2012年数学建模课程结业论文题目
2012年全国数学建模B题优秀论文

B 题 太阳能小屋的设计摘要本题要求设计一个太阳能光伏电池的铺设方案,使得太阳能小屋的年发电量尽可能大,同时单位发电量的费用尽可能小。
为此我们首先研究了了太阳能发电原理,然后运用太阳能辐射原理以及布格——朗伯定律,计算出每种型号光伏电池在小屋的不同表面的发电年收益率,经过计算我们得出了A 类型光伏电池铺设在小屋顶面不能收益等(见附录)有益于简化模型的结论。
在模型建立过程中,我们首先通过计算每种型号光伏电池在不同表面的收益率的大小,进而选择各个表面要铺设的光伏电池型号。
由于不同型号的电池不能串联,我们规定每个表面铺设多于两种型号的光伏电池,来进一步优化了模型。
问题一,在模型求解中,我们使用Excel 软件,首先穷举出每个表面铺设一种型号光伏电池的35年收益,然后穷举出每个表面铺设两种型号光伏电池时的收益。
最后得出最优解是年收入为:13330元,35年的收益320536元。
铺设方案见模型求解,当民用电价Wh k /5.0元不变时,小屋的投资回收年限为:7年。
针对问题二,我们考虑到小屋表面电池板的朝向与倾角均会影响到光伏电池的工作效率。
在问题一的基础上,我们为了使房顶能够获取最大的辐射能,通过查阅文献,并通过相关计算得出:当大倾斜面的光伏电池的倾斜角度为5°,小倾斜面的光伏电池的倾斜角度为45°,光伏电池的朝向为北偏西23.10°时电池所受到的辐射最强,太阳能小屋的收益最大。
针对问题三,我们充分利用前两问的结果,我们注意到房屋的北面和东面的太阳能辐射较弱,所以我们选择在这两面设计了最大窗墙比。
同时对太阳能小屋的朝向和屋顶的角度进行了优化,使得小屋的表面尽可能大,接收的总辐射强度最大,最后建立模型求出经济效益。
关键词: 多目标 整数规划 Excel 软件一、问题重述在设计太阳能小屋时,需在建筑物外表面(屋顶及外墙)铺设光伏电池,光伏电池组件所产生的直流电需要经过逆变器转换成220V 交流电才能供家庭使用,并将剩余电量输入电网。
2012国赛A题数学建模论文

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第二组得分 77.9 75.8 75.6 76.9 81.5 75.5 74.2 72.3 80.4 79.8 71.4 72.4 73.9 77.1 78.4 67.3 80.3 76.7 76.4 76.6 79.2 79.4 77.4 76.1 79.5 74.3 77 79.6
我们参赛选择的题号是(从 A/B/C/D 中选择一项填写) : 我们的参赛报名号为(如果赛区设置报名号的话) : 所属学校(请填写完整的全名) : 参赛队员 (打印并签名) :1. 2. 3. 指导教师或指导教师组负责人 (打印并签名): 日期: 日
A
年
月
2012 高教社杯全国大学生数学建模竞赛
编 号 专 用 页
第一组得分 62.7 80.3 80.4 68.6 73.3 72.2 67.5 72.3 81.5 67.5 70.1 53.9 74.6 69.2 58.7 74.6 79.3 59.9 78.6 78.6 77.1 77.2 85.6 78 69.2 73.8 73
2012年高教社杯全国大学生数学建模竞赛D题国家二等奖论文

承诺书我们仔细阅读了中国大学生数学建模竞赛的竞赛规则.我们完全明白,在竞赛开始后参赛队员不能以任何方式(包括电话、电子邮件、网上咨询等)与队外的任何人(包括指导教师)研究、讨论与赛题有关的问题。
我们知道,抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他公开的资料(包括网上查到的资料),必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。
我们郑重承诺,严格遵守竞赛规则,以保证竞赛的公正、公平性。
如有违反竞赛规则的行为,我们将受到严肃处理。
我们授权全国大学生数学建模竞赛组委会,可将我们的论文以任何形式进行公开展示(包括进行网上公示,在书籍、期刊和其他媒体进行正式或非正式发表等)。
我们参赛选择的题号是(从A/B/C/D中选择一项填写): D我们的参赛报名号为(如果赛区设置报名号的话):Y 0802所属学校(请填写完整的全名):西安理工大学高等技术学院参赛队员(打印并签名) :1. 熊**2. 胡**3. 杨**指导教师或指导教师组负责人(打印并签名):教练组日期:年月日赛区评阅编号(由赛区组委会评阅前进行编号):编号专用页赛区评阅编号(由赛区组委会评阅前进行编号):全国统一编号(由赛区组委会送交全国前编号):全国评阅编号(由全国组委会评阅前进行编号):机器人避障问题摘要机器人避障问题主要考虑机器人的路径选择。
本文问题是地图已知情况下,机器人从区域中一点到达另一点的避障最短路径和最短时间路径问题。
利用几何学的路径规划算法对机器人避障问题建立几何模型,并使用matlab 软件和mathematica 软件求解,用图论知识进行分析得出局部最优路径,最终比较得出机器人避障的全局最优路径。
问题一:建立区域中一点到达任一点的避障最短路径和最短时间路径的数学模型,将具体问题分解成三种线圆结构,并运用图论知识中的方法、穷举法以及几何知识进行优化求出最短路径,最终比较得到各个路段机器人避障得最短路径。
2012年 全国数学建模大赛A题获奖论文英文版English

The Evaluation of WinesSummaryThe general way is to employ a number of qualified wine critics to taste the wi nes when needing to determine the quality of the wines. But the grapes of making wines are able to influence the quality of the wines in acertain extent.In Task 1, we firstly solve the arithmetic mean to the two groups of the same s ample wine ratings of Appendix I of the wine critic Members , then prove and verif y two groups Tasting ratings results have the existence of significant differences using SPSS software by paired T test ,finally solve the second assessment wine grou p more reliable by analysis of variance method.In Task 2, by an accurate analysis of the impact of the physical and•chemic al indicators of wine grape and the quality of wine to wine grapes ,we extract the pri ncipal component that embodies the basic characteristics of the object of study, so w e can reduce redundancy, and reduce the dimension of the physical and chemical in dicators of wine grapes, which of the various samples conduct a comprehensive e valuation and ranking grapes .Red grapes into four categories on this basis, the thr ee levels of white grape.In Task 3, we analyze the correlation degree of both using the typical correlation, it is concluded that both has the very high correlation, that is, the better the quality of wine grape, the higher the quality of the wine.In Task 4,we again use SPSS software to visually show the correlation coefficient between the three study and concluded that the impact on wine quality is more than two, there are other factors not