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European Mathematical Society
CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF MARTIN RAUSSEN Department of Mathematical Sciences, Aalborg University Fredrik Bajers Vej 7G DK-9220 Aalborg, Denmark e-mail: [email protected] ASSOCIATE EDITORS VASILE BERINDE Department of Mathematics, University of Baia Mare, Romania NEWSLETTER No. 52 e-mail: [email protected] KRZYSZTOF CIESIELSKI Mathematics Institute June 2004 Jagiellonian University Reymonta 4, 30-059 Kraków, Poland EMS Agenda ........................................................................................................... 2 e-mail: [email protected] STEEN MARKVORSEN Editorial by Ari Laptev ........................................................................................... 3 Department of Mathematics, Technical University of Denmark, Building 303 EMS Summer Schools.............................................................................................. 6 DK-2800 Kgs. Lyngby, Denmark EC Meeting in Helsinki ........................................................................................... 6 e-mail: [email protected] ROBIN WILSON On powers of 2 by Pawel Strzelecki ........................................................................ 7 Department of Pure Mathematics The Open University A forgotten mathematician by Robert Fokkink ..................................................... 9 Milton Keynes MK7 6AA, UK e-mail: [email protected] Quantum Cryptography by Nuno Crato ............................................................ 15 COPY EDITOR: KELLY -
The Bibliography
Referenced Books [Ach92] N. I. Achieser. Theory of Approximation. Dover Publications Inc., New York, 1992. Reprint of the 1956 English translation of the 1st Rus- sian edition; the 2nd augmented Russian edition is available, Moscow, Nauka, 1965. [AH05] Kendall Atkinson and Weimin Han. Theoretical Numerical Analysis: A Functional Analysis Framework, volume 39 of Texts in Applied Mathe- matics. Springer, New York, second edition, 2005. [Atk89] Kendall E. Atkinson. An Introduction to Numerical Analysis. John Wiley & Sons Inc., New York, second edition, 1989. [Axe94] Owe Axelsson. Iterative Solution Methods. Cambridge University Press, Cambridge, 1994. [Bab86] K. I. Babenko. Foundations of Numerical Analysis [Osnovy chislennogo analiza]. Nauka, Moscow, 1986. [Russian]. [BD92] C. A. Brebbia and J. Dominguez. Boundary Elements: An Introductory Course. Computational Mechanics Publications, Southampton, second edition, 1992. [Ber52] S. N. Bernstein. Collected Works. Vol. I. The Constructive Theory of Functions [1905–1930]. Izdat. Akad. Nauk SSSR, Moscow, 1952. [Russian]. [Ber54] S. N. Bernstein. Collected Works. Vol. II. The Constructive Theory of Functions [1931–1953]. Izdat. Akad. Nauk SSSR, Moscow, 1954. [Russian]. [BH02] K. Binder and D. W. Heermann. Monte Carlo Simulation in Statistical Physics: An Introduction, volume 80 of Springer Series in Solid-State Sciences. Springer-Verlag, Berlin, fourth edition, 2002. [BHM00] William L. Briggs, Van Emden Henson, and Steve F. McCormick. A Multigrid Tutorial. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, second edition, 2000. [Boy01] John P. Boyd. Chebyshev and Fourier Spectral Methods. Dover Publi- cations Inc., Mineola, NY, second edition, 2001. [Bra84] Achi Brandt. Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, volume 85 of GMD-Studien [GMD Studies]. -
How a Minimal Surface Leaves an Obstacle
