美国数学建模MCM_ICM论文模版

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 typical 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

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）

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 consider ation 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……

全国数学建模竞赛一等奖论文

交巡警服务平台的设置与调度 摘要 由于警务资源有限，需要根据城市的实际情况与需求建立数学模型来合理地确定交巡警服务平台数目与位置、分配各平台的管辖范围、调度警务资源。设置平台的基本原则是尽量使平台出警次数均衡，缩短出警时间。用出警次数标准差衡量其均衡性，平台与节点的最短路衡量出警时间。 对问题一，首先以出警时间最短和出警次数尽量均衡为约束条件，利用无向图上任意两点最短路径模型得到平台管辖范围，并运用上下界网络流模型优化解,得到A区平台管辖范围分配方案。发现有6个路口不能在3分钟内被任意平台到达，最长出警时间为5.7分钟。 其次，利用二分图的完美匹配模型得出20个平台封锁13个路口的最佳调度方案，要完全封锁13个路口最快需要8.0分钟。 最后，以平台出警次数均衡和出警时间长短为指标对方案优劣进行评价。建立基于不同权重的平台调整评价模型，以对出警次数均衡的权重u和对最远出警距离的权重v 为参数，得到最优的增加平台方案。此模型可根据实际需求任意设定权重参数和平台增数，由此得到增加的平台位置，权重参数可反映不同的实际情况和需求。如确定增加4个平台，令u=0.6，v=0.4，则增加的平台位置位于21、27、46、64号节点处。 对问题二，首先利用各区平台出警次数的标准差和各区节点的超距比例分析评价六区现有方案的合理性，利用模糊加权分析模型以城区的面积、人口、总发案次数为因素来确定平台增加或改变数目。得出B、C区各需改变2个平台的位置，新方案与现状比较，表明新方案比现状更合理。D、E、F区分别需新增4、2、2个平台。利用问题一的基于不同权重的平台调整评价模型确定改变或新增平台的位置。 其次，先利用二分图的完美匹配模型给出80个平台对17个出入口的最优围堵方案，最长出警时间12.7分钟。在保证能够成功围堵的前提下，若考虑节省警力资源，分析全市六区交通网络与平台设置的特点，我们给出了分阶段围堵方案，方案由三阶段构成。最多需调动三组警力，前后总共需要29.2分钟可将全市路口完全封锁。此方案在保证成功围堵嫌疑人的前提下，若在前面阶段堵到罪犯，则可以减少警力资源调度，节省资源。 【关键字】：不同权重的平台调整评价模糊加权分析最短路二分图匹配

葡萄酒的评价_全国数学建模大赛优秀论文

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。 我们授权全国大学生数学建模竞赛组委会，可将我们的论文以任何形式进行公开展示（包括进行网上公示，在书籍、期刊和其他媒体进行正式或非正式发表等）。 我们参赛选择的题号是（从A/B/C/D中选择一项填写）： A 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）：重庆工商大学 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)： 日期： 2012 年 9 月 10 日赛区评阅编号（由赛区组委会评阅前进行编号）：

编号专用页 赛区评阅编号（由赛区组委会评阅前进行编号）： 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）：

葡萄酒的评价 摘要 酿酒葡萄的好坏与所酿葡萄酒的质量有直接的关系，葡萄酒和酿酒葡萄检测的理化指标会在一定的程度上反映葡萄酒和葡萄的质量。本论文主要研究葡萄酒的评价、酿酒葡萄的分级以及酿酒葡萄与葡萄酒的理化指标之间的相互关系问题。 对于问题一:我们从假设检验的角度出发分析，对两组的评分进行均值和方差运算，并在零假设成立的前提下通过使用Matlab 做T 检验，得出两组评酒员对于红葡萄酒的评价结果无显著性差异，而对于白葡萄酒的评价结果存在显著性差异的结果。再建立可信度模型 = H ，计算结果如下表， 对于问题二:根据葡萄酒质量的综合得分，将其划分为优、良、合格、不合格四个等级，并对酿酒葡萄的理化指标进行主成分分析，得出对葡萄影响较大的 到了它们的偏相关系矩阵。利用通径方法建立了数学模型，得出了它们之间的线性回归方程： 11231123=2.001x 0.0680.015x +........=0.0540.7580.753x ......... y x y x x ----+红红红红白白白白 对于问题四:在前面主成分分析和葡萄酒分级的基础上，建立Logistic 回归模型，并利用最大似然估计法求出线性回归方程的参数，得出线性回归方程。运用SPSS 软件，通过matlab 编程运算，求出受它们综合影响的线性回归方程。在验证时，随机从上面选取理化指标，将它们带入P 的计算式中，通过所求P 值判断此时葡萄酒质量所属级别，得出了不能用葡萄和葡萄酒的理化指标来评价葡萄酒的质量的结论。

