2017年美国大学生数学建模E题获奖优秀论文
2017年全国大学生数学建模竞赛优秀论文
2017年全国大学生数学建模竞赛优秀论文数学是知识的工具，亦是其它知识工具的泉源。
所有研究顺序和度量的科学均和数学有关，数学建模是培养学生运用数学工具解决实际问题的最好表现。
下文是店铺为大家搜集整理的关于2017年全国大学生数学建模竞赛优秀论文的内容，欢迎大家阅读参考!2017年全国大学生数学建模竞赛优秀论文篇1浅析数学建模课程改革及其教学方法论文关键词:数学课程;数学建模;课程设置;课程改革论文摘要:数学建模教学和竞赛的开展,是培养学生创新能力的重要途径。
对数学建模竞赛中出现的问题进行分析,找出问题产生的根源与必修课和专业课设置不合理有关,应对高校数学课程的设置、教学方式等进行改革,并提出具体改革建议。
1. 前言数学建模,从宏观上讲是人们借助数学改造自然、征服自然的过程,从微观上讲是把数学作为一种工具并应用它解决实际问题的教学活动方式。
数学建模教育本身是一种素质教育,数学建模的教学与竞赛是实施素质教育的有效途径,它既增强了学生的数学应用意识,又提高了学生运用数学知识和计算机技术分析和解决问题的能力。
因而加强数学建模教育,培养学生的数学应用意识与能力已成为我国高校数学建模课程改革的重要目标之一。
虽然目前我国许多高校在数学建模方面取得了一些成绩,但大学生们在竞赛中也暴露出了许多问题,引发出对传统的课程设置和教学方法的思考。
2. 数学建模的现状和所存在问题与原因分析2.1 建模竞赛的现状根据竞赛时间(九月中下旬),我国大部分高校每年一般在七月中旬便开始组织学生的报名培训工作。
培训内容分为两个部分:首先集中讲解一些基础知识,主要包括常微分方程、概率与数理统计、运筹学、数学实验、建模基础等课程;然后进行建模的模拟训练,以往届国内外普通组和大专组的部分竞赛题为选题,让学生自愿结组,在规定时间内完成,并自愿为同学讲解各自的解题思路和方法。
参赛学生首先要参加培训,他们一般是先关注校园网上的通知,再到各院系自愿报名而组成,经培训后选拔出参赛队员。
2017年全国数学建模大赛获奖优秀论文
2017年全国数学建模大赛获奖优秀论文数学建模就是通过计算得到的结果来解释实际问题，并接受实际的检验，来建立数学模型的全过程。
下文是店铺为大家整理的关于2017年全国数学建模优秀论文的范文，欢迎大家阅读参考!2017年全国数学建模优秀论文篇1基于EXCEL的层次分析法模型设计摘要：层次分析法是美国学者T.L.Satty于20世纪70年代提出了以定性与定量相结合，系统化、层次化分析解决问题的方法，简称AHP。
传统的层次分析法算法具有构造判断矩阵不容易、计算繁多重复且易出错、一致性调整比较麻烦等缺点。
本文利用微软的Excel电子表格的强大的函数运算功能，设置了简明易懂的计算表格和步骤，使得判断矩阵的构造、层次单排序和层次总排序的计算以及一致性检验和检验之后对判断矩阵的调整变得十分简单。
关键词：Excel 层次分析法模型一、层次分析法的基本原理层次分析法是解决定性事件定量化或定性与定量相结合问题的有力决策分析方法。
它主要是将人们的思维过程层次化、，逐层比较其间的相关因素并逐层检验比较结果是否合理，从而为分析决策提供较具说服力的定量依据。
层次分析法不仅可用于确定评价指标体系的权重，而且还可用于直接评价决策问题，对研究对象排序，实施评价排序的评价内容。
用AHP分析问题大体要经过以下七个步骤：⑴建立层次结构模型;首先要将所包含的因素分组，每一组作为一个层次，按照最高层、若干有关的中间层和最低层的形式排列起来。
对于决策问题，通常可以将其划分成层次结构模型，如图1所示。
其中，最高层：表示解决问题的目的，即应用AHP所要达到的目标。
中间层：它表示采用某种措施和政策来实现预定目标所涉及的中间环节，一般又分为策略层、约束层、准则层等。
最低层：表示解决问题的措施或政策(即方案)。
⑵构造判断矩阵;设有某层有n个元素，X={Xx1,x2,x3……xn}要比较它们对上一层某一准则(或目标)的影响程度，确定在该层中相对于某一准则所占的比重。
2017数学建模优秀论文d题方面的
2017数学建模优秀论文d题方面的数学建模就是学习如何把物理的复杂的世界用适当的数学语言描述出来，进而用数学的手段对模型加以分析，然后再用所得结论回归现实，指导实践。
下文是店铺为大家搜集整理的关于2017数学建模优秀论文的内容，欢迎大家阅读参考!2017数学建模优秀论文篇1浅谈大学生数学建模的意义【摘要】本文重点分析了数学建模对当前数学教育教学改革的现实意义，探讨了数学建模对学生应用数学能力的培养，阐述了计算机在数学建模竞赛中的作用和地位，最后介绍了数学建模对数学教学改革的启示意义。
【关键词】数学建模;综合素质;教学改革长期以来，我国的数学教学中一直普遍存在着重结论而轻过程、重形式而轻内容、重解法而轻应用等弊端，不注重学生数学能力和素质的培养;过分强调对定义、定理、法则、公式等知识的灌输与讲授，不注重这些知识的应用，割断了理论与实际的联系，造成学与用的严重脱节，致使在我们的数学教育体制下培养出来的学生的能力结构都形成了一种严重的病态，主要表现在：数学理论知识掌握得还可以，但应用知识的能力很差，不能学以致用，缺乏创造力和解决实际问题的能力，这些问题使我们的学生在走向工作岗位时上手速度慢，面对新的数学问题时束手无策，不能将所学的知识灵活运用到实际中去。
显然，这种教育体制和理念与现代教育理念是背道而驰的，是必须抛弃的。
开展数学建模教学或数学建模竞赛，能够培养学生各方面的综合能力，提高学生的综合素质，对于当前数学教育教学改革有着极为重要的现实意义。
1 数学建模能够丰富和优化学生的知识结构，开拓学生的视野数学建模所涉及到的许多问题都超出了学生所学的专业，例如“基金的最佳适用”、“会议筹备”、“地震搜索”等许多建模问题，分别属于不同的学科与专业，为了解决这些问题，学生必须查阅和学习与该问题相关的专业书籍和科技资料，了解这些专业的相关知识，从而软化或削弱了目前教育中僵死的专业界限，使学生掌握宽广而扎实的基础知识，使他们不断拓宽分析问题、解决问题的思路，朝着复合型人才和具备全面综合素质人才的方向发展。
2017美赛数学建模M奖论文
For office use onlyT1________________ T2________________ T3________________ T4________________ Team Control Number70028Problem ChosenBFor office use onlyF1________________F2________________F3________________F4________________2017MCM/ICMSummary Sheet(Your team's summary should be included as the first page of your electronic submission.)Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page.SummaryThe performance of highway toll plaza directly affects the capacity of the highway, so the design of road toll plaza is imperative.In this paper, we conduct performance analysis for a specific toll plaza in New Jersey, USA, including accident prevention, throughput and cost. First of all, we usegrey model to predict the future output of the toll plaza, and compared with the realdata, the average value of the residual value is 0.429. Then we can draw a conclusionthat the throughput performance of the toll plaza is secondary. Next, we use queuingtheory to get the service index of the toll plaza in the light and heavy traffic, and thecellular automaton model is used to consider the changing circumstances of servicelevel, uses regression model to establish a function relation between traffic accidentand four factors. Then, we find that the rate of change has the greatest influence onit and the pavement performance has the least influence . In terms of cost, weconsider the toll plaza land and road construction. And the cost of road constructionis divided into the labor cost and material cost.Next, according to the influence of road geometry on the traffic performance of Toll Plaza, we select the transition curve trajectory model to improve the toll plazatransition, which can also have an improvement on the size and shape of the toll plazaand merge mode.Finally, we do a series of performance studies for our improved toll plaza. First of all, the improvement in the square flow and car flow under the condition of servicelevel are determined respectively through simulation .Next, we draw a conclusion thatthe service performance of the toll plaza is not obvious in small car flow, but there is amarked increase in large flow. Then, due to the fact that the unmanned vehicle coulddeal with a variety of road conditions, it undoubtedly expands our improved optionalscheme. Eventually, we obtain the throughput of toll before and after the improvementunder the different proportion of mixed charge mode and find that the improvedthroughput in the toll plaza has been increased on the performance.contents1 Introduction: (1)1.1 Problem background: (1)1.2 Steps: (1)1.3 Our work: (1)2 Assumptions (2)3 Nomenclature (2)4 Throughput analysis of grey forecasting model (3)5 error analysis (4)6 Service level of toll station (5)7 Vehicle lane changing rules based on Cellular Automata (6)8 Security analysis based on multivariate statistical regression mode (8)8.1 Study on the rate of change of Toll Plaza (8)8.2 Study on the longitudinal slope of entrance section of Toll Plaza (9)8.3 Research on service level of toll station (10)8.4 Study on pavement performance of toll station (10)9 Safety performance evaluation model of toll station (11)10 Cost analysis model of toll station (11)11 Analysis of the influence of lane geometry parameters on its capacity (12)11.1 Determination of lane changing rate (12)11.2 Influence of geometric parameters on the flow of the car lane (14)11.3 Energy consumption analysis based on cellular automata model (15)Definition of energy consumption: (16)Numerical simulation and analysis of the results: (17)Influence of curvature radius on energy consumption (17)Influence of arc length on energy consumption (18)12 The effect of traffic flow on service performance based on improved queuing theory 1913 The influence of unmanned vehicles on the improved model of Toll Plaza .. 2114 The influence of charging method on improving model of Toll Plaza (21)15 Strengths and Weaknesses (22)15.1 Strengths: (22)15.2 Weaknesses: (22)15.3 Future Model Development: (22)Comprehensive improvement strategy of tollplaza1Introduction:1.1Problem background:Highway toll and toll plaza is to ensure traffic safety and unimpeded, however because of lack of unified design specification, toll station and its square construction exists many problems. Such as: low value because of the technical indicators to make square construction scale too small and cause the toll plaza opened only few years as the traffic bottleneck, and use the high value on the one hand, because of the technical indicators and make the toll station construction scale is too large, waste a lot of money and resources. Due to incorrect linear indicators, or too short, the gradual square square length is insufficient, square road centerline offset, etc., it is too difficult to use after the completion of the square.so establishing the toll gates and the toll plaza design norms, as soon as possible, has the very vital significance in standardizing the construction of the toll station, ensuring the smooth general characteristic of toll plaza and traffic safety, improving the charging efficiency and management level, reducing the land acquisition and controlling investment and so on .1.2Steps:·A performance analysis of any particular toll plaza design that may already be implemented through the following three factors: accident prevention, throughput and cost .·Determine if there are better solutions (shape, size, and merging pattern) than any in common use.·Consider the performance of your solution in light and heavy traffic.·Consider the situation where more autonomous (self-driving) vehicles are added and how the solution is affected by the proportions of conventional (human-staffed) tollbooths, exact-change (automated) tollbooths, and electronic toll collection booths (such as electronic toll collection via a transponder in the vehicle)1.3Our work:·Based on the available data ,we make a performance analysis of any particulartoll plaza design that may already be implemented .·According to the problem from the performance analysis ,we make out a better solutions (shape, size, and merging pattern) than any in common use.·Determine the performance of the solution in light and heavy traffic ,how the solution change as more autonomous (self-driving) vehicles are added to the traffic mix and how the solution is affected by the proportions of conventional (human-staffed) tollbooths, exact-change (automated) tollbooths, and electronic toll collection booths.2AssumptionsTo simplify the problem and make it convenient for us to simulate real-life conditions, we make the following basic assumptions.1. Each section of roads is one-way traffic2.Vehicles in the retention period of toll station can be neglected3.In any hour of the vehicle arrival rate is proportional to the length of time4.The probability of any vehicle arrival in one hour of time is not affected by the previous history .5. The vehicles arrive in line with the Poisson distribution, namely the headway is negative exponential distribution3Nomenclatureε(0)(t)the residual errorq(t)the relative errorc the variance ratioP the small error probabilityr the curvature of the bend radiusu the static friction coefficientl the gradual change ratiok the number of serving drivewayρ/k traffic intensityw mean time to stay at a toll stationd automotive braking distancef the tire and road surface friction coefficientY the number of traffic accidents in toll stations per year∆W Width of the gradualα1curve angle R 1the radius of convex curve points pdelay probability e(n,t) energy consumption of the first n vehicles from time t to t+14 Throughput analysis of grey forecasting modelFigure 4-0-1Schematic diagram of New Jersey toll plazaFirst of all, we chose a toll plaza on the New Jersey in the United States for a specific performance analysis of toll plaza, and it includes the accident prevention, throughput, and cost.In view of the throughput of the toll plaza, we choose the grey forecasting model GM(1,1) , to predict the throughput of the toll plaza. Due to the problem of uncertainty, so we take the grey prediction model to deal with it.Suppose x (0)(1),x (0)(2)…,x (0)(M )In order to overcome the irregular , we use accumulation processx (1)(t )=∑x (0)(i)M i<1 Such a relatively smooth new series approximation can be described by the following differential equation:dx (1)dt +ax (1)=μ Its an albino form discrete solution of differential equation is: x ̂(1)(i +1)=.x (1)−u a /e ;ai +u aThe type of the parameter a、u be determined by the least squares fitting method is as follows:（1）（2）（3）A ̂=0a u 1=(B T B);1B T Y N Among them the matrix is:B =[ −12,x (1)(1)+x (1)(2)-1−12,x (1)(2)+x (1)(3)-1⋯⋯−12,x (1)(m −1)+x (1)(m )-1] Y N =(x (0)(2),x (0)(3),⋯,x (0)(m ))TSo the original data fitting sequence is:x ̂(0)(1)=x (0)(1)x ̂(0)(i +1)=x (1)(i +1)−x (1)(i )Table 4-0-1 Traffic flow prediction table5 error analysisIn equation (11), and regulations, the original data of reducing value and its residual error and relative error between observed value is as follows{ε(0)(t )=x (0)(t )−x′(0)(t )q (t )=ε(0)(t )x (0)(t )×100%The following inspection of the accuracy: x(0)=1M ∑x (0)(t )M t<0 ε(0)=1M;1∑(ε(0)(t )−ε0M t<2)2Second, calculate the variance ratio c =s 2s 1and small error probability P =2|ε(0)(t )−ε(0)|<0.6745s 13（4）（5）（6） （7） （8） （9） （10） （11）Figure 5-0-2comparison chart of grey prediction modelWe use m、p、v max to represent quality of the vehicle, random delayprobability and maximum speed respectively, g represents the local acceleration of gravity, r represents curvature of the bend radius and u represents the static friction coefficient . With the road statistical analysis carried out on the real value and the error of predicted value, we obtain the following res ults:It shows that the GM(1,1)model prediction results have a better response to .reflect the actual situation.6 Service level of toll stationThe direct feeling of the driver to the traffic environment of the toll station is from the queue length of the toll lane, and the length of the queue depends on the service level of the toll station V/C. In this regard, we use the queuing theory model of multichannel Queuing service, in which the vehicle arrival time is in a Poisson distribution, which is the negative exponential distribution; Suppose m is random arrival rate ,c i is output rate,k is the number of serving driveway, ρ=m c .There is the probability of having no vehicle in the queuing theoryρ(0)=1,∑1n!k−1n=0p n :1k!ρk k k−ρ- Average number of vehicles in queueing theory:n =ρ+p n ρ(0)k!k n−k (1;ρk )2 （12）（13）queue length: q =n −ρ=p n ρ(0)k!k n−k (1;ρk )2 Average number of waiting vehicles per lanea =q kAverage waiting time in queue systems:d =n m =q m +1c Average waiting time in queue:W =q mMean tardinessDeceleration time of vehicle entering toll stationt 1=v 03.6a 1Mean time to stay at a toll stationw =E ,S -+W qVehicle acceleration time of leaving toll stationt 2=v 03.6a 2 In this equation, v 0 is the normal traffic flow (km/h); a 1 、a 2 are deceleration of the vehicle (m/s 2); W q is average queue time (s)； E ,S - is expected service time (s);7 Vehicle lane changing rules based on CellularAutomataWe apply the previous cellular automata model, which is now extended to multi Lane case. The main difference between multi lane and single lane is to consider the model of lane changing. In this paper, we take 4 lanes as an example.In reality, it may be possible to change lanes when the driver is found to be close to the exit and the front of the adjacent lane is empty. If you want to change lanes ,you should consider the vehicle behind the adjacent lane. When the distance （14）（15） （16） （17） （18） （19） （20）to the rear of the adjacent lane reaches to a certain length, you can change the road. Lane change scenarios can be shown in figure (), when the c car on the 1 Lane is blocked by the c 1 car, while the c 2 and c 3 cars on the 2 lanes are relatively large. in order to maintain the speed, c car will change to the road lane 2.Figure 7-0-3Schematic diagram of lane changingWhether or not the driver chooses the lane change is mainly decided by the d 0,d n,otℎer 、d n ,back three indicators, through the previous research, this paper thinks that the lane changing rule is:When d n,back >v maxC n ={1−C n d n <min{v n +1，v max } d n,otℎer >d n ,d n,back >v max c n Otℎer circumstancesWhen d n,back ≤v max ,C n ={1−C n d n <min{v n +1，v max } d n,otℎer >d nv max −θ(−∆x )α>1+min{d n,otℎer +1,v max }−min *V n +1，v max +c n Otℎer circumstancesAmong them, C n is the n car in the lane , C n =0 or 1,d n 、d n,otℎer andd n,back are the distance between the first n vehicle and the front vehicle, the distance from the adjacent lane and the distance from the vehicle in the adjacent lane, respectively. d safe is safety lane change model.d n,back −v max , ∆x <0, v max −θ(−∆x )α is the distance between the vehicle and the vehicle in the adjacent lane after correction by the value function, 1+min{d n,otℎer +1,v max }−min *V n +1，v max + is Limit Lane distance. The parameters α and θchange according to the psychological status of driver. If α>1, the greater α is, the more careful the driver is. If θ>1, the greater θis, the more careful the driver is. When α=1，θ=1,that ’s Lane changing model.