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 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。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 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 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：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 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. 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 for………By 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 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 reaches………by 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 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 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 na?ve 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 model 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 to…

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 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 presented……

c.说明模型可用于其他领域

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）介绍论文的重点内容或研究范围，常用词汇有study, present, include, focus, 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）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, 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 evaluating 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 following assumptions about……process 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 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：……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 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 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 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.

例3：An escort can 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 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

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 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

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 mass

Using 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=c

26．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, so

23．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

图

引用的文献数据所画的图：

1、分阶段图的引入：

First 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: ……deformation: After compression reaches the maximum, the rate of deformation starts to fall. The unrecoverable deformation goes on increasing. (2003—65)

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)(2005—53\54)

3、通过历史数据作图：

We validate our model by examining historical HIV rates from prenatal clinics in South Africa between 1995 and 2005(Figure 1). (2006—244)

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. (2003—260)

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. (2005—55)

We plot

W for values of B from 6 to 13, in steps of 0.25, together with the best-fit quartic, in Figure 2 1

(2005—92)

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). (2005—211)

We use the graph in Figure 1 to simulate the arrival of passengers. (2003—201)

The simulation model also generates system characteristics for the ETD machines at airport A. These results are shown in Figure 3. (2003—232)

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%,……. (2005—213\233)

4、用软件（如MA TLAB）画图：

To solve the differential equations in our model, we use (the ODE45 numerical integrator) in MA TLAB on (式子) to find the results in Figure 3.(2005—232)

5、图形的改进：

Generally speaking, the shape of the target is not too irregular, so we choose five typic al shapes of the targets 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 sizes of the helmets in 2D are indicated in Figure 3c, while 3D shot placements are shown in Figure 4. (2003—130)

6、画示意图：

The irrigation order and position of sprinklers are presented in Figure 4. (2006—127)

This algorithm can be viewed in the flowchart in Figure 3.We define some of the objects found in the chart. (2006—164\165)

表

表的格式：表头在上注：红字标记代表可通用的句子

1、在表前对表的来源和数据进行说明

例1In Table 1, we summarize the minimum number of escorts needed to reach each service level

表的解释部分

For each airport, the difference between the Good and Adequate service levels is roughly a factor of two, with slightly increasing returns to scale; with larger scales, the staff are spread more uniformly, so it is less likely that a job will crop up with nobody close enough to take it.

例2

表的解释部分

（前面的说出数据的来源，然后筛选出比较代表性的数据进行说明）。

We determined absolute and relative criticality values for each country for which all the data used in computing parameters was available (108 countries). We then used relative criticality in selecting our most critical countries, by continent. Had we used absolute criticality it would have given precedence to large nations, despite relatively mild HIV/AIDS situations.

例3

The table below is the generated irrigation schedule for the repositioning of the sprinklers, given 12-hour work day for a rancher. Each pipe is set in place for 5 hours.

例4

And some data processing we can get the relevant statistical data information of patient and donor characteristics for the simulation.

例5

The graft survival rates show in the following UNOS data for kidney transplants in the U.S (based on OPTN data as of 2006):

2、在表后对表的内容进行说明

例1

Table 9 shows linear fit parameters for all three models. Note that all three models are well described by a linear equation.

例2

Using the cellular automata model, we compute waiting time as a function of both the number of lanes and the number of tollbooths. For a fixed L, we compare all values of C total and choose the lowest one. The results of this method are presented in Table6.

例3

According to the above data,we can see that many of the European countries have the high rates of the donor, particularly in Spain. This phenomenon shows that the organ transplant is also hot in Europe. Although the relevant policies and statutes in these countries are less comprehensive than that in U.S, there still a lot what U.S could learn from. Here, we mainly analyze the organ transplant policies in Spain, U.K and Korea this three countries.

……The population contained in each region is summarized in table 1.（在表后对数据的内容进行总结）

例4

图表的解释部分

As indicated in Table 6, there is fairly good agreement between the recommended number of booths for a typical day and for peak hours. However, we note that the optimal booth number for a typical day never exceeds that for rush hour. Rush hour seems to require slightly more booths than a typical day in order for the plaza to operate most efficiently.

