Sequential parimutuel games
|
|
- Millicent Dawson
- 5 years ago
- Views:
Transcription
1 Sequetial parimutuel games Rob Feeey ad Stephe P. Kig Departmet of Ecoomics The Uiversity of Melboure Parkville, Vic Australia Abstract: I a parimutuel bettig system, a successful player s retur depeds o the umber of other players who choose the same actio. This paper examies a geeral solutio for two-actio sequetial parimutuel games, ad shows how the (uique) equilibrium of such games leads to simple patter of behavior. I particular, we show that there is a advatage to beig a early mover, that early players might choose actios with a ex ate low probability of success, ad that player actio choices ca flip with small chages i the parameters of the game. JEL umbers: C72, D84 Key Words: Parimutuel Bettig, Iterdepedecies, Ivestmet Clusters Correspodig author, Stephe P. Kig. We would like to thak Jeff Borlad for his useful commets. We would also like to thak the Faculty of Ecoomics ad Commerce at the Uiversity of Melboure for a grat to sposor this research.
2 1. Itroductio May ivestmets ivolve returs that are depedet o the actios of others. A simple case is a parimutuel gamblig system where bettors make a fiacial ivestmet o the outcome of a sportig evet. A example is the totalizer system at horse races where idividuals place bets o horses. If their chose horse wis, the the retur to a idividual is a fractioal proportio of the etire amout wagered o the race. The retur depeds o both the total bets of all gamblers ad the proportio who bet o the same horse. Parimutuel gamblig systems have log bee of iterest to ecoomists because they capture importat elemets of more geeral ivestmet decisios. They are aalogous to simplified fiacial markets where the scale of the pricig problem has bee reduced, with gamblers bettig o horses rather tha stocks ad comparig odds rather tha prices. Chadha ad Quadt (1996) argue that bettig markets ca provide a excellet test-bed for examiig market efficiecy. Parimutuel gamblig systems have also bee used to test for risk attitudes ad utility prefereces, for example Asch, Malkiel ad Quadt (1982) ad more recetly Hamid, Prakash ad Smyser (1996). Much of the theoretical work aalysig parimutuel systems, however, makes a critical small player assumptio that oe idividual caot ifluece the actios of others. I other words, there are always eough players i the system so that the effect of oe player s actios o the iformatio ad returs of other players ca be igored. For example, Potter ad Wit (1995) examie a parimutuel system where players idepedetly choose actios after receivig a idividual sigal that is draw from a commo distributio. But each player igores the cosequeces of their actio o the odds of the gamble. Similarly, Wataabe (1997) aalyses a parimutuel system with a cotiuum of players. 1 1 Plott, Wit, ad Yag (1997) cosider various models of parimutuel bettig markets, ad compare some experimetal results agaist models. They develop a model without the small player assumptio but are uable to solve for equilibrium i this model. Wataabe, ooyama, Mori (1994) cosider a fiite player game but where players have mutually icosistet beliefs. 1
3 The small player assumptio greatly simplifies the modelig of parimutuel systems, but it is very strog. For example, if there are few players or if some players wager relatively large sums of moey the the iterdepedecy of returs i a parimutuel system meas that the small player assumptio is likely to be violated. Further, as has bee observed i other cotexts, whe there is asymmetric iformatio, the actios of oe player ca result i sigificat iformatio trasmissio that affects the actios of other players eve whe returs are ot directly liked. The literature o herdig ad iformatio cascades aalyses this pheomeo (Baerjee (1992), Bikhchadai, Hirscheifer, ad Welch (1992, 1998), Welch (1992)). 2 While much of the work i related areas has focussed o iterdepedecy ad the trasmissio of iformatio, this paper focuses o iterdepedecy of player actios as govered by the parimutuel form of retur. We cosider a simple model of a parimutuel system where all players have idetical iformatio. This meas that each idividual s actio will affect the returs of all other players by (a) icreasig the size of the prize pool ad (b) raisig the expected retur associated with other actios. We cosider a sequece of players who must choose betwee two actios. Expected returs deped o the umber of players, the actios chose by all other players, ad a exogeous parameter such as the probability that oe actio is correct. Players must determie their optimal actio give their kowledge of the actios take by all precedig players ad their expectatio of the choices of all succeedig players. Our results highlight two importat features of sequetial decisio makig. First, players may cluster o choices, i that they will ofte make the same choice as the player who immediately precedes them. Such clusterig does ot reflect ay iformatio asymmetry or iferece process as i the literature o iformatio cascades. Rather, it reflects the iability of margial returs over actios to be perfectly equated i a fiite player game. Secodly, players who must make relatively early actio choices may choose a actio that ex ate appears to have a low expected payoff. Their decisio is drive by the ratioal belief that later players will cluster o the outcome that ex ate appears more 2 As the classic paper by Grossma ad Stiglitz (1980) poits out, eve if all players are price takers, i a ratioal expectatios equilibrium, aggregate actios by otherwise small agets ca covey 2
4 favorable. The iterdepedecy of returs meas that such clusterig ca result i a ex ate more favorable actio havig a lower expected retur ex post. To see a example of this secod pheomeo, cosider a situatio where three players sequetially choose the outcome of a football game betwee the Bears ad the Bulls. There is a total prize pool of $100, ad the ex ate probability of the Bears wiig is 60%. But returs are parimutuel, so that those players who correctly choose the wier of the game share the prize pool equally amog themselves. The i equilibrium, we would expect the first player to maximize his retur by choosig to back the Bulls while the secod ad third players support the favored Bears. Give the first player s choice, the secod ad third players idividually prefer to both support the Bears ad gai a expected retur of (at least) $30 rather tha to back the Bulls ad receive a expected retur of o more tha $20. The first player, who ca accurately ifer the behaviour of the other players, will back the Bulls ad receive a expected retur of $40. If, i cotrast, the first player had chose to support the favored Bears, the his expected retur would oly be $30 at best, as at least oe of the other players would also support the Bears. The first player maximizes his expected retur by isolatig himself through his choice of the ex ate worse alterative. Our results ca be applied to a variety of ivestmet situatios. For example, suppose that ivestors sequetially choose betwee two tows i which to locate similar retail stores. We should ot be surprised if early ivestors all choose the same tow ad later ivestors all choose the alterative locatio. Further, if oe tow has a larger populatio ad, as such, would appear ex ate to provide a preferred retail locatio, we should ot be surprised if early ivestors all choose to locate i the smaller tow. This behavior does ot reflect ay iformatio asymmetry or market-drive herdig. Rather, it simply reflects the parimutuel form of the payoffs associated with the ivestmets. iformatio. 3
