MODERN MATHEMATICS 1900 to 1950
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Power Values of Divisor Sums Author(S): Frits Beukers, Florian Luca, Frans Oort Reviewed Work(S): Source: the American Mathematical Monthly, Vol
Power Values of Divisor Sums Author(s): Frits Beukers, Florian Luca, Frans Oort Reviewed work(s): Source: The American Mathematical Monthly, Vol. 119, No. 5 (May 2012), pp. 373-380 Published by: Mathematical Association of America Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.119.05.373 . Accessed: 15/02/2013 04:05 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access to The American Mathematical Monthly. http://www.jstor.org This content downloaded on Fri, 15 Feb 2013 04:05:44 AM All use subject to JSTOR Terms and Conditions Power Values of Divisor Sums Frits Beukers, Florian Luca, and Frans Oort Abstract. We consider positive integers whose sum of divisors is a perfect power. This prob- lem had already caught the interest of mathematicians from the 17th century like Fermat, Wallis, and Frenicle. In this article we study this problem and some variations. We also give an example of a cube, larger than one, whose sum of divisors is again a cube. 1. INTRODUCTION. Recently, one of the current authors gave a mathematics course for an audience with a general background and age over 50. -
The History of the First Kidney Transplantation
165+3 14 mm "Service to society is the rent we pay for living on this planet" The History of the Joseph E. Murray, 1990 Nobel-laureate who performed the first long-term functioning kidney transplantation in the world First Kidney "The pioneers sacrificed their scientific life to convince the medical society that this will become sooner or later a successful procedure… – …it is a feeling – now I am Transplantation going to overdo - like taking part in creation...” András Németh, who performed the first – a European Overview Hungarian renal transplantation in 1962 E d i t e d b y : "Professor Langer contributes an outstanding “service” to the field by a detailed Robert Langer recording of the history of kidney transplantation as developed throughout Europe. The authoritative information is assembled country by country by a generation of transplant professionals who knew the work of their pioneer predecessors. The accounting as compiled by Professor Langer becomes an essential and exceptional reference document that conveys the “service to society” that kidney transplantation has provided for all mankind and that Dr. Murray urged be done.” Francis L. Delmonico, M.D. Professor of Surgery, Harvard Medical School, Massachusetts General Hospital Past President The Transplantation Society and the Organ Procurement Transplant Network (UNOS) Chair, WHO Task Force Organ and Tissue Donation and Transplantation The History of the First Kidney Transplantation – a European Overview European a – Transplantation Kidney First the of History The ISBN 978-963-331-476-0 Robert Langer 9 789633 314760 The History of the First Kidney Transplantation – a European Overview Edited by: Robert Langer SemmelweisPublishers www.semmelweiskiado.hu Budapest, 2019 © Semmelweis Press and Multimedia Studio Budapest, 2019 eISBN 978-963-331-473-9 All rights reserved. -
Scope of Various Random Number Generators in Ant System Approach for Tsp