Each value in Table 6 is representative of approximately 20 trials. Through these trials, we noted a

remarkable stability in our model. Despite the stochastic nature of our algorithm, each number of lanes was almost always optimized to the same number of tollbooths. There were a handful of exceptions; they occurred exclusively for small numbers of highway lanes (< 3 lanes). Integer values are presented in Table 6 only because fractional tollbooths have no physical meaning.

3、表前表后有引入引出，且中间对两表之间进行比较

例1

表的解释部分

We can obtain the data which is involved with the status of the American Organ

Transplant from the data banks. We have collected the demand of the various organs in United States to date, the annual donors，transplants and the demand (Here taking the kidney for example, by years 1995-2006)

From the above table1, we can see that the kidney accounts for 73% in the

total of the organ transplants. It accounts for a very large proportion as a most important organ which can be transplanted. Therefore, we only need to discuss the status of the kidney transplant here, being able to achieve the analysis and research on the organ transplant.

According to the above data, we can get the figures as follow:

例2

So after many times simulation under the conditions discussed above, we obtain statistic results as follow:

表的解释部分

By analyzing the above result, we can find: When there are more donors (more resources), the number of transplant will increase obviously, and the matching rate changes only a little; When the network is divided into 11 regions (small networks), the costs of the transport and preservation of the organ will be reduced greatly.

例3

Table 7 reports the general patient statistics under each regime in the columns. The first column in these tables reports the total live donor transplants as percentage of the population size, which is the sum of next two columns, transplants from own compatible donor and transplants from trades. The forth column is the percentage of patients upgraded to the top of the waitlist as heads of w-chains. The fifth and sixth columns report the quality of matches in the live donor transplants: the risk of graft failure relative to the risk under no-exchange mechanism with population size n=400 is reported in the fifth column and the number of HLA mismatches for an average transplant is reported in the sixth column. In the table 8, we change the n into 200.

表与表之间的比较

By comparison, we can found that the matching proportion become little and the matching quality will get worse as the total number of the patients decrease. The result is consistent with the reality. The 30% probability of the waiting list or low quality exchange is an adjustable parameter.

例4

表与表的比较

Also, we wish to explore the situation in which there is one lane per booth:

例5

The parameters we choose to modify are p (probability of advancement), …delay? (number of time steps required to serve a vehicle in a tollbooth), and q (the probability that a flagged vehicle opts to attempt a turn). The results of this analysis are presented in Table 7. Since we have used six lanes as our standard test case, we continue with this choice here.

As indicated in Table 7, our cellular automata model is relatively insensitive to both p and q. Changes of ± 11% and ± 5.2% in p and q, respectively, had no effect on the optimal number of tollbooths for a six lane highway. On the other hand, increasing the delay time by 25% shifted the optimal number of booths from 10 to 11 (10%). Decreasing the delay by 25% had no effect on the solution. Perhaps additional work could lead to an elucidation of the relation between delay and optimal booth number that could help stabilize the cellular automata model.

优缺点

Evaluations of solutions

Strengths

?Our main model's strength is its enormous edibility. For instance,……..Including all these factors

into a single, robust framework, our model enables

?We developed a theoretical line formation model which agrees without rough data. Our computer

model agrees with both despite working on different principles, implying it behaves as we want.

?This allows us to make substantive conclusions about

?Finally, our model is strong because of

?The Monte Carlo simulation has been perfectly used in our models, and the simulation

results are consistent with the reality.

?We introduced…… in order to improve the exchange quality. The chain rules can also

modified in a degree.

?The models used in our paper is promotional, in view of different consideration,

?we can modify our models conveniently.

?the model is independent of the site simulated( )…

?the( )model is .intuitive

?the algorithm is efficient ::

? a corresponding strength of our model is that it would be relatively easy to include a parameter for

probability of ……

?Our model is particularly appropriate for simulation of ……, a problem that naturally lends itself to

such discrete modeling.

?The fundamental strengths of our model are…

?The model is independent of…

?Processor-based model has few input parameters, leading to good robustness and sensitivity.

?Uses a variety of modeling techniques in an integrated, holistic model.

