In this paper we define and discuss the theory of abstract outer measures on a sequentially continuous(2) linear lattice S. This is a generalization of the concept of outer measure on a function space as used by Bourbaki [3]. H. Nakano [7] and M. H. Stone [8] have modernized Lebesgue's extension theory; our approach provides a common generalization of their theories. We show, for example, that ...

Temperature and relative humidity have opposing effects on evaporative water loss, the likely mediator of the temperature-dependence of nephrolithiasis. However, prior studies considered only dry-bulb temperatures when estimating the temperature-dependence of nephrolithiasis. We used distributed lag non-linear models and repeated 10-fold cross-validation to determine the daily temperature metri...

The lattice of ordered compactifications of a topological sum of a finite number of totally ordered spaces is investigated. This investigation proceeds by decomposing the lattice into equivalence classes determined by the identification of essential pairs of singularities. This lattice of equivalence classes is isomorphic to a power set lattice. Each of these equivalence classes is further deco...

1. Introduction Stone, in [8], developed for distributive lattices a representation theory generalizing that for Boolean algebras. This he achieved by topologizing the set X of prime ideals of a distributive lattice A (with a zero element) by taking as a base {P a : aeA} (where P a denotes the set of prime ideals of A not containing a), and by showing that the map a i-> P a is an isomorphism re...

This work is a primary achievement in studying the CO2 and N2–oil systems. To predict gas-liquid relative permeability curves, a Shan-Chen type multicomponent multiphase lattice Boltzmann model for two-phase flow through 2D porous media is developed. Periodic and bounce back boundary conditions are applied to the model with the Guo scheme for the external body force (i.e.,...

Rough relation algebras are a generalization of relation algebras such that the underlying lattice structure is a regular double Stone algebra. Standard models are algebras of rough relations. A discrete duality is a relationship between classes of algebras and classes of relational systems (frames). In this paper we prove a discrete duality for a class of rough relation algebras and a class of...