美国数学建模比赛-特等奖论文--MCM.pdf
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1、The LATEX Template for MCMWzlf11February 4,2009AbstractBut they also provided an early glimpse at the complex set of tradeoffsfacing party leaders,from their desire to make their own influence felt totheir worries about offending the candidates and particular constituenciesnot to mention the long,so
2、metimes troubled relationship between Mr.Goreand the Clintons.The issues party leaders are grappling with,they said,include how toavoid the perception of a back-room deal that thwarts the will of millionsof voters who have cast ballots in primaries and caucuses.That perceptioncould cripple the event
3、ual Democratic nominees chances of winning thepresidency in November,they said.ContentsAbstract.11Introduction.31.1 Other Assumptions.42Analysis of the Problem.43Calculating and Simplifying the Model.54The Model Results.55Validating the Model.66Conclusions.67A Summary.68Evaluate of the Mode.79Streng
4、ths and weaknesses.79.1 Strengths.7References.7Appendix.72page3 of 13Team#.1IntroductionShe said the nomi-nationshouldnotbede-cidedbydelegatesfromFloridaandMichiganal-located on the basis ofvotinginprimariestherelast month,as the Clin-ton campaign has pro-posed.Mrs.Clintongot more votes in bothplace
5、s,althoughneithercandidate actively cam-paigned there and Mr.Obamawasnotevenonthe ballot in Michigan.Thepartyhadpenalizedthose states for holding3210123202505xPeaksyFig 1:The figuretheirprimariesearlierthanthepartywantedbystrippingthemoftheirdelegatesto the convention.Although Mr.Gore has expressed
6、concerns to some associatesabout the damage a brokered convention could cause,several associates said hewas hopeful that one candidate would soon break through,sparing the partysuch an outcome.He told a close friend recently that his decision not to endorsefeels like the right thing and that he rema
7、ined optimistic the race is going to tipat some point,the friend said.Although Mr.Gore has expressed concerns to some associates about thedamage a brokered convention could cause,several associates said he was hope-ful that one candidate would soon break through,sparing the party such an out-come.He
8、 told a close friend recently that his decision not to endorse feels likethe right thing and that he remained optimistic the race is going to tip at somepoint,the friend said.is constant.do not affect the population.have no effect on.we can ignore it.is negligible3page4 of 13Team#.1.1Other Assumptio
9、nsAlthough Mr.Gore has expressed concerns to some associates about thedamage a brokered convention could cause,several associates said he was hope-ful that one candidate would soon break through,sparing the party such an out-come.He told a close friend recently that his decision not to endorse feels
10、 likethe right thing and that he remained optimistic the race is going to tip at somepoint,the friend said.Under the above and basic assumptions,we can set out to construct our model(show our approach in detail).2Analysis of the Problem3210123202505xPeaksyFig 2:aa4page5 of 13Team#.Although Mr.Gore h
11、as expressed concerns to some associates about thedamage a brokered convention could cause,several associates said he was hope-ful that one candidate would soon break through,sparing the party such an out-come.He told a close friend recently that his decision not to endorse feels likethe right thing
12、 and that he remained optimistic the race is going to tip at somepoint,the friend said.a11a12a13a21a22a23a31a32a33=OppositeHypotenusecos1arcsinAlthough Mr.Gore has expressed concerns to some associates about the damagea brokered convention could cause,several associates said he was hopeful thatone c
13、andidate would soon break through,sparing the party such an outcome.He told a close friend recently that his decision not to endorse feels like the rightthing and that he remained optimistic the race is going to tip at some point,thefriend said.pj=(0,if j is oddr!(1)j/2,if j is evenAlthough Mr.Gore
14、has expressed concerns to some associates about the damagea brokered convention could cause,several associates said he was hopeful thatone candidate would soon break through,sparing the party such an outcome.He told a close friend recently that his decision not to endorse feels like the rightthing a
15、nd that he remained optimistic the race is going to tip at some point,thefriend said.arcsin=ZZZKlimxn!r!(nr)!(1)3Calculating and Simplifying the Model“A is equivalent to B”Although Mr.Gore has expressed concerns to some as-sociates about the damage a brokered convention could cause,several associate
16、ssaid he was hopeful that one candidate would soon break through,sparing theparty such an outcome.He told a close friend recently that his decision notto endorse feels like the right thing and that he remained optimistic the race isgoing to tip at some point,the friend said.4The Model ResultsAlthoug
17、h Mr.Gore has expressed concerns to some associates about thedamage a brokered convention could cause,several associates said he was hope-5page6 of 13Team#.ful that one candidate would soon break through,sparing the party such an out-come.He told a close friend recently that his decision not to endo
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