AC 2007-458: SCOPE OF VARIOUS RANDOM NUMBER GENERATORS IN ANT SYSTEM APPROACH FOR TSP S.K. Sen, Florida Institute of Technology Syamal K Sen ([email protected]) is currently a professor in the Dept. of Mathematical Sciences, Florida Institute of Technology (FIT), Melbourne, Florida. He did his Ph.D. (Engg.) in Computational Science from the prestigious Indian Institute of Science (IISc), Bangalore, India in 1973 and then continued as a faculty of this institute for 33 years. He was a professor of Supercomputer Computer Education and Research Centre of IISc during 1996-2004 before joining FIT in January 2004. He held a Fulbright Fellowship for senior teachers in 1991 and worked in FIT. He also held faculty positions, on leave from IISc, in several universities around the globe including University of Mauritius (Professor, Maths., 1997-98), Mauritius, Florida Institute of Technology (Visiting Professor, Math. Sciences, 1995-96), Al-Fateh University (Associate Professor, Computer Engg, 1981-83.), Tripoli, Libya, University of the West Indies (Lecturer, Maths., 1975-76), Barbados.. He has published over 130 research articles in refereed international journals such as Nonlinear World, Appl. Maths. and Computation, J. of Math. Analysis and Application, Simulation, Int. J. of Computer Maths., Int. J Systems Sci., IEEE Trans. Computers, Internl. J. Control, Internat. J. Math. & Math. Sci., Matrix & Tensor Qrtly, Acta Applicande Mathematicae, J. Computational and Applied Mathematics, Advances in Modelling and Simulation, Int. J. Engineering Simulation, Neural, Parallel and Scientific Computations, Nonlinear Analysis, Computers and Mathematics with Applications, Mathematical and Computer Modelling, Int. J. Innovative Computing, Information and Control, J. Computational Methods in Sciences and Engineering, and Computers & Mathematics with Applications. -
Three Aspects of the Theory of Complex Multiplication
Three Aspects of the Theory of Complex Multiplication Takase Masahito Introduction In the letter addressed to Dedekind dated March 15, 1880, Kronecker wrote: - the Abelian equations with square roots of rational numbers are ex hausted by the transformation equations of elliptic functions with sin gular modules, just as the Abelian equations with integral coefficients are exhausted by the cyclotomic equations. ([Kronecker 6] p. 455) This is a quite impressive conjecture as to the construction of Abelian equations over an imaginary quadratic number fields, which Kronecker called "my favorite youthful dream" (ibid.). The aim of the theory of complex multiplication is to solve Kronecker's youthful dream; however, it is not the history of formation of the theory of complex multiplication but Kronecker's youthful dream itself that I would like to consider in the present paper. I will consider Kronecker's youthful dream from three aspects: its history, its theoretical character, and its essential meaning in mathematics. First of all, I will refer to the history and theoretical character of the youthful dream (Part I). Abel modeled the division theory of elliptic functions after the division theory of a circle by Gauss and discovered the concept of an Abelian equation through the investigation of the algebraically solvable conditions of the division equations of elliptic functions. This discovery is the starting point of the path to Kronecker's youthful dream. If we follow the path from Abel to Kronecker, then it will soon become clear that Kronecker's youthful dream has the theoretical character to be called the inverse problem of Abel. -
HISTORY of UKRAINE and UKRAINIAN CULTURE Scientific and Methodical Complex for Foreign Students
