Some examples for the Poincaré and Painlevé problems

In 1891, Poincaré started a series of three papers in which he tried to answer the following question (cf. [21-23]): “Is it possible to decide if an algebraic differential equation in two variables is algebraically integrable?” (in the sense that it has a rational first integral). More or less at the same time P. Painlevé asked the following question: “Is it possible to recognize the genus of the general solution of an algebraic differential equation in two variables which has a rational first integral?”. In this paper we give examples of one-parameter families which show that both problems have a negative answer. With some of the families we can also answer a question posed by M. Brunella in [5].     

Electrochemical impedance spectroscopy and linear polarization applied to evaluation of porosity of phosphate conversion coatings on electrogalvanized steels

In this work, electrochemical impedance spectroscopy and linear polarization are used in determining porosity of zinc phosphates, and of nickel and manganese modified zinc phosphates on electrogalvanized steel. The porosity of the phosphate layers ranges from 0.1% for the manganese-modified hopeite to 8% for hopeite, using the linear polarization and the electrochemical impedance spectroscopy techniques. The porosity values measured using the two techniques were in agreement. All impedance spectra of coated samples showed two steps, with two capacitive arcs and an inductive looping.     

Constructing saturating sets in projective spaces using subgeometries

Designs, Codes and Cryptography - A $$\varrho $$ -saturating set of $$\text {PG}(N,q)$$ is a point set $${\mathcal {S}}$$ such that any point of $$\text {PG}(N,q)$$ lies in a subspace of dimension...     

A new GROMOS force field for hexopyranose-based carbohydrates

A new parameter set (referred to as 45A4) is developed for the explicit-solvent simulation of hexopyranose-based carbohydrates. This set is compatible with the most recent version of the GROMOS force field for proteins, nucleic acids, and lipids, and the SPC water model. The parametrization procedure relies on: (1) reassigning the atomic partial charges based on a fit to the quantum-mechanical electrostatic potential around a trisaccharide; (2) refining the torsional potential parameters associated with the rotations of the hydroxymethyl, hydroxyl, and anomeric alkoxy groups by fitting to corresponding quantum-mechanical profiles for hexopyranosides; (3) adapting the torsional potential parameters determining the ring conformation so as to stabilize the (experimentally predominant) (4)C(1) chair conformation. The other (van der Waals and nontorsional covalent) parameters and the rules for third and excluded neighbors are taken directly from the most recent version of the GROMOS force field (except for one additional exclusion). The new set is general enough to define parameters for any (unbranched) hexopyranose-based mono-, di-, oligo- or polysaccharide. In the present article, this force field is validated for a limited set of monosaccharides (alpha- and beta-D-glucose, alpha- and beta-D-galactose) and disaccharides (trehalose, maltose, and cellobiose) in solution, by comparing the results of simulations to available experimental data. More extensive validation will be the scope of a forthcoming article. (c) 2005 Wiley Periodicals, Inc. J Comput Chem 26: 1400-1412, 2005.     

Thermal and viscosity characterization of two asphalt emulsions

Journal of Thermal Analysis and Calorimetry - Asphalt emulsion is a versatile product that can be used for different waterproofing applications in civil construction and highway constructions....     

Desorption/ionization efficiencies of triacylglycerols and phospholipids via EASI‐MS

Knowledge of the major effects governing desorption/ionization efficiency is required for the development and application of ambient mass spectrometry. Although all triacylglycerols (TAG) have the same favorable protonation and cationization sites, their desorption/ionization efficiencies can vary dramatically during easy ambient sonic‐spray ionization because of structural differences in the carbon chain. To quantify this somewhat surprising and drastic effect, we have performed a systematic investigation of desorption/ionization efficiencies as a function of unsaturation and length for TAG as well as for diacylglycerols, monoacylglycerols and several phospholipids (PL). Affinities for Na⁺ as a function of unsaturation level have also been assayed via comprehensive metadynamics calculations to understand the influence of this phenomenon on the ionization efficiency. The results suggest that dipole–dipole interactions within a carbon chain tuned by unsaturation sites govern ionization efficiency of TAG and PL. Copyright © 2014 John Wiley & Sons, Ltd.