（21） （22）In order to discuss the αandθ, we use Cellular automata simulation. In a two lane road with a length of7.5km, adopting the open boundary condition, each lane is composed of 1000cells with a length of7.5km, the maximum speed of vehicle v max=5. The random slowing down rate was 0.2.8Security analysis based on multivariate statistical regression modeAimed at the prevention of the accident, we use multiple linear regression to establish a function between the number of traffic accidents and the following four factors: toll square gradient, service level, Toll plaza entrance section of the longitudinal slope, the Pavement performance of Toll station .Figure 8-1Cause analysis of accident8.1Study on the rate of change of Toll PlazaFan in and fan out area of toll plaza are designed to make the gradual vehicles more natural smoothly in and out of the toll plaza. In order to drive vehicle easily , there has a requirement on its gentle gradient change. Otherwise the driver could produce driving deviation, which may cause improper operation and endangers safety.The relationship is as follow:（23）l=b,LAccording to the experience, the vehicles with straight into another lane deviation than at around 0.9m s⁄, drivers usually have no move feeling and uncomfortable feeling.Figure 8-1 The relationship between Accident number and Toll plaza ramp rateFigure 8-1 shows the relation curve between highway toll plaza ramp rate and traffic accident, the figure demonstrates that as the toll plaza ramp rate increases, the traffic accidents will increase, whereas the security of the toll plaza will decrease.Through the data regression analysis, we get the related models between toll plaza ramp rate and the number of traffic accidentsY =1.423e .0064xIn this equation, Y is the forecasted numbers of traffic accident corresponding to the toll plaza ramp rate , x is the toll plaza ramp rate of toll plaza.The correlation coefficient in the model R 2=0.8621, it shows that description model of correlation is higher, From the model ,we can learn that the occurrence of traffic accident frequency is proportional to the toll plaza ramp rate. Gradient length is insufficient, so it can't meet to slow down and change lanes entering the toll plaza vehicle safety requirements, resulting in the occurrence of traffic accidents .8.2 Study on the longitudinal slope of entrance section ofToll PlazaHighway toll entrance section of the longitudinal slope design without fully considering the characteristics of vehicles entering the toll plaza, a long downhill or turn downhill and so on bad road alignment, those will affect the normal operation of the pilot and make the vehicles entering the toll plaza slowdown not sufficient, longitudinal safe driving distance not enough and driving direction can't adjust to the charge lane ,which will causetraffic accidents. This will lead to serious losses. （24）Figure 8-0-4 entrance section of the longitudinal slope and accident numberThrough regression analysis, we get the relevant model between the toll plaza entrance section of longitudinal wave and traffic accidentsY =2.6254e 0.638xIn this equation, Y is the forecasted numbers of traffic accident corresponding to the toll plaza ramp rate , x is the longitudinal wave of t oll plaza’s entry section .The correlation coefficient in the model R 2=0.9219,it shows the correlation of this model is relatively high. But we can learn that toll station ‘s traffic accident and its entrance section of longitudinal wave have a positive correlation from figure model representation ,.The greater the slope, the lower charge war security.8.3 Research on service level of toll stationBased on the previous research of service performance of toll station, we take V C as the measure of service level and Cite previous results. 8.4 Study on pavement performance of toll stationAccording to the vehicle dynamics, the vehicle's braking distance can be expressed as follows:d =u 257.9(f:I) In this equation, d is automotive braking distance , u is the speed at the beginning of the automobile brake, f is the tire and road surface friction coefficient, Iis road longitudinal slope（25）9 Safety performance evaluation model of toll stationBased on the above analysis, the evaluation model of descriptive can be written as the equation form, using multiple linear regression model .Y is the number of traffic accidents in toll stations every year , x 1=1l ,x 2=V C ,x 3=i,则Y =β0+β1x 1+β2x 2+β3x 3N is sample size , Y i (i =1,2,…,N ) represent the Y value of sample i , x i 1,x i 2,…x i n (i =1,2…，N) represent the value of each variable insample I, respectively.令Y =[Y 1Y 2⋮Y n], X =[11⋮1x 11x 21⋮x n 1⋯⋯⋮⋯x 1n x 2n ⋮x n n ] β=[β0β1⋮βn ] Y =Xβ,making maximum likelihood estimate of each variable coefficient β1，β2，…βn , it can get a normal equations:X T Xβ=X T YSo you can get the following regression equationY =−4.4012−9.947511l +10.098V C +11.25i 10 Cost analysis model of toll stationWe selected the American New Jersey a toll plaza to make cost analysisFirstly, according to relevant data, we learn that New Jersey’s average price is （26） （27）（28）（29）（30）$3500 per mu,And the toll plaza which we analyzed occupies about 5 mu, therefore, the land price of the toll plaza is about $17500;Second, the road construction costs include labor and material cost, and the local construction industry ’s average monthly salary is $3000, we use it to calculate labor, this occupies the largest in the road construction costs; As for material cost, we calculate by the current prices in the United States, is about $40 per cubic meter, then according to the size of the toll plaza, it will cost about $45000.In conclusion, the cost of toll plaza spend mainly on the labor cost of highway construction, the material cost also accordingly account for part of it.11Analysis of the influence of lane geometry parameters on its capacity11.1Determination of lane changing rateAccording to the analysis of vehicle trajectory and running state of vehicle , vehicle trajectory in the middle of the gradual path is similar to vehicle lane changing trajectory, and considering the factors when the driver turns, we select the easement curve trajectory model to design the gradual change section of toll plaza. And in the middle of the two convex type curve , we join a long for L straight section , it is shown in the figure belowFigure 11-0-5Toll plaza improvementsAccording to characteristics of convex curve geometric elements, we can use the following formula to calculate the first period of convex curve of easement curve tangent length T1:T1=(R1+p1)tanα1+q1（31）2In this equation, R 1 is the radius of the first section of convex curve points , ρ1 is Within shift, q 1 is tangent increment, α1 is curve angle, and α1=2β1, β1 is easement curve angleSuppose the first and second convex curve gradient width are ∆W 1 and ∆W 2 respectively, the width of one side with the gradient is ∆W .Depending on the figure with the easement curve in orbit, there are: ∆W 1=T 1∙sin α1∆W 2=T 2∙sin α2∆W =∆W 1+∆W 2+Lsinα1∆W =0(R 1+p 1)(1−cos L S1R 1 )+q 11∙sin L S1R 1 +0(R 2+p 2)(1−cos L S2R 2)+q 21∙sin Ls2R 2 +Lsinα1 L S1 and L S2 are the length of easement curve of two convex curve respectivelyL is radial tangent of two convex curve, so α1=α2,then it Can be introduced as follows:L S1R 1 =L S2R 2 Associate (38) and (39),we can get the length of easement curve of two - Section convex curve L S1 and L S2, then the transition section longitudinal distance L y can use the following formula to calculate:L y =[(R 1+p 1)tan L S12R 1 +q 1+(R 2+p 2)tan L S22R 2 +q 2](1+cos L S1R 1 )+Lcosα1 Suppose the ramp rate of transition period is K ,then we can adopt the following equation:K =∆WL y From this equation , we can learn that the driving radius and the straight line segment L have a great influence on the length and the gradient of the gradient. The greater the radius, the longer the straight line, the longer the length of the gradient, the smaller the rate of change（32） （33） （34） （35） （36）（37）（38）11.2 I nfluence of geometric parameters on the flow of thecar laneAssuming C 0 and C 1=dC dl represent respectively bend and itsgradient , l represents the length of the curve itself , we can get C (l )=C 0+C 1lso ，the bend of the direction Angle isφ(l )=φ0+∫C(τ)l 0dτ=φ0+C 0l +12C 1l 2 The bend of the longitudinal distance x(l) and transverse distance y(l) are{x (l )=x 0+∫cosφ(τ)dτl 0y (l )=y 0+∫sinφ(τ)dτl 0 Assuming sinφ≈φ,cosφ≈1,and when x 0(l )=0,x (l )=l , then the bend of transverse distance y(x) and direction angle φ(x) can be expressed{φ(x )=φ0+C 0x +12C 1x 2y (x )=y 0+φl +12C 0x 2+16C 1l 3 Using the ideas of analytical mechanics, assuming that the longitudinal velocity along the x axis for x ′, along the y axis transverse speed for y ′ , along the z axis of horizontal pendulum angular velocity as the bits of ψ′, then from The Lagrange's equations we can get{ d dt .ðE T ðẋ/−ψðE T ðẏ=F Q 1d dt .ðE T ðẏ/+ψðE T ðẋ=F Q 2d dt .ðE T ðψ/+ẋ ðE T ðẏ−y ðE T ðẋ=F Q 3 Defining the system kinetic energy E T =12m (ẋ+ẏ)+12I z ψ2In the formula, m,I z respectively represent Vehicle quality and Rotary inertia take the derivative of (46),we can get{ d dt .ðE T ðẋ/−ψðE T ðẏ=d dt(mẋ)−ψ (mẏ)d dt .ðE T ðẏ/+ψðE T ðẋ=d dt (mẏ)−ψ (mẋ)d dt .ðE T ðψ/+ẋ ðE T ðẏ−y ðE T ðẋ=d dt (I z ψ)−x (mẏ)−y (mẋ) （39）（40）（41）（42）（43）Delimiting generalized force: {F Q 1=∑F xF Q 2=∑F y F Q 3=∑M zIn summary we can get the Vehicle longitudinal coupling model.We mainly consider the lateral situation∑F y =F yr +F xf +F xf cosδ If the vehicle driving in the bend is only disturbed by small disturbance near the equilibrium state, the front wheel angle is small enough , so cosδ≈1,sinδ≈δ ∑F y =−(C f +C r )y ẋ−(aC f −bC f )ψẋ+(F xf +C f )δ We put the formula () and formula () into ()y =−d 2ẏẋ−.ẋ+kd 3ẋ/ψ−(F xf :C f m )δ In the formula d 2=C f :C r m ,d 3=aC f ;bC rI z ,k =I z mThen, the resultant force ∑M z along the vertical direction is∑M z =aF xf sinδ+aF xf cosδ−bF yrWhen sinφ≈φ,cosφ≈1,then∑F y =−(a 2C f +b 2C r )ψẋ−(aC f −bC f )ẏẋ+a(F xf +C f )δψ=−d 4ψẋ−−d 3y ẋ+a I z (F xf :C f m )δ In the formula, d 4=(a 2C f :b 2C r )I z 11.3 E nergy consumption analysis based on cellularautomata modelConsidering the influence of different shapes on traffic performance is mainly reflected in the curve, we mainly study the influence of the curve on the whole problem. On the road segment, Lane set of sections containing only one plane curve, the curve is provided with the deceleration section of L , the road will be regarded as the length of the L 1D discrete lattice chain, each lattice point at each moment or is empty or occupied for a car.m 、p and v max represent the quality of the vehicle, the （44） （45）（46）（47） （48） （49） （50）（51）stochastic delay probability and maximum speed ,respectively, g is the local acceleration of gravity, r and u represent the static friction coefficient of curvature radius and static coefficient of friction between wheel and road, respectively. The vertical direction of the vehicle is subjected to a pair of balance forces, and the influence of tangential friction on the vehicle is mainly reflected in the change of the speed, Therefore , the centripetal force required for the safety of the vehicle is provided by the normal static friction force,v safe is maximum speed of safetyturning, then mv safe2r =μmg,⁄v safe =√μgr .In each step of t →t +1 , all vehicles are in accordance with the following rules of the evolution of the speed and location of the synchronization update :Determine the vehicle delay probability p ：When the vehicle is in the buffer section , if v >v safe,take the probability of delay p =p 1 (larger), in other cases, take p =p 2 (smaller),Acceleration process: v n (t)→min (v n (t )+1,v max );deterministic deceleration process: v n (t)→min (v n (t ),gap n (t))Stochastic deceleration process with probability p ：v n (t)→max (v n (t )−1,0) deceleration process ：When the vehicle is in the corner of the road, and the speed v (t )>v safe , in order to turn the corner ，it must be slowed down :v n (t)→min (v n (t ),v safe )location update process: x n (t )→x n (t )+v n (t)Among them, v n (t) and x n (t ) are the speed and position of the first n vehicle at time t respectively , x n:1(t ) is the position of the first n +1 vehicle at time t . gap n (t )=x n:1(t )−x n (t )−1is the spacing between the first n car and the foregoing vehicle which is close to it.Definition of energy consumptionSuppose the mass of vehicle is m , when it slows down, its kinetic energy is reduced, we define the kinetic energy reduction for energy consumption, e(n,t) represents that energy consumption of the first n vehicles from time t to t+1 .e (n,t )={m,v 2(n,,t );v 2(n,,t:1)-2v (n,t )>v (n,t +1);0,v (n,t )≤v (n,t +1)The average energy consumption per vehicle per unit time:E d =1T 1N ∑∑e(n,t) N n<1t0:T;1t<t0 N is the total number of vehicles on the driveway, t 0 is relaxation time. For（52） （53）the energy consumption of the vehicle, if it is because the speed of t moment is greater than the Vehicle-to-vehicle distance v(n,t)>gap n(t), the vehicle decelerates, thatis defined as the interaction energy, denoted by E di; If it is because of the random deceleration caused, defined as the random deceleration energy consumption, denotedby E dr;if it is because the car speed In the corner v(n,t)>v safe, there is deceleration for the sake of driving safely, defined as safe energy consumption, denoted by E ds.Then total energy consumption is:E d=E di+E dr+E ds（54）Numerical simulation and analysis of the resultsTo simplify the problem, assuming that the length of actual road is 7.5km, Divided into 1000lattices, equivalent to the actual length of each grid correspondsto 7.5m, Delay probability p1=0.8,p2=0.25,Quality unit is defined 1. Entering probability changes from 0~1.0.The state of each vehicle is represented by its own speed v, v∈,0,v max-We let v max=5cell he actual speed is135km/h.We take8×104time steps every run .Influence of curvature radius on energy consumptionThe arc length s, the friction coefficient μand the radius of curvature of r are carried out numerical simulation. parameters are as follows: s=30m,μ=0.5,r=10、50、100、200、300m.According to v max=5cell/s,the maximum speed of the vehicle v max=37.5m/s. Results show that when r=300m, the safetyspeed v safe=√μgr=38.73m/s,v safe>v max, the bottleneck of the curve disappears and the speed limit is lost. The change of the probability in_p of therandom energy consumption（E di、E dr、E ds、E d）is shown in the figure.。
建模美赛获奖范文
建模美赛获奖范文全文共四篇示例，供读者参考第一篇示例：近日，我校数学建模团队在全国大学生数学建模竞赛中荣获一等奖的喜讯传来，这是我校首次在该比赛中获得如此优异的成绩。
本文将从建模过程、团队合作、参赛经验等方面进行详细介绍，希望能为更多热爱数学建模的同学提供一些借鉴和参考。
让我们来了解一下比赛的背景和要求。
全国大学生数学建模竞赛是由中国工程院主办，旨在促进大学生对数学建模的兴趣和掌握数学建模的基本方法和技巧。
比赛通常会设置一些实际问题，参赛队伍需要在规定时间内通过建立数学模型、分析问题、提出解决方案等步骤来完成任务。
最终评选出的优胜队伍将获得一等奖、二等奖等不同级别的奖项。
在本次比赛中，我们团队选择了一道关于城市交通拥堵研究的题目，并从交通流理论、路网优化等角度进行建模和分析。
通过对城市交通流量、拥堵原因、路段限制等方面的研究，我们提出了一种基于智能交通系统的解决方案，有效缓解了城市交通拥堵问题。
在展示环节，我们通过图表、数据分析等方式清晰地呈现了我们的建模过程和成果，最终赢得了评委的认可。
在整个建模过程中，团队合作起着至关重要的作用。
每个成员都发挥了自己的专长和优势，在分析问题、建模求解、撰写报告等方面各司其职。
团队内部的沟通和协作非常顺畅，大家都能积极提出自己的想法和看法，达成共识后再进行实际操作。
通过团队合作，我们不仅完成了比赛的任务，也培养了团队精神和合作能力，这对我们日后的学习和工作都具有重要意义。
参加数学建模竞赛是一次非常宝贵的经历，不仅能提升自己的数学建模能力，也能锻炼自己的解决问题的能力和团队协作能力。
在比赛的过程中，我们学会了如何快速建立数学模型、如何分析和解决实际问题、如何展示自己的成果等，这些能力对我们未来的学习和工作都将大有裨益。
在未来，我们将继续努力，在数学建模领域不断学习和提升自己的能力，为更多的实际问题提供有效的数学解决方案。
我们也希望通过自己的经验和教训，为更多热爱数学建模的同学提供一些指导和帮助，共同进步，共同成长。
2017年大学生数学建模优秀论文发表（2）
2017年大学生数学建模优秀论文发表(2)2017年大学生数学建模优秀论文篇3试谈高职大学生数学建模竞赛的现状及对策全国大学生数学建模竞赛是教育部高等教育司和中国工业与应用数学学会共同主办的面向全国大学生的群众性科技活动，目前已经发展成为大学生四大赛事之一，在全国高校和社会上都有相当大的吸引力和影响力。
开展竞赛的目的在于激发大学生学习数学的积极性、主动性和创造性，提高大学生建立数学模型和运用计算机技术解决实际问题的综合能力，鼓励广大学生踊跃参加科技实践活动，拓展知识面，培养创新精神及团结合作意识，推动大学数学教学体系、教学内容和方法的改革。
一、大学生数学建模竞赛现状分析湖北工业职业技术学院(以下简称我院)于2006年首次参加全国大学生数学建模竞赛。
由于缺乏指导教师和充足的资金支持，宣传不到位、建模活动普及度不高等原因，我院的数学建模水平与省内同类院校相差较远，一直存在着参赛队少、获奖级别低等问题。
(一) 学生竞赛能力相对薄弱整体而言，湖北工业职业技术学院学生数学基础较差，专业知识掌握不牢，计算机应用能力较为薄弱，且各专业数学知识的侧重点不同。
由于高数课课时逐渐减少，教师正常指导教学时间不足，学生对学习数学的重要性缺乏认识，学习积极性降低，导致了在对学生进行数学建模竞赛的培训过程中仍然需要教师做较大的努力对学生的基础方面进行一个“补弱”的讲授环节，然后才能对学生进行一个有效的整合，进而开展创新思维和实践应用能力的培养\[1\]。
而学生计算机应用能力较低也导致了学生难以运用计算机进行模型的搭建、具体分析和快速解题。
而当今大学生的创造性思维普遍缺失，很多学生没有对生活中的一些数学现象做深入的分析和研究，难以提出创造性的对策解决一些高难度的建模问题，上述原因导致学生竞赛的整体成绩难以令人满意。
