WOLFRAM EDUCATION SOLUTIONS MATHEMATICA® TECHNOLOGIES for TEACHING and RESEARCH About Wolfram
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Jet Development in Leading Log QCD.Pdf
17 CALT-68-740 DoE RESEARCH AND DEVELOPMENT REPORT Jet Development in Leading Log QCD * by STEPHEN WOLFRAM California Institute of Technology, Pasadena. California 91125 ABSTRACT A simple picture of jet development in QCD is described. Various appli- cations are treated, including transverse spreading of jets, hadroproduced y* pT distributions, lepton energy spectra from heavy quark decays, soft parton multiplicities and hadron cluster formation. *Work supported in part by the U.S. Department of Energy under Contract No. DE-AC-03-79ER0068 and by a Feynman Fellowship. 18 According to QCD, high-energy e+- e annihilation into hadrons is initiated by the production from the decaying virtual photon of a quark and an antiquark, ,- +- each with invariant masses up to the c.m. energy vs in the original e e collision. The q and q then travel outwards radiating gluons which serve to spread their energy and color into a jet of finite angle. After a time ~ 1/IS, the rate of gluon emissions presumably decreases roughly inversely with time, except for the logarithmic rise associated with the effective coupling con 2 stant, (a (t) ~ l/log(t/A ), where It is the invariant mass of the radiating s . quark). Finally, when emissions have degraded the energies of the partons produced until their invariant masses fall below some critical ~ (probably c a few times h), the system of quarks and gluons begins to condense into the observed hadrons. The probability for a gluon to be emitted at times of 0(--)1 is small IS and may be est~mated from the leading terms of a perturbation series in a (s). -
T.C. Selçuk Üniversitesi Fen Bilimleri Enstitüsü Wolfram
T.C. SELÇUK ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ WOLFRAM|ALPHA BİLGİ MOTORUNDA MATEMATİKSEL VE İSTATİSTİKSEL İŞLEMLER Seçkin YILMAZ YÜKSEK LİSANS TEZİ İstatistik Anabilim Dalı Ekim-2011 KONYA Her Hakkı Saklıdır TEZ BİLDİRİMİ Bu tezdeki bütün bilgilerin etik davranış ve akademik kurallar çerçevesinde elde edildiğini ve tez yazım kurallarına uygun olarak hazırlanan bu çalışmada bana ait olmayan her türlü ifade ve bilginin kaynağına eksiksiz atıf yapıldığını bildiririm. DECLARATION PAGE I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Seçkin YILMAZ Tarih: ÖZET YÜKSEK LİSANS TEZİ WOLFRAM|ALPHA BİLGİ MOTORUNDA MATEMATİKSEL VE İSTATİSTİKSEL İŞLEMLER Seçkin YILMAZ Selçuk Üniversitesi Fen Bilimleri Enstitüsü İstatistik Anabilim Dalı Danışman: Yrd. Doç. Dr. Buğra SARAÇOĞLU Yıl, 2011 Sayfa 89 Jüri Yrd. Doç. Dr. Buğra SARAÇOĞLU Prof. Dr. Aşır GENÇ Yrd. Doç. Dr. Hasan KÖSE İstatistiksel ve matematiksel işlemlerin çözümünde paket programlar kullanılmaktadır. Paket programların çoğunun ücretli olması, kullanılacak bilgisayarda kurulu olması ve uygun işletim sisteminin yüklü olması gibi faktörler kullanıcıları birden fazla etmene bağlı kılmaktadır. Kullanıcıların istatistiksel ve matematiksel problemleri çözebilmesi için paket program kullanmak yerine internet üzerinden hizmet veren Wolfram|Alpha bilgi motorunu kullanarak bu işlemleri yapabilmektedir. Bu bilgi motorunun internetten ücretsiz hizmet vermesi, kullanıcıların bilgisayarlarına herhangi bir paket program kurmayı gerektirmemesi, kullanıcıların istatistik ve matematik ile ilgili herhangi bir konu arattığında detaylı bir şekilde bilgi sunması kullanıcıya sağlamış olduğu başlıca kolaylıklardır. Bu çalışmada Wolfram|Alpha bilgi motorunun bazı matematiksel ve istatistiksel uygulamaları verilmiştir. -
PARTON and HADRON PRODUCTION in E+E- ANNIHILATION Stephen Wolfram California Institute of Technology, Pasadena, California 91125