HOW A MINIMAL SURFACE LEAVES AN OBSTACLE BY DAVID KINDERLEHRER University of Minnesota, Minneapolis, MN 55455, USA (1) This paper is an investigation of the curve of separation determined by the solution to a variational inequality for minimal surfaces. A strictly convex domain ~ in the z = x 1 +ix~ plane is given together with a smooth function ~p which assumes a positive maxi- mum in ~ and is negative on ~, the boundary of ~. Let u denote the Lipschitz function which minimizes area among all Lipschitz functions in ~ constrained to lie above ~p in and to vanish on a~. For such u there is a coincidence set I c ~ consisting of those points z where u(z)=yJ(z). Let us call F={(xl, x~, xa): xa=u(z)=y~(z), zE~I} the "curve" of se- paration. The object of this paper is to show that F is analytic, as a function of its arc length parameter, provided that y; is strictly concave and analytic. The study of the coincidence set of the solution to a variational inequality and its curve of separation was originated, together with the study of the regularity of the solu- tion, by H. Lewy and G. Stampacchia ([11)]. They obtained, essentially, the result pre- sented here for the variational inequality derived from the Dirichlet Integral. The topo- logical conclusion that r is a Jordan curve was reached under the assumption that yJ E C2(~) be strictly concave, a conclusion valid for a wide variety of cases, in particular the problem treated in this paper ([6]). Our demonstration reties on the resolution of a system of differential equations and the utilization of the solution to extend analytically a conformal representation of the minimal surface which is the graph of u in the subset of ~ where u(z)>~(z). -
A Complete Bibliography of Publications in SIAM Journal on Mathematical Analysis, 1970–1999
A Complete Bibliography of Publications in SIAM Journal on Mathematical Analysis, 1970{1999 Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 13 March 2018 Version 3.14 ∗ Title word cross-reference aK(at);a! 0 [Log79b]. B [Rei79]. BC1 [Ask82]. β [HT87]. BV (Ω) [AK99]. C1 [Coh89]. C3 [McC97]. Cα [YL94]. Cα(Ω) [XA91]. Cp [Rea86b]. C [Yao95]. C (T ) #11889 [Spe79]. 0 0 [Wu90]. C` [Mil94]. A [FM99]. D [Har80]. D O(2) [ML93]. Dr u(x; t)=D u(x; t) (−1; 1) [LS93]. (−∞; 1)[Pas74]. n x t 0 0 [Kem82a]. (m(t)x (t)) + A(t)x(t)=0[Ede79]. k ∗ 0 0 0 D U(X1; ···;Xr)=DX U(X1; ···;Xr) (p(x)u (x)) + g(x)u (x)+qu(x)=f [Whi79]. X1 k [Kem85]. DA [Har80]. δ [Lan83b]. ∆2u = λu (φ(y0)) = qf(t; y; y0); 0 <t<1[O'R93]. [Cof82]. ∆ u(x)+F (x)u(x)=0[CG71]. (r(t) (x)x0)0 + a(t)f(x) = 0 [MR79a]. p+2 ∆ + K2 = 0 [Kal75]. 0 <p(x) 2 L1[a; b] [Whi79]. 0 ≤ x ≤ l − ∆u + K(jxj)jujp 1u = 0 [Yan96]. [CL73]. 2 [AJV94, CW99]. 2m + 1 [Sho70]. − − ∆u + jujp 1u −|ujq 1u = 0 [Tro90]. E3 2π [FR91]. 2π/m [FR91]. 3 [KoM98]. -
Writing the History of Dynamical Systems and Chaos
Historia Mathematica 29 (2002), 273–339 doi:10.1006/hmat.2002.2351 Writing the History of Dynamical Systems and Chaos: View metadata, citation and similar papersLongue at core.ac.uk Dur´ee and Revolution, Disciplines and Cultures1 brought to you by CORE provided by Elsevier - Publisher Connector David Aubin Max-Planck Institut fur¨ Wissenschaftsgeschichte, Berlin, Germany E-mail: [email protected] and Amy Dahan Dalmedico Centre national de la recherche scientifique and Centre Alexandre-Koyre,´ Paris, France E-mail: [email protected] Between the late 1960s and the beginning of the 1980s, the wide recognition that simple dynamical laws could give rise to complex behaviors was sometimes hailed as a true scientific revolution impacting several disciplines, for which a striking label was coined—“chaos.” Mathematicians quickly pointed out that the purported revolution was relying on the abstract theory of dynamical systems founded in the late 19th century by Henri Poincar´e who had already reached a similar conclusion. In this paper, we flesh out the historiographical tensions arising from these confrontations: longue-duree´ history and revolution; abstract mathematics and the use of mathematical techniques in various other domains. After reviewing the historiography of dynamical systems theory from Poincar´e to the 1960s, we highlight the pioneering work of a few individuals (Steve Smale, Edward Lorenz, David Ruelle). We then go on to discuss the nature of the chaos phenomenon, which, we argue, was a conceptual reconfiguration as -
UCLA Electronic Theses and Dissertations
