A note on the Lebesgue–Ljunggren–Nagell equation $$ax^2+b^{2m}=4y^n$$ a x 2 + b 2 m = 4 y n

Periodica Mathematica Hungarica - Let a, b be fixed positive integers such that $$2\not \mid {ab}$$ , $$\gcd (a,b)=1$$ and a is square-free, and let $$h(-a)$$ denote the class number of...     

Investigation of carotenoid composition of paprika paste

Summary The carotenoid compositions of four different, industrially-produced paprika pastes (Piros Arany delicacy; Piros Arany hot; Vega delicacy; Vega hot) were investigated by HPLC, and compared with the composition of fresh red, tomato-shaped paprika (Capsicum annuum var.lycopersice forme rubrum). In addition, two kinds of ground raw paprika (Er?s Pista; édes Anna) were also investigated. In total, 23 carotenoids have been identified or tentatively identified, based on their UV-Vis spectra and co-chromatography with authentic samples. Presented at Balaton Symposium '01 on High-Performance Separation Methods, Siófok, Hungary, September 2–4, 2001.     

New Versions of Some Classical Stochastic Inequalities

Motivated by an investigation of finding necessary and sufficient conditions for the Kolmogorov strong law of large numbers for the general Gini's mean difference, new versions of the classical Lévy, Ottaviani, and Hoffmann-J\ooTrgensen inequalities are obtained for a sequence of Banach space valued random variables. No geometric conditions are imposed on the Banach space. An application to the general Gini's mean difference in a Banach space setting is presented.     

Chiral Separation of Ketoprofen on a Chirobiotic T Column and Its Chiral Recognition Mechanisms

Purpose

In this study, direct separation of ketoprofen enantiomers was performed on a Chirobiotic T column.

Methods

The effects of the type and amount of the organic modifier, buffer concentration, pH value, temperature and flow rate on retention and selectivity were investigated. Experiments were carried out in the temperature range of 20–40 °C to study the effects of temperature. Thermodynamic parameters were calculated from plots of ln k or ln α versus 1/T. Molecular dynamics simulation was done to investigate interactions between ketoprofen enantiomers and the chiral selector—teicoplanin.

Results

It was observed that pH and flow rate had a large influence on resolution. Baseline separation of ketoprofen enantiomers could be achieved with low amounts of methanol, high temperature and high buffer concentrations.

Conclusions

Results from a thermodynamic study and molecular dynamics simulation show that steric hindrance effect, π–π complexation, hydrogen bonding and electrostatic forces are the main driving forces which cause chiral recognition of ketoprofen enantiomers.

     

Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media

Asymptotic error expansions in the sense of L ^∞-norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing technique, and the key point in deriving them is the establishment of the error estimates for the mixed regularized Green’s functions with memory terms presented in R. Ewing at al., Int. J. Numer. Anal. Model 2 (2005), 301–328. As a result of all these higher order numerical approximations, they can be used to generate a posteriori error estimators for this mixed finite element approximation. This project was supported in part by the Special Funds for Major State Basic Research Project (2007CB8149), the National Natural Science Foundation of China (10471103 and 10771158), the Social Science Foundation of the Ministry of Education of China (Numerical methods for convertible bonds, 06JA630047), the NSERC, Tianjin Natural Science Foundation (07JCYBJC14300), and Tianjin University of Finance and Economics.     

Potential of Applying the Geometry-Based Rover Slip Prediction Model Learned on the Earth to the Moon

Russian Physics Journal - Wheeled ground robots are widely used in planetary exploration missions, where slip can measure problems during driving and pre-acquisition slips play an important role....     

Experiments on the synthesis of carotenoid glycosides

Isozeaxanthin was treated with trifluoroacetic acid and tetra-O-benzoyl-1-thio-β-d-glucose to afford β,β-carotene-4,4′-bisthioglucoside isomers in good yields. The deprotected compounds are mimetics of naturally occurring thermoxanthins and can show favourable effects against oxidation stress.     

On the Kolmogorov–Feller law for exchangeable random variables

We prove a Kolmogorov–Feller weak law of large numbers for exchangeable sequences, under a second order hypothesis on the truncated mixands.     

Separation and Identification of Carotenoids in Flowers of Chelidonium majus L. and Inflorescences of Solidago canadensis L.

The current research project aimed at the carotenoid analysis of total extracts of the inflorescences of Canadian goldenrod (Solidago canadensis L.), and the flowers of greater celandine (Chelidonium majus L.). The plant extracts were separated and analyzed by column liquid chromatography (CLC) and LC. Carotenoids were identified on the basis of their UV–Vis spectroscopic properties in different solvents, chemical reactions [5,6-epoxide → 5,8-epoxide (furanoid oxide rearrangement), (E/Z)-isomerization] and by co-chromatography with authentic reference samples. The parallel use of CLC and LC allowed the identification of numerous minor carotenoids in all extracts and fractions.     

Pt-decorated PdCo@Pd/C core-shell nanoparticles with enhanced stability and electrocatalytic activity for the oxygen reduction reaction

A simple method for the preparation of PdCo@Pd core-shell nanoparticles supported on carbon based on an adsorbate-induced surface segregation effect has been developed. The stability of these PdCo@Pd nanoparticles and their electrocatalytic activity for the oxygen reduction reaction (ORR) were enhanced by decoration with a small amount of Pt deposited via a spontaneous displacement reaction. The facile method described herein is suitable for large-scale, lower-cost production and significantly lowers the Pt loading and thus the cost. The as-prepared PdCo@Pd and Pd-decorated PdCo@Pd nanocatalysts have a higher methanol tolerance than Pt/C in the ORR and are promising cathode catalysts for fuel cell applications.