On Cullen numbers which are both Riesel and Sierpiński numbers

We describe an algorithm to determine whether or not a given system of congruences is satisfied by Cullen numbers. We use this algorithm to prove that there are infinitely many Cullen numbers which are both Riesel and Sierpiński. (Such numbers should be discarded if you are searching prime numbers with Proth?s theorem.)     

Analysis of the antioxidant activity of an indole library: cyclic voltammetry versus ROS scavenging activity

The electrochemical behavior of an indole library of compounds, including several tryptophan and tryptamine derivatives previously demonstrated to be active against several reactive oxygen species (ROS), was investigated. For this purpose, a voltammetry study was undertaken and the oxidation potential was correlated to the scavenging activity reported for the studied indoles. All the compounds showed an oxidation potential peak lower than that observed for indole (Epox = 1.035 V), but higher than that described for the antioxidant melatonin (Epox = 0.715 V). The electrochemical behavior showed a high correlation with the scavenging activity of peroxyl radical, for selected compounds.     

Unexpected reactivity of trifluoromethylated olefins with indole: a mechanistic investigation

Several trifluoromethylated compounds were reacted with indole sodium salt, leading to monofluorinated compounds. The unexpected products formation was rationalized by DFT calculations.     

Hydrogen‐bonding controls the solid‐state and enantiomeric comformations of the amino alcohol ligand 2‐[(2‐hydroxyethyl)amino]cyclohexanol

The crystal structure of the title compound, C₈H₁₇NO₂, consists of (R,R) and (S,S) enantiomeric pairs packed in adjacent double layers which are characterized by centrosymmetric hydrogen‐bonded dimers, generated via N—H...O and O—H...O interactions, respectively. Intermolecular interactions, related to acceptor and donor molecule chirality, link the achiral double layers into tubular columns, which consist of a staggered hydrophilic inner core surrounded by a hydrophobic cycloalkyl outer surface and extend in the [011] direction.     

Vibrational analysis of d-PCL(530)/siloxane-based hybrid electrolytes doped with two lithium salts

The present study has been focused on environmentally friendly sol–gel-derived electrolytes based on a di-urethane cross-linked d-PCL(530)/siloxane network [where d represents di, PCL identifies the poly(ε-caprolactone) biopolymer, and 530 is the average molecular weight in grams per mole] doped with a wide range of concentration of lithium perchlorate and lithium bis(trifluoromethanesulfonyl)imide. Fourier Transform Infrared and Raman spectroscopies have been applied to evaluate the extent of ionic association. Characteristic bands of the PCL(530) segments, of the urethane cross-links, and of the anions have been examined to gain insight into the cation/biopolymer, cation/anion, and cation/cross-link interactions. In both electrolyte systems, “free” ions and contact ions have been identified. The addition of salt modifies the hydrogen-bonded array of the host matrix, causing the destruction/formation of the urethane/urethane aggregates.     

Hydro­gen bonding in 2-(hydroxy­methyl)-1,3-propane­diol and N,N′-bis­[2-hydroxy-1,1-bis­(hydroxy­methyl)­ethyl]­malon­amide

The mol­ecule of 2-(hydroxy­methyl)-1,3-propane­diol, C₄H₁₀O₃, lies across a mirror plane in space group P2₁/m, with disorder of both terminal hydroxyl H atoms. The molecules are linked by three O—H⋯O hydrogen bonds which combine to form sheets; in each O—H⋯O bond, the H atom resonates between the two O atoms. In the crystal structure of N,N′-­bis­[2-hydroxy-1,1-bis­(hydroxy­methyl)­ethyl]­malon­amide, C₁₁H₂₂N₂O₈, the molecule lies about a twofold axis and has four strong hydrogen bonds which form a mixture of chains and dimers; these combine to give a three-dimensional supramolecular framework.     

Galilean-Covariant Clifford Algebras in the Phase-Space Representation

We apply the Galilean covariant formulation of quantum dynamics to derive the phase-space representation of the Pauli–Schrödinger equation for the density matrix of spin-1/2 particles in the presence of an electromagnetic field. The Liouville operator for the particle with spin follows from using the Wigner–Moyal transformation and a suitable Clifford algebra constructed on the phase space of a (4 + 1)-dimensional space–time with Galilean geometry. Connections with the algebraic formalism of thermofield dynamics are also investigated.