Class Code List Report
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Tt-Satisfiable
CMPSCI 601: Recall From Last Time Lecture 6 Boolean Syntax: ¡ ¢¤£¦¥¨§¨£ © §¨£ § Boolean variables: A boolean variable represents an atomic statement that may be either true or false. There may be infinitely many of these available. Boolean expressions: £ atomic: , (“top”), (“bottom”) § ! " # $ , , , , , for Boolean expressions Note that any particular expression is a finite string, and thus may use only finitely many variables. £ £ A literal is an atomic expression or its negation: , , , . As you may know, the choice of operators is somewhat arbitary as long as we have a complete set, one that suf- fices to simulate all boolean functions. On HW#1 we ¢ § § ! argued that is already a complete set. 1 CMPSCI 601: Boolean Logic: Semantics Lecture 6 A boolean expression has a meaning, a truth value of true or false, once we know the truth values of all the individual variables. ¢ £ # ¡ A truth assignment is a function ¢ true § false , where is the set of all variables. An as- signment is appropriate to an expression ¤ if it assigns a value to all variables used in ¤ . ¡ The double-turnstile symbol ¥ (read as “models”) de- notes the relationship between a truth assignment and an ¡ ¥ ¤ expression. The statement “ ” (read as “ models ¤ ¤ ”) simply says “ is true under ”. 2 ¡ ¤ ¥ ¤ If is appropriate to , we define when is true by induction on the structure of ¤ : is true and is false for any , £ A variable is true iff says that it is, ¡ ¡ ¡ ¡ " ! ¥ ¤ ¥ ¥ If ¤ , iff both and , ¡ ¡ ¡ ¡ " ¥ ¤ ¥ ¥ If ¤ , iff either or or both, ¡ ¡ ¡ ¡ " # ¥ ¤ ¥ ¥ If ¤ , unless and , ¡ ¡ ¡ ¡ $ ¥ ¤ ¥ ¥ If ¤ , iff and are both true or both false. 3 Definition 6.1 A boolean expression ¤ is satisfiable iff ¡ ¥ ¤ there exists . -
Membership Policy
Membership Policy The General Committee annually determines the categories of membership and charges that will apply from September each year. Membership of SBSC provides the following benefits: 1. Right to store a supported class at the club (subject to availability) and other classes subject to General Committee approval on a case-by-case basis. 2. Free entry into all club races covered by season sailing instructions. 3. Access to discounted use of the clubhouse for private functions. 4. Right to use club on-water assets for private use, with conditions. The following table sets out the current categories and charges that apply to the 2016-17 sailing year: Annual Category Benefit Exclusions/Conditions Subscription Individual $300 Full benefits Family $500 Full benefits Life No Charge Full benefits * Social – Storage, entry fees and use of on water $150/$250 Individual/family asset not included 3 month individual membership to cover $20 per Schools Teams Racing roster, no other club Teams Racing term rights apply other than access to YA insurance. Participants and members of other clubs are deemed to be members of SBSC for the duration of training whilst participating in Training No Charge club run events. No club rights apply other than the ability to leave boats on club premises for the duration of the event. Benefits of Corporate Membership are Corporate $1000 detailed in individual agreements. *Life membership is bestowed on an individual or a couple and does not extend to family of a life member. Where a life member has family members who wish to join the club they are required to purchase a separate membership package. -
2021 Transpacific Yacht Race Event Program
