美赛-数学建模-写作模版(各部分)

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数学建模美赛

摘要：结合目前国内外对教练员的评价体系，我们对教练员评价系统的基本原理、基本模型和主要建模内容进行研究，对遇到和需要解决的相关理论和技术问题进行比较深入的分析、研究和探讨。

硬性指标通过增值性评价方法，由运动员比赛获胜率的斜率来表现；软性指标则运用了层次分析法，并依据教练员评价系统中操作的多主体评价指标体系求出每项指标的权重分布，目的在于通过查阅文献资料，经过比较、分析和综合，本文创造性地运用国外对教练员评价与中国对教练员评价的理论，对教练员评价方法进行研究，设计一套既能反映教练员能力素质的框架构成，又能客观区分软性指标中各要素重点与非重点的比例关系。

初步确定了如下两个因素作为衡量最优秀教练能力素质的标准，分别为硬性指标和软性指标，硬性指标我们运用了增值性评价的方法，这种评价方法的理念是：根据球队或运动员在大型比赛中成绩的进步和变化来评价教练员的绩效。

通过运动员成就（包括运动员比赛的成绩、态度及观念等）作为评价教练员的依据，通过分析 Pythagorean expectation找出足球、篮球、曲棍球三个不同领域的获胜率的公式，运用多元线性函数进行拟合，考虑时间跨度利用曲线拟合来表现出教练员的执教绩效，有针对性的选拔出优秀的教练。

而软性指标运用模糊层次分析法来定量的表示，并遵循多元化的原则，评价主体多元化是指运动员评价、教练员自我评价、专家评价、同行教练员评价都参与教练员的软性评价，多方面地呈现教练员的表现，从而为国家选拔出优秀教练员提供参考。

为了增加本文的实用性，我们编制了模糊矩阵乘法的运算程序，使评估的最后工作变得简单易行。

运用模糊矩阵乘法的运算程序，将得到各等级的模糊分布和加权平均后的直接得分。

实验中，在结合手工运算的基础上，对运算程序进行了有效性验证。

并且通过验证表明：该运算程序是有效的，可以推广使用。

为了验证模型的可行性，我们收集权威网站NBA十大教练排名，然后查找相关数据，在分析的基础上定义五个指标，并求出相对应于十大教练的值。

数学建模范文1

第二章方案报告一．背景介绍：一个工厂生产两种产品，甲产品每单位利润为0.5单位，乙产品每单位利润为0.3单位，产品仅能在周末运出。

产品的生产量必须与工厂仓库总量相适当，仓库容量为400000单位。

包装好的每单位产品通过相同的系统生产（例如烟厂生产不同品牌的香烟），产品甲的生产率为2000单位/小时，产品乙的生产率为2500单位/小时，系统每周可使用的工时是130小时，市场预测表明，在目前市场的状态和广告宣传作用下，每周最大的需求量甲产品250000单位，乙产品为350000单位。

另外，根据合同规定，工厂每周至少要生产50000单位乙产品，提供给某特殊用户。

我们遇到的问题如下：（1）在现有状态下，工厂应如何安排每周的生产计划，以获取最大利润？（2）工厂为获取更大利润，应如何挖潜改革？比如增加系统的生产时间（需新增生产线）;增加宣传力度，以提高市场需求量（需增宣传费用）；增加仓库的库容量（要付出额外租金）；不满足乙产品合同规定的部分生产量（要付罚金），哪些措施能使利润增加？（3）能使利润增加的措施，在多大的范围内是可取的（在影子价格不变的前提下），此时实际的利润是多少?(提示：利用参数规划，所需的参数可能不止一个。

)二．解决方案 ① 第一问求解设x 1为每周生产产品甲的单位数，x 2为每周生产产品乙的单位数。

该问题的数学模型为⎪⎪⎪⎪⎪⎩⎪⎪⎪⎪⎪⎨⎧≥≥≤≤≤≤+≤++0035000050000250000(13025002000(40000022..3.05.0max 2121212121x x x x xx x x t s x x ）（市场需求及合同约束生产时间限制）仓库限制）该问题用单纯形方法求解如下：首先把该问题化为标准LP 问题，其标准型为⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧=≥-≤+-≤+≤+≤++≤++--7,6,5,4,3,2,1,050000350000250000130000045200000..3.05.0min 72625142132121i x x x x x x x x x x x x x t s x x i然后依次有如下单纯形表x 1 2x 3x 4x 5x 6x 7x RHSx 1 2x 3x 4x 5x 6x 7x RHSx 1 2x 3x 4x 5x 6x 7x RHS所以，最优解x 1=150000 2x =50000 z=90000即每周生产甲产品15000个单位，生产乙产品50000个单位，可获得最大利润为90000. ②第二问求解当采取改革时，比如增加系统的生产时间（需新增生产线）;增加宣传力度，以提高市场需求量（需增宣传费用）；增加仓库的库容量（要付出额外租金）；不满足乙产品合同规定的部分生产量（要付罚金）。

MCM美国大学生数学建模竞赛模板-公式

由假设得到公式1．We assume laminar flow and use Bernoulli’s equation:（由假设得到的公式）公式Where符号解释According to the assumptions, at every junction we have（由于假设）公式由原因得到公式2．Because our field is flat, we have公式, so the height of our source relative to our sprinklers does not affect the exit speed v2 （由原因得到的公式）；公式Since the fluid is incompressible(由于液体是不可压缩的), we have公式Where公式用原来的公式推出公式3．Plugging v1 into the equation for v2 ,we obtain（将公式1代入公式2中得到）公式11．Putting these together(把公式放在一起), because of the law of conservation of energy, yields：[]公式12．Therefore, from (2),(3),(5), we have the ith junction（由前几个公式得）公式Putting (1)-(5) together, we can obtain pup at every junction. In fact, at the last junction, we have公式Putting these into (1) ,we get（把这些公式代入1中）公式Which means that theCommonly, h is aboutFrom these equations, （从这个公式中我们知道）we know that ………引出约束条件4．Using pressure and discharge data from Rain Bird 结果,We find the attenuation factor （得到衰减因子，常数，系数）to be公式计算结果6．To find the new pressure ,we use the ( 0 0),which states that the volume of water flowing in equals the volume of water flowing out : （为了找到新值，我们用什么方程）公式Where() is ;;7．Solving for VN we obtain (公式的解)公式Where n is the …..8．We have the following differential equations for speeds in the x- and y- directions:公式Whose solutions are （解）公式9．We use the following initial conditions ( 使用初值) to determine the drag constant:公式根据原有公式10．We apply the law of conservation of energy（根据能量守恒定律）. The work done by the forces is公式The decrease in potential energy is （势能的减少）公式The increase in kinetic energy is (动能的增加)公式Drug acts directly against velocity, so the acceleration vector from drag can be found Newton’s law F=ma as : (牛顿第二定律)Where a is the acceleration vector and m is massUsing the Newton’s Second Law, we have that F/m=a and公式So that公式Setting the two expressions for t1/t2 equal and cross-multiplying gives公式22．We approximate the binomial distribution of contenders with a normal distribution:公式Where x is the cumulative distribution function of the standard normal distribution. Clearing denominators and solving the resulting quadratic in B gives公式As an analytic approximation to . for k=1, we get B=c26．Integrating, （使结合）we get PVT=constant, where公式The main composition of the air is nitrogen and oxygen, so i=5 and r=1.4, so23．According to First Law of Thermodynamics, we get公式Where ( ) . we also then have公式Where P is the pressure of the gas and V is the volume. We put them into the Ideal Gas Internal Formula:公式Where对公式变形13．Define A=nlw to be the ( )（定义）; rearranging (1) produces （将公式变形得到）公式We maximize E for each layer, subject to the constraint (2). The calculations are easier if we minimize 1/E.（为了得到最大值，求他倒数的最小值）Neglecting constant factors （忽略常数）, we minimize公式使服从约束条件14．Subject to the constraint （使服从约束条件）公式Where B is constant defined in (2). However, as long as we are obeying this constraint, we can write （根据约束条件我们得到）公式And thus f depends only on h , the function f is minimized at （求最小值）公式At this value of h, the constraint reduces to公式结果说明15．This implies（暗示）that the harmonic mean of l and w should be公式So , in the optimal situation. ………5．This value shows very little loss due to friction.（结果说明）The escape speed with friction is公式16．We use a similar process to find the position of the droplet, resulting in公式With t=0.0001 s, error from the approximation is virtually zero.17．We calculated its trajectory(轨道) using公式18．For that case, using the same expansion for e as above,公式19．Solving for t and equating it to the earlier expression for t, we get公式20．Recalling that in this equality only n is a function of f, we substitute for n and solve for f. the result is公式As v=…, this equation becomes singular (单数的).由语句得到公式21．The revenue generated by the flight is公式24．Then we have公式We differentiate the ideal-gas state equation公式Getting公式25．We eliminate dT from the last two equations to get （排除因素得到）公式22．We fist examine the path that the motorcycle follows. Taking the air resistance into account, we get two differential equations公式Where P is the relative pressure, we must first find the speed v1 of water at our source: （找初值）公式自己根据计算所画的图：1、为了…….(目的)，我们作了…….图。