549 * PARTON AND HADRON PRODUCTION IN e+e- ANNIHILATION Stephen Wolfram California Institute of Technology, Pasadena, California 91125 Ab stract: The production of showers of partons in e+e- annihilation final states is described according to QCD , and the formation of hadrons is dis cussed. Resume : On y decrit la production d'averses d� partons dans la theorie QCD qui forment l'etat final de !'annihilation e+ e , ainsi que leur transform ation en hadrons. *Work supported in part by the U.S. Department of Energy under contract no. DE-AC-03-79ER0068. SSt1 Introduction In these notes , I discuss some attemp ts e ri the cl!evellope1!1t of - to d s c be hadron final states in e e annihilation events ll>Sing. QCD. few featm11res A (barely visible at available+ energies} of this deve l"'P"1'ent amenab lle· are lt<J a precise and formal analysis in QCD by means of pe·rturbatirnc• the<J ry. lfor the mos t part, however, existing are quite inadle<!i""' lte! theoretical mett:l�ods one must therefore simply try to identify dl-iimam;t physical p.l:ten<0melilla tt:he to be expected from QCD, and make estll!att:es of dne:i.r effects , vi.th the hop·e that results so obtained will provide a good appro�::illliatimn to eventllLal'c ex act calculations . In so far as such estllma�es r necessa�y� pre�ise �r..uan- a e titative tests of QCD are precluded . On the ott:her handl , if QC!Ji is ass11l!med correct, then existing experimental data to inve•stigate its be may \JJ:SE•«f havior in regions not yet explored by theoreticalbe llJleaums . -
The Problem of Distributed Consensus: a Survey Stephen Wolfram*
The Problem of Distributed Consensus: A Survey Stephen Wolfram* A survey is given of approaches to the problem of distributed consensus, focusing particularly on methods based on cellular automata and related systems. A variety of new results are given, as well as a history of the field and an extensive bibliography. Distributed consensus is of current relevance in a new generation of blockchain-related systems. In preparation for a conference entitled “Distributed Consensus with Cellular Automata and Related Systems” that we’re organizing with NKN (= “New Kind of Network”) I decided to explore the problem of distributed consensus using methods from A New Kind of Science (yes, NKN “rhymes” with NKS) as well as from the Wolfram Physics Project. A Simple Example Consider a collection of “nodes”, each one of two possible colors. We want to determine the majority or “consensus” color of the nodes, i.e. which color is the more common among the nodes. A version of this document with immediately executable code is available at writings.stephenwolfram.com/2021/05/the-problem-of-distributed-consensus Originally published May 17, 2021 *Email: [email protected] 2 | Stephen Wolfram One obvious method to find this “majority” color is just sequentially to visit each node, and tally up all the colors. But it’s potentially much more efficient if we can use a distributed algorithm, where we’re running computations in parallel across the various nodes. One possible algorithm works as follows. First connect each node to some number of neighbors. For now, we’ll just pick the neighbors according to the spatial layout of the nodes: The algorithm works in a sequence of steps, at each step updating the color of each node to be whatever the “majority color” of its neighbors is. -
Understanding Differential Equations Using Mathematica and Interactive Demonstrations Paritosh Mokhasi
CODEE Journal Volume 9 Article 8 11-25-2012 Understanding Differential Equations Using Mathematica and Interactive Demonstrations Paritosh Mokhasi James Adduci Devendra Kapadia Follow this and additional works at: http://scholarship.claremont.edu/codee Recommended Citation Mokhasi, Paritosh; Adduci, James; and Kapadia, Devendra (2012) "Understanding Differential Equations Using Mathematica and Interactive Demonstrations," CODEE Journal: Vol. 9, Article 8. Available at: http://scholarship.claremont.edu/codee/vol9/iss1/8 This Article is brought to you for free and open access by the Journals at Claremont at Scholarship @ Claremont. It has been accepted for inclusion in CODEE Journal by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. Understanding Differential Equations Using Mathematica and Interactive Demonstrations Paritosh Mokhasi, James Adduci and Devendra Kapadia Wolfram Research, Inc., Champaign, IL. Keywords: Mathematica, Wolfram Demonstrations Project Manuscript received on May 24, 2012; published on November 25, 2012. Abstract: The solution of differential equations using the software package Mathematica is discussed in this paper. We focus on two functions, DSolve and NDSolve, and give various examples of how one can obtain symbolic or numerical results using these functions. An overview of the Wolfram Demon- strations Project is given, along with various novel user-contributed examples in the field of differential equations. The use of these Demonstrations in a classroom setting is elaborated upon to emphasize their significance for education. 