1、MCM 写作模版(各部分) 摘要 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 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
2、 ：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
3、 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 analyz
4、ing 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 Without implementing defensive measure, the university is exposed to an expected loss of $8.9 million per
5、year. 3 总的解决概述 a 通过 什么 方法 解决 什么 问题 例：We address the problem of optimizing 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 We formulate the problem as a network flow in which
6、 vertices are the locations of escorts and wheelchair passengers. 例 2 : A nave 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 ：We divide the jump into three phases: flying through the air, punching through the s
7、tack, and landing on the ground. 第二、三 段：具 体 分析 1 在什么模型中/ 建立了什么模型 a. 主流 模型 例 1 ： We formulate a differential model to account for the rates of change of these uses, and how this change would affect the overall consumption of water within the studied region. - 1 - MCM 写作模版(各部分) 例 2:We examined the mat
8、hematical effects of. We developed a detailed (simulation methodology) to test our ideas and to quantify the differences between (among) different (strategies). 例 3：Based on (write your basis .such as the theory of supply and demand), we establish a model (such as differential equation system that i
9、ncludes demand, supply). 例 4：To (write the aims), we establish a criterion (write the criterion). b. 模型 非主 流 例 5 ：We build a model to determine how to lay out the pipe each time the equipment is moved. 例 6 ：We determine 例 7 ：We build a model to determine. 例 8 ：We formulate a model forBy analyzing an
10、d examining 2 分析模型（使用 什么数 据，怎么做，一般三 句话 ） a. 写历 史数 据 例 1 ： Using historical data from the United States, we determine initial conditions for our model. b. 写计 算机 模拟 例 1 ：this model leads to a computer simulation of catch-can tests of the irrigation system and 例 2:Software packing reachesby calculating
11、 and comparing c. 运用 数据 模拟 例 1 ：to ground this model in reality, we incorporate extensive demographic data and run 例 2 ：We fit the modified model to data (such as 1970-2003.). We conclude that (write the last conclude). d. 讲 详细 分析 例 1 ：We physically characterize the system that 例 2 ：We provide a str
12、ategy (write the logical strategy). 例 3 ：The model is (efficient, intuitive, and flexible) and could be applied to 例 4 ：To meet the needs of people today without, we establish a criterion of rational( 合理的 标准) oil allocation(分配). 3 总结该模型的结果/ 得 到什么结论 a. 说 明不 是最 优但 能产生 作用 例：We show that this strategy i
13、s not optimal but can be improved by assigning different numbers b. 说明 如果 用这 个模 型，结 果 如何 例 1 ：If Delta Airlines were to utilize the nave strategy at Atlanta International Airport, the cost would be 例 2：We modify the model to reflect (some trend such as exponentially increasing) and generalize the mo
14、del to (other field). 例 3 ：Our results are summarized in the formula for the optimal number Bof tollbooths for c 通过 其上 情况 的列 举得到 的 结论 例：For various situations, we propose an optimal solution. d. 得 出了 结论 例 1 ：we elicit that a conclusion. 例 2 ：We conclude with a series of recommendations for how best
15、to - 2 - MCM 写作模版(各部分) e. 进一步 说明其 他因素 对 模型的影 响 例 ：In addition to the model, we also discuss policies for f.用真 实数 据检 验模 型 例:To demonstrate how our model works, we apply it to 最后一段 ：写总 的 结论 a. 说明 结论 的可 行性 例：Our suggested solution, which is easy to implement, includes a detailed timetable and the arran
16、gement of pipes. b. 说明 算法 的广 泛性 例 1 ：Our algorithm is broad enough to accommodate various airport concourses, flight schedules, and flight delays. 例 2 ：Our analysis began by determining what factor impact, Our conclusions are presented c.说明 模型 可用 于其 他领域 例：Since our model is based on it can be applie
17、d to (other domain). 其他（承 上启下 的 连接词/ 常用词 组） 例:In addition to the model, we also discuss 引言部分 （1）回 顾研 究背 景， 常用词 汇有 review, summarize, present, outline, describe 等 （2）说 明写 作目 的， 常用词 汇有 purpose, attempt, aim 等， 另外 还可 以用 动 词不 定式 充当 目的 状 语来表达 （3 ） 介绍 论文 的重 点内 容或 研 究范 围， 常用 词汇有 study, present, include, fo