TRANSPACTHE FIFTY-FIRST RACE FROM LOS ANGELES 2021 TO HONOLULU 2 0 21 JULY 13-30, 2021 Comanche: © Sharon Green / Ultimate Sailing COMANCHE Taxi Dancer: © Ronnie Simpson / Ultimate Sailing • Hamachi: © Team Hamachi HAMACHI 2019 FIRST TO FINISH Official race guide - $5.00 2019 OVERALL CORRECTED TIME WINNER P: 808.845.6465 [email protected] F: 808.841.6610 OFFICIAL HANDBOOK OF THE 51ST TRANSPACIFIC YACHT RACE The Transpac 2021 Official Race Handbook is published for the Honolulu Committee of the Transpacific Yacht Club by Roth Communications, 2040 Alewa Drive, Honolulu, HI 96817 USA (808) 595-4124 [email protected] Publisher .............................................Michael J. Roth Roth Communications Editor .............................................. Ray Pendleton, Kim Ickler Contributing Writers .................... Dobbs Davis, Stan Honey, Ray Pendleton Contributing Photographers ...... Sharon Green/ultimatesailingcom, Ronnie Simpson/ultimatesailing.com, Todd Rasmussen, Betsy Crowfoot Senescu/ultimatesailing.com, Walter Cooper/ ultimatesailing.com, Lauren Easley - Leialoha Creative, Joyce Riley, Geri Conser, Emma Deardorff, Rachel Rosales, Phil Uhl, David Livingston, Pam Davis, Brian Farr Designer ........................................ Leslie Johnson Design On the Cover: CONTENTS Taxi Dancer R/P 70 Yabsley/Compton 2019 1st Div. 2 Sleds ET: 8:06:43:22 CT: 08:23:09:26 Schedule of Events . 3 Photo: Ronnie Simpson / ultimatesailing.com Welcome from the Governor of Hawaii . 8 Inset left: Welcome from the Mayor of Honolulu . 9 Comanche Verdier/VPLP 100 Jim Cooney & Samantha Grant Welcome from the Mayor of Long Beach . 9 2019 Barndoor Winner - First to Finish Overall: ET: 5:11:14:05 Welcome from the Transpacific Yacht Club Commodore . 10 Photo: Sharon Green / ultimatesailingcom Welcome from the Honolulu Committee Chair . 10 Inset right: Welcome from the Sponsoring Yacht Clubs . -
Chapter 9: Initial Theorems About Axiom System
Initial Theorems about Axiom 9 System AS1 1. Theorems in Axiom Systems versus Theorems about Axiom Systems ..................................2 2. Proofs about Axiom Systems ................................................................................................3 3. Initial Examples of Proofs in the Metalanguage about AS1 ..................................................4 4. The Deduction Theorem.......................................................................................................7 5. Using Mathematical Induction to do Proofs about Derivations .............................................8 6. Setting up the Proof of the Deduction Theorem.....................................................................9 7. Informal Proof of the Deduction Theorem..........................................................................10 8. The Lemmas Supporting the Deduction Theorem................................................................11 9. Rules R1 and R2 are Required for any DT-MP-Logic........................................................12 10. The Converse of the Deduction Theorem and Modus Ponens .............................................14 11. Some General Theorems About ......................................................................................15 12. Further Theorems About AS1.............................................................................................16 13. Appendix: Summary of Theorems about AS1.....................................................................18 2 Hardegree, -
NS14 ASSOCIATION NATIONAL BOAT REGISTER Sail No. Hull
NS14 ASSOCIATION NATIONAL BOAT REGISTER Boat Current Previous Previous Previous Previous Previous Original Sail No. Hull Type Name Owner Club State Status MG Name Owner Club Name Owner Club Name Owner Club Name Owner Club Name Owner Club Name Owner Allocated Measured Sails 2070 Midnight Midnight Hour Monty Lang NSC NSW Raced Midnight Hour Bernard Parker CSC Midnight Hour Bernard Parker 4/03/2019 1/03/2019 Barracouta 2069 Midnight Under The Influence Bernard Parker CSC NSW Raced 434 Under The Influence Bernard Parker 4/03/2019 10/01/2019 Short 2068 Midnight Smashed Bernard Parker CSC NSW Raced 436 Smashed Bernard Parker 4/03/2019 10/01/2019 Short 2067 Tiger Barra Neil Tasker CSC NSW Raced 444 Barra Neil Tasker 13/12/2018 24/10/2018 Barracouta 2066 Tequila 99 Dire Straits David Bedding GSC NSW Raced 338 Dire Straits (ex Xanadu) David Bedding 