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Graphs and Patterns in Mathematics and Theoretical Physics, Volume 73
http://dx.doi.org/10.1090/pspum/073 Graphs and Patterns in Mathematics and Theoretical Physics This page intentionally left blank Proceedings of Symposia in PURE MATHEMATICS Volume 73 Graphs and Patterns in Mathematics and Theoretical Physics Proceedings of the Conference on Graphs and Patterns in Mathematics and Theoretical Physics Dedicated to Dennis Sullivan's 60th birthday June 14-21, 2001 Stony Brook University, Stony Brook, New York Mikhail Lyubich Leon Takhtajan Editors Proceedings of the conference on Graphs and Patterns in Mathematics and Theoretical Physics held at Stony Brook University, Stony Brook, New York, June 14-21, 2001. 2000 Mathematics Subject Classification. Primary 81Txx, 57-XX 18-XX 53Dxx 55-XX 37-XX 17Bxx. Library of Congress Cataloging-in-Publication Data Stony Brook Conference on Graphs and Patterns in Mathematics and Theoretical Physics (2001 : Stony Brook University) Graphs and Patterns in mathematics and theoretical physics : proceedings of the Stony Brook Conference on Graphs and Patterns in Mathematics and Theoretical Physics, June 14-21, 2001, Stony Brook University, Stony Brook, NY / Mikhail Lyubich, Leon Takhtajan, editors. p. cm. — (Proceedings of symposia in pure mathematics ; v. 73) Includes bibliographical references. ISBN 0-8218-3666-8 (alk. paper) 1. Graph Theory. 2. Mathematics-Graphic methods. 3. Physics-Graphic methods. 4. Man• ifolds (Mathematics). I. Lyubich, Mikhail, 1959- II. Takhtadzhyan, L. A. (Leon Armenovich) III. Title. IV. Series. QA166.S79 2001 511/.5-dc22 2004062363 Copying and reprinting. Material in this book may be reproduced by any means for edu• cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg• ment of the source is given. -
Professor Peter Goldreich Member of the Board of Adjudicators Chairman of the Selection Committee for the Prize in Astronomy
The Shaw Prize The Shaw Prize is an international award to honour individuals who are currently active in their respective fields and who have recently achieved distinguished and significant advances, who have made outstanding contributions in academic and scientific research or applications, or who in other domains have achieved excellence. The award is dedicated to furthering societal progress, enhancing quality of life, and enriching humanity’s spiritual civilization. Preference is to be given to individuals whose significant work was recently achieved and who are currently active in their respective fields. Founder's Biographical Note The Shaw Prize was established under the auspices of Mr Run Run Shaw. Mr Shaw, born in China in 1907, was a native of Ningbo County, Zhejiang Province. He joined his brother’s film company in China in the 1920s. During the 1950s he founded the film company Shaw Brothers (HK) Limited in Hong Kong. He was one of the founding members of Television Broadcasts Limited launched in Hong Kong in 1967. Mr Shaw also founded two charities, The Shaw Foundation Hong Kong and The Sir Run Run Shaw Charitable Trust, both dedicated to the promotion of education, scientific and technological research, medical and welfare services, and culture and the arts. ~ 1 ~ Message from the Chief Executive I warmly congratulate the six Shaw Laureates of 2014. Established in 2002 under the auspices of Mr Run Run Shaw, the Shaw Prize is a highly prestigious recognition of the role that scientists play in shaping the development of a modern world. Since the first award in 2004, 54 leading international scientists have been honoured for their ground-breaking discoveries which have expanded the frontiers of human knowledge and made significant contributions to humankind. -
2011/2012 Black History Trivia Bowl Study Questions # CATEGORY
