Joint extension of two theorems of Kotzig on 3-polytopes

The weight of an edge in a graph is the sum of the degrees of its end-vertices. It is proved that in each 3-polytope there exists either an edge of weight at most 13 for which both incident faces are triangles, or an edge of weight at most 10 which is incident with a triangle, or else an edge of weight at most 8. All the bounds 13, 10, and 8 are sharp and attained independently of each other.     

Growth and study of single crystals of (Na,K)NbO<Subscript>3</Subscript> solid solutions

(Na, K)NbO₃ crystals with a perovskite structure and a KNbO₃ content up to 40 mol % were grown from flux with the use of the solvent NaBO₂. The dielectric measurements of the crystals grown revealed phase transitions that had never been observed before in ceramic samples.     

Control of the temperature hysteresis and diffuse dielectric anomaly in the temperature range of the ferroelectric-antiferroelectric phase transition in PbZr1 − x TixO3 (0.03 ≤ x ≤ 0.05) ceramics

The magnitudes of the temperature hysteresis and diffuse dielectric anomaly corresponding to the transition from the antiferroelectric phase to the ferroelectric phase in PbZr_{1 ? x} Ti_xO₃ (0.03 ≤ x ≤ 0.05) ceramics can be reversibly changed by varying the temperatures of heating and cooling in the course of thermocycling. The results obtained indicate that the antiferroelectric-ferroelectric transition in the PbZr_{1 ? x} Ti_xO₃ ceramics materials is a smeared first-order phase transition.     

Distribution of integral functionals of a Brownian motion process

In this paper one considers methods which enable one to determine the distribution of certain functionals of a Brownian motion process. Among such functionals we have: the positive continuous additive functional of a Brownian motion, defined by the formula $$A\left( t \right) = \int\limits_{ - \infty }^\infty {\hat t\left( {t, y} \right)dF\left( y \right),} $$ where \(\hat t\left( {t, y} \right)\) is the Brownian local time process while F(y) is a monotonically increasing right continuous function; the functional $$B\left( t \right) = \mathop {\mathop \smallint \limits_{ - \infty } }\nolimits^\infty f\left( {y,\hat t\left( {t, y} \right)} \right)dy,$$ where f(y, x) is a continuous function; and the functional $$C\left( t \right) = \mathop {\mathop \smallint \limits_0 }\nolimits^t f\left( {w\left( s \right),\hat t\left( {sr} \right)} \right)ds$$ As an application of these methods one considers some concrete functionals such that \(\hat t^{ - 1} \left( z \right) = \min \left\{ {s:\hat t\left( {s, o} \right) = z} \right\},\mathop {\mathop \smallint \limits_{ - \infty } }\nolimits^\infty \hat t^2 \left( {t, y} \right)dy,\mathop {\sup }\limits_{y \in R^1 } \hat t\left( {T, y} \right)\) , where T is an exponential random time, independent of \(\hat t\left( {t, y} \right)\) .     

A revised quantum chemistry-based potential for poly(ethylene oxide) and its oligomers in aqueous solution

We have conducted a high-level quantum chemistry study of the interactions of 1,2-dimethoxyethane (DME) with water for complexes representing both hydrophilic and hydrophobic hydration. It was found that our previous quantum chemistry-based force field for poly(ethylene oxide) (PEO) and its oligomers in aqueous solution did a poor job in describing the hydrophobic binding of water to the ether, consistent with our recent calculations of the excess free energy and entropy of hydration of DME. Our original force field was revised to more accurately reproduce the interaction of water with the carboneous portions of DME. Molecular dynamics simulations of aqueous DME solutions using the revised quantum chemistry-based potential yielded good agreement with experiment for excess free energy, enthalpy, and volume as well as excess solution viscosity and the self-diffusion of water. Comparison with our original potential revealed that the relatively hydrophobic ether-water interactions in the new potential strongly reduced the favorable excess free energy and enthalpy but have relatively little influence on the excess entropy for dilute DME solutions. Other properties of DME and PEO solutions including conformational populations and dynamics, solution viscosity, hydrogen bonding, water translational and rotational diffusion and neutron structure factor as a function of solution composition were found to be largely unchanged from those obtained using the original potential.     

A comparative investigation of the fatty acid compositions of the seeds of a number of lines of a genetic collection of Gossypium hirsutum

A comparative analysis has been made of the amounts of lipids and their fatty-acid compositions in the seeds of the lines of agenetic collection of cotton plants of the speciesGossypium hirsutum and their hybrids and the variety Tashkent-1. The results obtained on the fatty-acid compositions of some hybrids make it possible to recommend the use of individual lines of cotton plants as donors for improving the food-value indices of cottonseed oil.Institute of Chemsitry of Plant Substances, Academy of Sciences of the Uzbek SSR, Tashkent. V. I. Lenin Tashkent State University. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 173–176, March–April, 1991.     

Activity of γ-Al2O3 modified by NaOH in disproportionation of methanethiol

Na⁺/Al₂O₃ catalysts in disproportionation of methanethiol are highly selective towards dimethyl sulfide but less active compared to -Al₂O₃. Their activity falls with increasing Na⁺ in the sample. This decrease is due to the neutralization of Brönsted acid centers on the catalyst.

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Na⁺/Al₂O₃ , , -Al₂O₃. Na⁺ . .

     

Decomposition of alkanethiols to dialkyl sulfides and hydrogen sulfide

Disproportionation of thiol to sulfide and H₂S takes place on catalysts of various composition, the most active being those with paired acid-base centers. On these catalysts at 200–400°C methanethiol is quantitatively converted to dimethyl sulfide. Disproportionation of ethanethiol and particularly of 2-propanethiol is accompanied by the decomposition of sulfides formed and initial thiols to produce olefins and H₂S.

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H₂S , - . 200–400°C . 2- H₂S.