2013年小美赛c题特等奖1162队B题
第二届“认证杯”数学中国数学建模国际赛承诺书我们仔细阅读了第二届“认证杯”数学中国数学建模国际赛的竞赛规则。
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我们的参赛队号为：1162我们选择的题目是：PROBLEM B：Hermit Crabs Evolve Employment Pattern of Human参赛队员(签名) ：队员1：万方平队员2：姜冰心队员3：邢思雨参赛队教练员(签名)：第二届“认证杯”数学中国数学建模国际赛编号专用页参赛队伍的参赛队号：（请各个参赛队提前填写好）：1162 竞赛统一编号（由竞赛组委会送至评委团前编号）：竞赛评阅编号（由竞赛评委团评阅前进行编号）：Discussion of the Feasibility of the VacancyChainDecember9,2013SummaryRousseau once said Man was born free,and he is everywhere in chains.However,it is not trying to spread a pessimistic world outlook.Instead,it is through interaction among people that our society can make progress.Just like hermit crabs would group together to exchange shells so that every individual can get a larger size of home.Our human society also exists similar phenomenon which is called vacancy chain.However,allo-cating shells among is relatively a easy job,how to exchange job among people is a rather difficult problem.In order to address problems above.We conclude three sub-problems and its solution in our paper:1)Figure out the conditions need to meet so that vacancy chain can function as a tool to optimize every individual can benefit.2)Build a model to evaluate ones competencies and propose an algorithm as social strategies to exchange jobs in vacancy chains so that everyone benefits.3)Develop a inequality to answer how many job appli-cants do need to satisfy both employers and employees and run our model to predict the change of HR expends for some enterprise customers within the next5years.In thefirst sub-problem,we discuss the different effects of differen-t organizational hierarchies on vacancy chains.Then we successfullyfig-ure out that hierarchical organizational forms with less middle managers than straight pyramis are most likely to be regulated by vacancy chain-s.And fortunately,most enterprises’organizational forms are similar to it.That is to say,vacancy chain can be applicable to most cases.Next,in second sub-problemswe propose a linear equation as a evaluating function and get a overall score for every individual which represents one’s com-petencies.Then,based on the overall scores,we use a greedy algorithm to exchange jobs among people in vacancy chain.Peoples qualities will be compatible with the job requirement.In this case every individual will get the most appropriate job.Finally,in the third sub-problemsince vacancy chain also has its cost like replacement cost and training cost.We will not allow the total cost outweigh its benefits.So we will propose a inequation that need to meet so that the cost will not outweigh the benefits.That is to1Team#1162Page2of19 say,we willfigure out how many job applicants do need to satisfy both em-ployees and employers at certain situations.Finally,we will run our modelto show the change of HR expends for some enterprises customers withinthe nextfive years.In the whole modeling process,we give full consideration to validity, feasibility and cost-efficiency of our model.Team#1162Page3of19Contents1Introduction4 2Discussion of the feasibility of the vacancy chain42.1Introduction (4)2.2Background (5)2.3The influence of organizational hierarchies on vacancy chain (5)2.3.1Model of organization form (5)2.3.2Analysis (6)2.3.3Conclusions (7)3A Vacancy chain model83.1Introduction (8)3.2Assumption (8)3.3Procedure (8)3.3.1Analysis (8)3.3.2Model Solution (9)3.3.3An algorithm to allocate jobs in vacancy chain (10)3.4Conclusions (11)4Practice of model124.1Introduction (12)4.2Limitation of the number of people in vacancy chain (12)4.3Model Testing (13)4.4Conclusions (16)5Strengths and Weaknesses165.1Strengths (16)5.2Weaknesses (17)References17 6Advertisement17Team#1162Page4of19 1IntroductionAs we know,the concept of the term-vacancy chain is derived from the sci-entific observation from a kind of phenomena in hermit crab population.As the hermit crab grows in size,it has tofind a larger shell and abandon the previ-ous one.Several hermit crab species,both terrestrial and marine,use vacancy chains tofind new shells:when a new,bigger shell becomes available,hermit crabs gather around it and form a kind of queue from largest to smallest.When the largest crab moves into the new shell,the second biggest crab moves into the newly vacated shell,thereby making its previous shell available to the third crab,and so on.Since this biological discovery,more meanings have been added to the term of vacancy chain.Nowadays,a vacancy chain is a social structure through which resources are distributed to consumers.In a vacancy chain,a new resource unit that arrives into a population is taken by thefirst individual in line,who then leaves his or her old unit behind,this old unit is taken by a second individual,leaving his or her old unit behind,and so ually when a vacancy occurs the bulk of the people whofill the positions come from the inside the internal labor market rather than hiring someone new.The individuals being moved and or promoted to a new job or position often gain a higher salary of more benefits which has an important impact on the organization.In this paper,we propose a model of vacancy chain to maximize the total interests of employers and employees,then use it to predict the change of job movement in some enterprises.We conclude three sub-problems to tackle in our paper.We discuss when the vacancy chain can be used as a tool to optimize the jobs allocation among employees and what conditions need to meet so that vacancy chain can exert its function.Build a model to calculating employee’s competencies which can be used to arrange employees when vacancy chain happens and develop an algorithm of job allocation which tries to benefit every employee.Discuss how many job applicants do need to satisfy both employers and em-ployees and Run our model to predict the change of HR expends for some en-terprise customers within the next5years.In the whole modeling process,we give full consideration to validity,feasibility and cost-efficiency of our model. 2Discussion of the feasibility of the vacancy chain2.1IntroductionAlthough,theoretically,vacancy chain can improve the benefit of people in that chain and hence improve the overall well-being of the whole enterprise and society,whether such group phenomenon can be applicable to every allTeam#1162Page5of19 industrials or not is open to doubt.That is to say,the question that whether vacancy chain can exert its function as resource allocation on every industries should be answered.So,in this section,we should discuss the feasibility of vacancy chain at the frist.2.2BackgroundIndividuals affected by vacancy chains starting in an organization usually are upwardly mobile in small to moderate jumps in status or laterally mobile within their same status;they rarely experience downward mobility.In systems in which they operate,vacancy chains have a strong influence up-on organizational demographics.Such factors as length of service distributions for individuals within the organization,rates of advancement within the sys-tem,the age distribution of individuals within particular strata,cohort effects for mobility within the system,and waiting times for advancement.In the previously work of Guido Fioretti[1]have investigate the effect of va-cancy chain under certain circumstances,especially the hierarchies structure of enterprises.We will use his theory to evaluate the feasibility of vacancy chain in certain industries.2.3The influence of organizational hierarchies on vacancy chain 2.3.1Model of organization formAt the beginning,since vacancy chain is a social phenomenon,the spread of information is an indispensable factor in the effect of vacancy chain.Besides, hierarchies level and structure can affect information spread and hence affect the vacancy chainwe introduce