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Final Poster
Associating Finite Groups with Dessins d’Enfants Luis Baeza, Edwin Baeza, Conner Lawrence, and Chenkai Wang Abstract Platonic Solids Rotation Group Dn: Regular Convex Polygon Approach Each finite, connected planar graph has an automorphism group G;such Following Magot and Zvonkin, reduce to easier cases using “hypermaps” permutations can be extended to automorphisms of the Riemann sphere φ : P1(C) P1(C), then composing β = φ f where S 2(R) P1(C). In 1984, Alexander Grothendieck, inspired by a result of f : 1( ) ! 1( )isaBely˘ımapasafunctionofeither◦ zn or ' P C P C Gennadi˘ıBely˘ıfrom 1979, constructed a finite, connected planar graph 4 zn/(zn +1)! 2 such that Aut(f ) Z or Aut(f ) D ,respectively. ' n ' n ∆β via certain rational functions β(z)=p(z)/q(z)bylookingatthe inverse image of the interval from 0 to 1. The automorphisms of such a Hypermaps: Rotation Group Zn graph can be identified with the Galois group Aut(β)oftheassociated 1 1 rational function β : P (C) P (C). In this project, we investigate how Rigid Rotations of the Platonic Solids I Wheel/Pyramids (J1, J2) ! w 3 (w +8) restrictive Grothendieck’s concept of a Dessin d’Enfant is in generating all n 2 I φ(w)= 1 1 z +1 64 (w 1) automorphisms of planar graphs. We discuss the rigid rotations of the We have an action : PSL2(C) P (C) P (C). β(z)= : v = n + n, e =2 n, f =2 − n ◦ ⇥ 2 !n 2 4 zn · Platonic solids (the tetrahedron, cube, octahedron, icosahedron, and I Zn = r r =1 and Dn = r, s s = r =(sr) =1 are the rigid I Cupola (J3, J4, J5) dodecahedron), the Archimedean solids, the Catalan solids, and the rotations of the regular convex polygons,with 4w 4(w 2 20w +105)3 I φ(w)= − ⌦ ↵ ⌦ 1 ↵ Rotation Group A4: Tetrahedron 3 2 Johnson solids via explicit Bely˘ımaps. -
Light and Color
Light and Color Light is a complex phenomenon that is classically explained with a simple model based on rays and wavefronts. The Molecular Expressions Microscopy Primer explores many of the aspects of visible light starting with an introduction to electromagnetic radiation and continuing through to human vision and the perception of color. Each section outlined below is an independent treatise on a limited aspect of light and color. We hope you enjoy your visit and find the answers to your questions. Electromagnetic Radiation - Visible light is a complex phenomenon that is classically explained with a simple model based on propagating rays and wavefronts, a concept first proposed in the late 1600s by Dutch physicist Christiaan Huygens. Electromagnetic radiation, the larger family of wave-like phenomena to which visible light belongs (also known as radiant energy ), is the primary vehicle transporting energy through the vast reaches of the universe. The mechanisms by which visible light is emitted or absorbed by substances, and how it predictably reacts under varying conditions as it travels through space and the atmosphere, form the basis of the existence of color in our universe. Light: Particle or a Wave? - Many distinguished scientists have attempted to explain how electromagnetic radiation can display what has now been termed duality , or both particle-like and wave-like behavior. At times light behaves as if composed of particles, and at other times as a continuous wave. This complementary, or dual, role for the properties of light can be employed to describe all of the known characteristics that have been observed experimentally, ranging from refraction, reflection, interference, and diffraction, to the results with polarized light and the photoelectric effect. -
University of Copenhagen
Organ system development in recent lecithotrophic brachiopod larvae Altenburger, Andreas; Martinez, Pedro; Wanninger, Andreas Wilhelm Georg Published in: Geological Society of Australia. Abstracts Series Publication date: 2010 Document version Publisher's PDF, also known as Version of record Citation for published version (APA): Altenburger, A., Martinez, P., & Wanninger, A. W. G. (2010). Organ system development in recent lecithotrophic brachiopod larvae. Geological Society of Australia. Abstracts Series, 3-3. http://www.deakin.edu.au/conferences/ibc/spaw2/uploads/files/6IBC_Program%20&%20Abstracts%20volume.p df Download date: 25. Sep. 2021 Geological Society of Australia