Parallel coordinates in three dimensions and sharp spectral isoperimetric inequalities

In this paper we show how the method of parallel coordinates can be extended to three dimensions. As an application, we prove the conjecture of Antunes, Freitas and Krej\v{c}i\v{r}\'ik \cite{AFK} that "the ball maximises the first Robin eigenvalue with negative boundary parameter among all convex domains of equal surface area" under the weaker restriction that the boundary of the domain is diffeomorphic to the sphere and convex or axiconvex. We also provide partial results in arbitrary dimensions

Birational automorphism groups of Severi-Brauer surfaces over the field of rational numbers

We prove that the only non-trivial finite subgroups of birational automorphism group of non-trivial Severi-Brauer surfaces over the field of rational numbers are $\mathbb{Z}/3\mathbb{Z}$ and $(\mathbb{Z}/3\mathbb{Z})^2.$ Moreover, we show that $(\mathbb{Z}/3\mathbb{Z})^2$ is contained in $\mathrm{Bir}(V)$ for any Severi-Brauer surface $V$ over a field of characteristic zero, and $(\mathbb{Z}/3\mathbb{Z})^3$ is contained in $\mathrm{Bir}(V)$ for any Severi-Brauer surface $V$ over a field of characteristic zero which contains a non-trivial cube root of unity

Perpetual motion machine

For many centuries scientists and inventors have tried to create perpetual motion machines, but even in those times they understood that the attempts to build such machines were vain and foolish

Application of sociological methods and implements in distance learning of the staff of municipal libraries of Sverdlovsk region

The article examines the question of the application of methods and implements of sociology in the e-learning system of additional education. The author speaks of applying sociology in the library. Attention is paid to the monitoring of the process of distance learning of the staff of municipal libraries. The author discusses how feedback can be provided.В статье анализируется вопрос применения методов и инструментов социологии в дистанционной системе дополнительного образования. Автор говорит о применении социологии в библиотеке. Уделяется внимание проведению контроля в процессе дистанционного обучения сотрудников муниципальных библиотек. Рассматривается, как может осуществляться обратная связь

That multifacet english like: How do you like it?

The article is devoted to the English word like, its semantics and functions. It is derived from the Proto-Germanic root lik in galika ‘having the same form or body’. In the course of time the meaning of physical similarity underwent such processes as semantic bleaching and subjectification, which gave rise to the development of various lexico-grammatical and pragmatic functions. It is difficult to draw clear lines of demarcation between its traditional formal functions associated with such parts of speech as conjunction, preposition, particle and its pragmatic functions, such as emphatic, hesitational, metalinguistic, examplificatory, quotative, approximative. The latter express various subjective and abstract shades of meaning. The authors analyze them with reference to pragmatics, drawing on the theories of politeness, relevance and subjectification. Most scholars define like in these pragmatic functions as ‘discourse marker’; however, lexicographers refer to the word like in these discursive functions as ‘adverb’. The authors carried out research into the stylistic reference of the word like in its various functions. The text analysis of Helen Fielding’s Bridget Jones’s Diary and the Nature journal articles has shown that the formal and pragmatic like is prevalent in the work of fiction, especially in the parts presenting conversations; it has also revealed that such uses are absent in scientific texts. © 2017, Slovenska Vzdelavacia Obstaravacia. All rights reserved

Mechano-Electric Feedbacks in a New Model of the Excitation-Contraction Coupling in Human Cardiomyocytes

The study is aimed to develop a new human cardiomyocyte model, which describes electromechanical coupling and mechano-electric feedbacks. The combined electromechanical model (TP+M) links the TP06 electrophysiological model of the human cardiomyocyte with our earlier developed model of the myocardium mechanical activity and its calcium regulation. In the TP+M model, we tried to maintain principal features of calcium transients and action potentials during the twitches typical for the human cardiomyocytes. The developed TP+M model allows simulating several basic classic phenomena such as load-dependent relaxation and length-dependence of isometric twitches and respective changes in action potential duration. We have also simulated some age-dependent changes in the electrical and mechanical activity in the human cardiomyocytes. © 2018 Creative Commons Attribution.The work was carried out within the framework of the IIP UrB RAS themes (Nos. AAAA-A18-118020590031-8, АААА-А18-118020590134-6) and was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0006, and by RFBR (18-01-00059 - single cell modeling; 18-015-00368 – ageing simulation)

Perpetual motion machine

For many centuries scientists and inventors have tried to create perpetual motion machines, but even in those times they understood that the attempts to build such machines were vain and foolish

Mechano-calcium and mechano-electric feedbacks in the human cardiomyocyte analyzed in a mathematical model

Experiments on animal hearts (rat, rabbit, guinea pig, etc.) have demonstrated that mechano-calcium feedback (MCF) and mechano-electric feedback (MEF) are very important for myocardial self-regulation because they adjust the cardiomyocyte contractile function to various mechanical loads and to mechanical interactions between heterogeneous myocardial segments in the ventricle walls. In in vitro experiments on these animals, MCF and MEF manifested themselves in several basic classical phenomena (e.g., load dependence, length dependence of isometric twitches, etc.), and in the respective responses of calcium transients and action potentials. However, it is extremely difficult to study simultaneously the electrical, calcium, and mechanical activities of the human heart muscle in vitro. Mathematical modeling is a useful tool for exploring these phenomena. We have developed a novel model to describe electromechanical coupling and mechano-electric feedbacks in the human cardiomyocyte. It combines the 'ten Tusscher-Panfilov' electrophysiological model of the human cardiomyocyte with our module of myocardium mechanical activity taken from the 'Ekaterinburg-Oxford' model and adjusted to human data. Using it, we simulated isometric and afterloaded twitches and effects of MCF and MEF on excitation-contraction coupling. MCF and MEF were found to affect significantly the duration of the calcium transient and action potential in the human cardiomyocyte model in response to both smaller afterloads as compared to bigger ones and various mechanical interventions applied during isometric and afterloaded twitches. © 2020 The Author(s).Russian Foundation for Basic Research, RFBR: 18‑01‑00059The work was carried out within the framework of the IIP UrB RAS themes (Nos. AAAA‑A18‑118020590031‑8, AAAA‑A18‑118020590134‑6) and was supported by RFBR (18‑01‑00059) and by Act 211 Government of the Russian Federation, contract No. 02.A03.21.0006

Transmural cellular heterogeneity in myocardial electromechanics

Myocardial heterogeneity is an attribute of the normal heart. We have developed integrative models of cardiomyocytes from the subendocardial (ENDO) and subepicardial (EPI) ventricular regions that take into account experimental data on specific regional features of intracellular electromechanical coupling in the guinea pig heart. The models adequately simulate experimental data on the differences in the action potential and contraction between the ENDO and EPI cells. The modeling results predict that heterogeneity in the parameters of calcium handling and myofilament mechanics in isolated ENDO and EPI cardiomyocytes are essential to produce the differences in Ca2+ transients and contraction profiles via cooperative mechanisms of mechano-calcium-electric feedback and may further slightly modulate transmural differences in the electrical properties between the cells. Simulation results predict that ENDO cells have greater sensitivity to changes in the mechanical load than EPI cells. These data are important for understanding the behavior of cardiomyocytes in the intact heart. © 2017, The Physiological Society of Japan and Springer Japan.Japan Society for the Promotion of Science, JSPS: 16K1287