Cohomology relative to a system of closed forms on the torus

To a system of closed one‐forms on the torus, we associate a differential complex and compute the induced cohomology groups provided that a related matrix satisfies a Diophantine condition.     

On finite groups with automorphisms whose fixed points are Engel

The main result of the paper is the following theorem. Let q be a prime, n a positive integer, and A an elementary abelian group of order q². Suppose that A acts coprimely on a finite group G and assume that for each \({a \in A^{\#}}\) every element of C_G(a) is n-Engel in G. Then the group G is k-Engel for some \({\{n,q\}}\)-bounded number k.     

The real symmetric matrices of odd order with a P-set of maximum size

Suppose that A is a real symmetric matrix of order n. Denote by m_A(0) the nullity of A. For a nonempty subset α of {1, 2,..., n}, let A(α) be the principal submatrix of A obtained from A by deleting the rows and columns indexed by α. When m_A(α)(0) = m_A(0)+|α|, we call α a P-set of A. It is known that every P-set of A contains at most ?n/2? elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As a first step to the full characterization of these graphs of odd order, we establish some conditions for such graphs G under which there is a real symmetric matrix A whose graph is G and contains a P-set of size (n ? 1)/2.     

Nonsymmetric and symmetric fractional calculi on arbitrary nonempty closed sets

We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentiation and integration of non‐integer order on discrete, continuous, and hybrid settings. Main properties of the new fractional operators are investigated and some fundamental results presented, illustrating the interplay between discrete and continuous behaviors. Copyright © 2015 John Wiley & Sons, Ltd.     

An unprecedented Pd-catalyzed, water-promoted sequential oxidative aminocarbonylation-cyclocarbonylation process leading to 2-oxazolidinones

An unprecedented, PdI2-catalyzed, sequential oxidative aminocarbonylation-cyclocarbonylation process, leading to 2-oxazolidinone derivatives 3 in good to excellent yields starting from readily available alpha,alpha-disubstituted 2-ynylamines 1 and secondary amines 2, is reported. In the case of an alpha-monosubstituted substrate, the initially formed 2-oxazolidinone derivative underwent shift of the double bond to give a 3H-oxazol-2-one derivative in excellent isolated yield.     

Sesquiterpene lactones-based classification of the family asteraceae using neural networks and k-nearest neighbors

In a recent publication we described the application of an unsupervised learning method using self-organizing maps to the separation of three tribes and seven subtribes of the plant family Asteraceae based on a set of sesquiterpene lactones (STLs) isolated from individual species. In the present work, two different structure representations--atom counts (2D) and radial distribution function (RDF) (3D)--and two supervised classification methods--counterpropagation neural networks and k-nearest neighbors (k-NN)--were used to predict the tribe in which a given STL occurs. The data set was extended from 144 to 921 STLs, and the Asteraceae tribes were augmented from three to seven. The k-NN classifier with k = 1 showed the best performance, while the RDF code outperformed the atom counts. The quality of the obtained model was assessed with two test sets, which exemplified two possible applications: (1) finding a plant source for a desired compound and (2) based on a plant species chemical profile (STLs): (a) study the relationship between the current taxonomic classification and plant's chemistry and (b) assign a species to a tribe by majority vote. In addition, the problem of defining the applicability domain of the models was assessed by means of two different approaches-principal component analysis combined with Hotelling T2 statistic and an a posteriori probability-based rule.     

Comparative computational and experimental study on the thermochemistry of the chloropyrimidines

The standard (p0 = 0.1 MPa) molar enthalpies of formation, Delta fH(0)(M), for liquid 2,4,6-trichloropyrimidine and for crystalline 2-chloropyrimidine, 2,4- and 4,6-dichloropyrimidine, and 2,4,5,6-tetrachloropyrimidine compounds were determined at T = 298.15 K by rotating-bomb combustion calorimetry. The standard molar enthalpies of vaporization or sublimation, Delta (g)(cr,l) H(0)(M), of these compounds at T = 298.15 K were determined by Calvet microcalorimetry. The experimental standard molar enthalpies of formation of those compounds, in the gaseous state, at T = 298.15 K, were thus obtained by combining these two sets of results. The latter values have been employed in the calibration of the computational procedure, which has been used to estimate the gas-phase enthalpies of formation for the other chloropyrimidines that were not possible to obtain in a pure form for the experimental study. It is found that the exchange-correlation functional based on the local spin density approximation (LSDA) seems to be a cheap choice for the estimation of enthalpies of formation for heterocycles containing nitrogen atoms; the well-known B3LYP hybrid method yields larger differences, with respect to the experimental values, for 2,4,6-tri- and 2,4,5,6-tetrachloropyrimidines.     

Understanding solvation in hydrofluoroalkanes: ab initio calculations and chemical force microscopy

Understanding solvation in hydrofluoroalkane (HFA) propellants is of great importance for the development of novel pressurized metered-dose inhaler (pMDI) formulations. HFA-based pMDIs are not only the most widely used inhalation therapy devices for treating lung diseases, but they also hold promise as vehicles for the systemic delivery of biomolecules to and through the lungs. In this work we propose a combined microscopic experimental and computational approach to quantitatively relate the chemistry of moieties to their HFA-philicity. Binding energy calculations are used to determine the degree of interaction between a propellant HFA and candidate fragments. We define a new quantity, the enhancement factor E, which also takes into account fragment-fragment interactions. This quantity is expected to correlate well with the solubility and the ability of the moieties of interest to impart stability to colloidal dispersions in HFAs. We use a methyl-based (CH) segment and its fluorinated analog (CF) to test our approach. CH is an important baseline case since it represents the tails of surfactants in FDA-approved pMDIs. CF was chosen due to the improved solubility and ability of this chemistry to stabilize aqueous dispersions in HFAs. Adhesion force from Chemical Force Microscopy (CFM) is used as an experimental analog to the binding energy calculations. The force of interaction between a chemically modified AFM tip and substrate is measured in a model HFA, which is a liquid at ambient conditions. Silanes with the same chemistry as the fragments used in the ab initio calculations allow for direct comparison between the two techniques. The CFM results provide an absolute scale for HFA-philicity. Single molecule (pair) forces calculated from the CFM experiments are shown to be in very good agreement to the E determined from the ab initio calculations. The ab initio calculations and CFM are corroborated by previous experimental studies where propellants HFAs are seen to better solvate the CF functionality.     

Glass transition line in C60: a mode-coupling/molecular-dynamics study

We report a study of the mode-coupling theory (MCT) glass transition line for the Girifalco model of C60 fullerene. The equilibrium static structure factor of the model, the only required input for the MCT calculations, is provided by molecular dynamics simulations. The glass transition line develops inside the metastable liquid-solid coexistence region and extends down in temperature, terminating on the liquid side of the metastable portion of the liquid-vapor binodal. The vitrification locus does not show re-entrant behavior. A comparison with previous computer simulation estimates of the location of the glass line suggests that the theory accurately reproduces the shape of the arrest line in the density-temperature plane. The theoretical HNC and MHNC structure factors (and consequently the corresponding MCT glass line) compare well with the numerical counterpart. Our results confirm the conclusion drawn in previous works about the existence of a glassy phase for the fullerene model at issue.