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Arxiv:0705.1142V1 [Math.DS] 8 May 2007 Cases New) and Are Ripe for Further Study
A PRIMER ON SUBSTITUTION TILINGS OF THE EUCLIDEAN PLANE NATALIE PRIEBE FRANK Abstract. This paper is intended to provide an introduction to the theory of substitution tilings. For our purposes, tiling substitution rules are divided into two broad classes: geometric and combi- natorial. Geometric substitution tilings include self-similar tilings such as the well-known Penrose tilings; for this class there is a substantial body of research in the literature. Combinatorial sub- stitutions are just beginning to be examined, and some of what we present here is new. We give numerous examples, mention selected major results, discuss connections between the two classes of substitutions, include current research perspectives and questions, and provide an extensive bib- liography. Although the author attempts to fairly represent the as a whole, the paper is not an exhaustive survey, and she apologizes for any important omissions. 1. Introduction d A tiling substitution rule is a rule that can be used to construct infinite tilings of R using a finite number of tile types. The rule tells us how to \substitute" each tile type by a finite configuration of tiles in a way that can be repeated, growing ever larger pieces of tiling at each stage. In the d limit, an infinite tiling of R is obtained. In this paper we take the perspective that there are two major classes of tiling substitution rules: those based on a linear expansion map and those relying instead upon a sort of \concatenation" of tiles. The first class, which we call geometric tiling substitutions, includes self-similar tilings, of which there are several well-known examples including the Penrose tilings. -
Technological Entrepreneurship – a Key to World Peace and Prosperity”
cc MM CoCorrmickmick NorthwesternNorthwestern Engineering Engineering MaterialMaterialss ScienceScience and and EngineeringEngineering The 2014 McCormick Dean’s Seminar Series Dr. Dan Shechtman – Nobel Laureate Israel Institute of Technology Monday, October 20, 2014 4:00pm, McCormick Auditorium (Allen Center) Reception to follow north of McCormick Auditorium in the Allen Center “Technological Entrepreneurship – a Key to World Peace and Prosperity” Most of the countries in the world lack significant natural resources and are characterized by low standard of living with little hope for improvement due to population growth and mismanagement. This is true also for countries that are rich in natural resources, but do not use them wisely. People that live in countries that enjoy high standard of living are industrious and their countries industrial. The basic reason of this division is technological entrepreneurship nourished by free market economy. Technologically entrepreneurial people make the difference. So, is there hope for everybody on the globe to improve their lives? Can technological entrepreneurship be motivated and taught so that generations of determined entrepreneurs will build up thriving economies? The clear answer to both questions is yes, but the process will take time and dedication. It all starts with education in general and scientific- technical education in particular. There is also a way to expedite the process – start with the already educated engineers and scientists. These are the first candidates for entrepreneurial endeavors. They can do it, but need motivation, continuous instruction and encouraging economic environment until they create successful start-ups and serve as role models for others. The name of the game is motivation. -
Contents Contents