taken into account.Through the Third Schedule aromatic substances added argumentation analysis, we have confirmed the larger factors exist .Physical and chemical indicators of wine grapes and wine can not be very accurate assessment of the quality of the wine, you can consider the introduction of a sensory analysis of taste and smell. Keywords:Paired samples T-test Principal Component Analysis Canonical- correlation analysis Path AnalysisIntroductionThe general way is to employ a number of qualified wine critics to tast the wines when needing to determine the quality of the wines. First,each tasting member in the taste of the wine samples give rates in accordance with the classification index, then sum the total scores to determine the quality of the wines. Quality of wine grape has a direct bearing with the quality of the wines. the physical and chemical indicators of wine grape and the wine can reflect the quality of the wine and grape to some extent. Following issues need to be addressed :1. Analysis in Annex 1 two groups of evaluation of wine member of the evaluation results whether there were significant differences of both, which a set of results more reliable.2. According to the physical and chemical indicators of the wine grape and wine quality, how about were these wine grape classified ?3. Analyze the link between the physical and chemical indicators of wine grapes and wine.4. Analyze the physical and chemical index of the wine grape and wine to the influence on the quality of wine, and demonstrate the ability to use the physical and chemical indicators of grape and wine to evaluate the quality of the wine.The analysis of issueBackgroundThe high-quality wines are popular in 2012. It ’s seems to be urgent to study that the main raw materials - whether the quality of the red grapes and white grapes of the wine is good or bad a decisive role. Therefore analyzed the relationship between wines ’ and grapes ’ quality and physical and chemical indicators over thirty kinds of physical and chemical indicators of grape and wine.Assumptions1 Each tasting wine samples from an approximate normal distribution of the distribution of the overall ;2 Tasting members are normal senses, there is not much difference ;3 Annex all the physical and chemical indicators can be representative of the nature of the study, omission of the object of study have a significant impact on physical and chemical indicators ;Symbolic representationα: Significant parameters ;W : Rejection region range ;m : The number of indicator variables ; 12,,...,,m x x x : Evaluation object ;i j a⋅ Standardized index value ; ,j j s μ: Sample mean and sample standard deviation of the j-th indicator ; R : Correlation coefficient matrix ; A : Standardized matrix; (1,2,,)i i m λ= Eigenvalue ;(1,2,,)i e i m = Eigenvectors ;1V Eigenvectors of the correlation coefficient matrix of red wine grapes; 1D Red wine grape correlation coefficient matrix eigenvalue;2V White wine grape correlation coefficient matrix of eigenvectors; 2D Eigenvalues of the correlation matrix of white wine grapes;12,,,p λλλ The characteristic value corresponding to the first, second ...... p maincomponen ;p The number of indicators in the wine ;q The number of indicators of the wine grape ;11R The coefficient matrix of the first set of variables ;22R The coefficient matrix of the second set of variables ;11'R 、22'R The correlation coefficient of the first set of variables and the second setof variables ;1Z Comprehensive evaluation function of the principal component of red grape wine grape ;2Z Comprehensive evaluation function of the principal components of the white grape wine grape ;,1,2,...,28j x j = Transverse section of physical and chemical indicators in accordance with Annex II to turn on behalf of the 27-level indicators of the total amino acids, proteins, VC, ......, as well as wine quality and wine