Ministry of Education and Science of Ukraine Flight Academy of National Aviation University IRYNA ROMANKO HISTORY OF UKRAINE AND UKRAINIAN CULTURE Scientific and Methodical Complex for foreign students Part 3 GUIDELINES FOR SELF-STUDY Kropyvnytskyi 2019 ɍȾɄ 94(477):811.111 R e v i e w e r s: Chornyi Olexandr Vasylovych – the Head of the Department of History of Ukraine of Volodymyr Vynnychenko Central Ukrainian State Pedagogical University, Candidate of Historical Sciences, Associate professor. Herasymenko Liudmyla Serhiivna – associate professor of the Department of Foreign Languages of Flight Academy of National Aviation University, Candidate of Pedagogical Sciences, Associate professor. ɇɚɜɱɚɥɶɧɨɦɟɬɨɞɢɱɧɢɣɤɨɦɩɥɟɤɫɩɿɞɝɨɬɨɜɥɟɧɨɡɝɿɞɧɨɪɨɛɨɱɨʀɩɪɨɝɪɚɦɢɧɚɜɱɚɥɶɧɨʀɞɢɫɰɢɩɥɿɧɢ "ȱɫɬɨɪɿɹ ɍɤɪɚʀɧɢ ɬɚ ɭɤɪɚʀɧɫɶɤɨʀ ɤɭɥɶɬɭɪɢ" ɞɥɹ ɿɧɨɡɟɦɧɢɯ ɫɬɭɞɟɧɬɿɜ, ɡɚɬɜɟɪɞɠɟɧɨʀ ɧɚ ɡɚɫɿɞɚɧɧɿ ɤɚɮɟɞɪɢ ɩɪɨɮɟɫɿɣɧɨʀ ɩɟɞɚɝɨɝɿɤɢɬɚɫɨɰɿɚɥɶɧɨɝɭɦɚɧɿɬɚɪɧɢɯɧɚɭɤ (ɩɪɨɬɨɤɨɥʋ1 ɜɿɞ 31 ɫɟɪɩɧɹ 2018 ɪɨɤɭ) ɬɚɫɯɜɚɥɟɧɨʀɆɟɬɨɞɢɱɧɢɦɢ ɪɚɞɚɦɢɮɚɤɭɥɶɬɟɬɿɜɦɟɧɟɞɠɦɟɧɬɭ, ɥɶɨɬɧɨʀɟɤɫɩɥɭɚɬɚɰɿʀɬɚɨɛɫɥɭɝɨɜɭɜɚɧɧɹɩɨɜɿɬɪɹɧɨɝɨɪɭɯɭ. ɇɚɜɱɚɥɶɧɢɣ ɩɨɫɿɛɧɢɤ ɡɧɚɣɨɦɢɬɶ ɿɧɨɡɟɦɧɢɯ ɫɬɭɞɟɧɬɿɜ ɡ ɿɫɬɨɪɿɽɸ ɍɤɪɚʀɧɢ, ʀʀ ɛɚɝɚɬɨɸ ɤɭɥɶɬɭɪɨɸ, ɨɯɨɩɥɸɽ ɧɚɣɜɚɠɥɢɜɿɲɿɚɫɩɟɤɬɢ ɭɤɪɚʀɧɫɶɤɨʀɞɟɪɠɚɜɧɨɫɬɿ. ɋɜɿɬɭɤɪɚʀɧɫɶɤɢɯɧɚɰɿɨɧɚɥɶɧɢɯɬɪɚɞɢɰɿɣ ɭɧɿɤɚɥɶɧɢɣ. ɋɬɨɥɿɬɬɹɦɢ ɪɨɡɜɢɜɚɥɚɫɹ ɫɢɫɬɟɦɚ ɪɢɬɭɚɥɿɜ ɿ ɜɿɪɭɜɚɧɶ, ɹɤɿ ɧɚ ɫɭɱɚɫɧɨɦɭ ɟɬɚɩɿ ɧɚɛɭɜɚɸɬɶ ɧɨɜɨʀ ɩɨɩɭɥɹɪɧɨɫɬɿ. Ʉɧɢɝɚ ɪɨɡɩɨɜɿɞɚɽ ɩɪɨ ɤɚɥɟɧɞɚɪɧɿ ɫɜɹɬɚ ɜ ɍɤɪɚʀɧɿ: ɞɟɪɠɚɜɧɿ, ɪɟɥɿɝɿɣɧɿ, ɩɪɨɮɟɫɿɣɧɿ, ɧɚɪɨɞɧɿ, ɚ ɬɚɤɨɠ ɪɿɡɧɿ ɩɚɦ ɹɬɧɿ ɞɚɬɢ. ɍ ɩɨɫɿɛɧɢɤɭ ɩɪɟɞɫɬɚɜɥɟɧɿ ɪɿɡɧɨɦɚɧɿɬɧɿ ɞɚɧɿ ɩɪɨ ɮɥɨɪɭ ɿ ɮɚɭɧɭ ɤɥɿɦɚɬɢɱɧɢɯ -
Abstracts for 18 Category Theory; Homological 62 Statistics Algebra 65 Numerical Analysis Syracuse, October 2–3, 2010
A bstr bstrActs A A cts mailing offices MATHEMATICS and additional of Papers Presented to the Periodicals postage 2010 paid at Providence, RI American Mathematical Society SUBJECT CLASSIFICATION Volume 31, Number 4, Issue 162 Fall 2010 Compiled in the Editorial Offices of MATHEMATICAL REVIEWS and ZENTRALBLATT MATH 00 General 44 Integral transforms, operational calculus 01 History and biography 45 Integral equations Editorial Committee 03 Mathematical logic and foundations 46 Functional analysis 05 Combinatorics 47 Operator theory Robert J. Daverman, Chair Volume 31 • Number 4 Fall 2010 Volume 06 Order, lattices, ordered 49 Calculus of variations and optimal Georgia Benkart algebraic structures control; optimization 08 General algebraic systems 51 Geometry Michel L. Lapidus 11 Number theory 52 Convex and discrete geometry Matthew Miller 12 Field theory and polynomials 53 Differential geometry 13 Commutative rings and algebras 54 General topology Steven H. Weintraub 14 Algebraic geometry 55 Algebraic topology 15 Linear and multilinear algebra; 57 Manifolds and cell complexes matrix theory 58 Global analysis, analysis on manifolds 16 Associative rings and algebras 60 Probability theory and stochastic 17 Nonassociative rings and algebras processes Abstracts for 18 Category theory; homological 62 Statistics algebra 65 Numerical analysis Syracuse, October 2–3, 2010 ....................... 655 19 K-theory 68 Computer science 20 Group theory and generalizations 70 Mechanics of particles and systems Los Angeles, October 9–10, 2010 .................. 708 22 Topological groups, Lie groups 74 Mechanics of deformable solids 26 Real functions 76 Fluid mechanics 28 Measure and integration 78 Optics, electromagnetic theory Notre Dame, November 5–7, 2010 ................ 758 30 Functions of a complex variable 80 Classical thermodynamics, heat transfer 31 Potential theory 81 Quantum theory Richmond, November 6–7, 2010 .................. -
David Walker [Press Release]
