On pleated singular points of first order implicit differential equations

We study phase portraits of a first order implicit differential equation in a neighborhood of its pleated singular point that is a non-degenerate singular point of the lifted field. Although there is no a visible local classification of implicit differential equations at pleated singular points (even in the topological category), we show that there exist only six essentially different phase portraits, which are presented

Influence of the solvent on the equilibrium of 4-carbomethoxy-1, 3-dithiacyclohexanones-5

1. The position of equilibrium of 4-carbomethoxy-1, 3-dithiacyclohexanone-5 (I), 2-methyl-4-carbomethoxy-1,3-dithiacyclohexanone-5 (II), and 2, 2-dimethyl-4-carbomethoxy-1, 3-dithiacyclohexane-5 (III) in acetonitrile, 50% aqueous dioxane, methanol, ethanol (fractional distillate), abs. ethanol, isobutanol, dioxane, and heptane was determined. 2. The ratio of the equilibrium constants of (I) and (II) does not depend on the nature of the solvent. © 1970 Consultants Bureau

A method for determining the position of tautomeric equilibrium solely from infrared and ultraviolet spectral data

A method was described for determining the position of equilibrium in tautomeric systems, using only data from IR and UV spectra. © 1969 Consultants Bureau

Quantum theory of wave mixing on a two-level system

We apply the scattering matrix formalism to wave mixing on a quantum two-level system. We carry out the fermionization of the two-level system degrees of freedom using the Popov-Fedotov semions, calculate n-particle Green's function, and apply the Lehmann-Symanzik-Zimmermannn reduction procedure. Using the developed approach, we provide a consistent quantum explanation of the appearance of coherent side peaks observed in an experiment on the scattering of bichromatic radiation on a two-level artificial atom \cite{dmitriev2019probing}. We show that the spectrum observed in the experiment is the result of bosonic stimulated scattering of photons from one mode of the bichromatic drive to another and vice versa

Small conformationally mobile molecules as probes for molecular mobility in glassy polymers

A new method for studying molecular mobility in glassy polymers-the method of conformationally inhomogeneous probes-is described. A small quantity of a low-molecular-weight compound (probe) having unidentical conformations with different vibrational spectra is introduced into a polymer. The thermodynamic and activation parameters responsible for the concentrations of the conformers and the rates of conformational transitions are connected with both the intramolecular interactions and the properties of the medium (e.g. polymer). Information about the kinetics and equilibria of the conformers could be obtained by investigating the vibrational spectra. This information may be the key to understanding the molecular mobility and free-volume distribution in polymers. The following compounds were used as probes: 1,2-bromofluoroethane, methyl dichlorophosphate and trans-1,2-dichlorocyclohexane. The polymers poly-styrene, poly(vinyl chloride), poly(methyl methacrylate), poly(vinyl acetate), poly(vinylbutyral), poly-propylene and polybutadiene were investigated. The temperature dependences of the absorption-band intensities of the probes were studied. Freezing of the conformational transitions in the probe molecules was found at temperatures Tf characterizing specific polymer-probe systems. The Tf are close to the temperatures of the relaxation transitions in the pure polymers. The possibilities of the method are discussed. © 1994

Poly(methyl methacrylate)/1,2-dichloroethane system: Freezing of conformational mobility in the low-molecular component

The conformational dynamics in 1,2-dichloroethane (DCE)/poly(methyl methacrylate) (PMMA) mixtures has been studied at different concentrations of DCE. The intensities of the infrared absorption bands belonging to the trans and gauche conformers have been measured in the 77-300 K temperature range. Besides, the glass transition temperatures of the mixtures T g were determined by the differential scanning calorimetry. For all the systems under investigation the freezing of the conformational transitions has been found: below a certain temperature T f the trans/gauche ratio becomes temperature independent. The T f value for the lowest volume fraction of DCE (C = 0.01) was found to be close to the temperature of one of the secondary relaxation transitions of pure PMMA (195 K). At this temperature the free volume entities in PMMA should have the volume close to that of the conformationally mobile groups of DCE (∼25 Å 3). The concentration dependence of T f consists of two branches. At low concentrations of the diluent (C < 0.6) T f slowly decreases with the concentration of DCE, reflecting the concentration behaviour of the relaxation transition temperature. At the higher concentrations the freezing of the conformational equilibrium in DCE occurs at the glass transition of the mixtures, and the T f values are close to the T g ones. Copyright © 1996 Elsevier Science Ltd