On the adjacency quantization in the equation modelling the Josephson effect

We investigate two-parametric family of non-autonomous ordinary differential equations on the two-torus \dot x=\frac{dx}{dt}=\nu\sin x + a + s \sin t, \ a,\nu,s\in\rr; \ \nu\neq0 \text {is fixed}, that model the Josephson effect from superconductivity. We study its rotation number as a function of parameters $(a,s)$ and its {\it Arnold tongues}: the level sets of the rotation number that have non-empty interior. Its Arnold tongues have many non-typical properties: they exist only for integer rotation numbers (V.M.Buchstaber, O.V.Karpov, S.I.Tertychnyi (2010); Yu.S.Ilyashenko, D.A.Ryzhov, D.A.Filimonov (2011)); their boundaries are given by pairs of analytic curves (V.M.Buchstaber, O.V.Karpov, S.I.Tertychnyi (2004, 2012)). Numerical experiments and theoretical investigations (V.M.Buchstaber, O.V.Karpov, S.I.Tertychnyi (2006); A.V.Klimenko and O.L.Romaskevich (2012)) show that each Arnold tongue forms an infinite chain of adjacent domains separated by adjacency points and going to infinity in asymptotically vertical direction. Recent numerical experiments had also shown that the adjacencies of each Arnold tongue have one and the same integer abscissa $a$ equal to the corresponding rotation number. We prove this fact for every fixed $\nu$ with $|\nu|\leq1$. In the general case we prove a weaker statement: the abscissa of each adjacency point is integer; it has the same sign, as the rotation number; its modulus is no greater than that of the rotation number. The proof is based on the representation of the differential equations under consideration as projectivizations of complex linear differential equations on the Riemann sphere (V.M.Buchstaber, O.V.Karpov, S.I.Tertychnyi (2004); R.L.Foote (1998); Yu.S.Ilyashenko, D.A.Ryzhov, D.A.Filimonov (2011)), and the classical theory of complex linear equations.Comment: In Russian (18 pages, 1 figure); brief summary in English (7 pages

Groups with infinitely many ends acting analytically on the circle

This article takes the inspiration from two milestones in the study of non minimal actions of groups on the circle: Duminy's theorem about the number of ends of semi-exceptional leaves and Ghys' freeness result in analytic regularity. Our first result concerns groups of analytic diffeomorphisms with infinitely many ends: if the action is non expanding, then the group is virtually free. The second result is a Duminy's theorem for minimal codimension one foliations: either non expandable leaves have infinitely many ends, or the holonomy pseudogroup preserves a projective structure.Comment: We can now make a precise reference to Deroin's work arXiv:1811.10298. 54 pages, 2 figure

Legibility of Textbooks: A Literature Review

AbstractThe purpose of the study was to analyse findings in the field of the textbooks’ legibility, readability and visual word recognition. The paper focuses on the most significant findings for comprehending the texts’ spatial characteristics during reading, word and letter recognition. The aim of the study was to analyse the factors which have induced inconsistencies between the findings acquired by scientists, as well as to compare findings which continually lead to progression in this field

The education values of full-time and part-time students of a ministerial university

The article is based on the results of the sociological study on the value orientations of students in two traditional forms - full-time and part-time, the peculiarities of their educational trajectories, the motivation for choosing the form of education. The article tests the hypothesis about the presence (absence) of a pronounced connection between the organizational form of education at a university and the subsequent distribution of students, based on estimates of their level of education. The collection of empirical material on the research problem has been carried out in the course of planned research work devoted to the study of the image of the Academy of Management of the Ministry of Internal Affairs of Russia. A number of associations about the university among those who received education in different forms of education have been identified and described Two approaches of value expectations from education have been identified : the first is closely related to the strengthening of the resource of the prestige of academic education, the second - with the increase in the educational potential of the educational institution. It has been proved that in full-time students the desire to improve themselves as individuals and professionals who can compete on the basis of improved personal competencies, and not on the symbolic attributes of the social hierarchy prevail; the educational efforts of a significant part of students by correspondence are focused mainly on achieving a formal learning outcome - an increase in status, and do not consider a diploma as a document that reflects the qualifications and level of education of the owner. The article makes a substantiated conclusion about the need to differentiate the status of the received educational document depending on the form of study at a university

Spin-reorientation transitions in the Cairo pentagonal magnet Bi4 Fe5 O13 F

© 2017 American Physical Society. We show that interlayer spins play a dual role in the Cairo pentagonal magnet Bi4Fe5O13F, on one hand mediating the three-dimensional magnetic order, and on the other driving spin-reorientation transitions both within and between the planes. The corresponding sequence of magnetic orders unraveled by neutron diffraction and Mössbauer spectroscopy features two orthogonal magnetic structures described by opposite local vector chiralities, and an intermediate, partly disordered phase with nearly collinear spins. A similar collinear phase has been predicted theoretically to be stabilized by quantum fluctuations, but Bi4Fe5O13F is very far from the relevant parameter regime. While the observed in-plane reorientation cannot be explained by any standard frustration mechanism, our ab initio band-structure calculations reveal strong single-ion anisotropy of the interlayer Fe3+ spins that turns out to be instrumental in controlling the local vector chirality and the associated interlayer order