UCLA UCLA Electronic Theses and Dissertations Title Algorithms for Optimal Paths of One, Many, and an Infinite Number of Agents Permalink https://escholarship.org/uc/item/3qj5d7dj Author Lin, Alex Tong Publication Date 2020 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA Los Angeles Algorithms for Optimal Paths of One, Many, and an Infinite Number of Agents A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Mathematics by Alex Tong Lin 2020 c Copyright by Alex Tong Lin 2020 ABSTRACT OF THE DISSERTATION Algorithms for Optimal Paths of One, Many, and an Infinite Number of Agents by Alex Tong Lin Doctor of Philosophy in Mathematics University of California, Los Angeles, 2020 Professor Stanley J. Osher, Chair In this dissertation, we provide efficient algorithms for modeling the behavior of a single agent, multiple agents, and a continuum of agents. For a single agent, we combine the modeling framework of optimal control with advances in optimization splitting in order to efficiently find optimal paths for problems in very high-dimensions, thus providing allevia- tion from the curse of dimensionality. For a multiple, but finite, number of agents, we take the framework of multi-agent reinforcement learning and utilize imitation learning in order to decentralize a centralized expert, thus obtaining optimal multi-agents that act in a de- centralized fashion. For a continuum of agents, we take the framework of mean-field games and use two neural networks, which we train in an alternating scheme, in order to efficiently find optimal paths for high-dimensional and stochastic problems. -
Prizes and Awards Session
PRIZES AND AWARDS SESSION Wednesday, July 12, 2021 9:00 AM EDT 2021 SIAM Annual Meeting July 19 – 23, 2021 Held in Virtual Format 1 Table of Contents AWM-SIAM Sonia Kovalevsky Lecture ................................................................................................... 3 George B. Dantzig Prize ............................................................................................................................. 5 George Pólya Prize for Mathematical Exposition .................................................................................... 7 George Pólya Prize in Applied Combinatorics ......................................................................................... 8 I.E. Block Community Lecture .................................................................................................................. 9 John von Neumann Prize ......................................................................................................................... 11 Lagrange Prize in Continuous Optimization .......................................................................................... 13 Ralph E. Kleinman Prize .......................................................................................................................... 15 SIAM Prize for Distinguished Service to the Profession ....................................................................... 17 SIAM Student Paper Prizes .................................................................................................................... -
A Complete Bibliography of Publications in Nordisk Tidskrift for Informationsbehandling, BIT, and BIT Numerical Mathematics
A Complete Bibliography of Publications in Nordisk Tidskrift for Informationsbehandling, BIT,andBIT Numerical Mathematics Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 09 June 2021 Version 3.54 Title word cross-reference [3105, 328, 469, 655, 896, 524, 873, 455, 779, 946, 2944, 297, 1752, 670, 2582, 1409, 1987, 915, 808, 761, 916, 2071, 2198, 1449, 780, 959, 1105, 1021, 497, 2589]. A(α) #24873 [1089]. [896, 2594, 333]. A∗ [2013]. A∗Ax = b [2369]. n A [1640, 566, 947, 1580, 1460]. A = a2 +1 − 0 n (3) [2450]. (A λB) [1414]. 0=1 [1242]. 1 [334]. α [824, 1580]. AN [1622]. A(#) [3439]. − 12 [3037, 2711]. 1 2 [1097]. 1:0 [3043]. 10 AX − XB = C [2195, 2006]. [838]. 11 [1311]. 2 AXD − BXC = E [1101]. B [2144, 1953, 2291, 2162, 3047, 886, 2551, 957, [2187, 1575, 1267, 1409, 1489, 1991, 1191, 2007, 2552, 1832, 949, 3024, 3219, 2194]. 2; 3 979, 1819, 1597, 1823, 1773]. β [824]. BN n − p − − [1490]. 2 1 [320]. 2 1 [100]. 2m 4 [1181]. BS [1773]. BSI [1446]. C0 [2906]. C1 [1105]. 3 [2119, 1953, 2531, 1351, 2551, 1292, [3202]. C2 [3108, 2422, 3000, 2036]. χ2 1793, 949, 1356, 2711, 2227, 570]. [30, 31]. Cln(θ); (n ≥ 2) [2929]. cos [228]. D 3; 000; 000; 000 [575, 637]. -
