Influence of heat transfer on MHD Carreau fluid flow due to motile cilia in a channel

Journal of Thermal Analysis and Calorimetry - Mucus transport mediated by motile cilia in the airway is an important defense mechanism for prevention of respiratory infections. Cilia motility can...     

Studies on toxicity of aluminum oxide (Al<Subscript>2</Subscript>O<Subscript>3</Subscript>) nanoparticles to microalgae species: <Emphasis Type="Italic">Scenedesmus</Emphasis> sp. and <Emphasis Type="Italic">Chlorella</Emphasis> sp.

In view of increasing commercial applications of metal oxide nanoparticles their toxicity assessment becomes important. Alumina (Al₂O₃) nanoparticles have wide range of applications in industrial as well as personal care products. In the absence of prior report on toxicological impact of alumina nanoparticles to microalgae, the principal objective of this study was to demonstrate the effect of the nanoparticles on microalgae isolated from aquatic environment (Scenedesmus sp. and Chlorella sp.). The growth inhibitory effect of alumina nanoparticles was observed for both the species (72 h EC₅₀ value, 45.4 mg/L for Chlorella sp.; 39.35 mg/L for Scenedesmus sp.). Bulk alumina also showed toxicity though to a lesser extent (72 h EC₅₀ value, 110.2 mg/L for Chlorella sp.; 100.4 mg/L for Scenedesmus sp.). A clear decrease in chlorophyll content was observed in the treated cells compared to the untreated ones, more effect being notable in the case of nanoparticles. Preliminary results based on FT-IR studies, optical and scanning electron microscopic images suggest interaction of the nanoparticles with the cell surface.     

Global optimal approximate solutions

Given non-void subsets A and B of a metric space and a non-self mapping T:A? B{T:A\longrightarrow B}, the equation T x = x does not necessarily possess a solution. Eventually, it is speculated to find an optimal approximate solution. In other words, if T x = x has no solution, one seeks an element x at which d(x, T x), a gauge for the error involved for an approximate solution, attains its minimum. Indeed, a best proximity point theorem is concerned with the determination of an element x, called a best proximity point of the mapping T, for which d(x, T x) assumes the least possible value d(A, B). By virtue of the fact that d(x, T x) ≥ d(A, B) for all x in A, a best proximity point minimizes the real valued function x? d(x, T x){x\longrightarrow d(x, T\,x)} globally and absolutely, and therefore a best proximity in essence serves as an ideal optimal approximate solution of the equation T x = x. The aim of this article is to establish a best proximity point theorem for generalized contractions, thereby producing optimal approximate solutions of certain fixed point equations. In addition to exploring the existence of a best proximity point for generalized contractions, an iterative algorithm is also presented to determine such an optimal approximate solution. Further, the best proximity point theorem obtained in this paper generalizes the well-known Banach’s contraction principle.     

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.