18、cus, emphasize, emphasis, attention 等 方法部分 （1 ） 介绍 研究 或试 验过 程， 常用 词汇有 test study, investigate, examine, experiment, discuss, consider, analyze, analysis 等 （2）说 明研 究或 试验 方法， 常 用词 汇有 measure, estimate, calculate 等 （3 ）介 绍应 用、 用途 ，常 用词汇 有等 结果部分 （1）展 示研 究结 果， 常用词 汇有 show, result, present 等 （2）介 绍结 论， 常用
19、 词汇有 summary, introduce, conclude 等 讨论部分 （1）陈 述论 文的 论点 和作者 的 观点 ，常 用词 汇有 suggest, repot, present, expect, describe 等 （2 ）说明论证，常用词汇有等 support, provide, indicate, identify, find, demonstrate, confirm, clarify （3 ） 推荐 和建 议， 常用 词汇 有 suggest, suggestion, recommend, recommendation, propose, necessity, nec
20、essary, expect 等。 摘 要中 常用的 词语 汇 ： critical 至关重要 的 algorithm 运算法则 a method of evaluating 评 价方法 - 3 - MCM 写作模版(各部分) appropriate 近似 的 consider 考虑 configurations 布局 optimal 统一的 maximize 使最大 化 strategy 策略 parameter 参数，主 要的 决 定因素 accuracy 精确性 strengths and weaknesses 优点和 缺点 contact 相关 的 contract 建 立， 构造 c
21、alculate 计算 establish 建立 formula 公式 modify 改进 rational 合理的 countermeasure 对策 criterion 标准， 准则 Assumptions 引 出： We make the following assumptions aboutprocess in this paper. a. 不考虑因素 例1 ：We do not take into account interactions between factors. 例2 ：The influence of can be neglected 例3 ：is “ideal” in
22、, can be neglected. b. 为了简化模型，之后 反 驳 不正确，但是合理。 例 1： In fact （in reality ） factors effect each others, but in order to simplify the model ,we ignore the interactions between factors. 例2 ：In fact in reality factors effect each others, but in order to simplify the model ,we ignore the interactions betw
23、een factors. c. 近似 例1：can be approximated as a liner function of . 例 2： are assumed to be the same. In practice, there is a slight difference. 例3：can be approximated as a liner function of . d. 细致考虑（可附 原因） 例 1：An airport consists of 1 to 10 concourses, each of with consists of 2 to 50 gates. Gates i
24、n the same concourse are generally located close to one another, while the travel time between concourses can be quite lengthy. Hence, we assume that inter-concourse travel is much lengthier than intra-concourse travel. 例 2：A average fast walking speed is 250ft/min(3mph), but average speed when arms
25、 are immobilized (as when pushing a wheelchair) is only 180 ft/min (2 mph) Gross and Shi 2001. We assume that an escort walks at these speeds. - 4 - MCM 写作模版(各部分) 例 3：An escort can operate only one wheelchair at a time. U.S. Dept. of transportation guidelines discourages leaving WPs unattended. Henc
26、e, the escort takes a WP to the connecting flight and remains until the flight leaves. e. 直接定义( 假设) ： 例1：To measure the,we define 例2：Yearly industry statistics can be used valid. 例3：Sth may be represented by 例4：.are independent and randomly distributed 总结： Additional assumptions are made to simplify
27、 analysis for individual sections. These assumptions will be discussed at the appropriate locations. 公式 由 假设 得到公 式 1We assume laminar flow and use Bernoullis 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 2Because our field is fl
28、at, 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 3Plugging v1 into the equation for v2 ,we obtain （将公 式 1 代 入公式 2 中得 到） 公式 11 Putting the
29、se together( 把公式 放在 一起), because of the law of conservation of energy, yields ： 公式 12Therefore, 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
30、 入 1 中） 公式 Which means that the Commonly, h is about - 5 - MCM 写作模版(各部分) From these equations, （从这 个 公式 中我 们知 道）we know that 引 出约 束条件 4Using 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 6To find the new pressure ,we use the ( 0 0),
31、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 ; 7Solving for VN we obtain ( 公式 的解) 公式 Where n is the 8We have the following differential equations for speeds in the x- and y- directions: 公式 Whose solutions are （解 ） 公式
32、 9We use the following initial conditions ( 使 用初 值 ) to determine the drag constant: 公式 根 据原 有公式 10We 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 direc