Molecular mechanisms of neuroprotective effects of thyroid hormones and their metabolites in acute brain ischemia

As endovascular reperfusion advances and multimodal neuroimagimg is implemented, neuroprotection in ischemic stroke progresses to the next level. In the recent years, the focus of neuroprotection research has been gradually shifting towards the research of endogenous substances and their synthetic analogs. According to the available evidence, thyroid hormones (THs) and their metabolites are potentially effective neuroprotectors in brain ischemia. Objective. To identify and classify TH neuroprotective effects in acute brain ischemia by analyzing contemporary data. We studied and analyzed publications indexed in РubMed, SciElo, ScienceDirect, Scopus, Biomedical Data Journal, and eLibrary. The molecular basis of TH effects includes genomic and non-genomic mechanisms aimed at mitochondrial activity regulation, neuro- and angiogenesis, axonal transport, cytoskeleton maintenance, and impact on ion channels as well as activation and expression of specific proteins. TH effects on the central nervous system can be classified into following clusters: influence on neuronal and glial metabolism, apoptosis modulation, neuroplasticity and angiogenesis, impact on hemostasis, and local and systemic immune response. Conclusion. THs are multimodal and selective regulators of cellular processes that affect neuroplasticity and neuro-reintegration both in the brain ischemic zone and beyond it. Therefore, a promising research can cover THs and and their metabolites as cerebral cytoprotectors to improve functional outcomes of ischemic strokes

Nonreciprocity of spin waves in metallized magnonic crystal

The nonreciprocal properties of spin waves in metallized one-dimensional bi-component magnonic crystal composed of two materials with different magnetizations are investigated numerically. Nonreciprocity leads to the appearance of indirect magnonic band gaps for magnonic crystals with both low and high magnetization contrast. Specific features of the nonreciprocity in low contrast magnonic crystals lead to the appearance of several magnonic band gaps located within the first Brillouin zone for waves propagating along the metallized surface. Analysis of the spatial distribution of dynamic magnetization amplitudes explains the mechanism of dispersion band formation and hybridization between magnonic bands in magnonic crystals with metallization

Methods of Assessment of Dynamics of Change of Probability Characteristics of Recognition of Objects in Aerial Reconnaissance

В статье представлена методика оценки динамики изменения вероятностных характеристик распознавания и различения объектов воздушной разведки при операторном и автоматическом дешифрировании соответственно. Представлена математическая постановка задачи распознавания объектов воздушной разведки по инфракрасным изображениям. Приведены результаты оценки изменения вероятностных характеристик распознавания (различения) объектов воздушной разведки по результатам натурного экспериментаThe article presents a method of assessing the dynamics of changes in the probabilistic characteristics of recognition and distinction of objects of aerial reconnaissance in the operator and automatic decryption, respectively. The mathematical formulation of the problem of recognition of objects of aerial reconnaissance by infrared images is presented. The results of the evaluation of changes in the probabilistic characteristics of recognition (distinction) of objects of aerial reconnaissance on the results of full-scale experimen

Functional classification of proteins based on projection of amino acid sequences: application for prediction of protein kinase substrates

<p>Abstract</p> <p>Background</p> <p>The knowledge about proteins with specific interaction capacity to the protein partners is very important for the modeling of cell signaling networks. However, the experimentally-derived data are sufficiently not complete for the reconstruction of signaling pathways. This problem can be solved by the network enrichment with predicted protein interactions. The previously published <it>in silico </it>method PAAS was applied for prediction of interactions between protein kinases and their substrates.</p> <p>Results</p> <p>We used the method for recognition of the protein classes defined by the interaction with the same protein partners. 1021 protein kinase substrates classified by 45 kinases were extracted from the Phospho.ELM database and used as a training set. The reasonable accuracy of prediction calculated by leave-one-out cross validation procedure was observed in the majority of kinase-specificity classes. The random multiple splitting of the studied set onto the test and training set had also led to satisfactory results. The kinase substrate specificity for 186 proteins extracted from TRANSPATH^®database was predicted by PAAS method. Several kinase-substrate interactions described in this database were correctly predicted. Using the previously developed ExPlain™ system for the reconstruction of signal transduction pathways, we showed that addition of the newly predicted interactions enabled us to find the possible path between signal trigger, TNF-alpha, and its target genes in the cell.</p> <p>Conclusions</p> <p>It was shown that the predictions of protein kinase substrates by PAAS were suitable for the enrichment of signaling pathway networks and identification of the novel signaling pathways. The on-line version of PAAS for prediction of protein kinase substrates is freely available at <url>http://www.ibmc.msk.ru/PAAS/</url>.</p