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												How to Juggle the Proof for Every Theorem an Exploration of the Mathematics Behind Juggling
How to juggle the proof for every theorem An exploration of the mathematics behind juggling Mees Jager 5965802 (0101) 3 0 4 1 2 (1100) (1010) 1 4 4 3 (1001) (0011) 2 0 0 (0110) Supervised by Gil Cavalcanti Contents 1 Abstract 2 2 Preface 4 3 Preliminaries 5 3.1 Conventions and notation . .5 3.2 A mathematical description of juggling . .5 4 Practical problems with mathematical answers 9 4.1 When is a sequence jugglable? . .9 4.2 How many balls? . 13 5 Answers only generate more questions 21 5.1 Changing juggling sequences . 21 5.2 Constructing all sequences with the Permutation Test . 23 5.3 The converse to the average theorem . 25 6 Mathematical problems with mathematical answers 35 6.1 Scramblable and magic sequences . 35 6.2 Orbits . 39 6.3 How many patterns? . 43 6.3.1 Preliminaries and a strategy . 43 6.3.2 Computing N(b; p).................... 47 6.3.3 Filtering out redundancies . 52 7 State diagrams 54 7.1 What are they? . 54 7.2 Grounded or Excited? . 58 7.3 Transitions . 59 7.3.1 The superior approach . 59 7.3.2 There is a preference . 62 7.3.3 Finding transitions using the flattening algorithm . 64 7.3.4 Transitions of minimal length . 69 7.4 Counting states, arrows and patterns . 75 7.5 Prime patterns . 81 1 8 Sometimes we do not find the answers 86 8.1 The converse average theorem . 86 8.2 Magic sequence construction . 87 8.3 finding transitions with flattening algorithm . - 
												
												Revolutionary Flyer V2n2 Fall84for a PDF with Full
A FLYING DISC & FOOTBAG SPORTS DIGEST ~~~~~~~~~ ULTIMATE THE SINKHOLE CLASSIC DISC GOLF WORLD + STATE CHAMPIONSHIPS FOOTBAG NATIONAL CHAMPIONSHIPS «UPCOMING EVENTS» The Revolutionary Flyer FROM THE EDITORS With the passing of summer , autumn is falling upon us leaving time to reflect on the commitment we ' ve made to you , the readers . Making this flyer a subscription publication was essential for its growth. We are pleased with the response we have received over the summer , for it has helped to establish a foundation o~ which to build. Therefore we can pro cede with our goal of making this the best flyer of its type to be circulated throughout Florida. This issue covers Ultimate ' s exciting Sinkhole City Classic , disc golf from the State to the World Championshi ps . W. F. A. Footbag Nationals , and other little interesting tidbits that make for enjoyable reading. So go ahead , read , enjoy , and (if you haven ' t already) subscribe. It will be well worth the investment. Fantastic Flights! Bret & Dori Executive Editor EDITORIAL OFFICE : Bret Segrest The Revolutionary Flyer Assistant Editor 351 Montgomery Road Dori Segrest Alt. Spgs ., Fl. 32714 (05)862- 4852 Contributors Ed Aviles Jr. Lynn Finch Terry Hamlin Next Issue Nick Hart January 1st. Ace Mason The W.F.A. .................. r :' :' I ~ I . BRAND W s¢- S~ The ~ NEW DISC! I Danciny Footbag WOISCRAFT »The PHANTOM W ~ PROOUCTS ~ In,""""", the N'l:W'P.ST H 10 R QUAUTY P'CXYJ'BAO - B~R BY D!'.810N &nd ~NJOY!:D ~ Discraft Products has come out with by bolh recre&Uonal player and profes.slr, M.! altke a new golf and distance disc , the EASIEST 1'0 KICK I ITS PU$I1C BUDS MAK1!! IT PHANTOM. - 
												