33、tly against velocity, so the acceleration vector from drag can be found Newtons law F=ma as : ( 牛顿第 二定 律) Where a is the acceleration vector and m is mass Using the Newtons 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 22W
34、e 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=c 26In
35、tegrating, （ 使结 合）we get PVT=constant, where - 6 - MCM 写作模版(各部分) 公式 The main composition of the air is nitrogen and oxygen, so i=5 and r=1.4, so 23According 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
36、into the Ideal Gas Internal Formula: 公式 Where 对 公式 变形 13Define 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
37、 ）, we minimize 公式 使 服从 约束条 件 14Subject 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 const
38、raint reduces to 公式 结果 说明 15This implies （暗示） that the harmonic mean of l and w should be 公式 So , in the optimal situation. 5This 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
39、公式 With t=0.0001 s, error from the approximation is virtually zero. 17We calculated its trajectory( 轨道) using 公式 18For that case, using the same expansion for e as above, 公式 19Solving for t and equating it to the earlier expression for t, we get 公式 20Recalling that in this equality only n is a funct
40、ion of f, we substitute for n and solve for f. the result is 公式 - 7 - MCM 写作模版(各部分) As v=, this equation becomes singular ( 单数的). 由 语句 得到公 式 21The revenue generated by the flight is 公式 24Then we have 公式 We differentiate the ideal-gas state equation 公式 Getting 公式 25We eliminate dT from the last two e
41、quations to get （排除 因素 得到 ） 公式 22We 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 图 引用的文献数据所画 的图 ： 1、 分阶 段图 的引 入： Firs
42、t we study the (文献) ，showing under the situation. 分阶 段图 的引 出： The compression process is divided into three( 数字) phases, as shown in the figure: The first phase: deformation, according to ; the second phase: deformation. The compression grows more slowly and reaches the maximum. The third phase: def
43、ormation: After compression reaches the maximum, the rate of deformation starts to fall. The unrecoverable deformation goes on increasing. (200365) 2、引 用已 有的 模型 图： A model of flow rate for instant total failure is right triangular 【U.S. Army Corps of Engineers 1997 】. (see Figure 1)(20055354) 3、通 过历
44、 史数 据作 图： We validate our model by examining historical HIV rates from prenatal clinics in South Africa between 1995 and 2005(Figure 1). (2006244) 4、 拟合 的图 形： Figure 1 shows the number of bags still left for the EDS to process at airport A after each minute in airport B, the results are similar. (20
45、03260) 自己根据计算所画的 图： 1、 为了.(目的)，我 们作 了. 图。 To demonstrate better the change in flow rate with time when the breach begins t form, we plot over a shorter range of time in Figure 5. (200555) - 8 - MCM 写作模版(各部分) We plot 1 W for values of B from 6 to 13, in steps of 0.25, together with the best-fit quart
46、ic, in Figure 2 (200592) 2、根 据数 据拟 合的 图： Fitting ( 式子) to the data in ( 表), we get the curve in Figure 1, for the function ( 公式). (2005211) We use the graph in Figure 1 to simulate the arrival of passengers. (2003201) The simulation model also generates system characteristics for the ETD machines at
47、 airport A. These results are shown in Figure 3. (2003232) 3、根 据取 值不 同画 图： We take 2001as the starting point, when total remaining oil was 1.1178bbl.We calculate the time to oil exhaustion under different cases: GDP growing at 10%, 5%, 3%,and 1%.(Figure 3) For 10%, ; for 5%,;for 3%,;for 1%,. (200521
48、3233) 4、用 软件 （如 MATLAB ）画图 ： To solve the differential equations in our model, we use (the ODE45 numerical integrator) in MATLAB on ( 式子) to find the results in Figure 3.(2005232) 5、 图形 的改 进： Generally speaking, the shape of the target is not too irregular, so we choose five typical shapes of the ta
49、rgets in different sizes. In Figure 3a, we illustrate the maximum section of a typical bean-shaped target, whose maximum dimension is 35mm. Using the skeleton generation algorithm, we get corresponding skeleton shown in Figure 3b. Then we apply the GA-based shot placement algorithm, resulting in three shots for the target: one 14 mm helmet and two 8 mm helmets. The locations and s
