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3-Fermion Topological Quantum Computation [1]
3-Fermion topological quantum computation [1] Sam Roberts1 and Dominic J. Williamson2 1Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia 2Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305, USA I. INTRODUCTION Topological quantum computation (TQC) is currently the most promising approach to scalable, fault-tolerant quantum computation. In recent years, the focus has been on TQC with Kitaev's toric code [2], due to it's high threshold to noise [3, 4], and amenability to planar architectures with nearest neighbour interactions. To encode and manipulate quantum information in the toric code, a variety of techniques drawn from condensed matter contexts have been utilised. In particular, some of the efficient approaches for TQC with the toric code rely on creating and manipulating gapped-boundaries, symmetry defects and anyons of the underlying topological phase of matter [5{ 10]. Despite great advances, the overheads for universal fault-tolerant quantum computation remain a formidable challenge. It is therefore important to analyse the potential of TQC in a broad range of topological phases of matter, and attempt to find new computational substrates that require fewer quantum resources to execute fault-tolerant quantum computation. In this work we present an approach to TQC for more general anyon theories based on the Walker{Wang mod- els [11]. This provides a rich class of spin-lattice models in three-dimensions whose boundaries can naturally be used to topologically encode quantum information. The two-dimensional boundary phases of Walker{Wang models accommodate a richer set of possibilities than stand-alone two-dimensional topological phases realized by commuting projector codes [12, 13]. -
Boenig-Liptsin / Entrepreneurs of the Mind / 1 Citizen's Mind
Margo Boenig-Liptsin SIGCIS Workshop, November 9, 2014 Work in !rogress Session "orking draft – please do not cite (ear SIGCIS Workshop !articipants) *hank you $or reading this partial draft of one of my dissertation 'hapters) I-m submitting to your review a draft of a 'hapter $rom the mi##&e of my dissertation, therefore to contextualize the "riting that you "i&& be reading, I inc&ude be&ow an abstract of my "hole dissertation project and a chapter out&ine. 2s you "i&& see, this early draft of Chapter 2 is based primari&y on empirical research of my three national cases1 I haven't yet integrated into it any secondary &iterature. I "ould be very gratef,& $or your suggestions of re$erences that you $eel "ould be interesting $or me to incorporate/refect upon, especial&y $rom the &iterature on the history of computing, given the topi's that I am exploring in this chapter or in the dissertation as a "hole. *his early draft is also missing complete $ootnotes—they are current&y 0ust notes $or mysel$ and references that I need to tidy up. I-m gratef,& $or al& of your comments, "hich "i&& no doubt make the next #raft of this signifcant&y better) Best "ishes, Margo (issertation abstract Making the Citi/en of the Information 2ge7 2 comparative study of computer &iteracy programs $or 'hi&dren, 1960s-1990s My dissertation is a comparative history of the frst computer &iteracy programs $or chi&dren. *he project examines how programs to introduce 'hi&dren to computers in the 9nited States, :rance, and the Soviet 9nion $rom the 1960s to 1990s embodied political, epistemic, and moral debates about the kind of citi/en required $or &i$e in the 21st century. -
Nikolay Luzin, His Students, Adversaries, and Defenders (Notes
Nikolay Luzin, his students, adversaries, and defenders (notes on the history of Moscow mathematics, 1914-1936) Yury Neretin This is historical-mathematical and historical notes on Moscow mathematics 1914-1936. Nikolay Luzin was a central figure of that time. Pavel Alexandroff, Nina Bari, Alexandr Khinchin, Andrey Kolmogorov, Mikhail Lavrentiev, Lazar Lyusternik, Dmitry Menshov, Petr Novikov, Lev Sсhnirelman, Mikhail Suslin, and Pavel Urysohn were his students. We discuss the time of the great intellectual influence of Luzin (1915-1924), the time of decay of his school (1922-1930), a moment of his administrative power (1934-1936), and his fall in July 1936. But the thing which served as a source of Luzin’s inner drama turned out to be a source of his subsequent fame... Lazar Lyusternik [351] Il est temps que je m’arr ete: voici que je dis, ce que j’ai d´eclar´e, et avec raison, ˆetre inutile `adire. Henri Lebesgue, Preface to Luzin’s book, Leˇcons sur les ensembles analytiques et leurs applications, [288] Прошло сто лет и что ж осталось От сильных, гордых сих мужей, Столь полных волею страстей? Их поколенье миновалось Alexandr Pushkin ’Poltava’ There is a common idea that a life of Nikolay Luzin can be a topic of a Shakespeare drama. I am agree with this sentence but I am extremely far from an intention to realize this idea. The present text is an impassive historical-mathematical and historical investigation of Moscow mathematics of that time. On the other hand, this is more a story of its initiation and turning moments than a history of achievements. -