Contents CHEMISTRY International January-March 2019 Volume 41 No. 1 Introduction The International Year of the Periodic Table 2019 2 by Jan Reedijk and Natalia Tarasova Features IUPAC and the Periodic Table by G.J. Leigh 6 Criteria for New Element Discovery: Providing Assurance 10 in a Field of Allure and Romance by Sigurd Hofmann Looking Backwards and Forwards at the Development 16 of the Periodic Table by Eric Scerri Isotopic Abundances and Atomic Weights: History of IUPAC 21 Commission II.1 in the Service of Chemistry by John R. De Laeter IUPAC Commission II.1 Today by Juris Meija 24 Isotopes Matter by Norman E. Holden, Tyler B. Coplen, and Peter Mahaffy 27 The New SI: The International System of Units is Getting 32 a Makeover by Ian Mills and Roberto Marquardt IUPAC Wire Election of IUPAC Officers and Bureau Members 36 Juris Meija Made the Top 40 Under 40 37 C. Oliver Kappe is Awarded the 2018 IUPAC-ThalesNano Prize 37 for Flow Chemistry OPCW to Further Enhance Contributions to United Nations’ 38 Sustainable Development Goals 1001 Inventions: Journeys from Alchemy to Chemistry 38 Stamps International 39 Project Place Critical evaluation of homogeneous equilibrium and solubility 40 constants of gadolinium in environmental and biological- relevant conditions 23rd UNESCO/IUPAC Postgraduate Course in Polymer Science 40 Guidance for the Compilation, Critical Evaluation and 40 Dissemination of Chemical Data Making an imPACt On the Discovery of New Elements (IUPAC/IUPAP 42 Provisional Report) IUPAC Periodic Table of the Elements and Isotopes -
Arxiv:Math/0601064V1
DUALITY OF MODEL SETS GENERATED BY SUBSTITUTIONS D. FRETTLOH¨ Dedicated to Tudor Zamfirescu on the occasion of his sixtieth birthday Abstract. The nature of this paper is twofold: On one hand, we will give a short introduc- tion and overview of the theory of model sets in connection with nonperiodic substitution tilings and generalized Rauzy fractals. On the other hand, we will construct certain Rauzy fractals and a certain substitution tiling with interesting properties, and we will use a new approach to prove rigorously that the latter one arises from a model set. The proof will use a duality principle which will be described in detail for this example. This duality is mentioned as early as 1997 in [Gel] in the context of iterated function systems, but it seems to appear nowhere else in connection with model sets. 1. Introduction One of the essential observations in the theory of nonperiodic, but highly ordered structures is the fact that, in many cases, they can be generated by a certain projection from a higher dimensional (periodic) point lattice. This is true for the well-known Penrose tilings (cf. [GSh]) as well as for a lot of other substitution tilings, where most known examples are living in E1, E2 or E3. The appropriate framework for this arises from the theory of model sets ([Mey], [Moo]). Though the knowledge in this field has grown considerably in the last decade, in many cases it is still hard to prove rigorously that a given nonperiodic structure indeed is a model set. This paper is organized as follows. -
Nfap Policy Brief » October 2019
NATIONAL FOUNDATION FOR AMERICAN POLICY NFAP POLICY BRIEF» OCTOBER 2019 IMMIGRANTS AND NOBEL PRIZES : 1901- 2019 EXECUTIVE SUMMARY Immigrants have been awarded 38%, or 36 of 95, of the Nobel Prizes won by Americans in Chemistry, Medicine and Physics since 2000.1 In 2019, the U.S. winner of the Nobel Prize in Physics (James Peebles) and one of the two American winners of the Nobel Prize in Chemistry (M. Stanley Whittingham) were immigrants to the United States. This showing by immigrants in 2019 is consistent with recent history and illustrates the contributions of immigrants to America. In 2018, Gérard Mourou, an immigrant from France, won the Nobel Prize in Physics. In 2017, the sole American winner of the Nobel Prize in Chemistry was an immigrant, Joachim Frank, a Columbia University professor born in Germany. Immigrant Rainer Weiss, who was born in Germany and came to the United States as a teenager, was awarded the 2017 Nobel Prize in Physics, sharing it with two other Americans, Kip S. Thorne and Barry C. Barish. In 2016, all 6 American winners of the Nobel Prize in economics and scientific fields were immigrants. Table 1 U.S. Nobel Prize Winners in Chemistry, Medicine and Physics: 2000-2019 Category Immigrant Native-Born Percentage of Immigrant Winners Physics 14 19 42% Chemistry 12 21 36% Medicine 10 19 35% TOTAL 36 59 38% Source: National Foundation for American Policy, Royal Swedish Academy of Sciences, George Mason University Institute for Immigration Research. Between 1901 and 2019, immigrants have been awarded 35%, or 105 of 302, of the Nobel Prizes won by Americans in Chemistry, Medicine and Physics. -