?Our model effectively achieved all of the goals we set initially. It was fast and could handle large

quantities of data, but also had the flexibility we desired. Though we did not test all possibilities, we showed that our model optimizes state districts for any of a number of variables. If we had chosen to input income, poverty, crime or education data into our interest function, we could have produced high-quality results with virtually no added difficulty. As well, our method was robust.

?Our main model's strength is its enormous flexibility. For instance

?This allows us to make substantive conclusions about policy issues, even without extensive data

sets. By varying parameters, allocation rules, and our program's objective function——all quite feasible within the structure——we can examine the guts of policymaking: the ethical principles underlying a policy, the implementation rules designed to fulfill them, and the sometimes

nebulous numbers that govern the results.

?Finally, our model is strong because of its discrete setup.

?The fundamental strengths of our model are its robustness and flexibility. All of the data is

fully parameterized, so the model can be applied to……

Weaknesses

?Some special data can?t be found, and it makes that we have to do some proper assumption

before the solution of our models. A more abundant data resource can guarantee a better result in our models. Current line length is not taken into account by the line formation

model. In real life……

?Weaknesses of the model included assumptions made for simplicity that likely do not hold. For

instance, in most runs of our model on(sides……), cases (impact/conclusion) to…… This feature is likely a result of our assumption that /The primary weakness of this model is the( ), It should be possible to eliminate this, another weakness that could be corrected with more analysis is ( )`

?The primary weakness of this model is the…

Another weakness that could be corrected with more analysis is …

?Parameters have to be derived from physical occurrences.

?The other primary weakness of our model is our lack of metrics for comparison.

?Although we list the model's comprehensive, discrete simulation as a strength, it is

?(Paradoxically) also the most notable weakness. Our results lack clear….Second ,our model

demands great attention to….While its general structure and methodology are valid, the specific figures embedded in its code are not airtight.

?Although we list the model's comprehensive,……as a strength, it is (paradoxically) also

the most notable weakness. Our results lack clear illustrative power; data manipulated

through a computer program cannot achieve the same effect as……

?Indeed, there is a fundamental tradeoff here between realism and elegance, and our model

arguably veers toward over realism.

总结

Conclusions

1、A s our team set out to come up with a strategy on what would be the most efficient way to

我们提出了一种最有效的方法去解决……

2、T he first aspect that we took into major consideration was…….

Other important findings through research made it apparent that the standard

首先我们考虑到……，其他重要的是我们通过研究使

4、We have used mathematical modeling in a……to analyze some of the factors associated with such an activity。

为了分析这类问题的一些因素，我们运用数学模型……

5、This “cannon problem” has been used in many forms in many differential equations courses in the Department of Mathematical Sciences for several years.

这些年这些问题已经以不同的微分方程形式运用于自然科学部门。

6、In conclusion our team is very certain that the methods we came up with in

总之，我们很确定我们提出的方法

7、We already know how well our results worked for……

我们已经知道我们结果对……

8、Now that the problem areas have been defined, we offer some ways to reduce the effect of these problems.

既然已经定义了结果，我们提出一些方法减少对问题的影响。

9、There are many methods in existence for……Furthermore each is mostly successful in what is sets out to do. However, all of these seem to

有许多的方法研究……，因此最好的是我们要作的，然而，所有的这些好像……

10、While our approaches and models were effective and produced results, there remain several types of model weaknesses:

我们的方法和模型很有效对结果进行延伸，我们的模型也存在些缺点。

11、We next developed a detailed simulation engine to perform simulations. Our simulations allowed us to ……

我们接下来研究计算，我们的模拟允许我们……

12、We have reached several valuable conclusions about the nature of……and some of the possible policy solutions that can be implemented to make it more effective ，Most importantly, we believe in the absolute necessity of implementing

我们得到关于这类问题的结果，一些可能的政策结果使它很有效，最重要的是，我们认为……相当有必要性。

13、We use …to …

14、Thus, we recommend…

15、Considering the…

16、In this paper, we examine the results of some fundamental avaricious in structure:……