1 Introduction 1 Mathematica is a powerful software package used for all kinds of symbolic and numerical computations. It has been available for around 25 years. Mathematica is sometimes viewed as a very sophisticated calculator useful for solving a variety of different problems, including differential equations. -
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Mel says, “This is swell! But it’s not ideal—it’s a free, grainy PDF.” Attain your ideals! Purchase a nicer, printable PDF of this issue. Or nicest of all, subscribe to the paper version of the Annals of Improbable Research (six issues per year, delivered to your doorstep!). To purchase pretty PDFs, or to subscribe to splendid paper, go to http://www.improbable.com/magazine/ ANNALS OF Special Issue THE 2009 IG® NOBEL PRIZES Panda poo spinoff, Tequila-based diamonds, 11> Chernobyl-inspired bra/mask… NOVEMBER|DECEMBER 2009 (volume 15, number 6) $6.50 US|$9.50 CAN 027447088921 The journal of record for inflated research and personalities Annals of © 2009 Annals of Improbable Research Improbable Research ISSN 1079-5146 print / 1935-6862 online AIR, P.O. Box 380853, Cambridge, MA 02238, USA “Improbable Research” and “Ig” and the tumbled thinker logo are all reg. U.S. Pat. & Tm. Off. 617-491-4437 FAX: 617-661-0927 www.improbable.com [email protected] EDITORIAL: [email protected] The journal of record for inflated research and personalities Co-founders Commutative Editor VP, Human Resources Circulation (Counter-clockwise) Marc Abrahams Stanley Eigen Robin Abrahams James Mahoney Alexander Kohn Northeastern U. Research Researchers Webmaster Editor Associative Editor Kristine Danowski, Julia Lunetta Marc Abrahams Mark Dionne Martin Gardiner, Tom Gill, [email protected] Mary Kroner, Wendy Mattson, General Factotum (web) [email protected] Dissociative Editor Katherine Meusey, Srinivasan Jesse Eppers Rose Fox Rajagopalan, Tom Roberts, Admin Tom Ulrich Technical Eminence Grise Lisa Birk Psychology Editor Dave Feldman Robin Abrahams Design and Art European Bureau Geri Sullivan Art Director emerita Kees Moeliker, Bureau Chief Contributing Editors PROmote Communications Peaco Todd Rotterdam Otto Didact, Stephen Drew, Ernest Lois Malone Webmaster emerita [email protected] Ersatz, Emil Filterbag, Karen Rich & Famous Graphics Steve Farrar, Edinburgh Desk Chief Hopkin, Alice Kaswell, Nick Kim, Amy Gorin Erwin J.O. -
Cellular Automation
John von Neumann Cellular automation A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays.[2] A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton. The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. -
A New Kind of Science
Wolfram|Alpha, A New Kind of Science A New Kind of Science Wolfram|Alpha, A New Kind of Science by Bruce Walters April 18, 2011 Research Paper for Spring 2012 INFSY 556 Data Warehousing Professor Rhoda Joseph, Ph.D. Penn State University at Harrisburg Wolfram|Alpha, A New Kind of Science Page 2 of 8 Abstract The core mission of Wolfram|Alpha is “to take expert-level knowledge, and create a system that can apply it automatically whenever and wherever it’s needed” says Stephen Wolfram, the technologies inventor (Wolfram, 2009-02). This paper examines Wolfram|Alpha in its present form. Introduction As the internet became available to the world mass population, British computer scientist Tim Berners-Lee provided “hypertext” as a means for its general consumption, and coined the phrase World Wide Web. The World Wide Web is often referred to simply as the Web, and Web 1.0 transformed how we communicate. Now, with Web 2.0 firmly entrenched in our being and going with us wherever we go, can 3.0 be far behind? Web 3.0, the