some mathematics models which can be used to simulate some kinds of hierarchy structure and distribution of strata of organi-zation in enterprises.There are mainly four mathematics model we want to introduce.Thefirst model we introduce is a decreasing exponential distribution from low to high strata.The functional form isf(k)=e−αk(1) where s N is the number of strata and k=0,1,2,3...s.This distribution corre-sponds to the kind of a hierarchy structure with far less managerial positions than subordinate positions.In other words,such structures look like pyramids.The second model we introduce is a decreasing exponential distribution from high to low strata.The functional form isf(k)=e−α(s−k)(2) where s N is the number of strata and k=0,1,2,3...s.This distribution corre-sponds to an inversed hierarchy with much more managers than subordinates.Team #1162Page 6of 19Some people may argue that such hierarchy is obviously unlikely in real world.Indeed,we do not want to deny the fact that such structure is unrealistic.How-ever,given that we want to evaluate the effect of different hierarchies on vacan-cy chain comprehensively,we still introduce this model in this paper.The third 246810k 0.10.20.30.4 ak1246810k0.10.20.30.4a s k 2246810k 0.51.01.52.03246810k0.10.20.30.4a a s ks k4Figure 1:strata −distributionmodel we introduce is a uniform distribution.The functional form isf (k )=1(3)where s N is the number of strata and k =0,1,2,3...s .The distribution corre-sponds to an organization where there are as many managers as subordinates.This model is a midpoint between model 1and model 2.The fourth model we introduce is a mixed one.That is to say,half the posi-tions assigned to strata according to a decreasing exponential distribution from low to high strata as in model 1.Half the positions assigned to strata according to a positions distribution from high to low strata as in model 2.The functional form isf (k )=e −αα(s −k )/(s −k )!(4)where s N is the number of strata and k =0,1,2,3...s .This hybrid distribution generates a hierarchy with proportionately less middle managers than a simple pyramid as in model 1.2.3.2AnalysisAccording to work of Guido Fioretti[1],in both of the model 1and model 2,the spread of information has positive impact on the proportion of vacancyTeam#1162Page7of19Figure2:Left to right,the charts obtained when strata−distribution is equal to 1,2,3and4,respectively.chains when contiguous strata have a very different number of positions.In model3,more information never has a positive effect on the proportion of va-cancy chains.The impact is even negative.Finally,in model4,such hierarchy can not only have positive impact on the proportional of vacancy chains when information spreads,but also can make a large use of vacancy chains in order to allocate resources.2.3.3ConclusionsTo sum up,from the discussion above,hierarchical organizational forms with less middle managers than straight pyramis are most likely to be regulated by vacancy chains.That is to say,vacancy chains can exert its power on industries whose organizational form is similar to model4.Team#1162Page8of193A Vacancy chain model3.1IntroductionWhen studying the behavior of hermit crabs,scientistsfind that instead of gathering in a random arrangement,hermit crabs tend to behave more rational-ly.That is to say,hermit crabs will gather around the new shell and form a kindof queue from largest to smallest in size so that every crab can receive benefits.In order to function as a tool of resources allocation,vacancy chain should not be work automatically.Insteadsome rules or strategies need to be involved so that everyones interests can be ensured and enhanced,just like hermit crabs do.Hermit crabs will arrange themselves according to their size,in this sec-tionwe will mimic such behavior.We will introduce a mathematics model to evaluate employees’competence and then every employee will get a overall s-core.Then according to these scores,we will use a greedy algorithm to allocate jobs among these employees.3.2Assumption•We assume that the organizational form is similar to the model4in formersection.•We assume that job requirement,employees’competence and welfare thejob brings can all be quantized.•We assume that people in relatively lower strata will obey the arrangementconducted by higher strata.•We assume that the initial arrangement is reasonable.That is to say,joband people in this job are compatible.People with high competence willhave high position in enterprise which asks for a high requirement andreceive high welfare.3.3Procedure3.3.1AnalysisAt the beginning,we will discuss how to evaluate a person’s”size”(competence) and factors that can reflect one’s competence.In1973American psychological theorist David Clarence McClelland proposed the term”Competence Model”[2].He defined competence asfive parts,knowl-edge,skill,self-concept,traits,motives.Figure3shows thefive parts of compe-tence.Although the concept of competence model is appealing,how to apply such abstract model to real world is a rather complicated and harsh mission.Indeed,Team#1162Page9of19Figure3:Five parts of competence defined by McClellandIceberg Theory is applicable to this case[3].As stated infigure4,surface knowl-edge and skill competences were relatively easy to develope and assess;Core motive and trait competencies at the base of the personality iceberg are moredifficult to assess and develop;Self-concept competencies lie somewhere in be-tween.3.3.2Model SolutionFurthermore,they experts have developed methods to evaluate one’s compe-tencies.According to the work of Lyle M.Spencer and Signe M.Spencer[4],thereare mainly eight kinds of method we can use to evaluate employees.Further-morethey proposed a quantitative way to evaluate the correlation coefficients among these eight kinds of method.Table1shows Spencer’s work.Since Spencer’s work is comprehensive and robust,we will use their conclu-sion as basis for our model.In here,we propose a linear equation.This equation is shown below.F(x1,x2,x3,x4,x5,x6,x7,x8)=a1x1+a2x2+a3x3+a4x4+a5x5+a6x6+a7x7+a8x8(5) F(x1,x2,x3,x4,x5,x6,x7,x8)is defined as the overall scores for employees.The higher the score is,the more competent the employee is.x1,x2,x3,x4,x5,x6,x7,x8Team#1162Page10of19Figure4:The Iceberg Model and Central and Surface Competences Source:Spencer and Spencer(1993:11)evaluation method R(correlation coefficient)Assessment center0.65Behavioral event interview0.48-0.61Work sample test0.54Ability test0.53Personality test0.39Resume0.38Recommendation0.23Non-behavioral interview0.05-0.19source:Spencer,Competence at workare the scores of test from Assessment center,Behavioral event interview,Work sample test,Ability test,Personality test,Resume,Recommendation,Non-behavioral interview,respectively.a1,a2,a3,a4,a5,a6,a7,a8are the normalization result of those correlation coefficients shown in the table2.Table2shows the actual number ofa1to a8.3.3.3An algorithm to allocate jobs in vacancy chainNow that we develop a method to evaluate peoples competencies.It’s timeto develop a way to arrange employees just like hermit crabs when vacancy chain appears.We use Greedy Algorithm to allocate jobs.The algorithm are stated as follows:Before the algorithm,we should use(5)to calculate all employees’overallTeam#1162Page11of19evaluation method w(weight)Behavioral event interview0.16Work sample test0.16Ability test0.16Personality test0.12Resume0.11Recommendation0.07Non-behavioral interview0.04scores.Once a employee leaves his/her job,according to his/her overall scores,we can limit the employees who will be involved in vacancy chain in those people whose overall scores are lower than the leaving one.This is because Individuals affected by vacancy chains starting in an organization usually are upwardly mo-bile in small to moderate jumps in status or laterally mobile within their same status;they rarely experience downward mobility.Once a new job appears in a company,than we can compare this job with other jobs that are already existing to estimate its relative position among all the jobs in this company.Remember the assumption that the general welfare of a job is proportional to its requirement and therefore it is also proportional to the overall scores we proposed.And now,we can use this estimated value to limit the employees who will be involved in vacancy chain in those people whose overall scores are lower than the estimated value.Now that we have defined the domain,we can describe the allocation algo-rithm.