(完整)数学建模美赛试题

地球资源的消耗速度快,越来越多的人关注人类社会的未来。

自1960年以来，已经有许多专家研究可持续发展。

然而大多数人的研究对象是整个世界，一个国家或一个地区。

几乎没有人选择48个最不发达国家(LDC)在联合国为研究对象列表。

然而，LDC国家集团共享许多相同的点.他们的发展道路也有法律的内涵。

本文选择这些国家为研究对象针对发现常规的可持续发展道路。

本文组织如下。

第二部分介绍研究的背景和本研究的意义。

第三节描述了我们对可持续发展的理解细节和显示我们的评估系统的建立过程和原理，那么我们估计每一个国家的LDC和获得可持续发展的能力和等级。

第四节提供了一个最糟糕的国家毛里塔尼亚计划指数在第三节。

第五节演示了在第四节的合理性和可用性计划。

最后在第六节总结本文的主要结论和讨论的力量和潜在的弱点。

地球上的资源是有限的。

三大能源石油、天然气和煤炭可再生。

如何避免人类的发展了资源枯竭和实现可持续发展目标是现在的一个热门话题。

在过去的两个世纪，发达国家已经路上,先污染,再控制和达到高水平的可持续发展。

发展中国家希望发展和丰富。

然而,因为他们的技术力量和低水平的经济基础薄弱，浪费和低效率的发展在这些国家是正常的.所以本文主要关注如何帮助发展中国家特别是48在联合国最不发达国家实现可持续发展是列表可持续发展的理解是解决问题的关键。

可持续发展的定义经历了一个长期发展的过程.在这里,布伦特兰可持续发展委员会的简短定义的”能力发展可持续- - — - - -以确保它既满足现代人的需求又不损害未来的能力代来满足自己的需求”[1]无疑是最被广泛接受的一个在各种内吗定义。

这个定义方面发挥了重要作用在很多国家的政策制定的过程。

然而,为了证明一个国家的现状是否可持续不可持续的,更具体的定义是必要的更具体的概念，我们认为,如果一个国家的发展是可持续的，它应该有一个基本的目前的发展水平，一个平衡的国家结构和一个光明的未来.基本的发展水平反映了国家的基础和潜力。

全国大学生数学建模竞赛论文超级模板

第二部分问题分析………………………………………… ………………()
第三部分模型的假设…………………………………………………………()
第四部分定义与符号说明……………………………… …………………()
第五部分模型的建立与求解………………………………… ……………()
1．问题1的模型………………………………………………………………()
第三部分：问题2的。。。个模型（4号宋体）
。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。
第四部分：问题3的。。。个模型（4号宋体）
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六、模型评价与推广
对本文中的模型给出比较客观的评价，必须实事求是，有根据，以便评卷人参考。
（数学建模论文书写基本框架,仅供参考）
题目（黑体不加粗三号居中）
摘要（黑体不加粗四号居中）
（摘要正文小4号，写法如下）
（第1段）首先简要叙述所给问题的意义和要求，并分别分析每个小问题的特点（以下以三个问题为例）。根据这些特点我们对问题1用。。。。。。。。的方法解决；对问题2用。。。。。。。。的方法解决；对问题3用。。。。。。。。的方法解决。
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三、模型假设（4号黑体）
（以下小4号）
1.假设题目所给的数据真实可靠；
2．
3．
4．
5．
6．
。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。
注意：假设对整篇文章具有指导性，有时决定问题的难易。一定要注意假设的某种角度上的合理性，不能乱编，完全偏离事实或与题目要求相抵触。注意罗列要工整。

美国大学生数学建模大赛英文写作

Conference Interpreting and Its Effect Evaluation, Nonlinear Waves in Elastic Rods， Introducing Management into…
写作要求： 1. 简短论文标题一般在10个字内，最多不超过15个词。
多用复合词
如：self-design, cross-sectional, dust-free, water-proof, input-orientation, piece-wiselinear 利用缩略词如：e.g., i.e., vs.（与…相对), ibid.(出处相同）， etc., cit.(在上述引文中), et al.(等人), viz.(即,就是), DEA (data envelopment analysis), OLS(Ordinary least-squares)
“Investigation on …”, “Observation on …”, “The Method of …”, “Some thought on…”, “A research on…”等冗余套语。
4. 少用问题性标题 5. 避免名词与动名词混杂使用如:标题是 “The Treatment of Heating and Eutechticum of Steel” 宜改为 “Heating and Eutechticuming of Steel” 6. 避免使用非标准化的缩略语论文标题要求简洁,但一般不使用缩略语 ,更不能使用非标准化的缩略语。
关键词（Keywords)
基本功能：顾名思义；便于检索语言特点：多用名词；字数有限（4-6）；出处明确写作要求 :论文的关键字一般列在作者与单位之下，论文摘要之上。也有列在论文摘要之下的。关键词除第一个字母大写外，一般不要求大写。关键词间用逗号、分号或大间隔隔开。最末一个关键词一般不加用逗号、分号或句号。

