This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to...

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...

In the late 1930's Garrett Birkhoff [3] pioneered the theory of distributive lattices. An important component in this theory is the concept of exponentiation of lattices [4]: for a lattice L and a partially ordered set P let L denote the set of all order-preserving maps of P to L partially ordered b y / ^ g if and only if/(;c) ^ g(x) for each x e P (see Figure 1). Indeed, If is a lattice. This ...

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, routing nodes are proposed to provide speedup and parallel processing capability in Data Vortex network architectures. The new design not only significantly improves network throughput and latency, but also eliminates the need for distributive traffic control mechanism originally embedded among nodes and the need for nodal buffering. The cost effectiveness is studied by a compari...

ground penetrating radar (gpr) is one of high resolution geophysical methods for locating missed objects, buried equipments. gpr is a nondestructive testing method that is useful in various kinds of explorations such as mapping the archaeological sites. the safety of the archaeological sites is one of the most concerns of the archaeologists. one of the best gpr applications is in archaeology as...

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