Addressing in Substitution Tilings
Addressing in substitution tilings Chaim Goodman-Strauss DRAFT: May 6, 2004 Introduction Substitution tilings have been discussed now for at least twenty-five years, initially motivated by the construction of hierarchical non-periodic structures in the Euclidean plane [?, ?, ?, ?]. Aperiodic sets of tiles were often created by forcing these structures to emerge. Recently, this line was more or less completed, with the demonstration that (essentially) every substitution tiling gives rise to an aperiodic set of tiles [?]. Thurston and then Kenyon have given remarkable characterizations of self- similar tilings, a very closely related notion, in algebraic terms [?, ?]. The dynamics of a species of substitution tilings under the substitution map has been extensively studied [?, ?, ?, ?, ?]. However, to a large degree, a great deal of detailed, local structure appears to have been overlooked. The approach we outline here is to view the tilings in a substitution species as realizations of some algorithmicly derived language— in much the same way one can view a group’s elements as strings of symbols representing its generators, modulo various relations. This vague philosophical statement may become clearer through a quick discussion of how substitution tilings have often been viewed and defined, com- pared to our approach. The real utility of addressing, however, is that we can provide detailed and explicit descriptions of structures in substitution tilings. Figure 1: A typical substitution We begin with a rough heuristic description of a substitution tiling (formal definitions will follow below): One starts in affine space Rn with a finite col- lection T of prototiles,1, a group G of isometries to move prototiles about, an 1In the most general context, we need assume little about the topology or geometry of the 1 expanding affine map σ and a map σ0 from prototiles to tilings– substitution rules. -
Dan Shechtman
University of Haifa The Senate of the University of Haifa, by virtue of the authority vested in it by the constitution of the University and in accordance with the recommendations of the President and the Executive Committee hereby confers upon Dan Shechtman the degree of Doctor of Philosophy, Honoris Causa in recognition of his scientific breakthrough resulting in the birth of a new field in science, a unique accomplishment achieved by few others; his uncompromising belief in the scientific truth of his discovery despite persistent opposition from senior researchers in the scientific community, and the lesson he teaches that loyalty to truth will ultimately defeat critics; his reminding us that science deals first and foremost with findings and that scientists must never distort findings to serve any other interests; for his deep friendship with the University of Haifa and the great honor his excellence has brought to the city of Haifa and the State of Israel. Conferred in Haifa, Israel 13 Sivan 5772/June 3, 2012 Ami Ayalon Prof. Aaron Ben–Ze’ev Prof. David Faraggi Chairman of the Executive Committee President Rector PROFESSOR DAN SHECHTMAN Nobel Laureate in Chemistry for 2011 Prof. Dan Shechtman was born in 1941 in Tel Aviv. He earned a bachelor’s degree in Mechanical Engineering in 1966, a master’s degree in Materials Engineering in 1968 and a Ph.D. in the same field in 1972 – all from the Technion-Israel Institute of Technology. The following three years, he worked in the American Air Force Aerospace Research Laboratories, where he studied the microstructure and physical metallurgy of titanium aluminides. -
Visualization of Regular Maps
Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps Jarke J. van Wijk Dept. of Mathematics and Computer Science Technische Universiteit Eindhoven [email protected] Abstract The first puzzle is trivial: We get a cube, blown up to a sphere, which is an example of a regular map. A cube is 2×4×6 = 48-fold A regular map is a tiling of a closed surface into faces, bounded symmetric, since each triangle shown in Figure 1 can be mapped to by edges that join pairs of vertices, such that these elements exhibit another one by rotation and turning the surface inside-out. We re- a maximal symmetry. For genus 0 and 1 (spheres and tori) it is quire for all solutions that they have such a 2pF -fold symmetry. well known how to generate and present regular maps, the Platonic Puzzle 2 to 4 are not difficult, and lead to other examples: a dodec- solids are a familiar example. We present a method for the gener- ahedron; a beach ball, also known as a hosohedron [Coxeter 1989]; ation of space models of regular maps for genus 2 and higher. The and a torus, obtained by making a 6 × 6 checkerboard, followed by method is based on a generalization of the method for tori. Shapes matching opposite sides. The next puzzles are more challenging. with the proper genus are derived from regular maps by tubifica- tion: edges are replaced by tubes. Tessellations are produced us- ing group theory and hyperbolic geometry. The main results are a generic procedure to produce such tilings, and a collection of in- triguing shapes and images. -
Media Information Press Talks at #Lino16, Mo.-We., Marionettenoper
Kuratorium für die Tagungen der Nobelpreisträger in Lindau Council for the Media Information Lindau Nobel Laureate Meetings Ehrenpräsident | Honorary President Press talks at #LiNo16, Mo.-We., Marionettenoper (Stadttheater) Prof. Dr. h. c. mult. Graf Lennart Bernadotte af Wisborg (†) Aimed at the accredited journalists, select media partners of the Lindau Vorstand | Executive Commitee Countess Bettina Bernadotte af Wisborg Nobel Laureate Meetings will present a “press talk” to cover topical (Präsidentin | President) Prof. Dr. Wolfgang Lubitz issues of wide interest. A panel of Nobel Laureates, young scientists, (Vizepräsident | Vice-President) and expert guests will discuss the given topic with each other and then Prof. Dr. Helga Nowotny (Vizepräsidentin | Vice-President) take questions from the audience. Nikolaus Turner (Schatzmeister | Treasurer) Stiftung Scientists in motion: how immigration continues to shape the Lindauer Nobelpreisträgertagungen Foundation scientific world Lindau Nobel Laureate Meetings pres. by Physics World, Mo. 27 June, 16.45-17.30 hrs. Ehrenpräsidium | Honorary Presidents moderator: Hamish Johnston, editor of physicsworld.com Prof. Dr. h. c. mult. Graf Lennart Bernadotte af Wisborg (†) Prof. Dr. Roman Herzog A recent study by Physics World shows that more than 25% of physics Bundespräsident a. D. Nobel laureates are immigrants, a figure that reflects the importance of Vorstand | Board of Directors human migration in science. Scientists move country for many Jürgen Kluge (Vorsitzender | Chairman) different reasons. Some are seeking better professional opportunities Bettina Gräfin Bernadotte af Wisborg Thomas Ellerbeck while others move for family reasons. And unfortunately, some Reinhard Pöllath scientists are forced to leave their home countries to escape political, Nikolaus Turner (Geschäftsführer | Managing Director) religious or other persecution. -
Branched Surfaces and Colored Patterns Juan
BRANCHED SURFACES AND COLORED PATTERNS JUAN ESCUDERO A cell complex is defined in the analysis of the topological invariants of tiling spaces. In some cases the complex contains collared tiles. The representation of the corresponding branched surface can be done by assigning colors to the collared tiles. This allows to distinguish tiles with the same shape but different edge identifications. Fig.1 Level-4 supertiles for the octagonal tiling Fig 2. A fragment of “Branched Manifold" Fig 3. “Nueve y 220-A” is based on a nodal surface with degree nine and cyclic symmetry. 1.-Introduction Artists, scientists and mathematicians share instinctive feelings about order and disorder. One of the fields where this is apparent is the mathematical theory of long range aperiodic order, because of its im- plications in the arts. Aperiodic tilings are geometric objects lying somewhere between periodicity and randomness. In the 1960´s Wang and Berger introduced aperiodic sets of tiles in the treatment of certain problems in logic. The question was whether or not it is possible to determine algorithmically if given a set of tiles they tile the plane. The cardinal of the tile sets was very high and examples with few prototiles were constructed later by Robinson, Penrose, Ammann, and others. Since the discovery of quasicrystals in the 1980´s, the generation of ideal quasiperiodic structures has been a problem studied mainly by mathematicians and physicists. Recently it has been suggested that aperiodic order already was present in the medieval islamic archi- tecture. [8] Periodic and non-periodic girih (geometric star-and-polygon, or strapwork) patterns were on the basis of the designs. -