美赛格式要求范文

美赛格式要求范文美赛（MCM/ICM）是美国大学生数学建模竞赛的英文缩写，是一项面向全球大学生的数学建模竞赛。

MCM/ICM每年提供若干个实际问题供参赛者选择，并规定参赛者提交一份由三人组成的队伍作品，要求队伍在规定的时间内解答问题并撰写一篇报告。

以下是美赛格式的一般要求：1.报告页数要求：参赛队伍通常需要撰写一篇1200字以上的报告。

具体的页数要求可以根据不同的问题和竞赛要求略有变化，但一般不超过20页。

尽管有页数限制，但在撰写报告时需要全面、清晰地阐述问题、解决方法和结论。

2.章节结构：一篇标准的美赛报告通常包括以下几个部分：-引言：介绍问题的背景和目的，明确解决问题的方法和目标。

-问题分析：对问题进行深入的分析和理解，包括重新表述问题、提出假设和限制条件，展开问题讨论。

-模型建立：建立一个或多个数学模型，以解决问题。

需要解释模型背后的理论基础和假设，并给出模型的描述和方程。

-模型求解：详细描述解决模型的方法、步骤和计算过程。

需要标注具体的计算公式、算法、图表和详细的计算结果。

-结果分析：对所得结果进行详细的解释和分析，包括结果的合理性和局限性，对模型的优缺点进行评价。

-结论与建议：总结所得结论，并提出可能的进一步研究方向和改进建议。

3.图表和数学符号的使用：美赛报告通常需要使用多个图表和数学符号，以支持和解释问题的分析和解决方法。

图表应该清晰、简洁，并配有必要的标注和说明。

数学符号应该统一、准确地使用，避免造成混淆。

5.语言表达：报告应使用准确、简练、清晰的语言表达问题、论证思路和解决方案。

语法、拼写和标点符号应正确无误。

尽管以上是一般的美赛报告要求，但具体的格式要求可能会因竞赛规则和题目的特殊性而有所不同。

建议参赛队伍在参赛前详细了解官方提供的竞赛规则和报告要求，并遵循官方给出的指导进行撰写报告。

同时，可以参考以往的优秀报告和获奖队伍的经验，借鉴其写作技巧和结构。

数学建模美赛2012MCM B论文

Camping along the Big Long RiverSummaryIn this paper,the problem that allows more parties entering recreation system is investigated.In order to let park managers have better arrangements on camping for parties,the problem is divided into four sections to consider.The first section is the description of the process for single-party's rafting.That is, formulating a Status Transfer Equation of a party based on the state of the arriving time at any campsite.Furthermore,we analyze the encounter situations between two parties.Next we build up a simulation model according to the analysis above.Setting that there are recreation sites though the river,count the encounter times when a new party enters this recreation system,and judge whether there exists campsites available for them to station.If the times of encounter between parties are small and the campsite is available,the managers give them a good schedule and permit their rafting,or else, putting off the small interval time t∆until the party satisfies the conditions.Then solve the problem by the method of computer simulation.We imitate the whole process of rafting for every party,and obtain different numbers of parties,every party's schedule arrangement,travelling time,numbers of every campsite's usage, ratio of these two kinds of rafting boats,and time intervals between two parties' starting time under various numbers of campsites after several times of simulation. Hence,explore the changing law between the numbers of parties(X)and the numbers of campsites(Y)that X ascends rapidly in the first period followed by Y's increasing and the curve tends to be steady and finally looks like a S curve.In the end of our paper,we make sensitive analysis by changing parameters of simulation and evaluate the strengths and weaknesses of our model,and write a memo to river managers on the arrangements of rafting.Key words:Camping；Computer Simulation;Status Transfer Equation1IntroductionThe number of visits to outdoor recreation areas has increased dramatically in last three decades.Among all those outdoor activities,rafting is often chose as a family get-together during May to September.Rafting or white water rafting is a kind of interesting and challenging recreational outdoor activity,which uses an inflatable raft to navigate a river or sea [1].It is very popular in the world,especially in occidental countries.This activity is commonly considered an extreme sport that usually done to thrill and excite the raft passengers on white water or different degrees of rough water.It can be dangerous.During the peak period,there are many tourists coming to experience rafting.In order to satisfy tourists to the maximum,we must make full use of our facilities in hand,which means we must do the utmost to utilize the campsites in the best way possible.What's more,to make more people feel the wildness life,we should minimize the encounters to the best extent;meanwhile no two sets of parties can occupy the same campsite at the same time.It is naturally coming into mind that we should consider where to stop,and when to stop of a party [2].In previous studies [3-5],many researchers have simulated the outdoor creation based on real-life data,because the approach is dynamic,stochastic,and discrete-event,and most recreation systems share these traits.But there exists little research aiming at describing the way that visitors travel and distribute themselves within a recreation system [6].Hence,in our paper,we consider the whole process of parties in detail and simulate every party ’s behavior,including the location of their campsites,and how long it will last for them to stay in a campsite to finish their itineraries.Meanwhile minimize the numbers of encounters.Aiming at showing the whole process of rafting,we firstly focus on analyzing the situation s of a single-party's rafting by using status transfer equation,then consider the problems of two parties'encounters on the river.Finally,after several times of simulation on the whole process of rafting,we obtain the optimal value of X .2Symbols and DefinitionsIn this section,we will give some basic symbols and definitions in the following for the convenience.Table 1.Variable Definition Symbols Definitioni v i p j i q ,S dThe velocity of oar or motor0-1variables on choosing rafting transportation0-1variables on the occupation of campsitesLength of the riverAverage distance between two campsites3General AssumptionsIn order to have a better study on this paper,we simplify our model by thefollowing assumptions:1)19:00to 07:00is people's sleeping time,during this time,people are stationedin the campsite.The total time of sleeping is 12hours,as rafting is an exiting sport game,after a day's entertainment,people have cost a lot of energy,and nearly tired out.So in order to have a better recreation for the next day,we set that people begin their trip at 07:00,and end at 19:00for a day's schedule.2)Oar-powered rubber rafts and motorized parties can successfully raft from FirstLaunch to Final Exit,there exist no accident over the whole trips.3)All the rubber rafts and motorized boats have the same exterior except velocities;we regard a rubber raft or a motorized boat as a party and don't consider the tourists individuals on the parties.4)There is only one entrance for parties to enter the recreation system.5)Regardless of the effects that the physical features of the river brings to oar andmotorized parties,that is to say we ignore the stream ’s propulsion and resistance to both kinds of rafting boats.Oar and motorized parties can keep the average velocity of 4mph and 8mph.6)Divide the whole river into N segments.4Analysis of This Rafting ProblemRafting is a very popular spots game world-wide.In the peak period of rafting,there are more people choosing to raft,it often causes congestion that not all people can raft at any time they want.Hence,it is important for managers to set an optimal schedule for every party (from our assumptions,we regard a rafting boat as a party)in advance.Meanwhile,the parties need to experience wildness life,so the managers should arrange the schedules which minimize the encounters'time between parties to the best extent.What's more,no two sets of parties can occupy the same site at the same time.Our aim is to determine an optimal mix of trips over varying duration (measured YXNj i t ,jT t∆KNumbers of campsites Numbers of parties Numbers of attraction sites Time of the i th party finishing the whole trip ranges from6days to 18daysRandom staying time at each campsiteDelay time of rafting from beginning Threshold value of encounterin nights on the river.That is to say,we must obtain an optimal value of X through lots of trails.This optimal value represents that the campsites have a high usage while more people are available to raft.The Long Big River is 225miles long,if we discuss the river as a whole and consider all the parties together,it will be difficult for us to have a clear recognition on parties'behaviors.Hence,we divide the river into N attraction sites.Each of the attraction sites has Y/N campsites since the campsites are uniformly distributed throughout the river corridor.So build up a model based on single-party ’s behavior of rafting in small distance.At last,we can use computer simulation to imitate more complex situations with various rafting boats and large quantities of parties.5Mathematic Models5.1Rafting of the Single-party Model （Status Transfer Equation [7]）From the previous analysis,in order to have a clear recognition of the whole rafting process,we must analyze every single-party's state at any time.In this model,we consider the situation that a single-party rafts from the First Launch to the Final Exit.So we formulate a model that focus on the behavior of one single-party.For a single-party,it must satisfy the following equation:status transfer equation.it represents the relationships between its former state and the latter state.State here means:when the i th party arrives at the j th campsites,the party may occupy the j th campsite or not.As a party can choose two kinds of transportation to raft:oar-powered rubber rafts(i v =4mph)and motorized rafts(i v =8mph).i v is the velocity of the rafting boats,and i p is the 0-1variables of the selecting for boats.Therefore,we can obtainthe following equation:)1(84i i i p p v −+=(i=1,2,…,X ).(1)where i p =0if the i th party uses motorized boat as their rafting tool,at thistime i v =8mph ;while i p =1when ,the i th party rafts with oar-powered rubber raft with i v =4mph.In fact,Eq.(1)denotes which kind of rafting boat a party can choose.A party not only has choice on rafting boats,but also can select where to camp based on whether the campsites are occupied or not.The following formulation shows the situation whether this party chooses this campsite or not:⎩⎨⎧=party previous a by occupied is campsite the 0,party previous a by occupied not is campsite the q ij ,1(2)where i =1,2,…,X ;j =1,2,…,Y .Where the next one can’t set their camp at this place anymore,that is to say thelatter party’s behavior is determined by the former one.As campsites are fairly uniformly distributed throughout the river corridor,hence,we discrete the whole river into segments,and regard Y campsites as Y nodes which leaves out (Y +1)intervals.Finally we get the average distance between th e j th campsite and (j+1)th campsite:1+=Y Sd (3)where is the length of the river,and its value is 225miles.What’s more,the trip-days for a party is not infinite,it has fluctuating intervals:h t h j i 432144,≤≤(4)where is the t i ，j itinerary time for a party ranges from 144hours to 432hours (6to 18nights).From Eq.(1),(2)and (3),the status transfer equation is given as follows:),...2,1,,...2,1(11,1,,Y j X i T q v d t t j j i i j i j i ==×++=−−−（5）The i th party’s arriving time at the j th campsite is determined by the time when the i th arrived at （j-1）campsite,the time interval i v d ,and the time T j-1random generated by computer shown in Eq.(5).It is a dynamic process and determined by its previous behavior.5.2The Analysis of Two Parties Parties’’Encounter on the River Our goal is to making full use of the campsites.Hence,the objective of all the formulation is to maximize the quantities of trips （parties ）X while consider getting rid of the congestion.If we reduce the numbers of the encounters among parties,there will be no congestion.In order to achieve this goal,we analysis the situations of when two parties’to encounter,and where they will encounter.In order to create a wildness environment for parties to experience wildness life,managers arrange a schedule that can make any two parties have minimal encounters with each other.Encounter is that parties meet at the same place and at the same time.Regarding the river as a whole is not convenient to study,hence,our discussion is based on a small distance where distance=d (Eq.3),between the j th and (j+1)th campsites.Finally the encounter problem of the whole river is transferred into small fractions.On analyzing encounter problem in d and count numbers of each encounter in d together,we get a clear recognition of the whole process and the total numbers of encounter of two parties.The following Figure 1represents random two parties rafting in d :Figure 1.Random two parties'encounter or not on the riverThe i th party arrives at j th campsite (t j k ,-t j i ,)time earlier than the k th party reaches the j th campsite.After t time,interval distance between the i th party and the k th party can be denoted by the following function:)()(t t t v t v t S ij kj i k j +−×−×=∆(6)Where k,i =1,2,…,X ,j =1,2,…,Y .k i ≠.Whether the two parties stationed on the j th campsite and(j +1)th campsite are based on the state of the campsites’occupation,yields we obtain:⎩⎨⎧=×01,,j k j i q q (i,k =1,2,…,X ;j =1,2,…,Y ;k ≠i )(7)Note that Eq.6is constrained by Eq.7,for different value of )(t S J ∆andj k j i q q ,,×we can obtain the different cases as follows:Case 1:⎩⎨⎧=×=∆10)(,,j k j i j q q t S (8)Which means both the i th and k th party don’t choose the j th campsite,they are rafting on the river.Hence,when the interval distance between the two parties is 0,that is )(t S J ∆=0,they encounter at a certain place in d on the river.Cases2:⎩⎨⎧=×=∆00)(,,j k j i j q q t S (9)Although the interval distance between the two parties is 0,the j th campsite is occupied by the i th party or the k th party.That is one of them stop to camp at a certain place throughout the river corridor.Hence,there is no possibility for them to encounter on the river.Cases 3:⎩⎨⎧=×≠∆10)(,,j k j i j q q t S ⎩⎨⎧=×≠∆00)(,,j k j i j q q t S (10)No matter the j th campsite is occupied or not for )(t S J ∆≠0,that is at the same time,they are not at the same place.Hence,they will not encounter at any place in d .5.3Overview of Computer Simulation Modeling to Rafting5.3.1Computer SimulationSimulation modeling is a kind of method to imitate the real-word process or a system.This approach is especially suited to those tasks which are too complex for direct observation,manipulation,or even analytical mathematical analysis (Banks and Carson 1984,Law and Kelton 1991,Pidd 1992).The most appropriate approach for simulating out-door recreation is dynamic,stochastic,and discrete-event model,since most recreation systems share these traits.In all,simulation models can reflect the real-world accurately.5.3.2Simulation for the Whole Process of Parties on Rafting [8]This simulation can approximate show a party’s behavior on the river under a wide rang of conditions.From the analysis of the previous study,we have known that the next party’s behavior is affected by the former one.Hence,when the first party enters the rafting system,there is no encounter,and it can choose every campsite.then the second party comes into the rafting system ,at this time,we must consider the encounter between them,and the limit on choosing the campsite.As time goes by,more and more parties enter this system to raft which lead to a more complex situation.A party who satisfies the following two conditions will be removed from the current order to the next order.So he can’t “finish his trip”right away.The two conditions are as follows:(1)He chooses a campsite where has been occupied by other parties.