2011/2012 Black History Trivia Bowl Study Questions # CATEGORY QUESTION ANSWER Along the Gulf Coast of Louisiana, what type of music is played 1 Arts with the accordion? Zydeco 2 Arts Who wrote "Their Eyes Were Watching God" ? Zora Neale Hurston Which one of composer/pianist Anthony Davis' operas premiered in Philadelphia in 1985 and was performed by the X: The Life and Times of 3 Arts New York City Opera in 1986? Malcolm X Since 1987, who has held the position of director of jazz at 4 Arts Lincoln Center for the Performing Arts in New York City? Wynton Marsalis Of what profession were Langston Hughes, Zora Neale Hurston, and Countee Cullen, major contributors to the Harlem 5 Arts Renaissance? Writers Who wrote Clotel , or The President’s Daughter , the first 6 Arts published novel by a Black American in 1833? William Wells Brown Who published The Escape , the first play written by a Black 7 Arts American? William Wells Brown 8 Arts What is the given name of blues great W.C. Handy? William Christopher Handy What aspiring fiction writer, journalist, and Hopkinsville native, served as editor of three African American weeklies: the Indianapolis Recorder , the Freeman , and the Indianapolis William Alexander 9 Arts Ledger ? Chambers 10 Arts Nat Love wrote what kind of stories? Westerns Cartoonist Morrie Turner created what world famous syndicated 11 Arts comic strip? Wee Pals Who was born in Florence, Alabama in 1873 and is called 12 Arts “Father of the Blues”? WC Handy Georgia Douglas Johnson was a poet during the Harlem Renaissance era. -
ABSTRACT Chaos in Dendritic and Circular Julia Sets Nathan Averbeck, Ph.D. Advisor: Brian Raines, D.Phil. We Demonstrate The
ABSTRACT Chaos in Dendritic and Circular Julia Sets Nathan Averbeck, Ph.D. Advisor: Brian Raines, D.Phil. We demonstrate the existence of various forms of chaos (including transitive distributional chaos, !-chaos, topological chaos, and exact Devaney chaos) on two families of abstract Julia sets: the dendritic Julia sets Dτ and the \circular" Julia sets Eτ , whose symbolic encoding was introduced by Stewart Baldwin. In particular, suppose one of the two following conditions hold: either fc has a Julia set which is a dendrite, or (provided that the kneading sequence of c is Γ-acceptable) that fc has an attracting or parabolic periodic point. Then, by way of a conjugacy which allows us to represent these Julia sets symbolically, we prove that fc exhibits various forms of chaos. Chaos in Dendritic and Circular Julia Sets by Nathan Averbeck, B.S., M.A. A Dissertation Approved by the Department of Mathematics Lance L. Littlejohn, Ph.D., Chairperson Submitted to the Graduate Faculty of Baylor University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Approved by the Dissertation Committee Brian Raines, D.Phil., Chairperson Will Brian, D.Phil. Markus Hunziker, Ph.D. Alexander Pruss, Ph.D. David Ryden, Ph.D. Accepted by the Graduate School August 2016 J. Larry Lyon, Ph.D., Dean Page bearing signatures is kept on file in the Graduate School. Copyright c 2016 by Nathan Averbeck All rights reserved TABLE OF CONTENTS LIST OF FIGURES vi ACKNOWLEDGMENTS vii DEDICATION viii 1 Preliminaries 1 1.1 Continuum Theory and Dynamical Systems . 1 1.2 Unimodal Maps . -
ABSTRACT the Specification Property and Chaos In
ABSTRACT The Specification Property and Chaos in Multidimensional Shift Spaces and General Compact Metric Spaces Reeve Hunter, Ph.D. Advisor: Brian E. Raines, D.Phil. Rufus Bowen introduced the specification property for maps on a compact met- ric space. In this dissertation, we consider some implications of the specification d property for Zd-actions on subshifts of ΣZ as well as on a general compact metric space. In particular, we show that if σ : X X is a continuous Zd-action with ! d a weak form of the specification property on a d-dimensional subshift of ΣZ , then σ exhibits both !-chaos, introduced by Li, and uniform distributional chaos, intro- duced by Schweizer and Smítal. The !-chaos result is further generalized for some broader, directional notions of limit sets and general compact metric spaces with uniform expansion at a fixed point. The Specification Property and Chaos in Multidimensional Shift Spaces and General Compact Metric Spaces by Reeve Hunter, B.A. A Dissertation Approved by the Department of Mathematics Lance L. Littlejohn, Ph.D., Chairperson Submitted to the Graduate Faculty of Baylor University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Approved by the Dissertation Committee Brian E. Raines, D.Phil., Chairperson Nathan Alleman, Ph.D. Will Brian, D.Phil. Markus Hunziker, Ph.D. David Ryden, Ph.D. Accepted by the Graduate School August 2016 J. Larry Lyon, Ph.D., Dean Page bearing signatures is kept on file in the Graduate School. Copyright c 2016 by Reeve Hunter All rights reserved TABLE OF CONTENTS LIST OF FIGURES vi ACKNOWLEDGMENTS vii DEDICATION viii 1 Introduction 1 2 Preliminaries 4 2.1 Dynamical Systems . -