5 2. The Model idividuals sequetially choose oe of two possible actios, a { A, B}. Each idividual receives a payoff that depeds o both the specific actio that they choose ad the umber of other players that have chose the idetical actio. Deote the umber of players choosig A as. The payoff to player i from choosig A is give by pm while the payoff from choosig B is ( 1 M where p ad M are exogeous parameters. All players ca observe the history of the game. We wish to examie the subgame perfect equilibria of this game. This game ca be iterpreted i (at least) two ways: Dividig a fixed moetary pool: each player kows ex ate the total payoff associated with ay actio. This is give by pm for actio A ad by (1-M for actio B. The payoff to a player i from actio a is equal to the total payoff associated with actio a divided by the umber of players who choose that actio. I other words, a idividual s retur from choosig A or B is pm ad ( 1 M respectively. A simple parimutuel game: There exists a true state of the world Ω where { α, β} where p [ 0,1] Ω. The probability that Ω= α is p ad the probability that Ω= β is 1 p. Idividuals are uaware of the true state ex ate but they do kow the value of p. Actio A is correct whe the true state is α, while actio B is correct whe the true state is β. Each idividual pays oe dollar to play the game. If a idividual i chooses actio A ad this is the correct actio the they receive a gross retur equal to M. If they choose B ad this is correct the they receive a gross retur of is pm ad M. So a idividual s expected retur from choosig A or B give ( 1 M respectively. 4
6 3. Geeral Results The followig two theorems apply to the model preseted above. The proofs are give i the appedix. Theorem 1 Give ad p, cosider such that + 1 p. 3 The: Theorem 2 a) If p ( 1 the there is a subgame perfect ash equilibrium where players 1,2,, choose A ad the remaider choose B. i.e. a equilibrium of the form AAA AB BBB. b) If p ( 1 the there is a subgame perfect ash equilibrium where players 1,2,,- choose B ad the remaider choose A. i.e. a equilibrium of the form BBB BA AAA. + 1 Give ad p, cosider such that < p < ad p ( 1. The the equilibrium defied i Theorem 1 is uique. These two theorems show that the equilibrium outcomes of the sequetial parimutuel ivestmet game will follow a simple patter. The players break ito two simple groups accordig to their order i the sequece ad their actio choice. Either the first players will all choose actio A with the remaider choosig actio B, or the first players will all choose B with the remaider choosig A. Further the subgame perfect equilibrium is geerally uique i the sese that give a fiite value of, multiple equilibria oly exist for a fiite umber of values of p. 3 ote that such a will always exist but eed ot be uique. 5
7 The equilibrium ivolves a early mover advatage. While the first group (either or - players) all receive the same payoff, this payoff is greater tha that received by the remaider of the players. But this advatage does ot mea that early movers choose the ex ate more likely outcome or the actio associated with the ex ate larger 1 pool of fuds. With p > 2, the first players may still all choose actio B i equilibrium ad receive a higher payoff tha those player who choose actio A. If we iterpret p as a probability, the the uique equilibrium ca ivolve early movers backig a extreme log-shot. For example, suppose that p = 0.99 ad = 101. The the two theorems imply that the uique equilibrium ivolves the first player choosig B ad the remaiig 100 choosig A. The theorems show how the equilibrium behavior of the players ca be very sesitive to the parameters of the game. The additio of a extra player, for example, ca cause the equilibrium to flip so that almost all players alter their choice. To see this, 11 suppose that p = 20. If there are iitially eight players the the uique equilibrium outcome is for the first four players to choose actio A ad the remaiig players to choose actio B. But if we add a extra player to the game, the the uique equilibrium ivolves the first four players choosig actio B while the remaiig players choose A. If the extra player moves last, the the additio of this player has led each of the origial players to chage their choice. Similarly, as p chages, the equilibrium actios will alter, followig a predictable patter. For example, as p falls from oe to oe-half, successively more players will choose actio B rather tha A. Further, the choice of early movers will flip betwee A 3 ad B as p falls. To see this, suppose that = 3. It is easy to cofirm that if p (,1] the the uique equilibrium outcome ivolves all three players choosig A. If p falls 2 3 so that p (, ) 3 4 the the uique outcome ivolves the first two players choosig A ad the last choosig B. But if p falls further, so that p ( 1, 2 ) will choose B ad the latter two players will choose A. 2 3 the the first player 4 6
8 Multiple equilibria oly exist for specific values of ad p. Whe p = ( 1 there are C equilibrium outcomes. I each, players choose actio A ad ( ) players choose actio B but all possible combiatios of orderigs ca 2 arise as equilibria. For example, with = 3 ad p = ay outcomes where oe player chooses actio B ad the other two players choose actio A ca occur i equilibrium. Whe p = ( 1 there are C +1 + C equilibrium +1 outcomes. I equilibrium either + 1 players choose A ad 1 players choose B or players choose A ad ( ) choose B. I either case, all possible combiatios of orderigs ca arise Coclusio I this paper we have aalyzed a sequetial parimutuel gamblig game ad have characterized the equilibria of this game. While our model is relatively simple, our results provide isight ito the behavior of other systems that ivolve iterdepedet ivestmet decisios. For example, our results ca explai why a early retailer of a ew product might prefer to locate i a relatively small tow rather tha close to a larger market, or why sequetial ivestmet decisios might appear to be characterized by clusterig subject to sudde switches i choice. Our results do ot deped o iformatio asymmetries or icosistet beliefs, but simply reflect the iterdepedet ature of ivestmet returs. I this sese, our results provide a simple explaatio for observed pheomeo, like clusterig. This said, the model could obviously be exteded to allow for iformatio asymmetry ad the aggregatio of iformatio as the game progresses. As oted i the literature o iformatio cascades, eve with idepedet returs, sequetial iformatio aggregatio ca ivolve sigificat imperfectios. This will be complicated by parimutuel returs as ay cascade dilutes the retur to early players. However, this remais the topic of future research. 7
