Action of a Graph Automorphism on the Space of Flows

Mathematical Notes -     

Synthesis of ethyl 5-aryl-5-(trifluoromethyl)-4,5-dihydroisoxazole-3-carboxylates,exhibiting plant growth-regulating properties

Russian Chemical Bulletin - A convenient method for the synthesis of high-boiling-point α-(trifluoromethyl)styrenes was proposed. The regioselective synthesis of a series of ethyl...     

Synthesis and study of yttrium aluminum garnets doped with neodymium and ytterbium

Ytterbium- and neodymium-substituted yttrium aluminum garnets were obtained by hydroxide coprecipitation and by the cryochemical method. A continuous series of solid solutions in the Y₃Al₅O₁₂ — Yb₃Al₅O₁₂ system and limited solid solutions (Nd _x Y_{1 ? x} )₃Al₅O₁₂ (0 ≤ x ≤ 0.19) were obtained. The synthetic methods used made it possible to reduce the synthesis temperature from 1800 to 950°C and to obtain more homogeneous and nanosized material.     

Superconformal Indices of $${{\mathcal N}=4}$$ SYM Field Theories

Superconformal indices (SCIs) of 4d N = 4{{\mathcal N} = 4} SYM theories with simple gauge groups are described in terms of elliptic hypergeometric integrals. For F ₄, E ₆, E ₇, E ₈ gauge groups this yields first examples of integrals of such type. S-duality transformation for G ₂ and F ₄ SCIs is equivalent to a change of integration variables. Equality of SCIs for SP(2N) and SO(2N + 1) group theories is proved in several important special cases. Reduction of SCIs to partition functions of 3d N=2{{\mathcal N}=2} SYM theories with one matter field in the adjoint representation is investigated, corresponding 3d dual partners are found, and some new related hyperbolic beta integrals are conjectured.     

Copper complexes: cytotoxicity and transport possibilities

Russian Chemical Bulletin - A copper complex with N-(5,6-dihydro-4H-1,3-thiazin-2-yl)benzamide was synthesized for the first time and characterized by 1H NMR spectroscopy, LETDY mass spectrometry,...     

Aftereffect relaxation processes in lead zirconate titanate

Relaxation processes in lead zirconate titanate after switching-off perturbations of different physical nature have been considered. The model of the process, which accounts for the partial depolarization during perturbations, the formation of charged F-centers during released charge trapping, and their relaxation, has been proposed.     

Technology of liquid-phase compounding of ultra-high-molecular-weight polyethylene with nanoparticles of inorganic compounds under the action of ultrasonic vibrations

A novel technology for preparing nanocomposites on the basis of ultra-high-molecular-mass polyethylene and nanoparticles of inorganic compounds (SiO₂, Al₂O₃, ZrO₂, AlN, Si₃N₄) was developed and tested. The technology consists in liquid-phase compounding of nanocomposite components under the continuous action of ultrasonic vibrations. The developed technology ensures dispersion of nanopaticle agglomerates in a liquid medium, efficient mixing of components of the powder blend, and uniform distribution of nanoparticles in the polymer matrix. The nanocomposites obtained exhibit increased levels of strength and elasticity.     

Synthesis of ethyl α-nitro-β-trifluoromethyl acrylate and β-trifluoromethyl-substituted tryptophan analogs and their plant growth regulating activity

Russian Chemical Bulletin - Ethyl α-nitro-β-trifluoromethyl acrylate was synthesized by nucleophile-catalyzed reaction of ethyl nitroacetate with excess trifluoroacetaldehyde methyl...     

Interaction of components in the NaOH-TiO<Subscript>2</Subscript> · H<Subscript>2</Subscript>O-H<Subscript>2</Subscript>O system at 25°C

Solubilities in the NaOH-TiO₂ · H₂O-H₂O system at 25°C were studied. The solubility isotherm was found to have two maxima. The formation of two compounds, Na₂Ti₅O₁₁ · 10H₂O and Na₂Ti₃O₇ · 7H₂O, was established.     

Elliptic Hypergeometry of Supersymmetric Dualities

We give a full list of known ${\mathcal{N}=1}$ supersymmetric quantum field theories related by the Seiberg electric-magnetic duality conjectures for SU(N), SP(2N) and G ₂ gauge groups. Many of the presented dualities are new, not considered earlier in the literature. For all these theories we construct superconformal indices and express them in terms of elliptic hypergeometric integrals. This gives a systematic extension of the related R?melsberger and Dolan-Osborn results. Equality of indices in dual theories leads to various identities for elliptic hypergeometric integrals. About half of them were proven earlier, and another half represents new challenging conjectures. In particular, we conjecture a dozen new elliptic beta integrals on root systems extending the univariate elliptic beta integral discovered by the first author.