Measuring Complexity in Cantor Dynamics
Measuring Complexity in Cantor Dynamics Karl Petersen cantorsalta2015: Dynamics on Cantor Sets CIMPA Research School, 2-13 November 2015 December 11, 2017 1 Contents Contents 2 1 Introduction 5 1.1 Preface . 5 1.2 Complexity and entropy . 5 1.3 Some definitions and notation . 5 1.4 Realizations of systems . 7 2 Asymptotic exponential growth rate 9 2.1 Topological entropy . 9 2.2 Ergodic-theoretic entropy . 9 2.3 Measure-theoretic sequence entropy . 13 2.4 Topological sequence entropy . 13 2.5 Slow entropy . 14 2.6 Entropy dimension . 17 2.7 Permutation entropy . 18 2.8 Independence entropy . 19 2.9 Sofic, Rokhlin, na¨ıve entropies . 20 2.10 Kolmogorov complexity . 23 3 Counting patterns 25 3.1 The complexity function in one-dimensional symbolic dynamics . 25 3.2 Sturmian sequences . 26 3.3 Episturmian sequences . 28 3.4 The Morse sequence . 29 3.5 In higher dimensions, tilings, groups, etc. 29 3.6 Topological complexity . 31 3.7 Low complexity, the number of ergodic measures, automorphisms . 31 3.8 Palindrome complexity . 33 3.9 Nonrepetitive complexity and Eulerian entropy . 35 3.10 Mean topological dimension . 36 3.11 Amorphic complexity via asymptotic separation numbers . 37 3.12 Inconstancy . 38 3.13 Measure-theoretic complexity . 38 3.14 Pattern complexity . 39 4 Balancing freedom and interdependence 41 4.1 Neurological intricacy . 41 4.2 Topological intricacy and average sample complexity . 43 4.3 Ergodic-theoretic intricacy and average sample complexity . 46 4.4 The average sample complexity function . 46 4.5 Computing measure-theoretic average sample complexity . -
Order-Of-Magnitude Physics: Understanding the World with Dimensional Analysis, Educated Guesswork, and White Lies Peter Goldreic
Order-of-Magnitude Physics: Understanding the World with Dimensional Analysis, Educated Guesswork, and White Lies Peter Goldreich, California Institute of Technology Sanjoy Mahajan, University of Cambridge Sterl Phinney, California Institute of Technology Draft of 1 August 1999 c 1999 Send comments to [email protected] ii Contents 1 Wetting Your Feet 1 1.1 Warmup problems 1 1.2 Scaling analyses 13 1.3 What you have learned 21 2 Dimensional Analysis 23 2.1 Newton’s law 23 2.2 Pendula 27 2.3 Drag in fluids 31 2.4 What you have learned 41 3 Materials I 43 3.1 Sizes 43 3.2 Energies 51 3.3 Elastic properties 53 3.4 Application to white dwarfs 58 3.5 What you have learned 62 4 Materials II 63 4.1 Thermal expansion 63 4.2 Phase changes 65 4.3 Specific heat 73 4.4 Thermal diffusivity of liquids and solids 77 4.5 Diffusivity and viscosity of gases 79 4.6 Thermal conductivity 80 4.7 What you have learned 83 5 Waves 85 5.1 Dispersion relations 85 5.2 Deep water 88 5.3 Shallow water 106 5.4 Combining deep- and shallow-water gravity waves 108 5.5 Combining deep- and shallow-water ripples 108 5.6 Combining all the analyses 109 5.7 What we did 109 Bibliography 110 1 1 Wetting Your Feet Most technical education emphasizes exact answers. If you are a physicist, you solve for the energy levels of the hydrogen atom to six decimal places. If you are a chemist, you measure reaction rates and concentrations to two or three decimal places. -
ONE HUNDRED YEARS of COMPLEX DYNAMICS the Subject of Complex Dynamics, That Is, the Behaviour of Orbits of Holomorphic Functions
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by University of Liverpool Repository ONE HUNDRED YEARS OF COMPLEX DYNAMICS MARY REES The subject of Complex Dynamics, that is, the behaviour of orbits of holomorphic functions, emerged in the papers produced, independently, by Fatou and Julia, almost 100 years ago. Although the subject of Dynami- cal Systems did not then have a name, the dynamical properties found for holomorphic systems, even in these early researches, were so striking, so unusually comprehensive, and yet so varied, that these systems still attract widespread fascination, 100 years later. The first distinctive feature of iter- ation of a single holomorphic map f is the partition of either the complex plane or the Riemann sphere into two