ABSTRACTS Number 95 6th International Brachiopod Congress Melbourne, Australia 1-5 February 2010 Geological Society of Australia, Abstracts No. 95 6th International Brachiopod Congress, Melbourne, Australia, February 2010 Geological Society of Australia, Abstracts No. 95 6th International Brachiopod Congress, Melbourne, Australia, February 2010 Geological Society of Australia Abstracts Number 95 6th International Brachiopod Congress, Melbourne, Australia, 1‐5 February 2010 Editors: Guang R. Shi, Ian G. Percival, Roger R. Pierson & Elizabeth A. Weldon ISSN 0729 011X © Geological Society of Australia Incorporated 2010 Recommended citation for this volume: Shi, G.R., Percival, I.G., Pierson, R.R. & Weldon, E.A. (editors). Program & Abstracts, 6th International Brachiopod Congress, 1‐5 February 2010, Melbourne, Australia. Geological Society of Australia Abstracts No. 95. Example citation for papers in this volume: Weldon, E.A. & Shi, G.R., 2010. Brachiopods from the Broughton Formation: useful taxa for the provincial and global correlations of the Guadalupian of the southern Sydney Basin, eastern Australia. In: Program & Abstracts, 6th International Brachiopod Congress, 1‐5 February 2010, Melbourne, Australia; Geological Society of Australia Abstracts 95, 122. -
Clinical Optics Elkington
Document file:///C|/download/www.netlibrary.com/nlreader/nlreader.dll@bookid=51924&Filename=cover.html9/30/2006 2:34:05 PM Document Page i Clinical Optics file:///C|/download/www.netlibrary.com/nlreader/nlreader.dll@bookid=51924&Filename=Page_I.html9/30/2006 2:34:28 PM Document Page ii Other books of interest Clinical Orthoptics Fiona Rowe 0 632 04274 5 Diagnosis and Management of Ocular Mobility Disorders Second Edition A. Anson & H. Davis 0 632 04798 4 Ocular Anatomy and Physiology T. Saude 0 632 03599 4 Clinical Anatomy of the Eye R.S. Snell & M.A. Lemp 0 632 04344 X Orthoptic Assessment and Management Second Edition D. Stidwill 0 632 05012 8 file:///C|/download/www.netlibrary.com/nlreader/nlreader.dll@bookid=51924&Filename=Page_II.html9/30/2006 2:34:29 PM Document Page iii Clinical Optics Third Edition Andrew R. Elkington CBE, MA, FRCS, FRCOphth Consultant Ophthalmologist Southampton Eye Unit Southampton General Hospital. Professor of Ophthalmology University of Southampton. President, Royal College of Ophthalmologists (1994–1997). Helena J. Frank BMedSci, FRCS, FRCOphth Consultant Ophthalmologist Royal Victoria Hospital Bournemouth. Michael J. Greaney MD, FRCSEd, FRCOphth Specialist Registrar Southampton Eye Unit Southampton General Hospital. file:///C|/download/www.netlibrary.com/nlreader/nlreader.dll@bookid=51924&Filename=Page_III.html (1 of 2)9/30/2006 2:34:30 PM Document Page iv © 1984, 1991, 1999 by Blackwell Science Ltd Editorial Offices: Osney Mead, Oxford OX2 0EL 25 John Street, London WC1N 2BL 23 Ainslie Place, Edinburgh EH3 6AJ 350 Main Street, Malden MA 02148 5018, USA 54 University Street, Carlton Victoria 3053, Australia 10, rue Casimir Delavigne 75006 Paris, France Other Editorial Offices: Blackwell Wissenschafts-Verlag GmbH Kurfürstendamm 57 10707 Berlin, Germany Blackwell Science KK MG Kodenmacho Building 7–10 Kodenmacho Nihombashi Chuo-ku, Tokyo 104, Japan The right of the Author to be identified as the Author of this Work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. -
WRAP Theses Earle 1994.Pdf
A Thesis Submitted for the Degree of PhD at the University of Warwick Permanent WRAP URL: http://wrap.warwick.ac.uk/104927 Copyright and reuse: This thesis is made available online and is protected by original copyright. Please scroll down to view the document itself. Please refer to the repository record for this item for information to help you to cite it. Our policy information is available from the repository home page. For more information, please contact the WRAP Team at: [email protected] warwick.ac.uk/lib-publications THE BRITISH LIBRARY BRITISH THESIS SERVICE THE RESTORATION AND FALL OF ROYAL TITLE GOVERNMENT IN NEW GRANADA 1815-1820 AUTHOR Rebecca A. EARLE DEGREE Ph.D AWARDING Warwick University BODY DATE 1994 THESIS DX184477 NUMBER THIS THESIS HAS BEEN MICROFILMED EXACTLY AS RECEIVED The quality of this reproduction is dependent upon the quality of the original thesis submitted for microfilming. Every effort has been made to ensure the highest quality of