Boundary Value Problems for Systems That Are Not Strictly
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Applied Mathematics Letters 24 (2011) 757–761 Contents lists available at ScienceDirect Applied Mathematics Letters journal homepage: www.elsevier.com/locate/aml On mixed initial–boundary value problems for systems that are not strictly hyperbolic Corentin Audiard ∗ Institut Camille Jordan, Université Claude Bernard Lyon 1, Villeurbanne, Rhone, France article info a b s t r a c t Article history: The classical theory of strictly hyperbolic boundary value problems has received several Received 25 June 2010 extensions since the 70s. One of the most noticeable is the result of Metivier establishing Received in revised form 23 December 2010 Majda's ``block structure condition'' for constantly hyperbolic operators, which implies Accepted 28 December 2010 well-posedness for the initial–boundary value problem (IBVP) with zero initial data. The well-posedness of the IBVP with non-zero initial data requires that ``L2 is a continuable Keywords: initial condition''. For strictly hyperbolic systems, this result was proven by Rauch. We Boundary value problem prove here, by using classical matrix theory, that his fundamental a priori estimates are Hyperbolicity Multiple characteristics valid for constantly hyperbolic IBVPs. ' 2011 Elsevier Ltd. All rights reserved. 1. Introduction In his seminal paper [1] on hyperbolic initial–boundary value problems, H.O. Kreiss performed the algebraic construction of a tool, now called the Kreiss symmetrizer, that leads to a priori estimates. Namely, if u is a solution of 8 d X C >@ u C A .x; t/@ u D f ;.t; x/ 2 × Ω; <> t j xj R jD1 (1) C >Bu D g;.t; x/ 2 @ × @Ω; :> R ujtD0 D 0; C Pd where the operator @t jD1 Aj@xj is assumed to be strictly hyperbolic and B satisfies the uniform Lopatinski˘ı condition, there is some γ0 > 0 such that u satisfies the a priori estimate p γ kuk 2 C C kuk 2 C ≤ C kf k 2 C C kgk 2 C ; (2) Lγ .R ×Ω/ Lγ .R ×@Ω/ Lγ .R ×Ω/ Lγ .R ×@Ω/ 2 2 −γ t for γ ≥ γ0. -
Calculus Redux
THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA VOLUME 6 NUMBER 2 MARCH-APRIL 1986 Calculus Redux Paul Zorn hould calculus be taught differently? Can it? Common labus to match, little or no feedback on regular assignments, wisdom says "no"-which topics are taught, and when, and worst of all, a rich and powerful subject reduced to Sare dictated by the logic of the subject and by client mechanical drills. departments. The surprising answer from a four-day Sloan Client department's demands are sometimes blamed for Foundation-sponsored conference on calculus instruction, calculus's overcrowded and rigid syllabus. The conference's chaired by Ronald Douglas, SUNY at Stony Brook, is that first surprise was a general agreement that there is room for significant change is possible, desirable, and necessary. change. What is needed, for further mathematics as well as Meeting at Tulane University in New Orleans in January, a for client disciplines, is a deep and sure understanding of diverse and sometimes contentious group of twenty-five fac the central ideas and uses of calculus. Mac Van Valkenberg, ulty, university and foundation administrators, and scientists Dean of Engineering at the University of Illinois, James Ste from client departments, put aside their differences to call venson, a physicist from Georgia Tech, and Robert van der for a leaner, livelier, more contemporary course, more sharply Vaart, in biomathematics at North Carolina State, all stressed focused on calculus's central ideas and on its role as the that while their departments want to be consulted, they are language of science. less concerned that all the standard topics be covered than That calculus instruction was found to be ailing came as that students learn to use concepts to attack problems in a no surprise. -
