exclusively专门
undobtedly毫无疑问的
notable 值得注意的
tremedous/significant极大的
notion概念
definition定义——define
Interpret……as…… 理解……为
invoke(+模型援引，引用
equation方程式，等式
function因变量——提示符号的含义
matrix矩阵，模型
constant 常数，常量It requires I t o be a constant for …to be true
algorithm演算方法——a general algorithm 通用算法simplify the algorithm 简化算法we have produced a general algrrithm to solve this tpye of problems.
derivative微分，倒数antiderivative 不定积分
optimal results 最优结果
invesgate the problem from different point of view调查问题——investgation调查survey 调查
subproblem 子问题，次要问题——major problem 主要问题
metric 度量标准，指标
digit 数字delete some digits
element /component 元素
解题思路seek/explore——
explore different ideas探索不同的想法
we seek to device a new model for solving the problem by exploring the new direction suggested by their investigations.
解决方案design/device ——develop/establish/conduct
Based on our analysis, we design a model for the problem using integral linear programming(线性积分). We then devise a polynominal-time apprximation algorithm to
produce near optimal https://www.doczj.com/doc/c4767588.html,ing integral linear programming.We then device a polynominal-time approximation to
We conduct sensitivity analysis on…to find…xxx analysis is also performed.
解决结果tackle/solve
We tackle the problem using the new technique we developed in the previous section.While it is difficult to solve the problem completely, we are able to solve a major subproblem.
计划与打算approach/propose
We approach the problem using the proposed method.
We propose a new approach to tackling the problem.
词组
Basedon…以……为基础
According to根据
Devide …into…——subdivide into细分
…is applied to…使用了……模型来……——we apply our model into将我们的模型运用于
Model proves to be efficient in other sports.模型被证明在其他方面有效
….,which indicates that………反映了
…,which led to the change of…导致了……的变化
We…..only to find that..我们……只是发现了……
… doesn’tmatter……是无关的
Take…as example/as a case study举例
formulate and justify the assumptions 阐述并证明假说
design/establish a model设计模型
devise an algorithm 设计一个运算法/计算程序
carry out numerical simulations 进行数学模拟
for our problem a relationship exists that(… 我们的问题中存在一个关系式，使……
we will assume/suppose that…我们假设……
compare with different approaches 与不同的措施相比较
There are at least two notions of where the sweet spot should be—an impact location on the bat that either
· minimizesthe discomforttothehands, or
· maximizes the outgoing velocity Of the ball.
We focus exclusively on the second definition我们专注于第二种定义
We interpret the error of +2 as a normal distribution,.一with standard deviation of 1。
To illustrate the upon two points,we choose the following two norms.为了说明上述两个观点，我们选择了下面两种标准
What follows in the chapter will hammer at…本章节接下来会集中……
…system works by………系统通过……工作
类比手法as for…..,similarly there are…
对比a ….while b…
连缀词fir st,…second,…,after that…,at last…
Summary
1Restatement of the problem（introduction）
Problem background,previous study,our work
2Assumptions
（symbols,definitions and assumptions）
3Justification ofOur Approach
4The Model
4．1 Dissatisfaction of a passenger needing a connection
4．2 Dissatisfaction of a passenger not needing a connection
4．3 Total dissatisfaction on an aircraft
5Testing the Model
6Results
7Strengths and Meaknesses
References
标题：
how to please most of the people most of the time
locating a drug runner:miami vice style
centroids,clusters,and crime:anchor ing the geographic profile s of serial criminals(固定轮廓
loading two railroad cars
taking the mystery out of sudoku difficulty:an oracular model
计算
The total wins a could be calculated as follows:
a = aaii(3.1)
-Where aaii denotes wins for the iitt? year. The total loses b could be calculated as follows: Let r denotes …,then it can be calculated as follows:
Symbols for ………的符号（后接表格）symbol——definition
summary
·赛题重述与阐明：用自己的语言描述将要解决的问题。
·解释假设条件及其合理性：强调建模所用的假设，而且清楚地列出建模所需的所有变
量。
·模型设计及合理性论证：指出所用模型的类型或构造新的模型。
·描述模型的测试情况及灵敏度分析：包括误差分析等检测项目。
·优缺点讨论：包括模型及解题方法的优点与不足。
长度稍超过半页即可。
In the last few years，the 9-by-9 puzzle grid known as Sudoku has gone from being a popular Japanese puzzle to a global craze.用吸引人的语言激发读者兴趣
不包含太多的细节
简明扼要地将解题方法描述清楚，包括全部要点及主要思路，并阐明所得出的结论。如果有数值运算，还应该给出重要的计算结果
最好不要在摘要中使用数学公式。
We study the sweet spot on a baseball bat. We begin by establishing a model of a bat hitting a ball by analyzing a video of a professional https://www.doczj.com/doc/c4767588.html,ing this model, we determine that hitting a ball with a bat can be seen as an imperfect collision of two balls,where the bat is replaced by a hitting ball.