(二) 缺乏竞赛的氛围数学建模竞赛在世界范围内产生的影响是很大的，在我国也日益引起各高等院校的重视，热度有增无减，但是并没有给我院带来预期的影响。
2017年数学建模优秀论文
2017年数学建模优秀论文数学是人类知识活动留下来最具威力的知识工具，是一些现象的根源。
数学是不变的，是客观存在的。
下文是店铺为大家搜集整理的关于2017年数学建模优秀论文的内容，欢迎大家阅读参考!2017年数学建模优秀论文篇1浅谈初中生数学问题意识的培养一、初中生问题意识培养的意义问题意识即在学科学习过程中能够主动思考、认真探究，从而针对某个方面提出问题的思想准备。
在数学课堂上，学生常常不敢或不愿回答课堂提问，不能或不善提出问题，能够经常积极回答问题的只有少数学生，能够在课堂中提出问题的学生更是少之又少。
学生缺少问题意识，不能提出问题，不利于学生思维的发展，不利于学习能力的进一步提升。
朱永新关于新课程的核心理念之一：教给学生一生有用的东西。
而学生自主学习、勤学好问的习惯一定是学生一辈子受益的。
心理学研究表明，意识到问题的存在是思维的起点，学生没有问题本身就是大问题.被称为现代科学之父的爱因斯坦曾指出：“提出一个问题往往比解决一个问题更重要。
”初中生数学问题意识的培养，是学习习惯和学习能力培养的重要方面，是新课程改革的需要。
二、初中生问题意识培养策略如何培养学生问题意识呢?我们通过教学实践进行了相关探索，并初步形成了一些策略。
1、改变评价方式，鼓励提问造成学生问题意识缺失的原因是多方面的。
我们的评价导向不利于学生问题意识的培养是原因之一，多数时候我们对回答问题对、考试分数高大加赞赏，对于学习有困难的学生缺少鼓励指导。
大批循规蹈矩的学生，不敢也不会去质疑。
学生学习中的问题本应该由学生主动提出，而实际教学中常常是学生被老师问。
如何改变这一现状?我们可以采用多种方式鼓励学生提问。
(1)注意运用表扬或激励性语言，逐步使学生感受到课堂中能提出问题和敢于回答问题一样都是值得肯定和鼓励的。
(2)把学生课堂提问是否积极作为对学生评价的一个重要方面。
(3)有目的进行一些提问竞赛等活动。
2、夯实学习基础，让学生能问教学实践中我们体会到学生能否提出问题与学生学习基础有密切关系，学习基础较好的学生更容易提出问题。
数学建模美赛一等奖优秀专业论文
For office use onlyT1________________ T2________________ T3________________ T4________________ Team Control Number52888Problem ChosenAFor office use onlyF1________________F2________________F3________________F4________________Mathematical Contest in Modeling (MCM/ICM) Summary SheetSummaryIt’s pleasant t o go home to take a bath with the evenly maintained temperature of hot water throughout the bathtub. This beautiful idea, however, can not be always realized by the constantly falling water temperature. Therefore, people should continually add hot water to keep the temperature even and as close as possible to the initial temperature without wasting too much water. This paper proposes a partial differential equation of the heat conduction of the bath water temperature, and an object programming model. Based on the Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), this paper illustrates the best strategy the person in the bathtub can adopt to satisfy his desires. First, a spatiotemporal partial differential equation model of the heat conduction of the temperature of the bath water is built. According to the priority, an object programming model is established, which takes the deviation of temperature throughout the bathtub, the deviation of temperature with the initial condition, water consumption, and the times of switching faucet as the four objectives. To ensure the top priority objective—homogenization of temperature, the discretization method of the Partial Differential Equation model (PDE) and the analytical analysis are conducted. The simulation and analytical results all imply that the top priority strategy is: The proper motions of the person making the temperature well-distributed throughout the bathtub. Therefore, the Partial Differential Equation model (PDE) can be simplified to the ordinary differential equation model.Second, the weights for the remaining three objectives are determined based on the tolerance of temperature and the hobby of the person by applying Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Therefore, the evaluation model of the synthesis score of the strategy is proposed to determine the best one the person in the bathtub can adopt. For example, keeping the temperature as close as the initial condition results in the fewer number of switching faucet while attention to water consumption gives rise to the more number. Third, the paper conducts the analysis of the diverse parameters in the model to determine the best strategy, respectively, by controlling the other parameters constantly, and adjusting the parameters of the volume, shape of the bathtub and the shape, volume, temperature and the motions and other parameters of the person in turns. All results indicate that the differential model and the evaluation model developed in this paper depends upon the parameters therein. When considering the usage of a bubble bath additive, it is equal to be the obstruction between water and air. Our results show that this strategy can reduce the dropping rate of the temperatureeffectively, and require fewer number of switching.The surface area and heat transfer coefficient can be increased because of the motions of the person in the bathtub. Therefore, the deterministic model can be improved as a stochastic one. With the above evaluation model, this paper present the stochastic optimization model to determine the best strategy. Taking the disparity from the initial temperature as the suboptimum objectives, the result of the model reveals that it is very difficult to keep the temperature constant even wasting plentiful hot water in reality.Finally, the paper performs sensitivity analysis of parameters. The result shows that the shape and the volume of the tub, different hobbies of people will influence the strategies significantly. Meanwhile, combine with the conclusion of the paper, we provide a one-page non-technical explanation for users of the bathtub.Fall in love with your bathtubAbstractIt’s pleasant t o go home to take a bath with the evenly maintained temperature of hot water throughout the bathtub. This beautiful idea, however, can not be always realized by the constantly falling water temperature. Therefore, people should continually add hot water to keep the temperature even and as close as possible to the initial temperature without wasting too much water. This paper proposes a partial differential equation of the heat conduction of the bath water temperature, and an object programming model. Based on the Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), this paper illustrates the best strategy the person in the bathtub can adopt to satisfy his desires. First, a spatiotemporal partial differential equation model of the heat conduction of the temperature of the bath water is built. According to the priority, an object programming model is established, which takes the deviation of temperature throughout the bathtub, the deviation of temperature with the initial condition, water consumption, and the times of switching faucet as the four objectives. To ensure the top priority objective—homogenization of temperature, the discretization method of the Partial Differential Equation model (PDE) and the analytical analysis are conducted. The simulation and analytical results all imply that the top priority strategy is: The proper motions of the person making the temperature well-distributed throughout the bathtub. Therefore, the Partial Differential Equation model (PDE) can be simplified to the ordinary differential equation model.Second, the weights for the remaining three objectives are determined based on the tolerance of temperature and the hobby of the person by applying Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Therefore, the evaluation model of the synthesis score of the strategy is proposed to determine the best one the person in the bathtub can adopt. For example, keeping the temperature as close as the initial condition results in the fewer number of switching faucet while attention to water consumption gives rise to the more number. Third, the paper conducts the analysis of the diverse parameters in the model to determine the best strategy, respectively, by controlling the other parameters constantly, and adjusting the parameters of the volume, shape of the bathtub and the shape, volume, temperature and the motions and other parameters of the person in turns. All results indicate that the differential model and the evaluation model developed in this paper depends upon the parameters therein. When considering the usage of a bubble bath additive, it is equal to be the obstruction between water and air. Our results show that this strategy can reduce the dropping rate of the temperature effectively, and require fewer number of switching.The surface area and heat transfer coefficient can be increased because of the motions of the person in the bathtub. Therefore, the deterministic model can be improved as a stochastic one. With the above evaluation model, this paper present the stochastic optimization model to determine the best strategy. Taking the disparity from the initial temperature as the suboptimum objectives, the result of the model reveals that it is very difficult to keep the temperature constant even wasting plentiful hotwater in reality.Finally, the paper performs sensitivity analysis of parameters. The result shows that the shape and the volume of the tub, different hobbies of people will influence the strategies significantly. Meanwhile, combine with the conclusion of the paper, we provide a one-page non-technical explanation for users of the bathtub.Keywords:Heat conduction equation; Partial Differential Equation model (PDE Model); Objective programming; Strategy; Analytical Hierarchy Process (AHP) Problem StatementA person fills a bathtub with hot water and settles into the bathtub to clean and relax. However, the bathtub is not a spa-style tub with a secondary hearing system, as time goes by, the temperature of water will drop. In that conditions,we need to solve several problems:(1) Develop a spatiotemporal model of the temperature of the bathtub water to determine the best strategy to keep the temperature even throughout the bathtub and as close as possible to the initial temperature without wasting too much water;(2) Determine the extent to which your strategy depends on the shape and volume of the tub, the shape/volume/temperature of the person in the bathtub, and the motions made by the person in the bathtub.(3)The influence of using b ubble to model’s results.(4)Give a one-page non-technical explanation for users that describes your strategyGeneral Assumptions1.Considering the safety factors as far as possible to save water, the upper temperature limit is set to 45 ℃;2.Considering the pleasant of taking a bath, the lower temperature limit is set to 33℃;3.The initial temperature of the bathtub is 40℃.Table 1Model Inputs and SymbolsSymbols Definition UnitT Initial temperature of the Bath water ℃℃T∞Outer circumstance temperatureT Water temperature of the bathtub at the every moment ℃t Time hx X coordinates of an arbitrary point my Y coordinates of an arbitrary point mz Z coordinates of an arbitrary point mαTotal heat transfer coefficient of the system 2（）⋅/W m K1SThe surrounding-surface area of the bathtub 2m 2S The above-surface area of water2m 1H Bathtub’s thermal conductivity/W m K ⋅（） D The thickness of the bathtub wallm 2H Convection coefficient of water2/W m K ⋅（） a Length of the bathtubm b Width of the bathtubm h Height of the bathtubm V The volume of the bathtub water3m c Specific heat capacity of water/()J kg ⋅℃ ρ Density of water3/kg m ()v t Flooding rate of hot water3/m s r TThe temperature of hot water ℃Temperature ModelBasic ModelA spatio-temporal temperature model of the bathtub water is proposed in this paper. It is a four dimensional partial differential equation with the generation and loss of heat. Therefore the model can be described as the Thermal Equation.The three-dimension coordinate system is established on a corner of the bottom of the bathtub as the original point. The length of the tub is set as the positive direction along the x axis, the width is set as the positive direction along the y axis, while the height is set as the positive direction along the z axis, as shown in figure 1.Figure 1. The three-dimension coordinate systemTemperature variation of each point in space includes three aspects: one is the natural heat dissipation of each point in space; the second is the addition of exogenous thermal energy; and the third is the loss of thermal energy . In this way , we build the Partial Differential Equation model as follows:22212222(,,,)(,,,)()f x y z t f x y z t T T T T t x y z c Vαρ-∂∂∂∂=+++∂∂∂∂ (1) Where● t refers to time;● T is the temperature of any point in the space;● 1f is the addition of exogenous thermal energy;● 2f is the loss of thermal energy.According to the requirements of the subject, as well as the preferences of people, the article proposes these following optimization objective functions. A precedence level exists among these objectives, while keeping the temperature even throughout the bathtub must be ensured.Objective 1(.1O ): keep the temperature even throughout the bathtub;22100min (,,,)(,,,)t t V V F t T x y z t dxdydz dt t T x y z t dxdydz dt ⎡⎤⎡⎤⎛⎫=-⎢⎥ ⎪⎢⎥⎢⎥⎣⎦⎝⎭⎣⎦⎰⎰⎰⎰⎰⎰⎰⎰ (2) Objective 2(.2O ): keep the temperature as close as possible to the initial temperature;[]2200min (,,,)tV F T x y z t T dxdydz dt ⎛⎫=- ⎪⎝⎭⎰⎰⎰⎰ (3) Objective 3(.3O ): do not waste too much water;()30min tF v t dt =⋅⎰ (4) Objective 4(.4O ): fewer times of switching.4min F n = (5)Since the .1O is the most crucial, we should give priority to this objective. Therefore, the highest priority strategy is given here, which is homogenization of temperature.Strategy 0 – Homogenization of T emperatureThe following three reasons are provided to prove the importance of this strategy. Reason 1-SimulationIn this case, we use grid algorithm to make discretization of the formula (1), and simulate the distribution of water temperature.(1) Without manual intervention, the distribution of water temperature as shown infigure 2. And the variance of the temperature is 0.4962. 00.20.40.60.8100.51 1.5200.5Length WidthH e i g h t 4242.54343.54444.54545.5Distribution of temperature at the length=1Distribution of temperatureat the width=1Hot water Cool waterFigure 2. Temperature profiles in three-dimension space without manual intervention(2) Adding manual intervention, the distribution of water temperature as shown infigure 3. And the variance of the temperature is 0.005. 00.5100.51 1.5200.5 Length WidthH e i g h t 44.744.7544.844.8544.944.9545Distribution of temperatureat the length=1Distribution of temperature at the width=1Hot water Cool waterFigure 3. Temperature profiles in three-dimension space with manual interventionComparing figure 2 with figure 3, it is significant that the temperature of water will be homogeneous if we add some manual intervention. Therefore, we can assumed that222222()0T T T x y zα∂∂∂++≠∂∂∂ in formula (1). Reason 2-EstimationIf the temperature of any point in the space is different, then222222()0T T T x y zα∂∂∂++≠∂∂∂ Thus, we find two points 1111(,,,)x y z t and 2222(,,,)x y z t with:11112222(,,,)(,,,)T x y z t T x y z t ≠Therefore, the objective function 1F could be estimated as follows:[]2200200001111(,,,)(,,,)(,,,)(,,,)0t t V V t T x y z t dxdydz dt t T x y z t dxdydz dt T x y z t T x y z t ⎡⎤⎡⎤⎛⎫-⎢⎥ ⎪⎢⎥⎢⎥⎣⎦⎝⎭⎣⎦≥->⎰⎰⎰⎰⎰⎰⎰⎰ (6) The formula (6) implies that some motion should be taken to make sure that the temperature can be homogeneous quickly in general and 10F =. So we can assumed that: 222222()0T T T x y zα∂∂∂++≠∂∂∂. Reason 3-Analytical analysisIt is supposed that the temperature varies only on x axis but not on the y-z plane. Then a simplified model is proposed as follows:()()()()()()()2sin 000,0,,00,000t xx x T a T A x l t l T t T l t t T x x l π⎧=+≤≤≤⎪⎪⎪==≤⎨⎪⎪=≤≤⎪⎩ (7)Then we use two ways, Fourier transformation and Laplace transformation, in solving one-dimensional heat equation [Qiming Jin 2012]. Accordingly, we get the solution:()()2222/22,1sin a t l Al x T x t e a l πππ-=- (8) Where ()0,2x ∈, 0t >, ()01|x T f t ==(assumed as a constant), 00|t T T ==.Without general assumptions, we choose three specific value of t , and gain a picture containing distribution change of temperature in one-dimension space at different time.00.20.40.60.811.2 1.4 1.6 1.8200.511.522.533.54Length T e m p e r a t u r e time=3time=5time=8Figure 4. Distribution change of temperature in one-dimension space at different timeT able 2.V ariance of temperature at different timet3 5 8 variance0.4640 0.8821 1.3541It is noticeable in Figure 4 that temperature varies sharply in one-dimensional space. Furthermore, it seems that temperature will vary more sharply in three-dimension space. Thus it is so difficult to keep temperature throughout the bathtub that we have to take some strategies.Based on the above discussion, we simplify the four dimensional partial differential