•According to the scores of eight tests mentioned above,use(5)to calculate the overall scores for every employees in that vacancy chain.•Sort employees by overall scores in descending order.•The one who has highest scores will occupy the vacant job;The one who has second highest scores will occupy the job that the highest one leaves, the rest may be deduced by analogy.•If all employees in chain change their algorithm will end.3.4ConclusionsTo sum up,from the discussion above,we develop a mathematics model to comprehensively evaluate and calculate employee’s competencies.Then by using Greedy Algorithm,we optimize job allocation in vacancy chain so that ev-eryone in this chain can improve their benefits.Just like Adam Smith once said,Team#1162Page12of19the improvement of personal welfare can lead to the improvement of social ing our model,vacancy chain can improve the interests of individuals, then the interests of enterprises,andfinally well-being of the society as a whole.4Practice of model4.1IntroductionSo far,our discussion and model are based on theoretical and ideal situation. We do not consider external factors like competitors in job markets and costs from vacancy chain.Since the purpose of enterprises is maximize the profits with least costs.In this section,we will consider the limitation of the number of people in vacancy chain to ensure that the cost may not outweigh the benefits it brings.And then, we will run our model to predict the expenses in exchanging jobs.4.2Limitation of the number of people in vacancy chainEvery coin has two sides.In other words,vacancy chain can also bring po-tential negative effects like some overhead costs.According to the work of Wayne F.Cascio[5],there are mainly three kinds of costs when exchanging job.They are separation cost,replacement costs and training ually,separation cost consists of exit processing,separation pay and unemployment tax impact and so on.Replacement cost consists of com-munication of vacancy,pre-employment admin,selection interviews,relocation expense and so on.Training cost consists of formal training,OJT observation, training wages and so on.Now that we have a brief outlook of costs,it is reasonable to assume that if there are100people in vacancy change,that is to say,there100people need to exchange their jobs,the costs of changing job maybe extremely high.In this case, perhaps hiring some people from job markets may cost much lower.Indeed,in reality world,employers usually tend to hire people from job markets in order to save money if exchanging cost is much more higher.In here,we propose a inequality to describe the case mentioned above.(A1+A2+...+A i)+(B1+B2+...+B j)<=C1+C2+...+C k(6) The inequality shown above can help us answer the question that how many job applicants do need to satisfy both employers and employees.An(n for1to i) means the costs of exchanging job for employee n.Bn(n for1to j)means the costs of hiring person n from outside markets when vacancy chain (n for 1to k)means the cost of hiring person n from outside markets when vacancy chain does not ually,the subscript k is equal to subscript j.Team#1162Page13of19 This inequality tells us the cost of vacancy chain(cost of exchanging people and hiring some people)should not outweigh the cost of directly hiring peo-ple.Some people may argue that both cases we need to hire the same number of people,then why should we use vacancy change.This is easy to explain,al-though the number of people hired from outside markets is equal,their cost is not.Through vacancy chain we should only hire people for jobs whose require-ments are relatively lower and thus the costs are also relatively lower.Let me use an example illustrate it,when selecting a president for a country,the cost is usually extremely high.It’s been a practice that once running for a leading position in government,those candidates will competefiercely on screens and in newspaper for more supportors.Costs are the last thing that is taken into ac-count,for they are all aware the important role an appealing image plays in their pared with selecting president,the cost of selecting local gover-nor is much more lower.Through vacancy chain,high positions are occupied by employees in internal enterprise and low positions are left to be occupied by hiring outside people.In this case,it is possible that vacancy chain can save money than directly hiring people from markets.From the discussion above,we can draw the conclusion that if the inequality can be satisfiedthen both employees and employers can benefit.Otherwisewe should hire people from outside markets instead of using vacancy chain to ex-change jobs.4.3Model TestingNow,we will run our model tofind out the expenses.At the beginning,there are four people in an enterprise registered in our website.(seefigure5)Then employee A left.If directly hiring a person for A’original position costs10,000dollars.The costs of exchanging jobs for B,C,D are3,000,2,000, 1,000dollars,respectively and the cost of hiring people for D’s position cost2, 000dollars.Then according to the inequality we mentioned above,we will use vacancy chain instead of directly hiring people.figure6shows the change(We hire E to occupy D’s original position).Team#1162Page14of19Figure5:Figure6:Then,employer C left(seefigure7).If directly hiring a person for C’s posi-tion costs8,000dollars.The costs of exchanging jobs for D,E are2,500,1,500 dollars,respectively and the cost of hiring people for E’s position cost2,000dol-lars.Then according to the inequality we mentioned above,we will use vacancy chain instead of directly hiring people.Figure8shows the change(We hire F to occupy E’s original position).Team#1162Page15of19Figure7:Figure8:Then,a new job is created above B’s position(seefigure9).If directly hiring a person for this new position costs11,000dollars.The costs of exchanging jobs for B,D,E,F are4,000,3,000,2,000,1,000dollars,respectively and the cost of hiring people for F’s position cost3,000dollars.Then according to the inequality we mentioned above,we will directly hire people for the new position instead of using vacancy chain to exchange job.Figure10shows the change(We hire H to occupy the new position).Team#1162Page16of19Figure9:Figure10:If in the nextfive years,there will be m hirings and n exchanges and the aver-age costs are x dollars and y dollars respectively.Then,we predict the change of HR expends for some enterprise customers within thesefive years is x∗m+y∗n.4.4ConclusionsSo far,we have discussed the conditions need to meet so that both employees and employers can benefit when vacancy chain happens.Besides,we run our model to predict the cost of change of HR.5Strengths and Weaknesses5.1StrengthsOur competency evaluation model is based on quantitative analysis,so our results of evaluation are objective and efficient.Team#1162Page17of19 The conditions need to meet so that vacancy chain can function well are based on expert’s research,so our results are more convincing and persuasive.Our prediction is also based on quantitative analysis,enterprises can use this quantitative results to adjust their arrangement.5.2WeaknessesOur model(in section3)is restricted by limited data.We define several assumptions and restrictions to simplify our model build-ing process,which may undermine its feasibility in real world.In the process of prediction(in section4),we don’t get the exact value of the change costs due to lack of data.References[1]uido Fioretti University of Bologna A Model of Vacancy Chains as a Mecha-nism for Resource Allocation7.March2007Online at http://mpra.ub.uni−muenchen.de/8205/[2]avid McClelland /wiki/David C larence M cClelland.[3]eveloping Competency Model for Middle Managers in Medium-sizedManufacturing Sector WANG Li WANG Hongmei School of Economic-s and Management Beijing Jiaotong University,P.R.China,100044http: ///wiki/David C larence M cClelland[4]yle M.Spencer,Phd Signe M.Spencer Competence at Work Models for Su-perior Performance Wiley India Pvt.Limited.MPRA Paper No.8205,posted10.April200813:49UTC[5]ayne F.Cascio Costing Human Resources The Financial Impact of Behaviorin Organizations.6AdvertisementTeam#1162Page18of19Team#1162Page19of19。