28/07/2018 Barracouta 2065 Moondance Cat In The Hat Frans Bienfeldt CHYC NSW Raced 435 Cat In The Hat Frans Bienfeldt 27/02/2018 27/02/2018 Mid Coast 2064 Tiger Nth Degree Peter Rivers GSC NSW Raced 416 Nth Degree Peter Rivers 13/12/2017 2/11/2013 Herrick/Mid Coast 2063 Tiger Lambordinghy Mark Bieder PHOSC NSW Raced Lambordinghy Mark Bieder 6/06/2017 16/08/2017 Barracouta 2062 Tiger Risky Too NSW Raced Ross Hansen GSC NSW Ask Siri Ian Ritchie BYRA Ask Siri Ian Ritchie 31/12/2016 Barracouta 2061 Tiger Viva La Vida Darren Eggins MPYC TAS Raced Rosie Richard Reatti BYRA Richard Reatti 13/12/2016 Truflo 2060 Tiger Skinny Love Alexis Poole BSYC SA Raced Skinny Love Alexis Poole 15/11/2016 20/11/2016 Barracouta -
Repalrlng Radio Sets
repalrlng radio sets PART 2 H.W. HELLYER Inthefirst article of this series, Gordon J. King has compressed a wealth of technical information. My brief is to discuss the important mechanical aspects of servicing. Before we can do this, it is necessary to review the tools, instruments and other commonly needed. There are two principal sizes, bench aids that are necessary, and others but tight clhassis screws often need one of the that are desirable though not indispensable. larger types, with a cross-bar, such as used in The emphasis is on tidy and method:cal cycle 'shops. The screwdrivers should preferably service procedure; hence the treatment of have insulated plastic handles. A number of makers the subiect which regards even the kitchen market these especially for electrical work. 'service table workshop as a department'. Beginning at the beginning, we take a * PTIERS look at the basic tools of our trade or hobby. A large pair are essential with square, parallel jaws, a serrated circular section and strong edge cutting blade to deal with iron wire, bolt ends, TOOLS chassis burrs. A pair of long-nosed "electrician's" pliers, with insulated ffiOOLS are personal items. A toolkit is built handle and a smaller. flat- ended pair I up from humble beginnings.with experience for delicate work are also recom- r proving the worth of some tools, modifying the mended. use of others. One or two favourites will be to hand at all times; others are rarely needed. The follow- * CUTTERS list is a suggestion of basic tools most ing often Side and top-cutters of various styles and sizes a't the bench. -
Chapter 13: Formal Proofs and Quantifiers
Chapter 13: Formal Proofs and Quantifiers § 13.1 Universal quantifier rules Universal Elimination (∀ Elim) ∀x S(x) ❺ S(c) Here x stands for any variable, c stands for any individual constant, and S(c) stands for the result of replacing all free occurrences of x in S(x) with c. Example 1. ∀x ∃y (Adjoins(x, y) ∧ SameSize(y, x)) 2. ∃y (Adjoins(b, y) ∧ SameSize(y, b)) ∀ Elim: 1 General Conditional Proof (∀ Intro) ✾c P(c) Where c does not occur outside Q(c) the subproof where it is introduced. ❺ ∀x (P(x) → Q(x)) There is an important bit of new notation here— ✾c , the “boxed constant” at the beginning of the assumption line. This says, in effect, “let’s call it c.” To enter the boxed constant in Fitch, start a new subproof and click on the downward pointing triangle ❼. This will open a menu that lets you choose the constant you wish to use as a name for an arbitrary object. Your subproof will typically end with some sentence containing this constant. In giving the justification for the universal generalization, we cite the entire subproof (as we do in the case of → Intro). Notice that although c may not occur outside the subproof where it is introduced, it may occur again inside a subproof within the original subproof. Universal Introduction (∀ Intro) ✾c Where c does not occur outside the subproof where it is P(c) introduced. ❺ ∀x P(x) Remember, any time you set up a subproof for ∀ Intro, you must choose a “boxed constant” on the assumption line of the subproof, even if there is no sentence on the assumption line. -
The First Fifty Years People, Memories and Reminiscences Contents