reproduction. Some pages may have indistinct print, especially if the original papers were poorly produced or if awarding body sent an inferior copy. If pages are missing, please contact the awarding body which granted the degree. Previously copyrighted materials (journals articles, published texts etc.) are not filmed. This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that it's copyright rests with its author and that no information derived from it may be published without the author's prior written consent. Reproduction of this thesis, other than as permitted under the United Kingdom Copyright Designs and Patents Act 1988, or under specific agreement with the copyright holder, is prohibited. -
Mapa Geologico Del Departamento De Boyaca
MAPA GEOLOGICO DEL DEPARTAMENTO DE BOYACA Memoria explicativa Elaborado por: ANTONIO JOSÉ RODRÍGUEZ PARRA ORLANDO SOLANO SILVA Enero DEL 2000 REPÚBLICA DE COLOMBIA MINISTERIO DE MINAS Y ENERGÍA INSTITUTO COLOMBIANO DE GEOLOGÍA Y MINERÍA MAPA GEOLOGICO DEL DEPARTAMENTO DE BOYACA Memoria explicativa Elaborada por: ANTONIO JOSÉ RODRÍGUEZ PARRA ORLANDO SOLANO SILVA MINISTERIO DE MINAS Y ENERGIA INSTITUTO DE INVESTIGACIONES EN GEOCIENCIAS, MINERIA Y QUIMICA “INGEOMINAS” Enero del 2000 i CONTENIDO RESUMEN .................................................................................................................... 1 1. INTRODUCCION.................................................................................................... 2 2. ASPECTOS FISICOS Y SOCIALES DEL DEPARTAMENTO DE BOYACA ......... 3 2.1 LOCALIZACIÓN GEOGRÁFICA Y FISIOGRAFÍA............................................ 3 2.2 HIDROGRAFIA ..................................................................................................... 7 2.3 CLIMA.................................................................................................................... 8 2.4 SUELOS Y VEGETACION .................................................................................... 8 2.5 POBLACION - ACTIVIDAD ECONOMICA ....................................................... 12 2.6 VIAS Y TRANSPORTE....................................................................................... 12 2.7 METODOLOGIA - FUENTES DE INFORMACION ........................................... 13 3. ESTRATIGRAFIA -
On Some Properties of Distance in TO-Space
Aksaray University Aksaray J. Sci. Eng. Journal of Science and Engineering Volume 4, Issue 2, pp. 113-126 e-ISSN: 2587-1277 doi: 10.29002/asujse.688279 http://dergipark.gov.tr/asujse http://asujse.aksaray.edu.tr Available online at Research Article On Some Properties of Distance in TO-Space Zeynep Can* Department of Mathematics, Faculty of Science and Letters, Aksaray University, Aksaray 68100, Turkey ▪Received Date: Feb 12, 2020 ▪Revised Date: Dec 21, 2020 ▪Accepted Date: Dec 24, 2020 ▪Published Online: Dec 25, 2020 Abstract The aim of this work is to investigate some properties of the truncated octahedron metric introduced in the space in further studies on metric geometry. With this metric, the 3- dimensional analytical space is a Minkowski geometry which is a non-Euclidean geometry in a finite number of dimensions. In a Minkowski geometry, the unit ball is a certain symmetric closed convex set instead of the usual sphere in Euclidean space. The unit ball of the truncated octahedron geometry is a truncated octahedron which is an Archimedean solid. In this study, 2 first, metric properties of truncated octahedron distance, 푑푇푂, in ℝ has been examined by 3 metric approach. Then, by using synthetic approach some distance formulae in ℝ푇푂, 3- dimensional analytical space furnished with the truncated octahedron metric has been found. Keywords Metric, Convex polyhedra, Truncated octahedron, Distance of a point to a line, Distance of a point to a plane, Distance between two lines *Corresponding Author: Zeynep Can, [email protected], 0000-0003-2656-5555 2017-2020©Published by Aksaray University 113 Zeynep Can (2020). -
Global Lithium Sources—Industrial Use and Future in the Electric Vehicle Industry: a Review