quality ratings;,1,2,...,14,15;i y i = Wine quality, peel quality juice rate (%), respectively, in turn, said, stems ratio (%), one hundred quality / g, ear quality / g dry matter content g/100g solid acid than titratable acidity (g/l), PH value, soluble solids g/l, the reducing sugars g/L, total sugar g/L, and flavonols (mg/kg), resveratrol (mg/kg) and other physical and chemical indicators ;Model establishments and solutionsTask1:Analysis in Annex 1 two groups of evaluation of wine member of the evaluationresults whether there were significant differences of both, which a set of results more reliable.To review the wine member of the evaluation result, significant difference and credibility evaluation calculation methods are varied ,mainly including Sensory evaluation of significant differences, based on the evaluation of the credibility of the Analytic Hierarchy Process, discriminant analysis, T value analysis, F value analysis,etc.Firstly, in accordance with the principle of the score with the same sample that 10 Tasting 'average score obtained in Schedule I of the first and second sets each red and white wine sample tasting ratings. Are listed below:two tables of very difference.Establishments of Model 11-1 For the evaluation of red wine :First of all by the data observation, it is known that on the whole, in view of the same sample wine in the first group and the second group of score difference are more prominent,therefore the relationship between the two with a Broken line vividly expressed. From the sensory ,image display greater differences in two groups Tasting set of evaluation criteria, shown in the following figure line chart:Figure 1 the overall rating of FirstSet and SecondSet for each of the red wine samplesThen, the overall rating results of the two rating wine group in a significant level 0.05α= are made a significant difference test. Firstly, each wine sample is selected from the large number of the same kind of samples wine from testing samples ,sample population can be approximated as a normal distribution . Secondly, Of all samples tested constitute 27 paired samples tested overall. Therefore we paired samples T-test two samples. The results are as follows:Table 3 The paired samples T-test the first and second Sets(The red)Inspection objectthe difference with 95% confidence interval tNPLowerlimitCeilingFirst and Second0.41569 4.66579 2.458 26 0.021In fact, P<0.05α=and 1/2,0.975,262.458 2.0555n t t α->==, the result falls into Rejection region {}1/2W t t α-=≥.Therefore the overall evaluation criteria of the members of the twogroups of wine critic has a significant difference.Which is trustworthier : The smaller the v ariance,the trustworthier the group’s evaluate ,when we study a single kind of wine sample. In that ,we compare the variance of these two groups to define the trustworthier group which have a smaller variance .Table 4 The credibility test for red wineWine sample sFirstSet ’s Variance Second’sVarianceThetrustworthiergroupWine sample sFirstSet ’s Variance Second’sVarianceThetrustworthiergroup1 236.1 736.9 一 15 770.1 372.1 二2 358.1 146 二 16 112.9 180.9 一3 412.4 276.4 二 17 792.1 82.5 二 4 972.4 371.6 二 18 424.9 452.4 一which is the better,the ratio of the two groups for 8:19;therefore the Second is trustworthier.1 -1 For the evaluation of white wine :Firstly,in a word,only studying the same sample wine,two groups are in small diference., therefore the relationship between the two with a Broken line vividly expressed.Said out as follows:Figure 2 the overall rating of FirstSet and SecondSet for each of the white wine samples Because wo use the same way to answer about the white wines’ question , There is no longer the detailed solution process .In summary,the evaluation results of both show significant differences,and the Second is trustworthier wherever in the red wines or the white wines. At the same