												Children Bond with SJSU Parents Employees Fired
SERVING SAN JOSE STATE UNIVERSITY SINCE 1934 SPARTANSPARTAN DAILYDAILY WWW.THESPARTANDAILY.COM VOLUME 122, NUMBER 53 FRIDAY, APRIL 23, 2004 Children bond with SJSU parents Employees fi red for taking photos of soldiers’ caskets Associated Press WASHINGTON — The Pentagon lost its tight control over the images of coffi ns returning from Iraq as about 350 such images were released under the Freedom of Information Act and a Seattle newspaper published a similar photo taken by a military contractor. After Dover Air Force Base, the main port for returning remains, released hundreds of government photos of the ceremonies, the Defense Department ordered Thursday that no more photographs be released. In addition, two employees for defense contractor Maytag Aircraft were fi red after the Pentagon complained about a photo of fl ag-draped caskets taken by one of them appeared in the Seattle Times. In March 2003, on the eve of war in Iraq, the Pentagon ordered an end to all media coverage of ceremonies for the returning remains of soldiers killed overseas. Although Dover already had such a policy, the Pentagon action enforced a military-wide ban on images of fl ag-draped caskets that dated from late 2000 but had not been followed. With few exceptions, the ban had remained in force until recent days. But last week, about 350 photos from Dover were released under a Freedom of Information Act request by Russ Kick, a First Amendment advocate who runs a Web site called the Memory Hole (www.thememoryhole.org). Dover had recommended that Kick’s request be denied, but offi cials at Air Mobility Command headquarters at Scott Air Force Base in Illinois authorized the release on appeal. - 
												
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Cairns, John William (1976) The strength of lapped joints in reinforced concrete columns. PhD thesis. http://theses.gla.ac.uk/1472/ Copyright and moral rights for this thesis are retained by the author A copy can be downloaded for personal non-commercial research or study, without prior permission or charge This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the Author The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the Author When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given Glasgow Theses Service http://theses.gla.ac.uk/ [email protected] THE STRENGTHOF LAPPEDJOINTS IN REINFORCEDCONCRETE COLUMNS by J. Cairns, B. Sc. A THESIS PRESENTEDFOR THE DEGREEOF DOCTOROF PHILOSOPHY Y4 THE UNIVERSITY OF GLASGOW by JOHN CAIRNS, B. Sc. October, 1976 3 !ý I CONTENTS Page ACKNOWLEDGEIvIENTS 1 SUMMARY 2 NOTATION 4 Chapter 1 INTRODUCTION 7 Chapter 2 REVIEW OF LITERATURE 2.1 Bond s General 10 2.2 Anchorage Tests 12" 2.3 Tension Lapped Joints 17 2.4 Compression Lapped Joints 21 2.5 End Bearing 26 2.6 Current Codes of Practice 29 Chapter 3 THEORETICALSTUDY OF THE STRENGTHOF LAPPED JOINTS 3.1 Review of Theoretical Work on Bond Strength 32 3.2 Theoretical Studies of Ultimate Bond Strength 33 3.3 Theoretical Approach 42 3.4 End Bearing 48 3.5 Bond of Single Bars Surrounded by a Spiral 51 3.6 Lapped Joints 53 3.7 Variation of Steel Stress Through a Lapped Joint 59 3.8 Design of Experiments 65 Chapter 4 DESCRIPTION OF EXPERIMENTALWORK 4.1 General Description of Test Specimens 68 4.2 Materials 72 4.3 Fabrication of Test Specimens 78 4.4 Test Procedure 79 4.5 Instrumentation 80 4.6 Push-in Test Specimens 82 CONTENTScontd. - 
												
												Siteswap-Notes-Extended-Ltr 2014.Pages
Understanding Two-handed Siteswap http://kingstonjugglers.club/r/siteswap.pdf Greg Phillips, [email protected] Overview Alternating throws Siteswap is a set of notations for describing a key feature Many juggling patterns are based on alternating right- of juggling patterns: the order in which objects are hand and lef-hand throws. We describe these using thrown and re-thrown. For an object to be re-thrown asynchronous siteswap notation. later rather than earlier, it needs to be out of the hand longer. In regular toss juggling, more time out of the A1 The right and lef hands throw on alternate beats. hand means a higher throw. Any pattern with different throw heights is at least partly described by siteswap. Rules C2 and A1 together require that odd-numbered Siteswap can be used for any number of “hands”. In this throws end up in the opposite hand, while even guide we’ll consider only two-handed siteswap; numbers stay in the same hand. Here are a few however, everything here extends to siteswap with asynchronous siteswap examples: three, four or more hands with just minor tweaks. 3 a three-object cascade Core rules (for all patterns) 522 also a three-object cascade C1 Imagine a metronome ticking at some constant rate. 42 two juggled in one hand, a held object in the other Each tick is called a “beat.” 40 two juggled in one hand, the other hand empty C2 Indicate each thrown object by a number that tells 330 a three-object cascade with a hole (two objects) us how many beats later that object must be back in 71 a four-object asynchronous shower a hand and ready to re-throw. - 
												