(2)He has two many encounters with other parties.So in order to determine typical trip itineraries for various types of rafting boat ,campsite,and time intervals （See Trip Schedule Sheet 1），we need to perform a series of trails run that can represent the real-life process of rafting based on these considerations,.A main flowchart of the program is shown in Figure 2.Figure2.Main simulation flowchartAfter several times of simulation,we obtain the optimal X(the numbers of campsites),minimal E(Encounter)and TP(Trip Time).Followed by Figure2,we simulate the behavior of a party whether it can enterthe rafting system or not in Figure3.Figure3.Sub flowchart5.3.3The Results of SimulationAfter simulating the whole process of parties rafting on the river,we get three figures(Figure4,Figure5and Figure6)to present the results.In order to simulate the rafting process more conveniently,we divide the whole river into31segments(31attraction sites),and input an initial value of Y=155(numbers of campsites),where there are5campsites in every attraction sites.We represent the times of campsites occupied by various parties on Figure2by coordinates(x,y),where x is the order of the campsites from0to155（these campsites are all uniformly distributed thorough the corridor）,and y is the numbers of each campsite occupied by different parties.For example,(140，1100)represents that at the campsite,there exists nearly1100times of occupation in total by parties over180days. Hence,the following Figure4shows the times of campsites’usage from March to September.Figure4.Numbers of campsites'usage during six-month period from March to SeptemberFrom Figure4,The numbers of campsites’usage can be identified the efficiency of every campsites’usage.The higher usage of the campsites,the higher efficiency they are.Based on these,we give a simple suggestion to managers(see in Memo to Managers).Figure5.the ratio of usage on campsites with time going byFigure5shows the changes of the ratio on campsites.when t=0,the campsites are not used,but with time going by,the ratio of the usage of campsites becomes higher and higher.We can also obtain that when t>20,the ratio keeps on a steady level of65%;but when t >176,the ratio comes down,that is,there are little parties entering the recreation system.In all,these changes are rational very much,and have high coincidence with real-world.Then we obtain1599parties arranged into recreation system after inputting the initial value Y=155,and set orders to every party from number0to number1599.Plotting every party's travelling time of the whole process on a map by simulating,as follows:Figure6.Every party’s travelling timeFigure6shows the itinerary of the travelling time,most of the travelling time is fluctuating between13days and15.3days,and most of travelling time are concentrated around14days.In order to create an outdoor life for all parties,we should minimize the numbers of encounter among different parties based on equations(6)and(7)：So we get every party’s numbers of encounter by coordinates(x,y),where x is the order of the parties from0to1600,y is the numbers of encounters.Shown in Figure7,as follows:Figure7.Every party’s numbers of encounterFigure7shows every party’s numbers of encounter at each campsite.From this figure,we can know that the numbers of their encounter are relatively less,the highest one is8times,and most of the parties don’t encounter during their trips,which is coincident with the real-world data.Finally,according to the travelling time of a party from March to September,we set a plan for river managers to arrange the number of parties.Hence,by simulating the model,we obtain the results by coordinate(x,y),where y is the days of travelling time,x is the numbers of parties on every day.The figure is shown as follows:Figure8.Simulation on travelling days versus the numbers of parties From Figure8.we set a suitable plan for river manager,which also provide reference on his managements.6Sensitive AnalyzeSensitive analysis is very critical in mathematical modeling,it is a way to gauge the robustness of a model with respect to assumptions about the data and parameters. We try several times of simulation to get different numbers of parties on changing the numbers of campsites ceaselessly.Thus using the simulative data,we get the relationship between the numbers of campsites and parties by fitting.On the basis of this fitting,we revise the maximal encounter times(Threshold value)continually,and can also get the results of the relationships between the numbers of campsites and parties by fitting.Finally,we obtain a Figure9denoting the relations of Y(numbers of campsites)and X(numbers of parties),as follows:Figure9.Sensitive analysis under different threshold values Given the permitted maximal numbers of encounters(threshold value=K),we obtain the relationships between Y(numbers of campsites)and X(numbers of trips). For example,when K=1,it means no encounters are allowed on the river when rafting;when K=2,there is less than2chances for the boats to meet.So we can define the K=4,6,8to describe the sensitivity of our model.From Figure9,we get the information that with the increase of K,the numbers of boats available to rafts till increase.But when K>6,the change of the numbers of boats is inconspicuous,which is not the main factor having appreciable impact on the numbers of boats.>In all,when the numbers of campsites(Y)are less than250,they would have a great effect on the numbers of boats.But in the diverse situations,like when Y>250, the effect caused by adding the numbers of campsites to hold more boats is not notable.When K<6,the numbers of boats available increases with the ascending of K, While K>6,the numbers of boats don’t have great change.Take all these factors into consideration,it reflects that the numbers of the boats can’t exceed its upper limit.Increase the numbers of campsites and numbers of encounter blindly can’t bring back more profits.7Strengths and WeaknessesStrengthsOur model has achieved all of the goals we set initially effectively.It is not only fast and could handle large quantities of data,but also has the flexibility we desire.Though we don’t test all possibilities,if we had chosen to input the numbers of campsites data into our program,we could have produced high-quality results with virtually no added difficulty.Aswell,our method was robust.Based on general assumptions we have made in previous task,we consider a party’s state in the first place,then simulate the whole process of rafting.It is an exact reflection of the real-world.Hence,our main model's strength is its enormousedibility and stability and there are some key strengths:(1)The flowchart represents the whole process of rafting by given different initialvalues.It not only makes it possible to develop trip itineraries that are statistically more representatives of the total population of river trips,but also eliminates the tedious task of manual writing.(2)Our model focuses on parties’behavior and interactions between each other,notthe managers on the arrangement of rafting,which can also get satisfactory and high-quality results.(3)Our model makes full use of campsites,while avoid too many encounters,whichleads to rational arrangements.WeaknessesOn the one hand,although we list the model's comprehensive simulation as a strength,it is paradoxically also the most notable weakness since we don’t take into account the carrying capacity of the water when simulates,and suppose that a river can bear as much weight as possible.But in reality,that is impossible.On the other hand,our results are not optimal,but relative optimal.8ConclusionsAfter a serial of trials,we get different values of X based on the general assumptions we make.By comparing them,we choose a relative better one.From this problem,it verifies the important use of simulation especially in complex situations. Here we consider if we change some of the assumptions,it may lead to various results. For example,(a)Let the velocity of this two kinds of boats submit to normal distribution.In this paper,the average velocity of oar-powered rubber rafts and motorized boats are 4mphand8mph,respectively.But in real-world,the speed of the boats can’t get rid of the impacts from external force like stream’s propulsion and resistance.Hence,they keep on changing all the time.(b)Add and reduce campsites to improve the ratio of usage on campsites.By analyzing and simulating,the usage of each campsite is different which may lead to waste or congestion at a campsite.Hence,we can adjust the distribution of campsites to arrive the best use.A Memo to River ManagersOur simulation model is with high edibility and stability in many occasions.It can imitate every party’s behavior when rafting so as to make a clear recognition of the process.Internal Workings of The ModelInputsOur model needs to input initial value of Y,as well as the numbers of attraction sites. Algorithm(Figure2,and Figure3)Our algorithm represents the whole process of rafting,so we can use it to simulate the process of rafting by inputting various initial values.OutputsBased on the algorithm in our paper,our model will output the relative optimalnumbers of parties X.Furthermore,we can also get other information,such as the interval time between two parties at First Launch,a detailed schedule for each party of rafting,the relationship between X and Y and so on.Summary and RecommendationsAfter100times of simulating,we come to two conclusions:(a)The numbers of parties(X)have relations with the numbers of campsites(Y), that is to say,with the increasing of Y,the increasing speed of X goes fast at the first place and then goes down,finally it tends to be steady.Hence,we advice river managers to adjust the numbers of campsites properly to get the optimal numbers of parties.(b)Add campsites to the high usage of the former campsites and deduce campsites at the low usage of the former campsites.From Figure4,we know that the ratios of every campsites are different,some campsites are frequently used,but some are not.Thus we can infer that the scenic views are attractive,and have attracted lots of parties camping at the campsite.so we can add campsites to this nodes.Else the campsites with low usage have lost attractions which we should reduce the numbers of campsites at those nodes.References[1]KarloŠimović，Wikipedia，Rafting，/wiki/Rafting.[2] C.A.Roberts and R.Gimblett，Computer Simulation for Rafting Traffic on theColorado River，COMPUTER SIMULATION FOR RAFTING TRAFFIC,2001, 19-30.[3] C.A.Roberts,D.Stallman，J.A.Bieri.Modeling complex human-environmentinteractions:the Grand Canyon river trip simulator，Ecological Modeling153(2002)181-196.[4]J.A.Bieri and C.A.Roberts，Using the Grand Canyon River Trip Simulator toTest New Launch Scheduleson the Colorado River，Washington DC,AWISMagazine,Vol.29,No.3,2000,6-10.[5] A.H.Underhill and A.B.Xaba，The Wilderness Simulation Model as aManagement Tool for the Colorado River in Grand Canyon National Park，NATIONAL PARK SERVICE/UNIVERSITY OF ARIZONA Unit SupportProject CONTRIBUTION NO.034/03.[6] B.Wang and R.E.Manning，Computer Simulation Modeling for RecreationManagement:A Study on Carriage Road Use in Acadia National Park,Maine,USA,USA,Vermont05405,1999.[7]M.M.Meerschaert，Mathematical Modeling(Third Edition).China MachinePress publishing,2009.[8]A.H.Underhill，The Wilderness Use Simulation Model Applied to Colorado RiverBoating in Grand Canyon National Park,USA，Environmental Management Vol.10,No.3,1986,367-374.。