2013年全国大学生数学建模竞赛B题全国一等奖论文
碎纸片的拼接复原【摘要】破碎文件的拼接在司法物证复原、历史文献修复以及军事情报获取等领域都有着重要的应用。
本文主要解决碎纸机切割后的碎纸片拼接复原问题。
针对第一问，附件1、2分别为沿纵向切割后的19张中英文碎纸片，本文在考虑破碎纸片携带信息量较大的基础上，利用MATLAB对附件1、2的碎纸片图像分别读入，以数字矩阵的方式进行存储。
利用数字矩阵中包含图像边缘灰度这一特征，本文采用贪心算法的思想，在首先确定原文件左右边界的基础上，以Manhattan距离来度量两两碎纸片边界差异度，利用计算机搜索依次从左往右搜寻最匹配的碎纸片进行横向配对并达成排序目的。
最终，本文在没有进行人工干预，成功地将附件1、2碎纸片分别拼接复原，得到复原图片见附录2.1、2.2，纵切中文及英文结果表分别如下:为先对本文3、第4行及第9Spearman拼接复原1. 对于给定的来自同一页印刷文字文件的碎纸机破碎纸片（仅纵切），建立碎纸片拼接复原模型和算法，并针对附件1、附件2给出的中、英文各一页文件的碎片数据进行拼接复原。
如果复原过程需要人工干预，请写出干预方式及干预的时间节点。
复原结果以图片形式及表格形式表达。
2. 对于碎纸机既纵切又横切的情形，请设计碎纸片拼接复原模型和算法，并针对附件3、附件4给出的中、英文各一页文件的碎片数据进行拼接复原。
如果复原过程需要人工干预，请写出干预方式及干预的时间节点。
复原结果表达要求同上。
3. 上述所给碎片数据均为单面打印文件，从现实情形出发，还可能有双面打印文件的碎纸片拼接复原问题需要解决。
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请尝试设计相应的碎纸片拼接复原模型与算法，并就附件5的碎片数据给出拼接复原结果，结果表达要求同上。
二、模型假设1. 假设原题附件给出的破碎纸片图像是完好无损的。
2. 假设原题附件给出的破碎纸片仅包含纯文字内容（中英文），不含表格线等。
3. 假设原题附件给出的破碎纸片在切割时无油墨损失。
2013年全国大学生英语竞赛决赛C类
2013 NationalEnglish ContestforCollegeStudents(LevelC - Final)参考答案及作文评分标准PartIListening Com prehension (30 marks)Section A (5 marks)1—5 ACBBCSection B (10 marks)6—10 CCABA11—15 BCBCASection C (5 marks)16—20 ACBACSection D (10 marks)21.prescription22.drugaddiction23.lenientapproach24.distinguished between25.arelicensed to 26.singletransaction27.Proponents28.legitimate29.campaigns30.therebyPartIIVocabulary and Structure(15 marks)31—35 DBBCB36—40 CABAD41—45 ABACAPartIIICloze(10 marks)46.height47.both48.surprising49.mistakenly50.through51.hungry52.scientific53.Sleepiness54.connection55.evilPartIV Reading Com prehension (40 marks)Section A (10 marks)56.risks57.innocentrmation59.gang60.requestingSection B (10 marks)61.F62.T63.F64.Itprovidesstudentswith an onlinelearningenvironment.65.Theyreceivetheindividualsupportandadvicetheyneedtosucceed in theirstudy.Section C (10 marks)66.enduring 67.starved68.moredramatically69.D70.CSection D (10 marks)71.BecausetheEgyptiansworshipedcatsasholyanimalsandtherewerelawsprotectingthem.72.TheDarkAgesin Europe.1--73.About10 percent.74.猫惯有“巫师的助手”之称。
2013年美赛真题题目
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*请务必变更控制之前选择打印出来的页面的数量和问题。
团队可以自由选择之间MCM问题MCM问题A，B或ICM问题C.COMAP镜像站点：更多：/undergraduate/contests/mcm/MCM：数学建模竞赛ICM：交叉学科建模竞赛2013年赛题MCM问题问题A：终极布朗尼潘当在一个矩形的锅热烘烤时的4个角落中浓缩，并在拐角处（以及在较小程度上在边缘处）：产品会过头。
在一个圆形盘的热量被均匀地分布在整个外缘和在边缘处的产品不过头。
然而，因为大多数烤炉使用圆形平底锅的形状是矩形的是效率不高的相对于使用在烘箱中的空间。
开发一个模型来显示横跨平底锅平底锅不同形状 - 矩形之间的圆形和其他形状的外边缘的热量分布。
假设1。
的宽度与长度之比的W / L的形状是矩形的烘箱。
2。
- 每个盘必须具有的区域A的3。
最初，两个机架在烤箱，间隔均匀。
建立一个模型，可用于选择最佳的泛类型（形状）在下列情况下：1。
适合在烤箱的锅，可以最大限度地提高数（N）2。
最大限度地均匀分布热量（H），泛3。
优化的组合的条件（1）和（2）式中的权重p和（为1 - p）被分配的结果来说明如何随不同的值的W / L和p。
在除了MCM格式解决方案中，准备一到两页的广告片的新布朗尼美食杂志突出自己的设计和结果。
问题B：水，水，无处不在新鲜的白开水是在世界大部分地区的发展限制约束。
建立一个数学模型，为确定有效的，可行的和具有成本效益的水资源战略于2013年，以满足预计的用水需求，从下面的列表]中选择一个国家，到2025年，确定最佳的水战略。
2013年美国数学建模竞赛B题
水资源计划摘要本文是要设计一个有效的，可行的，低成本的用水计划，来满足某国2025年的用水需求。
我们选择中国为研究对象，根据中国各地区历年的水资源总量并求出其均值，参考各地区历年用水总量来预测2025年的用水总量，将两者相减得出差值，并以此为依据将中国各地区分为缺水地区，不缺水地区，水资源丰富地区三类。
经研究分析有两种可行性高的方案。
第一种，由水资源丰富地区向缺水地区提供水。
第二种，是由沿海缺水城市进行海水淡化并运往其他缺水城市。
我们主要考虑经济因素对两种方案进行分析研究，最终得出结论由水资源丰富地区铺设管道向缺水地区提供水为最优方案。
并以各省的省会作为核心城市，说明全省的需水和调水情况，并以省会城市或直辖市为顶点构成一个赋权图，即把问题转换为求水资源丰富地区到缺水地区的最短路问题，并用图论的知识来解决问题。
在此基础上考虑到此方案会改变就业，生产力，水资源利用等因素，从而对经济，物理，环境产生不同程度的影响，并用层次分析加以研究，最终以报告的方式向政府反映。
关键词：回归分析最小生成树层次分析法一、问题重述淡水是世界大部分地区的发展限制。
试建立一个数学模型，用来确定一个有效的、可行的和低成本的水资源战略，以满足2025年预计的用水需求，特别是，您的数学模型必须解决存储和输送，去盐碱化和环境保护等问题。
如果可能的话，用你的模型探讨此战略在经济，物理和环境等方面的影响。
试提供一个非技术性的文件，向政府相关部门介绍你的方法以及其可行性和成本，并说明为什么它是“最好的水战略”。
二、符号说明ˆy：预测得出的2025年用水量；S：输水的造价；1S：海水淡化的造价；2d1: 输水工程的单位造价；d2：海水淡化的单位造价；2R：拟合度.三、模型假设1.从2013年到2025年各外部因素对水资源总量无影响，例如：雪灾、地震、洪水、战争等对环境的影响；2.各地区海水淡化单位费用相同；3.不同地区淡水转移的单位费用相同；4.人们的消费水平及劳动力费用不会随意外事故发生明显改变。
历届美国数学建模竞赛赛题(汉语版)
历届美国数学建模竞赛赛题, 1985－2006AMCM1985问题-A 动物群体的管理AMCM1985问题-B 战购物资储备的管理AMCM1986问题-A 水道测量数据AMCM1986问题-B 应急设施的位置AMCM1987问题-A 盐的存贮AMCM1987问题-B 停车场AMCM1988问题-A 确定毒品走私船的位置AMCM1988问题-B 两辆铁路平板车的装货问题AMCM1989问题-A 蠓的分类AMCM1989问题-B 飞机排队AMCM1990问题-A 药物在脑内的分布AMCM1990问题-B 扫雪问题AMCM1991问题-A 估计水塔的水流量AMCM1992问题-A 空中交通控制雷达的功率问题AMCM1992问题-B 应急电力修复系统的修复计划AMCM1993问题-A 加速餐厅剩菜堆肥的生成AMCM1993问题-B 倒煤台的操作方案AMCM1994问题-A 住宅的保温AMCM1994问题-B 计算机网络的最短传输时间AMCM1995问题-A 单一螺旋线AMCM1995问题-B A1uacha Balaclava学院AMCM1996问题-A 噪音场中潜艇的探测AMCM1996问题-B 竞赛评判问题AMCM1997问题-A Velociraptor(疾走龙属)问题AMCM1997问题-B为取得富有成果的讨论怎样搭配与会成员AMCM1998问题-A 磁共振成像扫描仪AMCM1998问题-B 成绩给分的通胀AMCM1999问题-A 大碰撞AMCM1999问题-B “非法”聚会AMCM1999问题- C 大地污染AMCM2000问题-A空间交通管制AMCM2000问题-B: 无线电信道分配AMCM2000问题-C：大象群落的兴衰AMCM2001问题- A: 选择自行车车轮AMCM2001问题-B：逃避飓风怒吼（一场恶风…）AMCM2001问题-C我们的水系-不确定的前景AMCM2002问题-A风和喷水池AMCM2002问题-B航空公司超员订票AMCM2002问题-C蜥蜴问题AMCM2003问题-A: 特技演员AMCM2003问题-C航空行李的扫描对策AMCM2004问题-A：指纹是独一无二的吗？AMCM2004问题-B：更快的快通系统AMCM2004问题-C：安全与否？AMCM2005问题-A：.水灾计划AMCM2005问题-B：TollboothsAMCM2005问题-C：.Nonrenewable ResourcesAMCM2006问题-A：用于灌溉的自动洒水器的安置和移动调度AMCM2006问题-B：通过机场的轮椅AMCM2006问题-C：在与HIV/爱滋病的战斗中的交易AMCM85问题-A 动物群体的管理在一个资源有限，即有限的食物、空间、水等等的环境里发现天然存在的动物群体。
2013美赛ABC试题及翻译
2013 Contest ProblemsMCM PROBLEMSPROBLEM A: The Ultimate Brownie PanWhen baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners (and to a lesser extent at the edges). In a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.当在一个矩形的锅中烘烤时热量集中在烤箱的4个角落中，并在角落处的食物烤的过了（在某种程度上边缘也是这样）。
在一个圆形盘的热量被均匀地分布在整个外缘，在边缘处的食物烤的不会过头。
然而，因为大多数烤箱是方形的，使用原型的平底锅效率是不高的相对于烤箱中的空间。
Develop a model to show the distribution of heat across the outer edge of a pan for pans of different shapes - rectangular to circular and other shapes in between.建立一个模型来说明不同形状的锅(圆形方形或其他形状)的外边缘热量的不同分布。
Assume1. A width to length ratio of W/L for the oven which is rectangular in shape.2. Each pan must have an area of A.3. Initially two racks in the oven, evenly spaced.假设1.矩形烤箱的的宽度与长度之比是W / L。
2012-2013年全国大学生英语竞赛C类试题