Arxiv:1705.01740V1 [Cond-Mat.Str-El] 4 May 2017 2
Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections M. Hermanns1, I. Kimchi2, J. Knolle3 1Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany 2Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA and 3T.C.M. group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge, CB3 0HE, United Kingdom Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking the topological order underlying quantum spin liquids is hard to detect exper- imentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tri-coordinated lattices are chief counterexamples | they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li)2IrO3 Iridates and RuCl3. In this review, we give an overview of the rich physics of the Kitaev model, including 2D and 3D fractionalization as well as dynamical correlations and behavior at finite temperatures. We discuss the different materials, and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures. arXiv:1705.01740v1 [cond-mat.str-el] 4 May 2017 2 CONTENTS I. Introduction 2 II. Kitaev quantum spin liquids 3 A. The Kitaev model 3 B. Classifying Kitaev quantum spin liquids by projective symmetries 4 C. Confinement and finite temperature 5 III. Symmetry and chemistry of the Kitaev exchange 6 IV. -
Chapter 10 Orderings and Valuations
Chapter 10 Orderings and valuations 10.1 Ordered fields and their natural valuations One of the main examples for group valuations was the natural valuation of an ordered abelian group. Let us upgrade ordered groups. A field K together with a relation < is called an ordered field and < is called an ordering of K if its additive group together with < is an ordered abelian group and the ordering is compatible with the multiplication: (OM) 0 < x ^ 0 < y =) 0 < xy . For the positive cone of an ordered field, the corresponding additional axiom is: (PC·)P · P ⊂ P . Since −P·−P = P·P ⊂ P, all squares of K and thus also all sums of squares are contained in P. Since −1 2 −P and P \ −P = f0g, it follows that −1 2= P and in particular, −1 is not a sum of squares. From this, we see that the characteristic of an ordered field must be zero (if it would be p > 0, then −1 would be the sum of p − 1 1's and hence a sum of squares). Since the correspondence between orderings and positive cones is bijective, we may identify the ordering with its positive cone. In this sense, XK will denote the set of all orderings resp. positive cones of K. Let us consider the natural valuation of the additive ordered group of the ordered field (K; <). Through the definition va+vb := vab, its value set vK becomes an ordered abelian group and v becomes a homomorphism from the multiplicative group of K onto vK. We have obtained the natural valuation of the ordered field (K; <). -
Sculptor Nina Slobodinskaya (1898-1984)
1 de 2 SCULPTOR NINA SLOBODINSKAYA (1898-1984). LIFE AND SEARCH OF CREATIVE BOUNDARIES IN THE SOVIET EPOCH Anastasia GNEZDILOVA Dipòsit legal: Gi. 2081-2016 http://hdl.handle.net/10803/334701 http://creativecommons.org/licenses/by/4.0/deed.ca Aquesta obra està subjecta a una llicència Creative Commons Reconeixement Esta obra está bajo una licencia Creative Commons Reconocimiento This work is licensed under a Creative Commons Attribution licence TESI DOCTORAL Sculptor Nina Slobodinskaya (1898 -1984) Life and Search of Creative Boundaries in the Soviet Epoch Anastasia Gnezdilova 2015 TESI DOCTORAL Sculptor Nina Slobodinskaya (1898-1984) Life and Search of Creative Boundaries in the Soviet Epoch Anastasia Gnezdilova 2015 Programa de doctorat: Ciències humanes I de la cultura Dirigida per: Dra. Maria-Josep Balsach i Peig Memòria presentada per optar al títol de doctora per la Universitat de Girona 1 2 Acknowledgments First of all I would like to thank my scientific tutor Maria-Josep Balsach I Peig, who inspired and encouraged me to work on subject which truly interested me, but I did not dare considering to work on it, although it was most actual, despite all seeming difficulties. Her invaluable support and wise and unfailing guiadance throughthout all work periods were crucial as returned hope and belief in proper forces in moments of despair and finally to bring my study to a conclusion. My research would not be realized without constant sacrifices, enormous patience, encouragement and understanding, moral support, good advices, and faith in me of all my family: my husband Daniel, my parents Andrey and Tamara, my ount Liubov, my children Iaroslav and Maria, my parents-in-law Francesc and Maria –Antonia, and my sister-in-law Silvia. -
Leonhard Euler: His Life, the Man, and His Works∗