9 Bibliography Asch, P., Malkiel, B., Quadt, R.(1982) "Racetrack Bettig ad Iformed Behavior", Joural of Fiacial Ecoomics, 10, Baerjee, A. (1992) "A simple model of herd behavior", The Quarterly Joural of Ecoomics, 107, Bikhchadai, S., Hirshleifer, D., Welch, I. (1992) "A Theory of Fads, Fashio, Custom, ad Cultural Chage as Iformatioal Cascades", The Joural of Political Ecoomy, 100, Bikhchadai, S., Hirshleifer, D., Welch, I. (1998) "Learig from the behavior of others: coformity, fads ad iformatioal cascades", Joural of Ecoomic Perspectives, 12, Chadha, S., Quadt, R. (1996) "Bettig bias ad market equilibrium i racetrack bettig", Applied Fiacial Ecoomics, 6, Hamid, S., Prakash, A., Smyser, M. (1996) "Margial risk aversio ad prefereces i a bettig market", Applied Ecoomics, 28, Grossma, S., ad Stiglitz, J. (1980) "O the impossibility of iformatioally efficiet markets", America Ecoomic Review, 70, Plott, C., Wit, J., Yag, W. (1997) "Parimutuel Bettig Markets as Iformatio Aggregatio Devices: Experimetal Results", Califoria Istitute of Techology Social Sciece Workig Paper 986, April. Potters, J., Wit, J. (1995) "Bets ad bids: favorite-logshot bias ad wier s curse", Katholieke Uiversiteit Brabat, etherlads: CetER, Discussio Paper, Jue. Wataabe, T. (1997) "A parimutuel system with two horses ad a cotiuum of bettors", Joural of Mathematical Ecoomics, 28,
10 Wataabe, T., H. ooyama, M. Mori (1994) "A Model of a Geeral Parimutuel System: Characterizatios ad Equilibrium Selectio", Iteratioal Joural of Game Theory, 23, Welch, I. (1992) "Sequetial sales, learig ad cascades", The Joural of Fiace, 47,
11 Appedix. For the proofs of theorems 1 ad 2 it is coveiet to itroduce the followig otatio. Let P aη be the retur to a player choosig actio a whe η players i total choose actio a. 1. Proof of Theorem 1 Cosider the putative equilibrium where p ( 1 ad the first players choose A, ad the remaider choose B, i.e. a equilibrium of the form AAA AB BBB. (The proof of the symmetric case where p ( 1 is aalogous.) From our parameter restrictios it is easy to show that the followig iequalities hold: P A P B P A + 1 P B 1 P A 1 P B + 1 P A + x < P B x P A x > P B + x We ow show that o player will fid it desirable to uilaterally deviate from the putative equilibrium. First, cosider the players who choose A i the putative equilibrium. Suppose a subset of Z of these players deviate ad choose B. From the above iequalities, these players are oly strictly better off if at least Z + 1 players who would have chose B i the putative equilibrium ow choose A. ow, cosider the players who choose B i the putative equilibrium. Suppose a subset of Z of these players deviate ad choose A. From the above iequalities, these players are oly strictly better off if at least Z + 1 players who would have chose A i the putative equilibrium ow choose B. ote that this implies that ay deviatios must make some players worse off tha i equilibrium as it caot be the case that Z Z + 1 ad Z Z + 1 simultaeously. It remais to show that the first player who uilaterally deviates caot be made strictly better off. Let the first player deviate by choosig actio a rather tha actio a. The first player will oly strictly gai if all the players who choose actio a are strictly worse off. But this caot occur. To see this, suppose the coverse ad cosider the last player that chooses a. otig that P aη is decreasig i η ad from the above iequalities, this player will always gai by choosig a rather tha a regardless of the behavior of subsequet players. So this player will ot choose actio a ad we have a cotradictio. 10
12 As o player i the putative equilibrium ca ever strictly gai by deviatig, the putative equilibrium is a subgame perfect ash equilibrium. Q.E.D. 2. Proof of Theorem 2 The followig lemmas are useful i the proof of theorem 2. Lemma Cosider, p, ad such that < p <. The, i ay subgame perfect ash equilibrium, players will choose A ad - players will choose B. Proof: From theorem 1 we kow that there exists a equilibrium where players choose A ad players choose B. Cosider ay other putative equilibrium. Suppose that i this putative equilibrium + x players choose A, ad x players choose B. Cosider the last player that chose A ad call this player i. If i deviates ad chooses B, the i is strictly better off regardless of the actios of ay subsequet players i+ 1,, sice P B x+ 1 > P A + x. Therefore i will deviate ad the putative equilibrium where more tha players choose A caot be a actual equilibrium. Similarly if -x players choose A. Therefore, i equilibrium, players choose A ad - players choose B. Q.E.D. Lemma 2. Cosider ay subgame of the whole game, begiig with the i th player ad ay subgame perfect ash equilibria of this subgame give the choices of players 1,, i 1. This equilibrium oly depeds o the umber of players before i who choose A ad B, ot their specific order. Proof: This trivially follows as the payoffs for each player oly deped o the umber of other players associated with each actio ad ot their order. Q.E.D. Proof of Theorem 2. From lemma 1 we ca restrict attetio to equilibria where players choose actio A ad the remaider choose actio B. We begi with the case where p > ( 1. From theorem 1 we kow that the relevat equilibrium exists. To show that it is uique, cosider ay other putative equilibrium. I this putative equilibrium, there must exist two players, i ad i+1, where i plays B ad i+1 plays A. 11
13 Cosider the last such pair of players. We show that such a player i will always fid it optimal to deviate so that the putative equilibrium is ot a actual equilibrium. To see this, if i deviates ad chooses A, the player i+1 chooses either B or A. Suppose i+1 chooses B, the by lemma 2 o player i+ 2,, will fid it desirable to deviate. But the player i receives p rather tha ( 1 ad is better off ad will therefore deviate. Alteratively, suppose player i+1 chooses A after player i deviates. Player i+1 will oly fid this optimal if p > (1, where x is the umber of players x + 1 i+ 2,, that deviate from B to A i the subgame perfect ash equilibrium after i+1 chooses A. This is because player i+1 could choose B ad get ( 1. But player i also gets p > (1 ad will therefore deviate. x + 1 As player i always deviates, there is o equilibrium with player i that plays B where i+1 plays A. The aalogous proof holds for the symmetric case where p > ( 1, ad a ( 1 p ) > p. Therefore, the equilibrium characterized i theorem 1 is uique. Q.E.D. 12
A SECOND SOLUTION FOR THE RHIND PAPYRUS UNIT FRACTION DECOMPOSITIONS
Fudametal Joural of Mathematics ad Mathematical Scieces Vol., Issue, 0, Pages -55 This paper is available olie at http://www.frdit.com/ Published olie November 9, 0 A SECOND SOLUTION FOR THE RHIND PAPYRUS
More informationThe structure of the Fibonacci numbers in the modular ring Z 5
Notes o Number Theory ad Discrete Mathematics Vol. 19, 013, No. 1, 66 7 The structure of the iboacci umbers i the modular rig Z J. V. Leyedekkers 1 ad A. G. Shao 1 aculty of Sciece, The Uiversity of Sydey
More information8.5. Solving Equations II. Goal Solve equations by balancing.