2012 National English Contest for College Students(Level C – Preliminary)(总分：150分时间：120分钟)Part I listening Comprehension (30 marks)Section A (5 marks)In this section, you will hear five short conversations. Each conversation will be read only once .After each conversation, there will be a twenty-second pause. During the pause, read the question and the three choices marked A, B and C, and decide which is the best answer .Then mark the corresponding letter on the answer sheet with a single line through the centre.1.What does the man say we can do to deal with oil crisis?A. To make full use of oil.B. To use as little oil aspossibleC. To find alternative energy.2. Where does this conversation most probably take place?A. In an insurance company.B. In a bank.C. In a supermarket.3. According to the man, who is going to take over the position they are talking about?A. Janice.B. Someone else.C. Meryl.4. What does the woman say about the man’s report for the meeting?A. He has to get it ready before tomorrow noon.B. He has done well enough.C. He has enough time to prepare it.5. How many people will be on the earth by the year 2020 according to the professor?A. Some 5.8 billion.B. Nearly 7 billion.C. Over 8.5 billion.Section B (10 marks)I n this section, you will hear two long conversations. Each conversation will be read only once. At the end of each conversation, there will be a one-minute pause. During the pause, read the questions and the three choices marked A, Band C, and decide which is the best answer. Then mark the corresponding letter on the answer sheet with a single line through the centreConversation One6. What’s the main job of Simon’s organization?A. They send out radio signals to communicate with other planets.B. They look for life and intelligence on other planets.C. They study stars that have planets orbiting around them.7. Why does the organization search for radio signals from space?A. Their presence may prove the existence of aliens.B. They may help scientists find out how the universe started.C. They convey messages about life on the earth.8. Does Simon believe those stories about aliens visiting our planet?A. No, he doesn’t believe them at all.B. Yes, he does believe those stories because of his study.C. Yes, he believes them although he has no evidence.9. Which of the following factor is considered to be important in forming life according to the passage?A. Gravity.B. Minerals.C. Water.10. When did the “big bang” occur?A. No one knows.B. 12 billion years ago.C. 20 billion year ago.Conversation Two11. Why did Bob make the news last month?A. Because he criticized traditional jobsB. Because he earned a lot of money.C. Because he tried new strategies in finding a job.12. In which way do the bestsellers like “The Brand Called You”and “The Personal BrandingPhenomenon” help people?A. They advise people to promote themselves as brands.B. They teach people how to be a perfect partner.C. They give people tips for job interview.13. When did Bob come up with the idea of using the internet to find a job?A. Ten years ago when he was a college student.B. When he began to do research between jobs.C. After he launched the campaign “Give Bob a Job”.14. What was the purpose of Bob’s making the video?A. To fulfill his ambition as a director.B. To sell his products like Teddy bears and T-shirts.C. To advertise his skills and talents.15. How can the internet help Bob in his job search exactly?A. By helping him make friends.B. By passing on the video he made.C. By providing job information for him.Section C (5 marks)In this section, you will hear five short news items. After each item, which will be read only once,there will be a pause. During the pause, read the question and the three choices marked A, B and C, and decide which is the best answer. Then mark the corresponding letter on the answer sheet with a single line through the centre.16. How many troops are going to withdraw from Afghanistan by the end of next year?A. 43,000.B. 10,000.C. 33,000.17. What is the finding of the study?A. Low-calorie foods may lead to more weight.B. High-calorie foods may lead to more weight.C. High-calorie foods may lead to less weight.18. What do the conflicting reports show about radiation?A. The radiation level given by Tokyo Electric is much smaller than that given by other tests.B. The radiation level given by other tests is smaller than that given by Tokyo Electric.C. The radiation level is close to 10,000 times the normal level.19. Why are Caribbean Service and Europe Today shut down by BBC?A. Because of their outdated services.B. Because of cuts in government funding.C. Because of lack of target audience.20. What’s the cause of demonstrations in cities and towns across Syria?A. They are calling for more freedom.B. Workers demand higher pay.C. Some thirty people were killed by the police.Section D (10 marks)In this section, you will hear a short passage. There are 10 missing words or phrases. Fill in the blanks with the exact words or phrases you hear. The passage will be read twice. Remember to write the answers on the answer sheet.Recovery from jetlag can take as long as a day for every time zone crossed. So if you’re flying east-west for your holiday or on business, it is likely to mean a few days of feeling tired or even unwell.Jetlag is the (21)__________ of the body’s natural cycle and some factors make it worse. The artificial atmosphere inside a plane can affect the body in a number of ways and add to the effects of jetlag.Exercising before flights helps to offset the effects on the body of reduced (22) _________, and aerobic exercise afterwards helps to reoxygenate it. Drink plenty of water. Children may need more. Drinking carrot juice before flying overcomes oxygen deficiency.Eat light, frequent meals. Heavy meals (23) __________ the blood circulation, which can lead to dizziness and fainting. For two weeks before you fly, eat plenty of food containing vitamins A and E; theywill build up your (24) __________ and help to keep you fit. Sleep as much as you can before the flight and on it. On board, wear earplugs and eye pads because darkness (25) __________ secretion of the hormones that enhance sleep.Avoid alcohol, which restricts the brain’s oxygen intake. Like tea and coffee, alcohol increases the dehydration effect of flying. If you need to drink to relax, (26) __________ that the cabin environment intensifies the effect of alcohol.Wear loose, comfortable, warm clothes and limber up during flight. Sitting down for several hours slows down the (27) _________, leading to local stiffness, cramps and dizziness. Re-adjust to local time as soon as you can. Bright light helps the body stay alert, so if you are going somewhere sunny, stay outside.Do not smoke before or during the flight since smoking (28) ___________ the blood oxygen level. If you need to calm your nerves, try aromatherapy oils which have a sedative effect. (29) _________ your doctor before flying if you are on medication. The effects of some drugs are strengthened at high altitudes and some may produce (30) _________.Part II Vocabulary and Structure (15 marks)There are 15 incomplete sentences in this section. For each blank there are four choices marked A, B, C and D. Choose the one that best completes the sentence. Then mark the corresponding letter on the answer sheet with a single line through the centre.31. What we all work for is to free ________ time for the things we really want to do.A. offB. upC. asideD. in32. You _________ his words seriously. He was talking nonsense.A.won’t.takeB. may not takeC. mustn’t have takenD. needn’t have taken33. Never hesitate to _________ the first opportunity that comes along.A. seizeB. drawC. who; thatD. obtain34. His mother ________ hated city life longed to return to the village in _______she grew up.A. that; whereB. who; whichC. who; thatD. who; where35. All things _______, I think I’d better take your advice.A. consideringB. to be consideredC. consideredD. have been considered36. Twelve European countries ________ over to the Euro on January 1st, 2002.A. transformedB. switchedC. reversedD. altered37. She isn’t anything ________ unpleasant as people say she is.A. as likeB. likeC. asD. like as38. Stop complaining. You really ________ my nerves.A. get downB. get alongC. get offD. get on39. There wasn’t _______ truth in what he said.A. a grain ofB. a ray ofC. a point ofD. a drop of40. ________ for my savings, I wouldn’t be able to survive these miserable days.A. Was it notB.Were it notC.Had it been notD. Hadn’t it been41. There was a power cut this morning. ________, I couldn’t do anything with my computer.A. SupposedlyB. PresumablyC. ConsequentlyD. Essentially42. Alarm clocks needlessly wake ______ households. I want to design something targeted at theindividual sleeper.A. wholeB. totalC. fullD. high43. _______ both parties agree on these issues will a contract be signed soon.A. If onlyB. UnlessC. ShouldD. Only if44.