Two-Parameter Fuzzy-Valued Stochastic Integrals and Equations

This article is concerned with notions of fuzzy-valued stochastic integrals driven by two-parameter martingales and increasing processes. We present their main properties and formulate next two-parameter fuzzy-valued stochastic integral equations. We establish the existence and uniqueness of solutions to such equations as well as their additional properties.     

Can 2‐acylpyrroles form an intramolecular hydrogen bond?

The formation of intramolecular hydrogen bonding by certain N‐substituted 2‐acylpyrroles has been demonstrated by B3LYP/aug‐cc‐pVDZ calculations, the quantum theory of atoms in molecules, and the natural bond orbital method. Total electron energy densities H_BCP at the bond critical point of the H?O bond were applied to analyze the strength of these interactions. The relations between quantum theory of atoms in molecules, carbonyl stretching vibrational modes ν_{C = O}, and natural bond orbital parameters associated with the formation of the C–H?O interaction have been established. The short contacts were found experimentally in the crystal structure of a new 2‐acylpyrrole derivative 5‐chloro‐2‐oxopentyl‐1‐(5‐chloro‐2‐oxopentyl)pyrrolo‐2‐carboxylate. The influence of 2‐ and N‐substitution of 2‐acylpyrroles on C‐H?O interaction energy is discussed. It was found that the methylene group may act as a proton donor leading to a red‐shift or blue‐shift phenomenon of the ν_C–H stretching mode. Copyright © 2015 John Wiley & Sons, Ltd.     

Chiral Sulfinimines in Asymmetric Synthesis of Enantiomeric Aminophosphonic Acids

Abstract

Aminophosphonic acids have become important in different fields of chemistry, medicine and agriculture. In this review article, we highlight a new strategy developed in the author's laboratory of asymmetric synthesis of enantiomeric aminophosphonic acid that users chiral sulfinimines as reagents. A key reaction in the synthesis of enantiopure α-, β- and γ-aminophosphonic acids is a highly or fully diastereoselective addition of trivalent phosphorus nucleophiles and α-phosphonate carbanions to enantiopure sulfinimines. The steric course of these addition reactions is rationalized. The usefulness of the sulfinimine methodology is demonstrated by the synthesis of biologically active enantiopure 2-amino-3-phosphonopropanoic acid (AP3), 2-amino-4-phosphonobutanoic acid (AP4) and phosphoemeriamine.     

Hydrogen‐Bonding in Aminocatalysis: From Proline and Beyond

This Concept article summarizes recent progress in the field of hydrogen‐bonding aminocatalysis using proline‐derived systems. The aminocatalysts available in the literature are categorized by the incorporated hydrogen‐bonding scaffold and its mode of recognition. Both mono‐ and double‐hydrogen‐bonding motifs are discussed and examples of their application in asymmetric synthesis are given.     

Effect of temperature on the equilibrium and kinetics of galactose,glucose, and lactose adsorption on a cation exchanger

Galacto-oligosaccharides are typically produced by an enzymatic reaction when the post-reaction mixture contains considerable amounts of lactose and glucose and a smaller amount of galactose. In order to develop a process of chromatographic removal of saccharide impurities, adsorption equilibria and kinetics of these di- and monosaccharides were investigated for Diaion UBK 530, an industrialgrade strong cation-exchanger in the Na⁺ form. Frontal chromatographic experiments were carried out in the temperature range of 30–70°C and a broad interval of saccharide concentrations up to 350 g L^?1. Breakthrough curves were described using the equilibrium-dispersive model with the linear adsorption isotherm. Both the distribution and the axial dispersion coefficient values depended on the saccharide molecule type and size. No significant effect of temperature or concentration on the distribution coefficient was observed. The apparent dispersion coefficients of all saccharides exhibited some decrease with the temperature, which was caused by the decrease of the intraparticle mass transfer resistance. An analysis showed that both the intraparticle mass transfer and the axial dispersion had a significant influence on the front dispersion.     

Solution and asymptotic analysis of a boundary value problem in the spring–mass model of running

We consider the classic spring–mass model of running which is built upon an inverted elastic pendulum. In a natural way, there arises an interesting boundary value problem for the governing system of two nonlinear ordinary differential equations. It requires us to choose the stiffness to ascertain that after a complete step, the spring returns to its equilibrium position. Motivated by numerical calculations and real data, we conduct a rigorous asymptotic analysis in terms of the Poicaré–Lindstedt series. The perturbation expansion is furnished by an interplay of two time scales what has an significant impact on the order of convergence. Further, we use these asymptotic estimates to prove that there exists a unique solution to the aforementioned boundary value problem and provide an approximation to the sought stiffness. Our results rigorously explain several observations made by other researchers concerning the dependence of stiffness on the initial angle of the stride and its velocity. The theory is illustrated with a number of numerical calculations.

     

Preparation of thin SnO2 layers by inorganic sol-gel process

SnO₂ sols were prepared in the following way: (1) precipitation of metastannic acid with aqueous ammonia from aqueous solutions of SnCl₄, (2) washing the precipitates with NH₄NO₃ solution and water, (3) peptization of precipitates in water, sometimes with an addition of HNO₃, at elevated temperature using mechanical stirring. In those sols, sometimes diluted with water or ethanol, substrates (glass or silica derived wafers) were dipped and withdrawn at various rates. Gel coatings were converted into crystalline SnO₂ by thermal treatment at 600°C. Coatings with thickness between 300–2000 Å were prepared.     

Independent Components Analysis of the Overlapping Voltammetric Signals

This paper introduces the Independent Components Analysis (ICA) to voltammetry and extends possibility of the qualitative and quantitative analysis of binary mixtures of similar oxidation/reduction potentials. It was demonstrated that even in the case of distance between peaks potentials equal to 10 mV, determinations may be realized according to typical validation criteria. The methodology was presented using the simulated data and capabilities and limitations of the method were described. Further, the usefulness of ICA was presented for voltammograms registered during simultaneous determination of copper and antimony, and thallium and indium. The results of high practical importance for chemical analysis were achieved and documented. In the quantitative analysis a property was extensively used, that ICA is an unsupervised method.