8.5 Solvig Equatios II Goal Solve equatios by balacig. STUDENT BOOK PAGES 268 271 Direct Istructio Prerequisite Skills/Cocepts Solve a equatio by ispectio or systematic trial. Perform operatios usig itegers,
More informationWelcome to the world of the Rube Goldberg!
Welcome to the world of the Rube Goldberg! Sice 1988, tes of thousads of studets have competed i our aual Rube Goldberg Machie Cotests where they are challeged to build the wackiest workig Rube Goldberg
More informationPolicy sensitivity analysis of Karachi commuters
Policy sesitivity aalysis of Karachi commuters A. Q. Memo 1 & K. Sao 2 1 Departmet of Civil Egieerig, NED Uiversity of Egieerig ad Techology, Karachi, Pakista 2 Departmet of Civil ad Evirometal Egieerig,
More informationTHE EFFECTS OF COUPLED INDUCTORS IN PARALLEL INTERLEAVED BUCK CONVERTERS
THE EFFECTS OF COUPED INDUCTORS IN PARAE INTEREAVED BUCK CONVERTERS Paul Seria, David Fi ad Geoff Walker pseria@itee.uq.edu.au School of Iformatio Techology ad Electrical Egieerig Uiversity of Queeslad
More informationGENETICS 101 GLOSSARY
GENETICS 101 This documet is iteded to provide a basic uderstadig of caie geetics to the America Eskimo Dog (AED) ower ad breeder. It is simplified from scietific facts ad uderstadig. It is ot iteded to
More informationICC WORLD TWENTY ( WORLD CUP-2014 )- A CASE STUDY
INTERNATIONAL JOURNAL OF MATHEMATICAL SCIENCES AND APPLICATIONS Volume 5 Number 1 Jauary-Jue 215 ICC WORLD TWENTY2-214 ( WORLD CUP-214 )- A CASE STUDY Bhavi Patel 1 ad Pravi Bhathawala 2 1 Assistat Professor,
More informationActive Travel The Role of Self-Selection in Explaining the Effect of Built Environment on Active Travel
Active Livig Research Buildig Evidece to Prevet Childhood Obesity ad Support Active Commuities RESE ARCH brief Fall 2009 activelivigresearch.org Active Travel The Role of Self-Selectio i Explaiig the Effect
More informationThe Analysis of Bullwhip Effect in Supply Chain Based on Strategic Alliance
The Aalysis of Bullwhip Effect i Supply Chai Based o Strategic Alliace Rui Xu, Xiaoli Li, Xiaomi Sog, Gag Liu School of Busiess, Hubei Uiversy, Wuha, 430062, P. R. Chia, wdxj826@126.com Abstract. Bullwhip
More informationSPH4U Transmission of Waves in One and Two Dimensions LoRusso
Waves travelig travellig from oe medium to aother will exhibit differet characteristics withi each medium. Rules A wave of fixed frequecy will have a shorter wavelegth whe passig from a fast medium to
More informationOutline. Changing needs in Urban Traffic. Introduction The starting point Basic principles Analysis Facts Changes Context Solutions Key messages
Chagig eeds i Urba Traffic Rob Methorst Chair COST 358 Pedestrias Quality Needs Cetre for Trasport ad Navigatio 27th of October 2011 Outlie Itroductio The startig poit Basic priciples Aalysis Facts Chages
More informationIntroduction to Algorithms 6.046J/18.401J/SMA5503
Itroductio to Algorithms 6.046J/8.40J/SMA5503 Lecture 4 Prof. Charles E. Leiserso Quicsort Proposed by C.A.R. Hoare i 962. Divide-ad-coquer algorithm. Sorts i place lie isertio sort, but ot lie merge sort.
More informationGamblers Favor Skewness, Not Risk: Further Evidence from United States Lottery Games
Gamblers Favor Skewness, Not Risk: Further Evidence from United States Lottery Games Thomas A. Garrett Russell S. Sobel Department of Economics West Virginia University Morgantown, West Virginia 26506
More informationCorruption on the Court: The Causes and Social Consequences of Point-Shaving in NCAA Basketball
Corruptio o the Court: The Causes ad Social Cosequeces of Poit-Shavig i NCAA Basketball by Yag-Mig Chag * ad Shae Saders ** October 8, 007 * Departmet of Ecoomics, Kasas State Uiversity, 39 Waters Hall,
More informationnumber in a data set adds (or subtracts) that value to measures of center but does not affect measures of spread.