In order to….,we…
To evaluate the accuracy of the two models,…is defined.It is supposed to…为了评价两个模型的准确性
Introduction——
1重述赛题
2明确解题目标（可以用列表形式）
3澄清原题中的模糊概念
4对现有文献在相似问题的研究进行综述和评论
5简要描述参赛小组的解题方法和主要结果
已有调查previous research：
There are some models which can solve such problem.One is..,another is…
…provides a comprehensive and rational framework for…
我们的工作our work
In section 1,we…,section 2 proviedes/shows…
主体body
描述模型设计（列出和论证建立模型所用的假设，对赛题的分析）
1将模型设计所用的假设条件一一列出并解释清楚
Criminal's movement is unconstrained.Because of thedifficulty of finding real-world distance data, we invoke the 'Manhattan assumption’:There are enough streets and sidewalks in a sufficiently grid-like patternthat movements along real-world movement routes is the same as 'straight-line’movement in a space discretized into city blocks
We have produced a general algorithm to solve this type ofproblem, but for our problem arelationship exists that greatlysimplified the algorithm.
We will make the following simplifying assumptions.——简化条件要在模型缺陷中讨论
结尾conclusion
描述模型测试方法以及所得到的结果
结论在结尾的开始就写出来
对结论进行适当的讨论，指出哪些是作者观点哪些是结果
模型中用到的参数值的变化对模型及结论产生的影响
再次指出论文缺陷
假如有充足时间和计算资源，能够解决的问题
Attention：
1使用we做人称，需要指明作者用the authors/one of the authors
使用they表示泛指的第三人称a student should be careful not to lose their books.
2使用简单时态（一般现在时，一般过去时，一般将来时）定理和事实用一般过去式3使用主动语态the model produced a disirable conclusion
4写简单句。一句话表达一个意思，谓语紧跟主语，不要包含副词。
5写简短的段落（停顿）
6使用具体的词汇
7减少琐碎的细节
8突出重点重要的论点用黑体字写在段落之首新概念也用黑体assumption可以直接用列表
9删掉多余词汇名词换成动词find the solution—solve
10使用并列短语强调联系if a is a root of the function x, then b is a root of the function y. 11避免单调重复
first we solved an equation, the solution of the first equation allowed us to solve the second equation.
We know equation a has a solution, which implies equation b has a solution.thus, equation c also has a solution.(有关联句的时候还是要用复杂句的
12不使用同一词汇描述不同的对象
We ran into several obstales when trying to solve the problem.