												Understanding Siteswap Juggling Patterns a Guide for the Perplexed by Greg Phillips, [email protected]
Understanding Siteswap Juggling Patterns A guide for the perplexed by Greg Phillips, [email protected] Core rules (for all patterns) Synchronous siteswap (simultaneous throws) C1 We imagine a metronome ticking at some constant rate. Some juggling patterns involve both hands throwing at the Each tick is called a “beat.” same time. We describe these using synchronous siteswap. C2 We indicate each thrown object by a number that tells us how many beats later that object must be back in a hand S1 The right and left hands throw at the same time (which and ready to re-throw. counts as two throws) on every second beat. We group C3 We indicate a sequence of throws by a string of numbers the simultaneous throws in parentheses and separate the (plus punctuation and the letter x). We imagine these hands with commas. strings repeat indefinitely, making 531 equivalent to S2 We indicate throws that cross from hand to hand with an …531531531… So are 315 and 153 — can you see x (for ‘xing’). why? C4 The sum of all throw numbers in a siteswap string divided Rules C2 and S1 taken together demand that there be only by the number of throws in the string gives the number of even numbers in valid synchronous siteswaps. Can you see objects in the pattern. This must always be a whole why? The x notation of rule S2 is required to distinguish number. 531 is a three-ball pattern, since (5+3+1)/3 patterns like (4,4) (synchronous fountain) from (4x,4x) equals three; however, 532 cannot be juggled since (synchronous crossing). - 
												
												General Catalog.Pdf
ICM ID UPC Item Description Manufacturer MFG ID Min Retail 00105071 024291115229 Bamboo Stir Fry Set 3 Pc Navajo Manufacturing Co, Inc. 25805 2 $ 4.99 00105230 046354315407 Magnetic Numbers & Letters Ja-Ru, Inc. 1405 2 $ 2.99 00105256 046354732600 Glider Air Force Foam Jet 1/cd Ja-Ru, Inc. 2311 2 $ 2.99 00105277 047878650005 Cooler Can Holder U.S. Poly Enterprise, Inc. S650A-BK200 2 $ 2.99 00105283 714415016807 Neon Shot Glasses 12ct Evriholder Products, LLC. SGLSICM0672 2 $ 2.99 00106116 039052810138 TS Luggage Smart Tags 2ct Conair Corporation TS92NLT 3 $ 4.99 00106119 039052008993 TS Adapter Plug 4pc Insulated Plugs Conair Corporation M500ENR 1 $ 17.99 00106133 039052813603 TS Deluxe PVC Luggage Tags 2ct Conair Corporation TS02VB 3 $ 4.99 00183145 085455201578 Opener Beer Bottle/Can Tapper Chef Craft Corporation 20157-TKT 2 $ 2.99 00183699 085455210808 Cocktail Sword Spears Asst 30ct Chef Craft Corporation 21080-TKT 2 $ 1.99 00183913 815290025011 Sink Scents Assorted Liv-It! LLC 501 2 $ 2.99 00184879 871290005941 Foot File - Perfect Pair 1/cd Donnamax, Inc. 134148 2 $ 2.99 00185272 616513704351 Eye Care Essentials 4pc Kit Cala - Shin's Trading Co. 70-435B 2 $ 4.99 00185579 769898062278 Blending Wedge - Flower Shaped 6 ct Swissco LLC 6227 2 $ 4.99 00186171 769898070198 Pumice Sponge Swissco LLC 7019 2 $ 4.99 00186775 687969001394 Comb - Soft Touch Shower Comb Swissco LLC 50383 2 $ 4.99 00186858 085455205682 Opener Jar and Cap Rubber 2pk Chef Craft Corporation 20568-TKT 2 $ 1.99 00187062 705654017045 Doggie Clean Up Bags 20pk Pet King Inc PK1704 2 $ 1.69 00187070 763615802512 Combo Cutlery Clear Plastic 48ct King Zak, Inc. - 
												
