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The Ties That Bind Olga Alexandrovna Ladyzhenskaya and the 2022 ICM in St. Petersburg
University of Richmond UR Scholarship Repository Math and Computer Science Faculty Publications Math and Computer Science 3-2020 The Ties That Bind Olga Alexandrovna Ladyzhenskaya and the 2022 ICM in St. Petersburg Della Dumbaugh University of Richmond, [email protected] Panagiota Daskalopoulos Anatoly Vershik Lev Kapitanski Nicolai Reshetikhin See next page for additional authors Follow this and additional works at: https://scholarship.richmond.edu/mathcs-faculty-publications Recommended Citation Dumbaugh, Della, Panagiota Daskalopoulos, Anatoly Vershik, Lev Kapitanski, Nicolai Reshetikhin, Darya Apushkinskaya, and Alexander Nazarov. “The Ties That Bind: Olga Alexandrovna Ladyzhenskaya and the 2022 ICM in St. Petersburg.” Notices of the American Mathematical Society 67 (March 2020): 373–81. https://doi.org/10.1090/noti2047. This Article is brought to you for free and open access by the Math and Computer Science at UR Scholarship Repository. It has been accepted for inclusion in Math and Computer Science Faculty Publications by an authorized administrator of UR Scholarship Repository. For more information, please contact [email protected]. Authors Della Dumbaugh, Panagiota Daskalopoulos, Anatoly Vershik, Lev Kapitanski, Nicolai Reshetikhin, Darya Apushkinskaya, and Alexander Nazarov This article is available at UR Scholarship Repository: https://scholarship.richmond.edu/mathcs-faculty-publications/ 237 HISTORY The Ties That Bind Olga Alexandrovna Ladyzhenskaya and the 2022 ICM in St. Petersburg Della Dumbaugh, Panagiota -
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. -
Why Wirtinger Derivatives Behave So Well
Why Wirtinger derivatives behave so well Bart Michels∗ April 14, 2019 Contents 1 Introduction 2 2 Partial derivatives revisited 2 3 Complexification 3 3.1 Complexified differentials: two variables . .4 3.2 Complexified differentials: multiple variables . .4 3.3 Conjugation . .5 4 Chain rule 7 5 Holomorphic functions 10 6 Power series 11 7 Concluding remarks 12 ∗Universit´eParis 13, LAGA, CNRS, UMR 7539, F-93430, Villetaneuse, France. Email: [email protected] 1 1 Introduction Given a smooth function f : C ! C, it makes a priori no sense to talk about @f @f the Wirtinger derivatives and . We could define them by @z @z¯ @f 1 @f @f = − i @z 2 @x @y (1) @f 1 @f @f = + i @z¯ 2 @x @y but that does not explain why we denote them like partial derivatives, where the confusing sign convention comes from, why they behave like partial derivatives, and why they act on power series in z and z in the way they should. Here follows a construction of Wirtinger derivatives that avoids the explicit formula (1). The reader may be interested in the definitions in section 3, in the sanity check in Proposition 3.2, the chain rule from Proposition 4.3 and the results from section 6. 2 Partial derivatives revisited It is worthwhile to take a second look at what a partial derivative is. Con- sider finite-dimensional real vector spaces V and W .1 They carry a canonical smooth structure. Consider a differentiable function f : V ! W . At every point p 2 V , f has a differential Dpf : V ! W , an R-linear map. -
Vector and Tensor Analysis, 1950, Harry Lass, 0177610514, 9780177610516, Mcgraw- Hill, 1950
Vector and tensor analysis, 1950, Harry Lass, 0177610514, 9780177610516, McGraw- Hill, 1950 DOWNLOAD http://bit.ly/1CHWNWq http://www.powells.com/s?kw=Vector+and+tensor+analysis DOWNLOAD http://goo.gl/RBcy2 https://itunes.apple.com/us/book/Vector-and-tensor-analysis/id439454683 http://bit.ly/1lGfW8S Vector & Tensor Analysis , U.Chatterjee & N.Chatterjee, , , . Tensor Calculus A Concise Course, Barry Spain, 2003, Mathematics, 125 pages. A compact exposition of the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry, elasticity, and. The Art of Modeling Dynamic Systems Forecasting for Chaos, Randomness and Determinism, Foster Morrison, Mar 7, 2012, Mathematics, 416 pages. This text illustrates the roles of statistical methods, coordinate transformations, and mathematical analysis in mapping complex, unpredictable dynamical systems. It describes. Partial differential equations in physics , Arnold Sommerfeld, Jan 1, 1949, Mathematics, 334 pages. Partial differential equations in physics. Tensor Calculus , John Lighton Synge, Alfred Schild, 1978, Mathematics, 324 pages. "This book is an excellent classroom text, since it is clearly written, contains numerous problems and exercises, and at the end of each chapter has a summary of the. Vector and tensor analysis , Harry Lass, 1950, Mathematics, 347 pages. Abstract Algebra and Solution by Radicals , John Edward Maxfield, Margaret W. Maxfield, 1971, Mathematics, 209 pages. Easily accessible undergraduate-level text covers groups, polynomials, Galois theory, radicals, much more. Features many examples, illustrations and commentaries as well as 13. Underwater Missile Propulsion A Selection of Authoritative Technical and Descriptive Papers, Leonard Greiner, 1968, Fleet ballistic missile weapons systems, 502 pages. -