17、We also wish to tie our exploration of sensitive……

18、we suspect that such system are in general less effective than simpler ones……

数学建模论文格式说明

摘 认真书写摘要（注意篇幅不能超过一页，但要充分利用本页），勿庸置疑，摘要 在整个数模论文中占有及其重要的地位，它是评委对你所写论文的第一印象，因此在这一部分的写作上一定要花大功夫， 千万不能马虎。摘要是论文是否取得好名次的决定性因素，评委们通过你的摘要就决定是否继续阅读你的论文。换句话说，就算你的论文其他方面写得再好，摘要不行，你的论文也不会得到重视。我认为在写摘要时应包括6个方面：对问题稍做描述（问题的研究有什么意义），用了什么方法，建立了什么样的模型（线性规化模形），针对所建立的模型用什么算法、软件解的，得到什么结论，模型、结论有什么特色。 简而言之，摘要应该体现你用什么方法，解决了什么问题，得出了什么结论。另外，好的摘要都包含了两个共同的特点：简要simple 和明确clear 。 学术论文要求：括地陈述论文研究的目的、方法、结果、结论，要求200～300字．应排除本学科领域已成为常识的内容；不要把应在引言中出现的内容写入摘要，不引用参考文献；不要对论文内容作诠释和评论．不得简单重复题名中已有的信息．用第三人称，不使用“本文”、“作者”等作为主语．使用规范化的名词术语，新术语或尚无合适的汉文术语的，可用原文或译出后加括号注明．除了无法变通之外，一般不用数学公式和化学结构式，不出现插图、表格．缩略语、略称、代号，除了相邻专业的读者也能清楚理解的以外，在首次出现时必须加括号说明．结构严谨，表达简明，语义确切。 摘要是论文的门面，摘要写的不好评委后面就不会去看了，自然只能给个成功参赛奖。摘要首先不要写废话，也不要照抄题目的一些话，直奔主题，要写明自己怎样分析问题，用什么方法解决问题，最重要的是结论是什么要说清楚，在中国的竞赛中结论如果正确一般得奖是必然的，如果不正确的话评委可能会继续往下看，也可能会扔在一边，但不写结论的话就一定不会得奖了，所以要认真写。摘要至少需要琢磨两个小时，不要轻视了它的重要性。很有必要多看看优秀论文的摘要是如何写的，并要作为赛前准备的内容之一。 关键词：关键词1；关键词2；关键词3用的方法中的重要术语） 其它汉字 小四号宋字，行距用单倍行距（由于数学论文中通常有汉字和公式，建议行距用固定行距22磅。）

2014年数学建模美赛ABC_题翻译

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.wendangku.net/doc/3f7910224.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.wendangku.net/doc/3f7910224.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.wendangku.net/doc/3f7910224.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

全国大学生数学建模竞赛论文模板

2009高教社杯全国大学生数学建模竞赛 承诺书 我们仔细阅读了中国大学生数学建模竞赛的竞赛规则. 我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师）研究、讨论与赛题有关的问题。 我们知道，抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他公开的资料（包括网上查到的资料），必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。 我们郑重承诺，严格遵守竞赛规则，以保证竞赛的公正、公平性。如有违反竞赛规则的行为，我们将受到严肃处理。 我们参赛选择的题号是（从A/B/C/D中选择一项填 写）： 我们的参赛报名号为（如果赛区设置报名号的 话）： 所属学校（请填写完整的全 名）： 参赛队员 (打印并签名) ： 1. 2.

3. 指导教师或指导教师组负责人 (打印并签名)：指导教师组 日期：年月日 赛区评阅编号（由赛区组委会评阅前进行编号）： 2009高教社杯全国大学生数学建模竞赛 编号专用页 赛区评阅编号（由赛区组委会评阅前进行编号）： 赛区评阅记录（可供赛区评阅时使用）：

全国统一编号（由赛区组委会送交全国前编号）： 全国评阅编号（由全国组委会评阅前进行编号）： 论文标题 摘要 摘要是论文内容不加注释和评论的简短陈述，其作用是使读者不阅读论文全文即能获得必要的信息。 一般说来，摘要应包含以下五个方面的内容： ①研究的主要问题； ②建立的什么模型； ③用的什么求解方法； ④主要结果（简单、主要的）； ⑤自我评价和推广。

