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On the Density of Nice Friedmans
On the density of nice Friedmans Michael Brand [email protected] Monash University School of IT Clayton, VIC 3800 Australia May 26, 2018 Abstract A Friedman number is a positive integer which is the result of an expression combining all of its own digits by use of the four basic op- erations, exponentiation and digit concatenation. A “nice” Friedman number is a Friedman number for which the expression constructing the number from its own digits can be represented with the original order of the digits unchanged. One of the fundamental questions re- garding Friedman numbers, and particularly regarding nice Friedman numbers, is how common they are among the integers. In this paper, we prove that nice Friedman numbers have density 1, when considered in binary, ternary or base four. arXiv:1310.2390v1 [math.NT] 9 Oct 2013 1 Introduction Friedman numbers [2, 3] are numbers that can be computed from their own digits, each digit used exactly once, by use of the four basic arithmetic opera- tions, exponentiation and digit concatenation (as long as digit concatenation is not the only operation used). Parentheses can be used at will. An example of a Friedman number is 25, which can be represented as 52. An example of a non-Friedman number is any power of 10, because no power of 10 can 1 be expressed as the result of a computation using only arithmetic operations and exponentiation if the initial arguments in the computation are a smaller power of 10 and several zeros. Several interesting subsets of Friedman numbers have been defined since the introduction of Friedman numbers. -
National Collegiate ) Athletic Association ) No
Case 4:14-md-02541-CW Document 941 Filed 07/25/18 Page 1 of 119 PAGES 1 - 118 UNITED STATES DISTRICT COURT NORTHERN DISTRICT OF CALIFORNIA BEFORE THE HONORABLE CLAUDIA WILKEN, JUDGE IN RE: NATIONAL COLLEGIATE ) ATHLETIC ASSOCIATION ) NO. 14-MD-2541 CW ATHLETIC GRANT-IN-AID CAP ) ANTITRUST LITIGATION ) ) MARTIN JENKINS, ET AL., ) NO. C-14-2758 CW ) PLAINTIFFS, ) ) THURSDAY, JULY 19, 2018 VS. ) ) NATIONAL COLLEGIATE ) OAKLAND, CALIFORNIA ATHLETIC ASSOCIATION, ET AL.) ) PRETRIAL CONFERENCE DEFENDANTS. ) ____________________________) REPORTER'S TRANSCRIPT OF PROCEEDINGS FOR PLAINTIFFS: HAGENS BERMAN SOBOL SHAPIRO LLP 1918 EIGHTH AVENUE, SUITE 3300 SEATTLE, WASHINGTON 98101 BY: STEVE W. BERMAN, ESQUIRE JEFF D. FRIEDMAN, ESQUIRE WINSTON & STRAWN LLP 200 PARK AVENUE NEW YORK, NEW YORK 10166 BY: JEFFREY L. KESSLER, ESQUIRE JOSEPH A. LITMAN, ESQUIRE DAVID L. GREENSPAN, ESQUIRE (APPEARANCES CONTINUED) REPORTED BY: DIANE E. SKILLMAN, CSR NO. 4909 OFFICIAL COURT REPORTER TRANSCRIPT PRODUCED BY COMPUTER-AIDED TRANSCRIPTION DIANE E. SKILLMAN, OFFICIAL COURT REPORTER, USDC Case 4:14-md-02541-CW Document 941 Filed 07/25/18 Page 2 of 119 2 1 FOR PLAINTIFFS: WINSTON & STRAWN LLP 101 CALIFORNIA STREET 2 SAN FRANCISCO, CALIFORNIA 94111 BY: SEAN D. MEENAN, ESQUIRE 3 JEANIFER E. PARSIGIAN, ESQUIRE 4 FOR PLAINTIFFS : PEARSON SIMON WARSHAW LLP 44 MONTGOMERY STREET, SUITE 2450 5 SAN FRANCISCO, CALIFORNIA 94104 BY: BENJAMIN E. SHIFTAN, ESQUIRE 6 BRUCE L. SIMON, ESQUIRE 7 PRITZKER LEVINE LLP 8 180 GRAND AVNEUE, SUITE 1390 OAKLAND, CALIFORNIA 94612 9 BY: ELIZABETH C. PRITZKER, ESQUIRE 10 11 FOR DEFENDANT WILKINSON WALSH + ESKOVITZ NCAA: 2001 M STREET NW, 10TH FLOOR 12 WASHINGTON, DC 20036 BY: BETH A. -
Anita Roddick