Wirtinger Kalman Overdrive
Wirtinger Kalman Overdrive O. Smirnov (Rhodes & SKA SA) C. Tasse (Obs. Paris Meudon & Rhodes) The 3GC Culture Wars Two approaches to dealing with DD effects The “NRAO School”: Represent everything by the A-term Correct during imaging (convolutional gridding) Solve for pointing offsets Sky models are images The “ASTRON School”: Solve for DD gains towards (clusters of) sources Make component sky models, subtract sources in uv-plane while accounting for DD gains O. Smirnov & C. Tasse - Wirtinger Kalman Overdrive - SPARCS 2015 2 Why DD Gains Cons: non-physical, slow & expensive But, DD+MeqTrees have consistently delivered the goods with all major pathfinders Early LOFAR maps and LOFAR EoR (S. Yatawatta) Beautiful ASKAP/BETA maps (I. Heywood) JVLA 5M+ DR (M. Mitra earlier) Fair bet that we'll still be using them come MeerKAT and SKA O. Smirnov & C. Tasse - Wirtinger Kalman Overdrive - SPARCS 2015 3 DD Gains Are Like Whiskey The smoother the better Make everything look more attractive If you overindulge, you wake in in the morning wondering where your {polarized foregrounds, weak sources, science signal} have gotten to differential source gain & bandpass gain beam coherency (s) (s) (s)H (s)H H Vpq= G⏞p ∑ ⏞Δ Ep E⏞p ⏞Xpq Eq Δ Eq Gq ⏟( s ) sum over sources O. Smirnov & C. Tasse - Wirtinger Kalman Overdrive - SPARCS 2015 4 The One True Way O. Smirnov & C. Tasse - Wirtinger Kalman Overdrive - SPARCS 2015 5 The Middle Way DR limited by how well we can subtract the brighter source population thus bigger problem for small dish/WF Subtract the first two-three orders of magnitude in the uv-plane good source modelling and (deconvolution and/or Bayesian) PB models, pointing solutions, +solvable DD gains Image and deconvolve the rest really well A-term and/or faceting O. -
A Contextual Analysis of the Early Work of Andrzej Trautman and Ivor
A contextual analysis of the early work of Andrzej Trautman and Ivor Robinson on equations of motion and gravitational radiation Donald Salisbury1,2 1Austin College, 900 North Grand Ave, Sherman, Texas 75090, USA 2Max Planck Institute for the History of Science, Boltzmannstrasse 22, 14195 Berlin, Germany October 10, 2019 Abstract In a series of papers published in the course of his dissertation work in the mid 1950’s, Andrzej Trautman drew upon the slow motion approximation developed by his advisor Infeld, the general covariance based strong conservation laws enunciated by Bergmann and Goldberg, the Riemann tensor attributes explored by Goldberg and related geodesic deviation exploited by Pirani, the permissible metric discontinuities identified by Lich- nerowicz, O’Brien and Synge, and finally Petrov’s classification of vacuum spacetimes. With several significant additions he produced a comprehensive overview of the state of research in equations of motion and gravitational waves that was presented in a widely cited series of lectures at King’s College, London, in 1958. Fundamental new contribu- tions were the formulation of boundary conditions representing outgoing gravitational radiation the deduction of its Petrov type, a covariant expression for null wave fronts, and a derivation of the correct mass loss formula due to radiation emission. Ivor Robin- son had already in 1956 developed a bi-vector based technique that had resulted in his rediscovery of exact plane gravitational wave solutions of Einstein’s equations. He was the first to characterize shear-free null geodesic congruences. He and Trautman met in London in 1958, and there resulted a long-term collaboration whose initial fruits were the Robinson-Trautman metric, examples of which were exact spherical gravitational waves. -
Blind Demixing Via Wirtinger Flow with Random Initialization