美赛-数学建模模版

摘要第一段：写论文解决什么问题1．问题的重述其中主要的内容是a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An (effective plan) is crucial to………b. 直接指出问题：例1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.例4: After mathematically analyzing the ……problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goal is... that (minimizes the time )……….2．解决这个问题的伟大意义反面说明。

数学建模美国赛2002ABC

AMCM2002问题-A风和喷水池在一个楼群环绕的宽阔的露天广场上，装饰喷泉把水喷向高空。

刮风的日子，风把水花从喷泉吹向过路行人。

喷泉射出的水流受到一个与风速计（用于测量风的速度和方向）相连的机械装置控制，前者安装在一幢邻近楼房的顶上。

这个控制的实际目标，是要为行人在赏心悦目的景象和淋水浸湿之间提供可以接受的平衡：风刮得越猛，水量和喷射高度就越低，从而较少的水花落在水池范围以外。

你的任务是设计一个算法，随着风力条件的变化，运用风速计给出的数据来调整由喷泉射出的水流。

AMCM2002问题-B航空公司超员订票你备好行装准备去旅行，访问New York城的一位挚友。

在检票处登记之后，航空公司职员告诉说，你的航班已经超员订票。

乘客们应当马上登记以便确定他们是否还有一个座位。

航空公司一向清楚，预订一个特定航班的乘客们只有一定的百分比将实际乘坐那个航班。

因而，大多数航空公司超员订票?也就是，他们办理超过飞机定员的订票手续。

而有时，需要乘坐一个航班的乘客是飞机容纳不下的，导致一位或多位乘客被挤出而不能乘坐他们预订的航班。

航空公司安排延误乘客的方式各有不同。

有些得不到任何补偿，有些改订到其他航线的稍后航班，而有些给予某种现金或者机票折扣。

根据当前情况，考虑超员订票问题：航空公司安排较少的从A地到B地航班机场及其外围加强安全性乘客的恐惧航空公司的收入迄今损失达数千万美元建立数学模型，用来检验各种超员订票方案对于航空公司收入的影响，以求找到一个最优订票策略，就是说，航空公司对一个特定的航班订票应当超员的人数，使得公司的收入达到最高。

确保你的模型反映上述问题，而且考虑处理“延误”乘客的其他办法。

此外，书写一份简短的备忘录给航空公司的CEO（首席执行官），概述你的发现和分析。

AMCM2002问题-C如果我们过分扫荡自己的土地，将会失去各种各样的蜥蜴。

佛罗里达灌木蜥蜴是一种灰色或灰褐色小蜥蜴，遍布于佛罗里达中部和大西洋沿岸地区的沙质高地上。

数学建模美赛B题论文

2013建模美赛B题思路数学建模美赛B题论文摘要水资源是极为重要生活资料，同时与政治经济文化的发展密切相关，北京市是世界上水资源严重缺乏的大都市之一。

本文以北京为例，针对影响水资源短缺的因素，通过查找权威数据建立数学模型揭示相关因素与水资源短缺的关系，评价水资源短缺风险并运用模型对水资源短缺问题进行有效调控。

首先，分析水资源量的组成得出影响因素。

主要从水资源总量（供水量）和总用水量（需水量）两方面进行讨论。

影响水资源总量的因素从地表水量，地下水量和污水处理量入手。

影响总用水量的因素从农业用水，工业用水，第三产业及生活用水量入手进行具体分析。

其次，利用查得得北京市2001-2008年水量数据，采用多元线性回归，建立水资源总量与地表水量，地下水量和污水处理量的线性回归方程yˆ=-4.732+2.138x1+0.498x2+0.274x3根据各个因数前的系数的大小，得到风险因子的显著性为rx1>rx2>rx3(x1, x2，x3分别为地表水、地下水、污水处理量)。

再次，利用灰色关联确定农业用水、工业用水、第三产业及生活用水量与总用水量的关联程度ra =0.369852，rb= 0.369167，rc=0.260981。

从而确定其风险显著性为r a>r b>r c。

再再次，由数据利用曲线拟合得到农业、工业及第三产业及生活用水量与年份之间的函数关系，a=0.0019（t-1994）3-0.0383（t-1994）2-0.4332（t-1994）+20.2598;b=0.014（t-1994）2-0.8261t+14.1337;c=0.0383（t-1994）2-0.097（t-1994）+11.2116;D=a+b+c；预测出2009-2012年用水总量。

最后，通过定义缺水程度S=（D-y）/D=1-y/D，计算出1994-2008的缺水程度，绘制出柱状图，划分风险等级。

我们取多年数据进行比较，推测未来四年地表水量和地下水量维持在前八年的平均水平，污水处理量为近三年的平均水平，得出2009-2012年的预测值，并利用回归方程yˆ=-4.732+2.138x1+0.4982x2+0.274x3计算出对应的水资源总量。

数学建模美赛论文标准格式参考--中英文对照

Your Paper's Title Starts Here: Please Centeruse Helvetica (Arial) 14论文的题目从这里开始：用Helvetica (Arial)14号FULL First Author1, a, FULL Second Author2,b and Last Author3,c第一第二第三作者的全名1Full address of first author, including country第一作者的地址全名，包括国家2Full address of second author, including country第二作者的地址全名，包括国家3List all distinct addresses in the same way第三作者同上a email,b email,c email第一第二第三作者的邮箱地址Keywords:List the keywords covered in your paper. These keywords will also be used by the publisher to produce a keyword index.关键字：列出你论文中的关键词。

这些关键词将会被出版者用作制作一个关键词索引。

For the rest of the paper, please use Times Roman (Times New Roman) 12论文的其他部分请用Times Roman (Times New Roman) 12号字Abstract. This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.Please make the page settings of your word processor to A4 format (21 x 29,7 cm or 8 x 11 inches); with the margins: bottom 1.5 cm (0.59 in) and top 2.5 cm (0.98 in), right/left margins must be 2 cm (0.78 in).摘要：这个模板解释和示范供稿技术刊物有限公司时，如何准备你的供相机使用文件。

数学建模格式要点（大全5篇）

数学建模格式要点（大全5篇）第一篇：数学建模格式要点1编号问题。

公式用math type自动编号。

图在下面编号并命名。

表在上面编号并命名。

○2摘要问题。

首段本文研究什么，建立了什么模型，得到了什么结论。

对于各问题，考虑到○什么因素，建立什么模型，得到什么结果，最好能体现具体数据。

摘要很重要，一般来说至少占总分的20%，所以要尽量写得充实一点。

3参考文献的引用要体现出来。

○4要学会分层，突出要点。

○5表格尽量用三线表。

○6公式编号要右对齐。

○7图和表都要居中。

○8matlab里的图应该直接从matlab菜单里复制，最好不要剪切，否则会有灰色部分。

○9每段开头要空2个格。

○10画图形尽量用VISIO。

○11各参考文献都要在正文中体现出来。

○第二篇：数学建模既科学论文写作要点附件2科技学术论文的写作要求随着科学技术的发展，越来越多的学者涉及到学术论文的写作领域，那么怎样写学术论文，学术论文写作是怎样要求的，格式如何，下面就介绍一下学术论文的写作要求。