摘要中不要有关键字和数学表达式。 数学建模竞赛章程规定，对竞赛论文的评价应以： ①假设的合理性 ②建模的创造性 ③结果的正确性 ④文字表述的清晰性 为主要标准。 所以论文中应努力反映出这些特点。 注意：整个版式要完全按照《全国大学生数学建模竞赛论文格式规范》的要求书写，否则无法送全国评奖。 一、问题的重述 数学建模竞赛要求解决给定的问题，所以一般应以“问题的重述”开始。 此部分的目的是要吸引读者读下去，所以文字不可冗长，内容选择不要过于分散、琐碎，措辞要精练。 这部分的内容是将原问题进行整理，将已知和问题明确化即可。 注意： 在写这部分的内容时，绝对不可照抄原题！

数学建模解答和论文格式说明

数学建模题目解答说明 ●解答按照范文要求进行，附上相关程序和运行状态截图。 ●上交纸质文档和电子文档。电子文档考给班长，一起交给我。 注：用“选作题目+学号+姓名”作为文件夹的文件名。文件夹中应包含正文word2003格式和附录-----程序源文件和结论。 ●交卷时间：2010年6月22日之前。过期视为缺考。 数学建模论文格式规范 ●论文用白色A4纸单面打印；上下左右各留出至少2.5厘米的页边距；从 左侧装订。 ●论文第一页为承诺书，具体内容和格式见本规范第二页。 ●论文题目和摘要写在论文第二页上，从第三页开始是论文正文。 ●论文从第二页开始编写页码，页码必须位于每页页脚中部，用阿拉伯数 字从“1”开始连续编号。 ●论文不能有页眉 ●论文题目用三号黑体字、一级标题用四号黑体字，并居中；二级、三级 标题用小四号黑体字，左端对齐（不居中）。论文中其他汉字一律采用小四号宋体字，行距用单倍行距，打印时应尽量避免彩色打印。 ●提请大家注意：摘要应该是一份简明扼要的详细摘要（包括关键词）， 在整篇论文评阅中占有重要权重，请认真书写（注意篇幅不能超过一页，且无需译成英文）。 ●引用别人的成果或其他公开的资料(包括网上查到的资料) 必须按照规 定的参考文献的表述方式在正文引用处和参考文献中均明确列出。正文引用处用方括号标示参考文献的编号，如[1][3]等；引用书籍还必须指出页码。参考文献按正文中的引用次序列出，其中书籍的表述方式为：[编号] 作者，书名，出版地：出版社，出版年。 参考文献中期刊杂志论文的表述方式为： [编号] 作者，论文名，杂志名，卷期号：起止页码，出版年。 参考文献中网上资源的表述方式为： [编号] 作者，资源标题，网址，访问时间（年月日）。

数学建模美赛2012MCM B论文

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

美赛数学建模比赛论文模板

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

数学建模论文格式说明

摘 要 认真书写摘要（注意篇幅不能超过一页，但要充分利用本页），勿庸置疑，摘要 在整个数模论文中占有及其重要的地位，它是评委对你所写论文的第一印象，因此在这一部分的写作上一定要花大功夫，千万不能马虎。摘要是论文是否取得好名次的决定性因素，评委们通过你的摘要就决定是否继续阅读你的论文。换句话说，就算你的论文其他方面写得再好，摘要不行，你的论文也不会得到重视。我认为在写摘要时应包括6个方面：对问题稍做描述（问题的研究有什么意义），用了什么方法，建立了什么样的模型（线性规化模形），针对所建立的模型用什么算法、软件解的，得到什么结论，模型、结论有什么特色。 简而言之，摘要应该体现你用什么方法，解决了什么问题，得出了什么结论。另外，好的摘要都包含了两个共同的特点：简要simple 和明确clear 。 学术论文要求：括地陈述论文研究的目的、方法、结果、结论，要求200～300字。应排除本学科领域已成为常识的内容；不要把应在引言中出现的内容写入摘要，不引用参考文献；不要对论文内容作诠释和评论。不得简单重复题名中已有的信息。不使用“我”、“我们”、“作者”等作为主语，应使用“本文”。使用规范化的名词术语，新术语或尚无合适的汉文术语的，可用原文或译出后加括号注明。除了无法变通之外，一般不用数学公式和化学结构式，不出现插图、表格。缩略语、略称、代号，除了相邻专业的读者也能清楚理解的以外，在首次出现时必须加括号说明。结构严谨，表达简明，语义确切。 摘要是论文的门面，摘要写的不好评委后面就不会去看了，自然只能给个成功参赛奖。摘要首先不要写废话，也不要照抄题目的一些话，直奔主题，要写明自己怎样分析问题，用什么方法解决问题，最重要的是结论是什么要说清楚，在中国的竞赛中结论如果正确一般得奖是必然的，如果不正确的话评委可能会继续往下看，也可能会扔在一边，但不写结论的话就一定不会得奖了，所以要认真写。摘要至少需要琢磨两个小时，不要轻视了它的重要性。很有必要多看看优秀论文的摘要是如何写的，并要作为赛前准备的内容之一。 关键词：关键词1；关键词2；关键词3用的方法中的重要术语） 其它汉字小四号宋字，行距用单倍行距（由于数学论文中通常有汉字和公式，建议行距用固定行距22磅。）