semantic web, is a web that endeavors to understand meaning rather than syntactically precise commands (Andersen, 2010). Enter Wolfram|Alpha. Wolfram Alpha, officially launched in May 2009, is a rapidly evolving "computational search engine,” but rather than searching pre‐existing documents, it actually computes the answer, every time (Andersen, 2010). Wolfram|Alpha relies on a knowledgebase of data in order to perform these computations, which despite efforts to date, is still only a fraction of world’s knowledge. Scientist, author, and inventor Stephen Wolfram refers to the world’s knowledge this way: “It’s a sad but true fact that most data that’s generated or collected, even with considerable effort, never gets any kind of serious analysis” (Wolfram, 2009-02). -
Downloadable PDF of the 77500-Word Manuscript
From left: W. Daniel Hillis, Neil Gershenfeld, Frank Wilczek, David Chalmers, Robert Axelrod, Tom Griffiths, Caroline Jones, Peter Galison, Alison Gopnik, John Brockman, George Dyson, Freeman Dyson, Seth Lloyd, Rod Brooks, Stephen Wolfram, Ian McEwan. In absentia: Andy Clark, George Church, Daniel Kahneman, Alex "Sandy" Pentland (Click to expand photo) INTRODUCTION by Venki Ramakrishnan The field of machine learning and AI is changing at such a rapid pace that we cannot foresee what new technical breakthroughs lie ahead, where the technology will lead us or the ways in which it will completely transform society. So it is appropriate to take a regular look at the landscape to see where we are, what lies ahead, where we should be going and, just as importantly, what we should be avoiding as a society. We want to bring a mix of people with deep expertise in the technology as well as broad 1 thinkers from a variety of disciplines to make regular critical assessments of the state and future of AI. —Venki Ramakrishnan, President of the Royal Society and Nobel Laureate in Chemistry, 2009, is Group Leader & Former Deputy Director, MRC Laboratory of Molecular Biology; Author, Gene Machine: The Race to Decipher the Secrets of the Ribosome. [ED. NOTE: In recent months, Edge has published the fifteen individual talks and discussions from its two-and-a-half-day Possible Minds Conference held in Morris, CT, an update from the field following on from the publication of the group-authored book Possible Minds: Twenty-Five Ways of Looking at AI. As a special event for the long Thanksgiving weekend, we are pleased to publish the complete conference—10 hours plus of audio and video, as well as this downloadable PDF of the 77,500-word manuscript. -
WOLFRAM EDUCATION SOLUTIONS MATHEMATICA® TECHNOLOGIES for TEACHING and RESEARCH About Wolfram Research
WOLFRAM EDUCATION SOLUTIONS MATHEMATICA® TECHNOLOGIES FOR TEACHING AND RESEARCH About Wolfram Research For over two decades, Wolfram Research has been dedicated to developing tools that inspire exploration and innovation. As we work toward our goal to make the world’s data computable, we have expanded our portfolio to include a variety of products and technologies that, when combined, provide a true campuswide solution. At the center is Mathematica—our ever-advancing core product that has become the ultimate application for computation, visualization, and development. With millions of dedicated users throughout the technical and educational communities, Mathematica is used for everything from teaching simple concepts in the classroom to doing serious research using some of the world’s largest clusters. Wolfram’s commitment to education spans from elementary education to research universities. Through our free educational resources, STEM teacher workshops, and on-campus technical talks, we interact with educators whose feedback we rely on to develop tools that support their changing needs. Just as Mathematica revolutionized technical computing 20 years ago, our ongoing development of Mathematica technology and continued dedication to education are transforming the composition of tomorrow’s classroom. With more added all the time, Wolfram educational resources bolster pedagogy and support technology for classrooms and campuses everywhere. Favorites among educators include: Wolfram|Alpha®, the Wolfram Demonstrations Project™, MathWorld™, -