sets which are totally invariant under f: the Julia set | closed, nonempty, perfect, with dynamics which might loosely be called chaotic | and its complement | open, possibly empty, but, if non-empty, then with dynamics which were completely classified by the two pioneering researchers, modulo a few simply stated open questions. Before the subject re-emerged into prominence in the 1980's, the Julia set was alternately called the Fatou set, but Paul Blanchard introduced the idea of calling its complement the Fatou set, and this was immediately universally accepted. Probably the main reason for the remarkable rise in interest in complex dynamics, about thirty-five years ago, was the parallel with the subject of Kleinian groups, and hence with the whole subject of hyperbolic geome- try. A Kleinian group acting on the Riemann sphere is a dynamical system, with the sphere splitting into two disjoint invariant subsets, with the limit set and its complement, the domain of discontinuity, having exactly similar properties to the Julia and Fatou sets. -
Arxiv:1111.3682V1 [Astro-Ph.EP] 15 Nov 2011 Ant Planets, As Well As Their Dynamical Architecture (I.E
Draft version November 17, 2011 Preprint typeset using LATEX style emulateapj v. 11/10/09 INSTABILITY-DRIVEN DYNAMICAL EVOLUTION MODEL OF A PRIMORDIALLY 5 PLANET OUTER SOLAR SYSTEM Konstantin Batygin1, Michael E. Brown1 & Hayden Betts2 1Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 and 2Polytechnic School, Pasadena, CA 91106 Draft version November 17, 2011 ABSTRACT Over the last decade, evidence has mounted that the solar system's observed state can be favorably reproduced in the context of an instability-driven dynamical evolution model, such as the \Nice" model. To date, all successful realizations of instability models have concentrated on evolving the four giant planets onto their current orbits from a more compact configuration. Simultaneously, the possibility of forming and ejecting additional planets has been discussed, but never successfully implemented. Here we show that a large array of 5-planet (2 gas giants + 3 ice giants) multi-resonant initial states can lead to an adequate formation of the outer solar system, featuring an ejection of an ice giant during a phase of instability. Particularly, our simulations demonstrate that the eigenmodes which characterize the outer solar system's secular dynamics can be closely matched with a 5-planet model. Furthermore, provided that the ejection timescale of the extra planet is short, orbital excitation of a primordial cold classical Kuiper belt can also be avoided in this scenario. Thus the solar system is one of many possible outcomes of dynamical relaxation and can originate from a wide variety of initial states. This deems the construction of a unique model of solar system's early dynamical evolution impossible. -
CV Background
Steven Soter CV 2013 Research Associate, Department of Astrophysics, American Museum of Natural History, Central Park West at 79th Street, New York, NY 10024. Visiting Professor, Environmental Studies Program, New York University, 285 Mercer Street, 9th Floor, New York, NY 10003, and Email: <[email protected]>. Tel: 212-769-5230. RECENT ACTIVITIES Research in astronomy and geoarchaeology. Teaching at NYU: courses on Scientific Thinking and Speculation, Geology and Antiquity in the Mediterranean, Life in the Universe, Climate Change, and Energy and Environment. BACKGROUND AND EDUCATION Born in Los Angeles, California, May 1943 BSc in Astronomy/Physics, 1965 University of California at Los Angeles (Advisors: George Abell and Peter Goldreich) PhD in Astronomy, 1971 Cornell University, Ithaca, New York (Advisors: Thomas Gold, Carl Sagan, Joseph Burns) PREVIOUS POSITIONS 1964-66 Research Assistant, Radio Astronomy Project, Aerospace Corporation, El Segundo, California 1966-71 Research Assistant, Center for Radiophysics and 1973-79 Space Research, Cornell University, Ithaca, N.Y. 1971-73 Postdoctoral Fellow, Miller Institute for Basic Research in Science, UC Berkeley 1973-79 Assistant Editor, ICARUS: International Journal of Solar System Studies (Carl Sagan, editor) 1977-80 Co-Writer and Head of Research, COSMOS Television Series, KCET/Los Angeles 1980-87 Senior Research Associate, Center for Radiophyscs and Space Research, Cornell University 1988-97 Special Assistant to the Director, National Air and Space Museum, Smithsonian Institution, Washington, DC 1997-03 Scientist, Hayden Planetarium American Museum of Natural History, New York 2004-13 Research Associate, Department of Astrophysics, American Museum of Natural History, New York 2005-07 Scientist-in-Residence, Center for Ancient Studies, New York University, New York 2008-12 Visiting Professor, Environmental Studies Program, New York University, New York . -