(一)题名（Title,Topic）题名又称题目或标题。

题名是以最恰当、最简明的词语反映论文中最重要的特定内容的逻辑组合。

论文题目是一篇论文给出的涉及论文范围与水平的第一个重要信息，也是必须考虑到有助于选定关键词和编制题录、索引等二次文献可以提供检索的特定实用信息。

论文题目十分重要，必须用心斟酌选定。

有人描述其重要性，用了下面的一句话：“论文题目是文章的一半”。

对论文题目的要求是：准确得体，简短精练，外延和内涵恰如其分，醒目。

对这四方面的要求分述如下。

1．准确得体。

要求论文题目能准确表达论文内容，恰当反映所研究的范围和深度。

常见毛病是：过于笼统，题不扣文。

关键问题在于题目要紧扣论文内容，或论文内容与论文题目要互相匹配、紧扣，即题要扣文，文也要扣题。

这是撰写论文的基本准则。

是论文撰写必须注意的问题。

2．简短精练。

力求题目的字数要少，用词需要精选。

至于多少字算是合乎要求，并无统一的“硬性”规定，一般希望一篇论文题目不要超出20个字，不过，不能由于一味追求字数少而影响题目对内容的恰当反映，在遇到两者确有矛盾时，宁可多用几个字也要力求表达明确。

2024数学建模美赛a题

2024数学建模美赛a题全文共四篇示例，供读者参考第一篇示例：2024年数学建模美赛A题的题目是一个挑战性的问题，需要参赛选手在短时间内进行思考和分析，然后给出一个合理的解决方案。

这个题目涉及到了数学建模、数据分析和计算机编程等多个领域，需要选手具备较强的逻辑思维能力和解决问题的能力。

题目要求参赛选手利用给定的数据集，对某个特定问题进行建模和分析，然后给出解决方案。

选手需要根据现有的数据集进行数据清洗和预处理，然后利用统计学和数学建模的方法对数据进行分析和建模，最终提供一个可行的解决方案。

在解题过程中，选手需要运用各种数学工具和编程语言来处理数据和进行计算，例如Python、R语言等。

选手还需要结合实际问题的背景知识和专业知识，对数据进行合理的解释和分析。

在解题过程中，选手需要注意数据的质量和可靠性，同时还需要对模型的准确性和稳定性进行评估。

最终，选手需要给出一个详细的报告，说明解决问题的方法和步骤，以及给出相关的结论和建议。

参加数学建模比赛可以锻炼选手的团队合作能力和解决问题的能力，同时也能够提高选手的数学建模和数据分析能力。

希望参赛选手在比赛中能够充分发挥自己的潜力，充分展现出自己的优势和才华，最终取得优异的成绩。

【字数不足，正在努力补充中……】第二篇示例：2024数学建模美赛a题分析数学建模是一门涵盖数学、计算机科学和工程等多学科知识的综合性学科，应用广泛，涉及领域广泛。

每年举办的数学建模比赛更是为广大热爱数学和挑战智力的学生提供了一个展示自己才华的舞台。

今天我们就来分析一下2024年数学建模美赛的a题。

让我们来看一下2024年数学建模美赛a题的具体问题描述：根据指定信息，设计出最佳的实体投资组合。

实体投资组合包括个人、公司、政府、银行等单位所投资的资金和资产，投资的目的是为了获得更高的回报率。

在实际投资中，投资者需要根据市场行情、经济形势等因素来选择不同的投资产品，以实现最大化的利润。

我们需要通过收集数据来分析市场行情和经济形势，以确定合适的投资产品。

2021年美国大学生数学建模竞赛题目A--真菌范文六篇(含Matlab源代码)

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2021年美国大学生数学建模竞赛题目A--真菌范文六
篇（含Matlab源代码）
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Your complete solution.

