Applications of Polymeric Reagents in Organic Synthesis

Polymer supported reagents have found many applications in recent years. Scientists in research laboratories of agrochemical and pharmaceutical industries now routinely utilize these compounds to prepare ensembles of small organic molecules for screening. This review is aimed to highlight some of the most important applications of these promising materials in organic synthesis. Furthermore, an extensive listing of polymeric reagents that were recently used in organic synthesis is included.     

Indoor radon monitoring in some buildings surrounding the national Hydroelectric Power Corporation (NHPC) project at upper Siang in Arunachal Pradesh, India

In the present study measurement of radon and its progeny concentration has been undertaken in the buildings constructed in the surroundings of National Hydroelectric Power Corporation (NHPC). LR-115 Type-II solid state nuclear track detectors fixed on a thick flat card were exposed in bare mode. Track etch technique has been used to estimate the radon concentration in the rooms of some buildings. Annual effective dose has been calculated from the radon concentration to carry out the assessment of the variability of expected radon exposure of the population due to radon and its progeny. The radon levels in these dwellings vary from 9±4 to 472±28 Bq m⁻³ with an average value of 158±14.9 Bq m⁻³ whereas annual effective dose varies from 0.1±0.04 to 7±0.4 mSv y⁻¹ with an average value of 2.3±0.2 mSv y⁻¹. These values are below the recommended action levels.     

Fixed points of fuzzy contractive and fuzzy locally contractive maps

We establish some fixed point theorems for fuzzy contractive and fuzzy locally contractive mappings on a compact metric space with the d_∞-metric for fuzzy sets. Our results generalized well-known classical results of Edelstein.     

Discrete optimization in partially ordered sets

The primary aim of this article is to resolve a global optimization problem in the setting of a partially ordered set that is equipped with a metric. Indeed, given non-empty subsets A and B of a partially ordered set that is endowed with a metric, and a non-self mapping ${S : A \longrightarrow B}$ , this paper discusses the existence of an optimal approximate solution, designated as a best proximity point of the mapping S, to the equation Sx?=?x, where S is a proximally increasing, ordered proximal contraction. An algorithm for determining such an optimal approximate solution is furnished. Further, the result established in this paper realizes an interesting fixed point theorem in the setting of partially ordered set as a special case.     

Common best proximity points: global minimization of multi-objective functions

Given non-empty subsets A and B of a metric space, let ${S{:}A{\longrightarrow} B}$ and ${T {:}A{\longrightarrow} B}$ be non-self mappings. Due to the fact that S and T are non-self mappings, the equations Sx = x and Tx = x are likely to have no common solution, known as a common fixed point of the mappings S and T. Consequently, when there is no common solution, it is speculated to determine an element x that is in close proximity to Sx and Tx in the sense that d(x, Sx) and d(x, Tx) are minimum. As a matter of fact, common best proximity point theorems inspect the existence of such optimal approximate solutions, called common best proximity points, to the equations Sx = x and Tx = x in the case that there is no common solution. It is highlighted that the real valued functions ${x{\longrightarrow}d(x, Sx)}$ and ${x{\longrightarrow}d(x, Tx)}$ assess the degree of the error involved for any common approximate solution of the equations Sx = x and Tx = x. Considering the fact that, given any element x in A, the distance between x and Sx, and the distance between x and Tx are at least d(A, B), a common best proximity point theorem affirms global minimum of both functions ${x{\longrightarrow}d(x, Sx)}$ and ${x{\longrightarrow}d(x, Tx)}$ by imposing a common approximate solution of the equations Sx = x and Tx = x to satisfy the constraint that d(x, Sx) = d(x, Tx) = d(A, B). The purpose of this article is to derive a common best proximity point theorem for proximally commuting non-self mappings, thereby producing common optimal approximate solutions of certain simultaneous fixed point equations in the event there is no common solution.     

Correlated percolation in a film-deposition model

Clustering phenomenon has been studied in a film-deposition model in which a monolayer of particles is deposited onto a substrate. The occupation of a given site is assumed to depend on the occupation states of its nearest neighbouring sites as well as on the temperature of the particles being deposited. It is found that the percolating clusters remain ramified in that the number of their boundary sites are proportional to the number of particles in the cluster. The percolation threshold, however is lowered to (54±2)% as compared to 59% density for the uncorrelated case.