equation to an ordinary differential equation. Thus, we take the first strategy that make some motion to meet the requirement of homogenization of temperature, that is 10F =.ResultsTherefore, in order to meet the objective function, water temperature at any point in the bathtub needs to be same as far as possible. We can resort to some strategies to make the temperature of bathtub water homogenized, which is (,,)x y z ∀∈∀. That is,()(),,,T x y z t T t =Given these conditions, we improve the basic model as temperature does not change with space.112213312()()()()/()p r H S dT H S T T H S T T c v T T c V V dt D μρρ∞⎡⎤=++-+-+--⎢⎥⎣⎦(9) Where● 1μis the intensity of people’s movement ;● 3H is convection between water and people;● 3S is contact area between water and people;● p T is body surface temperature;● 1V is the volume of the bathtub;● 2V is the volume of people.Where the μ refers to the intensity of people ’s movement. It is a constant. However , it is a random variable in reality, which will be taken into consideration in the following.Model T estingWe use the oval-shaped bathtub to test our model. According to the actual situation, we give initial values as follows:0.19λ=,0.03D =,20.54H =,25T ∞=,040T =00.20.40.60.8125303540Time T e m p e r a t u r eFigure 5. Basic modelThe Figure 5 shows that the temperature decreases monotonously with time. And some signs of a slowing down in the rate of decrease are evident in the picture. Reaching about two hours, the water temperature does not change basically and be closely to the room temperature. Obviously , it is in line with the actual situation, indicating the rationality of this model.ConclusionOur model is robust under reasonable conditions, as can be seen from the testing above. In order to keep the temperature even throughout the bathtub, we should take some strategies like stirring constantly while adding hot water to the tub. Most important of all, this is the necessary premise of the following question.Strategy 1 – Fully adapted to the hot water in the tubInfluence of body surface temperatureWe select a set of parameters to simulate two kinds of situation separately.The first situation is that do not involve the factor of human1122()()/H S dT H S T T cV dt D ρ∞⎡⎤=+-⎢⎥⎣⎦(10) The second situation is that involves the factor of human112213312()()()/()p H S dT H S T T H S T T c V V dt D μρ∞⎡⎤=++-+--⎢⎥⎣⎦(11) According to the actual situation, we give specific values as follows, and draw agraph of temperature of two functions.33p T =,040T =204060801001201401601803838.53939.540TimeT e m p e r a t u r eWith body Without bodyFigure 6a. Influence of body surface temperature50010001500200025003000350025303540TimeT e m p e r a t u r eWith body Without bodyCoincident pointFigure 6b. Influence of body surface temperatureThe figure 6 shows the difference between two kinds of situation in the early time (before the coincident point ), while the figure 7 implies that the influence of body surface temperature reduces as time goes by . Combing with the degree of comfort ofbath and the factor of health, we propose the second optimization strategy: Fully adapted to the hot water after getting into the bathtub.Strategy 2 –Adding water intermittentlyInfluence of adding methods of waterThere are two kinds of adding methods of water. One is the continuous; the other is the intermittent. We can use both different methods to add hot water.1122112()()()/()r H S dT H S T T c v T T c V V dt D μρρ∞⎡⎤=++-+--⎢⎥⎣⎦(12) Where r T is the temperature of the hot water.To meet .3O , we calculated the minimum water consumption by changing the flow rate of hot water. And we compared the minimum water consumptions of the continuous with the intermittent to determine which method is better.A . Adding water continuouslyAccording to the actual situation, we give specific values as follows and draw a picture of the change of temperature.040T =, 37d T =, 45r T =5001000150020002500300035003737.53838.53939.54040.5TimeT e m p e r a t u r eadd hot waterFigure 7. Adding water continuouslyIn most cases, people are used to have a bath in an hour. Thus we consumed that deadline of the bath: 3600final t =. Then we can find the best strategy in Figure 5 which is listed in Table 2.T able 3Strategy of adding water continuouslystart t final tt ∆ vr T varianceWater flow 4 min 1 hour56 min537.410m s -⨯45℃31.8410⨯0.2455 3mB . Adding water intermittentlyMaintain the values of 0T ,d T ,r T ,v , we change the form of adding water, and get another graph.5001000150020002500300035003737.53838.53939.540TimeT e m p e r a t u r et1=283(turn on)t3=2107(turn on)t2=1828(turn off)Figure 8. Adding water intermittentlyT able 4.Strategy of adding water intermittently()1t on ()2t off 3()t on vr T varianceWater flow 5 min 30 min35min537.410m s -⨯45℃33.610⨯0.2248 3mConclusionDifferent methods of adding water can influence the variance, water flow and the times of switching. Therefore, we give heights to evaluate comprehensively the methods of adding hot water on the basis of different hobbies of people. Then we build the following model:()()()2213600210213i i n t t i F T t T dtF v t dtF n -=⎧=-⎪⎪⎪=⎨⎪⎪=⎪⎩⎰∑⎰ (13) ()112233min F w F w F w F =++ (14)12123min ..510mini i t s t t t +>⎧⎨≤-≤⎩Evaluation on StrategiesFor example: Given a set of parameters, we choose different values of v and d T , and gain the results as follows.Method 1- AHPStep 1:Establish hierarchy modelFigure 9. Establish hierarchy modelStep 2: Structure judgment matrix153113511133A ⎡⎤⎢⎥⎢⎥=⎢⎥⎢⎥⎢⎥⎣⎦Step 3: Assign weight1w 2w3w 0.650.220.13Method 2-TopsisStep1 ：Create an evaluation matrix consisting of m alternatives and n criteria, with the intersection of each alternative and criteria given as ij x we therefore have a matrixStep2：The matrix ij m n x ⨯（）is then normalised to form the matrix ij m n R r ⨯=（）, using thenormalisation method21r ,1,2,,;1,2,ijij mij i x i n j m x====∑…………，Step3：Calculate the weighted normalised decision matrix()(),1,2,,ij j ij m n m nT t w r i m ⨯⨯===⋅⋅⋅where 1,1,2,,nj j jj w W Wj n ===⋅⋅⋅∑so that11njj w==∑, and j w is the original weight given to the indicator,1,2,,j v j n =⋅⋅⋅.Step 4： Determine the worst alternative ()w A and the best alternative ()b A()(){}{}()(){}{}max 1,2,,,min 1,2,,1,2,,n ,min 1,2,,,max 1,2,,1,2,,n ,w ij ij wjbijij bjA t i m j J t i m j J t j A t i m j J t i m j J tj -+-+==∈=∈====∈=∈==where, {}1,2,,J j n j +==⋅⋅⋅ associated with the criteria having a positive impact, and {}1,2,,J j n j -==⋅⋅⋅associated with the criteria having a negative impact. Step 5： Calculate the L2-distance between the target alternative i and the worst condition w A()21,1,2,,m niw ij wj j d tt i ==-=⋅⋅⋅∑and the distance between the alternative i and the best condition b A()21,1,2,,m nib ij bj j d t t i ==-=⋅⋅⋅∑where iw d and ib d are L2-norm distances from the target alternative i to the worst and best conditions, respectively .Step 6 ：Calculate the similarity to the worst condition Step 7 ： Rank the alternatives according to ()1,2,,iw s i m =⋅⋅⋅ Step 8 : Assign weight1w2w 3w 0.55 0.170.23ConclusionAHP gives height subjectively while TOPSIS gives height objectively. And the heights are decided by the hobbies of people. However, different people has different hobbies, we choose AHP to solve the following situations.Impact of parametersDifferent customers have their own hobbies. Some customers prefer enjoying in the bath, so the .2O is more important . While other customers prefer saving water, the .3O is more important. Therefore, we can solve the problem on basis of APH . 1. Customers who prefer enjoying: 20.83w =,30.17w =According to the actual situation, we give initial values as follows:13S =,11V =,2 1.4631S =,20.05V =,33p T =,110μ=Ensure other parameters unchanged, then change the values of these parameters including 1S ,1V ,2S ,2V ,d T ,1μ. So we can obtain the optimal strategies under different conditions in Table 4.T able 5.Optimal strategies under different conditions2.Customers who prefer saving: 20.17w =,30.83w =Just as the former, we give the initial values of these parameters including1S ,1V ,2S ,2V ,d T ,1μ, then change these values in turn with other parameters unchanged. So we can obtain the optimal strategies as well in these conditions.T able 6.Optimal strategies under different conditionsInfluence of bubbleUsing the bubble bath additives is equivalent to forming a barrier between the bath water and air, thereby slowing the falling velocity of water temperature. According to the reality, we give the values of some parameters and gain the results as follows:5001000150020002500300035003334353637383940TimeT e m p e r a t u r eWithour bubbleWith bubbleFigure 10. Influence of bubbleT able 7.Strategies (influence of bubble)Situation Dropping rate of temperature (the larger the number, the slower)Disparity to theinitial temperatureWater flow Times of switchingWithout bubble 802 1.4419 0.1477 4 With bubble 34499.85530.01122The Figure 10 and the Table 7 indicates that adding bubble can slow down the dropping rate of temperature effectively . It can decrease the disparity to the initial temperature and times of switching, as well as the water flow.Improved ModelIn reality , human ’s motivation in the bathtub is flexible, which means that the parameter 1μis a changeable measure. Therefore, the parameter can be regarded as a random variable, written as ()[]110,50t random μ=. Meanwhile, the surface of water will come into being ripples when people moves in the tub, which will influence the parameters like 1S and 2S . So, combining with reality , we give the range of values as follows:()[]()[]111222,1.1,1.1S t random S S S t random S S ⎧=⎪⎨=⎪⎩Combined with the above model, the improved model is given here:()[]()[]()[]11221121111222()()()/()10,50,1.1,1.1a H S dT H S T T c v T T c V V dt D t random S t random S S S t random S S μρρμ∞⎧⎡⎤=++-+--⎪⎢⎥⎣⎦⎨⎪===⎩(15)Given the values, we can get simulation diagram:050010001500200025003000350039.954040.0540.140.15TimeT e m p e r a t u r eFigure 11. Improved modelThe figure shows that the variance is small while the water flow is large, especially the variance do not equals to zero. This indicates that keeping the temperature of water is difficult though we regard .2O as the secondary objective.Sensitivity AnalysisSome parameters have a fixed value throughout our work. By varying their values, we can see their impacts.Impact of the shape of the tub0.70.80.91 1.1 1.2 1.3 1.433.23.43.63.84Superficial areaT h e t i m e sFigure 12a. Times of switching0.70.80.91 1.11.21.31.43890390039103920393039403950Superficial areaV a r i a n c eFigure 12b. V ariance of temperature0.70.80.91 1.1 1.2 1.3 1.40.190.1950.20.2050.21Superficial areaW a t e r f l o wFigure 12c. Water flowBy varying the value of some parameters, we can get the relationships between the shape of tub and the times of switching, variance of temperature, and water flow et. It is significant that the three indexes will change as the shape of the tub changes. Therefore the shape of the tub makes an obvious effect on the strategies. It is a sensitive parameter.Impact of the volume of the tub0.70.80.91 1.1 1.2 1.3 1.4 1.533.544.55VolumeT h e t i m e sFigure 13a. Times of switching。
2017全国数学建模优秀论文
2017全国数学建模优秀论文数学建模竞赛是实现数学教育创新的重要载体，下文是小编为大家整理的关于2017全国数学建模优秀论文的范文，欢迎大家阅读参考!2017全国数学建模优秀论文篇1关于数学建模方法的几点思考【摘要】首先阐述数学建模内涵;其次分析数学建模与数学教学的关系;最后总结出提高数学教学效果的几点思考。
【关键词】数学建模;数学教学;教学模式什么是数学建模，为什么要把数学建模的思想运用到数学课堂教学中去?经过反复阅读有关数学建模与数学教学的文章，仔细研修数十个高校的数学建模精品课程，数学建模优秀教学案例等，笔者对数学教学与数学建模进行初步探索，形成一定认识。
一、数学建模数学建模即运用数学知识与数学思想，通过对实际问题数学化，建立数学模型，并运用计算机计算出结果，对实际问题给出合理解决方案、建议等。
系统的谈数学建模需从以下三个方面谈起。
1.数学建模课程。
“数学建模”课程特色鲜明，以综合门类为基础，重实践，重应用。
旨在使学生打好数学基础，增强应用数学意识，提高实践能力，建立数学模型解决实际问题。
注重培养学生参与现代科研活动主动性与参与工程技术开发兴趣，注重培养学生创新思维及创新能力等相关素质。
2.数学建模竞赛。
1985年，美国工业与应用数学学会发起的一项大学生竞赛活动名为“数学建模竞赛”。
旨在提高学生学习数学主动性，提高学生运用计算机技术与数学知识和数学思想解决实际问题综合能力。
学生参与这项活动可以拓宽知识面，培养自己团队意识与创新精神。
同时这项活动推动了数学教师与数学教学专家对数学体系、教学方式与教学知识重新认识。
1992年，教育部高教司和中国工业与数学学会创办了“全国大学生数学建模竞赛”。
截止2012年10月已举办有21届。
大力推进了我国高校数学教学改革进程。
3.数学建模与创新教育。
创新教育是现代教育思想的灵魂。
数学建模竞赛是实现数学教育创新的重要载体。
如2012年A题，葡萄酒的评价中，要求学生对葡萄酒原料与酿造、储存于葡萄酒色泽、口味等有全面认识;而2012年D题，机器人行走避障问题，要求学生了解对机器人行走特点;2008年B题，乘公交看奥运，要求学生了解公交换乘系统。
2017数学建模获奖论文
2017数学建模获奖论文在我国倡导素质教育的今天，数学建模受到的关注与日俱增。
数学建模已成为国际、国内数学教育中稳定的内容和热点之一。
下文是店铺为大家搜集整理的关于2017数学建模获奖论文的内容，欢迎大家阅读参考!2017数学建模获奖论文篇1浅谈初中生数学建模能力的培养摘要：在中学数学教学中，加强数学建模能力的培养有助于数学应用意识的渗透，培养学生用数学解决实际问题的能力。
关键词：数学建模能力在中学数学教学中，加强数学建模能力的培养有助于数学应用意识的渗透，培养学生用数学解决实际问题的能力。
那么，如何培养初中生数学的建模能力呢?一、初中生数学建模能力培养的意义。
根据数学建模的特点，在初中数学教学中，渗透建模思想，开展建模活动，具有重要意义。
1、促进理论与实践相结合，培养学生应用数学的意识。
数学建模的过程，是实践―理论―实践的过程，是理论与实践的有机结合。
强化数学建模的教学，不仅能使学生更好地掌握数学基础知识，学会数学的思想、方法、语言，也是为了学生树立正确的数学观，增强应用数学的意识，全面认识数学及其与科学、技术、社会的关系，提高分析问题和解决问题的能力。
2、培养学生的能力。
数学建模的教学体现了多方面能力的培养：①翻译能力，能将实际问题用数学语言表达出来，建立数学模型，并能把数学问题的解用一般人所能理解的非数学语言表达出来;②运用数学能力;③交流合作能力;④创造能力。
3、发挥了学生的参与意识，体现了学生的主体性。
根据现代建构主义学习观，知识不能简单地由教师或其他人传授给学生，而只能由学生依据自身已有的知识和经验主动地加以建构。
所以数学建模的教学，符合现代教学理念，必将有助于教学质量的提高。
二、数学建模思想培养的基本原则在课堂设计方面，数学建模教学要遵循下列教学设计原则：1、所有的学习活动都应该与教学的任务或目标挂钩。
也就是说，学习活动应带有明确的目的性，学以致用。
2、把支持学习者发掘问题作为学习活动的刺激物，使学习成为自愿的事，而不是强加给他们学习目标和以通过测试为目的。
美赛e题优秀论文翻译
美赛e题优秀论文翻译E题中文翻译：问题E：需要可持续城市！背景：许多社区正在实施智能增长计划，以考虑长期，可持续的规划目标。
“聪明的成长是关于帮助每个城镇和城市变得更加经济繁荣，社会公平和环境可持续的生活地方。
”[2]智能增长的重点是建设拥抱可持续发展的城市 - 经济繁荣，社会公平，环境可持续。
这个任务比以往任何时候都重要，因为世界正在迅速城市化。
预计到2050年，世界人口的66％将是城市人口 - 这将导致25亿人口被纳入城市人口。
[3]因此，城市规划变得越来越重要和必要，以确保人们获得公平和可持续的家园，资源和就业机会。
智能增长是一种城市规划理论，起源于1990年代，作为遏制城市持续蔓延和减少城市中心周围农田损失的手段。
智能增长的十大原则是[4]1混合土地利用2利用紧凑的建筑设计3创造一系列住房机会和选择4创建可步行的社区5培养独特的，有吸引力的社区，具有强烈的地方感6保留开放空间，农田，自然美景和关键环境区域7加强和指导现有社区的发展8提供多种交通选择9使开发决策具有可预测性，公平性和成本效益10鼓励社区和利益相关者在发展决策中进行合作这些广泛的原则必须适应社区的独特需求，才能有效。
因此，任何成功的衡量都必须包括一个城市的人口统计，增长需求和地理条件，以及坚持三个E的目标。
任务：国际城市管理集团（ICM）需要您帮助实施智能增长理论到世界各地的城市设计。
在两个不同的大陆选择两个中型城市（人口在10万和50万之间的任何城市）。
1.定义衡量城市智能增长成功率的指标。
它应该考虑可持续性的三个E和/或智能增长的十个原则。
2.研究选定城市的当前增长计划。
衡量和讨论每个城市目前的增长计划是否符合智能增长原则。
根据您的指标，当前的计划是否成功？3.使用智能增长原则在未来几十年内为两个城市制定增长计划。
支持您为什么根据您的城市的地理位置，预期增长率和经济机会选择您的计划的组件和计划。
使用您的指标评估您的智能增长计划的成功。
数学建模美赛优秀论文
A Summary
Our solution consists of three mathematical models, offering a thorough perspective of the leaf. In the weight evaluation model, we consider the tree crown to be spherical, and leaves reaching photosynthesis saturation will let sunlight pass through. The Fibonacci number is helping leaves to minimize overlapping each other. Thus, we obtain the total leaf area and by multiplying it to the leaf area ratio we will get the leaf weight. Furthermore, a Logistic model is applied to depict the relationship between the leaf weight and the physical characteristic of a tree, making it easy to estimate the leaf weight by simply measure the circumstance of the trunk. In the shape correlation model, the shape of a leaf is represented by its surface area. Trees living in different habitats have different sizes of leaves. Mean annual temperature(T) and mean annual precipitation(P) are supposed to be significant in determining the leaf area. We have also noticed that the density of leaves and the density of branches greatly affect the size of leaf. To measure the density, we adopt the number of leaves per unit-length branch(N) and the length of intervals between two leaf branches(L) in the model. By applying multiple linear regression to data of six tree species in different habitats, we lately discovered that leaf area is positively correlated with T, P and L. In the leaf classification model, a matter-element model is applied to evaluate the leaf, offering a way of classifying leaf according to preset criteria. In this model, the parameters in the previous model are applied to classify the leaf into three categories: Large, Medium, and Small. Data of a tree species is tested for its credit, proving the model to be an effective model of classification especially suitable for computer standardized evaluation. In sum, our models unveil the facts concerning how leaves increase as the tree grows, why different kinds of trees have different shapes of leaves, and how to classify leaves. The imprecision of measurement and the limitedness of data are the main impediment of our modeling, and some correlation might be more complicated than our hypotheses.