resources Review Global Lithium Sources—Industrial Use and Future in the Electric Vehicle Industry: A Review Laurence Kavanagh * , Jerome Keohane, Guiomar Garcia Cabellos, Andrew Lloyd and John Cleary EnviroCORE, Department of Science and Health, Institute of Technology Carlow, Kilkenny, Road, Co., R93-V960 Carlow, Ireland; [email protected] (J.K.); [email protected] (G.G.C.); [email protected] (A.L.); [email protected] (J.C.) * Correspondence: [email protected] Received: 28 July 2018; Accepted: 11 September 2018; Published: 17 September 2018 Abstract: Lithium is a key component in green energy storage technologies and is rapidly becoming a metal of crucial importance to the European Union. The different industrial uses of lithium are discussed in this review along with a compilation of the locations of the main geological sources of lithium. An emphasis is placed on lithium’s use in lithium ion batteries and their use in the electric vehicle industry. The electric vehicle market is driving new demand for lithium resources. The expected scale-up in this sector will put pressure on current lithium supplies. The European Union has a burgeoning demand for lithium and is the second largest consumer of lithium resources. Currently, only 1–2% of worldwide lithium is produced in the European Union (Portugal). There are several lithium mineralisations scattered across Europe, the majority of which are currently undergoing mining feasibility studies. The increasing cost of lithium is driving a new global mining boom and should see many of Europe’s mineralisation’s becoming economic. The information given in this paper is a source of contextual information that can be used to support the European Union’s drive towards a low carbon economy and to develop the field of research. -
Strontium-Isotope Stratigraphy As a Constraint on the Age of Condensed Levels: Examples from the Jurassic of the Subbetic
Strontium-isotope stratigraphy as a constraint on the age of condensed levels: examples from the Jurassic of the Subbetic Zone (southern Spain) LUIS M. NIETO*, PEDRO A. RUIZ-ORTIZ*, JAVIER REY and Ma ISABEL BENITOà * Dpto. de Geologı´a, Universidad de Jae´n, E-23071 Jae´n, Spain (E-mail: [email protected]) Dpto. de Geologı´a, EPS Linares, Universidad de Jae´n, E-23700 Jae´n, Spain àDpto. de Estratigrafı´a, U.E.I. Correlaciones Estratigra´ ficas, Universidad Complutense de Madrid-CSIC, E-28040 Madrid, Spain ABSTRACT Condensed levels are often characterized by reworked fossils that may lead to incorrect age assessments. Strontium-isotope stratigraphy is an important chronostratigraphic tool that can be used to verify the biostratigraphic information from condensed beds. This paper describes a study of the 87 Sr/86Sr isotope ratios of 56 belemnite samples collected from 28 stratigraphic sections of the boundary between the Upper Member of the Gavila´n Formation and the Zegrı´ Formation (Pliensbachian, Subbetic Zone). The petrographic and geochemical data (d18O, d13C, concentrations of Fe, Mn and Mg, and the Sr/Mn ratio) suggest that the belemnites have preserved their original marine geochemical composition. After plotting the samples in diagrams of 87Sr/86Sr values against time according to their biostratigraphic age, four different groups (A, B, C and D) were obtained with respect to the reference curve. In groups A and B, the age deduced from the Sr-isotope ratio is in total or partial agreement, respectively, with the biostratigraphic age; therefore the 87Sr/86Sr ratio is a good method for the dating, correlation and assessment of biostratigraphic results. -
X-Ray Spectroscopic Characterization of Laser–Produced Hot Dense Plasmas
THESIS presented at École Polytechnique to obtain the degree of DOCTOR OF ECOLE POLYTECHNIQUE specialization : physics by Nikolaos Kontogiannopoulos Title of the thesis : X-ray spectroscopic characterization of laser–produced hot dense plasmas defended publicly in 6 December 2007 in front of the jury composed of : Jean–Claude Gauthier President Anne Sylvie Gary Referee Jean–Francois Wyart Referee Patrick Audebert Victor Malka Claude Chenais–Popovics Invited Michel Poirier Research Director Acknowledgements This thesis was realized in the laboratory LULI (“Laboratoire pour l’Utilisation des Lasers Intenses”) of Ecole Polytechnique between 2004 and 2007. I would like to thank Francois Amiranoff director of laboratory for providing all the technical and material support and resources for implementing this work. I thank all the members of the jury. Especially Anne Sylvie Gary and Jean–Francois