—I’ve run out of cash. Could you lend me a few pounds this evening?—_____ I’ll just have to find time to get to the bank and make a withdrawal.A.I can lend you some now.B. I’m not sure I’ve got any either.C. Sorry, I haven’t got a penny in my account.D. My credit card must be left home.45. —We’re all going to the New Skyline Restaurant for our end-of-year get-together. Can we countyou in?—Oh, thanks, Sara, but _____A. I didn’t find you then.B. I’ve been to the restaurant once.C. I’ll pass this time.D. I’ll meet you there at 5:00.Part III Cloze (10 marks)Read the following passage and fill in each blank with one word. Choose the correct word in one of the following three ways: according to the context, by using the correct form of the given word, or by using the given letters of the word. Remember to write the answers on the answer sheet.Did you know that for every 20,000 novels written, only one gets published? So the (46) ____ (likely) that I’ll ever fulfill my ambition of becoming a professional mystery writer doesn’t seem very high. But the prospect of turning my lifelong passion into my livelihood and achieving fame and (47) for ______ at the same time is just too exciting for me to be put off by dull statistics.So what does it (48) t_______ to become a writer? Reading is important—all writers need to research their genre thoroughly to familiarize themselves (49) _______ its codes and conventions. My bookshelves at home are stacked with the novels of all the great mystery writers, which I’ve read and in many cases, re-read, despite (50) _______ (know) all the time “who’d done it”.Of course, being a writer requires imagination. You have to develop your own personal style rather than simply copy the work of “the greats”. I’ve turned out (51) d________ of short crime stories for my university student magazine—some have been published, some not, but I’ve always aimed to produce original and imaginative material.Last but not (52) ________, successful writers possess enormous self-discipline. I’ve often sacrificed my social life in order to devote the necessary time and effort to producing a good quality story. And more than once that has meant (53) _______ the midnight oil.We’ve got a novel inside us. Getting it out in anywhere near publishable form is no (54) ______ task, but with imagination and determination, and the help of an expert on “master class”, who could possibly fail to (55) re_______ their ambition?Part IV Reading Comprehension (40 marks)Read the following passages. Each passage is followed by several questions. Respond to the questions using information from the passage. Remember to write the answers on the answer sheet.Section A (10 marks)Questions 56—60 are based on the following passage.The term culture shock was introduced for the first time in 1958 to describe the anxiety produced when a person moves to a completely newenvironment. This term expresses the feeling of not knowing what to do or how to do things in a new environment. This term expresses the feeling of not knowing what to do or how to do things in a new environment. We can describe culture shock as the physical and emotional discomfort a person suffers when coming to live in a place different from the place of origin.Often, the way that we live before is not accepted or considered as normal in the new place. Everything is different, for example, not speaking the language, not knowing how to use banking machines, not knowing how to use telephones, and so forth.The symptoms of culture shock can appear at different times. Although a person can experience real pain from culture shock, it is also an opportunity for growing and learning new perspectives. Culture shock can help people develop a better understanding of themselves and stimulate personal creativity.Culture shock has many stages. Each stage can be ongoing, or appear only at certain times. In the first stage, the new arrival may feel very happy about all of the new experience. This time is called the honeymoon stage. Afterward, the second stage presents itself. A person may encounter some difficulties in daily life. For example, communication difficulties may occur, such as not being understood. In this stage, there may be feelings of impatience, anger and sadness. Transition betweenthe old methods and those of the new country is a difficult process and takes time to complete. The third stage is characterized by gaining some understanding of the new culture. A new feeling of pleasure and sense of humor may be experienced. A person may start to feel a psychological balance. The individual is more familiar with the environment and wants to belong. This starts an evaluation of the old ways versus those of the new. In the fourth stage, the person realizes that the new culture has good and bad things to offer. This stage can be one of double integration or triple integration, depending on the number of cultures that the person has to process. This integration is characterized by a more solid feeling of belonging. The person starts to define himself or herself and establish goals for living. The fifth stage is the stage that is called the reentry shock. This occurs when a person returns to the newly acquired customs are considered improper in the old culture.Questions 56—60Complete the summary with words from the passage, changing the form where necessary, with only one word for each blank.Introduced in 1958, culture shock is a term used to (56) __________ physical and emotional discomfort people experience when they come to or live in a new place. Although many people suffer a lot from culture shock, it is an (57) _________ for personal improvement. The five stages of culture shock may last for a long time or show up once in a while. In the first stage, the (58) __________ stage, the new arrival might be OK with everything. Afterward, (59) ________ from old methods to the new one calls for time and energy. During the third and fourth stage, people may gain more understanding of the new culture and possess objective views. The double or triple integration is (60) __________ by a feeling of belonging. The last stage, called reentry shock, refers to the feeling people have when returning to their home country.Section B (10 marks)Questions 61-65 are based on the following passage.For some people, it would be unthinkable. But Gabe Henderson is finding freedom in a recent decision; he canceled his MySpace account. The 26 years old graduate student stopped his account after realizing that a lot of his online friends were really just acquaintances. “The superficial emptiness clouded the excitement I had once felt,”Henderson wrote in an article. “It seems we have lost, to some degree, the special depth that true friendship is about.”Journalism professor Michael Bugeja, who is a strong supporter of face-to-face communication,read Henderson’s column and saw it was a sign of hope. Though he’s not anti-technology, Bugeja often lectures students about “interpersonal intelligence”—knowing when, where, and for what purpose technology is most appropriate. He points out the students he’s seen walking across campus, holding hands with each other while talking on cell phones to someone else He’s also seen them in coffee shops, surrounded by people, but staring instead at a computer screen. “True friends,” he says, “need to learn when to stop blogging and go across campus to help a friend.”These days, young people are more wired than ever—but they’re also getting more worried. Increasingly, they’ve had to deal with online bullies, who are posting anything from embarrassing photos