time ,we find a standard to measure the quality of wine—the tasing ratings of the trustworthier sommeliers. Task2: According to the physical and chemical indicators of the wine grape and wine quality, how about were these wine grape classified ?Analysis of Model 2:There are a lot of the physical and chemical indicators of wine grapes that include more than 30 level indicators and some secondary indicators in Annex 2.we hope that many high correlation variables in wine grape physicochemical indicators are converted into mutually independent or uncorrelated variables,to choose only a small amount of indicators that can reflect most of the nature of the object of study. There are so-called Principal component which can be used to explain the research object indicators.2-1 The Step of using Principal Component Analisis way:(1) Standardize raw dataThere are m indicator variables that can be used to Principal Component Analisis way,namedas 12,,...,.m x x x There are all (1n or )2n evaluation objects.In there ,128,27m n ==,and 228n =( 1n represents the red wine as a research object, 2nrepresents the white wine as aresearch object ). The value of the j th indicator of the ith evaluation object is i j a ⋅,thereforewe gain the initial matrix of the object of study:1111m n n m a a A a a ⋅⋅⋅⋅⎛⎫ ⎪= ⎪ ⎪⎝⎭ ,The value of each indicator is converted to a standardized indicator value.As follows:,1,2,...,;1,2,...,,i j i i j ja ai n j m s μ⋅⋅-=== Among :11,1,2,...,,n i i j j i a s j m n μ⋅====∑At the same time,j and j srespectively is the sample’s mean and standard deviation Correspondingly ,1,2,...,j j j jx xj m s μ-==It ’s a standardized indicator variable.(2)Calculting the Correlation coefficient matrix R: the Correlation coefficient matrix()i j m n R r ⋅⨯=11122122212m m m m m m m r r r r r r R r r r ⋅⋅⋅⋅⋅⋅⋅⋅⋅⎡⎤⎢⎥⎢⎥=⎢⎥⎢⎥⎣⎦ TR A A =*,among : A represents A’s standardized matrix .By nature that R is a realsymmetric matrix (j i i j r r ⋅⋅=r ij =r ji ),therefore we only need to calculate on the upper triangle element or lower triangular elements to seek R . The Correlation coefficient matrix of the red wine grapes is R1,and the Correlation coefficient matrix of the white is R2. Specific data, see Annex 1.0 and Annex 3.0.(3)Calculating eigenvalues and eigenvectorsFirstly , we have solved the characteristic equation 0=-R I λ. We usually obtain eigenvalues (1,2,,)i i m λ= by Jacobi method , then arrange its in order of size 12,0m λλλ≥≥≥≥Secondly ,we respectively obtain the eigenvector (1,2,,)i e i m = corresponding to theeigenvalue i λ. Here is a requirement ,means i e =1,211mijj e ==∑,of which ij e represents the j-th component of the vector i e .The eigenvector V1 and eigenvalue D1 of the red wine grapes’ Correlation coefficient matrix , see Annex 2.0.The Characteristic roots of red wine grapes D1 Sequence :-0.0000 0.0000 0.0016 0.0058 0.0112 0.0156 0.0299 0.0504 0.0652 0.0826 0.1764 0.2025 0.2275 0.2350 0.3019 0.3712 0.5499 0.6844 0.7307 0.8076 0.9969 1.2228 1.5217 1.9934 2.8682 3.2615 4.7702 6.8158The eigenvector V2 and eigenvalue D2 of the white wine grapes’ Correlation coefficient matrix , see Annex 4.0.The Characteristic roots of white wine grapes D2 Sequence :-0.0000 0.0008 0.0026 0.0060 0.0250 0.0441 0.0634 0.0790 0.0953 0.1352 0.2719 0.3142 0.3156 0.3798 0.4458 0.6326 0.7267 0.8919 0.9663 1.0753 1.2937 1.4996 1.6175 1.7869 2.0894 2.9810 4.6623 5.5981(4)Calculation of the contribution rate and cumulative contribution rate of the main componentsThe contribution rate of main component i z :1(1,2,,)imkk i m λλ==∑The cumulative contribution rate :11(1,2,,)ikk mkk i m λλ===∑∑We generally take the characteristic values of 85-95% of the cumulatiive contribution rate corresponding to 1-st,2-nd,…,p-th(p≤m) main cpmponent.2-2 The results of principal component analysis :The eigenvalues 123,,,.....p λλλλwhose accumulative contribution rate of 85-95% can be