Blind Demixing via Wirtinger Flow with Random Initialization Jialin Dong Yuanming Shi [email protected] [email protected] ShanghaiTech University ShanghaiTech University Abstract i = 1; ··· ; s, i.e., s This paper concerns the problem of demixing X \ \ a series of source signals from the sum of bi- yj = bj∗hixi∗aij; 1 ≤ j ≤ m; (1) linear measurements. This problem spans di- i=1 verse areas such as communication, imaging N K processing, machine learning, etc. However, where faijg 2 C , fbjg 2 C are design vectors. semidefinite programming for blind demixing Here, the first K columns of the matrix F form the ma- m K m m is prohibitive to large-scale problems due to trix B := [b1; ··· ; bm]∗ 2 C × , where F 2 C × high computational complexity and storage is the unitary discrete Fourier transform (DFT) ma- cost. Although several efficient algorithms \ trix with FF ∗ = Im. Our goal is to recover fxig and have been developed recently that enjoy the \ fhig from the sum of bilinear measurements, which is benefits of fast convergence rates and even known as blind demixing [1, 2]. regularization free, they still call for spec- tral initialization. To find simple initial- This problem has spanned a wide scope of applications ization approach that works equally well as ranging from imaging processing [3, 4] and machine spectral initialization, we propose to solve learning [5, 6] to communication [7, 8]. Specifically, blind demixing problem via Wirtinger flow by solving the blind demixing problem, both original with random initialization, which yields a images and corresponding convolutional kernels can be natural implementation. -
LOCAL WELL-POSEDNESS for the QUASI-LINEAR HAMILTONIAN SCHRÖDINGER EQUATION on TORI Roberto Feola, Felice Iandoli
LOCAL WELL-POSEDNESS FOR THE QUASI-LINEAR HAMILTONIAN SCHRÖDINGER EQUATION ON TORI Roberto Feola, Felice Iandoli To cite this version: Roberto Feola, Felice Iandoli. LOCAL WELL-POSEDNESS FOR THE QUASI-LINEAR HAMIL- TONIAN SCHRÖDINGER EQUATION ON TORI. 2020. hal-02504490v2 HAL Id: hal-02504490 https://hal.archives-ouvertes.fr/hal-02504490v2 Preprint submitted on 16 Mar 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. LOCAL WELL-POSEDNESS FOR THE QUASI-LINEAR HAMILTONIAN SCHRODINGER¨ EQUATION ON TORI ROBERTO FEOLA AND FELICE IANDOLI ABSTRACT. We prove a local in time well-posedness result for quasi-linear Hamiltonian Schrodinger¨ equa- d s tions on T for any d ≥ 1. For any initial condition in the Sobolev space H , with s large, we prove the existence and unicity of classical solutions of the Cauchy problem associated to the equation. The lifespan of such a solution depends only on the size of the initial datum. Moreover we prove the continuity of the solution map. CONTENTS 1. Introduction . 1 2. Functional setting . 3 3. Paralinearization of NLS . 13 4. Basic energy estimates . 15 5. Proof of the main Theorem 1.2 . -
June 1976 Table of Contents
CALENDAR This Calendar lists all of the meetings which have been approved by the Council up to the date this issue of the c}I/;Jiiai) was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Abstracts should be submitted on special forms which are available in most departments of mathematics; forms can also be obtained by writing to the headquarters of the Society. Abstracts to be presented at the meeting in person must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline for the meeting. Meeting Deadline for Abstracts* Number Date Place and News Items 737 August 24-28, 1976 Toronto, Canada June 15, 1976 (80th Summer Meeting) 738 October 30, 1976 Storrs, Connecticut September 7, 1976 739 November 6, 1976 Ann Arbor, Michigan September 7, 1976 740 November 19-20, 1976 Columbia, South Carolina September 28, 1976 741 November 19-20, 1976 All:uquerque, New Mexico September 28, 1976 742 January 27-31, 1977 St. Louis, Missouri November 3, 1976 (83rd Annual Meeting) March 31-Aprll 1, 1977 Huntsville, Alabama April15-16, 1977 Evanston, Wlnois April 22-23, 1977 Hayward, California August 14-18, 1977 Seattle, Washington (Slat Summer Meeting) November 11-12, 1977 Memphis, Tennessee Ja1Bl8ry 18-22, 1978 Atlanta, Georgia (84th Annual Meeting) January 11-15, -
Relativistic Astrophysics: the View from Texas in Baltimore (Review)