David A. Walker, Ph.D. Associate Dean for Academic Affairs, College of Education Professor of Educational Technology, Research, and Assessment Lagomarcino Laureate Northern Illinois University College of Education 325 Graham DeKalb, IL 60115 ACADEMIC DEGREES Ph.D. - Iowa State University of Science and Technology M.A. - Iowa State University of Science and Technology B.A. - St. Olaf College UNIVERSITY POSITIONS 2016 – Present: Associate Dean for Academic Affairs, College of Education, Northern Illinois University 2012 – Present: Professor, Department of Educational Technology, Research, and Assessment, Northern Illinois University 2006 – 2012: Associate Professor, Department of Educational Technology, Research, and Assessment, Northern Illinois University 2006 – 2011: Coordinator of Assessment, College of Education, Northern Illinois University 2003 – 2006: Assistant Professor, Department of Educational Technology, Research, and Assessment, Northern Illinois University 2000 – 2003: Assistant Professor, Department of Educational Technology and Research, Florida Atlantic University 1999 – 2000: Post-Doctorate, Research Institute for Studies in Education, Iowa State University of Science and Technology David A. Walker 2 SCHOLARSHIP REFEREED JOURNAL PUBLICATIONS 1. Smith, T. J., Walker, D. A., Chen, H.- T., & Hong, Z.-. R., & Lin, H.-S. (2021). School belonging and math attitudes among high school students in advanced math. International Journal of Educational Development, 80. doi: 10.1016/j.ijedudev.2020.102297 2. Smith, T. J., Walker, D. A., Chen, H.- T., & Hong, Z.-. R. (2020). Students' sense of school belonging and attitude towards science: A cross-cultural examination. International Journal of Science and Mathematics Education, 18(5), 855-867. doi: 10.1007/s10763-019-10002-7 3. Chomentowski, P. J., Alis, J. P., Nguyen, R. K., Lukaszuk, J. -
About Logic and Logicians
About Logic and Logicians A palimpsest of essays by Georg Kreisel Selected and arranged by Piergiorgio Odifreddi Volume 2: Mathematics Lógica no Avião ABOUT LOGIC AND LOGICIANS A palimpsest of essays by Georg KREISEL Selected and arranged by Piergiorgio ODIFREDDI Volume II. Mathematics Editorial Board Fernando Ferreira Departamento de Matem´atica Universidade de Lisboa Francisco Miraglia Departamento de Matem´atica Universidade de S~aoPaulo Graham Priest Department of Philosophy The City University of New York Johan van Benthem Department of Philosophy Stanford University Tsinghua University University of Amsterdam Matteo Viale Dipartimento di Matematica \Giuseppe Peano" Universit`adi Torino Piergiorgio Odifreddi, About Logic and Logicians, Volume 2. Bras´ılia: L´ogicano Avi~ao,2019. S´erieA, Volume 2 I.S.B.N. 978-65-900390-1-9 Prefixo Editorial 900390 Obra publicada com o apoio do PPGFIL/UnB. Editor's Preface These books are a first version of Odifreddi's collection of Kreisel's expository papers, which together constitute an extensive, scholarly account of the philo- sophical and mathematical development of many of the most important figures of modern logic; some of those papers are published here for the first time. Odifreddi and Kreisel worked together on these books for several years, and they are the product of long discussions. They finally decided that they would collect those essays of a more expository nature, such as the biographical memoirs of the fellows of the Royal Society (of which Kreisel himself was a member) and other related works. Also included are lecture notes that Kreisel distributed in his classes, such as the first essay printed here, which is on the philosophy of mathematics and geometry. -
Origin of Irrational Numbers and Their Approximations