INFORMATION– CONSCIOUSNESS– REALITY How a New Understanding of the Universe Can Help Answer Age-Old Questions of Existence the FRONTIERS COLLECTION
THE FRONTIERS COLLECTION James B. Glattfelder INFORMATION– CONSCIOUSNESS– REALITY How a New Understanding of the Universe Can Help Answer Age-Old Questions of Existence THE FRONTIERS COLLECTION Series editors Avshalom C. Elitzur, Iyar, Israel Institute of Advanced Research, Rehovot, Israel Zeeya Merali, Foundational Questions Institute, Decatur, GA, USA Thanu Padmanabhan, Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India Maximilian Schlosshauer, Department of Physics, University of Portland, Portland, OR, USA Mark P. Silverman, Department of Physics, Trinity College, Hartford, CT, USA Jack A. Tuszynski, Department of Physics, University of Alberta, Edmonton, AB, Canada Rüdiger Vaas, Redaktion Astronomie, Physik, bild der wissenschaft, Leinfelden-Echterdingen, Germany THE FRONTIERS COLLECTION The books in this collection are devoted to challenging and open problems at the forefront of modern science and scholarship, including related philosophical debates. In contrast to typical research monographs, however, they strive to present their topics in a manner accessible also to scientifically literate non-specialists wishing to gain insight into the deeper implications and fascinating questions involved. Taken as a whole, the series reflects the need for a fundamental and interdisciplinary approach to modern science and research. Furthermore, it is intended to encourage active academics in all fields to ponder over important and perhaps controversial issues beyond their own speciality. Extending from quantum physics and relativity to entropy, conscious- ness, language and complex systems—the Frontiers Collection will inspire readers to push back the frontiers of their own knowledge. More information about this series at http://www.springer.com/series/5342 For a full list of published titles, please see back of book or springer.com/series/5342 James B. -
Recursos Informáticos Para La Docencia En Matemáticas Y Finanzas: the Wolfram Demonstrations Project
Recursos informáticos para la docencia en Matemáticas y Finanzas: The Wolfram Demonstrations Project Recursos informáticos para la docencia en Matemáticas y Finanzas: The Wolfram Demonstrations Project Muñoz Torrecillas, Mª José Departamento de Dirección y Gestión de Empresas Universidad de Almería Rodríguez Alcantud, José Carlos Departamento de Economía e Historia Económica Universidad de Salamanca RESUMEN En este trabajo ofrecemos información sobre las posibilidades del Wolfram Demonstrations Project como herramienta pedagógica. Las herramientas necesarias para aprovecharlo son de libre uso, multiplataforma, y accesibles desde el navegador. Describimos sus características principales y nos centramos en sus potencialidades para la docencia en Finanzas, Matemáticas y Teoría de Juegos. Palabras claves: Computable Document Format; Wolfram Demonstrations Project; Docencia, Finanzas; Docencia, Teoría de Juegos; Docencia, Matemáticas. Área temática: Metodología y Didáctica. XIX Jornadas ASEPUMA – VII Encuentro Internacional 1 Anales de ASEPUMA nº 19: 0407 Muñoz Torrecillas, Mª José; Rodríguez Alcantud, José Carlos ABSTRACT Our work offers detailed information about the possibilities of The Wolfram Demonstrations Project as a teaching resource. The tools that permit to use it are free, multi- platform, and accessible from the browser. We describe its main features and focus on its potential for teaching in Finance, Mathematics and Game Theory. Keywords: Computable Document Format; Wolfram Demonstrations Project; Teaching, Finance; Teaching, Game Theory; Teaching, Mathematics. Acknowledgments: José Carlos Rodríguez quiere agradecer la financiación parcial de este trabajo a través del proyecto ECO2009-07682 del Ministerio de Ciencia e Innovación, Gobierno de España. XIX Jornadas ASEPUMA – VII Encuentro Internacional 2 Anales de ASEPUMA nº 19: 0407 Recursos informáticos para la docencia en Matemáticas y Finanzas: The Wolfram Demonstrations Project 1.