generally selected as principal component parameters . According to theconclusion of the Principal Component Analysis , whenever in red wine or the white wine, the quality of wine is regarded as the first principal component. This shows that the quality of the evaluation of the grade of wine grapes wine share an important role .In addition ,we also gain:1. In the system which the red wine grapes act as study ,the effect of the principal component analysis of the first eleven characteristic roots whose cumulative contribution rate achieves 90% above is very great . Therefore we choose the first fourteen principal components []121314,,...,,y y y yto run a comprehensive evaluation. The contributions of fourteen principal component variables are the weight tobuild principal component comprehensive evaluation model of the red wine grapes , namly:345678910111213112140.116482559y +0.10243608y 0.0711931110.054346623+0.043671585y +0.035603699y +0.02884296y +0.026096522y +0.024442944y +0.019639356y +0.0.243422980.17036401325719y 894y 0.010782181y Z y y y ++++=+Therefore, we put all the objects corresponding to factors of the various principal components into the model ,to gain the comprehensive evaluation and sort results of the red wine grapes.2-3 ConclutionFor the red wine grapes , there are quite difference to various samples of grapes , therefore the red wine grape samples are divided into four grades: "Premium", "Great", "Qualified" and "Bad" .No. 26 sample is classified as "Premium" level by visible quality and particularly high comprehensive evaluation ;No. 17,24,5, and 20 are classified as "Great" level by great quality and high comprehensive evaluation ;No. 23,25,10,12,18,27,6,8,14,9,19,and sample is classified as "Qualified" level ;And , No. 15,3,13,4,21,7,11,2,22,and 16 sample are only classified as "Bad" , because their evaluateons are less than 60.For the white wine grapes,…Task3:Analyze the link between the physical and chemical indicators of wine grapes and wine.3-1 Model preparation :Introduced the idea of canonical correlation analysis In task 3 , we study the correlation relationship between 27 physical and chemical indicators of wine grapes ,10 of the red wines and 9 of the white wines ; the method which is similar to the main component is used, to respectively find the linear combination of the two sets of variables.Can make the number of variables to simplify, and can achieve the purpose of analysis correlation.3-2 Modeling steps :一、According to the purpose of the analysis to establish the original matrixAmong: p is the number of indicators in the wines, q is the wine grape number of indicators11111111p q n np n nq x x y y x x y y ⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦;二、Standardization of the original data , and calculating a correlation coefficient matrix11212122R R R R R ⎡⎤=⎢⎥⎣⎦Among: 11R ,22R respectively is the correlation coefficient matrix of the first set ofvariables and a second set of variables .三、Seeking canonical correlation coefficient and canonical variablesCalculate the eigenvalues and eigenvectors of the matrix A and B ,to gain the canonical correlation coefficient and canonical variables.Among:1111122221A R R R R --= ,1122211112B R R R R --=.四、Making canonical aorrelation analysis by using SPSS,to analysis of the link between the physical and chemical indicators of the wine grape and wine.The first step, the original data entry wine grapes and wines .As follows : X1,X2, X3 ,X4 ,X5 respectively represents Anthocyanin ,Tannin, Total phenolic , Wine total flavonoids , DPPH half inhibition volume ; Y1 ,Y2 ,Y3 …Y16 respectively represents the original data of the wine grapes of Annex II (Vertical indicators from the total amino acids ). Due to the limited space here is only part of the data is given. Detailed data see Annex Table 5.0(redpu.xls).Run in SPSS results are as follows:between the