13使it指代的名词显而易见
14不直接渲染，不使用感叹号
15单数可数名词前一定要加冠词唯一the 泛指a
在表示某一类物体的名词前不加冠词
16不用firstly,已经过时了，可以改用begin by
17标题的重要的词要大写
18文字叙述字体times new roman 小节与下节标题与正文不同
19不在标题中使用数字符号
20 数字变量符号字母使用斜体
21矩阵符号用黑斜体大写，矩阵元素用黑斜体小写
22句中出现的同一符号读法一致，都是is equal to
23 不用符号取代文字，since…, we know…
24数字用文字书写，除了the rod is 5 feet long.是计量单位的一部分
25避免不必要的上下标，使用x，yax+by，顺序尽量一致
26删除只用过一次的上下标
27给图标编号并使用简要的文字说明。表明变量，标题行，图例。
28不要把数字符号用作句子的开头
29两个相邻的数字表达式用文字隔开
中间加上we have
30 if与then匹配
31新术语在第一次定义的时候使用黑体
32不要为表达式添加冒号或者其他标点符号。表达式可以同行也可以单行，看重要性。大段式子用单行。尽量用加号，减号断行。一系列等式要在等号处对齐！包括连等式。Following,below,as follows,用冒号
33省略号：
问题A：除非超车否则靠右行驶的交通规则 在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。建立数学模型来分析这条规则在低负荷和高负荷状态下的交通路况的表现。你不妨考察一下流量和安全的权衡问题,车速过高过低的限制，或者这个问题陈述中可能出现的其他因素。这条规则在提升车流量的方面是否有效？如果不是，提出能够提升车流量、安全系数或其他因素的替代品（包括完全没有这种规律）并加以分析。在一些国家，汽车靠左形式是常态，探讨你的解决方案是否稍作修改即可适用，或者需要一些额外的需要。最后，以上规则依赖于人的判断，如果相同规则的交通运输完全在智能系统的控制下，无论是部分网络还是嵌入使用的车辆的设计，在何种程度上会修改你前面的结果？ 问题B：大学传奇教练 体育画报是一个为运动爱好者服务的杂志，正在寻找在整个上个世纪的“史上最好的大学教练”。建立数学模型选择大学中在一下体育项目中最好的教练：曲棍球或场地曲棍球，足球，棒球或垒球，篮球，足球。 时间轴在你的分析中是否会有影响？比如1913年的教练和2013年的教练是否会有所不同？清晰的对你的指标进行评估，讨论一下你的模型应用在跨越性别和所有可能对的体育项目中的效果。展示你的模型中的在三种不同体育项目中的前五名教练。 除了传统的MCM格式，准备一个1到2页的文章给体育画报，解释你的结果和包括一个体育迷都明白的数学模型的非技术性解释。 使用网络测量的影响和冲击 学术研究的技术来确定影响之一是构建和引文或合著网络的度量属性。与人合写一手稿通常意味着一个强大的影响力的研究人员之间的联系。最著名的学术合作者是20世纪的数学家保罗鄂尔多斯曾超过500的合作者和超过1400个技术研究论文发表。讽刺的是,或者不是,鄂尔多斯也是影响者在构建网络的新兴交叉学科的基础科学,尤其是，尽管他与Alfred Rényi的出版物“随即图标”在1959年。鄂尔多斯作为合作者的角色非常重要领域的数学,数学家通常衡量他们亲近鄂尔多斯通过分析鄂尔多斯的令人惊讶的是大型和健壮的合著网络网站(见http:// https://www.doczj.com/doc/c4767588.html,/enp/)。保罗的与众不同、引人入胜的故事鄂尔多斯作为一个天才的数学家,才华横溢的problemsolver,掌握合作者提供了许多书籍和在线网站(如。,https://www.doczj.com/doc/c4767588.html,/Biographies/Erdos.html)。也许他流动的生活方式,经常住在带着合作者或居住,并给他的钱来解决问题学生奖,使他co-authorships蓬勃发展并帮助构建了惊人的网络在几个数学领域的影响力。为了衡量这种影响asErdos生产,有基于网络的评价工具,使用作者和引文数据来确定影响因素的研究,出版物和期刊。一些科学引文索引,Hfactor、影响因素,特征因子等。谷歌学术搜索也是一个好的数据工具用于网络数据收集和分析影响或影响。ICM 2014你的团队的目标是分析研究网络和其他地区的影响力和影响社会。你这样做的任务包括: 1)构建networkof Erdos1作者合著者(你可以使用我们网站https://files.oak https://www.doczj.com/doc/c4767588.html,/users/grossman/enp/Erdos1.htmlor的文件包括Erdos1.htm)。你应该建立一个合作者网络Erdos1大约有510名研究人员的文件,与鄂尔多斯的一篇论文的合著者,他但不包括鄂尔多斯。这将需要一些技术数据提取和建模工作获
For office use only T1________________ T2________________ T3________________ T4________________ Team Control Number 55069 Problem Chosen A For office use only F1________________ F2________________ F3________________ F4________________ 2017 MCM/ICM Summary Sheet The Rehabilitation of the Kariba Dam Recently, the Institute of Risk Management of South Africa has just warned that the Kariba dam is in desperate need of rehabilitation, otherwise the whole dam would collapse, putting 3.5 million people at risk. Aimed to look for the best strategy with the three options listed to maintain the dam, we employ AHP model to filter factors and determine two most influential criteria, including potential costs and benefits. With the weight of each criterion worked out, our model demonstrates that option 3is the optimal choice. According to our choice, we are required to offer the recommendation as to the number and placement of the new dams. Regarding it as a set covering problem, we develop a multi-objective optimization model to minimize the number of smaller dams while improving the water resources management capacity. Applying TOPSIS evaluation method to get the demand of the electricity and water, we solve this problem with genetic algorithm and get an approximate optimal solution with 12 smaller dams and determine the location of them. Taking the strategy for modulating the water flow into account, we construct a joint operation of dam system to simulate the relationship among the smaller dams with genetic algorithm approach. We define four kinds of year based on the Kariba’s climate data of climate, namely, normal flow year, low flow year, high flow year and differential year. Finally, these statistics could help us simulate the water flow of each month in one year, then we obtain the water resources planning and modulating strategy. The sensitivity analysis of our model has pointed out that small alteration in our constraints (including removing an important city of the countries and changing the measurement of the economic development index etc.) affects the location of some of our dams slightly while the number of dams remains the same. Also we find that the output coefficient is not an important factor for joint operation of the dam system, for the reason that the discharge index and the capacity index would not change a lot with the output coefficient changing.