美国大学生数学建模一等奖31552
Best all time college coachAbstractIn order to select the “best all time college coach” in the last century fairly, We take selecting the best male basketball coach as an example, and establish the TOPSIS sort - Comprehensive Evaluation improved model based on entropy and Analytical Hierarchy Process.The model mainly analyzed such indicators as winning rate, coaching time, the time of winning the championship, the number of races and the ability to perceive .Firstly ，Analytical Hierarchy Process and Entropy are integratively utilized to determine the index weights of the selecting indicators Secondly，Standardized matrix and parameter matrix are combined to construct the weighted standardized decision matrix. Finally, we can get the college men's basketball composite score, namely the order of male basketball coaches, which is shown in Table 7.Adolph Rupp and Mark Few are the last century and this century's "best all time college coach" respectively. It is realistic. The rank of college coaches can be clearly determined through this methods.Next, ANOVA shows that the scores of last century’s coaches and this century’s coaches have significant difference, which demonstrates that time line horizon exerts influence upon the evaluation and gender factor has no significant influence on coaches’ score. The assessment model, therefore, can be applied to both male and female coaches. Nevertheless, based on this, we have drawn coaches’ coaching ability distributing diagram under ideal situation and non-ideal situation according to the data we have found, through which we get that if time line horizon is chosen reasonably, it will not affect the selecting results. In this problem, the time line horizon of the year 2000 will not influence the selecting results.Furthermore, we put the data of the three types of sports, which have been found by us, into the above Model, and get the top 5 coaches of the three sports, which are illustrated in Table10, Table 11, Table12 and Table13 respectively. These results are compared with the results on the Internet[7], so as to examine the reasonableness of our results. We choose the sports randomly which undoubtedly shows that our model can be applied in general across both genders and all possible sports. At the same time, it also shows the practicality and effectiveness of our model.Finally, we have prepared a 1-2 page article for Sports Illustrated that explains our results and includes a non-technical explanation of our mathematical model that sports fans will understand.Key words: TOPSIS Improved Model; Entropy; Analytical Hierarchy Process;Comprehensive Evaluation Model; ANOV AContents Abstract (1)Contents (2)I. Introduction (3)П. The Basic Assumption (4)Ⅲ. Nomenclature (5)Ⅳ. Model (5)4.1 Data Processing (5)4.2 Model analysis (6)4.3 Model building (6)4.3.1 Dominant index weights calculation (7)4.3.2 Hidden index weights calculation (9)4.3.3 Positive and negative ideal solution building (12)4.3.4 Distance calculation (12)4.3.5 Comprehensive evaluation value (13)4.4 Model solution (13)4.4.1 Dominant index weights calculation (13)4.4.2 Hidden factors weights calculation (14)4.4.3 Consolidated score (16)4.5 Judgment of significant differences between the last century’s andthis century’s coaching score. (16)4.5.1 Preliminary investigation of the last century and the coach ofthe century standards (16)4.5.2 Further exploration on the influence of different time linehorizons on the assessment results (18)4.6 Test of model’s applicability to both gender (19)4.7 The selection for the top five college coaches of three sports (20)V. Analysis of our Model (22)5.1 Applications of our models (22)5.2 Strengths (22)5.3 Weaknesses (22)5.4 Future Improvements (22)Ⅵ. Conclusions (23)Ⅶ.A letter to the sports enthusiasts (23)Ⅷ. References (24)I. IntroductionTh e paper is to help "Sports Illustrated" to find the “best all time college coach” male or female.We tackle five main problems:●Build a mathematical model to choose the best college coach or coaches (past orpresent) from among either male or female coaches in such sports as college hockey or field hockey, football, baseball or softball, basketball, or soccer, and clearly articulate our metrics for assessment.●Does it make a difference which time line horizon that you use in your analysis,i.e., does coaching in 1913 differ from coaching in 2013?●Present our model’s top 5 coaches in each of 3 different sports.●Discuss how our model can be applied in general across both genders and allpossible sports.●In addition to the MCM format and requirements, prepare a 1-2 page article forSports Illustrated that explains our results and includes a non-technical explanation of our mathematical model that sports fans will understand.To tackle the first problem, we searched the indicators of Top 600 men’s basketball coaches of the American colleges. Take selecting the best male basketball coach as an example: for the explicit factors that affect assessment standards, we calculate each indicator’s weight by using Entropy method; for those implicit factors, we calculate the weight through experts’evaluation. The determination of each indicator’s score should be given by experts evaluation of each indicator. These indicators are then numericalized, and the importance of each indicator is determined through weight coefficients. Then through the multiplication of the scores of coaches’different ability indicator with corresponding weight coefficients, we get the corresponding scores, and the highest score indicates the best choice.For the second question, we first use ANOV A to determine whether significant difference exists between the scores of coaches in the last century and this century and the gender factor Significance difference shows that the time line horizon, the gender factor has influence on the assessment, whereas insignificant difference shows no influence. And based on this, we have drawn coaches’coaching ability distributing diagram under ideal situation and non-ideal situation according to the data we have found, which help us further research the influence of time line horizon on the assessment.For question 3 and 4, we put the data of the three types of sports, which have been found by us, into the Model , and get the top 5 coaches of the three sports, which are illustrated in Table10, Table 11, Table 12 and Table 13 respectively. These results are compared with the results on the Internet, so as to examine the reasonableness of our results. We choose the sports randomly, which undoubtedly shows that our model can be applied in general across both genders and all possible sports. At the same time, it also shows the practicality and effectiveness of our model.Figure1. The source of the best college coachesП. The Basic Assumption●Experts recessive factors evaluation criteria evaluation is fair and equitable.●Coaches’coaching level will increase with increasing age, but it will decline due to mental declination and the lack of the physical strength.●Assessment experts are fully known on college coaches.●The evaluation criteria only consider the factors enumerated in this paper, without considering other factors.●The evaluation criteria apply equally to men and women coaches.●We used the general data from a reliable website,Website (see Appendix).Ⅲ. NomenclatureXIndex data normalization matrix j w j Index weightsij θ Transformed normalized matrixθ+ "Positive ideal solution"θ- "Negative ideal solution"i φi comprehensive evaluation index values of being evaluated j ej Index entropy j ψ j Index Information utilityFF statisticⅣ. Model4.1 Data ProcessingIn order to better assess the extent of outstanding coaches, we selected a number of indicators to determine the coach for the "best all time college sports coach". We found information on the various indicators of data on the site and get some reliable indicators data of these college coaches. Due to the dimensions of each index inconsistencies exist, so we transformed the data to eliminate the effects of dimensionless. And through poor conversion get a normalized matrix ij m n X x ⨯⎡⎤=⎣⎦ ,1111n X m mn x x x x =, 1,2,;1,2,i m j n == ()41-ij r x =1,2,;1,2,i m j n == ()42-ij x is a dimensionless quantity and ij x []0,1∈, 1,2,;1,2,i m j n ==.4.2 Model analysisIn order to address the problems mentioned above and provide a valid, feasible assessment strategy for Sports Illustrated, we decide to select softball, basketball and football by reviewing the relevant literature. Coaching time, Competition winning rate, Cultural qualities, Athletic ability, Social skills, Ability to withstand, Innovation capacity, Ability to perceive, and so on, which are evaluation indexes. These evaluation indexes are divided into dominant factors and recessive factors. Specific factors of affecting the evaluation criteria are shown in Figure X. These indicators will be quantified and determine the degree of importance of each index by weight coefficient. When selecting coaches, the scores of the indicators multiply corresponding weight coefficient, getting corresponding scores, and the person with the highest score is the best candidate.Multi-level analysis method to determine the weight is more subjective. It is suitable to determine the weights for hidden factors, which are not used widely in both sexes and all possible requirements for sport. We need to build a more reasonable model to determine the weight for the dominant factor and recessive factors. Finally, we determine the “best all time college coach”.4.3 Model buildingWe look for the “best all time college coach” by establishing a mathematical model in Technique for Order Preference by Similarity to Ideal Solution. Take choosing the best college coach or coaches from among male coaches in such sports as basketball as an example. For the dominant factor, we calculate the weight of each indicator in Entropy Method; For the hidden factors, we calculate the weight of each indicator in expert assessment method. According to the situation of the coaches , the scores of all levels should be determined by experts, and these indicators should be quantified. Weighting coefficients represent the importance of each indicator. The scores of the indicators multiply corresponding weight coefficient to obtain the total score, and the person of highest score is the best candidate. This method is more objective, comprehensive, accurate and wide-applicable than the previous evaluation model.Flow chart of looking for the “best all time college coach” is shown in Figure 2.Figure 2.Flow chart of ModelTOPSIS Model (Technique for Order Preference by Similarity to an Ideal Solution ) was firstly introduced by C.L.Hwang and K.Yoon in 1981.TOPSIS Model is based on the proximity of a limited number of evaluation objects and idealistic goals and evaluate the relative merits of existing objects.Meanwhile, TOPSIS Model is an approximation of the ideal solution in order model, the model requires only a monotonically increasing (or decreasing) of each Utility function.Furthermore, TOPSIS multi-objective decision analysis model is a commonly used and effective model, also known as the merits of the solution from the law. The basic principle is evaluated by detecting the distance the optimal solution and the solution of the worst sort, if the evaluation of the optimal solution while the object closest to farthest from the worst solution, the result is optimal; otherwise, is not optimal，ｗhere the value of each index has reached the optimal solution for the optimal value of each index. Each index value solution has reached the worst the worst value of each index."Positive ideal solution" and "negative ideal solution" are two basic concepts TOPSIS Model. "Positive ideal solution" is an envisaged optimal solution (program), it's the individual attribute values to achieve the best value of each option; rather negative ideal solution is a solution envisaged for the worst (program ), each of which have reached the attribute value of each option in the worst value. Program to sort the various alternative rules are the ideal solution and the negative ideal solution for comparison, if one has a solution closest to the ideal solution, while away from the negative ideal solution, the solution is the best alternative solution.4.3.1 Dominant index weights calculationFor the dominant factor, we calculate the entropy method using the weight of each indicator.According to the data we found, we list the dominant influence coaches criteria indicators (see Figure 3). These dominant indicators are intuitive and easy to quantify,due to the weight of these data to calculate the specific rights-based approach, with strong objectivity. Degree of dispersion of data can be seen as the degree of disorder (entropy), the greater the entropy index data, the smaller the proportion of the index.Figure 3. Th e diagram of the entropy and weightsInformation entropy method is a method completely dependent on the data, but it is not affected by subjective factors.Figure 4. The structure of influence the selection criteria for the dominant factorsFormula to calculate the information entropy index for item j :11ln ln j ij mij i e x x m ==-∑，ij x []0,1∈ ()43- Information utility depends on the difference between the value of an index of the index information entropy between A and 1. It directly affects the size of the weight : the greater the utility value of the information , the greater the importance of the evaluation, and the greater the weight .1j je ψ=- ()43- Estimating the weight of each index using entropy method, its essence is to use the value of the coefficient to calculate the index information, the higher the value ofthe coefficient, the greater the importance of the evaluation (or the greater the weight, the bigger contribution to the evaluation results).Right item j index weight is:1j j jmi w ψψ==∑ ()43- 4.3.2 Hidden index weights calculationFor recessive factors, we take expert assessment method to calculate weights. The determination of index score at all levels should be carried out by an expert score for each indicator according to the situation of the coaches.According to the data we found, we cited the impact coach implicit criteria indicators (see Figure 4). These indicators are visually hidden but not easy to quantify. Because of these hidden right index weight calculation method based on highly subjective, we used AHP to accurately calculate the weights of these hidden indicators.AHP is a decision problem in terms of total goals layers of sub-goals, evaluation criteria and specific equipment investment program in order to break down the different hierarchies, then use judgment matrix eigenvector method to obtain the elements of each level of priority on a certain level of heavy elements, and finally re-weighted and hierarchical approach to merge the various alternative solutions to the overall goal of the final weights. "Priorities" is a relative measure, which indicates the alternative criteria for the evaluation of a program or sub-features of the target, which means excellent measure of the relative degree of each sub-target and the target level for the purposes of the relative importance of measure. Specific usage is to judge the matrix, find the maximum eigenvalue, then the corresponding feature vector normalization, finally we can get a level indicator on one level for a related indicators relative importance weights.Features of AHP are based on the nature of complex decision problems, influencing factors and internal factors affecting the relationship between in-depth analysis, and use less quantitative information to make decisions mathematical thinking process, so as to multi-target, multi-standard or non-structural properties of the complex issues simple decision making methods. Especially suitable the occasion for decision-making results difficult to directly and accurately measure.Figure 5. The structure of influence the selection criteria for the hidden factors We can know from the Figure 5 , the hierarchy is divided into one-level indicator, two-level indicators, so it belongs to the multi-level hierarchical structure model.Comparison matrix constructionAccording to the analysis of psychologists, the importance of being divided into nine grades, and secondary indicators for the level indicators can be pairwise comparison of their importance to quantify the value using the following scale.Table 1. Evaluation scaleScale Definition1 i is for j equally important3 i is for j slightly important5 i is more important for j7 i is very important for j9 i is absolutely vital for j2,4,6,8 Two intermediate value corresponding to the scaleReciprocal i compared with j,1ijijcc=or 1ijc=are obtained for the judge valueAccording to the above scale, relative matrix is as follows:By comparison, the comparison matrix of level indicators and secondary indicators are as follows:1111ni n nn c c C c c =()44-Due to the above judgment matrix symmetry, so when filling out, usually the first to fill 1ii c =section, and then judge and triangular or lower triangular() 1/2n n -elements on the form. In exceptional circumstances, the judgment matrix is transitive, that satisfies the equation ：ik kj ij c c c *= .When the formula to determine all the elements of the matrix are established, the consistency of judgment matrix is a matrix.Level single-sorting (Weight vector calculation) and TestFor the judgment of experts to fill in the matrix ，we took advantage of some mathematical methods for sorting. Level single-sorting refers to the various factors of each judgment matrix for weight relative weights of the criteria, so essentially calculating the weight vector. There are many ways to calculate the weight vector, such as the eigen value method, and the method, the root method, power method. Here is a brief overview and method.Principle "and the law", for consistency of judgment matrix, each column after normalization, we can get the corresponding weights. For non-consistency of judgment matrix, each column after normalization, which can be approximated by the corresponding weights, n column vectors and these strike the arithmetic average as the final weight of the weight. Specific formula is:111n iji nj klk c W n c ===∑∑ ()45- It should be noted that, in the layers of the sort , you need to test the consistency of judgment matrix . In exceptional circumstances , determining the matrix has passed and consistency. Under normal circumstances, the judge is not required to meet the strict nature of the matrix . But looking at the human understanding of the law , a right to judge the importance of the matrix there is some sort of logical law . For example, if A is more important than B, and B surpasses C importantly , from a logical perspective , A should be significantly more important than C, if the two a comparison of two important results than C , then the consistency of judgment matrix in violation of norms, logically unreasonable. If pairwise comparisons, C is more important than the result of A, the consistency of judgement matrix in violation of the guidelines, it was logically irrational.Therefore, in practice it is required to meet the general consistency of judgment matrix, which requires consistency checking. Only by testing can it illustrate that the logical judgment matrix is reasonable and to continue to analyze the results. Steps of consistency test are as follows.First , calculate the consistency index ..C I (consistency index).max..1nC I n λ-=- ()46- Second , look-up table to determine the corresponding average random consistency index ..R I （random index ）According to the different order of judgment matrix, we check the table below, and get the average random consistency index ..R I For example, for a 5-order judgment matrix, we can get ..R I = 1.12 easily.0 0 0.52 0.89 1.12 1.26 1.36 1.411.41.491.521.541.561.581.59Third , calculate the proportion of consistency ..C R (consistency ratio) and determine.......C I C R R I = ()47- When ..0.1C R <, the consistency of judgment matrix is considered acceptable and when .. 0.1C R >, it is considered the consistency of judgment matrix does not meet the requirements, we need to re-amend the judgment matrix. 