McCrae Yacht Club – the First Fifty Years People, Memories and Reminiscences Contents Championships Hosted at McCrae ...................................................................................................2 Our champion sailors...........................................................................................................................5 Classes Sailed over the years.......................................................................................................... 12 Stories from various sailing events.............................................................................................. 25 Rescues and Tall Tales...................................................................................................................... 31 Notable personalities........................................................................................................................ 37 Did you know? – some interesting trivia.................................................................................... 43 Personal Recollections and Reminiscences .............................................................................. 46 The Little America’s Cup – what really happened ….. ............................................................ 53 McCrae Yacht Club History - firsts ................................................................................................ 58 Championships Hosted at McCrae The Club started running championships in the second year of operation. The first championships held in 1963/64 -
Logic and Proof Release 3.18.4
Logic and Proof Release 3.18.4 Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn Sep 10, 2021 CONTENTS 1 Introduction 1 1.1 Mathematical Proof ............................................ 1 1.2 Symbolic Logic .............................................. 2 1.3 Interactive Theorem Proving ....................................... 4 1.4 The Semantic Point of View ....................................... 5 1.5 Goals Summarized ............................................ 6 1.6 About this Textbook ........................................... 6 2 Propositional Logic 7 2.1 A Puzzle ................................................. 7 2.2 A Solution ................................................ 7 2.3 Rules of Inference ............................................ 8 2.4 The Language of Propositional Logic ................................... 15 2.5 Exercises ................................................. 16 3 Natural Deduction for Propositional Logic 17 3.1 Derivations in Natural Deduction ..................................... 17 3.2 Examples ................................................. 19 3.3 Forward and Backward Reasoning .................................... 20 3.4 Reasoning by Cases ............................................ 22 3.5 Some Logical Identities .......................................... 23 3.6 Exercises ................................................. 24 4 Propositional Logic in Lean 25 4.1 Expressions for Propositions and Proofs ................................. 25 4.2 More commands ............................................ -
Portsmouth Number List 2016
Portsmouth Number List 2016 The RYA Portsmouth Yardstick Scheme is provided to enable clubs to allow boats of different classes to race against each other fairly. The RYA actively encourages clubs to adjust handicaps where classes are either under or over performing compared to the number being used. The Portsmouth Yardstick list combines the Portsmouth numbers with class configuration and the total number of races returned to the RYA in the annual return. This additional data has been provided to help clubs achieve the stated aims of the Portsmouth Yardstick system and make adjustments to Portsmouth Numbers where necessary. Clubs using the PN list should be aware that the list is based on the typical performance of each boat across a variety of clubs