to online threats. And increasingly, young people also are realizing that things they post on their profiles can come back to hurt them when applying for schools or jobs.Social networking can be an “extremely effective” way to publicize events to large groups. It can even help build a sense of community on campus. People joined Facebook as a way to meet others. However, it has limitations. A good Internet profile could make even the most boring person seem some what interesting. People are also not always happy with text messages on the cell phones. Cell phones can be a quick way to say “have a good day”. But friends can also cancel a night out with a text message to avoid having to explain. “Our generation needs to get over this fear of confrontation and rejection.” Henderson says. “The focus needs to be on quality communication, in all ways.” Back in his life, Henderson is enjoying spending more face-to-face time with his friends and less with his computer. He says his decision to quit his social-networking Internet accounts was a good one. “I’m not sacrificing friends,” he says, “because if a picture, some basic information about their life and a Web page is all my friendship has become, then there was nothing to sacrifice to begin with.”Questions 61—63Decide whether the following statements are true (T) or false (F) according to the passage.61. Although Henderson quit MySpace, most of his online friends are actually close friends.62. According to Bugeja, young people should know when to use technology and when to stop using it.63. Social networking helps build a sense of community but has a negative effect on young people’s life if it is used inappropriately.Questions 64—65Answer the following questions briefly according to the passage.64. What does Henderson lose by using social networking websites like Myspace?65. What do young people need to overcome in order to focus on quality communication?Section C (10 marks)Questions 66—70 are based on the following passage.“Five …Four …Three …Two …One …See ya! ”and Chance McGuire, twenty-five, isairborne off a 600 –foot concrete dam in NorthernCalifornia. In one second he falls 15 feet, in twoseconds 60 feet, and after three seconds and 130feet, he is flying at 66 miles an hour.McGuire is a practitioner of what he calls theking of all extreme sports. BASE—an acronym forbuilding, antenna, span (bridge) and earth (cliffs)—jumping has one of the sporting world’s highestfatality rates: in its 18-year history, forty –sixparticipants have been killed. Yet the sport has never been more popular, with more than a thousand jumpers in the United States, and more seeking to get into it every day. It is an activity without margin for error. If your chute malfunctions, don’t bother researching for a reserve—there isn’t time. There are no second chances.Still, the sport may be a perfect fit with the times. Americans may have more in common with McGuire than they know or care to admit. America has embarked on a national orgy of thrill seeking and risk taking. The rise of adventure and extreme sports such as BASE jumping, snowboarding, ice climbing, skateboarding, and paragliding is merely the most vivid manifestation of this new national behavior.The rising popularity of extreme sports speaks of an eagerness on the part of millions of Americans to participate in activities closer to the edge, where danger, skill, and fear combine to give weekend warriors and professional athletes alike a sense of pushing out personal boundaries. According to American Sports Data Inc., a consulting firm, participation in so-called extreme sports is way up. Snowboarding has grown 113 percent in five years and now boasts nearly 5.5 million participants. Mountain hiking, skateboarding, scuba diving—their growth curves reveal a nation that loves to play with danger. Contrast that with activities such as baseball, touch football, and aerobics, all of which were in steady decline throughout the 1990s.The pursuits that are becoming more popular have one thing in common: the perception that they are somehow more challenging than a game of touch football. “Every human being with two legs and two arms is going to wonder how fast, how strong, how enduring he or she is,” says Eric Perlman, a mountaineer and film maker specializing in extreme sports. “We are designed to experience or die.”Questions 66—68Complete the following sentences with information given in the passage in a maximum of 4 words for each blank.66. _______ rates doesn’t stop people from getting into BASE jumping every day.67. The rise of extreme sports manifests the national behavior of _______ and ________.68. The combination of fear, skill and danger gives both amateurs and professionals a sense of______.Questions 69—70Choose the best answer according to the passage.69. Which of the following activities reveals a nation that loves to play activities closer to the edge?A. Touch football.B. Baseball.C. Scuba diving.D. Aerobics.70. What does Eric mean by saying “We are designed to experience or die”?A. Life with great challenges is a meaningful one.B. Life without great experiences is very common.C. People may die while doing extreme sports.D. Extreme sports are essential parts of human life.Section D (10 marks)Questions 71—75 are based on the following passage.Albert Einstein was one of the greatest thinkers the world has ever known. He formulated theories of relativity, successfully described the nature of the universe and came up with the most famous equation in the world. David Beckham is the footballer whose skills and precision have made him one of the most gifted sportsmen of his generation. Who is more intelligent?How Gardner’s theory of multiple intelligences (MI) dares us to put these two men on neighboring pedestals. Instead of regarding intelligence as a single quantity measurable by pen-and-paper tests, Gardner, an education professor at Harvard University, divides human intelligence into no fewer than eight separate categories ranging from mathematical to musical competence. (74)His ideas have provoked vigorous debate about how one defines intelligence. Gardner’s point is that quantity measures only one capacity, the sort of mental agility that is valued in academic achievement, and that this single number does not do justice to human potential. So he has created his own spheres of achievement. Some categories are easily reconcilable with general perceptions about IQ. For example, “linguistic” intelligence confers a mastery of language, and is the preserve of such people as poets, writers and linguists. “Logical mathematical” intelligence marks out people who take a reasoning approach to physical things, and seek underlying principles. Einstein is the standard –bearer of this group, which also includes philosophers. These two categories are the main components of what we generally think of as “intelligence”.“Musical”intelligence characterizes musicians, composers and conductors. “Spatial”intelligence is about being able to picture perspective, to visualize a world in one’s head with great accuracy. Chess players, artists and architects would rate highly in this category. Dancers, athletes and actors are lumped under the “bodily-kinesthetic” heading; these individual, like Beckham, are able to control their bodies and movements very carefully.Then come two types of “personal”intelligence-intrapersonal, the ability to gauge one’s own mood, feelings and mental states, and interpersonal, being able to gauge it in others and use the information. These two categories could be interpreted as emotional intelligence. Psychiatrists are particularly adept at the former, while religious leaders and politicians are seen as people who can exploit the latter.Charles Darwin is perhaps the perfect embodiment of the eighth intelligence –“naturalist”. This label describes people with a deep understanding of the natural world and its objects. Zoologists and botanists can count themselves among this group.