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...     

Best proximity points: approximation and optimization

A best proximity point theorem explores the existence of an optimal approximate solution, known as a best proximity point, to the equations of the form Tx = x where T is a non-self mapping. The purpose of this article is to establish some best proximity point theorems for non-self non-expansive mappings, non-self Kannan- type mappings and non-self Chatterjea-type mappings, thereby producing optimal approximate solutions to some fixed point equations. Also, algorithms for determining such optimal approximate solutions are furnished in some cases.     

Common best proximity point theorems: Global minimization of some real-valued multi-objective functions

Let us deliberate the question of computing a solution to the problems that can be articulated as the simultaneous equations \({Sx = x}\) and \({Tx = x}\) in the framework of metric spaces. However, when the mappings in context are not necessarily self-mappings, then it may be consequential that the equations do not have a common solution. At this juncture, one contemplates to compute a common approximate solution of such a system with the least possible error. Indeed, for a common approximate solution \({x^*}\) of the equations, the real numbers \({d(x^*, Sx^*)}\) and \({d(x^*,Tx^*)}\) measure the errors due to approximation. Eventually, it is imperative that one pulls off the global minimization of the multiobjective functions \({x \rightarrow d(x, Sx)}\) and \({x \rightarrow d(x, Tx)}\). When S and T are mappings from A to B, it follows that \({d(x, Sx) \geq d(A, B)}\) and \({d(x, Tx) \geq d(A, B)}\) for every \({x \in A}\). As a result, the global minimum of the aforesaid problem shall be actualized if it is ascertained that the functions \({x \rightarrow d(x, Sx)}\) and \({x \rightarrow d(x, Tx)}\) attain the lowest possible value d(A, B). The target of this paper is to resolve the preceding multiobjective global minimization problem when S is a T-cyclic contraction or a generalized cyclic contraction, thereby enabling one to determine a common optimal approximate solution to the aforesaid simultaneous equations.     

Low-Lying Isomers of (TiO\begin{document}$_{2}$\end{document})\begin{document}$_{n}$\end{document} (\begin{document}${n}$\end{document}=2-8) Clusters

Although there are diverse bond features of Ti and O atoms, so far only several isomers have been reported for each (TiO\begin{document}$_2$\end{document})\begin{document}$_n$\end{document} cluster. Instead of the widely used global optimization, in this work, we search for the low-lying isomers of (TiO\begin{document}$_2$\end{document})\begin{document}$_n$\end{document} (\begin{document}$n$\end{document}=2\begin{document}$-$\end{document}8) clusters with up to 10000 random sampling initial structures. These structures were optimized by the PM6 method, followed by density functional theory calculations. With this strategy, we have located many more low-lying isomers than those reported previously. The number of isomers increases dramatically with the size of the cluster, and about 50 isomers were found for (TiO\begin{document}$_2$\end{document})\begin{document}$_7$\end{document} and (TiO\begin{document}$_2$\end{document})\begin{document}$_8$\end{document} with the energy within kcal/mol. Furthermore, new lowest isomers have been located for (TiO\begin{document}$_2$\end{document})\begin{document}$_5$\end{document} and (TiO\begin{document}$_2$\end{document})\begin{document}$_8$\end{document}, and isomers with three terminal oxygen atoms, five coordinated oxygen atoms as well as six coordinated titanium atoms have been located. Our work highlights the diverse structural features and a large number of isomers of small TiO\begin{document}$_2$\end{document} clusters.     

An algorithm for primary decomposition in polynomial rings over the integers

We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals, resp. over finite fields, and the idea of Shimoyama-Yokoyama, resp. Eisenbud-Hunecke-Vasconcelos, to extract primary ideals from pseudo-primary ideals. A parallelized version of the algorithm is implemented in Singular. Examples and timings are given at the end of the article.     

The use of the <Emphasis Type="Italic">k</Emphasis><Subscript>0</Subscript>-IAEA program in NIRR-1 NAA laboratory

The k ₀-IAEA program developed for implementation of the single comparator instrumental neutron activation analysis method (k ₀-INAA) has been used for elemental analysis with NIRR-1 irradiation and counting facilities. The existing experimental protocols for routine analysis based on the relative method were used to test the capability and reliability of the program for the analyses of geological and biological samples. The Synthetic Multi-element Standards (SMELS) types I, II and III recommended by the international k ₀ user community for the validation of k ₀-NAA method in NAA laboratories, furthermore, the following standard reference materials: NIST-1633b (Coal Fly Ash) and IAEA-336 (Lichen) were analyzed. Results obtained with the version 3.12 of the k ₀-IAEA program were found to be in good agreement with the data obtained with the established relative method using WINSPAN-2004 software. Detection limits for elemental analysis of geological and biological samples with NIRR-1 facilities are provided.     

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.     

The F<Subscript>4</Subscript>-algorithm for Euclidean rings

In this short note, we extend Faugére’s F₄-algorithm for computing Gröbner bases to polynomial rings with coefficients in an Euclidean ring. Instead of successively reducing single S-polynomials as in Buchberger’s algorithm, the F₄-algorithm is based on the simultaneous reduction of several polynomials.