various indicators are small.If the correlation coefficient of the two indicators, two indicators may reflect the same ,and you can consider the merger.Analyze the physical and chemical index of the wine grape and wine to the influence on the quality of wine, and demonstrate the ability to use the physical and chemical indicators of grape and wine to evaluate the quality of the wine.4-1 The idea of Model 4:In order to analysis of wine grape and wine physical and chemical index to the influence on the quality of wine , we introduce linear regression theory to realize size analysis method . Using the Path Analysis on the basis of multiple regression , correlation coefficient iy r is decomposed into the direct path coefficients and indirect path coefficients .Path Analysis of the theory has been proved that any simple Correlation coefficient (iy r)between an independent variable i x and dependent variable y= Direct path (iy P)coefficient between x and y+ Indirect path coefficients of all the i x and y;Indirect path coefficients ibetween an independent variable any i x and dependent variable any y=Correlation coefficient (iy r)×Path coefficients (jy p) .Making Path Analysis process, it is generally believed that the most difficult part to calculate is the path coefficients. In fact , the path coefficients that we need to can be obtained by liner regression calculation . Then Indirect path coefficients can be multiplied by the correlation coefficient .4-2Problem-solving steps :4.2-1Data entryStart SPSS program, data input SPSS,name of each variable, andset the variable label.Wine quality is acted as the dependent variable y, and the physical and chemical indicators of the wine grape and wine including Anthocyanins, Tannins, Total Phenols, Wine Total Flavonoids, Resveratrol,Trans polydatin,Cis polydatin,Trans-resveratrol,Cis-resveratrol,DPPH half inhibition volume,and Color were the independent variables x1, x2, x3,x4,x5,x6,x7,x8,x9,x10.4.2-2Normality test on the dependent variable yFigure 3y s Standard Q-Q diagramStrengths and Weaknesses1.The strengths of model(1) The model established by the questions one to four are in strict theory based on analysis derived,comparing theoretical calculations with actual background, we have amended ,therefore it makes model more reasonable.(2) The use of paired samples T-test makes the results more reliable . This paper originality is very strong,because of the most of the models in the article derived and established strictly.(3) All calculations are used to specialized mathematical software and processing large amounts of data, such conclusions credibility is higher.We quantitative analysis many influencing factors that model involves, to make the paper more persuasive.2.The weaknesses of modelIn questionI and II ,due to the choice of the numerical inevitably produce a slight error and the complexity of factors affect ,so the calculation results inevitably produce certain error. References[1] Dongyan Chen , Dongmei Li , Shuzhong Wang , Mathematical Model [M].Beijing:Science Press,2007[2] Fengqiu Liu , Shanqiang Li , Zuobao Cao, Mathematical experiment [M].Harbin: HarbinInstitute of Technology Press,2010[3] Shisong Mao,Yiming Cheng,Xiaolong Pu, Probability theory and mathematical statisticstutorial [M].Beijing: Higher Education Press,2004[4] Shoukui Si,Xi Sun, Algorithm and application of mathematical modeling [M].Beijing:National Defence Industry Press,2011[5] Zhixing Zhang, Design and Application of the MATLAB program [M].Beijing: TsinghuaUniversity Press,2002。
2012数学建模题目3篇

2012数学建模题目一、题目描述近年来,随着互联网技术的不断进步,移动互联网已经成为人们生活中不可或缺的一部分,而移动互联网产业的发展也越来越成熟。
然而,随着移动互联网用户数量的不断增长,如何提高移动互联网用户的使用体验成为了重要的问题。
本题要求通过对用户行为分析,建立数学模型,预测用户在移动互联网上的行为,并通过模型优化提高用户使用体验。
二、问题分析基于移动互联网用户的行为特征,我们可以将用户的使用过程分为以下几个阶段:1. 需求获取阶段:用户首先会通过各种渠道获取使用移动互联网的需求信息,例如通过搜索引擎、社交媒体等方式获取信息。
在这个阶段,用户主要进行信息搜索和筛选,并逐渐形成清晰的需求。
2. 功能使用阶段:在用户确定了需求之后,用户会选择相应的应用程序进行使用。