Lesso 3-3 Lesso 3-3 Traslatios of Data Vocabulary ivariat BIG IDEA Addig (or subtractig) the same value to every umber i a data set adds (or subtracts) that value to measures of ceter but does ot affect
More informationLoad Calculation and Design of Roller Crowning of Truck Hub Bearing
Sed Orders for Reprits to reprits@bethamsciece.ae 106 The Ope Mechaical Egieerig Joural, 2015, 9, 106-110 Ope Access Load Calculatio ad Desig of Roller Crowig of Truck Hub Bearig Xitao Xia,1, Shujig Dog
More informationTHE LATENT DEMAND METHOD
THE LATENT DEMAND METHOD Bruce W. Ladis, Russell M. Otteberg, Vekat R. Vattikuti SCI, Ic., 18115 U.S. Highway 41North, Suite 600, Lutz, FL 33549, USA Email: bladis@sciworld.et Travel patters i a metropolita
More informationThe Real Thing?: Representing the Bullfight and Spain in Death in the Afternoon by Peter Messent
The Real Thig?: Represetig the Bullfight ad Spai i Death i the Afteroo by Peter Messet Hemigway does t give us the real thig i the book; istead he gives us his versio of it Phrase used several times (both
More informationA Data Envelopment Analysis Evaluation and Financial Resources Reallocation for Brazilian Olympic Sports
WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza A Data Evelopmet Aalysis Evaluatio ad Fiacial Resources Reallocatio for Brazilia Olympic Sports RENATO PESCARINI VALÉRIO LIDIA ANGULO-MEZA
More informationHeadfirst Entry - Diving and Sliding
5/31/2011 Safe divig board use, safe slide use, usi Headfirst Etry - Divig ad Slidig POOLALARMS.COM HOME POOL SAFETY PRODUCTS POOL SAFETY ARTICLES & REPORTS POOL SAFETY LINKS & RESOURCES POOLALARMS.COM
More informationPERFORMANCE TEAM EVALUATION IN 2008 BEIJING OLYMPIC GAMES
XV INTERNATIONAL CONFERENCE ON INDUSTRIAL ENGINEERING AND OPERATIONS MANAGEMENT The Idustrial Egieerig ad the Sustaiable Developmet: Itegratig Techology ad Maagemet. Salvador, BA, Brazil, 06 to 09 October
More informationMINNESOTA DEER MANAGEMENT
MINNESOTA DEER MANAGEMENT A study of huter opiios about deer populatios ad maagemet: Blocks H H5 Fial Report A cooperative study coducted by: Miesota Cooperative Fish ad Wildlife Research Uit Miesota Departmet
More informationPatrick Boston (Leeds University) and Mark Chapman (Edinburgh University)
Iversio o requecy-depedet AVO data or luid properties Patric Bosto (Leeds Uiversity) ad Mar Chapma (Ediburgh Uiversity) Summary A umber o methods to estimate the requecy-depedece o relectivity have bee
More informationFootwork is the foundation for a skilled basketball player, involving moves
The Complete Book of Offesive Basketball Drills Basic Footwork ad Cuts Drills 2 Equipmet 16 chairs (or less) Persoel The etire team Basic Footwork ad Cuts Drills Two coaches How to Ru the Drill Five feet
More informationoperate regenerator top without boiling aq. amine solution.
HSRemoval-MaterialBalacemcd Rough material balace for removal of H S from shale gas with MDEA ad recovery of elemetal sulfur via the Claus process The solvet has bee dow-selected to be methyldiethaolamie
More informationRange St. Dev. n Mean. Total Mean % Competency. Range St. Dev. n Mean. Total Mean % Competency
CSWE Core Competecies - MSW 2013 MSW Program Dual Degree MSW/JD Program* *Due to the curret limited umber of Dual Degree studets, the MSW outcomes data represets outcomes for both programs. 1 : Idetify
More informationSt. Paul Midway YMCA Swim Lessons Schedule
St. Paul Midway YMCA Swim Lessos Schedule 2018 Late Fall October 29 - December 16 (651) 646-4557 ymcam.org/midway ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay safe
More informationInfluences of Teaching Styles and Motor Educability on Learning Outcomes of Volleyball
Asia Social Sciece; Vol., No. 5; 14 ISSN 1911-17 E-ISSN 1911-5 Published by Caadia Ceter of Sciece ad Educatio Iflueces of Teachig Styles ad Motor Educability o Learig Outcomes of Volleyball Syamsuddi
More informationEquipment. Rackets are fragile. Handle the shuttlecocks carefully and only by their rubber tips.
Badmito Overvie ad History Badmito is a racket sport that is played o a court divided by a et five feet high. The game is played ith a shuttlecock ( bird ). Ca be played as sigles or doubles. The object
More informationELIGIBILITY / LEVELS / VENUES
ELIGIBILITY / LEVELS / VENUES 10U - SQUIRT MINOR '09 & MAJOR '08 Eligibility: Top six teams i the league at each level will qualify based o regular seaso league play. Format: Divisioal crossover with semi-fial
More informationEagan YMCA Swim Lessons Schedule
Eaga YMCA Swim Lessos Schedule 2018 Early Fall September 10 - October 28 (651) 456-9622 www.eagaymca.org ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay safe aroud
More informationCorruption on the Court: The Causes and Social Consequences of Point-Shaving in NCAA Basketball
Corruptio o the Court: The Causes ad Social Cosequeces of Poit-Shavig i NCAA Basketball YANG-MING CHANG, SHANE SANDERS * Kasas State Uiversity; Nicholls State Uiversity This paper is cocered with the ecoomic
More informationEmma B. Howe YMCA Swim Lessons Schedule
Emma B. Howe YMCA Swim Lessos Schedule 2018 Summer Jue 4 - September 9 (763) 785-7882 ymcam.org/emmabhowe ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay safe aroud
More informationUniversity of California, Los Angeles Department of Statistics. Measures of central tendency and variation Data display
Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 13 Istructor: Nicolas Christou Measures of cetral tedecy Measures of cetral tedecy ad variatio Data display 1. Sample mea: Let x 1,
More informationDEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING, THE UNIVERSITY OF NEW MEXICO ECE-238L: Computer Logic Design Fall Notes - Chapter 6.
PARTMNT OF LCTRICAL AN COMPUTR NGINRING, TH UNIVRSITY OF NW MXICO C-238L: Computer Logic esig Fall 23 RGISTRS: Notes - Chapter 6 -bit Register: This is a collectio of '' -type flip flops, where each flip
More informationP h o t o g r a p h i c L i g h t i n g ( 1 1 B )
9 1 5 9 P h o t o g r a p h i c L i g h t i g ( 1 1 B ) 30S/30E/30M A Photography Course 9 1 5 9 : P h o t o g r a p h i c L i g h t i g ( 1 1 B ) 3 0 S / 3 0 E / 3 0 M Course Descriptio This course focuses
More informationELIGIBILITY / LEVELS / VENUES
ELIGIBILITY / LEVELS / VENUES 10U - SQUIRT MINOR '08 & MAJOR '07 Eligibility: Top six teams i the league at each level will qualify based o regular seaso league play. Format: Divisioal crossover with semi-fial
More information(612)
Shoreview YMCA Swim Lessos Schedule Late Sprig 2019 - April 15 - Jue 2 (612) 230-9622 www.shoreviewymca.org ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay safe aroud
More informationELIGIBILITY / LEVELS / VENUES
ELIGIBILITY / LEVELS / VENUES 10U - SQUIRT MINOR '08 & MAJOR '07 Eligibility: Top six teams i the league at each level will qualify based o regular seaso league play. Format: Divisioal crossover with semi-fial
More informationIntersleek Pro. Divers Manual. Our World is Water CONTENTS
Itersleek Pro Divers Maual CONTENTS Itroductio.......................................2 Expectatios for Itersleek Pro........................3 I-Water Maiteace...............................4 Haulig the
More informationWondering where to start?