and locations. Experimental numbers are based on fewer returns and are to be used as a guide for clubs to allocate as a starting number before reviewing and adjusting where necessary. The list of experimental Portsmouth Numbers will be periodically reviewed by the RYA and is based on data received from the PY Online website (www.pys.org.uk). Users of the PY scheme are reminded that all Portsmouth Numbers published by the RYA should be regarded as a guide only. The RYA list is not definitive and clubs should adjust where necessary. For further information please visit the RYA website: http://www.rya.org.uk/racing/Pages/portsmouthyardstick.aspx RYA PN LIST - Dinghy Change Class Name No. of Crew Rig Spinnaker Number Races Notes from '15 420 2 S C 1105 0 278 2000 2 S A 1101 1 1967 29ER 2 S A -
A Case Study of the Power Section in India
Indira Gandhi Institute of Development Research Bombay, India /N/fcX'DK'" ~ Environmentally sound energy efficient strategies: a case study of the power sector in India Prof. Jyoti Parikh Dr. J.P. Painuly Dr. Kankar Bhattacharya Working Paper No. 6 UNEP Collaborating Centre on Energy and Environment Risp National Laboratory, Denmark February 1997 of tw tmiMBfr b wtairreD ENVIRONMENTALLY SOUND ENERGY EFFICIENT STRATEGIES A CASE STUDY OF THE POWER SECTOR IN INDIA Working Paper No. 6 Printed by: Grafisk Service, Ris0 National Laboratory ISBN 87-550-2285-5 ISSN 1025-2258 Prof. Jyoti Parikh Dr. J.P. Painuly Dr. Kankar Bhattacharya Indira Gandhi Institute of Development Research Gen. Vaidya Marg, Goregaon (East) Bombay 400 065 India Tel: +91 22 840 0920/21 Fax: +91 22 840 2752/840 2026 UNEP Collaborating Centre on Energy and Environment Ris0 National Laboratory P.O. Box 49 DK-4000 Roskilde Denmark Tel: +45 46 32 22 88 Fax: +45 46 32 19 99 n DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document Foreword This report is the sixth in a series of working papers on energy and environment issues published by the UNEP Collaborating Centre on Energy and Environment at Ris0 National Laboratory, Denmark. The UNEP Collaborating Centre was established in 1990 with a primary mission of furthering the incorporation of environmental issues in energy planning and policy, particularly in developing countries. The work of the Centre is to a great extent catalytic, involving close collaboration with researchers, planners, government agencies, etc. -
1 Symbols (2286)
1 Symbols (2286) USV Symbol Macro(s) Description 0009 \textHT <control> 000A \textLF <control> 000D \textCR <control> 0022 ” \textquotedbl QUOTATION MARK 0023 # \texthash NUMBER SIGN \textnumbersign 0024 $ \textdollar DOLLAR SIGN 0025 % \textpercent PERCENT SIGN 0026 & \textampersand AMPERSAND 0027 ’ \textquotesingle APOSTROPHE 0028 ( \textparenleft LEFT PARENTHESIS 0029 ) \textparenright RIGHT PARENTHESIS 002A * \textasteriskcentered ASTERISK 002B + \textMVPlus PLUS SIGN 002C , \textMVComma COMMA 002D - \textMVMinus HYPHEN-MINUS 002E . \textMVPeriod FULL STOP 002F / \textMVDivision SOLIDUS 0030 0 \textMVZero DIGIT ZERO 0031 1 \textMVOne DIGIT ONE 0032 2 \textMVTwo DIGIT TWO 0033 3 \textMVThree DIGIT THREE 0034 4 \textMVFour DIGIT FOUR 0035 5 \textMVFive DIGIT FIVE 0036 6 \textMVSix DIGIT SIX 0037 7 \textMVSeven DIGIT SEVEN 0038 8 \textMVEight DIGIT EIGHT 0039 9 \textMVNine DIGIT NINE 003C < \textless LESS-THAN SIGN 003D = \textequals EQUALS SIGN 003E > \textgreater GREATER-THAN SIGN 0040 @ \textMVAt COMMERCIAL AT 005C \ \textbackslash REVERSE SOLIDUS 005E ^ \textasciicircum CIRCUMFLEX ACCENT 005F _ \textunderscore LOW LINE 0060 ‘ \textasciigrave GRAVE ACCENT 0067 g \textg LATIN SMALL LETTER G 007B { \textbraceleft LEFT CURLY BRACKET 007C | \textbar VERTICAL LINE 007D } \textbraceright RIGHT CURLY BRACKET 007E ~ \textasciitilde TILDE 00A0 \nobreakspace NO-BREAK SPACE 00A1 ¡ \textexclamdown INVERTED EXCLAMATION MARK 00A2 ¢ \textcent CENT SIGN 00A3 £ \textsterling POUND SIGN 00A4 ¤ \textcurrency CURRENCY SIGN 00A5 ¥ \textyen YEN SIGN 00A6