在这个阶段,用户主要进行应用程序的功能使用。
3. 反馈阶段:用户使用应用程序的过程中会对应用程序的界面、功能、速度等方面进行评价,并可能会向软件开发者反馈问题。
通过对这三个阶段的分析,我们可以发现用户行为具有以下特征:1. 多样性:用户的需求各不相同,对应用程序的评价也因人而异。
2. 实时性:用户使用移动互联网的过程中可能会随时变化,需要及时调整模型。
3. 复杂性:用户使用移动互联网的过程中涉及到多种维度的信息,需要通过数学模型进行分析和预测。
基于以上特征,我们需要建立合适的数学模型进行分析和预测。
三、模型建立为了建立数学模型,我们需要对用户行为数据进行采集、处理和分析。
具体地,我们需要考虑以下几个问题:1. 数据采集:我们需要通过各种手段进行数据的采集,例如使用爬虫技术对用户行为数据进行抓取。
2. 数据处理:在获取了足够的用户行为数据之后,我们需要对数据进行清洗、转换和统计,以便于进行数学模型的分析。
3. 数据分析:我们需要对数据进行统计分析,了解用户的行为特征和规律,并构建对应的数学模型进行预测。
基于以上思路,我们可以建立以下数学模型:1. 需求获取模型在需求获取阶段,用户通过搜索引擎、社交媒体等方式进行信息获取。
2012年“高教社杯”全国大学生数学建模竞赛(CUMCM)国家一等奖优秀论文C题目

承诺书我们仔细阅读了中国大学生数学建模竞赛的竞赛规则。
我们完全明白,在竞赛开始后参赛队员不能以任何方式(包括电话、电子邮件、网上咨询等)与队外的任何人(包括指导教师)研究、讨论与赛题有关的问题。
我们知道,抄袭别人的成果是违反竞赛规则的,如果引用别人的成果或其他公开的资料(包括网上查到的资料),必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。
我们郑重承诺,严格遵守竞赛规则,以保证竞赛的公正、公平性。
如有违反竞赛规则的行为,我们将受到严肃处理。
我们参赛选择的题号是(从A/B/C/D中选择一项填写): C 我们的参赛报名号为(如果赛区设置报名号的话): 4052 所属学校(请填写完整的全名): XXXXXX参赛队员(打印并签名):1.2. (隐去论文作者相关信息等)3.指导教师或指导教师组负责人(打印并签名):日期: 2012 年 9 月 9 日赛区评阅编号(由赛区组委会评阅前进行编号):编号专用页赛区评阅编号(由赛区组委会评阅前进行编号):赛区评阅记录(可供赛区评阅时使用):评阅人评分备注全国统一编号(由赛区组委会送交全国前编号):全国评阅编号(由全国组委会评阅前进行编号):基于逐步回归的脑卒中发病环境因素分析及干预模型摘要本文通过建立合理的假设,对某地区2009-2010年脑卒中发病率与8种气象因素进行了相关分析,并经多元逐步回归建立了脑卒中发病率的预报模型进行了定量分析,得到了较为合理的结论。
考虑到发病率与气象因素的复杂关系,在逐步线性回归模型的基础上,引进广义线性回归模型(GLM)进行推广。
针对问题一,本文对性别、年龄段、职业和时间序列以及4年的平均发病例数进行统计和分析,在删除了一些缺失或失真数据的基础上,对数据分别进行整理分析。
最后,在性别方面,得到脑卒中发病率男性比女性的高。
从年龄结构看,发病人数主要集中在50~90这一年龄区间内,其所占比例达81.10%。
从职业结构看,农民的发病率最大。
数学建模课程优秀论文题目

嘉兴学院2012-2013年度第2学期数学建模课程论文题目要求:按照数学建模论文格式撰写论文,以A4纸打印,务必于2013年5月31日前纸质交到8号楼214室,电子版发邮箱:*************。
并且每组至少推荐1人在课堂上做20分钟讲解。
题目1、产销问题某企业主要生产一种手工产品,在现有的营销策略下,年初对上半年6个月的产品需求预测如表1所示。
班时间不得超过10个小时。
1月初的库存量为200台。
产品的销售价格为240元/件。
该产品的销售特点是,如果当月的需求不能得到满足,顾客愿意等待该需求在后续的某个月内得到满足,但公司需要对产品的价格进行打折,可以用缺货损失来表示。
6月末的库存为0(不允许缺货)。
各种成本费用如表2所示。
(1)若你是公司决策人员,请建立数学模型并制定出一个成本最低、利润最大的最优产销方案;(2)公司销售部门预测:在计划期内的某个月进行降价促销,当产品价格下降为220元/件时,则接下来的两个月中6%的需求会提前到促销月发生。
试就一月份(淡季)促销和四月份(旺季)促销两种方案以及不促销最优方案(1)进行对比分析,进而选取最优的产销规题目2、汽车保险某保险公司只提供一年期的综合车险保单业务,这一年内,若客户没有要求赔偿,则给予额外补助,所有参保人被迫分为0,1,2,3四类,类别越高,从保险费中得到的折扣越多。
在计算保险费时,新客户属于0类。
在客户延续其保险单时,若在上一年没有要求赔偿,则可提高一个类别;若客户在上一年要求过赔偿,如果可能则降低两个类别,否则为0类。
客户退出保险,则不论是自然的还是事故死亡引起的,将退还其保险金的适当部分。
现在政府准备在下一年开始实施安全带法规,如果实施了该法规,虽然每年的事故数量不会减少,但事故中受伤司机和乘员数肯定会减少,从而医药费将有所下降,这是政府预计会出现的结果,从而期望减少保险费的数额。
这样的结果真会出现吗?这是该保险公司目前最关心的问题。
2012年“高教社杯”全国大学生数学建模竞赛(CUMCM)国家一等奖优秀论文C题目

承诺书我们仔细阅读了中国大学生数学建模竞赛的竞赛规则。
我们完全明白,在竞赛开始后参赛队员不能以任何方式(包括电话、电子邮件、网上咨询等)与队外的任何人(包括指导教师)研究、讨论与赛题有关的问题。
我们知道,抄袭别人的成果是违反竞赛规则的,如果引用别人的成果或其他公开的资料(包括网上查到的资料),必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。
我们郑重承诺,严格遵守竞赛规则,以保证竞赛的公正、公平性。
如有违反竞赛规则的行为,我们将受到严肃处理。
我们参赛选择的题号是(从A/B/C/D中选择一项填写): C 我们的参赛报名号为(如果赛区设置报名号的话): 4052 所属学校(请填写完整的全名): XXXXXX参赛队员(打印并签名):1.2. (隐去论文作者相关信息等)3.指导教师或指导教师组负责人(打印并签名):日期: 2012 年 9 月 9 日赛区评阅编号(由赛区组委会评阅前进行编号):编号专用页赛区评阅编号(由赛区组委会评阅前进行编号):赛区评阅记录(可供赛区评阅时使用):评阅人评分备注全国统一编号(由赛区组委会送交全国前编号):全国评阅编号(由全国组委会评阅前进行编号):基于逐步回归的脑卒中发病环境因素分析及干预模型摘要本文通过建立合理的假设,对某地区2009-2010年脑卒中发病率与8种气象因素进行了相关分析,并经多元逐步回归建立了脑卒中发病率的预报模型进行了定量分析,得到了较为合理的结论。
考虑到发病率与气象因素的复杂关系,在逐步线性回归模型的基础上,引进广义线性回归模型(GLM)进行推广。
针对问题一,本文对性别、年龄段、职业和时间序列以及4年的平均发病例数进行统计和分析,在删除了一些缺失或失真数据的基础上,对数据分别进行整理分析。
最后,在性别方面,得到脑卒中发病率男性比女性的高。
从年龄结构看,发病人数主要集中在50~90这一年龄区间内,其所占比例达81.10%。
从职业结构看,农民的发病率最大。
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2012年数学模型课程结业论文题目1.某厂用原料A,B生产甲、乙、丙三种产品,已知生产单件产品所需原料、所获利润等有关数据如下表所示:(1)建立线性规划模型,求使该厂获利最大的生产计划;(2)若产品乙、丙的单件利润不变,甲的单件利润增加到6,是否改变生产计划?(3)若原料A市场紧缺,除拥有量外一时无法购进,而原料B如数量不足可去市场购买,单价为0.5,问该厂是否购买,以购进多少为宜。
2.下表是1980年到1999年世界人口统计数据(单位:百万)。
请利用1980年到1998年世界人口数据建立世界人口模型,用所建立的模型预测1999年人口,并与实际人口进行对比,表1 世界人口统计数据表3.一垂钓俱乐部鼓励垂钓者将钓上的鱼放生,打算按照放生的鱼的重量给予奖励,俱乐部只准备了一把软尺用于测量。
请你设计按照测量的长度估计鱼的重量的方法。
假定鱼池中只有一种鲈鱼,并且得到8条鱼的如下数据(胸围指鱼身的最大周长):先用机理分析建立模型,再用数据确定参数。
4.在甲乙双方的一次战役中,甲乙双方在开始时投入士兵数分别为x0和y0,t时刻甲乙双方的士兵数分别为x(t)和y(t),甲乙双方战斗的有效系数(包括士气、武器装备、指挥艺术等)分别为b和a,即甲方平均一个士兵使乙方士兵在单位时间内的减员数为b。
若甲乙双方都不考虑增援兵力,也不考虑士兵病故、逃亡等因素,试研究甲乙双方士兵人数的变化规律,并判断战役的结局情况。
5.硬盘振动测量硬盘是计算机上的重要部件,正向着更小、更快、密度更高的方向发展。