computation Review Origin of Irrational Numbers and Their Approximations Ravi P. Agarwal 1,* and Hans Agarwal 2 1 Department of Mathematics, Texas A&M University-Kingsville, 700 University Blvd., Kingsville, TX 78363, USA 2 749 Wyeth Street, Melbourne, FL 32904, USA; [email protected] * Correspondence: [email protected] Abstract: In this article a sincere effort has been made to address the origin of the incommensu- rability/irrationality of numbers. It is folklore that the starting point was several unsuccessful geometric attempts to compute the exact values of p2 and p. Ancient records substantiate that more than 5000 years back Vedic Ascetics were successful in approximating these numbers in terms of rational numbers and used these approximations for ritual sacrifices, they also indicated clearly that these numbers are incommensurable. Since then research continues for the known as well as unknown/expected irrational numbers, and their computation to trillions of decimal places. For the advancement of this broad mathematical field we shall chronologically show that each continent of the world has contributed. We genuinely hope students and teachers of mathematics will also be benefited with this article. Keywords: irrational numbers; transcendental numbers; rational approximations; history AMS Subject Classification: 01A05; 01A11; 01A32; 11-02; 65-03 Citation: Agarwal, R.P.; Agarwal, H. 1. Introduction Origin of Irrational Numbers and Their Approximations. Computation Almost from the last 2500 years philosophers have been unsuccessful in providing 2021, 9, 29. https://doi.org/10.3390/ satisfactory answer to the question “What is a Number”? The numbers 1, 2, 3, 4, , have ··· computation9030029 been called as natural numbers or positive integers because it is generally perceived that they have in some philosophical sense a natural existence independent of man. -
Dictionary of Mathematics
Dictionary of Mathematics English – Spanish | Spanish – English Diccionario de Matemáticas Inglés – Castellano | Castellano – Inglés Kenneth Allen Hornak Lexicographer © 2008 Editorial Castilla La Vieja Copyright 2012 by Kenneth Allen Hornak Editorial Castilla La Vieja, c/o P.O. Box 1356, Lansdowne, Penna. 19050 United States of America PH: (908) 399-6273 e-mail: [email protected] All dictionaries may be seen at: http://www.EditorialCastilla.com Sello: Fachada de la Universidad de Salamanca (ESPAÑA) ISBN: 978-0-9860058-0-0 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording or by any informational storage or retrieval system without permission in writing from the author Kenneth Allen Hornak. Reservados todos los derechos. Quedan rigurosamente prohibidos la reproducción de este libro, el tratamiento informático, la transmisión de alguna forma o por cualquier medio, ya sea electrónico, mecánico, por fotocopia, por registro u otros medios, sin el permiso previo y por escrito del autor Kenneth Allen Hornak. ACKNOWLEDGEMENTS Among those who have favoured the author with their selfless assistance throughout the extended period of compilation of this dictionary are Andrew Hornak, Norma Hornak, Edward Hornak, Daniel Pritchard and T.S. Gallione. Without their assistance the completion of this work would have been greatly delayed. AGRADECIMIENTOS Entre los que han favorecido al autor con su desinteresada colaboración a lo largo del dilatado período de acopio del material para el presente diccionario figuran Andrew Hornak, Norma Hornak, Edward Hornak, Daniel Pritchard y T.S. Gallione. Sin su ayuda la terminación de esta obra se hubiera demorado grandemente. -
Tutorme Subjects Covered.Xlsx
