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.     

Subregular Representations of {\mathfrak{s}}{\mathfrak{l}}_n and Simple Singularities of Type A n−1

Alexander Premet has stated the following problem: what is a relation between subregular nilpotent representations of a classical semisimple restricted Lie algebra and non-commutative deformations of the corresponding singularities? We solve this problem for type A.     

Polyfunctional compounds containing the 4,6-dialkoxy-7-arylthioheptene moiety as synthetically useful intermediates. The course of lewis acid-induced transformations

Data on the selectivity of the Lewis acids induced transformations of the title compounds are presented, and the routes leading to formation of products containing either cyclohexane or 1,3-diene units are described.     

Synthesis of functionalized m-bistrifluoromethylbenzenes via cyclocondensation of 1,1,1,5,5,5-hexafluoroacetylacetone with enamines

The reaction of 1,1,1,5,5,5-hexafluoroacetylacetone with push-pull enamines having a methyl group at the α-position was investigated. It was found that the reaction is sensitive both to the structure of enamines and to reaction conditions. As a result, a set of bistrifluoromethyldialkylanilines and ethyl bistrifluoromethylsalicylate was prepared. Plausible mechanisms and factors influencing the course of the reaction are discussed.     

Highly selective mono-substitution in Pd-catalyzed cross-coupling reactions of 3,6-dichloropyridazine with organozinc compounds

Pd-catalyzed cross-coupling reactions of 3,6-dichloropyridazine (1) with benzyl, aryl, and alkyl organozinc compounds led to selective mono-substitution of one of the chlorine atoms. The subsequent cross-coupling of the resulting monochlorides with RZnCl afforded unsymmetrical 3,6-carbon-disubstituted pyridazines.     

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.     

The electronic structure of FeV-cofactor in vanadium-dependent nitrogenase

The electronic structure of the active-site metal cofactor (FeV-cofactor) of resting-state V-dependent nitrogenase has been an open question, with earlier studies indicating that it exhibits a broad S = 3/2 EPR signal (Kramers state) having g values of ∼4.3 and 3.8, along with suggestions that it contains metal-ions with valencies [1V³⁺, 3Fe³⁺, 4Fe²⁺]. In the present work, genetic, biochemical, and spectroscopic approaches were combined to reveal that the EPR signals previously assigned to FeV-cofactor do not correlate with active VFe-protein, and thus cannot arise from the resting-state of catalytically relevant FeV-cofactor. It, instead, appears resting-state FeV-cofactor is either diamagnetic, S = 0, or non-Kramers, integer-spin (S = 1, 2 etc.). When VFe-protein is freeze-trapped during high-flux turnover with its natural electron-donating partner Fe protein, conditions which populate reduced states of the FeV-cofactor, a new rhombic S = 1/2 EPR signal from such a reduced state is observed, with g = [2.18, 2.12, 2.09] and showing well-defined ⁵¹V (I = 7/2) hyperfine splitting, a_iso = 110 MHz. These findings indicate a different assignment for the electronic structure of the resting state of FeV-cofactor: S = 0 (or integer-spin non-Kramers state) with metal-ion valencies, [1V³⁺, 4Fe³⁺, 3Fe²⁺]. Our findings suggest that the V³⁺ does not change valency throughout the catalytic cycle.

Active site FeV-cofactor of the V-nitrogenase and the EPR spectrum of the reduced cofactor showing ⁵¹V-hyperfine coupling.