如何减小盘片的振动,成为关键问题,于是怎样检测盘片的振动更加重要。
由于硬盘转速很高,不适宜接触式测量,容易想到光学测量。
有一种新技术测量物体表面获得振动情况,是利用类似镜面反射的几何光学原理工作的:选用同一点光源发出两束光线,照射有反射能力的被测物体平面,产生的两条反射光线再照射到水平放置的接受屏上。
接受屏能够检测出光线照射点在接受屏平面上的坐标位置,问题是怎样利用图2中O ’x ’y ’平面的两个坐标值反算出被测物体当前的平面方程,就可利用平面方程的变化得到振动情况。
图1是用两条光线检测的原理图,点光源O 为坐标原点,E1和E2是盘片瞬间位置的反射点,此时盘片局部表面方程为z=ax+by+(c+D),其中a,b,c 为未知量,由于硬盘在振动,平面就偏离了初始位置z=D(D<0);接受屏方程为z=h ,其中h>0为接受屏的高度,B1和B2是其上的照射点,这样利用它们确定a 、b 和c 获得盘片局部表面方程。
(本题作到确定出a 、b 和c 即可,不必分析振动情况)问题 1:请解释这种测量技术采用两束光线的原因。
问题 2:请建数学模型分析盘片局部表面方程的测量原理。
问题 3:试分析接受屏分辨率(测量精度)对盘片局部表面方程的影响。
6. 配件厂为装配线生产若干种部件,轮换生产不同的部件时因更换设备要付出生产准备费(与生产数量无关)。
同一部件的产量大与需求量时因积压资金、占用仓库要付贮存费。
今已知某一部件厂的日需求量为常数r ,日生产速率为常数k ,k>r ,每次生产准备费为c1,每天每件产品贮存费为c2。
假设不允许缺货,当存量降到零时立即开始生产(不计生产准备时间),并且在每个生产周期T 内,开始的一段时间(0<t<T0)一边生产一边销售,后来的一段时间(T0<t<T )只销售不生产。
试安排该产品的生产计划,即确定生产周期T ,使总费图2 接受屏示意图)D c +hz =图1 原理图用最小?7我国公务员制度已实施多年,1993年10月1日颁布施行的《国家公务员暂行条例》规定:“国家行政机关录用担任主任科员以下的非领导职务的国家公务员,采用公开考试、严格考核的办法,按照德才兼备的标准择优录用”。
目前, 我国招聘公务员的程序一般分三步进行:公开考试(笔试)、面试考核、择优录取。
现有某市直属单位因工作需要,拟向社会公开招聘8名公务员,具体的招聘办法和程序如下:(一)公开考试:凡是年龄不超过30周岁,大学专科以上学历,身体健康者均可报名参加考试,考试科目有:综合基础知识、专业知识和“行政职业能力测验”三个部分,每科满分为100分。
根据考试总分的高低排序按1:2的比例(共16人)选择进入第二阶段的面试考核。
(二)面试考核:面试考核主要考核应聘人员的知识面、对问题的理解能力、应变能力、表达能力等综合素质。
按照一定的标准,面试专家组对每个应聘人员的各个方面都给出一个等级评分,从高到低分成A/B/C/D四个等级,具体结果见表1所示。
(三)由招聘领导小组综合专家组的意见、笔初试成绩以及各用人部门需求确定录用名单,并分配到各用人部门。
该单位拟将录用的8名公务员安排到所属的7个部门,并且要求每个部门至少安排一名公务员。
这7个部门按工作性质可分为四类:(1)行政管理、(2)技术管理、(3)行政执法、(4)公共事业。
见表2所示。
招聘领导小组在确定录用名单的过程中,本着公平、公开的原则,同时考虑录用人员的合理分配和使用,有利于发挥个人的特长和能力。
招聘领导小组将7个用人单位的基本情况(包括福利待遇、工作条件、劳动强度、晋升机会和学习深造机会等)和四类工作对聘用公务员的具体条件的希望达到的要求都向所有应聘人员公布(见表2)。
每一位参加面试人员都可以申报两个自己的工作类别志愿(见表1)。
请研究下列问题:(1)如果不考虑应聘人员的意愿,择优按需录用,试帮助招聘领导小组设计一种录用分配方案;(2)在考虑应聘人员意愿和用人部门的希望要求的情况下,请你帮助招聘领导小组设计一种分配方案;(3)你的方法对于一般情况,即N个应聘人员M个用人单位时,是否可行?(4) 你对上述招聘公务员过程认为还有哪些地方值得改进,给出你的建议。
表1:招聘公务员笔试成绩,专家面试评分及个人志愿表 2: 用人部门的基本情况及对公务员的期望要求8.非线性交调的频率设计如果一非线性器件的输入)(t u 与输出)(t y 的关系是)()()(2t u t u t y +=(其中t 是时间),那么当输入是包含频率21,f f 的信号t f t f t u 212cos 2cos )(ππ+=时,输出)(t y 中不仅包含输入信号21,f f ,而且还会出现21f ,21f f ±等新的频率成分,这些新的频率称为交调,如果交调出现在原有频率21,f f 的附近,就会形成噪声干扰,因此工程设计中对交调的出现有一定的要求。
现有一SCS(非线性)系统,其输入输出关系由如下一组数据给出: 输入信号为t f A t f A t f A t u 3322112cos 2cos 2cos )(πππ++=,其中251=A ,45,1032==A A 是输入信号的振幅,对输入信号的频率321,,f f f 的设计要求为:1)5546,5041,4036321≤≤≤≤≤≤f f f 。
2)输出中的交调均不得出现在5±i f 的范围内(i=1,2,3),此范围称为i f 的接受带(参见下图)i B (信号振幅)n C (交调振幅)6-=i n f f 5-i f i f 5+i f 6+i f接收带3)定义输出中的信噪比SNR=2210log 10ni C B (单位:分贝),其中i B 是输出中对应于频率为if 的信号的振幅,n C 是某一频率为n f 的交调的振幅。
若n f 出现在6±=i n f f 处(i=1,2,3),则对应的SNR 应大于10分贝(参见上图)。
4)i f 不得出现在j f 的接收带内(i,j=1,2,3,i ≠j )5)为简单起见,i f 只取整数值,且交调只考虑2阶类型(即{j i f f ±},i,j=1,2,3)和3阶类型(即{k j i f f f ±±},i,j,k=1,2,3)试按上述要求设计输入信号频率k j i f f f ,,。
9.公平的竞赛评卷系统数学建模竞赛吸引了众多的大学生、研究生甚至中学生的参与,越来越多的人关心竞赛评卷的公平性。
现今大多数的评卷工作是这样进行的:先将答卷编成密号,评委由各参赛学校(20-50所)派出,按不同的题目分成几个题组,每个题组由M 个评委组成,评阅N 份答卷,每份答卷经L 个评委评阅,评委对每份答卷给出等级分(A+,A ,A-,B+,B ,B-,C+ ,C ,C-,D ),如果L 个评委给出的分数基本一致,就给出这份答卷的平均分,否则需讨论以达成一致(其中M = 5-10,N = 60-200,L = 3-5)。
现在需要你解决如下问题:(1)有A,B,C,D 四个题目,P (P ≥ M )所学校参赛,给出一种答卷编号加密和解密的数学公式方法(其中题号为明号);要求方法简单易算、可随意变换且保密性能好;对你的方法给出分析。
(2)每个题组的M 个评委来自不同学校,给出一种评阅答卷分配的数学公式方法,要求回避本校答卷,并且每个评委评阅的答卷尽可能广泛,并满足某些特殊的要求。
(3)给出评分一致性或公正性的检验方法,该方法要求对每个评委的公平性给出评价(某评委分数普遍给的偏高或低属于尺度偏差,不应算作不公平,可在下面的问题中调整)。
(4)给出最终的分数调整计算公式。
该公式要处理那些可能出现的“不公平”,及尺度偏差。
对可能出现的“不公平”构造例子,说明你的方法。
(5)对评卷中的其他问题(如采用百分制还是等级分,一份答卷由几个评委评阅可以满足既经济又公平,等等)提出你的看法和根据。
(6)假定有35所学校298个参赛队参赛,数据如附表。
其中:数字前两位代表学校,甲组选做A,B题;乙组选做C,D题;25名评委所属的学校编号为:1-17,20,21,22,24,26,28,29,30。
每份试卷经四位评委评阅,编号为15,22的只容许评C,D题,编号为26的只容许评A,B题,编号为1,4,6,12,16的评委要求评A题,编号为2,5,7,10的评委要求评B 题;编号为24的评委要求评C题,编号为29的评委要求评D题。
其余按所在学校的甲、乙组别及个人的要求安排。
要求对问题1,2给出具体的算法及结果。
对问题3,4,5给出模拟数据再进行分析和运算。
附表:XX赛区参赛情况表10.某装饰材料公司欲以每桶2元的价钱购进一批彩漆以供日后销售。
为了尽快收回资金并获得较多的赢利,公司经理李先生打算做广告,于是便找到广告公司的王经理进行咨询。
李经理认为,随彩漆售价的提高,预期销售量将减少,并对此进行了估算(见表2)。
他问王经理广告有多大的效应。
王经理说“投入一定的钢管费后,销售量将有一个增长,这由销售增长因子来表示。
例如,投资3万元的广告费,销售增长因子为1.85,即销售量将是预期表2 售价与预期销售量表3 广告费与销售增长因子问李经理如何确定彩漆的售价和广告费,才能使公司获得的利润最大?11.某公司有4万元,可向A,B,C三个项目投资,已知各项目投资额的相应效益值如下表,12.为了更好地引进优秀人才,需要对应招人员的情况进行综合考虑,并量化打分。