《数学建模》论文word模板

《数学建模》论文（宋体、小三、居中）题目：数学与信息科学学院学院：专业：班级：姓名：学号：2015 年月日1车道被占用对城市道路通行能力的影响摘要本文针对交通事故占用车道对城市道路通行能力的影响进行分析，通过采集附件1、附件2中的数据，对横断面实际通行能力、上游车流量与时间的函数关系运用拟合，通过判断车辆排队长度与实际通行能力、事故持续时间、上游车流量的关系，并建立了它们之间的微分方程模型.运用Matlab 软件，对模型进行分析和求解.对于问题一，为得出事故发生到撤离期间，横断面实际通行能力和时间的函数关系.对事故发生即刻起每10秒统计通过横断面汽车的标准当量数，再转化为单位为/pcu h 来表示实际通行能力，通过对附件1所给视频中车辆数据的统计与筛选，用Matlab 软件将统计筛选数据进行多项式拟合，得到该函数关系为21()0.305622.22941392.0532f t t t =-+.对于问题二，运用问题一的方法对处理附件2，同理得出函数关系为20()0.0106 2.34661365.7067f t t t =-+，根据两图曲线走势得出两图趋势大体相当，但图4.2较图4.1曲线平缓，说明图4.2的横断面实际通行能力受事故影响较小.产生差异的原因是根据附件3上左转流量比例35%、直行流量比例44% 和右转流量比例21%，即三车道比一车道车流量大，导致二三车道占用后需要换道的较多于一二车道占用，从而二三车道被占用时对横断面实际通行能力影响大，符合曲线走势.对于问题三，根据路段上游车流量与事故横断面实际通行能力对路段车辆排队长度变化率的关系为基础，利用问题一求横断面实际通行能力的时间变化函数的方法得出路段上游车流量与时间的函数，建立车辆排队长度与横断面实际通行能力、事故持续时间、上游车流量间的微分方程模型，假设车辆排队单位长度与横断面实际同行能力、路段上游车流量均称正比例关系，与事故持续时间之间的关系可以忽略不计，即得该微分方程模型为'2211()()()f t k f t k f t =+，再利用Maple 及初始值解出所设参量1k ，2k .对于问题四，由于题设条件符合上述模型，故将所给数据带入问题三所建模型当中求出时间即可.事故所处位置距离上游路口变为140米，根据视频中的实地情况，该路段中的支路位置将处在事故发生的下游，会相对减弱道路拥堵程度即提高实际通行能力，则运用原始模型求出时间相对应该偏小，但误差不会太大.关键词：实际通行能力；微分方程模型；拟合；Maple 软件目录(由域生成的目录，交稿前此页可以保留或删掉)摘要 (1)1、问题重述与问题分析 (3)1.1 问题重述（大家一定要注意样式的使用） (3)1.2 问题分析 (3)2、模型假设 (4)3、符号说明 (4)4、模型的建立与求解 (5)4.1 问题一的模型建立与求解 (5)4.2 问题二的模型建立与求解 (5)4.3 问题三的模型建立与求解 (6)4.4 问题四的求解 (7)5、模型的评价与改进 (8)5.1 对现有模型进行评价 (8)5.2 对现有模型的改进 (8)参考文献 (8)附录A (9)附录B (10)21、问题重述与问题分析1.1 问题重述（大家一定要注意样式的使用）随着城市化进程的加快，城市车辆数量剧增，交通事故日显突出，交通事故车道被占用导致车道或道路横断面通行能力在单位时间内降低.由于城市道路具有交通流密度大、连续性强等特点，一条车道被占用，也可能降低路段所有车道的通行能力，即使时间短，也可能引起车辆排队，出现交通阻塞.如处理不当，甚至出现区域性拥堵.就针对交通事故降低车道通行能力方面解决如下问题：(1) 描述视频中交通事故发生至撤离期间,事故所处横断面实际通行能力的变化过程.(2) 分析说明同一横断面交通事故所占车道不同对该横断面实际通行能力影响的差异.(3) 构建数学模型，分析交通事故所影响的路段车辆排队长度与事故横断面实际通行能力、事故持续时间、路段上游车流量间的关系.(4) 假如视频1（附件1）中的交通事故所处横断面距离上游路口变为140米，路段下游方向需求不变，路段上游车流量为1500/pcu h,事故发生时车辆初始排队长度为零，且事故持续不撤离.则求从事故发生开始到车辆排队长度将到达上游路口的时间.1.2 问题分析本题给出了两个交通事故发生时道路通行情况的视频及其示意图，通过视频采集数据来建立数学模型.针对问题一：根据实际通行能力的概念，在交通事故出现之前，道路保持基本通行能力，不必考虑实际通行能力，在事故出现即刻到撤离时间段内，通过视频1每10秒逐一统计标准车当量数（统计表见附件6），再转化为/pcu h为单位表示实际通行能力，利用Matlab软件将所统计筛选的数据拟合出一条曲线，筛选的目的是将视频中出现跳跃产生模糊的剪去，该曲线的走势及拟合出的函数反应实际通行能力的变化过程.针对问题二：就视频2采用问题一相同的方法统计，拟合出一条曲线及函数，将曲线一二进行比较，从而得出所占车道不同对横断面实际通行能力影响的差异.产生差异的原因是根据附件3上左转流量比例35%、直行流量比例44% 和右转流量比例21%，说明三车道比一车道车流量大，则所占二三车道比一二车道对降低实际通行能力影响大.3针对问题三：构建路段车辆排队长度与事故横断面实际通行能力、事故持续时间、路段上游车流量间的模型，利用问题一所求出的实际通行能力的函数，用同样的方法求出上游车流量的函数关系及车辆排队长度与时间的函数关系（统计表见附录）.根据车流量排队长度的变化率与横断面实际通行能力、路段上游车流量间的关系为基础，建立一个微分方程模型，再利用Maple软件及初始值解微分方程中的参量.针对问题四：问题四条件基本吻合问题三所建的模型，则直接将数据带进模型求出即可.事故所处位置距离上游路口变为140米，该路段中的支路位置将处在事故发生的下游，会相对减弱道路拥堵程度即提高实际通行能力，则运用原始模型求出时间相对应该偏小，但误差不会太大，则直接代入模型求解.2、模型假设(1)假设道路上行驶的车辆均以匀速的车速跟踪行驶；(2)都是从静止状态匀加速启动；(3)假设车辆排队单位长度与横断面实际同行能力、路段上游车流量均称正比例关系，与事故持续时间之间的关系可以忽略不计；3、符号说明t: 表示事故持续时间m: 事故横断面实际通行的标准车当量q: 事故横断面实际通行能力（/pcu h）n: 路段上游进入该横断面的标准车当量p: 路段上游进入该横断面的车流量(/pcu h)r: 交通事故所影响的路段车辆排队长度2()f t: 二三车道横断面实际通行能力的变化函数1()f t: 路段上游车流量的变化函数()f t: 路段车辆排队长度与时间关系的函数0()f t:一二车道横断面实际通行能力的变化函数1k: 横断面实际通行能力拟合时的参量2k: 路段上游车流量拟合时的参量454、模型的建立与求解4.1 问题一的模型建立与求解经分析，问题一是通过拟合曲线和函数来定量描述事故发生到撤离期间，横断面实际通行能力的变化，其实际通行能力是用每10秒统计通过横断面汽车的标准当量数，再转化为单位为/pcu h 来表示实际通行能力.图4.1实际通行能力的时间变化图（占用二三车道）是通过Matlab 拟合得到，从而得到实际通行能力与时间的关系21()0.305622.22941392.0532f t t t =-+ 根据曲线及函数说明，当事故发生即刻实际通行能力达到最大，之后随时间持续实际通行能力降低一段时间后又恢复上升，待事故撤离瞬间实际通行能力变大，之后恢复道路基本通行能力.可得出实际通行能力与事故持续时间之间并非单调关系，近似拟合方程有个最低点.图4.1 实际通行能力的时间变化图（占用二三车道）4.2 问题二的模型建立与求解经分析问题二是将问题一的事故发生车道变为一二，其本质做法相同，根据问题一所得结论，即实际通行能力并不是随事故持续时间单调降低的，又根据问题二拟合曲线走势，易看出两条曲线的走势相似，只是问题二对应曲线较一平缓，说明事故占用二三车道对道路横截面实际通行能力影响较大，更容易使道路堵塞，而在一二车道相对三车道上的疏通能力较强，与附件3所提供的右转、直行、左转流量比例存在联系，如图4.2实际通行能力的时间变化图（占用一二车道）图4.2 实际通行能力的时间变化图（占用一二车道）4.3 问题三的模型建立与求解根据交通事故所影响的路段车辆排队长度与横断面实际通行能力、事故持续时间和路段上游车流量间的关系得出，把持续时间当作自变量，运用微分方程，如方程显示不全就用单位行距即可(Mathtype的插入Right-numbered).67(8.1)由问题一及（1.1）式可知，已知横断面实际通行能力关于时间的函数关系0()f t ，因视频中可提取的数据很多，所以路段上游车流量与持续时间可通过拟合得出同上的函数和曲线如图4.3上游车流量的时间变化图()!!!n r n r - .再用相同的方式得出路段车辆排队长度随时间变化的函数关系及曲线.由假设条件知假设车辆排队单位长度与横断面实际同行能力、路段上游车流量均称正比例关系，与事故持续时间之间的关系可以忽略不计.根据'2211()()()f t k f t k f t =+利用Maple 软件及初始值计算得出1k 2k (如表1.1所示)则模型求得函数为1k = —1.6903， 2k =1.8 ,即12() 1.6903() 1.8()f t f t f t '=-+.表1.1 示例表格五号黑体（尽可能用三线表）五号五号五号宋体宋体4.4 问题四的求解由题意可知，此时最大车辆排队长度为140，而()f t 是排队长度与持续时间的函数关系，因此，欲求达到最大车辆排队长度所需的时间，只需用maple 软件直接把140代入即可，解得t =98s ，其中位于事故下游的支路不加考虑.5、模型的评价与改进5.1 对现有模型进行评价优点：(1)通过数据的拟合，弱化了数据的随机性，强化了其规律性；(2)模型的参数是通过回归参数的最小二乘估计法得到的，精确度较高；(3)采用微分方程模型建立起问题三中的各个关系，同时得到函数与问题四条件吻合.(4)在采用微分方程的同时考虑周期性相结合更切合实际.缺点：(1)对数据的拟合会产生较大的误差，并且丧失一些特征点，使得函数与实际相差大(2) 采用微分方程需针对连续函数，而此模型中以10秒为间隔相当于连续.会存在一定偏差.5.2 对现有模型的改进未考虑红绿灯对路段上游车流量的影响，即对模型所建立的函数没有周期性的影响.参考文献[1]姜启源，数学模型（第二版），北京:高等教育出版社，1993年.[2]王松桂，陈兰红，陈立萍，论线性统计模型的应用，中国科学，28（2）：1228-1239，1999年.[3]王高雄，论文的模板，/,2014年5月21日.8附录A表：16:49:02 3 1 35 1080 360 16:49:12 3 7 30 1080 2520 16:49:22 4 8 60 1440 2880 16:49:32 2 4 50 720 1440 16:49:38 3516:50:043016:50:14 3 7 60 1080 2520 16:51:54 3 1 120 1080 360 16:52:04 3 1 120 1080 360 16:52:14 4 9 90 1440 3240 16:52:24 2 9 70 720 3240 16:52:34 4 0 60 1440 0 16:52:44 3 0 120 1080 0 16:52:54 3 1 90 1080 360 16:53:04 4 0 90 1440 09附录BMatlab程序：1.第一个视频数据代码t=0:84;q=[1440 1080 1800 1440 1080 1080 2160 1080 1440 1440 720 720 1440 1080 720 720 1080 720 1080 1080 360 1080 1440 1080 1440 1080 1080 720 1080 360 1080 1080 1440 1440 1080 1080 1440 1080 1080 1080 1440 720 1080 1080 720 1080 1080 1440 1440 1080 720 1080 1080 1080 1440 720 1440 1080 1080 1440 1080 720 1080 1080 1800 720 1080 1800 1440 720 720 720 1440 1440 1080 1080 1440 1800 720 1080 1080 1800 1440 1080 4680];A=polyfit(t,q,2)z=polyval(A,t);plot(t,q,'+',t,z,'.')2.第二个视频数据代码t=0:174;q=[720 360 1800 1440 1800 1800 720 1800 2160 1440 1080 1080 1080 720 720 1800 1800 1080 1440 1440 2160 1800 720 1080 1440 1440 1080 2160 1440 720 1080 1080 1800 1800 1080 360 720 1800 2160 1440 1080 720 1080 1440 1440 1080 1440 1440 1440 1440 1800 1800 2160 1440 1080 1440 1080 1440 720 720 360 1080 1440 1800 1080 720 720 1800 1080 1440 1080 1080 1440 1080 1800 720 720 360 360 1440 1440 1800 1080 1800 1440 1080 1080 1800 1080 1080 720 1440 1440 1800 1440 1440 1440 1440 1080 1080 1080 1440 1440 1080 1080 1440 1080 1080 1080 1440 1440 1080 1080 720 1080 1440 1080 1440 1440 1080 1800 1080 1440 1440 1440 1080 1080 1440 1440 1080 1080 1440 1440 1800 1080 1440 1440 1080 1440 1080 1440 1080 1440 1080 1080 1440 1080 1080 360 720 1080 1080 1440 1440 1080 1440 1440 1080 1440 1080 1440 1080 720 1080 1080 1080 1440 1800 1440 1440 1080 1440 1440 1440 1440];12 10 11 10 14 13 24 13];A=polyfit(t,q,2)z=polyval(A,t);plot(t,q,'+',t,z,'.')103.路段上游车流量与时间的函数源程序：t=0:92;y=[360 360 360 2880 1440 0 360 360 0 1800 2520 0 0 360 360 2520 2880 0 0 0 360 1800 1800 0 0 360 360 2520 3240 2160 0 0 0 2520 1800 1080 360 0 360 2520 2880 1440 0 0 2520 3240 1440 0 0 0 3600 2880 1440 360 360 360 3240 3240 0 0 360 0 3960 2520 1440 0 2520 2880 3600 1440 0 0 0 0 2160 1800 720 0 0 0 0 0 0 2880 0 0 3600 2520 0 0 720 0 1800];A=polyfit(t,,p,3)z=polyval(A,t);plot(t,p,'+',t,z,'.')4.路段车辆排队长度与时间的函数源程序：t=0:87;r=[90 90 60 40 60 80 50 30 10 0 0 0 0 0 0 0 0 0 30 50 40 30 0 30 30 30 10 0 0 0 60 40 40 30 30 45 30 60 50 35 30 60 50 35 30 60 30 30 40 120 60 60 45 35 45 120 120 90 70 60 120 90 90 60 60 60 100 120 120 80 90 120 120 120 90 90 90 90 100 90 60 90 90 90 120 120 120 0];A=polyfit(t,r,3)z=polyval(A,t);plot(t,r,'+',t,z,'.')11。