Curriculum Vitae
Umberto Mosco WPI Harold J. Gay Professor of Mathematics May 18, 2021 Department of Mathematical Sciences Phone: (508) 831-5074, Worcester Polytechnic Institute Fax: (508) 831-5824, Worcester, MA 01609 Email: [email protected] Curriculum Vitae Current position: Harold J. Gay Professor of Mathematics, Worcester Polytechnic Institute, Worcester MA, U.S.A. Languages: English, French, German, Italian (mother language) Specialization: Applied Mathematics Research Interests:: Fractal and Partial Differential Equations, Homog- enization, Finite Elements Methods, Stochastic Optimal Control, Variational Inequalities, Potential Theory, Convex Analysis, Functional Convergence. Twelve Most Relevant Research Articles 1. Time, Space, Similarity. Chapter of the book "New Trends in Differential Equations, Control Theory and Optimization, pp. 261-276, WSPC-World Scientific Publishing Company, Hackenseck, NJ, 2016. 2. Layered fractal fibers and potentials (with M.A.Vivaldi). J. Math. Pures Appl. 103 (2015) pp. 1198-1227. (Received 10.21.2013, Available online 11.4.2014). 3. Vanishing viscosity for fractal sets (with M.A.Vivaldi). Discrete and Con- tinuous Dynamical Systems - Special Volume dedicated to Louis Niren- berg, 28, N. 3, (2010) pp. 1207-1235. 4. Fractal reinforcement of elastic membranes (with M.A.Vivaldi). Arch. Rational Mech. Anal. 194, (2009) pp. 49-74. 5. Gauged Sobolev Inequalities. Applicable Analysis, 86, no. 3 (2007), 367- 402. 6. Invariant field metrics and dynamic scaling on fractals. Phys. Rev. Let- ters, 79, no. 21, Nov. (1997), pp. 4067-4070. 7. Variational fractals. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997) No. 3-4, pp. 683-712. 8. A Saint-Venant type principle for Dirichlet forms on discontinuous media (with M. -
Fourth SIAM Conference on Applications of Dynamical Systems
Utah State University DigitalCommons@USU All U.S. Government Documents (Utah Regional U.S. Government Documents (Utah Regional Depository) Depository) 5-1997 Fourth SIAM Conference on Applications of Dynamical Systems SIAM Activity Group on Dynamical Systems Follow this and additional works at: https://digitalcommons.usu.edu/govdocs Part of the Physical Sciences and Mathematics Commons Recommended Citation Final program and abstracts, May 18-22, 1997 This Other is brought to you for free and open access by the U.S. Government Documents (Utah Regional Depository) at DigitalCommons@USU. It has been accepted for inclusion in All U.S. Government Documents (Utah Regional Depository) by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. tI...~ Confers ~'t' '"' \ 1I~c9 ~ 1'-" ~ J' .. c "'. to APPLICAliONS cJ May 18-22, 1997 Snowbird Ski and Summer Resort • Snowbird, Utah Sponsored by SIAM Activity Group on Dynamical Systems Conference Themes The themes of the 1997 conference will include the following topics. Principal Themes: • Dynamics in undergraduate education • Experimental studies of nonlinear phenomena • Hamiltonian systems and transport • Mathematical biology • Noise in dynamical systems • Patterns and spatio-temporal chaos Applications in • Synchronization • Aerospace engineering • Biology • Condensed matter physics • Control • Fluids • Manufacturing • Me;h~~~~nograPhY 19970915 120 • Lasers and o~ • Quantum UldU) • 51a m.@ Society for Industrial and Applied Mathematics http://www.siam.org/meetingslds97/ds97home.htm 2 " DYNAMICAL SYSTEMS Conference Prl Contents A Message from the Conference Chairs ... Get-Togethers 2 Dear Colleagues: Welcoming Message 2 Welcome to Snowbird for the Fourth SIAM Conference on Applications of Dynamica Systems. Organizing Committee 2 This highly interdisciplinary meeting brings together a diverse group of mathematicians Audiovisual Notice 2 scientists, and engineers, all working on dynamical systems and their applications.