Ridgedale YMCA Swim Lessos Schedule 2019 Witer Jauary 1 - February 24 (952) 544-7708 www.ridgedaleymca.org ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay safe aroud
More informationHuman-Robot Interaction: Group Behavior Level
SPECOM'006, St. Petersburg, 5-9 Jue 006 Huma-Robot Iteractio: Group Behavior Level Lev Stakevich, Deis Trotsky Sait Petersburg State Techical Uiversity 9, Politechicheskaya, St. Petersburg, 955, Russia
More informationASSESSMENT SCORING SYSTEM OF ROAD SAFETY INFRASTRUCTURE
ASSESSMENT SCORING SYSTEM OF ROAD SAFETY INFRASTRUCTURE Case Study of Mihag District i Shaghai, Chia Yue Wag, Daocheg Su 2 School of Traffic ad Trasportatio Egieerig, Togi Uiversity, Shaghai, Chia ABSTRACT
More informationRochester YMCA Swim Lessons Schedule
Rochester YMCA Swim Lessos Schedule 2018 Early Fall September 10 - October 28 (507) 287-2260 www.ymcam.org/rochester ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay
More informationSYMMETRY AND VARIABILITY OF VERTICAL GROUND REACTION FORCE AND CENTER OF PRESSURE IN ABLE-BODIED GAIT
SYMMETRY AND VARIABILITY OF VERTICAL GROUND REACTION FORCE AND CENTER OF PRESSURE IN ABLE-BODIED GAIT Yu Wag ad Kazuhiko Wataabe Graduate School of Educatio, Hiroshima Uiversity, Hiroshima, Japa, wagyu@hiroshima-u.ac.jp
More informationELIGIBILITY / LEVELS / VENUES
ELIGIBILITY / LEVELS / VENUES 10U - SQUIRT MINOR '09 & MAJOR '08 Eligibility: Top six teams i the league at each level will qualify based o regular seaso league play. Format: Divisioal crossover with semi-fial
More informationsecuring your safety
securig your safety LIFE POINT PRO DEFIBRILLATOR AN AUTOMATED EXTERNAL DEFIBRILLATOR (AED) CAN BE THE DIFFERENCE BETWEEN LIFE AND DEATH. Statistics show that early 200,000 people die each year as a result
More informationA Comparison of MOEA/D, NSGA II and SPEA2 Algorithms
Iteratioal Joural of Egieerig Treds ad Applicatios (IJETA) Volume 4 Issue 6, Nov-Dec 7 RESEARCH ARTICLE A Comparo of MOEA/D, ad Algorithms Rajai [1], Dr. Aad Prakash [] Asstat Professor of Computer Sciece
More informationHERKIMER CENTRAL SCHOOL DISTRICT Herkimer Elementary School 255 Gros Boulevard Herkimer, New York 13350
HERKIMER CENTRAL SCHOOL DISTRICT Herkimer Elemetary School 255 Gros Boulevard Herkimer, New York 13350 Robert J. Miller Superitedet ofschools 315-866-2230, Ext. 1302 FAX 315-866-2234 Reee L. Vogt, Pricipal
More informationWondering where to start?
New Hope YMCA Swim Lessos Schedule 2018 Early Fall September 10 - October 28 (763) 535-4800 www.ewhopeymca.org ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay safe
More informationAvailable online at ScienceDirect. Procedia Engineering 113 (2015 )
Available olie at www.sciecedirect.com ScieceDirect rocedia Egieerig 3 (205 ) 30 305 Iteratioal Coferece o Oil ad Gas Egieerig, OGE-205 The twi spool efficiecy cotrol Michuri A.I. a *, Avtoomova I.V. a
More informationHazard Identificaiton of Railway Signaling System Using PHA and HAZOP Methods
www.ijape.org Iteratioal Joural of Automatio ad Power Egieerig (IJAPE) Volume 2 Issue 2, February 2013 Hazard Idetificaito of Railway Sigalig System Usig PHA ad HAZOP Methods Jog Gyu Hwag *1, Hyu Jeog
More informationHastings YMCA Swim Lessons Schedule
Hastigs YMCA Swim Lessos Schedule 2018 Early Fall September 10 - October 28 (651) 480-8887 www.hastigsareaymca.org ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay
More informationAndover YMCA Swim Lessons Schedule
Adover YMCA Swim Lessos Schedule 2018 Early Fall September 10 - October 28 (763) 230-9622 www.adoverymca.org ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay safe aroud
More informationWondering where to start?
Blaisdell YMCA Swim Lessos Schedule 2018 Early Fall September 10 - October 28 (612) 827-5401 www.blaisdellymca.org ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay
More informationWondering where to start?
Woodbury YMCA Swim Lessos Schedule 2017 Late Fall October 30 - December 17 (651) 731-9507 ymcam.org/woodbury ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay safe aroud
More informationIRS ISSUES PROPOSED REGULATIONS FOR COMPARATIVE EFFECTIVENESS RESEARCH FEES
HUMAN CAPITAL PRACTICE ALERT: HEALTH CARE REFORM BILL July 2012 www.willis.com IRS ISSUES PROPOSED REGULATIONS FOR COMPARATIVE EFFECTIVENESS RESEARCH FEES The Comparative Effectiveess Research (CER) fee
More informationSPEED OF SOUND MEASUREMENTS IN GAS-MIXTURES AT VARYING COMPOSITION USING AN ULTRASONIC GAS FLOW METER WITH SILICON BASED TRANSDUCERS
SPEED OF SOUND MEASUREMENTS IN GAS-MIXTURES AT VARYING COMPOSITION USING AN ULTRASONIC GAS FLOW METER WITH SILICON BASED TRANSDUCERS Torbjör Löfqvist, Kęstutis Sokas, Jerker Delsig EISLAB, Departmet of
More informationWondering where to start?
Bursville YMCA Swim Lessos Schedule 2018 Witer Jauary 8 - February 25 (952) 898-9622 ymcam.org/bursville ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay safe aroud
More informationWest St Paul YMCA Swim Lessons Schedule
West St Paul YMCA Swim Lessos Schedule 2018 Early Fall September 10 - October 28 (651) 457-0048 www.weststpaulymca.org ABOUT Y SWIM LESSONS The Y strives to help all ages lear how to swim, so they ca stay
More informationCatenary Analysis and Calculation Method of Track Rope of Cargo Cableway with Multiple Loads
MATEC Web of Cofereces 8, 01008 (016) DOI: 10.1051/ mateccof/016801008 DME 016 Cateary Aalysis ad Calculatio Method of Track Rope of Cargo Cableway with Multiple Loads Jia Qi a, Ju Che, Liag Qiao, Jiacheg
More informationdraft final report NGSIM Arterial-Lane Selection Mode Federal Highway Administration Cambridge Systematics, Inc.