Camping along the Big Long River Summary In 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 Equation
The Keep-Right-Except-To-Pass Rule Summary As for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clearly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle density is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic. As for the second question, it requires us to testify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left. As for the third question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow . Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solution to accelerate the traffic flow overall. Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic control
Team Control Number For office use only 13215 For office use only T1 ________________ F1 ________________ T2 ________________ F2 ________________ T3 ________________ Problem Chosen F3 ________________ T4 ________________ F4 ________________ C 2012 Mathematical Contest in Modeling (MCM) Summary Sheet (Attach a copy of this page to each copy of your solution paper.) Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page. Message Network Modeling for Crime Busting Abstract A particularly popular and challenging problem in crime analysis is to identify the conspirators through analysis of message networks. In this paper, using the data of message traffic, we model to prioritize the likelihood of one’s being conspirator, and nominate the probable conspiracy leaders. We note a fact that any conspirator has at least one message communication with other conspirators, and assume that sending or receiving a message has the same effect, and then develop Model 1, 2 and 3 to make a priority list respectively and Model 4 to nominate the conspiracy leader. In Model 1, we take the amount of one’s suspicious messages and one’s all messages with known conspirators into account, and define a simple composite index to measure the likelihood of one’s being conspirator. Then, considering probability relevance of all nodes, we develop Model 2 based on Law of Total Probability . In this model, probability of one’s being conspirator is the weight sum of probabilities of others directly linking to it. And we develop Algorithm 1 to calculate probabilities of all the network nodes as direct calculation is infeasible. Besides, in order to better quantify one’s relationship to the known conspirators, we develop Model 3, which brings in the concept “shortest path” of graph theory to create an indicator evaluating the likelihood of one’s being conspirator which can be calculated through Algorithm 2. As a result, we compare three priority lists and conclude that the overall rankings are similar but quite changes appear in some nodes. Additionally, when altering the given information, we find that the priority list just changes slightly except for a few nodes, so that we validate the models’ stability. Afterwards, by using Freeman’s centrality method, we develop Model 4 to nominate three most probable leaders: Paul, Elsie, Dolores (senior manager). What’s more, we make some remarks about the models and discuss what could be done to enhance them in the future work. In addition, we further explain Investigation EZ through text and semantic network analysis, so to illustrate the models’ capacity of applying to more complicated cases. Finally, we briefly state the application of our models in other disciplines.