Wyart who carried out the demanding work of being referees. Also, Jean–Claude Gauthier, Patrick Audebert and Victor Malka, who accepted to judge this work. This work had the particular advantage to be accomplished, having as directors Claude Chenais–Popovics and Michel Poirier, which I gratefully thanks for their continuous help in every different problem that I found during my thesis. My gratitude to the members of research group that I had the pleasure to work with : Serena Bastiani–Ceccoti, Jean–Raphael Marques, and Olivier Peurysse. Special thanks to Thomas Blenski the theoretical work of which was a invaluable support in accomplishing my thesis. My grateful thanks to Frederic Thais. Apart from physics, its humor and its positive view gave to me a real reference to continue over the difficulties that I found during this work. -
[ENTRY POLYHEDRA] Authors: Oliver Knill: December 2000 Source: Translated Into This Format from Data Given In
ENTRY POLYHEDRA [ENTRY POLYHEDRA] Authors: Oliver Knill: December 2000 Source: Translated into this format from data given in http://netlib.bell-labs.com/netlib tetrahedron The [tetrahedron] is a polyhedron with 4 vertices and 4 faces. The dual polyhedron is called tetrahedron. cube The [cube] is a polyhedron with 8 vertices and 6 faces. The dual polyhedron is called octahedron. hexahedron The [hexahedron] is a polyhedron with 8 vertices and 6 faces. The dual polyhedron is called octahedron. octahedron The [octahedron] is a polyhedron with 6 vertices and 8 faces. The dual polyhedron is called cube. dodecahedron The [dodecahedron] is a polyhedron with 20 vertices and 12 faces. The dual polyhedron is called icosahedron. icosahedron The [icosahedron] is a polyhedron with 12 vertices and 20 faces. The dual polyhedron is called dodecahedron. small stellated dodecahedron The [small stellated dodecahedron] is a polyhedron with 12 vertices and 12 faces. The dual polyhedron is called great dodecahedron. great dodecahedron The [great dodecahedron] is a polyhedron with 12 vertices and 12 faces. The dual polyhedron is called small stellated dodecahedron. great stellated dodecahedron The [great stellated dodecahedron] is a polyhedron with 20 vertices and 12 faces. The dual polyhedron is called great icosahedron. great icosahedron The [great icosahedron] is a polyhedron with 12 vertices and 20 faces. The dual polyhedron is called great stellated dodecahedron. truncated tetrahedron The [truncated tetrahedron] is a polyhedron with 12 vertices and 8 faces. The dual polyhedron is called triakis tetrahedron. cuboctahedron The [cuboctahedron] is a polyhedron with 12 vertices and 14 faces. The dual polyhedron is called rhombic dodecahedron. -
Review of the Rare Earth Elements and Lithium Mining Sectors
CHEMINFO Review of the Rare Earth Elements and Lithium Mining Sectors FINAL REPORT March 2012 Prepared for: Environment Canada Mining Section Mining and Processing Division Prepared By: Cheminfo Services Inc. 30 Centurian Drive, Suite 205 Markham, Ontario L3R 8B8 Phone: (905) 944-1160 Fax: (905) 944-1175 CHEMINFO Table of Contents 1. EXECUTIVE SUMMARY .....................................................................................1 1.1 INTRODUCTION ....................................................................................................1 1.2 RARE EARTHS .....................................................................................................1 1.2.1 Presence in Canada ...................................................................................5 1.3 LITHIUM ..............................................................................................................5 1.3.1 Presence in Canada ...................................................................................7 1.4 RARE EARTHS AND LITHIUM MINING AND PROCESSING METHODS .....................7 1.4.1 Rare Earth Mining and Processing Methods.............................................7 1.4.2 Lithium Mining and Processing Methods..................................................8 1.5 SUBSTANCES OF ENVIRONMENTAL CONCERN IN RARE EARTH AND LITHIUM MINING AND PROCESSING ...............................................................................................8 1.5.1 Substances of Concern for Rare Earths.....................................................9