btropliysica/ Letters, 1981, Vol. 22, pp. 21-30 C> 1981 Gordon and Breach, Science Publishers, Inc. 0004-6388/81/2201-002 I $06.5010 Printed in the United States of America Relativistic Astrophysics: The View from Texas in Baltimore (Review) V. L. TRIMBLE Department of Physics, University of'Ca/ifornia. Irvine CA 92717 and Astronomy Program, University of Maryland College Park MD 20742 S. P. MARAN Laborarory for Astronomy and Solar Physics. NASA Goddard Space Flight Center, Greenbelt MD 20771 (Received July 7, 1981) · INTRODUCTION quantum theory and cannot be turned into one. It 0 is not renormalizable. That is, many seemingly The phrase relativistic astrophysics" was in sensible calculations yield infinite answers, and vented by Ivor Robinson, the late Alfred Schild, there is no coherent prescription for subtracting and Englebert Schucking on July 4th, 1963, as the infinite part to leave a finite, correct answer, part of the title of a symposium they were then in the way that quantum electrodynamics deals organizing at Dallas ("Conference on Gravita with the infinities of electromagnetism. tional Collapse and Other Topics in Relativistic 0 Even at the classical level, there may be linger Astrophysics ). The glory of the name, according ing doubts: Thomas Van Flandern (U.S. Naval to Robinson (who claims to have been out of the Observatory) finds, primarily from precise timings room at the crucial moment), was that no one of lunar occultations, that the constant of gravity knew what it meant, so they could have anything is decreasing by 3 parts in 10 11 per year, which is they wanted at the conference. -
Olga Ladyzhenskaya and Olga Oleinik: Two Great Women Mathematicians of the 20Th Century
“olga-ladyz-73” — 2004/12/15 — 10:21 — page 621 — #1 LA GACETA DE LA RSME, Vol. 7.3 (2004), 621–628 621 Olga Ladyzhenskaya and Olga Oleinik: two great women mathematicians of the 20th Century Susan Friedlander and Barbara Keyfitz This short article celebrates the contributions of women to partial dif- ferential equations and their applications. Although many women have made important contributions to this field, we have seen the recent deaths of two of the brightest stars –Olga Ladyzhenskaya and Olga Oleinik– and in their memory we focus on their work and their lives. The two Olgas had much in common and were also very different. Both were born in the 1920s in the Soviet Union and grew up during very diffi- cult years and survived the awful death and destruction of the 2nd world war. Shortly after the war they were students together at Moscow State University where they were both advised by I.G. Petrovsky, whose influ- ence on Moscow mathematics at the time was unsurpassed. Both were much influenced by the famous seminar of I.M.Gelfand and both young women received challenging problems in PDE from Gelfand. In 1947 both Olga’s graduated from Moscow State University and then their paths di- verged. Olga Oleinik remained in Moscow and continued to be supervised by Petrovsky. Her whole career was based in Moscow and after receiv- ing her PhD in 1954 she became first a professor and ultimately the Head of the department of Differential Equations at Moscow State Uni- versity. Olga Ladyzhenskaya moved in 1947 to Leningrad and her career developed at the Steklov Institute there. -
Phase Retrieval Via Wirtinger Flow: Theory and Algorithms
Phase Retrieval via Wirtinger Flow: Theory and Algorithms Emmanuel J. Cand`es∗ Xiaodong Li† Mahdi Soltanolkotabi‡ July 3, 2014; Revised January 2015 Abstract We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x ∈ Cn about which we have phaseless samples of the 2 form yr = S⟨ar; x⟩S , r = 1; : : : ; m (knowledge of the phase of these samples would yield a linear system). This paper develops a non-convex formulation of the phase retrieval problem as well as a concrete solution algorithm. In a nutshell, this algorithm starts with a careful initialization obtained by means of a spectral method, and then refines this initial estimate by iteratively applying novel update rules, which have low computational complexity, much like in a gradient descent scheme. The main contribution is that this algorithm is shown to rigorously allow the exact retrieval of phase information from a nearly minimal number of random measurements. Indeed, the sequence of successive iterates provably converges to the solution at a geometric rate so that the proposed scheme is efficient both in terms of computational and data resources. In theory, a variation on this scheme leads to a near-linear time algorithm for a physically realizable model based on coded diffraction patterns. We illustrate the effectiveness of our methods with various experiments on image data. Underlying our analysis are insights for the analysis of non- convex optimization schemes that may have implications for computational problems beyond phase retrieval. 1 Introduction We are interested in solving quadratic equations of the form 2 yr = S⟨ar; z⟩S ; r = 1; 2; : : : ; m; (1.1) n n where z ∈ C is the decision variable, ar ∈ C are known sampling vectors, and yr ∈ R are observed measurements.