												Volume 4 No 4 (October 1977)
VOLOMB 4 110 •• OCT. 197? ( 592 Miami Street Of'ticial Organ UMICYCLINO socmY OF &MER!Cl Inc. (§)1977 ill Rts Rea. Marion, Ohio 43302 Year}J' Membership S5 Includes 1'enletter (4) ID Card - See Blank Pg.18 omcERS FEL!m UNICYCLISTS: The 1977 National trnieycle Meet went off on sched w.e Aug. 20,21.st in Marion, <llio arxl the general conaensus seems to Pree. Paul Fox be that it was eTen better than last year's• Saturday's weather was a V.Pree. R.Tschud:1.n bit cooler than previous years, a trley beautiful day, and just per Sec. T. Di.ck Haines fect for unicycling. At last minute the meet host The Paul Fox Uni cycle Club Iie. ot Marion vaa able to make arrangements to hold the POUNDER MPMBEBS races at the Tri Rivera SChool about two miles from the site of the Bernard Crandall morning activities at the Marion Catholic High School. The races were Paul & Nancy Fox run oft there Saturday aftemoon am many boys and girls made happy. Peter Hangach A comment received by 70ur ed. in mall this week fran one contestant Patricia Herron stated: nI likedthe informality of. the races am believe most of the Bill Jenack kids did - it took a lot of pressure off everyone and made the whole Gordon Kruse meet most enjoyable". The Sur.da;r morning meeting at MoDonalda proved Steve McPeak , to be an excellent idea with a far larger attendance than ever before Fr. Ju. J. Moran and the business meeting was carried on smoot~ and quic~ and was Dr. - 
												
												(Multiplex) Juggling Sequences
Enumerating (multiplex) juggling sequences Steve Butler∗ Ron Grahamy Abstract We consider the problem of enumerating periodic σ-juggling sequences of length n for multiplex juggling, where σ is the initial state (or landing schedule) of the balls. We first show that this problem is equivalent to choosing 1's in a specified matrix to guarantee certain column and row sums, and then using this matrix, derive a recursion. This work is a generalization of earlier work of Fan Chung and Ron Graham. 1 Introduction Starting about 20 years ago, there has been increasing activity by discrete mathe- maticians and (mathematically inclined) jugglers in developing and exploring ways of representing various possible juggling patterns numerically (e.g., see [1, 2, 3, 4, 5, 6, 10, 12, 14]). Perhaps the most prominent of these is the idea of a juggling sequence (or \siteswap", as it is often referred to in the juggling literature). The idea behind this approach is the following. For a given sequence T = (t1; t2; : : : ; tn) of nonnega- tive integers, we associate a (possible) periodic juggling pattern in which at time i, a ball is thrown so that it comes down at time i + ti. This is to be true for each i; 1 ≤ i ≤ n. Because we assume this is to be repeated indefinitely with period n, then in general, for each i and each k ≥ 0, a ball thrown at time i + kn will come down at time i + ti + kn. The usual assumption made for a sequence T to be a valid juggling sequence is that at no time do two balls come down at the same time. - 
												
