Highly selective PVC-membrane electrodes based on Co(II)-Salen for determination of nitrite ion.

A cobalt(II) derivative was used as a suitable ionophore for the preparation of a polymeric membrane nitrite-selective electrode. The electrode reveals a Nemstian behavior over a very wide NO2- ion concentration range (1.0 x 10(-6)-1.0 x 10(-1) M) and a very low detection limit (5.0 x 10(-7) M). The potentiometric response is independent of the pH of solution in the pH range 4.0-9.5. The electrode shows advantages such as low resistance, fast response and, most importantly, good selectivity relative to a wide variety of inorganic and organic anions. In fact, the selectivity behavior of the proposed NO2- ion-selective electrode shows great improvements compared to the previously reported electrodes for nitrite ion. The proposed electrodes could be used for at least 2 months without any significant changes in potentials. The electrode was successfully applied to the determination of nitrate ion concentrations in sausage and milk samples.     

ε-WEAKLY CHEBYSHEV SUBSPACES OF BANACH SPACES

We will define and characterize c-weakly Chebyshev subspaces of Banach spaces. We will prove that all closed subspaces of a Banach space X are ε-weakly Chebyshev if and only if X is reflexive.     

Heavy tails for an alternative stochastic perpetuity model

In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten (1973) and Goldie (1991) all discount factors in the model are mutually independent. We prove that the tails of the distribution of this model are regularly varying both in the univariate and multivariate cases. Due to the additional randomness in the model the tails are not pure power laws as in the Kesten–Goldie setting but involve a logarithmic term.     

Selective complexation of alkali metal ions and nanotubular cyclopeptides: a DFT study

A density functional theory based on interaction of alkali metal cations (Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺) with cyclic peptides constructed from 3 or 4 alanine molecule (CyAla3 and CyAla4), has been investigated using mixed basis set (C, H, O, Li⁺, Na⁺ and K⁺ using 6-31+G(d), and the heavier cations: Rb⁺ and Cs⁺ using LANL2DZ). The minimum energy structures, binding energies, and various thermodynamic parameters of free ligands and their metal cations complexes have been determined with B3LYP and CAM-B3LYP functionals. The order of interaction energies were found to be Li⁺ > K⁺ > Na⁺ > Rb⁺ > Cs⁺ and Li⁺ > Na⁺ > K⁺ ? Rb⁺ > Cs⁺, calculated at CAM-B3LYP level for the M/CyAla3 and M/CyAla4 complexes, respectively. Their selectivity trend shows that the highest cation selectivity for Li⁺ over other alkali metal ions has been achieved on the basis of thermodynamic analysis. The main types of driving force host–guest interactions are investigated, the electron-donating O offers lone pair electrons to the contacting LP* of alkali metal cations.     

On simultaneous weakly-Chebyshev subspaces

In this paper, we shall introduce and characterize simultaneous quasi-Chebyshev (and weakly-Chebyshev) subspaces of normed spaces with respect to a bounded set S by using elements of the dual space.     

Efficacy of cones on topological vector spaces and application to common fixed points of multifunctions

Let (E, τ) be a topological vector space and P a cone in E. We shall define a topology τ _P on E so that (E, τ _P ) is a normable topological vector space and P is a normal cone with normal constant M = 1. Then by using the norm, we shall give some results about common fixed points of two multifunctions on cone metric spaces.     

Some fixed point results on a metric space with a graph

Combining some branches is a typical activity in different fields of science, especially in mathematics. Naturally, it is notable in fixed point theory. Over the past few decades, there have been a lot of activity in fixed point theory and another branches in mathematics such differential equations, geometry and algebraic topology. In 2006, Espinola and Kirk made a useful contribution on combining fixed point theory and graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using main idea of their work and the idea of combining fixed point theory and graph theory, we present some iterative scheme results for G-contractive and G-nonexpansive mappings on graphs.