SIAM REVIEW c 2008 Walter Gautschi Vol. 50, No. 1, pp. 3–33 Leonhard Euler: His Life, the Man, and His Works∗ Walter Gautschi† Abstract. On the occasion of the 300th anniversary (on April 15, 2007) of Euler’s birth, an attempt is made to bring Euler’s genius to the attention of a broad segment of the educated public. The three stations of his life—Basel, St. Petersburg, andBerlin—are sketchedandthe principal works identified in more or less chronological order. To convey a flavor of his work andits impact on modernscience, a few of Euler’s memorable contributions are selected anddiscussedinmore detail. Remarks on Euler’s personality, intellect, andcraftsmanship roundout the presentation. Key words. LeonhardEuler, sketch of Euler’s life, works, andpersonality AMS subject classification. 01A50 DOI. 10.1137/070702710 Seh ich die Werke der Meister an, So sehe ich, was sie getan; Betracht ich meine Siebensachen, Seh ich, was ich h¨att sollen machen. –Goethe, Weimar 1814/1815 1. Introduction. It is a virtually impossible task to do justice, in a short span of time and space, to the great genius of Leonhard Euler. All we can do, in this lecture, is to bring across some glimpses of Euler’s incredibly voluminous and diverse work, which today fills 74 massive volumes of the Opera omnia (with two more to come). Nine additional volumes of correspondence are planned and have already appeared in part, and about seven volumes of notebooks and diaries still await editing! We begin in section 2 with a brief outline of Euler’s life, going through the three stations of his life: Basel, St. -
Leonhard Euler Moriam Yarrow
Leonhard Euler Moriam Yarrow Euler's Life Leonhard Euler was one of the greatest mathematician and phsysicist of all time for his many contributions to mathematics. His works have inspired and are the foundation for modern mathe- matics. Euler was born in Basel, Switzerland on April 15, 1707 AD by Paul Euler and Marguerite Brucker. He is the oldest of five children. Once, Euler was born his family moved from Basel to Riehen, where most of his childhood took place. From a very young age Euler had a niche for math because his father taught him the subject. At the age of thirteen he was sent to live with his grandmother, where he attended the University of Basel to receive his Master of Philosphy in 1723. While he attended the Universirty of Basel, he studied greek in hebrew to satisfy his father. His father wanted to prepare him for a career in the field of theology in order to become a pastor, but his friend Johann Bernouilli convinced Euler's father to allow his son to pursue a career in mathematics. Bernoulli saw the potentional in Euler after giving him lessons. Euler received a position at the Academy at Saint Petersburg as a professor from his friend, Daniel Bernoulli. He rose through the ranks very quickly. Once Daniel Bernoulli decided to leave his position as the director of the mathmatical department, Euler was promoted. While in Russia, Euler was greeted/ introduced to Christian Goldbach, who sparked Euler's interest in number theory. Euler was a man of many talents because in Russia he was learning russian, executed studies on navigation and ship design, cartography, and an examiner for the military cadet corps. -
Slavic Scholar and Educator Pyotr Bezsonov (1827-1898): a Life and Legacy
E-ISSN 2281-4612 Academic Journal of Interdisciplinary Studies Vol 10 No 3 May 2021 ISSN 2281-3993 www.richtmann.org . Research Article © 2021 Kaplin et al.. This is an open access article licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (https://creativecommons.org/licenses/by-nc/4.0/) Received: 17 February 2021 / Accepted: 9 April 2021 / Published: 10 May 2021 Slavic Scholar and Educator Pyotr Bezsonov (1827-1898): A Life and Legacy Alexander Kaplin Department of Historiography, Source Studies and Archeology, V.N. Karazin Kharkiv National University, Kharkiv, Ukraine Olha Honcharova Department of Theory and Practice of the English Language, H.S. Skovoroda Kharkiv National Pedagogical University, Kharkiv, Ukraine Valentyna Hlushych Professor Leonid Ushkalov Ukrainian Literature and Journalism Department, H.S. Skovoroda Kharkiv National Pedagogical University, Kharkiv, Ukraine Halyna Marykivska Department of Social and Humanitarian Disciplines, Kharkiv National University of Internal Affairs, Kharkiv, Ukraine Viktoriia Budianska Department of Pedagogy, Foreign Philology and Translation, Simon Kuznets Kharkiv National University of Economics, Kharkiv, Ukraine Svitlana Lavinda Department of Ukrainian and Russian as Foreign Languages, O.M. Beketov Kharkiv National University of Urban Economy, Kharkiv, Ukraine DOI: https://doi.org/10.36941/ajis-2021-0070 Abstract Nowadays the name of Pyotr Bezsonov, the acknowledged in pre-revolutionary Russia scholar, is known to but a narrow circle of researchers as some myths and stereotypes about him have proved difficult to overwhelm. Yet, he traced in the history of Slavic studies as an assiduous collector of ancient Russian and Slavic literature works and explorer of Bulgarian, Belarusian and Serbian folklore, folk songs in particular, a scrutinizer of the Slavic languages and dialects, a talented pedagogue and editor. -
