Some common properties of certain continual and discrete convolutions

We consider discrete analogues of general Calderon–Zygmund operators and study their Fredholm properties in corresponding discrete spaces. We give also a comparison between discrete and continual cases. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multi-channel transformations of 1,3-diarylpropynones under superelectrophilic activation conditions: concurrence of intra- and intermolecular reactions. Experimental and theoretical study

1,3-Diarypropynones undergo concurrent multi-channel transformations in Bronsted (FSO₃H, TfOH) and Bronsted–Lewis (HF–SbF₅, TfOH-SbF₅) superacids, leading intramolecularly to 3-arylindenones, or intermolecularly to 1,3,3-triarylpropenones, and dimeric structures. The outcome depends on the electronic donor-acceptor properties of the substituents in the aromatic rings of the 1,3-diarylpropynones, and on the added aromatic external π-nucleophiles. The orbital energies, atom charges, orbital contributions, and global electrophilicity indices of the cationic intermediates have been calculated by DFT methods to explain these transformations.     

Study of the formation kinetics of Metastable phases in quenched Al-Mg-Si Alloys

The results of the experimental study of the formation kinetics of metastable phases during decomposition of supersaturated solid solutions of quenched Al-Mg-Si alloys are presented. The process has been studied by measuring the electrical conductivity at low temperatures (18–85°C) and by measuring the Young’s modulus using the acoustic method in the temperature range 120–220°C. The method of measuring the Young’s modulus is characterized by a high precision and has made it possible to distinguish between the successive stages of the decomposition due to the formation of Guinier-Preston zones, particles of the pre-β″/β″ and β′-phases. The effective activation energies have been calculated using the obtained data on the characteristic durations of the stages of the process at different temperatures. It has been shown that the activation energy of the formation and evolution of particles in the β″-phase is considerably lower than the activation energy of diffusion of alloying element atoms at equilibrium conditions, which is caused by the effect of long-lived quenching vacancies. This energy is close to the activation energy of migration of the ν + Mg complex and, according to the obtained results, is equal to 0.58 eV.     

The group Sp<Subscript>10</Subscript>(ℤ) is (2,3)-generated

It is proved that the group Sp₁₀(ℤ) is generated by an involution and an element of order 3.     

On reasons for the hysteresis of melting and crystallization of nanoparticles

The specific features of the EPR spectra of Tm³⁺ impurity ions in synthetic forsterite have been studied by continuous-wave EPR spectroscopy in the frequency range of 270–310 GHz at a temperature of 4.2 K in weak magnetic fields. Narrow resonance signals unrelated to the modulation of the resonance conditions of EPR under the modulation of the external magnetic field have been discovered in measurements at frequencies corresponding to the zero field splitting between the ground and first excited singlet electron states of Tm³⁺ ions in zero magnetic field. The origin of these narrow lines is discussed.     

Modeling of an Asymptotically Central Markov Process on 3D Young Graph

The paper discusses the asymptotics of path probabilities in Markov processes close to a central one on 3D Young graph. We consider a one-parameter family of such processes and compute the parameter value in such a way that the centrality condition is satisfied with the greatest possible accuracy. We defined a normalized dimension of paths in the 3D Young graph. We study the growth and oscillations of these normalized dimensions along greedy and random trajectories of the processes using large computer experiments involving 3D Young diagrams with millions of boxes.     

Cinnamonitrile as a precursor of a bi-centered electrophile in reactions with arenes in triflic acid

The reaction of cinnamonitrile [PhCH?=?CHCN] with arenes in the superacid TfOH at room temperature for 1?h gave two types of compounds, 3-aryl-3-phenyl propionitriles [Ar(Ph)CHCH₂CN] and/or 3-phenylindanones in 28–76% yield. The formation of these two reaction products depends on the nucleophilicity of the arene. In these reactions, carbocations generated upon the protonation of cinnamonitrile in TfOH behave as bi-centered electrophiles possessing reactive centers on the C3 carbon of the double bond and on the C1 carbon of the nitrile group.     

Multicomponent reaction of conjugated enynones with malononitrile and sodium alkoxides: Complex reaction mechanism of the formation of pyridine derivatives

Reaction of conjugated enynones,1,5-diarylpent-2-en-4-yn-1-ones, with malononitrile and sodium alkoxides in the corresponding alcohols at room temperature for 3–23 h results in the formation of two types of compounds (E)-/(Z)-6-aryl-4-(2-arylethenyl)-2-alkoxypyridine-3-carbonitriles (substituted nicotinonitriles), as the major reaction products in yields up to ca. 40–80%, and 6-aryl-4-arylethynyl-2-alkoxypyridines, as the minor reaction products in yields of 5–17%. Plausible mechanism of this complex and multistep reaction is discussed. The obtained pyridines possess fluorescent properties.     

Mechanisms of Coalescence of Metallic Nanodroplets and Sintering of Metallic Nanoparticles

Doklady Physics - The regularities and mechanisms of coalescence of Au nanodroplets and sintering of solid Au nanoparticles are investigated using molecular dynamics experiments and some...