Asymptotic formulas for nonoscillatory solutions of conditionally oscillatory half-linear equations

We establish asymptotic formulas for nonoscillatory solutions of a special conditionally oscillatory half-linear second order differential equation, which is seen as a perturbation of a general nonoscillatory half-linear differential equation

Distortion Varieties

The distortion varieties of a given projective variety are parametrized by duplicating coordinates and multiplying them with monomials. We study their degrees and defining equations. Exact formulas are obtained for the case of one-parameter distortions. These are based on Chow polytopes and Gröbner bases. Multi-parameter distortions are studied using tropical geometry. The motivation for distortion varieties comes from multi-view geometry in computer vision. Our theory furnishes a new framework for formulating and solving minimal problems for camera models with image distortion.     

Testing of the influenza virus purification by CIEF

In virological practice, the pre‐concentration, purification and subsequent determination of the purity and concentration of the viruses from the cultural medium and/or from the real sample are required. The conventional techniques used today are equipment demanding, time‐consuming and laborious. In this study, the CIEF of influenza viruses with UV detection has been developed and subsequently used to test the purification of the virus from the biological samples. The equine and swine influenza viruses present in infected allantoic fluid of specific pathogen free embryonated chicken eggs were precipitated by using PEG 6000 and sodium chloride. The precipitated viruses were centrifuged at 14 000×g, and the impurities of different densities were removed by using the sucrose gradients. The efficiency of the virus purification technique was examined by the CIEF and compared to the results of real‐time PCR. The pIs of both influenza viruses were determined. Simultaneously, the CIEF was found to be a suitable method for the rapid testing of the efficiency of the virus purification.     

The thermodynamic dissociation constants of methotrexate by the nonlinear regression and factor analysis of multiwavelength spectrophotometric pH-titration data

The mixed dissociation constants of methotrexate — chemically (2S)-2-[(4-{[(2,4-diamino-7,8-dihydropteridin-6-yl)methyl] (methyl)amino}phenyl)formamido]pentanedioic acid (the cas number 59-05-2) at various ionic strengths I of range 0.01–0.4, and at temperatures of 25°C and 37°C, were determined with the use of two different multiwavelength and multivariate treatments of spectral data, SPECFIT32 and SQUAD(84) nonlinear regression analyses and INDICES factor analysis according to a general rule of first, determining the number of components, and then calculating the spectral responses and concentrations of the components. Concurrently, the experimental determination of the thermodynamic dissociation constants was in agreement with its computational prediction of the PALLAS programme based on knowledge of the chemical structures of the drug. The factor analysis in the INDICES programme predicts the correct number of light-absorbing components when the data quality is high and the instrumental error is known. Three thermodynamic dissociation constants were estimated by nonlinear regression of {pK _a , I} data: for methotrexate pK_a1^T= 2.895(13), pK_a2^T= 4.410(14), pK_a3^T= 5.726(15) at 25°C and pK_a1^T= 3.089(15), pK_a2^T= 4.392(12), pK_a3^T= 5.585(11) at 37°C, where the figure in brackets is the standard deviation in last significant digits. The reliability of the dissociation constants of the drug were proven by conducting goodness-of-fit tests of the multiwavelength spectrophotometric pH-titration data.      

A generalization of Lyapunov's convexity theorem with applications in optimal stopping

Lyapunov proved that the range of finite measures defined on the same -algebra is compact, and if each measure also is atomless, then the range is convex. Although both conclusions may fail for measures on different -algebras of the same set, they do hold if the -algebras are nested, which is exactly the setting of classical optimal stopping theory.

     

Stereoselectivity of 1,3-dipolar cycloadditions of l-valine-derived nitrones with methyl acrylate

Chiral nitrones derived from l-valine react with methyl acrylate to afford the corresponding diastereomeric 3,5-disubstituted isoxazolidines. The dibenzylsubstituted nitrone gave also 3,4-disubstituted isoxazolidine in 4% yield, additionally. The stereoselectivity was dependent on the steric hindrance of the nitrone and reaction conditions. High pressure decreased the reaction time of the cycloadditions. The major products were found to have the C-3/C-6 erythro and C-3/C-5 trans relative configuration. The major cycloadduct undergoes N-O cleavage and deprotection to a chiral diaminodiol derivative.     

Reduced–size polarized basis sets for calculations of molecular electric properties. III. Second–row atoms

Reduced–size polarized (ZmPolX) basis sets are developed for the second–row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced–size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.     

Distinguishing standard SBL‐algebras with involutive negations by propositional formulas

Propositional fuzzy logics given by a combination of a continuous SBL t‐norm with finitely many idempotents and of an involutive negation are investigated. A characterization of continuous t‐norms which, in combination with different involutive negations, yield either isomorphic algebras or algebras with distinct and incomparable sets of propositional tautologies is presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microflow Vessel Improving Reproducibility and Sensitivity of Electrochemical Measurements

A new microflow system was designed and developed for electrochemical measurements. The electrochemical electrodes prepared using thick film technology were used in this arrangement. Results of various measurements such as simple amperometric measurement on the example of H₂O₂ detection, measurement with glucose oxidase (GOx) biosensor, soluble enzyme activity measurement etc. carried out using this system are reported. It was observed that the sensitivity and reproducibility of the electrochemical measurements is improved significantly. The new device performance was proved on H₂O₂ detection, activity of GOx measurement and heavy metals detection (measured concentration range: H₂O₂ 10^?9 to 10^?1 M, glucose 10^?6 to 10^?2 M, activity of GOx 10^?1 to 10² IU, heavy metals (Cu, Pb) 10^?4 to 10^?3 M). The microflow insert greatly reduces the overall size of the electrolyte vessel and measurements with sample quantity as low as 2 mL can be accomplished.