4.3.3 Positive and negative ideal solution buildingWe define ,1,2,;1,2,;ij ij ij w x i m j n θ=•==Determine the positive idealsolution θ+and negative ideal solution θ-；Assuming positive ideal solution θ+Negative ideal solution ：{}min ,1,2,;1,2,;j ij ii m j n θθ-=== Positive ideal solution ：{}min ,1,2,;1,2,;j ij ii m j n θθ+===4.3.4 Distance calculationT he Euclidean distance between being evaluated and Positive ideal solution1,2,i d i m +==⋅⋅⋅ ()48-The Euclidean distance between being evaluated and Negative ideal solution_1,2,i d i m ==⋅⋅⋅ ()49-4.3.5 Comprehensive evaluation valueThe value of comprehensive evaluation index evaluated is,1,2,i i i id i m d d φ-+-==⋅⋅⋅+ ()410- 4.4 Model solution4.4.1 Dominant index weights calculationWe find four dominant indicators for the last century of the impact evaluation criteria through the network, namely, "The time of winning the championship", "The number of races", "Coaching time", "Completion wining rate". Specific data are in Table 3.Table 3. Four indicators for men's basketball coachesHank Iba 29 1085 40 0.693 Ray Meyer 20 1078 42 0.672 Don Haskins 29 1072 38 0.671 Adolph Rupp 71 1066 41 0.822 E.A. Diddle 17 1061 42 0.715 Ralph Miller 17 1044 38 0.646 Slats Gill 13 992 36 0.604 Norm Stewart 30 967 32 0.656 Tony Hinkle 4 952 41 0.586 Norm Sloan 14 917 33 0.609 Jack Friel 3 872 30 0.568 Guy Lewis 26 871 30 0.68 Ned Wulk 17 837 31 0.59 JohnThompson 37835 27 0.714 John Wooden 54 826 29 0.804 Bill E. Foster 7 820 30 0.515 Johnny Orr 13812 29 0.574 … …………We will enter the above data by calculated entropy method to get the dominant index weights as follows:Table 4. Men's basketball coach dominant index weights tableDominant indexThe time ofwinning thechampionshipThe number ofraceCoachingtimeCompletionwinning rateweight0.7481 0.1195 0.1145 0.0178From the Table 4 we can observe "The time of winning the championship" share of the weight is larger than the "Completion wining rate". But the proportion of "The number of race" and "Coaching time", is less. This shows that the dominant indicators, "The time of winning the championship" for the selection of the coach plays a very important role.Figure 6. Men's basketball coach dominant index weights pie From Figure6, we can observe that"The time of winning the championship" significant weightings are larger in the share of other indicators. On the surface this is actually somewhat contradictory, but in fact, as "The time of winning the championship"indicators of the degree of dispersion is larger, therefore,its impact is huge coach rankings, while the smaller degree of dispersion of other indicators,so they rank impact on the coach is smaller.4.4.2 Hidden factors weights calculationUsing the comparison scale of the model we c an go to the comparison matrix level indicators and secondary indicators. Since the pairwise comparison is subjective, the Hidden factors weight is subjective. Using the way of expert reviewing, finding information or questionnaires to get the comparison matrix. Then calculate the weights. Then we examined whether it could through consistency test.We did a series of comparison matrix and then through examination we selected the following comparison matrix.Table 5. The best comparison matrix of the University men's basketball coach indicatorsHidden factors CulturalqualitiesAthleticabilitySocialskillsAbility towithstandInnovationcapacityThe abilityto perceiveCultural qualities 1 1/3 1/3 1/3 1/6 1/7 Athletic ability 3 1 1/3 1/3 1/5 1/5Social skills 3 3 1 1/3 1/5 1/4 Ability to withstand 5 3 3 1 1/3 1/5 Innovation capacity 6 5 5 3 1 1/4 The ability toperceive7 5 4 5 4 1Known by its consistency index, ..0.98700.10C R=<，.. 0.1360C I=, so it can go through consistency test. The maximum value weight , 6.6799λ=,which we calculated are shown in Table 5.The consistency is index..0.98700.10C R=<，.. 0.1360C I=. Through consistency test, the maximum characteristic value is 6.6799λ=. Weights form table below.Table 6. Best college men's basketball coach recessive factor index weights tableHidden factors CulturalqualitiesAthleticabilitySocialskillsAbility towithstandInnovationcapacityThe abilityto perceiveWeights 0.0345 0.0554 0.0836 0.1340 0.2491 0.4435Figure 7. Best college men's basketball coach recessive factor index weights pieWe obtain the weight values though consistency test and Analytic Hierarchy Process, Athletic ability of coaches is great importance of hidden index. Second, the cultural qualities, the innovation capacity is not important. The results are subjective more or less. We can not be generalized, with the development of society, the proportion of innovative indicators may increase.4.4.3 Consolidated scoreweights above put in TOPSIS model can get a score for each coach. Because hidden indicators expert review in our paper is difficult to achieve. Thus weakened expert evaluation index, highlighting calculations dominant indicators.Thus, we get the following scoring table.Table 7. Last century University men's basketball coach total scoreDean Smith 70 1133 36 0.776 0.0181 John Wooden 54 826 29 0.804 0.0139 John Thompson 37 835 27 0.714 0.0097 Norm Stewart 30 967 32 0.656 0.0081 Hank Iba 29 1085 40 0.693 0.0080 Don Haskins 29 1072 38 0.671 0.0080 Guy Lewis 26 871 30 0.68 0.0071 Everett Case 27 511 19 0.738 0.0071 Lou Carnesecca 26 726 24 0.725 0.0070 Gene Bartow 25 744 24 0.66 0.0067 Neil McCarthy 23 681 23 0.665 0.0062 Pete Carril 22 798 30 0.658 0.0061 Frank McGuire 22 785 30 0.699 0.0061 Joe B. Hall 23 463 16 0.721 0.0060 Jack Gardner 22 721 28 0.674 0.0060 Ray Meyer 20 1078 42 0.672 0.0058 Terry Holland 21 634 21 0.659 0.0057 ………………As can be seen from Table 7Adolph Rupp's highest overall score, it is reasonable to judge him in the last century's "best all time college coach". Due to the weakening of the influence of implicit indicators, so here was "best all time college coach" on the hidden indicators may have less. Using the same method to evaluate the coach of the century can be the century of the "best all time college coach" is Mark Few.4.5 Judgment of significant differences between the last century’s and this century’s coaching score.4.5.1 Preliminary investigation of the last century and the coach of the century standards.Taking into account the tremendous changes in the last century and this century,。
美国大学生数学建模大赛优秀论文一等奖摘要
SummaryChina is the biggest developing country. Whether water is sufficient or not will have a direct impact on the economic development of our country. China's water resources are unevenly distributed. Water resource will critically restrict the sustainable development of China if it can not be properly solved.First, we consider a greater number of Chinese cities so that China is divided into 6 areas. The first model is to predict through division and classification. We predict the total amount of available water resources and actual water usage for each area. And we conclude that risk of water shortage will exist in North China, Northwest China, East China, Northeast China, whereas Southwest China, South China region will be abundant in water resources in 2025.Secondly, we take four measures to solve water scarcity: cross-regional water transfer, desalination, storage, and recycling. The second model mainly uses the multi-objective planning strategy. For inter-regional water strategy, we have made reference to the the strategy of South-to-North Water Transfer[5]and other related strategies, and estimate that the lowest cost of laying the pipeline is about 33.14 billion yuan. The program can transport about 69.723 billion cubic meters water to the North China from the Southwest China region per year. South China to East China water transfer is about 31 billion cubic meters. In addition, we can also build desalination mechanism program in East China and Northeast China, and the program cost about 700 million and can provide 10 billion cubic meters a year.Finally, we enumerate the east China as an example to show model to improve. Other area also can use the same method for water resources management, and deployment. So all regions in the whole China can realize the water resources allocation.In a word, the strong theoretical basis and suitable assumption make our model estimable for further study of China's water resources. Combining this model with more information from the China Statistical Yearbook will maximize the accuracy of our model.。
2017年建模美赛E题带翻译
Problem E: Sustainable Cities Needed!Background:Many communities are implementing smart growth initiatives in an effort to consider long range, sustainable planning goals. “Smart growth is about helping every town and city become a more economically prosperous, socially equitable, and environmentally sustainable place to live.”Smart growth focuses on building cities that embrace theE’s of sustainability—Economically prosperous, socially Equitable, and Environmentally Sustainable. This task is more important than ever because the world is rapidly urbanizing. It is projected that by 2050, 66 percent of the world’s population will be urban—this will result in a projected 2.5 billion people being added to the urban population.Consequently, urban planning has become increasingly important andnecessary to ensure that people have access to equitable and sustainable homes, resources and jobs.Smart growth is an urban planning theory that originated in 1990’s as a means to curb continued urban sprawl and reduce the loss of farmland surrounding urban centers. The ten principles for smart growth are1 Mix land uses2 Take advantage of compact building design3 Create a range of housing opportunities and choices4 Create walkable neighborhoods5 Foster distinctive, attractive communities with a strong sense of place6 Preserve open space, farmland, natural beauty, and critical environmental areas7 Strengthen and direct development towards existing communities8 Provide a variety of transportation choices9 Make development decisions predictable, fair, and cost effective10 Encourage community and stakeholder collaboration in development decisions These broad principles must be tailored to a community’s unique needs to be effective. Thus, any measure of success must incorporate the demographics, growth needs, and geographical conditions of a city as well as the goal to adhere to the three E’s.2017 ICMProblem E: Sustainable Cities Needed!Tasks:The International City Management Group (ICM) needs your help implementing smart growth theories into city design around the world. Select two mid-sized cities (any city with a population of between 100,000 and 500,000 persons), on two different continents.1. Define a metric to measure the success of smart growth of a city. It should consider the three E’s of sustainability and/or the 10 principles of smart growth.2. Research the current growth plan of the selected cities. Measure and discusshow the current growth plan of each city meets the smart growth principles. How successful are the current plans according to your metric?3. Using smart growth principles develop a growth plan for both cities over the nextfew decades. Support why you chose the components and initiatives of yourplans based on the geography, expected growth rates, and economicopportunities of your cities. Use your metric to evaluate the success of yoursmart growth plans.4. Also using your metric, rank the individual initiatives within your redesigned smart growth plan as the most potential to the least potential. Compare and contrastthe initiatives and their ranking between the two cities.5. Suppose the population of each city will increase by an additional 50% by 2050,explain in what way(s) your plan supports this level of growth?Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages. Note: The appendix and references do not count toward the 20 page limit.References:[1] Smart Growth: Improving lives by improving communities.https:///[2] EPA, “This is Smart Growth.” 2016https:///smartgrowth/smart-growth-publication[3] World Urbanization Prospects. United Nations. 2014.https:///unpd/wup/Publications/Files/WUP2014-Highlights.pdf[4] EPA, “Smart Growth: A Guide to Developing and Implementing Greenhouse Gas Reductions Programs.” 2011./Documents/SCI/Report_Guide/Guide_EPA_SmartGrowthGHGReduction_2011.pdf[5] Duany, Andres, Jeff Speck and Mike Lydon. The Smart Growth Manual.McGraw-Hill. 2010.问题E：需要可持续城市！背景：许多社区正在实施智能增长计划，以努力考虑远程，可持续规划目标。
2017数学建模一等奖论文
2017数学建模一等奖论文数学建模的模型是对于现实世界的一个特定对象，一个特定目的，根据特有的内在规律，做出一些必要的假设，运用适当的数学工具，得到的一个数学结构。
下文是店铺为大家搜集整理的关于2017数学建模一等奖论文的内容，欢迎大家阅读参考!2017数学建模一等奖论文篇1谈中学生数学建模思想的培养【摘要】现如今的中学数学在新课程标准下要讲背景，重应用。
本文主要从数学建模的本质和如今中学的数学建模教学的现实情况出发，主要讲述了中学数学建模一些基本的方法和题型。
在教育部颁布的《全日制普通高级中学数学教学大纲(试验修订版)》中对学生提出新的教学要求，包括学会提出问题和明确探究方向;体验数学活动的过程; 培养创新精神和应用能力共3点内容。
所以在高中阶段可以利用假期时时间指导学生展开研究性学习的活动，要使学生学会自己提出实际问题和它的探究方向，讲实际问题抽象为数学问题，运用已有的数学知识尝试初步解决这些问题，这本身就是个建模的过程。
【关键词】数学建模;数学建模思想;建模能力本世纪初世界上很多国家的课程改革都把培养学生的数学建模思想作为教育的重要目标。
如德国的课程改革中，数学建模的能力位列学生的六大能力之一。
相比之下，我国的学生在数学建模这方面的能力要更弱一些，比如2010年广东省高考题一道营养配餐的问题，就是用高中数学知识中的线性规划的方法求解，题目中涉及的实际条件，问题限制很多很杂，这就需要学生有将实际问题转化成数学问题的能力，也就是建模的能力。
近几年高考的出题方向也在向这方面倾斜，应用题是一个常见的题型。
那么如何将如此重要的一种能力培养给学生掌握呢?本文就这个问题进行进一步的探讨：1.数学建模的基本内涵当需要从定量的角度分析和研究一个实际问题时，人们就要在深入调查研究、了解对象信息、作出简化假设、分析内在规律等工作的基础上，用数学的符号和语言，把它表述为数学式子，也就是数学模型，然后用通过计算得到的模型结果来解释实际问题，并接受实际的检验。
美国大学生数学建模竞赛二等奖论文
美国⼤学⽣数学建模竞赛⼆等奖论⽂The P roblem of R epeater C oordination SummaryThis paper mainly focuses on exploring an optimization scheme to serve all the users in a certain area with the least repeaters.The model is optimized better through changing the power of a repeater and distributing PL tones,frequency pairs /doc/d7df31738e9951e79b8927b4.html ing symmetry principle of Graph Theory and maximum coverage principle,we get the most reasonable scheme.This scheme can help us solve the problem that where we should put the repeaters in general cases.It can be suitable for the problem of irrigation,the location of lights in a square and so on.We construct two mathematical models(a basic model and an improve model)to get the scheme based on the relationship between variables.In the basic model,we set a function model to solve the problem under a condition that assumed.There are two variables:‘p’(standing for the power of the signals that a repeater transmits)and‘µ’(standing for the density of users of the area)in the function model.Assume‘p’fixed in the basic one.And in this situation,we change the function model to a geometric one to solve this problem.Based on the basic model,considering the two variables in the improve model is more reasonable to most situations.Then the conclusion can be drawn through calculation and MATLAB programming.We analysis and discuss what we can do if we build repeaters in mountainous areas further.Finally,we discuss strengths and weaknesses of our models and make necessary recommendations.Key words:repeater maximum coverage density PL tones MATLABContents1.Introduction (3)2.The Description of the Problem (3)2.1What problems we are confronting (3)2.2What we do to solve these problems (3)3.Models (4)3.1Basic model (4)3.1.1Terms,Definitions,and Symbols (4)3.1.2Assumptions (4)3.1.3The Foundation of Model (4)3.1.4Solution and Result (5)3.1.5Analysis of the Result (8)3.1.6Strength and Weakness (8)3.1.7Some Improvement (9)3.2Improve Model (9)3.2.1Extra Symbols (10)Assumptions (10)3.2.2AdditionalAdditionalAssumptions3.2.3The Foundation of Model (10)3.2.4Solution and Result (10)3.2.5Analysis of the Result (13)3.2.6Strength and Weakness (14)4.Conclusions (14)4.1Conclusions of the problem (14)4.2Methods used in our models (14)4.3Application of our models (14)5.Future Work (14)6.References (17)7.Appendix (17)Ⅰ.IntroductionIn order to indicate the origin of the repeater coordination problem,the following background is worth mentioning.With the development of technology and society,communications technology has become much more important,more and more people are involved in this.In order to ensure the quality of the signals of communication,we need to build repeaters which pick up weak signals,amplify them,and retransmit them on a different frequency.But the price of a repeater is very high.And the unnecessary repeaters will cause not only the waste of money and resources,but also the difficulty of maintenance.So there comes a problem that how to reduce the number of unnecessary repeaters in a region.We try to explore an optimized model in this paper.Ⅱ.The Description of the Problem2.1What problems we are confrontingThe signals transmit in the way of line-of-sight as a result of reducing the loss of the energy. As a result of the obstacles they meet and the natural attenuation itself,the signals will become unavailable.So a repeater which just picks up weak signals,amplifies them,and retransmits them on a different frequency is needed.However,repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies.In addition to geographical separation,the“continuous tone-coded squelch system”(CTCSS),sometimes nicknamed“private line”(PL),technology can be used to mitigate interference.This system associates to each repeater a separate PL tone that is transmitted by all users who wish to communicate through that repeater. The PL tone is like a kind of password.Then determine a user according to the so called password and the specific frequency,in other words a user corresponds a PL tone(password)and a specific frequency.Defects in line-of-sight propagation caused by mountainous areas can also influence the radius.2.2What we do to solve these problemsConsidering the problem we are confronting,the spectrum available is145to148MHz,the transmitter frequency in a repeater is either600kHz above or600kHz below the receiver frequency.That is only5users can communicate with others without interferences when there’s noPL.The situation will be much better once we have PL.However the number of users that a repeater can serve is limited.In addition,in a flat area ,the obstacles such as mountains ,buildings don’t need to be taken into account.Taking the natural attenuation itself is reasonable.Now the most important is the radius that the signals transmit.Reducing the radius is a good way once there are more users.With MATLAB and the method of the coverage in Graph Theory,we solve this problem as follows in this paper.Ⅲ.Models3.1Basic model3.1.1Terms,Definitions,and Symbols3.1.2Assumptions●A user corresponds a PLz tone (password)and a specific frequency.●The users in the area are fixed and they are uniform distribution.●The area that a repeater covers is a regular hexagon.The repeater is in the center of the regular hexagon.●In a flat area ,the obstacles such as mountains ,buildings don’t need to be taken into account.We just take the natural attenuation itself into account.●The power of a repeater is fixed.3.1.3The Foundation of ModelAs the number of PLz tones (password)and frequencies is fixed,and a user corresponds a PLz tone (password)and a specific frequency,we can draw the conclusion that a repeater can serve the limited number of users.Thus it is clear that the number of repeaters we need relates to the density symboldescriptionLfsdfminrpµloss of transmission the distance of transmission operating frequency the number of repeaters that we need the power of the signals that a repeater transmits the density of users of the areaof users of the area.The radius of the area that a repeater covers is also related to the ratio of d and the radius of the circular area.And d is related to the power of a repeater.So we get the model of function()min ,r f p µ=If we ignore the density of users,we can get a Geometric model as follows:In a plane which is extended by regular hexagons whose side length are determined,we move a circle until it covers the least regular hexagons.3.1.4Solution and ResultCalculating the relationship between the radius of the circle and the side length of the regular hexagon.[]()()32.4420lg ()20lg Lfs dB d km f MHz =++In the above formula the unit of ’’is .Lfs dB The unit of ’’is .d Km The unit of ‘‘is .f MHz We can conclude that the loss of transmission of radio is decided by operating frequency and the distance of transmission.When or is as times as its former data,will increase f d 2[]Lfs .6dB Then we will solve the problem by using the formula mentioned above.We have already known the operating frequency is to .According to the 145MHz 148MHz actual situation and some authority material ,we assume a system whose transmit power is and receiver sensitivity is .Thus we can conclude that ()1010dBm mW +106.85dBm ?