Cobb Plummer, Jewel Dates
Cal State LA Special Collections & Archives Jewel Plummer Cobb Collection Title: Jewel Plummer Cobb Collection Collection Number: 2015.012 Creator: Cobb Plummer, Jewel Dates: 1964-1995 Extent: 16.25 linear ft. Repository: California State University, Los Angeles, John F. Kennedy Memorial Library, Special Collections and Archives Location: Special Collections & Archives, Palmer, 4th floor Room 4048 - A Provenance: Donated by Jewel Plummer Cobb Processing Information: Processed by Amalia Castañeda 2015 Arrangement: The collection is organized into seven series: I. Publications; II. Writings and Research; III. Conferences, Meetings, Seminars and Workshops; IV. Topical Files; IV. Clippings; VI. Legislation Related Documents Acts; VII. Biographical Copyright: The Cobb Collection is the physical property of California State University, Los Angeles, John F. Kennedy Memorial Library, Special Collections and Archives. Preferred Citation: Folder title, Series, Box number, Collection tile, followed by Special Collections and Archives, John F. Kennedy Memorial Library, California State University, Los Angeles Historical/Biographical Note Jewel Plummer Cobb (1924- ), a distinguished African American biologist and academic administrator, is widely credited for her contributions to the scientific community, both through her cancer research and her commitment to equal access to educational and professional opportunities for women and minorities. The daughter of a physician and school teacher, Cobb developed interested in a science career as a high school student. She began her undergraduate career at University of Michigan but transferred to a historically black college after encountering a campus climate plagued by racial discrimination. After earning a PhD in Cell Physiology from NYU in 1950, she became a fellow at the National Cancer Institute. After directing the Tissue Culture Laboratory at the University of 1 Illinois, in 1967 she was appointed Dean and Professor of Zoology at Connecticut College. -
PUZZLES and PROSPECTS in PLANETARY RING DYNAMICS PETER GOLDREICH California Institute of Technology Abstract. I Outline Some Of
PUZZLES AND PROSPECTS IN PLANETARY RING DYNAMICS PETER GOLDREICH California Institute of Technology Abstract. I outline some of the main processes that shape planetary rings. Then I focus on two outstanding issues, the role of self-gravity in the precession of narrow rings and the dynamics of Neptune's arcs. By airing these well-defined but unsolved problems, I hope to encourage others to join me in the quest for their solutions. 1. Introduction The 15 years just past have witnessed an explosion in our knowledge of planetary rings. Jupiter, Uranus, and Neptune have joined Saturn as members of the family of ringed planets. We have come to appreciate that a few simple physical mechanisms account for the bewildering variety of structures displayed by ring systems. With the completion of the Voyager missions, the level of activity in this field will decline. Major new discoveries probably must await the arrival of the Cassini spacecraft at Saturn a decade hence. Planetary rings were the focus of my research for several years. Although this has not been the case for some time, and may never be again, they still hold my interest. After struggling to understand various issues, I feel well-situated to offer a commentary on unsolved problems. That is my aim here. After a brief review of some of the processes at work in rings, I shall focus attention on two outstanding puzzles. The first involves the precession of narrow rings and, in particular, the role played by the self-gravity of the ring material. The second concerns the mechanisms responsible for the unusual morphology of Neptune's ring arcs.