Life Stories Anita filling bottles at the first Body Shop, below, which opened in Brighton in 1976 life stories Anita Roddick She was a passionate s the morning sun streamed in through the windows of the human and animal A tiny green shop, a woman sat inside, frantically writing labels. ‘We’re rights campaigner nearly there. It will all be worth it,’ she who revolutionised the said, rallying the three friends pouring coconut shampoo into tiny plastic bottles. cosmetic industry by They had been working through the night. creating The Body Shop. The woman was Anita Roddick, and the date was 26 March 1976: the opening On the third anniversary of the first-ever Body Shop. What happened of her death, Mandy next reinvented the UK’s cosmetic industry and turned Anita into one of the world’s Appleyard celebrates the most famous and successful entrepreneurs. By bringing trade and ideals together, she extraordinary life of this was the first businesswoman who made it maverick entrepreneur sexy to care. The Body Shop {continued} september 2010 mArIe CLAIre <#R#> Life Stories Princess Diana meets Anita at The Body Shop HQ in With husband Visiting a forest tribe in Becoming a Littlehampton in 1986 Gordon in 1995 Brazil with daughter Sam dame in 2003 products came in simple packaging and aim was to create a product so good that voice of their campaigning. They were a At A GlANCe promoted health. The result was a multi- people would pay for it.’ formidable team: Gordon was the busi- 1942 Born in national company and a £51 million fortune. -
The Allergic Potential Arising from Proteinous Wine Fining Agents of Milk and Chicken Egg Albumen
JUSTUS-LIEBIG UNIVERSITY GIESSEN AND HOCHSCHULE GEISENHEIM UNIVERSITY THE ALLERGIC POTENTIAL ARISING FROM PROTEINOUS WINE FINING AGENTS OF MILK AND CHICKEN EGG ALBUMEN by MANUELLA WEBBER WITT M.Sc. Montpellier SupAgro, 2009 Submitted in partial fulfilment of the requirements for the degree of Dr. agr. 2014 THE ALLERGIC POTENTIAL ARISING FROM PROTEINOUS WINE FINING AGENTS OF MILK AND CHICKEN EGG ALBUMEN Submitted in partial fulfilment of the requirements for the degree of Dr. agr. 2014 First reviewer Prof Dr. Christmann Hochschule Geisenheim University (Professor for Œnology) Second reviewer Prof. Dr. Schnell Justus Liebig University of Giessen (Professor for General and Soil Microbiology) Declaration “I declare that the dissertation here submitted is entirely my own work, written without any illegitimate help by any third party and solely with materials as indicated in the dissertation. I have indicated in the text where I have used texts from already published sources, either word for word or in substance, and where I have made statements based on oral information given to me. At all times during the investigations carried out by me and described in the dissertation, I have followed the principles of good scientific practice as defined in the “Statutes of the Justus Liebig University Gießen for the Safeguarding of Good Scientific Practice” The 20th of March, 2014 Manuella Webber-Witt Note of thanks I met Prof. Dr. Monika Christmann in 2005 in Brazil. We had a friendly talk and it was the beginning of a long friendship and journey in my life. For all these years and for her patience I would like to thank Frau Christmann. -
To Serve Without Favor
TO SERVE WITHOUT FAVOR Policing, Human Rights, and Accountability in Northern Ireland Human Rights Watch/Helsinki Human Rights Watch New York AAA Washington AAA London AAA Brussels Copyright 8 May 1997 by Human Rights Watch All rights reserved. Printed in the United States of America. ISBN 1-56432-216-5 Library of Congress Catalog Card Number: 97-73331 Cover photograph copyright 8 1996 by Oistín Mac Bride. RUC riot squad in Drumcree. Addresses for Human Rights Watch 485 Fifth Avenue, New York, NY 10017-6104 Tel: (212) 972-8400, Fax: (212) 972-0905, E-mail: [email protected] 1522 K Street, N.W., #910, Washington, DC 20005-1202 Tel: (202) 371-6592, Fax: (202) 371-0124, E-mail: [email protected] 33 Islington High Street, N1 9LH London, UK Tel: (171) 713-1995, Fax: (171) 713-1800, E-mail: [email protected] 15 Rue Van Campenhout, 1000 Brussels, Belgium Tel: (2) 732-2009, Fax: (2) 732-0471, E-mail: [email protected] Web Site Address: http://www.hrw.org Gopher Address://gopher.humanrights.org:5000/11/int/Human Rights Watch Listserv address: To subscribe to the list, send an e-mail message to [email protected] with Asubscribe Human Rights Watch-news@ in the body of the message (leave the subject line blank). HUMAN RIGHTS WATCH Human Rights Watch conducts regular, systematic investigations of human rights abuses in some seventy countries around the world. Our reputation for timely, reliable disclosures has made us an essential source of information for those concerned with human rights. We address the human rights practices of governments of all political stripes, of all geopolitical alignments, and of all ethnic and religious persuasions. -