Geometry in Design Geometrical Construction in 3D Forms by Prof
D’source 1 Digital Learning Environment for Design - www.dsource.in Design Course Geometry in Design Geometrical Construction in 3D Forms by Prof. Ravi Mokashi Punekar and Prof. Avinash Shide DoD, IIT Guwahati Source: http://www.dsource.in/course/geometry-design 1. Introduction 2. Golden Ratio 3. Polygon - Classification - 2D 4. Concepts - 3 Dimensional 5. Family of 3 Dimensional 6. References 7. Contact Details D’source 2 Digital Learning Environment for Design - www.dsource.in Design Course Introduction Geometry in Design Geometrical Construction in 3D Forms Geometry is a science that deals with the study of inherent properties of form and space through examining and by understanding relationships of lines, surfaces and solids. These relationships are of several kinds and are seen in Prof. Ravi Mokashi Punekar and forms both natural and man-made. The relationships amongst pure geometric forms possess special properties Prof. Avinash Shide or a certain geometric order by virtue of the inherent configuration of elements that results in various forms DoD, IIT Guwahati of symmetry, proportional systems etc. These configurations have properties that hold irrespective of scale or medium used to express them and can also be arranged in a hierarchy from the totally regular to the amorphous where formal characteristics are lost. The objectives of this course are to study these inherent properties of form and space through understanding relationships of lines, surfaces and solids. This course will enable understanding basic geometric relationships, Source: both 2D and 3D, through a process of exploration and analysis. Concepts are supported with 3Dim visualization http://www.dsource.in/course/geometry-design/in- of models to understand the construction of the family of geometric forms and space interrelationships. -
On the 2011 Nobel Prize in Chemistry, Awarded to Dan Shechtman
DISTINGUISHED LECTURES CONTRIBUTIONS to SCIENCE 9 (2013) 17-23 Institut d’Estudis Catalans, Barcelona, Catalonia doi: 10.2436/20.7010.01.159 ISSN: 1575-6343 www.cat-science.cat OPENA ACCESS The Nobel Prizes of 2011 Crystallography and the Nobel Prizes: On the 2011 Nobel Prize in Chemistry, awarded to Dan Shechtman Joan F. Piniella Department of Geology, Autonomous University of Barcelona, Barcelona, Catalonia Based on the lecture given by the Summary. Crystallography has a considerable presence among Nobel Prize laureates. In- author at the IEC, Barcelona, on 13 deed, 48 of them have close links to crystallography. The 2011 Nobel Prize in Chemistry December 2011 for the Nobel Prizes was awarded to Dan Shechtman for his discovery of quasicrystals. In addition to the scien- of 2011 Sessions. tific merit of the work, the Prize is a personal recognition of Dan Shechtman, whose ideas Correspondence: were initially rejected by the international scientific community. Yet, reason prevailed in the Departament de Geologia end, supported by arguments that arrived from seemingly unrelated directions, such as the Facultat de Ciències Universitat Autònoma de Barcelona study of Arab building tiles and the mathematical concept of tessellation. Concepts of a 08193 Bellaterra, Catalonia more crystallographic nature, such as twinned crystals and modulated and incommensu- Tel. +34-935813088 rate crystal structures, also played an important role. Finally, in 1992, the International Fax +34-935811263 Union of Crystallography modified the definition of “crystal” to include quasicrystals. E-mail: [email protected] Received: 24.10.13 Keywords: crystal structure · electron diffraction · quasicrystals · tessellations Accepted: 25.11.13 Resum.