数学建模国家一等奖优秀论文

２01４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《全国大学生数学建模竞赛章程》和《全国大学生数学建模竞赛参赛规则》(以下简称为“竞赛章程和参赛规则”，可从全国大学生数学建模竞赛网站下载)。 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章程和参赛规则的，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，严格遵守竞赛章程和参赛规则，以保证竞赛的公正、公平性。如有违反竞赛章程和参赛规则的行为,我们将受到严肃处理。 我们授权全国大学生数学建模竞赛组委会，可将我们的论文以任何形式进行公开展示(包括进行网上公示，在书籍、期刊和其他媒体进行正式或非正式发表等)。 我们参赛选择的题号是(从Ａ/B/C/Ｄ中选择一项填写)：B 我们的报名参赛队号为（8位数字组成的编号）: 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): ?（论文纸质版与电子版中的以上信息必须一致,只是电子版中无需签名。以上内容请仔细核对，提交后将不再允许做任何修改。如填写错误，论文可能被取消评奖资格。) 日期： 20１4 年 9 月15日 赛区评阅编号(由赛区组委会评阅前进行编号）:

２０14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）：

2013全国数学建模大赛a题优秀论文

车道被占用对城市道路通行能力的影响 摘要 随着城市化进程加快，城市车辆数的增加，致使道路的占用现象日益严重，同时也导致了更多交通事故的发生。而交通事故发生过程中，路边停车、占道施工、交通流密增大等因素直接导致车道被占用，进而影响了城市道路的通行能力。本文在视频提供的背景下通过数据采集，利用数据插值拟合、差异对比、车流波动理论等对这一影响进行了分析，具体如下： 针对问题一，首先根据视频1中交通事故前后道路通行情况的变化过程运用物理观察测量类比法、数学控制变量法提取描述变量（如事故横断面处的车流量、车流速度以及车流密度）的数据，从而通过研究各变量的变化，来分析其对通行能力的影响。而视频1中有一些时间断层，我们可根据现有的数据先用统计回归对各变量数据插值后再进行拟合，拟合过程中利用残差计算值的大小来选择较好的模型来反应各变量与事故持续时间的关系，进而更好地说明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。 针对问题二：沿用问题一中的方法，对视频2中影响通行能力的各个变量进行数据采集，同样使用matlab对时间断层处进行插值拟合处理，再将所得到的的变化图像与题一中各变量的变化趋势进行对比分析，其中考虑到两视频的时间段与两视频的事故时长不同，从而采用多种对比方式（如以事故发生前、中、后三时段比较差值、以事故相同持续时间进行对比、以整个事故时间段按比例分配时间进行对比）来更好地说明这一差异。由于小区口的位置不同、时间段是否处于车流高峰期以及1、2、3道车流比例不同等因素的影响，采用不同的数据采集方式使采集的变量数据的实用性更强，从而最后得到视频1中的道路被占用影响程度高于视频2中的影响程度，再者从差异图像的变化波动中得到验证，使其合理性更强。 针对问题三：运用问题1、2中三个变量与持续时间的关系作为纽带，再根据附件5中的信号相位确定出车流量的测量周期为一分钟，测量出上游车流量随时间的变化情况，而事故横断面实际通行能力与持续时间的关系已在1、2问中由拟合得到，所以再根据波动理论预测道路异常下车辆长度模型的结论，结合采集数据得到的函数关系建立数学模型，最后得出事故发生后，车辆排队长度与事故横断面实际通行能力、事故持续时间以及路段上游车流量这三者之间的关系式。 针对问题四：在问题3建立的模型下，利用问题4中提供的变量数据推导出其它相关变量值，然后代入模型，估算出时间长度，以此检验模型的操作性及可靠性。 关键词：通行能力车流波动理论车流量车流速度车流密度