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数学建模论文标准格式 为了适应数学发展的潮流和未来社会人才培养的需要,美国、德国、日本等发达国家普遍都十分重视数学建模教学。以下是小编整理的数学建模论文标准格式，欢迎阅读。 1.数学建模简介 1985年，数学建模竞赛首先在美国举办，并在高等院校广泛开设相关课程。我国在1992年成功举办了首届大学生数学竞赛，并从1994年起，国家教委正式将其列为全国大学生的四项竞赛之一。数学建模是分为国内和国外竞赛两种，每年举行一次。三人为一队，成员各司其职：一个有扎实的数学功底，再者精于算法的实践，最后一个是拥有较好的文采。数学建模是运用数学的语言和工具，对实际问题的相关信息（现象、数据等）加以翻译、归纳的产物。数学模型经过演绎、求解和推断，运用数学知识去分析、预测、控制，再通过翻译和解释，返回到实际问题中[1]。数学建模培养了学生运用所学知识处理实际问题的能力，竞赛期间，对指导教师的综合能力提出了更高的要求。 2.数学建模科技论文撰写对学生个人能力成长的帮助 2.1.提供给学生主动学习的空间 在当今知识经济时代，知识的传播和更新速度飞快，推行素质教育是根本目标，授人与鱼不如授人与渔。学生掌握自学能力，能有效的弥补在课堂上学得的有限知识的不足。数学建模所涉及到的知识面广，除问题相关领域知识外，还要求学生掌握如数理统计、最优化、

图论、微分方程、计算方法、神经网络、层次分析法、模糊数学、数学软件包的使用等。多元的学科领域、灵活多变的技能方法是学生从未接触过的，并且也不可能在短时间内由老师一一的讲解清楚，势必会促使学生通过自学、探讨的方式来将其研懂。给出问题，让学生针对问题去广泛搜集资料，并将其中与问题有关的信息加以消化，化为己用，解决问题。这样的能力将对学生在今后的工作和科研受益匪浅[2]。 在培训期间，大部分学生会以为老师将把数学建模比赛所涉及到的知识全部传授给学生，学生只要在那里坐着听老师讲就能参加比赛拿到名次了。但是当得知竞赛主要由学生自学完成，老师只是起引导作用时，有部分学生选择了放弃。坚持下来的学生，他们感谢学校给与他们这样能够培养个人能力的机会，对他们今后受用匪浅！ 2.2.体验撰写综合运用知识和方法解决实际问题这一系列论文的过程 学生在撰写数学建模科技论文的时候，不光要求学生具备一定的数学功底、有良好的计算机应用能力、还要求学生具备相关领域知识，从实际问题中提炼出关键信息，并运用所学知识对这些关键信息加以抽象、建立模型。这也是教师一直倡导学生对所学知识不光要记住，而且要会运用。千万不要读死书，死读书，读书死。 2.3.培养了学生的创新意识和实践能力 在撰写过程中潜移默化的培养了学生获取新知识、新技术、新方法的能力，并在解决实际问题的过程中培养学生的创新意识和实践能

2019数学建模美赛论文

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