Generalizations of Tucker-Fan-Shashkin lemmas

Tucker and Ky Fan's lemma are combinatorial analogs of the Borsuk-Ulam theorem (BUT). In 1996, Yu. A. Shashkin proved a version of Fan's lemma, which is a combinatorial analog of the odd mapping theorem (OMT). We consider generalizations of these lemmas for BUT-manifolds, i.e. for manifolds that satisfy BUT. Proofs rely on a generalization of the OMT and on a lemma about the doubling of manifolds with boundaries that are BUT-manifolds.Comment: 10 pages, 2 figure

The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

Variations and conditions of the composition natural waters in the central european russia (On example of the Tatarstan republic)

© SGEM2017 All Rights Reserved. The upper part of the Tatarstan Republic section is complexed by sedimentary of multi facies complexes of Middle Upper Permian, Mesozoic and Pliocene-Quaternary rocks. The surface and ground water are characterized by a wide variability in composition, mineralization, water hardness and other parameters. These variations are determined by a complex of natural and technogenic factors. The most important natural factor is interaction of the atmospheric precipitation and their derivates with soils and rocks of the section. For assessment of this interaction, were analyzed water extracts and filtrates on the basis of distilled, snow melt and spring waters from the main types of soils and rocks. Additional determined the gradients of concentration changes by main parameters and components of the groundwater composition during their downward filtration in different regions of Tatarstan. The studies allows for predict hydrogeochemical conditions of active water exchange zone of cross section. First of all, this is necessary for the best location of water wells and efficient use of ground water

Electron spin resonance studies of the stabilization mechanism of cellulose nitrates

Although stabilization of polymer composites (specifically, cellulose nitrates (CN)) has been studied since fairly long time ago, no scrutiny of the nature of radical reactions underlying this process was undertaken. At the same time, as has been shown previously, ESR spectroscopy proved to be an efficient method for studying radical reactions taking place in thermal decomposition of CN. Therefore of interest is to employ the ESR technique in studies of the effect of diphenylamine (DPA), the most frequently used chemical stabilizer of cellulose nitrates, on these reactions and thereby to elucidate the appropriate stabilization mechanism

Study of correlation of oil flow properties with nuclear magnetic resonance and self-diffusion characteristics

© Copyright 2016.Correlation curves of viscosity, average spin-spin relaxation time, and average self-diffusion for crude oil samples from Tatarstan oil fields have been obtained. Two different averaging models were used to calculate mean values. It has been found that self-diffusion D and average spin-spin relaxation time R2 are best correlated in case reciprocal values 1/R and 1/D are averaged

EPR imaging study of paramagnetic centre distribution in thiokol-epoxy hermetics

The distribution of paramagnetic centres in carbon black filler in the interphase layer of the thiokol-epoxy hermetics on the border of brass or glass substrate was studied using EPR-imaging method. It was shown that the relative content of radicals decreases near the hermetic-"rigid" surface contact border. The thickness of the layer with a low concentration of radicals is estimated as 0.5±0.3 mm. The inhomogeneous distribution of radicals is more obvious in the case of hermetic hardening on a brass surface. These results are explained by a catalytic acceleration of the thiokol-epoxy polymerization reaction in the region of hermetic-metal surface contact. © 1996 Springer

Paper estimability of heavy oil viscosity by nuclear magnetic resonances researchestitle

Copyright © 2014, Society of Petroleum Engineers. This paper presents the results of laboratory and nuclear magnetic resonances researches of seventy-seven crude oil samples from the Devonian, Carboniferous and Permian formations of Tatarstan oil fields with a wide range of viscosity varying from several cps to 60,000 cps. The results can be used to estimate the viscosity of the oil, including in situ viscosity. It has been found that the NMR relaxation characteristics of the tested samples presented in the form of T2 time distribution spectra confirm that crude oil is multicomponent. Numerical characteristics resulting from the analysis of the spectrum of spin-spin relaxation time T2 have been determined, which show good correlation with the viscosity of the hydrocarbon fluid. The paper presents the obtained experimental correlations between the rheological properties and NMR characteristics for oil samples studied

Lithogenesis role in formation of zones with improved reservoir properties of subsalt carbonate sediments of venda and lower cambrian (Eastern Siberia)

The object of research is pre-salt deposits of carbonate complexes from Vendian and Lower Cambrian Nepa-Botuobiya anteclise (NBA), located in the central part of the Siberian platform, administratively dedicated to the Irkutsk region. The problems of fluid dynamics within the basement ledges are considered. Their role in the high productivity of overlying carbonate deposits is assessed. Reconstruction of sedimentation conditions and subsequent diagenesis and katagenesis of Nepa formation sediments is made that have the greatest impact on morphostructure of the sedimentary cover. Cuts of Vendian-Cambrian sediments before and after diagenesis and katagenesis are given. Detailed construction helped to establish antiform structure of the sedimentary cover deposition over the basement ledges, allowing visually see in retrospect a sediment`s restructuring and its influence on the formation of hydrocarbon traps. The information on the rising pore pressure within the ledges is provided, due to which there is a subvertical fluid migration through both sulfate-carbonate rocks and interformational mudstones which to the beginning of elysion processes in Nepa formation were also unlithified porous sediments. It is suggested that the most permeable zones in the sulfate-carbonate rocks were formed over the edge portions of the projections as the most deformed during compaction of sand and clay deposits Nepa formation and restructuring of the upper section of the sedimentary cover. It is suggested that the elysion stage of sedimentary basin development within ledges and arched structure of Vendian-Cambrian deposits leads to dissolution and mobilization by aqueous solutions of the sedimentary rocks substance at depth and their migration mostly up. The results outlined in this paper are supported by the core data analysis

Влияние вращения сферического тела, покрытого диэлектриком, на характеристики рассеяния

Dispersion ratio for sphere in diameter of 500 mm with the heat-shielding covering, for tree different angular velocities, was calculated. Produced the analysis of obtained results.Приведен расчет коэффициентов рассеяния для сферы радиусом 250 мм с диэлектрическим покрытием для трех различных угловых скоростей вращения рассеивателя. Пученные результаты проанализированы

Dentition simulator «Dentafit» - nnovation to improve dental health

Authors, based on the analysis of scientific literature, analyzed the possible use of an innovative product - the dentofacial simulator "Dentafit", which replenishes the deficit of the masticatory load.. The Company now its industrial production. Conduct research the necessity of using dentoalveolar training to improve the dental status, as well as the prevention and treatment of dentofacial anomalies.Авторами, на основании анализа научной литературы проведен анализ возможного использования инновационного изделия – зубочелюстного тренажера «Dentafit», восполняющего дефицит жевательной нагрузки. Начат его промышленный выпуск. Проведенными научными исследованиями обоснована необходимость использования зубочелюстного тренинга для улучшения стоматологического статуса, а также профилактики и лечения зубочелюстных аномалий