2014年数学建模美赛题目原文及翻译 作者：Ternence Zhang 转载注明出处：https://www.doczj.com/doc/c4767588.html,/zhangtengyuan23 MCM原题PDF： https://www.doczj.com/doc/c4767588.html,/detail/zhangty0223/6901271 PROBLEM A: The Keep-Right-Except-To-Pass Rule In countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane. Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be
2019 MCM/ICM Summary 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. Ecosystems provide many natural processes to maintain a healthy and sustainable environment after human life. However, over the past decades, rapid industrial development and other anthropogenic activities have been limiting or removing ecosystem services. It is necessary to access the impact of human activities on biodiversity and environmental degradation. The main purpose of this work is to understand the true economic costs of land use projects when ecosystem services are considered. To this end, we propose an ecological service assessment model to perform a cost benefit analysis of land use development projects of varying sites, from small-scale community projects to large national projects. We mainly focus on the treatment cost of environmental pollution in land use from three aspects: air pollution, solid waste and water pollution. We collect pollution data nationwide from 2010 to 2015 to estimate economic costs. We visually analyze the change in economic costs over time via some charts. We also analyze how the economic cost changes with time by using linear regression method. We divide the data into small community projects data (living pollution data) and large natural data (industrial pollution data). Our results indicate that the economic costs of restoring economical services for different scales of land use are different. For small-scale land, according to our analysis, the treatment cost of living pollution is about 30 million every year in China. With the rapid development of technology, the cost is lower than past years. For large-scale land, according to our analysis, the treatment cost of industrial pollution is about 8 million, which is lower than cost of living pollution. Meanwhile the cost is trending down due to technology development. The theory developed here provides a sound foundation for effective decision making policies on land use projects. Key words: economic cost , ecosystem service, ecological service assesment model, pollution. Team Control Number For office use only For office use only T1 ________________ F1 ________________ T2 ________________ F2 ________________ T3 ________________ Problem Chosen F3 ________________ T4 ________________ F4 ________________ E