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

数学建模优秀论文模板(全国一等奖模板)

Haozl觉得数学建模论文格式这么样设置 版权归郝竹林所有，材料仅学习参考 版权：郝竹林 备注☆ ※§等等字符都可以作为问题重述左边的。。。。。一级标题 所有段落一级标题设置成段落前后间距13磅 图和表的标题采用插入题注方式题注样式在样式表中设置居中五号字体 Excel中画出的折线表字体采用默认格式宋体正文10号 图标题在图上方段落间距前0.25行后0行 表标题在表下方段落间距前0行后0.25行 行距均使用单倍行距 所有段落均把4个勾去掉 注意Excel表格插入到word的方式在Excel中复制后，粘贴，word2010粘贴选用使用目标主题嵌入当前 Dsffaf 所有软件名字第一个字母大写比如E xcel 所有公式和字母均使用MathType编写 公式编号采用MathType编号格式自己定义

农业化肥公司的生产与销售优化方案 摘 要 要求总分总 本文针对储油罐的变位识别与罐容表标定的计算方法问题，运用二重积分法和最小二乘法建立了储油罐的变位识别与罐容表标定的计算模型，分别对三种不同变位情况推导出的油位计所测油位高度与实际罐容量的数学模型，运用matlab 软件编程得出合理的结论，最终对模型的结果做出了误差分析。 针对问题一要求依据图4及附表1建立积分数学模型研究罐体变位后对罐容表的影响，并给出罐体变位后油位高度间隔为1cm 的罐容表标定值。我们作图分析出实验储油罐出现纵向倾斜 14.时存在三种不同的可能情况，即储油罐中储油量较少、储油量一般、储油量较多的情况。针对于每种情况我们都利用了高等数学求容积的知识，以倾斜变位后油位计所测实际油位高度为积分变量，进行两次积分运算，运用MATLAB 软件推导出了所测油位高度与实际罐容量的关系式。并且给出了罐体倾斜变位后油位高度间隔为1cm 的罐容标定值（见表1），最后我们对倾斜变位前后的罐容标定值残差进行分析，得到样本方差为4103878.2-?，这充分说明残差波动不大。我们得出结论：罐体倾斜变位后，在同一油位条件下倾斜变位后罐容量比变位前罐容量少L 243。 表 1.1 针对问题二要求对于图1所示的实际储油罐，试建立罐体变位后标定罐容表的数学模型，即罐内储油量与油位高度及变位参数（纵向倾斜角度α和横向偏转角度β）之间的一般关系。利用罐体变位后在进/出油过程中的实际检测数据（附件2），根据所建立的数学模型确定变位参数，并给出罐体变位后油位高度间隔为10cm 的罐容表标定值。进一步利用附件2中的实际检测数据来分析检验你们模型的正确性与方法的可靠性。我们根据实际储油罐的特殊构造将实际储油罐分为三部分，左、右球冠状体与中间的圆柱体。运用积分的知识，按照实际储油罐的纵向变位后油位的三种不同情况。利用MATLAB 编程进行两次积分求得仅纵向变位时油量与油位、倾斜角α的容积表达式。然后我们通过作图分析油罐体的变位情况，将双向变位后的油位h 与仅纵向变位时的油位0h 建立关系表达式01.5(1.5)cos h h β=--，从而得到双向变位油量与油位、倾斜角α、偏转角β的容积表达式。利用附件二的数据，采用最小二乘法来确定倾斜角α、偏转角β的值，用matlab 软件求出03.3=α、04=β α=3.30，β=时总的平均相对误差达到最小，其最小值为0.0594。由此得到双向变位后油量与油位的容积表达式V ，从而确定了双向变位后的罐容表(见表2)。 本文主要应用MATLAB 软件对相关的模型进行编程求解，计算方便、快捷、准确，整篇文章采取图文并茂的效果。文章最后根据所建立的模型用附件2中的实际检测数据进行了误差分析，结果可靠，使得模型具有现实意义。 关键词：罐容表标定；积分求解；最小二乘法；MATLAB ；误差分