=.Substituting and to the above formula,we can get the Lfs 106.85dBm ?145MHz 148MHz average distance of transmission .()6.4d km =4mile We can learn the radius of the circle is 40mile .So we can conclude the relationship between the circle and the side length of regular hexagon isR=10d.1)The solution of the modelIn order to cover a certain plane with the least regular hexagons,we connect each regular hexagon as the honeycomb.We use A(standing for a figure)covers B(standing for another figure), only when As don’t overlap each other,the number of As we use is the smallest.Figure1According to the Principle of maximum flow of Graph Theory,the better of the symmetry ofthe honeycomb,the bigger area that it covers(Fig1).When the geometric centers of the circle andthe honeycomb which can extend are at one point,extend the honeycomb.Then we can get Fig2,Fig4:Figure2Fig3demos the evenly distribution of users.Figure4Now prove the circle covers the least regular hexagons.Look at Fig5.If we move the circle slightly as the picture,you can see three more regular hexagons are needed.Figure 52)ResultsThe average distance of transmission of the signals that a repeater transmit is 4miles.1000users can be satisfied with 37repeaters founded.3.1.5Analysis of the Result1)The largest number of users that a repeater can serveA user corresponds a PL and a specific frequency.There are 5wave bands and 54different PL tones available.If we call a code include a PL and a specific frequency,there are 54*5=270codes.However each code in two adjacent regular hexagons shouldn’t be the same in case of interfering with each other.In order to have more code available ,we can distribute every3adjacent regular hexagons 90codes each.And that’s the most optimized,because once any of the three regular hexagons have more codes,it will interfere another one in other regular hexagon.2)Identify the rationality of the basic modelNow we considering the influence of the density of users,according to 1),90*37=3330>1000,so here the number of users have no influence on our model.Our model is rationality.3.1.6Strength and Weakness●Strength:In this paper,we use the model of honeycomb-hexagon structure can maximize the use of resources,avoiding some unnecessary interference effectively.It is much more intuitive once we change the function model to the geometric model.●Weakness:Since each hexagon get too close to another one.Once there are somebuildingsor terrain fluctuations between two repeaters,it can lead to the phenomenon that certain areas will have no signals.In addition,users are distributed evenly is not reasonable.The users are moving,for example some people may get a party.3.1.7Some ImprovementAs we all know,the absolute evenly distribution is not exist.So it is necessary to say something about the normal distribution model.The maximum accommodate number of a repeater is 5*54=270.As for the first model,it is impossible that 270users are communicating in a same repeater.Look at Fig 6.If there are N people in the area 1,the maximum number of the area 2to area 7is 3*(270-N).As 37*90=3330is much larger than 1000,our solution is still reasonable to this model.Figure 63.2Improve Model3.2.1Extra SymbolsSigns and definitions indicated above are still valid.Here are some extra signs and definitions.symboldescription Ra the radius of the circular flat area the side length of a regular hexagon3.2.2Additional AdditionalAssumptionsAssumptions ●The radius that of a repeater covers is adjustable here.●In some limited situations,curved shape is equal to straight line.●Assumptions concerning the anterior process are the same as the Basic Model3.2.3The Foundation of ModelThe same as the Basic Model except that:We only consider one variable(p)in the function model of the basic model ;In this model,we consider two varibles(p and µ)of the function model.3.2.4Solution and Result1)SolutionIf there are 10,000users,the number of regular hexagons that we need is at least ,thus according to the the Principle of maximum flow of Graph Theory,the 10000111.1190=result that we draw needed to be extended further.When the side length of the figure is equal to 7Figure 7regular hexagons,there are 127regular hexagons (Fig 7).Assuming the side length of a regular hexagon is ,then the area of a regular hexagon is a .The area of regular hexagons is equal to a circlewhose radiusis 22a =1000090R.Then according to the formula below:.221000090a R π=We can get.9.5858R a =Mapping with MATLAB as below (Fig 8):Figure 82）Improve the model appropriatelyEnlarge two part of the figure above,we can get two figures below (Fig 9and Fig 10):Figure 9AREAFigure 10Look at the figure above,approximatingAREA a rectangle,then obtaining its area to getthe number of users..The length of the rectangle is approximately equal to the side length of the regular hexagon ,athe width of the rectangle is ,thus the area of AREA is ,then R ?*R awe can get the number of users in AREA is()，2**10000 2.06R a R π=????????9.5858R a =As 2.06<<10,000,2.06can be ignored ,so there is no need to set up a repeater in.There are 6suchareas(92,98,104,110,116,122)that can be ignored.At last,the number of repeaters we should set up is,1276121?=2)Get the side length of the regular hexagon of the improved modelThus we can getmile=km 40 4.1729.5858a == 1.6* 6.675a =3)Calculate the power of a repeaterAccording to the formula[]()()32.4420lg ()20lg Lfs dB d km f MHz =++We get32.4420lg 6.67520lg14592.156Los =++=32.4420lg 6.67520lg14892.334Los =++=So we get106.85-92.156=14.694106.85-92.334=14.516As the result in the basic model,we can get the conclusion the power of a repeater is from 14.694mW to 14.516mW.3.2.5Analysis of the ResultAs 10,000users are much more than 1000users,the distribution of the users is more close toevenly distribution.Thus the model is more reasonable than the basic one.More repeaters are built,the utilization of the outside regular hexagon are higher than the former one.3.2.6Strength and Weakness●Strength:The model is more reasonable than the basic one.●Weakness:Repeaters don’t cover all the area,some places may not receive signals.And thefoundation of this model is based on the evenly distribution of the users in the area,if the situation couldn’t be satisfied,the interference of signals will come out.Ⅳ.Conclusions4.1Conclusions of the problem●Generally speaking,the radius of the area that a repeater covers is4miles in our basic model.●Using the model of honeycomb-hexagon structure can maximize the use of resources,avoiding some unnecessary interference effectively.●The minimum number of repeaters necessary to accommodate1,000simultaneous users is37.The minimum number of repeaters necessary to accommodate10,000simultaneoususers is121.●A repeater's coverage radius relates to external environment such as the density of users andobstacles,and it is also determined by the power of the repeater.4.2Methods used in our models●Analysis the problem with MATLAB●the method of the coverage in Graph Theory4.3Application of our models●Choose the ideal address where we set repeater of the mobile phones.●How to irrigate reasonably in agriculture.●How to distribute the lights and the speakers in squares more reasonably.Ⅴ.Future WorkHow we will do if the area is mountainous?5.1The best position of a repeater is the top of the mountain.As the signals are line-of-sight transmission and reception.We must find a place where the signals can transmit from the repeater to users directly.So the top of the mountain is a good place.5.2In mountainous areas,we must increase the number of repeaters.There are three reasons for this problem.One reason is that there will be more obstacles in the mountainous areas. The signals will be attenuated much more quickly than they transmit in flat area.Another reason is that the signals are line-of-sight transmission and reception,we need more repeaters to satisfy this condition.Then look at Fig11and Fig12,and you will know the third reason.It can be clearly seen that hypotenuse is larger than right-angleFig11edge(R>r).Thus the radius will become smaller.In this case more repeaters are needed.Fig125.3In mountainous areas,people may mainly settle in the flat area,so the distribution of users isn’t uniform.5.4There are different altitudes in the mountainous areas.So in order to increase the rate of resources utilization,we can set up the repeaters in different altitudes.5.5However,if there are more repeaters,and some of them are on mountains,more money will be/doc/d7df31738e9951e79b8927b4.html munication companies will need a lot of money to build them,repair them when they don’t work well and so on.As a result,the communication costs will be high.What’s worse,there are places where there are many mountains but few persons. Communication companies reluctant to build repeaters there.But unexpected things often happen in these places.When people are in trouble,they couldn’t communicate well with the outside.So in my opinion,the government should take some measures to solve this problem.5.6Another new method is described as follows(Fig13):since the repeater on high mountains can beFig13Seen easily by people,so the tower which used to transmit and receive signals can be shorter.That is to say,the tower on flat areas can be a little taller..Ⅵ.References[1]YU Fei,YANG Lv-xi,"Effective cooperative scheme based on relay selection",SoutheastUniversity,Nanjing,210096,China[2]YANG Ming,ZHAO Xiao-bo,DI Wei-guo,NAN Bing-xin,"Call Admission Control Policy based on Microcellular",College of Electical and Electronic Engineering,Shijiazhuang Railway Institute,Shijiazhuang Heibei050043,China[3]TIAN Zhisheng,"Analysis of Mechanism of CTCSS Modulation",Shenzhen HYT Co,Shenzhen,518057,China[4]SHANGGUAN Shi-qing,XIN Hao-ran,"Mathematical Modeling in Bass Station Site Selectionwith Lingo Software",China University of Mining And Technology SRES,Xuzhou;Shandong Finance Institute,Jinan Shandon,250014[5]Leif J.Harcke,Kenneth S.Dueker,and David B.Leeson,"Frequency Coordination in the AmateurRadio Emergency ServiceⅦ.AppendixWe use MATLAB to get these pictures,the code is as follows:1-clc;clear all;2-r=1;3-rc=0.7;4-figure;5-axis square6-hold on;7-A=pi/3*[0:6];8-aa=linspace(0,pi*2,80);9-plot(r*exp(i*A),'k','linewidth',2);10-g1=fill(real(r*exp(i*A)),imag(r*exp(i*A)),'k');11-set(g1,'FaceColor',[1,0.5,0])12-g2=fill(real(rc*exp(i*aa)),imag(rc*exp(i*aa)),'k');13-set(g2,'FaceColor',[1,0.5,0],'edgecolor',[1,0.5,0],'EraseMode','x0r')14-text(0,0,'1','fontsize',10);15-Z=0;16-At=pi/6;17-RA=-pi/2;18-N=1;At=-pi/2-pi/3*[0:6];19-for k=1:2;20-Z=Z+sqrt(3)*r*exp(i*pi/6);21-for pp=1:6;22-for p=1:k;23-N=N+1;24-zp=Z+r*exp(i*A);25-zr=Z+rc*exp(i*aa);26-g1=fill(real(zp),imag(zp),'k');27-set(g1,'FaceColor',[1,0.5,0],'edgecolor',[1,0,0]);28-g2=fill(real(zr),imag(zr),'k');29-set(g2,'FaceColor',[1,0.5,0],'edgecolor',[1,0.5,0],'EraseMode',xor';30-text(real(Z),imag(Z),num2str(N),'fontsize',10);31-Z=Z+sqrt(3)*r*exp(i*At(pp));32-end33-end34-end35-ezplot('x^2+y^2=25',[-5,5]);%This is the circular flat area of radius40miles radius 36-xlim([-6,6]*r) 37-ylim([-6.1,6.1]*r)38-axis off;Then change number19”for k=1:2;”to“for k=1:3;”,then we get another picture:Change the original programme number19“for k=1:2;”to“for k=1:4;”,then we get another picture:。
2017数学建模优秀论文
2017数学建模优秀论文数学建模不仅为学生提供了一个参与实践、勇于创新的平台，也为学生的进一步发展打下了良好的基础。
下文是店铺为大家搜集整理的关于2017数学建模优秀论文的内容，欢迎大家阅读参考!2017数学建模优秀论文篇1浅析高职院校数学建模活动[摘要]文章以全国大学生数学建模竞赛为背景，简述了在高职院校学生中进行数学建模培训的意义，根据高职学生的数学基础知识掌握情况，结合数学建模竞赛的特点，探讨了高职院校开展数学建模培训的方法与具体内容，提出高职数学教学要精简数学理论、弱化系统性、突出数学应用、重在实用性的基本思想。
[关键词]高职学生数学建模数学建模是在20世纪六七十年代进入一些西方国家大学的，我国几所大学也在80年代初将数学建模引入课堂。
1992年由中国工业与应用数学学会组织举办了我国10城市的大学生数学模型联赛，74所院校参加了本次联赛。
教育部及时发现，并扶植、培育了这一新生事物，决定从1994年起由教育部高教司和中国工业与应用数学学会共同主办全国大学生数学建模竞赛，每年一届。
现在绝大多数本科院校和许多专科学校都开设了各种形式的数学建模课程和讲座，每年有几万名来自各个专业的大学生参加竞赛，有效激励了学生学习数学的积极性，提高了学生运用数学解决问题的能力，为培养学生利用数学方法分析、解决实际问题开辟了一条有效途径。
从1999年起，全国大学生数学建模竞赛设立了专科组，高职院校作为高等教育的重要组成部分，在开展数学建模活动中投入了极大的热情，数学建模也成为高职院校数学教学改革的一个热点。
作为高职院校的数学教师，笔者自2001年以来一直担负着学校的数学建模培训工作，每年学生们都积极参加数学建模竞赛，也取得了国家级、省级的奖励。
结合高职院校的学生特点，以及十年间高职数学教学和数学建模活动的实践，笔者对高职院校开展数学建模活动的意义进行了探讨，并总结了高职院校实行数学建模培训的思路与方法。
一、在高职院校开展数学建模活动的意义(一)数学建模活动能够满足部分学生的学习需求高职院校的学生大多是基础知识相对薄弱的，但是也有不少学生基础扎实，善于思考。
数学建模获奖论文(优秀范文10篇)11000字
数学建模获奖论文（优秀范文10篇）11000字数学建模竞赛从1992年始，到现如今已成为全国高校规模最大的基础性学科竞赛，也是世界上规模最大的数学建模竞赛。
本篇文章就为大家介绍一些数学建模获奖论文，供给大家欣赏和探讨。
数学建模获奖论文优秀范文10篇之第一篇：高中数学核心素养之数学建模能力培养的研究摘要：数学建模是一种比较重要的能力，教师在进行高中数学教学的过程中应该让学生们学习这种能力，这对于解决高中数学问题是比较有效的，而且对于学生们未来接受高等教育有更重要的意义。
教师在进行高中数学教学的过程中需要让学生们的能力得到锻炼，提升能力是教学的主要目的，学习知识是比较基础的教学目的，教师如果想让学生们的能力得到锻炼应该对教学方法进行更新，高中数学对于很多学生们来说都是比较困难的，所以教师应该不断更新教学方法，让学生们能理解教师的教学目的，而且找到适合自己的学习方法，这也是核心素养的基本内涵。
本文将对高中数学核心素养之数学建模能力培养进行研究。
关键词：高中数学; 核心素养; 数学建模; 能力培养; 应用研究;建模活动是一项比较有创造性的活动，学生们在学习的过程中一定要具备创新思维和自主学习能力，建模活动进行过程中可以让学生们独立，自觉运用数学理论知识去探索以及解决问题，构建模型解决实际问，教学活动中，让学生们的基础知识更加牢固、基本技能得到锻炼是最根本的目的。
学生们的运算能力以及逻辑思维能力也能在建模活动中得到锻炼，提升学生们的空间观念以及增强应用数学意识是延伸目的。
一、对数学建模的基本理解概述高中数学建模最简单的解释就是利用学生们学习过的理论知识来建立数学模型解决遇到的问题。
数学建模的基本过程就是对生活中或者课本中比较抽象问题解决的过程。
通过抽象可以建立刻画出一种较强的数学手段，通过运用数学思维也能观察分析各种事物的基本性质和特点。
学生们可以从复杂的问题中抽离出自己熟悉的模型，然后在利用好数学模型去解决实际问题基本就是事半功倍。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
For office use onlyT1________________ T2________________ T3________________ T4________________ Team Control Number59496Problem ChosenEFor office use onlyF1________________F2________________F3________________F4________________2017MCM/ICMSummary Sheet(Your team's summary should be included as the first page of your electronic submission.)Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page.In this paper, on the basis of three goals and ten principles,we define UrbanSustainability Index (USI) to measure the success rate of urban "smart growth".Weconstruct a comprehensive evaluation model to make a reliable and effectiveevaluation of USI and put forward reasonable suggestions.In Problem 1, we define USI as a measure of the success rate of smart cities, andpropose three-dimensional model and sixteen indicators of evaluation system. Then,the computational model is established, and the model is supplemented by thenormalization method of index data, the discrete treatment method and the balancedweight method. Finally, the neutralization evaluation model of urban sustainabledevelopment ability is constructed.In question 2, Shangri-La in China and Colorado Springs in the US were selected asrepresentative cities were studied and evaluated according to the ten principles of"smart growth". We deal with various indicators according to the comprehensiveevaluation model that we established in first question. According to the results of thetreatment, Colorado Springs' "Urban Sustainability" value is slightly higher than it ofShangri-La, so Colorado Springs’ "smart growth" obtain a higher degree of success.In Question 3, based on the geographic location of the sample cities, expected growthrates and economic opportunities and combine with own development strategies, wemake the future "smart growth" plan for two cities and the expected success rate ofthe program will be re-evaluated by using the indicator system.In Question4,we use the improved principal component analysis to analyze thedevelopment potential.In Question 5, the ecological environment, the economic level and the quality of lifeare discussed from the planned sub-items according to conclusion in Question 3. Inaddition,we compare the expected population growth rate of the city with the assumedgrowth rate in Question 5 and consider that in which way that the promotion of socialeffects support the growth of such a development.Key words: Smart Growth Gray Prediction Normalization ProcessingContentIntroduction (3)General Assumptions and Variable Description (3)General Assumptions (3)Definitions (4)Model Definitions (4)The Ability of Urban Sustainable Development (4)Indicator system (5)The Calculation Model of Urban "Smart Growth" (7)Establish the comprehensive evaluation model (10)Application of the Refined Model to the sample cities (12)Results and Discussion (13)Future plans and strategies for Smart growth (13)Colorado Springs (17)Shangri-La (18)Compared And Discussion (19)Conclusions (19)Strengths (20)Weakness (20)References (21)IntroductionThere are many problems exist in the process of urban planning and management in many countries. It is clear that the world urbanization trend is accelerated.The emerging economic globalization has made cities in all countries develop at an unprecedented speed. The followings are the basic form of urban sprawl:a) Urban land growth outstrips population growth.b) Dwellings, shops and workplaces are strictly separate.c) The lack of high-density economic center and it is difficult to walk.d) A road network characterized by large blocks.Rapid urbanization of population leads to the disorderly spread and expansion of urban space, which causes tremendous pressure on resources and environment, and makes the relationship between people and land tighter.A s Theodore Parker said that:“The city has always been a civilized fireplace, emitting light and heat in the dark.”Smart growth theory was firstly proposed by American scholars in the 90s of last century. This was because of the continued expansion of city public space, the loss caused by the spread of serious road congestion, environmental deterioration, and the scarcity of natural resources and a series of problems that existed in city growth plans. The scholars and the government hoped to establish a new plan and management was pretty fine, and the ultimate goal is to achieve coordinated economic social ecological development. It is defined as a planned and resource-saving urban development model. The development of our city requires promoting the city economy to run well and improving the urban livability and quality of life. As the city itself is the collection of nature, society and economic, as well as human and many other attributes, the content of smart growth research will be in a multi-disciplinary cross.General Assumptions and Variable DescriptionGeneral Assumptions• Our data are derived from the websites of international organizations and the city's official website, and it is reasonable to assume the high quality of their data. So the data we collect from online databases are accurate, reliable and mutually consistent. •Based on three E goals and ten principles, we select three secondary indicators and sixteen tertiary indicators as the city’s “smart growth" model. We assume that the unselected indicator data have no impact on the city's "Smart Growth "of comprehensive evaluation system of the weight and the results.•We selected Shangri-La in China, Colorado in the United States as the sample of middle-sized cities to validate our model, and we reasonably assume that the cities that were chosen were representative.•Assuming that the selected samp le cities have no more serious disasters in the next five years, this assumption implies that government decision-making, human behavior and natural activities have the least impact and the model we proposed is rational . •Assuming that within one year, the development plan of the sample cities has not changed much. In this way, we can use the recent year's data to validate our model and obtain reasonable and accurate results.DefinitionsIn order to measure the success of smart growth of a city, we state the following variables and concept:•Social harmony degree: our personal feeling about our physical condition, mental function ,social ability and personal comprehensive state on the basis of social economy, cultural background and value orientation•Urban economy sustainability: a specific system in the specified objectives and the default stage, it can successfully constrain its degree of coordination and the degree of stability within the threshold of sustainable development rate, that is to say, the ability of a particular system to successfully extend to economy sustainable development goals.