点评：航空货运问题 一、基本参数 1、货机：假设均匀分布 每天三架货机。 2、工作时间5：00—20：00设置为 t ：[0，15]？ 每天货机到达时间：5：00—20：00； 一工作组装满装卸场：6小时；一货机装满：3小时； 装卸台的容量：1.5货机； 3、费用系数： 停机费（等待装货）：15000元/小时架 一工作组：每小时9000元；二工作组：每小时12000元 4、服务原则：假设先来先服务 二、模型建立：概率计算模型 （一）概率分布 1、三架货机到达的时刻3,2,1,=i t i 服从[0，15]上的均匀分布，则： 密度函数：()1 ,01515 f t t = ≤≤ 分布函数：(),01515 t F t t = ≤≤ 2、设τ,δ,ε分别是首架货机到达时刻、第一架与第二架间隔、第二架与第三架间隔，
（1）τ的分布函数 3 31321321321321321))(1(1))(1(1)()()(1),,(1) ()()},,(min{) ()(1t F t t P t t P t t P t t P t t t t t t P t t t t t t P t t t t t t P t t t t P t P t F t --=≤--=>>>-=>>>-=≤?≤?≤-Ω=≤?≤?≤=≤=≤=ττ τ 的密度函数： ()()()1125 15151)151(3]1[3)(')(2 22 11-=-=-==t t t f t F t F t f t t ττ ]15,0[∈t （2）其余两货机到达与第一个到达的货机的间隔21,t t ??在0到15-τ之间是均匀分布的 于是： τ -=?151)(t f i t , τ-≤≤150t ；τ-=?15)(t t F i t , τ-≤≤150t ，i =1,2 δ 的密度函数 /121212()()()1() 1()() F t P t P t t t t P t t t t P t t P t t δτδ=≤=?≤?≤=-?>?>=-?>?> 221)](1[1)](1[11t F t t P t ?--=≤?--= ()()2//15152)()](1[2)(')(11---= -==??τττδτδt t f t F t F t f t t （3）第三架货机到达与第二个到达的货机的间隔ε在0和15-δ-τ之间是均匀分布的， 于是： ε 的密度函数
你的论文需要从此开始 请居中 使用Arial14字体 第一作者，第二作者和其他（使用Arial14字体） 1.第一作者的详细地址，包括国籍和email(使用Arial11) 2.第二作者的详细地址，包括国籍和email(使用Arial11) 3.将所有的详细信息标记为相同格式 关键词 列出文章的关键词。这些关键词会被出版方用作关键词索引(使用Arial11字体） 论文正文使用Times New Roman12字体 摘要 这一部分阐述说明了如何为TransTechPublications.准备手稿。最好阅读这些用法说明并且整篇论文都是遵照这个提纲。手稿的正文部分应该是17cm*25cm（宽*高）的格式（或者是6.7*9.8英尺）。请不要在这个区域以外书写。请使用21*29厘米或8*11英尺的质量较好的白纸。你的手稿可能会被出版商缩减20%。在制图和绘表格时候请特别注意这些准则。 引言 所有的语言都应该是英语。请备份你的手稿（以防在邮寄过程中丢失）我们收到手稿即默认为原作者允许我们在期刊和书报出版。如果作者在论文中使用了其他刊物中的图表，他们需要联系原作者，获取使用权。将单词或词组倾斜以示强调。除了每一部分的标题（标记部分的标题），不要加粗正文或大写首字母。使用激光打印机，而不是点阵打印机 正文的组织： 小标题 小标题应该加粗并注意字母的大小写。第二等级的小标题被视为后面段落的一部分（就像这一大段的一小部分的开头） 页码 不要打印页码。请用淡蓝色铅笔在每一张纸的左下角（在打印区域以外）标注数字。 脚注 脚注应该单独放置并且和正文分开理想地情况下，脚注应该出现在参考文献页，并且放在文章的末尾，和正文用分割线分开。 表格 表格（如表一，表二，...）应该放在正文当中，是正文的一部分，但是，要避免文本混乱。一个描述性的表格标题要放在图表的下方。标题应该独立的放在表格的下方或旁边。 表中的单位应放在中括号中[兆伏]如果中括号不可用，需使用大括号{兆}或小括号（兆)。1.这就是脚注
当我谈数学建模时我谈些什么——美赛一等奖经验总结 作者：彭子未 前言：2012 年3月28号晚，我知道了美赛成绩，一等奖（Meritorus Winner），没有太多的喜悦，只是感觉释怀，一年以来的努力总算有了回报。从国赛遗憾丢掉国奖，到美赛一等，这一路走来太多的不易，感谢我的家人、队友以及朋友的支持，没有你们，我无以为继。 这篇文章在美赛结束后就已经写好了，算是对自己建模心得体会的一个总结。现在成绩尘埃落定，我也有足够的自信把它贴出来，希望能够帮到各位对数模感兴趣的同学。 欢迎大家批评指正，欢迎与我交流，这样我们才都能进步。 个人背景：我2010年入学，所在的学校是广东省一所普通大学，今年大二，学工商管理专业，没学过编程。 学校组织参加过几届美赛，之前唯一的一个一等奖是三年前拿到的，那一队的主力师兄凭借这一奖项去了北卡罗来纳大学教堂山分校，学运筹学。