NGSIM Arterial-Lae Selectio Mode draft fial report prepared for Federal Highway Admiistratio prepared by Cambridge Systematics, Ic. with Itelliget Trasportatio Systems Laboratory Massachusetts Istitute
More informationCapacity of Shared-Short Lanes at Unsignalised Intersections
Nig Wu itle ad Abstract Author's Address apacity of Shared-Short aes at Usigalised Itersectios Nig Wu ABSA he calculatio procedures i recet highway capacity mauals do ot eactly treat ared/ort laes at usigalized
More informationHeld under the sanction of USA Swimming, issued by North Carolina Swimming, Inc. Sanction No. NC11117
The Greesboro Swimmig Associatio's 2011 Joh Gordo Dewey Ivitatioal Swim Meet November 19-20, 2011 The Greesboro Aquatic Ceter 1921 West Lee Street, Greesboro, NC 27403 SANCTION: HOST: FACILITY: Held uder
More informationIntroductory Rules of Officiating Small Sided Games Under 6 &Under 8 HANDBOOK
Itroductory Rules of Officiatig Small Sided Games Uder 6 &Uder 8 O F F I C I A L S HANDBOOK 1 T his hadbook is iteded to be used i cojuctio with the US Youth Soccer Small-sided Game Official s classroom
More informationBIKE MS: THE CITRUS TOUR, MAY 21-22, 2016 PARTNERSHIP PROPOSAL
BIKE MS: THE CITRUS TOUR, MAY 21-22, 2016 PARTNERSHIP PROPOSAL 1 Bike MS: 2016 Partership Proposal VISION STATEMENT For cyclists ad all those seekig a persoal challege ad a world free of MS, Bike MS is
More informationSeries 600 Accessories
Series 600 Geeral These accessories are a rage of devices for completig a peumatic circuit. These valves, with their special fuctios, are iserted betwee two valves, betwee a valve ad a cylider, or followig
More informationJOBST Elvarex Plus Feel the difference in seamless 3D!
JOBST Elvarex Plus Feel the differece i seamless 3D! Custom-made flat-kit compressio garmets for the maagemet of lymphatic diseases of the hads ad feet 3D Comfort, Compressio ad Techology JOBST Elvarex
More informationcase five Wal-Mart Stores Inc., March 2004
case five Wal-Mart Stores Ic., March 2004 TEACHING NOTE SYNOPSIS By 2004, Wal-Mart (W-M) was ot oly the world s biggest retailer, it was also (i terms of sales reveue) the world s largest corporatio. I
More information» WYOMING s RIDE 2013
» WYOMING s RIDE 2013 WYOMING S RIDE 2013 preseted by First Iterstate Bak of Wyomig bikemswyomig.org 1 We are people who wat to do somethig about ow.» Our Wyomig Bike MS Ride Two-Day Wyomig Ride: To view
More informationn UL Listed and FM Approved for n Solenoid control n Quick pressure relief valve 73Q n Pressure sustaining & reducing valve 723
Pressure Relief/Sustaiig Valve Prioritizig pressure zoes Esurig cotrolled pipelie fill-up Prevetig pipelie emptyig Pump overload & cavitatio protectio Safeguardig pump miimum flow Excessive lie pressure
More informationExistence of Nash Equilibria
Existence of Nash Equilibria Before we can prove the existence, we need to remind you of the fixed point theorem: Kakutani s Fixed Point Theorem: Consider X R n a compact convex set and a function f: X
More informationModelling Lane Changing Behaviour of Heavy Commercial Vehicles
Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles Modellig Lae Chagig Behaviour of Heavy Commercial Vehicles Sara Moridpour 1, Majid Sarvi 2, Geoff Rose 3 1 Post Graduate Studet, Moash Uiversity,
More informationANALYSIS AND MODELING TIME HEADWAY DISTRIBUTIONS UNDER HEAVY TRAFFIC FLOW CONDITIONS IN THE URBAN HIGHWAYS: CASE OF ISFAHAN
TRANSPORT ISSN 648-442 prit / ISSN 648-348 olie 2 Volume 26(4): 375 382 doi:.3846/648442.2.635694 ANALYSIS AND MODELING TIME HEADWAY DISTRIBUTIONS UNDER HEAVY TRAFFIC FLOW CONDITIONS IN THE URBAN HIGHWAYS:
More informationA Comparative Investigation of Reheat In Gas Turbine Cycles
Proceedigs of the Iteratioal Gas Turbie ogress 3 Tokyo November -7, 3 IGT3Tokyo TS-86 A omparative Ivestigatio of Reheat I Gas Turbie ycles K. Sarabchi Departmet of Mechaical egieerig Uiversity of Tabriz
More informationThe budget for the London 2012 Olympic and Paralympic Games
The budget for the Lodo 2012 Olympic ad Paralympic Games REPORT BY THE COMPTROLLER AND AUDITOR GENERAL HC 612 Sessio 2006-2007 20 July 2007 The Natioal Audit Office scrutiises public spedig o behalf of
More informationWhen rule-based models need to count
Whe rule-based models eed to cout Pierre Boutillier, Ioaa Cristescu To cite this versio: Pierre Boutillier, Ioaa Cristescu. Whe rule-based models eed to cout. [Research Reort] Harvard Medical School. 2017.
More informationANNUAL REPORT OF THE PZU GROUP
PZU G ANN RE 2007 ANNUAL REPORT OF THE PZU GROUP Table of cotets 1. Basic iformatio o the PZU Group... 3 2. Fiacial highlights of the PZU Group i 2007... 6 3. Letter from the Presidet of PZU SA... 7 4.
More informationELIGIBILITY / LEVELS / VENUES
ELIGIBILITY / LEVELS / VENUES 10U - SQUIRT MINOR '08 & MAJOR '07 Eligibility: Top six teams i the league at each level will qualify based o regular seaso league play. Format: Divisioal crossover with semi-fial
More informationChance and Uncertainty: Probability Theory
Chance and Uncertainty: Probability Theory Formally, we begin with a set of elementary events, precisely one of which will eventually occur. Each elementary event has associated with it a probability,
More informationThis report presents an assessment of existing and future parking & traffic requirements, for the site based on the current development proposal.
