Carbon and diamond paste microelectrodes based on Mn(III) porphyrins for the determination of dopamine

Three Mn(III) porphyrins were used for the design of carbon paste and diamond paste based microelectrodes, which were employed for the determination of dopamine in pharmaceutical and biological samples using differential pulse voltammetry (DPV). The limits of detection lie between 1.6 × 10⁻¹³ and 2.0 × 10⁻⁶ mol L⁻¹ while the sensitivities were between 230 pA μmol L⁻¹ and 3.24 μA mol L⁻¹. Dopamine was recovered reliable from pharmaceutical and biological samples in percentages higher than 91.00% and 92.00%, respectively. The surface of the microelectrodes can easily be renewed by simple polishing, obtaining a fresh surface ready for use in a new assay.     

Steric control over hydrogen bonding in crystalline organic solids: a structural study of N,N'-dialkylthioureas

Hydrogen bonding in crystalline N,N'-dialkylthioureas was examined with the help of single-crystal X-ray diffraction, DFT calculations, and Cambridge Structural Database (CSD) analysis. A CSD survey indicated that unlike the related urea derivatives, which persistently self-assemble into one-dimensional hydrogen-bonded chains, the analogous thioureas can form two different hydrogen-bonding motifs in the solid state: chains, structurally similar with those found in ureas, and dimers, that further associate into hydrogen-bonded layers. The formation of one motif or another can be manipulated by the bulkiness of the organic substituents on the thiourea group, which provides a clear example of steric control over the hydrogen bonding arrangement in crystalline organic solids.     

The influence of fluorine on the asymmetric reduction of fluoromethyl ketones

A comparative study of the asymmetric reduction of representative aryl and alkyl α-fluoro- and α-chloromethyl ketones using (−)-diisopinocampheylchloroborane [(−)-DIP-Chloride™] and (−)-B-isopinocampheyl-9-borabicyclo[3.3.1]nonane [R-Alpine-Borane^®] has been made. It was observed that DIP-Chloride™ is superior in terms of the rate and enantioselectivity for both classes of halo-ketones. While the reduction of monofluoroacetone and trifluoroacetone with DIP-Chloride™ provided the product alcohols in 61% ee and 96% ee, respectively, the reduction of difluoroacetone yielded only 5% ee. The influence of a lone halogen atom was not observed for monochloroacetone, all of which point towards a chelating effect of monofluoroacetone on the Lewis acidic chloroborane.     

Generalized Iterated Function Systems with Place Dependent Probabilities

In the present paper we introduce the concept of generalized iterated function system with place dependent probabilities (GIFSpdp). In this framework, we provide sufficient conditions under which the Markov operator associated to a GIFSpdp is Lipschitz. We also prove, under certain conditions, the existence of an analogue of Hutchinson measure associated to a GIFSpdp and study its properties.     

Stability of the vortex defect in the Landau–de Gennes theory for nematic liquid crystals

We analyze the radially symmetric solution corresponding to the vortex defect (the so-called melting hedgehog) in the Landau–de Gennes theory for nematic liquid crystals. We prove the existence, uniqueness and stability results of the melting hedgehog.     

Multiple positive solutions of non-local initial value problems for first order differential systems

The paper gives a new and natural method for the existence of multiple positive solutions for first order differential systems with non-local initial value conditions involving linear functionals. The case of higher order differential equations is also considered. The results are accompanied by numerical examples confirming the theory and proving for practice the importance of the bounds in solution localization.     

Fixed Point Theorems Under Combined Topological and Variational Conditions

The new idea is to replace part of the conditions on the operator involved in the classical fixed point theorems of Schauder, Krasnoselskii, Darbo and Sadovskii, by assumptions upon the associated functional, in case that the fixed point equation has a variational form. Fixed points minimizing the associated functionals are obtained via Ekeland’s variational principle and the Palais–Smale compactness condition guaranteed by the topological properties of the nonlinear operators.     

Vectorial penalization for generalized functional constrained problems

In this paper we use a double penalization procedure in order to reduce a set-valued optimization problem with functional constraints to an unconstrained one. The penalization results are given in several cases: for weak and strong solutions, in global and local settings, and considering two kinds of epigraphical mappings of the set-valued map that defines the constraints. Then necessary and sufficient conditions are obtained separately in terms of Bouligand derivatives of the objective and constraint mappings.     

Nonexistence of some Antipodal Distance-regular Graphs of Diameter Four

We find an inequality involving the eigenvalues of a regular graph; equality holds if and only if the graph is strongly regular. We apply this inequality to the first subconstituents of a distance-regular graph and obtain a simple proof of the fundamental bound for distance-regular graphs, discovered by Juri i , Koolen and Terwilliger. Using this we show that for distance-regular graphs with certain intersection arrays, the first subconstituent graphs are strongly regular. From these results we prove the nonexistence of distance-regular graphs associated to 20 feasible intersection arrays from the book Distance-Regular Graphs by Brouwer, Cohen and Neumaier .