(75)These eight categories certainly reflect the fact that, in these areas, there is a spectrum of human ability ranging from the hopeless to the brilliant. But are these really intelligences, or could these competences be more accurately described as gifts or talents?Questions 71—73Answer the following questions briefly according to the passage.71. What are the main components of “intelligence” we generally think of?72. What kind of abilities does emotional intelligence involve?73. Which intelligences are represented by Einstein and Beckham respectively?Questions 74—75Translate the underlined sentences in the passage into Chinese.74. His ideas have provoked vigorous debate about how one defines intelligence.75. These eight categories certainly reflect the fact that, in these areas, there is a spectrum of human ability ranging from the hopeless to the brilliant.Part V Translation (10 marks)Translate the following sentences into English, using the hints given in brackets. Remember to write the answer on the answer sheet.76. 既然没有退路了，我们不妨试试他的方法。
2013年数学建模美赛B题论文
2013建模美赛B题思路摘要水资源是极为重要生活资料，同时与政治经济文化的发展密切相关，北京市是世界上水资源严重缺乏的大都市之一。
本文以北京为例，针对影响水资源短缺的因素，通过查找权威数据建立数学模型揭示相关因素与水资源短缺的关系，评价水资源短缺风险并运用模型对水资源短缺问题进行有效调控。
首先，分析水资源量的组成得出影响因素。
主要从水资源总量（供水量）和总用水量（需水量）两方面进行讨论。
影响水资源总量的因素从地表水量，地下水量和污水处理量入手。
影响总用水量的因素从农业用水，工业用水，第三产业及生活用水量入手进行具体分析。
其次，利用查得得北京市2001-2008年水量数据，采用多元线性回归，建立水资源总量与地表水量，地下水量和污水处理量的线性回归方程yˆ=-4.732+2.138x1+0.498x2+0.274x3根据各个因数前的系数的大小，得到风险因子的显著性为r x1>r x2>r x3(x1, x2，x3分别为地表水、地下水、污水处理量)。
再次，利用灰色关联确定农业用水、工业用水、第三产业及生活用水量与总用水量的关联程度r a=0.369852，r b= 0.369167，r c=0.260981。
从而确定其风险显著性为r a>r b>r c。
再再次，由数据利用曲线拟合得到农业、工业及第三产业及生活用水量与年份之间的函数关系，a=0.0019（t-1994）3-0.0383（t-1994）2-0.4332（t-1994）+20.2598;b=0.014（t-1994）2-0.8261t+14.1337;c=0.0383（t-1994）2-0.097（t-1994）+11.2116;D=a+b+c；预测出2009-2012年用水总量。
最后，通过定义缺水程度S=（D-y）/D=1-y/D，计算出1994-2008的缺水程度，绘制出柱状图，划分风险等级。
我们取多年数据进行比较，推测未来四年地表水量和地下水量维持在前八年的平均水平，污水处理量为近三年的平均水平，得出2009-2012年的预测值，并利用回归方程yˆ=-4.732+2.138x1+0.4982x2+0.274x3计算出对应的水资源总量。
2013年美赛数学建模b题的分析
美国2025年可提供的实际淡水量怎样预测？
（ 可以先预测不同地区不同领域供水量，再相加）
如果实际淡水量小于需求量，可通过那些 方法提供不足的淡水？ （例如：海水淡化、不同地区淡水转移）
这些方法那个更好？（比较的依据是什么？ 例如费用，环境） 需要做出那些假设？
1. 从现在到2025年之前不会有战争，自然灾害等 影响因素 2.同一个地区的居民年用水量相同 3.同一个地区的居民量的年增长率为常数 4.不同地区海水淡化的单位费用相同 5.不同地区淡水转移的单位费用相同
注：模型假设一般是在问题分析中根据需要提出的，所以可以先提出 基本假设，以后再补充
Vx pre S
1.预测2025年供水量的模型（以一个州 的降水量为例）
其中， 表示州i 的可用降水量， 表示 该州的单位面积平均年降水量， Si 表示该 州的淡水地表面积
Vx pre S
2.预测2025年需水量的模型（以一个州的居民 用水量为例）
若 V大于0，则说明2025年美国的淡水量是足够 的，然后再看每个州需要补充的淡水量， 即 V V ，
si ri
若每个州需要补充的淡水量均大于0，则不需要采 取任何措施，
否则，需要在不通州之间进行淡水调度。
若 V小于0，则说明2025年美国的淡水量是不足的， 需要采取海水淡化等措施
注：为使表达更清晰，可以在论文中采用图、表等形式
其中， 表示州i 在2025年人口数量， 表示该 州在2010年人口数量， 表示该州的人口平均年增 长率则该州在2025年的居民用水量为
i Vri w N 2 0 0 5
其中 ，w 表示该州居民的平均年用水量
3. 2025年美国需要补充的淡水量
2013年最新美国数学竞赛试题及答案(AMC2013A)
A1Square has side length . Point is on , and the area of is . What is ?2A softball team played ten games, scoring , and runs. They lost by one run inexactly five gam es. In each of the other gam es, they scored twice as m any runs as their opponent.How many total runs did their opponents score?3 A flower bouquet contains pink roses, red roses, pink carnations, and red carnations. One third of thepink flowers are roses, three fourths of the red flowers are carnations, and six tenths of the flowers are pink. What percent of the flowers are carnations?4What is the value of5Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their tripTom paid , Dorothy paid , and Sammy paid . In order to share the costs equally, Tom gave Sammy dollars, and Dorothy gave Sammy dollars. What is ?6In a recent basketball game, Shenille attem pted only three-point shots and two-point shots. She wassuccessful on of her three-point shots and of her two-point shots. Shenille attem pted shots. How m any points did she score?7The sequence has the property that every term beginning with the third is thesum of the previous two. That is, Suppose that and. What is ?8Given that and are distinct nonzero real numbers such that , what is ?9In , and . Points and are on sides , , and ,respectively, such that and are parallel to and , respectively. What is the perimeter of parallelogram?(9th)（11 th）10Let be the set of positive integers for which has the repeating decimal representationwith and different digits. What is the sum of the elem ents of ?11Triangle is equilateral with . Points and are on and points and are onsuch that both and are parallel to . Furthermore, triangle and trapezoidsand all have the sam e perimeter. What is ?12he angles in a particular triangle are in arithmetic progression, and the side lengths are . Thesum of the possible values of equals where , and are positive integers. What is ?13Let points and . Quadrilateral is cut intoequal area pieces by a line passing through . This line intersects at point , where thesefractions are in lowest term s. What is ?14The sequence, , , ,is an arithm etic progression. What is ?15Rabbits Peter and Pauline have three offspring—Flopsie, Mopsie, and Cotton-tail. These five rabbits are to be distributed to four different pet stores so that no store gets both a parent and a child. It is not required that every store gets a rabbit. In how many different ways can this be done?16, , are three piles of rocks. The m ean weight of the rocks in is pounds, the m ean weightof the rocks in is pounds, the m ean weight of the rocks in the com bined piles and ispounds, and the m ean weight of the rocks in the combined piles and is pounds. What is thegreatest possible integer value for the mean in pounds of the rocks in the com bined piles and ?17A group of pirates agree to divide a treasure chest of gold coins am ong them selves as follows. Thepirate to take a share takes of the coins that rem ain in the chest. The number of coins initially in the chest is the sm allest number for which this arrangement will allow each pirate to receive apositive whole number of coins. How many coins doe the pirate receive?18Six spheres of radius are positioned so that their centers are at the vertices of a regular hexagon of side length . The six spheres are internally tangent to a larger sphere whose center is the center ofthe hexagon. An eighth sphere is externally tangent to the six sm aller spheres and internally tangent to the larger sphere. What is the radius of this eighth sphere?19In , , and . A circle with center and radius intersects at pointsand . Moreover and have integer lengths. What is ?20Let be the set . For , define to m ean that either or. How m any ordered triples of elem ents of have the property that ,, and ?21Consider . Which of the following intervals contains ?22A palindrome is a nonnegatvie integer number that reads t he sam e forwards and backwards when written in base 10 with no leading zeros. A 6-digit palindrome is chosen uniformly at random. Whatis the probability that is also a palindrome?23is a square of side length . Point is on such that . The square regionbounded by is rotated counterclockwise with center , sweeping out a region whosearea is , where , , and are positive integers and . What is ?24Three distinct segm ents are chosen at random among the segments whose end-points are the vertices of a regular 12-gon. What is the probability that the lengths of these three segm ents are the three side lengths of a triangle with positive area?25Let be defined by . How m any complex numbers are there suchthat and both the real and the imaginary parts of are integers with absolute value atmost ?1. E2. C3. E4. C5. B6. B7. C8. D9. C10. D11. C12. A13. B14. B15. D16. E17. D18. B19. D20. B21. A22. E23. C24. E25. A。