CR166916b02 20 Jue 2017 Melida Dodso Melida Dodso Architects PO Box 5635 Hughes ACT 2605 Email: mdodso@melidadodsoarchitects.com.au Dear Melida, Project: Dickso Apartmets Lowrie St Re: Statemet o Parkig
More informationTravel Demand Management Implementation in Bandar Lampung
Travel Demad Maagemet Implemetatio i Badar Lampug Rahayu Sulistyorii 1, a, 1 Lampug Uiversity Istitute Techology of Sumatera a Keywords: Traffic
More informationIndividual Behavior and Beliefs in Parimutuel Betting Markets
Mini-Conference on INFORMATION AND PREDICTION MARKETS Individual Behavior and Beliefs in Parimutuel Betting Markets Frédéric KOESSLER University of Cergy-Pontoise (France) Charles NOUSSAIR Faculty of Arts
More informationCurrent as of September 20, 2013 (red items are new entries since last TAAHC meeting)
Tag Allocatio ad Applicatio Hut Committee Topic List Reiitiated i December 0 Nevada Board of Wildlife Documet prit size 8/ x 4 of Category Applicatio Hut (A) Curret as of September 0, 0 (red items are
More informationMST 121: Supplementary resource material for Chapter A1, Sequences
MST : Supplemetary resource material for Chapter A Sequeces For each of the followig sequeces (a) 9 (b) (c) 8 7 Write ow the et terms of the sequece Write ow a epressio for the close form of the sequece
More informationVersion IV: April a publication from
Versio IV: April 2013 a publicatio from AWRF Associated Wire Rope Fabricators Recommeded Practice ad Guidelie Disclaimer for AWRF Recommeded Guidelie Swager Safety Guide Associated Wire Rope Fabricators
More information» COLORADO s RIDE 2013
» COLORADO s RIDE 2013 COLORADO S RIDE 2013 bikemscolorado.org 1 We are people who wat to do somethig about ow.» COlorado 2-Day Ride Caledar of Evets o back 2 2013 Bike MS COLORADO MS Society Missio Statemet
More informationGame Indicators Determining Sports Performance in the NBA
Joural of Huma Kietics volume 37/013, 145-151 DOI:10.478/huki-013-0035 145 Sectio III Sports Traiig Game Idicators Determiig Sports Performace i the NBA by Kazimierz Mikołajec 1, Adam Maszczyk,Tomasz Zając
More informationBasic Gas Spring Theory
Calculatig the iitial force The iitial force of the gas sprig ca be calculated as the sealed area of the pisto rod or the pisto (depedig o desig) multiplied by the pressure iside the gas sprig. The larger
More informationHypothesis testing: ANOVA Test of the equality of means among c groups. Flow-chart
Hypothesis testig: ANOVA Test of the equality of meas amog groups February 6, 200 Moez Hababou() Flow-hart Desribig iformatios Drawig olusios Foreastig Improve busiess proesses Data Colletio Probability
More informationTilburg University. Bets and Bids Potters, Jan; Wit, J. Publication date: Link to publication
Tilburg University Bets and Bids Potters, Jan; Wit, J. Publication date: 1996 Link to publication Citation for published version (APA): Potters, J. J. M., & Wit, J. (1996). Bets and Bids: Favorite-Longshot
More informationDFC NIST DIGITAL MASS FLOW CONTROLLERS. DFC with optional LCD readout PROG RS485. Programmable Mass Flow Controller with Digital Signal Processing
Programmable Mass Flow Cotroller with Digital Sigal Processig Microprocessor drive digital flow cotrollers allow oe to program, record, ad aalyze flow rates of various gases with a computer via a RS-485
More informationEuropean Works Council Developments Before, During and After the Crisis
Corell Uiversity ILR School DigitalCommos@ILR Iteratioal Publicatios Key Workplace Documets 2015 Europea Works Coucil Developmets Before, Durig ad After the Crisis Eurofoud Follow this ad additioal works
More informationDAMAGE ASSESSMENT OF FIBRE ROPES FOR OFFSHORE MOORING
RECOMMENDED PRACTICE DNV-RP-E304 DAMAGE ASSESSMENT OF FIBRE ROPES FOR OFFSHORE MOORING APRIL 2005 FOREWORD (DNV) is a autoomous ad idepedet foudatio with the objectives of safeguardig life, property ad
More information"The twisting movement of any hoof should, for physiological reasons, not be hindered by Shoeing." (Lungwitz 1884)
Volume 15: Issue 2 Shoeig for Rotatioal Deviatio of the Equie Limb by Michael J. Wildestei CJF, FWCF (Hos) Examiatio of a horse prelimiary to shoeig should be made while the aimal is at rest ad afterwards
More information1. Write down the ideal gas law and define all its variable and parameters. 2. Calculate the values and units of the ideal gas law constant R.
Ideal Gases Objectives:. Write dow the ideal gas law ad defie all its variable ad parameters.. Calculate the values ad uits of the ideal gas law costat R. 3. Calculate the value of oe variable,, T, or,
More informationPolynomial functions have graphs that are smooth and continuous. c) Use your knowledge of quadratic functions to sketch the graph.
Math 165 4.1 Polyomial fuctios I class work Polyomial fuctios have graphs that are smooth ad cotiuous 1) For the fuctio: y 2 = x 9. a) Write the fuctio i factored form. b) Fid the x-itercepts or real zeros
More informationComparison of Mathematical Approximation Methods for Mine Ventilation Network Analysis
Iteratioal Joural o Miig Scie IJMS Volume, Issue, 6, PP -4 ISSN 454-946 Olie wwwarcjouralsorg Compariso o Mathematical Approimatio Methods or Mie Vetilatio Network Aalysis Farhag Sereshki Associate Proessor
More informationThe Complete Book of Offensive. Basketball Drills GAME-CHANGING DRILLS FROM AROUND THE WORLD GIORGIO GANDOLFI
The Complete Book of Offesive Basketball Drills GAME-CHANGING DRILLS FROM AROUND THE WORLD GIORGIO GANDOLFI New York Chicago Sa Fracisco Lisbo Lodo Madrid Mexico City Mila New Delhi Sa Jua Seoul Sigapore
More information