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

SARS传播的数学模型 数学建模全国赛优秀论文

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城市表层土壤重金属污染分析 摘要 本文旨在对城市土壤地质环境的重金属污染状况进行分析，建立模型对金属污染物的分布特点、污染程度、传播特征以及污染源的确定进行有效的描述、评价和定位。 对于重金属空间分布问题，首先基于克里金插值法，应用Surfer 8软件对各数据点的分布情况进行模拟，得到了直观的重金属污染空间分布图形；随后，分别用内梅罗综合污染指数以及模糊评价标准和模型对城区内不同区域重金属的污染程度进行了评判。 对于金属污染的主要原因分析问题，基于因子分析法、问题一的结果和对各个金属污染物的来源分析等因素，判断出金属污染的主要原因有：工业生产、汽车尾气排放、石油加工并推测该区域是镍矿富集区。随后讨论了污染源之间的相互关系和不同金属的污染贡献率。 针对污染源位置确定问题，我们建立了两个模型：模型一以流程图的形式出现，基于污染传播的一般规律建立模型，求取污染源范围，模型作用更倾向于确定污染源的位置；模型二基于最小二乘法原理，建立了拟合二次曲面方程，在有效确定污染源的同时也反映了其传播特征，模型更加清楚，理论性也更强。 在研究城市地质环境的演变模式问题中，我们对针对污染源位置确定问题所建模型的优缺点进行了评价，同时建立了考虑了时间，地域环境和传播媒介的污染物传播模型，从而反映了地质的演变。 综上所述，本文模型的特点是从简单的模型建立起，强更准确的数学模型发展，逐步达到目标期望。 关键词：重金属污染，克里金插值最小二乘法因子分析流程图

一、问题重述 1.1问题背景 随着城市经济的快速发展和城市人口的不断增加，人类活动对城市环境质量的影响日显突出。对城市土壤地质环境异常的查证，以及如何应用查证获得的海量数据资料开展城市环境质量评价，研究人类活动影响下城市地质环境的演变模式，日益成为人们关注的焦点。评价和研究城市土壤重金属污染程度，讨论土壤中重金属的空间分布，研究城市土壤重金属污染特征、污染来源以及在环境中迁移、转化机理，并对城市环境污染治理和城市进一步的发展规划提出科学建议，不仅有利于城市生态环境良性发展，有利于人类与自然和谐，也有利于人类社会 健康和城市可持续发展[1] 。按照功能划分，城区一般可分为生活区、工业区、山区、主干道路区及公园绿地区等，不同的区域环境受人类活动影响的程度不同。 现对某城市城区土壤地质环境进行调查。为此，将所考察的城区划分为间距1公里左右的网格子区域，按照每平方公里1个采样点对表层土（0~10 厘米深度）进行取样、编号，并用GPS 记录采样点的位置。应用专门仪器测试分析，获得了每个样本所含的多种化学元素的浓度数据。另一方面，按照2公里的间距在那些远离人群及工业活动的自然区取样，将其作为该城区表层土壤中元素的背景值。 1.2 目标任务 (1) 给出8种主要重金属元素在该城区的空间分布，并分析该城区内不同区域重金属的污染程度。 (2) 通过数据分析，说明重金属污染的主要原因。 (3) 分析重金属污染物的传播特征，由此建立模型，确定污染源的位置。 (4) 分析所建立模型的优缺点，为更好地研究城市地质环境的演变模式，分析还应收集的信息，并进一步探索怎样利用收集的信息建立模型及解决问题。 二、 模型假设 1）忽略地下矿源对污染物浓度的影响； 2）认为海拔对污染物的分布较小，故只在少数模型中讨论其作用； 3）认为题目中的采样方式是科学的，能够客观反映污染源的分布。 三、 符号说明 3.1第一问中的符号说明 i p ——污染物i 的环境污染指数 i C ——污染物i 的实测值 i S ——污染物i 的背景值 m ax (/)i i C S ——土壤污染指数的最大值 (/)i i avg C S ——土壤污染指数的平均值