												Arizona Adult Protective Services Registry
Arizona Adult Protective Services Registry Generated 9/21/2021 To request this document in an ADA accessible format or for further information about this report, contact 602-542-4446 or [email protected]. To search this document, use 'Ctrl F'. Registered Date Placed Date of Birth Description of Disposition Findings Perpetrator Name on Registry Aarons, Courtney Renee 4/11/1982 Between approximately July 2 and July 7, 2020, COURTNEY Exploitation of Resources 12/30/2020 AARONS (date of birth 04/11/1982) exploited a vulnerable adult by illegally or improperly using the vulnerable adult’s resources for the profit or advantage of herself and persons other than the vulnerable adult. Specifically, Ms. Aarons used the vulnerable adult's ATM card to make six cash withdrawals totaling $1,800.00 from Wells Fargo ATM’s in both Kingman and Bullhead City, Arizona locations for purposes that did not benefit the vulnerable adult. These transactions were made without the vulnerable adult’s knowledge or informed consent. Such conduct constitutes exploitation pursuant to A.R.S. § 46-451(A)(5). Abbye, Christie N. 6/2/1986 From approximately November 2013 until approximately May 2014, Exploitation of Resources 2/23/2016 CHRISTIE ABBYE (date of birth 06/02/1986) exploited a vulnerable adult by illegally or improperly using the vulnerable adult’s resources for the profit or advantage of herself and persons other than the vulnerable adult. Specifically, while acting as the representative payee for the vulnerable adult’s Social Security benefits, Ms. Abbye made numerous transactions from the vulnerable adult’s bank account for purposes which did not benefit the vulnerable adult. - 
												
												Braids and Juggling Patterns Matthew Am Cauley Harvey Mudd College
Claremont Colleges Scholarship @ Claremont HMC Senior Theses HMC Student Scholarship 2003 Braids and Juggling Patterns Matthew aM cauley Harvey Mudd College Recommended Citation Macauley, Matthew, "Braids and Juggling Patterns" (2003). HMC Senior Theses. 151. https://scholarship.claremont.edu/hmc_theses/151 This Open Access Senior Thesis is brought to you for free and open access by the HMC Student Scholarship at Scholarship @ Claremont. It has been accepted for inclusion in HMC Senior Theses by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. Braids and Juggling Patterns by Matthew Macauley Michael Orrison, Advisor Advisor: Second Reader: (Jim Hoste) May 2003 Department of Mathematics Abstract Braids and Juggling Patterns by Matthew Macauley May 2003 There are several ways to describe juggling patterns mathematically using com- binatorics and algebra. In my thesis I use these ideas to build a new system using braid groups. A new kind of graph arises that helps describe all braids that can be juggled. Table of Contents List of Figures iii Chapter 1: Introduction 1 Chapter 2: Siteswap Notation 4 Chapter 3: Symmetric Groups 8 3.1 Siteswap Permutations . 8 3.2 Interesting Questions . 9 Chapter 4: Stack Notation 10 Chapter 5: Profile Braids 13 5.1 Polya Theory . 14 5.2 Interesting Questions . 17 Chapter 6: Braids and Juggling 19 6.1 The Braid Group . 19 6.2 Braids of Juggling Patterns . 22 6.3 Counting Jugglable Braids . 24 6.4 Determining Unbraids . 27 6.4.1 Setting the crossing numbers to zero. 32 6.4.2 The complete system of equations . - 
												
												Owner's Manual
Hyperion Hoop Owner’s Manual Revised 10/14/2014 This manual has information for casual and advanced users, plus troubleshooting and repair information. You probably don’t need to read the whole thing, but we recommend at least skimming the first section. 1 What is a Hyperion Hoop 2 Quick Start Instructions Your hoop comes pre-loaded with hundreds of patterns and is ready to use, but please read this section first! • Use only 14500 size lithium-ion rechargeable batteries in your hoop. • Don’t put the hoop’s batteries in a device designed for regular AA batteries. The higher voltage may cause damage to the device. • Don’t short the battery terminals! The battery can get extremely hot or even catch fire. Don’t keep it in a pocket with your car keys, for example. We’re speaking from personal experience on this one. • When the hoop shows a single flashing red light, the battery is nearly dead. Shut off the hoop, change batteries, or connect it to a USB charger. • If there’s a plastic tab sticking out of the remote control’s battery compartment, remove it before using the remote. Right out of the box your hoop may be a bit out of round. Leave it flat on the ground, preferably in a warm place, and it will return to its normal shape. Put a charged battery in the open end of the hoop, with the positive end (marked with a ‘+’) facing out. Be careful – installing the battery backwards could cause damage to the internal charging circuit.