1,184 research outputs found
Homotopical topology
No full textThis classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics—the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra—the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology—the Adams conjecture, Bott periodicity, the Hirzebruch–Riemann–Roch theorem, the Atiyah–Singer index theorem, to name a few—paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role in mathematics, and therefore in the presentation of this book, as well. A judicious focus on the key ideas, at an appropriate magnification of detail, enables the reader to navigate the breadth of material, confidently, without the disorientation of algebraic minutiae. Many exercises are integrated throughout the text to build up the reader’s mastery of concepts and techniques. Numerous technical illustrations elucidate geometric constructions and the mechanics of spectral sequences and other sophisticated methods. Over fifty hauntingly captivating images by A. T. Fomenko artistically render the wondrous beauty, and mystery, of the subject
Shifts of semi-invariants and complete commutative subalgebras in polynomial Poisson algebras
No full textWe study commutative subalgebras in the symmetric algebra
of a finite-dimensional Lie algebra . A. M. Izosimov introduced
extended Mischenko-Fomenko subalgebras and gave a
completeness criterion for them. We generalize his construction and extend
Mischenko-Fomenko subalgebras with the shifts of all semi-invariants of
. We prove that the new commutative subalgebras have the same
transcendence degree as
The Legacy of the Golden Horde in the European Cartography of 15th–18th Centuries (2)
No full textThe article presents the development of the European cartography of Eurasia as a reflection of the gradual accumulation of geographic and ethnographic information about the people and the state, which historical destiny was directly connected with the formation and subsequent dissolution of Genghis Khan’s empire. The author traces the gradual increase of information on eastern regions among western cartographers, which however consistently compared the strengthened Russian State with the “Tartar kingdoms”. The author emphasizes as well the importance of the information provided by the European maps for the study of the state structure of the Golden Horde, of the formation of the new Eurasian nations and of Russia’s relations with the Tatar states
The Legacy of the Golden Horde in the European Cartography of 15th–18th Centuries (1)
No full textThe article presents the development of the European cartography of Eurasia as a reflection of the gradual accumulation of geographic and ethnographic information about people and states, which history was directly connected with the formation and subsequent dissolution of Genghis Khan’s empire. The author traces the gradual increase in the information on eastern regions among western cartographers, which however consistently compared the strengthened Russian State with the “Tartar kingdoms”. The author emphasizes as well the importance of the information provided by the European maps for the study of the state structure of the Golden Horde, of the formation of the new Eurasian nations and of Russia’s relations with the Tatar states
Application of nanodimensional particles and aluminum hydroxide nanostructures for cancer diagnosis and therapy
No full text
Visual and hidden symmetry in geometry
No full textAbstractA symmetry appears in modern geometry and its numerous applications both in explicit form (visually trivial) and sometimes, through sufficiently complex mathematical transformations, in veiled, hidden form. This current paper is made up of commentaries to a series of mathematical, graphical works of the author. In these works an attempt was made to show some occurrences of symmetry in geometry, topology and mechanics
Features assessing the capital adequacy of banks under the countercyclical model of regulation
No full textThe article deals with fundamental issues of assessing the capital adequacy of banks, the evolution of ideas on how to assess it. The author has studied international and Russian practice of assessing capital adequacy oversight bodies, the current state of the capital adequacy of banking sector in Russia and abroad. Shows the effect of the global financial crisis of 2008 and 2010 to consolidate the capital of Russian banks. As part of the introduction of supervisory authorities' counter-cyclical regulatory model, the author developed intra-procedure assessment of capital adequacy; identified and justified by promising sources of capitalization of the banking system of Russia until 2015
Margarita N. Kozhina’s Way in Language Studies
No full textThe article was submitted on 22.12.2021.Представлена научная биография создателя Пермской стилистической школы, профессора Пермского государственного университета М. Н. Кожиной (1925–2012), разработавшей теорию функциональной стилистики, в рамках которой выявлены и описаны закономерности стилевой дифференциации литературного языка. В начале 60-х гг. ХХ в. М. Н. Кожина одной из первых в российском языкознании обратилась к изучению проблем функционирования языка и к формированию нового научного направления – речеведения. На базе междисциплинарного подхода она определила основные понятия и категории функциональной стилистики как важнейшей речеведческой науки. Труды М. Н. Кожиной органично вписались в эпистему второй половины ХХ – начала XXI в. и ознаменовали собой поворот лингвистики от системно-структурной парадигмы изучения языка к функциональной. Ею был разработан стилостатистический метод анализа речи. Статистическое обследование языковой стороны функциональных стилей привело к выводам о взаимодействии в речи лингвистических и экстралингвистических факторов. М. Н. Кожина – автор более 200 научных трудов, в том числе восьми монографий и первого в России учебника по стилистике русского языка. Профессор М. Н. Кожина входила в состав Международного комитета славистов и редколлегий ряда научных изданий, в том числе журналов Stylistyka (Польша) и Стил (Сербия). В предлагаемой статье М. Н. Кожина показана не только как крупный ученый-теоретик, но и как выдающийся организатор науки. По ее инициативе было подготовлено 20 сборников научных трудов по стилистике, проведено несколько масштабных конференций, опубликована трехтомная коллективная монография по истории русского научного стиля XVIII–XX вв., издан первый в России Стилистический энциклопедический словарь русского языка, ставший компендиумом знаний по функциональной стилистике. Маргарита Николаевна предстает талантливым исследователем и необыкновенно сильным человеком, которому удалось, преодолев драматические обстоятельства жизни, внести свой вклад в европейское языкознание.This article presents a scholarly biography of Margarita Kozhina (1925–2012), the founder of the well-known Perm School of Stylistics and professor at Perm State University. She developed the theory of functional stylistics, which revealed and described the regularities of stylistic differentiation in literary Russian. In the early 1960s, Kozhina was one of the first researchers in Russian linguistics to study issues of language functioning and form a new scholarly direction, namely speech studies. Based on an interdisciplinary approach, she defined the main categories of functional stylistics. The latter was regarded as the most important component of speech studies. Kozhina’s papers organically entered the episteme of the second half of the twentieth and early twentyfirst centuries. They marked the turn of linguistics from the system-structural paradigm of studying language to the functional one. Kozhina developed the stylistic-statistical method of speech analysis. A statistical survey of the linguistic side of functional styles allowed her to make conclusions about the interaction of linguistic and extra-linguistic factors in speech. Kozhina authored more than 200 scholarly publications, including 8 monographs and the first Russian textbook on Russian-language stylistics. She was a member of the International Committee of Slavists and the editorial boards of several scholarly journals, including Stylistyka (Poland) and Styl (Serbia). The article describes Kozhina both as a prominent theorist and a remarkable organiser of scholarship. She initiated 20 collections of academic works on stylistics, some international conferences, a three-volume collective monograph on the history of Russian scholarly style from the eighteenth to the twentieth centuries, and the first Stylistic Encyclopaedic Dictionary of the Russian Language (a compendium of knowledge on functional stylistics). The author describes Margarita Kozhina as a talented researcher and an unusually strong personality, who managed, having overcome dramatic circumstances, to make an important contribution to European studies of language
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