今年再次拿到一等奖，我创了两个校记录：一是第一个在大二拿到数模美赛一等奖，二是第一个在文科专业拿数模美赛一等奖。我的数模历程如下： 2011.4 校内赛三等奖 2011.8 通过选拔参加暑期国赛培训（学校之前不允许大一学生参加） 2011.9 国赛广东省二等奖 2011.11 电工杯三等奖 2012.2 美赛一等奖（Meritorious Winner） 动机：我参加数学建模的动机比较单纯，完全是出于兴趣。我的专业是工商管理，没有学过编程，觉得没必要学。我所感兴趣的是模型本身，它的思想，它的内涵，它的发展过程、它的适用问题等等。我希望通过学习模型，能够更好的去理解一些现象，了解其中蕴含的数学机理。数学模型中包含着一种简洁的哲学，深刻而迷人。 当然获得荣誉方面的动机可定也有，谁不想拿奖呢？ 模型：数学模型的功能大致有三种：评价、优化、预测。几乎所有模型都是围绕这三种功能来做的。比如，今年美赛A题树叶分类属于评价模型，B题漂流露营安排则属于优化模型。 对于不同功能的模型有不同的方法，例如评价模型方法有层次分析、模糊综合评价、熵值法等；优化模型方法有启发式算法（模拟退火、遗传算法等）、仿真方法（蒙特卡洛、元胞自动机等）；预测模型方法有灰色预测、神经网络、马尔科夫链等。在数学中国网站上有许多关于这些方法的相关介绍与文献。
MCM论文写作常用句型（长文，建议收藏） The expression of ... can be expanded as: ... ...的表达式可扩展为... A is exponentially smaller than B, so it can be neglected. A对B来说呈指数级减小，所以可以忽略不计。 Equation (1) is reduced to: 方程（1）化简为： Substitute the values into equation (3), we get... 把这些值代入方程3，我们得到... According to our first assumption on Page 1, 根据我们第一页的第一个假设， Thus we arrive at the conclusion： 因此我们得到结论： From the model of ..., we find that theoretically, it is almost true that ... 由...模型，我们从理论上证明了... 是真实可信的。 That is the theoretical basis for ... in many application areas. 这是...在很多领域应用的理论基础。 To quantitatively analyze the different requirements of the two applications, we intro duce two measures: 为了定量的分析这两种应用的不同要求，我们介绍来两个量度标准。 We give the criterion that... 我们给出了...的判别标准 According to the criterion of... 根据...的标准 So its expression can be derived from equation (3) with small change. 所以它的表达式可以由方程3做微小改动而推出。 Suppose that ...refers to... 假设...指的是...
第一段：写论文解决什么问题 1．问题的重述 a. 介绍重点词开头： 例1：“Hand move” irrigation, a cheap but labor-intensive small farms, 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：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 the engineering parameters of sprinklers available in the market. 数学建模美赛论文 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。如果没有…… implementing defensive measure, the university is exposed to an expected of $8.9 million per year. 3．总的解决概述 a．通过什么方法解决什么问题 例：amusement park enjoyment through distributing Quick Passes (QP), reservation slips that ideally allow an individual to spend less time waiting in line. b．实际问题转化为数学模型 例1 a network flow vertices are the locations of escorts and wheelchair passengers. 例2 : A na?ve strategy would be to employ the minimum number of escorts to guarantee that all passengers reach their gates on time. c.将问题分阶段考虑 例3：the jump three : flying through the air, punching through the stack, and landing on the ground. 第二、三段：具体分析