1、美赛数学建模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:An (effective p
2、lan) is crucial tob. 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 meas
3、ures 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 g
4、roup 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 year.3 总的解决概述 a通过什么方法解决什么问题 例:We address
5、 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 vertices are the locations of escorts and wheelchair p
6、assengers. 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 stack, 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
7、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.例2:We examined the mathematical effects of. We developed a detailed (simulation methodology) to test our ideas and to
8、 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 includes demand, supply).例4:To (write the aims), we establish a criterion (write the criterion).b.
9、 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 and 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
10、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 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
11、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 strategy (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
12、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 is 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 Airpo
13、rt, the cost would be 例2:We modify the model to reflect (some trend such as exponentially increasing) and generalize the model to (other field).例3:Our results are summarized in the formula for the optimal number Bof tollbooths forc通过其上情况的列举得到的结论例:For various situations, we propose an optimal solutio
14、n.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 toe.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
15、easy to implement, includes a detailed timetable and the arrangement 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 presentedc.说明模型可用于其他领域
16、例:Since our model is based on it can be applied 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)介绍论文的重点容或研究围,常用词汇有study, present, include, focus
17、, 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,常用词汇有summary, introduce, conclude等讨论部分(1)述论文的论点和作
18、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, necessary, 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 evaluati
19、ng 评价方法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 calculate 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
20、 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 , 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
21、 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 between 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:c
22、an 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 in the same concourse are generally located close to one another, while the travel time between concourses can be quite lengthy. Hence, we assume that i
23、nter-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 are immobilized (as when pushing a wheelchair) is only ft/min (2 mph) Gross and Shi 2001. We assume that an escort walks at these speeds.例3:An escort ca
24、n operate only one wheelchair at a time. U.S. Dept. of transportation guidelines discourages leaving WPs unattended. Hence, 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
25、may be represented by 例4:.are independent and randomly distributed总结:Additional assumptions are made to simplify 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 Acco
26、rding 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 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3Plugging v1 into t
27、he equation for v2 ,we obtain (将公式1代入公式2中得到)公式11Putting these 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
28、have 公式Putting these into (1) ,we get(把这些公式代入1中)公式Which means that the Commonly, h is about 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)
29、,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9We use the fol
30、lowing 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 directly against velocity, so the accel
31、eration 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 massUsing 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22We 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 re
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