International Research and Exchanges Board Records
International Research and Exchanges Board Records A Finding Aid to the Collection in the Library of Congress Prepared by Karen Linn Femia, Michael McElderry, and Karen Stuart with the assistance of Jeffery Bryson, Brian McGuire, Jewel McPherson, and Chanté Wilson-Flowers Manuscript Division Library of Congress Washington, D.C. 2011 International Research and Exchanges Board Records Page ii Collection Summary Title: International Research and Exchanges Board Records Span Dates: 1947-1991 (bulk 1956-1983) ID No: MSS80702 Creator: International Research and Exchanges Board Creator: Inter-University Committee on Travel Grants Extent: 331,000 items; 331 cartons; 397.2 linear feet Language: Collection material in English and Russian Repository: Manuscript Division, Library of Congress, Washington, D.C. Abstract: American service organization sponsoring scholarly exchange programs with the Soviet Union and Eastern Europe in the Cold War era. Correspondence, case files, subject files, reports, financial records, printed matter, and other records documenting participants’ personal experiences and research projects as well as the administrative operations, selection process, and collaborative projects of one of America’s principal academic exchange programs. International Research and Exchanges Board Records Page iii Contents Collection Summary .......................................................... ii Administrative Information ......................................................1 Organizational History..........................................................2 -
Underpinning of Soviet Industrial Paradigms
Science and Social Policy: Underpinning of Soviet Industrial Paradigms by Chokan Laumulin Supervised by Professor Peter Nolan Centre of Development Studies Department of Politics and International Studies Darwin College This dissertation is submitted for the degree of Doctor of Philosophy May 2019 Preface This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except as declared in the Preface and specified in the text. It is not substantially the same as any that I have submitted, or, is being concurrently submitted for a degree or diploma or other qualification at the University of Cambridge or any other University or similar institution except as declared in the Preface and specified in the text. I further state that no substantial part of my dissertation has already been submitted, or, is being concurrently submitted for any such degree, diploma or other qualification at the University of Cambridge or any other University or similar institution except as declared in the Preface and specified in the text It does not exceed the prescribed word limit for the relevant Degree Committee. 2 Chokan Laumulin, Darwin College, Centre of Development Studies A PhD thesis Science and Social Policy: Underpinning of Soviet Industrial Development Paradigms Supervised by Professor Peter Nolan. Abstract. Soviet policy-makers, in order to aid and abet industrialisation, seem to have chosen science as an agent for development. Soviet science, mainly through the Academy of Sciences of the USSR, was driving the Soviet industrial development and a key element of the preparation of human capital through social programmes and politechnisation of the society. -
«Numbers, Forms and Geometry»
INTERNATIONAL CONFERENCE «NUMBERS, FORMS AND GEOMETRY» August 21 - 26, 2017 Sochi, Russia CONFERENCE PROCEEDINGS KHABAROVSK 2017 International conference «Numbers, Forms and Geometry» August 21 – 26, 2017 Sochi, Russia Organizers: • Steklov Mathematical Institute, Russian Academy of Sciences • Moscow State University • Institute of Mathematics, The National Academy of Sciences, Belarus • Tula State Pedagogical University • Institute for Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences (IAM FEB RAS) • Sochi State University (SSU) Program committee: Yuri Nesterenko (Moscow State University, Moscow, chairman) Vasilij Bernik (Institute of Mathematics, The National Academy of Sciences, Belarus, vice-chairman) Victor Buchstaber (Steklov Mathematical Institute, Moscow, vice- chairman) 3 Mikhail Guzev (IAM FEB RAS, Vladivostok, vice-chairman) Vladimir Chubarikov (Moscow State University, Moscow) Maxim Vsemirnov (St.Petersburg Department of Steklov Mathematical Institute, St.Petersburg) Alexander Gaifullin (Steklov Mathematical Institute, Moscow) Nikolai Dobrovolskii (Tula State Pedagogical University, Tula) Vladimir Dubinin (IAM FEB RAS, Vladivostok) Henryk Iwaniec (Rutgers University, Rutgers) Sergei Konyagin (Moscow State University, Moscow) Yuri Matiyasevich (St.Petersburg Department of Steklov Mathematical Institute, St.Petersburg) Nikolai Moshchevitin (Moscow State University, Moscow) Taras Panov (Moscow State University, Moscow) Aleksei Parshin (Steklov Mathematical Institute, Moscow) Vladimir Platonov (Institute