proved that every Sectionally complemented nearlattice...

I consider abstract social systems where the distribution of wealth is an object of common concern. I study, in particular, the systems where liberal distributive social contracts consist of the Pareto-efficient distributions that are unanimously preferred to the initial distribution. I define a Dual Distributive Core from a process of decentralized auction on the budget shares of Lindahl assoc...

It is generally recognised that the potential positive and negative impacts of geoengineering will be distributed unevenly both geographically and temporally. The question of distributive justice in geoengineering thus is one of the major ethical issues associated with geoengineering. Currently, the question of distributive justice in geoengineering is framed in terms of who gets what (potentia...

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

Generalised Distributive laws in Computer Science are rules governing the transformation of one programming structure into another. In programming, they are programs satisfying certain formal conditions. Their importance has been to date documented in several isolated cases by diverse formal approaches. These applications have always meant leaps in understanding the nature of the subject. Howev...

The power set of a domain D can be seen as the function space D ! 2 of all functions in the pointwise order. One computational version thereof is the lifted lower powerdomain, which we can think of as the lattice of Scott-closed subsets or, alternatively, as the order dual of the function space D ! 2]. Therefore, logic and the ordinary power set, as well as its information-theoretic version, re...

BACKGROUND Intermittent glycemic measurements in patients admitted to the intensive care unit (ICU) can result in episodes of severe hypoglycemia or in a poor control of glycemia range. We designed a study to assess accuracy and reliability of continuous monitoring of tissue glucose for patients with distributive shock. METHODS Consecutive patients admitted to the ICU with a diagnosis of dist...

Let S be a distributive {∨, 0 }-semilattice. In a previous paper, the second author proved the following result: Suppose that S is a lattice. Let K be a lattice, let φ : Conc K → S be a {∨, 0 }-homomorphism. Then φ is, up to isomorphism, of the form Conc f , for a lattice L and a lattice homomorphism f : K → L. In the statement above, Conc K denotes as usual the {∨, 0 }-semilattice of all finit...

L. M/trki and R. P6schel have characterised the endoprimal distributive lattices as those which are not relatively complemented. The theory of natural dualities implies that any finite algebra A on which the endomorphisms of A yield a duality on the quasivariety DSP(A) is necessarily endoprimal. This note investigates endodualisability for finite distributive lattices, and shows, in a manner wh...