Mathfest 2018
Abstracts of Papers Presented at MathFest 2018 Denver, CO August 1 – 4, 2018 Published and Distributed by The Mathematical Association of America Contents Invited Addresses 1 Earle Raymond Hedrick Lecture Series by Gigliola Staffilani . 1 Nonlinear Dispersive Equations and the Beautiful Mathematics That Comes with Them Lecture 1: Thursday, August 2, 11:00–11:50 AM, Plaza Ballroom A, B, & C, Plaza Building Lecture 2: Friday, August 3, 10:30–11:20 AM, Plaza Ballroom A, B, & C, Plaza Building Lecture 3: Saturday, August 4, 10:00–10:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 AMS-MAA Joint Invited Address . 1 Gravity’s Action on Light: A Mathematical Journey by Arlie Petters Thursday, August 2, 10:00–10:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 MAA Invited Address . 1 Inclusion-exclusion in Mathematics: Who Stays in, Who Falls out, Why It Happens, and What We Should Do About It by Eugenia Cheng Friday, August 3, 11:30–12:20 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 Snow Business: Scientific Computing in the Movies and Beyond by Joseph Teran Saturday, August 4, 11:00–11:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 Mathematical Medicine: Modeling Disease and Treatment by Lisette de Pillis Thursday, August 2, 9:00–9:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 2 MAA James R.C. Leitzel Lecture . 2 The Relationship between Culture and the Learning of Mathematics by Talitha Washington Saturday, August 4, 9:00–9:50 AM, Plaza Ballroom A, B, & C, Plaza Building . -
Anita Roddick Founder of the Body Shop by Krista Mcluskey
PSSA ENGLISH LANGUAGE ARTS PASSAGE 3 Read the following passage about Anita Roddick. Then answer questions 20–29. Anita Roddick Founder of The Body Shop by Krista McLuskey Early Years Anita was born in Littlehampton, England, where her parents owned the Clifton Café. Anita’s father, Henry, turned the Clifton Café into an American-style diner like the ones he had seen while living in the United States. It was complete with pinball machines, a jukebox, and Coca-Cola, which was not well known in England at that time. Suddenly, the café became very popular. Anita realized that the atmosphere in a business can make it successful. When Anita was about ten years old, her mother took over the café. All the children were expected to work there after school and on weekends to help support the family. Meanwhile, Anita was completing her education. After finishing secondary school, she attended a teacher training college in the city of Bath. Developing Skills After graduating, Anita decided she wanted some adventure in her life. She traveled to Tahiti, New Hebrides, Australia, Madagascar, New Caledonia, and South Africa. In these places, Anita watched the local women use natural products to clean their skin and hair. She tried them and found they worked better than the products she used back in England. After Anita returned to England, she met and married Gordon Roddick, with whom she had two daughters. Anita and Gordon worked hard running a hotel and restaurant. One day, Gordon announced that he wanted to take two years off to ride on horseback from Buenos Aires, Argentina, to New York City. -
Number Games: Pandigital Numbers, Friedman Numbers, and E
