Markoff–Rosenberger triples and generalized Lucas sequences

Periodica Mathematica Hungarica - We consider the Markoff–Rosenberger equation $$\begin{aligned} ax^2+by^2+cz^2=dxyz \end{aligned}$$ with $$(x,y,z)=(U_i,U_j,U_k)$$ , where $$U_i$$ denotes the...     

Development of a Fast and Robust UHPLC Method for Apixaban In-Process Control Analysis

In-process control (IPC) is an important task during chemical syntheses in pharmaceutical industry. Despite the fact that each chemical reaction is unique, the most common analytical technique used for IPC analysis is high performance liquid chromatography (HPLC). Today, the so-called “Quality by Design” (QbD) principle is often being applied rather than “Trial and Error” approach for HPLC method development. The QbD approach requires only for a very few experimental measurements to find the appropriate stationary phase and optimal chromatographic conditions such as the composition of mobile phase, gradient steepness or time (tG), temperature (T), and mobile phase pH. In this study, the applicability of a multifactorial liquid chromatographic optimization software was studied in an extended knowledge space. Using state-of-the-art ultra-high performance liquid chromatography (UHPLC), the analysis time can significantly be shortened. By using UHPLC, it is possible to analyse the composition of the reaction mixture within few minutes. In this work, a mixture of route of synthesis of apixaban was analysed on short narrow bore column (50 × 2.1 mm, packed with sub-2 µm particles) resulting in short analysis time. The aim of the study was to cover a relatively narrow range of method parameters (tG, T, pH) in order to find a robust working point (zone). The results of the virtual (modeled) robustness testing were systematically compared to experimental measurements and Design of Experiments (DoE) based predictions.     

Determination of the geometrical configuration of the polyen chain of monocis C40-carotenoids—I: A 13C NMR study of monocis zeaxanthins and monocis capsorubins

¹³C NMR studies reveal that the polyen chain of neo-zeaxanthin A (2) and that of neo-capsorubin A (5) have 13-cis configuration, while those of neo-zeaxanthin B (3) and neo-capsorubin B (6) have 9-cis geometrical configuration. ¹³C NMR data on the corresponding all-trans carotenoids (1 and 4) are also reported.     

Structure of sodium alkyl sulfate micelles

Apparent and partial molar volumes of aggregated sodium octyl-, decyl-, dodecyl-, and tetradecyl sulfate molecules have been determined rigorously in terms of the pseudophase separation model. Mass density inside the micellar core—a basic thermodynamic parameter in the research of micelles by nuclear techniques—has been derived from the partial molar volumes.Micellar aggregation numbers of the same surfactants, obtained from small-angle neutron scattering [SANS] by systematically varying the surfactant concentration and solution temperature are published. A survey is given of the physical models and evaluation algorithms applied in SANS, together with a critical comparison of available experimental data published by various research teams.By utilizing a new least-squares fitting algorithm based on a microscopic diffusion model, the formation and annihilation parameters of ortho-positronium Co-Ps) in the micellar pseudophase and in the aqueous solvent, as well as the o-Ps diffusion coefficient in the solvent are deduced by evaluating conventionally measured positron lifetime spectra. From the pickoff annihilation rate of o-Ps in micelles the surface tension of the micellar core around the solubilization site of o-Ps is calculated. SANS results are utilized to determine the diffusion coefficient of o-Ps in normal and in 99.85% heavy water as a function of temperature. A definite isotopic effect in the two solvents can be seen from the results obtained for the diffusion coefficient and its activation energy. The Arrhenius plot of o-Ps diffusion coefficients indicates that o-Ps diffuses in both media without tunnelling.     

Direct coupling of size exclusion chromatography and mass spectrometry for the characterization of complex monoclonal antibody products

The present study describes the possibilities offered by an innovative bioinert size exclusion chromatography column for size variant characterization of complex monoclonal antibody products. This size exclusion chromatography column includes a novel column hardware surface. The column was prepared from metallic hardware components that were treated to have prototype hydrophilically modified hybrid organic–inorganic silica surfaces called hybrid surface technology. This provides a significant reduction in nondesired hydrophobic and electrostatic interactions that can occur between column and analyte when performing size exclusion chromatography analysis with volatile mobile phase. Compared to a reference stainless-steel column packed with the same batch of packing material, peak tailing, band broadening, and above all recovery of high molecular weight species were distinctly improved for all types of monoclonal antibody products. Based on our observations, we found that 50 mM ammonium acetate in water was a suitable mobile phase offering good compromise in terms of liquid chromatography performance and mass spectrometry sensitivity. In addition, method repeatability (intra- and interday relative standard deviations) on elution times and high molecular weight species peak areas were found to be excellent. By using this innovative size exclusion chromatography material, the low and high molecular weight species contained in various stressed and nonstressed monoclonal antibody products were successfully characterized with mass spectrometry detection.     

Synthesis of an amino-functionalized model of the Fe-only hydrogenase active site

A dinuclear 2Fe2S mimic 6 of the active site of the Fe-only hydrogenases has been synthesized. Complex 6 contains a free amino group which enables linkage to a protein backbone or to a redox active species for the study of electron transfer processes in proteins or in supramolecular systems. The structures of the complex 6 and its Boc-protected precursor 5 could be verified by X-ray crystallography.     

Pattern formation induced by ion-selective surfaces: models and simulations

Simple inorganic reactions in gels, such as NaOH + CuCl(2), NaOH + AgNO(3), and CuCl(2) + K(3)[Fe(CN)(6)], can yield to various precipitation patterns. The first compound penetrates in a hydrogel by diffusion, and reacts with the second compound homogenized in the gel. The precipitate patterns formed in these reactions have got two kinds of bordering surfaces. Recent experimental results suggested that one of these surfaces has an ion-selective (semipermeable) character: It restrains the diffusion of the reacting ion contained by the reactant that diffuses into the gel. In this paper, we built the above experimental observation into a reaction-diffusion cellular-automata model of the pattern formation. Computer simulations showed that the model is able to reproduce the basic building elements of the patterns.