Subject Group Subject Topic Computer Science Android Programming Computer Science Arduino Programming Computer Science Artificial Intelligence Computer Science Assembly Language Computer Science Computer Certification and Training Computer Science Computer Graphics Computer Science Computer Networking Computer Science Computer Science Address Spaces Computer Science Computer Science Ajax Computer Science Computer Science Algorithms Computer Science Computer Science Algorithms for Searching the Web Computer Science Computer Science Allocators Computer Science Computer Science AP Computer Science A Computer Science Computer Science Application Development Computer Science Computer Science Applied Computer Science Computer Science Computer Science Array Algorithms Computer Science Computer Science ArrayLists Computer Science Computer Science Arrays Computer Science Computer Science Artificial Neural Networks Computer Science Computer Science Assembly Code Computer Science Computer Science Balanced Trees Computer Science Computer Science Binary Search Trees Computer Science Computer Science Breakout Computer Science Computer Science BufferedReader Computer Science Computer Science Caches Computer Science Computer Science C Generics Computer Science Computer Science Character Methods Computer Science Computer Science Code Optimization Computer Science Computer Science Computer Architecture Computer Science Computer Science Computer Engineering Computer Science Computer Science Computer Systems Computer Science Computer Science Congestion Control -
Arquiteturas Digitais a Partir Do Diagrama De Voronoi E Triangulação De Delaunay
ARQUITETURAS DIGITAIS A PARTIR DO DIAGRAMA DE VORONOI E TRIANGULAÇÃO DE DELAUNAY DIGITAL ARCHITECTURES BY THE VORONOI DIAGRAM AND DELAUNAY TRIANGULATION LIMA, FABIO FERREIRA Dr, Faculdade de Artes Visuais - Universidade Federal de Goiás; email: [email protected]. RESUMO Muitos modelos encontrados na natureza inspiram diversos pesquisadores, podendo ser apropriadas formas, estruturas, parâmetros de usos aplicáveis à engenharia e arquitetura, principalmente por meio de instruções computacionais. Nessas condições, esse artigo se atém aos benefícios oriundos das técnicas da Triangulação de Delaunay e do Diagrama de Voronoi. Os métodos adotados foram: revisão da literatura quanto às principais características, tecnologia da informação na construção, sistemas estruturais. Os objetivos são: (1) compreender as principais qualidades que essas técnicas proporcionam, pelos padrões estendidos em nós e segmentos, conexões compositivas para pilares, treliças espaciais, grelhas metálicas. (2) apresentar alguns exemplos construídos, capazes de trazer demonstrações relevantes; (3) expor as qualidades expressivas advindas das técnicas. Esses modelos se configuram como estratégias computacionais a partir de geometrias estáveis e coesas, em abordagens estruturais consistentes. PALAVRAS-CHAVE: Triangulação de Delaunay; Diagrama de Voronoi; Performance arquitetônica e estrutural. ABSTRACT Many models found in nature inspire several researchers, and may be appropriate forms, structures, parameters of uses applicable to engineering and architecture, mainly through computational instructions. Under these conditions, this article is related to the benefits derived from the techniques of the Delaunay Triangulation and the Voronoi Diagram. The methods adopted were: literature review on the main characteristics, information technology in the construction, structural systems. The objectives are: (1) to understand the main qualities that these techniques provide, by the extended patterns in nodes and segments, composite connections for pillars, space trusses, metal grids.