Pandigital numbers Friedman numbers Approximating e Number Games: Pandigital Numbers, Friedman Numbers, and e Richard Wong SMMG 2020 Slides and worksheets can be found at http://www.ma.utexas.edu/users/richard.wong/Notes.html Richard Wong University of Texas at Austin Number Games: Pandigital numbers Friedman numbers Approximating e Pandigital Numbers Definition A pandigital number is an integer that uses each digit 0-9 exactly once in the significant digits of its decimal representation. Example I 1234567890 is a pandigital number. I 0123456789 is not. I 11234567890 is not a pandigital number, but it is a pandigital number with redundant digits. Richard Wong University of Texas at Austin Number Games: Pandigital numbers Friedman numbers Approximating e Pandigital Numbers Definition A pandigital number with redundant digits is an integer that uses each digit 0-9 at least once in the significant digits of its decimal representation. Definition A pandigital number is an integer that uses each digit 0-9 exactly once in the significant digits of its decimal representation. Richard Wong University of Texas at Austin Number Games: Pandigital numbers Friedman numbers Approximating e Work on the Pandigital numbers section of the worksheet! Richard Wong University of Texas at Austin Number Games: Pandigital numbers Friedman numbers Approximating e Friedman numbers Definition A Friedman number is an integer that can be non-trivially expressed as a formula using each of its significant digits exactly once, along with the operations (+, −, ×, ÷), additive inverses, parentheses, and exponentiation. Example I (n) is a trivial way to express an integer n. So that means that the single digit numbers cannot be Friedman numbers. -
“Business As Unusual ”: a Case Study on the Body Shop
Teaching Case ______________________________ Journal of Applied Case Research Sponsored by the Southwest Case Research Association “BUSINESS AS UNUSUAL”: A CASE STUDY ON THE BODY SHOP Subhadip Roy ICFAI University, India Lopamudra Ghosh ICFAI University, India © Journal of Applied Case Research Accepted: September 2008 2 “BUSINESS AS UNUSUAL1”: A CASE STUDY ON THE BODY SHOP “The business has existed for one reason only – to allow us to use our success to act as a force of change, to continue the education and consciousness-raising of our staff, to assist development in the Third World and above all, to help protect the environment. What we are trying to do is to create a new business paradigm, simply showing that business can have a human face and a social conscience”. - Anita Roddick (1991)2 ANITA RODDICK STEPPED DOWN AS THE BODY SHOP CHAIRPERSON February 2002, the founder of one of the biggest cosmetics companies in the world, Anita Roddick (Anita) stepped down as the chairperson of the Body Shop along with husband Gordon Roddick (Gordon), who was a co-chair along with her. A number of controversies in the mid and end 1990’s had badly affected the company’s image as doing “business with a human face” as opined by Anita in the quote given above. Periods of losses, coupled with poorly motivated shareholders, de-motivated franchisees, unsuccessful restructuring attempts and public propaganda against the company was proving to be too strong for the company to cope up. Thus, the decision of Anita and Gordon came up after several unsuccessful attempts to find a buyer for the firm. -
The Body Shop an Introduction Who Are We
The Body Shop An introduction Who are we A TRULY UNIQUE BRAND IN THE HEALTH & BEAUTY SECTOR - The original natural & ethical beauty brand DIFFERENT - A worldwide retail environment, providing direct connection with customers through a dedicated sales staff - Covering all beauty segments with more than 1200 products BEAUTY WITH HEART AN ALTERNATIVE VISION OF BEAUTY -Balance between beauty & values: 100% vegetarian, never tested on animal, NATURAL Community fair trade ingredients, responsibly sourced from around the world... - Always embracing diversity, never conformed to beauty industry stereotypes. 