•Policy-making degree: the proportion of urban residents who participate in policy-making accounts for of total population•The soundness of Medical Security System: as for a sound medical security system, it’s main body is basic medical insurance, and it should be supplemented by other forms of supplementary insurance and commercial health insurance. And a sound medical insurance system is expected to meet the demand of diversified medical treatment and provide safe, effective, convenient and inexpensive medical and health services for the masses.•Urbanization rate: the proportion of permanent resident population accounts for of the region total resident population•Urban spatial compact ratio: the degree of spatial compact in the process of urbanization, and whether it can produce a relatively high density of residential and multi-purposed mixed land.•Energy consumption per unit of output value: As for industrial enterprises, the industrial comprehensive energy consumption in ten thousand RMB divided by the total industrial output value in tons of standard coal.•Urban green coverage ratio: The percentage of green land area out of the total area of the urban land, which is an important indicator of urban environment quality. Model DefinitionsThe Ability of Urban Sustainable DevelopmentThe concept of the main sources of the following three aspects: Firstly, economic growth requirements and the uncontrolled expansion of the city makes the investment of public service facilities increase, as a consequence , the government finance is difficult to support, thus causing the economic growth rate to slow down. Secondly, the formation of private cars and the promotion of the road network and suburbanization spread rapidly. The occupation of the city public open space brings a heavy burden on land. And there are many ecological environmental problems caused by excessive use of resources and serious environmental pollution. Thirdly, the needs of society, a series of factors caused by the rapid spread of city and the fast pace of urbanization residents directly lead to reduced quality of life, the city's social equality is heavily influenced by the city and the harmonious degree of decline.After the implementation of "smart growth" plan in part of the city, good results are obtained in the city economic and social equality, as well as the environmental sustainability. In addition, sustainable development capacity of the city has been greatly improved, which, effectively curb the continued spread of city public space and the waste of resources. In order to measure the success rate of a city's "smart growth", we define the index of The Ability of Urban Sustainable Development as a measure.Indicator system1. Sustainable Development of Urban Economy（SDUE）. Economic sustainable development is a reasonable form of economic development. Through the implementation of sustainable economic development strategy we can form a sustainable social economic development model. In order to reflect the sustainable development level of the sample city economy objectively and completely, the paper also requests that the evaluation index system should be simple and clear enough so that the government and other decision-making organs can understand and respond to it. The GDP per person of the sample cities can be used to reflect the overall economic development of the region, which is the evaluation index of urban economic growth. In addition, we suggest that the index system should include urban spatial compact ratio, urban traffic quality indicators, urban land use efficiency, energy consumption per unit of output value, population growth rate and other evaluation indicators. At the same time, we can also use the relational matrix or vector graphics to reflect the relationship between the indicators, so that we can ensure that the index system is more complete, reliable and effective, and ultimately obtain aTable 2: Index System of Social Harmony(3) Urban Environmental Quality. The theory of “smart growth” is firstly proposed by American scholars in the 1990s. This is because the city continues to expand the urban green space due to the reduction of environmental pollution, land resourcesTable 3: Index System ofThe Calculation Model of Urban "Smart Growth"Through the above we build three-dimensional sixteen indicators of the evaluation index system, can be more comprehensive to the city's sustainable development capacity to make a reasonable calculation, get more accurate results.Establish the weight of each indexRatio, analytic hierarchy process and principal component analysis can be used to determine the index weight. However, both graded and analytic hierarchy processes involve subjective judgments, which are not objectivity to the data that we are evaluating. In order to avoid the interference of subjective factors and to meet the comparability of indicators, this paper chooses the arithmetic average weighting method as the basic synthesis method of urban sustainable development ability, which represents each of the main components of the method and indicator weight. It should be noted that the use of the method is not the ultimate goal, but just used in the indicators of the merger, and thus facilitate the research of results for further analysis, which in order to arrive at the target weight.Discrete Data ProcessingAccording to Table 3 we can know that a city's urbanization rate of the impact of the degree of harmony is two-sided. On the one hand, urbanization will be able to drive the economic growth, promote social harmony and improve the quality of life of residents. However, the high urbanization rate will cause over-exploitation of resources and increase the burden on the ecological environment. Based on these factors, we will do discrete data processing. We find that the best urbanization rate is 45%, or 45% of the discrete threshold (BSUR). According to this assumption, we can get the discrete treatment formula of the urbanization rate:UR*=|UR-BSUR|Where ER * is the discrete value of the population urbanization rate.Data Normalization ProcessingIn order to eliminate the dimensional effect between the indexes, we need to standardize the data (normalization processing) to solve the problem that the data are not consistent with each other. The comparability of indicators among these data . After the data are standardized, the indexes are in the same order of magnitude, which is suitable for comprehensive comparison and evaluation. There are two commonly used methods of normalization:1. min-max normalization （Min-Max Normalization ）Also known as dispersion normalization, is a linear transformation of the original data, the result value is mapped to [0 - 1] between. The conversion functions are as follows:*Max X X Max Min-=- （1） Max is the maximum value of the sample data and min is the minimum value of the sample data.However, the use of this method will produce a flaw. When new data are added, it may lead to changes in max and min, need to be redefined.2. The second method normalizes the data by giving the mean and standard deviation of the original data. The processed data are in accordance with the standard normal distribution, and the mean is 0 and the standard deviation is 1. The transformation function is: *X X μσ-= （2） Where μ is the mean of all sample data and σ is the standard deviation of all sample data.According to the nature of data and data results, we use the extreme value method to normalize the data, because the extreme value of the number of indicators and thedistribution of data requirements are lower, the transformed data are in an area asked, After transformation, the relative number of data is more obvious, at the same time to avoid the emergence of negative numbers, easy to do further data processing. Therefore, the entire index system processing, will use the extreme value method. The formula is as follows:Positive indexes ：min max minxi Xi -=- (3) Negative indexes ： max max minxi Xi -=- (4) Establish the comprehensive evaluation modelAssess the success rate of a city's "smart growth" program, which is to calculate the capacity of the city's sustainable development. After collecting and normalizing each index, we can synthesize 16 secondary indexes into three dimensions according to the weight of each indicator. Then we can get the success rate of the city's "smart growth" plan. In order to ensure that the influence which each index factor act on a more reasonable target in a model can adapt to more cities, which is more inclusive, we define a Ti variable and the mean weight, so that the results are more reasonable, more inclusive. Specific methods:()n 1F=ii i W X =∑ （5） Where F is the total index of the sample urban element index, and W i is the weight of the i-th index, X i is the value of the i-th objective index of the sample city..The current smart growth of Colorado Springs （2014）In order to study the model, we find some information about the current situation in two cities today on sustainable development and smart growth plan, and we state those information as follows:1. The Government has come up with a new concept: Scorecard. The scorecard is a community self-assessment tool that can help spur discussion and action on our community’s approach to growth and development issues. We can use it in a number of different ways. Such as:• As a concerned community member.You can use the scorecard to as an educational tool to better understand your community’s strengths and weaknesses in promoting smart growth. Individually answering the questions in the scorecard could also be the starting point for discussions with other members of your community.• In small group discussions or workshops.You can use the scorecard in small group discussion on your community’s approach togrowth and development to check your own and other people’s assumptions about what your community is and is not doing and what policies it may or may not have concerning growth and development (and even how effective the policies might be). Given the results of your small group discussion, you might be able to use the scorecard as part of more formal evaluation update of your community comprehensive master plan.2. Urban sprawl is an important reason for our intelligent growth, and the government emphasize the integrated use of land, and residential, office, commercial, kindergarten and some entertainment facilities are arranged in the community, and the government aims at community constructions. People can live in and work in communities, as well as run business and participate in entertainment activities, we look forward to form compact, suitable communities for walking, and mixed use. In this way, this plan can exactly meet the demand of taking advantage of compact building design.3. Take the City Lifestyle Apartment to Downtown Colorado Springs When developers work together on a pair of apartment buildings in the heart of Colorado Springs, the goal is to design projects that fit the city lifestyle rather than being suburban to the heart of the city. The result is that two buildings will have facilities that may be found in suburban buildings, but will have other features specifically designed to attract urban tenants, many of whom are young professionals. This exactly reflects the principle that creating a range of housing opportunities and choices.4. The related departments cooperate with each other to lower a major barrier, which is about the construction of affordable housing by passing a construction defects ordinance.The current smart growth of Shangri-La (2014)To enhance the urban functions, the city focuses on green development, the Sangria-La try to build a fine ecological environment, beautiful environment, livable city for people, the following are their future plans:1.Improve the basic conditions for the development of tourism in the traffic construction, speed up the construction of external roads, adjust the level of industrial structure, improve land utilization, Urban transport should establish the concept of pedestrian priority, improve the residents travel environment, protect the safety of travel, advocate green travel, which caters to the first principle of intelligent growth.2.Sangria-La population density is relatively low, and the government aims at promoting the urbanization process to some extend. The government is expected to strengthen urban construction and improve the urban system. In addition, we ought to take the path of sustainable urbanization, the road of intelligent urbanization, and theroad of harmonious urbanization.3.Increase public infrastructure Of the financial input，optimize the layout of urban infrastructure, insist the overall plan, improve the city open space, rational planning of urban space compactness. It is suggested that the city should build urban walkway and bicycle "green way", strengthen pedestrian crossing facilities, bicycle parking facilities, road greening, lighting and other facilities to effectively change the over-reliance on car travel traffic development model, and meet the needs of a variety of transportation choices.4.Improve the participation of citizens in government decision-making to participate in current affairs of the initiative. Promote the process of political modernization, improve the transparency of government management, and innovate the government management mechanism, which, is beneficial to encourage community and stakeholder collaboration in development decisions.The growth of urban population plays a significant role in assessing the viability of the programs that are being developed in the cities over the next few decades. Therefore, we analyze the population development trends of the selected cities by using the gray prediction model based on available data.Application of the Refined Model to the sample citiesWhen processing the selected sample cities, we define the Ti values according to the characteristics of the selected cities as follows: When the two dimensional indicators are combined to obtain the corresponding dimensional indicators, the factors considered are very comprehensive, and each index And the degree of influence on the upper-level indicators is approximately the same, Ti = 1 (i = 1, 2, ...) can be assumed at this time. According to the characteristics of the two sample cities and the policy of urban sustainable development (urban success rate), the paper analyzes the characteristics of urban sustainable development (the success rate of urban "smart growth") from the three dimensions of urban economy sustainable development, urban harmony and urban environmental quality. The impact of environmental quality on the model is the largest, and it should be defined as the Ti 1/2. The other two indicators of the degree of impact similar data, it is defined as 1/4.Results and DiscussionOur model shows that Colorado Springs has a sustainable urban capacity index of 52.47% and Shangri-La's urban sustainable development capacity of 46.38%.Finally, we can analyze the model test result is that the success rate of the current development plan in Colorado Springs is 52.74%, and Shangri-La current development plan success rate is 43.68%. Colorado Springs has been basically successful and achieved remarkable results. As for Shangri-La, due to the implementation of the plan for a short time, it has not shown significant performance. Future plans and strategies for Smart growthThrough our discussion on the principle of smart growth, we know that the principle mainly includes reducing travel distances, reducing travel times, avoiding single land uses, developing public transport, constructing pedestrian walkways, allocating public facilities and employment opportunities within walking distance, and increasing the number of industries that can promote economic growth Strength. As for a city, those industries are tourism and agriculture, forestry and so on.Colorado SpringsGeographic locationSmart Water Plans:The city lies in a high desert with the Southern Rocky Mountains to the west, the Palmer Divide to the north, high plains further east, and high desert lands to the south when leaving Fountain and approaching Pueblo. Colorado Springs has a semi-arid climate, and its location just east of the RockyMountains affords it the rapid warming influence from winds during winter but also subjects it to drastic day-to-day variability in weather conditions. Due to unusually low precipitation for several years, as such, protecting and enhancing and a community’s natural infrastructure are critical components of achieving Smart Growth.Intelligent Industry PlanDue to high-tech industry will relatively develop in the next few decades, the city are expected to seize the opportunity to recruit more high-tech talent, for example, in the city to establish a experimental base for migratory immigrants to attract more investment. In addition, the city ought to increase the information technology and complex electronic equipment research, since even after the next few decades, science and technology is still the primary productive force.Economy opportunityInvestment:A large percentage of Colorado Springs' economy is based on manufacturing high tech and complex electronic equipment.Attract foreign investors, and make a plan of investment. In addition, related departments can draw up a contract that fulfills the requirements and initiates a bidding process by calling for tenders.Increase employment:The city's location at the base of Pikes Peak and the Rocky Mountains makes it a popular tourism destination. Tourism is the third largest employer in the Pikes Peak region, accounting for more than 16,000 jobs. Nearly 5 million visitors come to the area annually, contributing $1.35 billion in revenue. Appropriate scale of the new tourism projects, the establishment of their own city characteristics of the ecological industry, science and technology into tourism. Shangri-LaGeographic locationEcological red lineShangri-La is located in the northwest of Yunnan Province, the city is surrounded by many mountains, so there is no doubt that the forest area is very large, green coverage in urban areas is very high, and the specific develop management is to build a global tourism system, scientifically determine the development intensity, and delimit red-line areas of ecology, and turned to the rational distribution of production space, living space and ecological space, as well as the construction of sustainable, livable and beautiful town, so that can retain enough open space, farmland and natural.Adjust the process of urbanizationShangri-La City is located in Yunnan Province, and it is one of the largest and the most densely populated cities, and the personnel are relatively scattered. We are expected to considering the carrying capacity of cities and towns and the capacity ofpopulation absorption, we should scientifically determine the scale of urbanization and reasonably grasp the pace and rhythm of urbanizationEconomy opportunityDiscover the great potential of tourismShangri-La is an important ecological function area in China. It is a multicultural and multicultural gathering place with broad development prospects. Its unique geographical advantages make the city's tourism and agriculture have great potential, so its future is very impressive.Expected growth ratesThe growth of urban population plays a significant role in assessing the viability of the programs that are being developed in the cities over the next few decades. Therefore, we analyze the population development trends of the selected cities by using the gray prediction model based on available data. In this part, we use gray forecasting to infer the variation tendency of the population.Gray forecasting is a method to predict the system with uncertain factors. The gray forecasting model can find out the regularity of the system variation by generating the correlation of the original data by differentiating the trend of development trend among the system factors, generating the data sequence with stronger regularity, and then establishing the corresponding differential Equation model, in order to predict the future trend of things the situation, which constructs a gray prediction model by using a series of quantitative values of the response prediction object characteristics observed at equal time intervals to predict the feature quantity at a certain time in the future or the time to reach a certain characteristic quantity.。