The Distributional Hankel Transform of Marcel Riesz's Ultrahyperbolic Kernel

In this article we give a sense to the distributional Hankel transform of Marcel Riesz's ultrahyperbolic kernel. First we evaluate Rα(u) in α = ?2k and α = 2k for the cases μ even and ν odd, μ even and ν even, and μ odd and ν odd, μ odd and ν even, where and Finally in Section 4 we obtain the distributional Hankel transform of Marcel Riesz's ultrahyperbolic kernel.     

Graph theoretical similarity approach to compare molecular electrostatic potentials

In this work we introduce a graph theoretical method to compare MEPs, which is independent of molecular alignment. It is based on the edit distance of weighted rooted trees, which encode the geometrical and topological information of Negative Molecular Isopotential Surfaces. A meaningful chemical classification of a set of 46 molecules with different functional groups was achieved. Structure--activity relationships for the corticosteroid binding affinity (CBG) of 31 steroids by means of hierarchical clustering resulted in a clear partitioning in high, intermediate, and low activity groups, whereas the results from quantitative structure--activity relationships, obtained from a partial least-squares analysis, showed comparable or better cross-validated correlation coefficients than the ones reported for previous methods based solely in the MEP.     

Insights into the algebraic structure of Lorenz-like systems using feedback circuit analysis and piecewise affine models

The characterization of chaotic attractors has been a widely addressed problem and there are now many different techniques to define their nature in a rather accurate way, at least in the case of a three-dimensional system. Nevertheless, the link between the structure of the ordinary differential equations and the topology of their solutions is still missing and only a few necessary conditions on the algebraic structure are known today. By using a feedback circuit analysis, it is shown that it is possible to identify the relevant terms of the equations, that is, the terms that really contribute to the structure of the phase portrait. Such analysis also provides some guidelines for constructing piecewise affine models. Moreover, equivalence classes can be defined on the basis of the active feedback circuits involved.     

Globalizations of partial actions on nonunital rings

In this note we prove a criteria for the existence of a globalization for a given partial action of a group on an -unital ring. If the globalization exists, it is unique in a natural sense. This extends the globalization theorem from Dokuchaev and Exel, 2005, obtained in the context of rings with

     

Density and refractive index in mixtures of ionic liquids and organic solvents: Correlations and predictions

Correlations between volumetric properties and refractive index of binary mixtures of room temperature ionic liquids (RTILs) and organic solvents were examined. To this end, the density and refractive index for a set of these systems were measured at atmospheric pressure at 298.15 K throughout the composition range. These data were used to calculate excess volumes and refractive index deviations by using expressions firmly based on the physical significance of each quantity, fact that allowed the expected relations between the two quantities to be confirmed. Based on these results, the molar refraction and free or void volume of the mixtures are calculated with a view to estimating the relative contribution of both quantities to the excess molar volume. Once molar refraction was confirmed to exhibit a near-ideal behaviour in all mixtures, a method for predicting the density and refractive index of RTIL + organic solvent mixtures was developed; the results show that this procedure can be a highly useful alternative to the usually complex experimental methods available for the thermophysical characterization of these systems.     

Stable numerical solution of the Cauchy problem for the Laplace equation in irregular annular regions

This article is mainly concerned with the numerical study of the Cauchy problem for the Laplace equation in a bounded annular region. To solve this ill‐posed problem, we follow a variational approach based on its reformulation as a boundary control problem, for which the cost function incorporates a penalized term with the input data. The cost function is minimized by a conjugate gradient method in combination with a finite element discretization. In the case where the input data is noisy, some preliminary error estimates, show that the penalization parameter may be chosen like the inverse of the level of noise. Numerical solutions in simple and complex domains show that this methodology produces stable and accurate solutions.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1799–1822, 2017     

Structure and Conformation of Photosynthetic Pigments and Related Compounds. 12. A Crystallographic Analysis of Porphyrin-quinones and Their Precursors

Abstract. A comprehensive crystallographic analysis of 10 porphyrin quinone precursors (dimethoxybenzene derivatives), and six porphyrin quinones has been performed. The free bases and zinc(II) complexes of the porphyrin quinones are of the 5,10,15-triaryl/alkyl-20-quinone-porphyrin type and carry various bridging and quinone units. The structural and conformational parameters were determined for all compounds; the donor-acceptor separation distances range from 6.3 to 10.9 Å. Knowledge of these data is a prerequisite for a detailed interpretation of theoretical and spectroscopic studies on such systems. Despite the obvious influence of the type and geometry of the bridging unit and quinone on the spatial arrangement of the donor and acceptor components, a large variety of different packing arrangements in the crystal were observed. These include π stacking, aggregate formation and axial ligation in the zinc(II) porphyrins. The latter often utilized the quinone (or dimethoxy) oxygen atoms for coordination to zinc(II) centers leading to porphyrin quinone dimers and even polymers.     

Modification of the Nutritional Quality and Oxidative Stability of Lupin (Lupinus mutabilis Sweet) and Sacha Inchi (Plukenetia volubilis L.) Oil Blends

Andean lupin (Lupinus mutabilis) oil is rich in monounsaturated (54.2%) and polyunsaturated (28.5%) fatty acids but has a ω-3:ω-6 ratio (1:9.2) above the recommended values for human health. Sacha inchi (Plukenetia volubilis) oil presents a high polyunsaturated fatty acid content (linolenic 47.2% and linoleic 34.7%), along a ω-3:ω-6 ratio (1:0.74) good for human consumption. The objective of this research was to study the physico-chemical properties and oxidative stability of tarwi and sacha inchi oil blends (1:4, 1:3, 1:1, 3:1 and 4:1 w:w) with suitable ω-3:ω-6 ratios. All blends showed ω-3:ω-6 ratios between 1:0.8 and 1:1.9, acceptable from a nutritional point of view, and high total tocopherols’ content (1834–688 mg/kg), thanks to sacha inchi. The oxidative stability index (OSI) of the mixtures by the Rancimat method at 120 °C ranged from 0.46 to 8.80 h. The shelf-life of 1:1 tarwi/sacha inchi oil blend was 1.26 years; its entropy (−17.43 J/mol), enthalpy (107.04 kJ/mol), activation energy (110.24 kJ/mol) and Gibbs energy (113.76 kJ/mol) suggest low oxidation reaction rates and good stability. Hence, balanced blends of tarwi/sacha inchi oils can achieve optimal nutritional properties and enhanced shelf-life.