数学建模范文模板

数学建模范文模板一、问题分析1. 问题的背景与意义：（1）简要介绍问题的相关背景与意义；（2）问题的研究价值和应用前景。

2. 问题的具体描述：（1）详细描述问题的具体内容，包括已知条件和需要求解的问题；（2）对问题进行可视化分析，如示意图、数据表格等。

3. 问题的假设：（1）对问题进行一些合理的假设，以简化问题；（2）明确各种假设的合理性和局限性。

二、模型的建立1. 模型的基本思路：（1）根据问题的具体情况，提出解决问题的基本思路、方法或策略；（2）形成数学模型的核心思想。

2. 模型的符号定义：（1）对模型中所用到的符号进行明确的定义；（2）解释符号的含义和用途。

3. 模型的建立与求解：（1）根据问题的具体要求，建立相应的数学模型；（2）通过数学方法对模型进行求解，得到问题的最优解或近似解。

三、模型的验证与分析1. 模型的验证：（1）对建立的数学模型进行验证，检验模型的合理性；（2）通过比较模型的预测结果与现实数据或实验结果的吻合程度，判断模型的有效性。

2. 模型的结果与讨论：（1）分析模型的求解结果，阐述其具体含义和实际意义；（2）对模型的局限性和改进方向进行讨论。

四、模型的应用与推广1. 模型的应用：（1）对模型的应用范围和条件进行说明；（2）通过实际案例分析，探讨模型在解决问题中的实际应用。

2. 模型的推广：（1）对模型的推广适用性进行分析；（2）针对其他类似问题，探讨模型的推广和改进方向。

五、总结与展望1. 研究总结：（1）对已完成的研究工作进行总结，强调研究的主要成果和创新之处；（2）指出问题研究中的不足和需要进一步探索的方向。

2. 研究展望：（1）对未来的研究方向和重点进行展望；（2）对进一步提高模型的精度、拓宽应用范围等方面提出建议。

美国中学生数学建模竞赛获奖论文

Abstract
In this paper, we undertake the search and find problem. In two parts of searching, we use different way to design the model, but we use the same algorithm to calculate the main solution. In Part 1, we assume that the possibilities of finding the ring in different paths are different. We give weight to each path according to the possibility of finding the ring in the path. Then we simplify the question as pass as more weight as possible in limited distance. To simplify the calculating, we use Greedy algorithm and approximate optimal solution, and we define the values of the paths(according to the weights of paths) in Greedy algorithm. We calculate the possibility according to the weight of the route and to total weights of paths in the map. In Part 2, firstly, we limit the moving area of the jogger according to the information in the map. Then we use Dijkstra arithmatic to analysis the specific area of the jogger may be in. At last, we use greedy algorithm and approximate optimal solution to get the solution.

数学建模美赛写作模版(包含摘要、格式、总结、表格、公式、图表、假设)

论文reference 格式中文解说版总体要求1 正文中引用的文献与文后的文献列表要完全一致.ν文中引用的文献可以在正文后的文献列表中找到；文献列表的文献必须在正文中引用。

2 文献列表中的文献著录必须准确和完备。

3 文献列表的顺序文献列表按著者姓氏字母顺序排列；姓相同,按名的字母顺序排列；著者姓和名相同，按出版年排列。

νν相同著者，相同出版年的不同文献，需在出版年后面加a、b、c、d……来区分，按文题的字母顺序排列。

如: Wang, M. Y。

（2008a). Emotional……Wang, M。

Y。

(2008b). Monitor……Wang，M。

Y. (2008c). Weakness……4 缩写chap. chapter 章ed。

edition 版Rev. ed。

revised edition 修订版2nd ed. second edition 第2版Ed. (Eds。

）Editor （Editors）编Trans. Translator（s) 译n.d. No date 无日期p。

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）page （pages）页Vol. Volume (as in Vol。

4) 卷vols。

volumes （as in 4 vols.）卷No。

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Part 部分Tech. Rep. Technical Report 技术报告Suppl. Supplement 增刊5 元分析报告中的文献引用ν元分析中用到的研究报告直接放在文献列表中，但要在文献前面加星号＊。

并在文献列表的开头就注明*表示元分析用到的的文献。

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美赛写作模板及参赛经验分享

Tittle of paperSummary/Abstract Key words:I.Introduction（引言）Organ transplantation is a preferable treatment for the most serious forms of end-stage diseases. In recent years, advances in medical science and technology have made solid organ transplantation an increasingly successful and common medical procedure, a literal ''second chance at life". Not only does it offer the best hope for complete rehabilitation, but it has also proved to be the most cost-effective of all treatment options, including dialysis. Consequently, more and more people are benefiting from organ transplants and their survival rates are steadily improving. The surgical techniques involved have been mastered for half a century and are now considered as routine. The two main sources of kidneys for transplantation are deceased-donor kidneys and live-donations from family and friends. However, unfortunately, there is a considerable shortage of donor organs, compared to demands. As a matter of fact, efficient matching and allocation of organs donated has become an exigent problem.The United Network for Organ Sharing (UNOS), as the operator of the Organ Procurement and Transplantation Network (OPTN), is responsible for transplant organ distribution in the United States. UNOS oversees the allocation of many different types of transplants,including liver, kidney, pancreas, heart, lung, and cornea.Focusing on kidney transplantation, based on UNOS Kidney Allocation Model, we develop a mathematical model for US transplant networks. First, incoming organs are matched with waiting candidates by medical institutions considering the factors as ABO blood compatibility, the degree of recipient major HLA mismatch in order to obtain a matching degree applied on the allocation part. After that, from the patients’perspective, on the basis of linear regression, priority weight is defined by pondering age, disease severity, time on waiting, PRA level, and region. Applying this mechanism of ranking, we realize MWBM (Maximum Weight Bipartite-graph Matching) and SMGS (Stable Matching based on Gale-Shapley algorithm). MWBM focuses on the optimal assignment of donors following the algorithm of bipartite-graph maximum weight matching; SMGS emphasizes the process of exchanges in order to obtain the stable exchanges between donors and candidates on the waiting list.II.T he Description of Problem（问题重述)III.Basic Assumptions●The level of mismatch is only relative to the number of antigens.●The data and information are accurately registered according tothe medical measures●The data and information are refreshed in time according to thestatus of the patients●No differences in the quality of the donor kidneys●The quality of the donor kidney is constantIV.D efinitions and Notations●Kidney transplantation: A kidney transplant is a surgical procedure to implant a healthykidney into a patient with kidney failure.●Prioritization●MD: Matching Degree●PW: Prioritization weight●MWSM: Maximum Weight Bipartite Matching●SMGS: Stable Matching based on Gale-Shapley algorithm或V.ModelsThrough the investigation of US transplantation network, we draw a general picture of the mechanism. With reference to some resources available on the website of UNOS, a flow chart (Figure 1) is developed showing the procedure of the network.Currently, the initial waiting list is composed of patients whoare waiting for a kidney or combined kidney-pancreas transplant. For the first time, the patients are requested to show the correct and scientific information to the US kidney transplant network which is needed for donor-recipient matching, the ranking of patients on the waiting list, and determining the outcome of those transplanted. The patients’waiting lists are composed of initial patients, historical patients and unsuccessful recipient after transplantation. Historical patients refer to registered patients whose status have changed and have an influence on the procedure.A patient is taken off the waiting list when a graft is offered and accepted by that patient or the patient is dead while waiting for a transplant. Unsuccessful recipients refer to the patients who have a bad result of transplantation calling for transplantation again, as it is so-called relistFigure 1. A schematic depicting the steps occurring in thetransplantation networks......Table 1.Survival rate involving HLA mismatchVI.C onclusions.Our model for the optimal allocation of the donor organs is established by three modules, procurement of MD and PW, optimal assignment by MWBM model and Stable Matching of Gale-Shapley algorithm. The model has offered a convincing procedure of the allocation with the ……VII.Strengths and weaknesses(模型优缺点)Strengths……WeaknessesVIII.References注意文献的积累，不要等到文章写完再去重新寻找文献。