5 CORES VALUES SINCE 1976 VALUES-DRIVEN The only brand that manages to change laws through long-standing campaigning. Our heritage Anita Roddick, the founder . A unique personality: Multi-award winner & Dame commander of the Order of the British Empire MAVERICK FAMOUS ACTIVIST A BELIEVER & AGITATOR IN THE IMPOSSIBLE EXPLOSIVE MADE POSITIVELY ENERGY POSSIBLE . A singular vision: ‘business as unusual’ - a force for good & change . Pioneered ethical business practice . Author of 6 books 5 It all started in 1976 . Started in Brighton England in 1976 by Dame Anita Roddick – motivated by need to feed her family while her husband fulfilled a lifelong ambition to ride from Buenos Aires to New York on horseback. The store opened with a range of 25 hand- mixed naturally inspired products. Anita initially attracted customers by sprinkling strawberry perfume oil on the street outside . The funeral parlour next door opposed the name ’The Body Shop’ but Anita retaliated, called the press resulting in significant publicity And has become an iconic natural brand known, loved & respected the world over The Body Shop: . -
A Balance of Business and Human Relations and the Contract Between
Neptunus, e-revue, CDMO, vol. 20, 2014/3, www.cdmo.univ-nantes.fr ! ! ! Human Sea Project www.humansea.univ-nantes.fr ! ! ! A balance of Business and Human Relations and the contract between a ship owner and the Flag State ! ! by Andria ALEXANDROU ! PhD Candidate, Queen Mary University of London ! ! ! !I. Introduction The shipping industry is one of the most powerful areas of transport which enables the carriage of goods from one country to another. Many countries base their economic grounds and accord their financial growth to this rapidly flourishing – if well functioned – industry. In this respect, globalisation is enhanced and it also plays a vital role, as the industry acts as a “facilitator1” for economic development. This is proven from the case which dates back to 1966, on April the 23rd when Fairland, “the first converted container ship, sailed from Port Elizabeth in the USA to Rotterdam, carrying with it 236 containers. This created a trend, for instance during the Vietnam War2, when the US government supplied its troops through !container shipping, which proved to be the most efficient option.” Nevertheless, it is important to state here, that there is a need for states to embrace social values and enhance the proper functioning of the shipping companies, on issues related to employment contracts. The main reason for arguing this emanates from the fact that the industry would have never functioned properly without the human presence. Machines do not constitute the source of profit but rather the crew in each company. Therefore, by keeping 1 W. R. GREGORY , B.A., Flags of Convenience: The Development of open registries in the global maritime business and implications from modern seafarers. -
Numbers 1 to 100
Numbers 1 to 100 PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Tue, 30 Nov 2010 02:36:24 UTC Contents Articles −1 (number) 1 0 (number) 3 1 (number) 12 2 (number) 17 3 (number) 23 4 (number) 32 5 (number) 42 6 (number) 50 7 (number) 58 8 (number) 73 9 (number) 77 10 (number) 82 11 (number) 88 12 (number) 94 13 (number) 102 14 (number) 107 15 (number) 111 16 (number) 114 17 (number) 118 18 (number) 124 19 (number) 127 20 (number) 132 21 (number) 136 22 (number) 140 23 (number) 144 24 (number) 148 25 (number) 152 26 (number) 155 27 (number) 158 28 (number) 162 29 (number) 165 30 (number) 168 31 (number) 172 32 (number) 175 33 (number) 179 34 (number) 182 35 (number) 185 36 (number) 188 37 (number) 191 38 (number) 193 39 (number) 196 40 (number) 199 41 (number) 204 42 (number) 207 43 (number) 214 44 (number) 217 45 (number) 220 46 (number) 222 47 (number) 225 48 (number) 229 49 (number) 232 50 (number) 235 51 (number) 238 52 (number) 241 53 (number) 243 54 (number) 246 55 (number) 248 56 (number) 251 57 (number) 255 58 (number) 258 59 (number) 260 60 (number) 263 61 (number) 267 62 (number) 270 63 (number) 272 64 (number) 274 66 (number) 277 67 (number) 280 68 (number) 282 69 (number) 284 70 (number) 286 71 (number) 289 72 (number) 292 73 (number) 296 74 (number) 298 75 (number) 301 77 (number) 302 78 (number) 305 79 (number) 307 80 (number) 309 81 (number) 311 82 (number) 313 83 (number) 315 84 (number) 318 85 (number) 320 86 (number) 323 87 (number) 326 88 (number)