A notion of reticulation which provides topological properties on algebras has introduced on commutative rings in 1980 by Simmons in [5]. For a given commutative ring A, a pair (L, λ) of a bounded distributive lattice and a mapping λ : A → L satisfying some conditions is called a reticulation on A, and the map λ gives a homeomorphism between the topological space Spec(A) consisting of prime fil...

BACKGROUND Households in dual reticulation developments are supplied with recycled water from sewage effluent for some non-potable purposes, and conventional tap water for other uses. Adverse health effects from recycled water exposure are considered unlikely; however, no epidemiological studies have been undertaken to assess the public health impact of such exposures. METHODS We compared the...

The reticulation L(R) of a commutative ring R was introduced by Joyal in 1975, then the theory developed Simmons remarkable paper published 1980. is bounded distributive algebra whose main property that Zariski prime spectrum Spec(R) and Stone SpecId (L(R)) are homeomorphic. construction lattice generalized Belluce for each unital defined axioms. In recent we algebras semidegenerate congruence-...

The problem of constructing an optimal rooted phylogenetic‎ ‎network from a set of rooted triplets is NP-hard. ‎In this paper‎, ‎we present a novel method called NCH‎, ‎which tries to construct a rooted phylogenetic network with the minimum number‎‎of reticulation nodes from an arbitrary set of rooted triplets based on the concept of the height function of a tree and a network. We report the pe...

UNLABELLED The purpose of this study was to evaluate integrated (18)F-FDG PET/CT in patients with idiopathic pulmonary fibrosis (IPF) and diffuse parenchymal lung disease (DPLD). METHODS Thirty-six consecutive patients (31 men and 5 women; mean age +/- SD, 68.7 +/- 9.4 y) with IPF (n = 18) or other forms of DPLD (n = 18) were recruited for PET/CT and high-resolution CT (HRCT), acquired on the...

BACKGROUND Emphysema and fibrosis, typically the idiopathic pulmonary fibrosis (IPF) form of usual interstitial pneumonia (UIP), can co-exist as combined pulmonary fibrosis emphysema (CPFE). It is unknown whether there is a pathobiologic basis for CPFE beyond the coexistence of fibrosis and emphysema. The aim of this study was to ascertain radiologic differences in severity of fibrosis and emph...

Failure of a liquid coating to remain continuous on a substrate that exhibits a significant equilibrium contact angle is a common occurrence in industrial applications. The term "reticulation" is sometimes used to describe the resulting formation of a pattern of defects. The failure may take the form of coating perforations and dewetting, and it may ultimately lead to a set of isolated drops. W...

Phylogeography, and its extensions into comparative phylogeography, have their roots in the layering of gene trees across geography, a paradigm that was greatly facilitated by the nonrecombining, fast evolution provided by animal mtDNA. As phylogeography moves into the era of next-generation sequencing, the specter of reticulation at several levels-within loci and genomes in the form of recombi...

Phylogenetic networks have emerged as a unifying evolutionary model of both vertical and horizontal inheritance. A major approach for reconstructing such networks is to reconcile gene trees that are reconstructed from various genomic regions. The Subtree Prune and Regraft (SPR) operation has been used to obtain lower bound estimates of the number of reticulation events from a pair of trees. How...