数学建模美赛论文中可以用到的短语
MCM美国大学生数学建模竞赛模板-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 theCommonly, h is aboutFrom 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 massUsing 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=c26．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, so23．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）公式自己根据计算所画的图：1、为了…….(目的)，我们作了…….图。
2014年美国大学生数学建模竞赛A题论文综述
数学建模综述2014年美国大学生数学建模竞赛A题论文综述我们小组精读两篇14年美赛A题论文，选择了其中一篇来进行学习，总结。
1、问题分析The Keep-Right-Except-To-Pass Rule除非超车否则靠右行驶的交通规则问题：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。
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论文：基于元胞自动机和蒙特卡罗方法,我们建立一个模型来讨论“靠右行”规则的影响。
首先,我们打破汽车的运动过程和建立相应的子模型car-generation的流入模型,对于匀速行驶车辆，我们建立一个跟随模型,和超车模型。
然后我们设计规则来模拟车辆的运动模型。
我们进一步讨论我们的模型规则适应靠右的情况和,不受限制的情况, 和交通情况由智能控制系统的情况。
我们也设计一个道路的危险指数评价公式。
我们模拟双车道高速公路上交通(每个方向两个车道,一共四条车道),高速公路双向三车道（总共6车道)。
通过计算机和分析数据。
我们记录的平均速度,超车取代率、道路密度和危险指数和通过与不受规则限制的比较评估靠右行的性能。
我们利用不同的速度限制分析模型的敏感性和看到不同的限速的影响。
左手交通也进行了讨论。
根据我们的分析,我们提出一个新规则结合两个现有的规则(靠右的规则和无限制的规则)的智能系统来实现更好的的性能。
该论文在一开始并没有作过多分析，而是一针见血的提出了自己对于这个问题的做法。
由于题目给出的背景只有一条交通规则，而且是题目很明确的提出让我们建立模型分析。
数学建模中的常用术语
数学建模中的常用术语数学建模是运用数学的语言和方法，通过建立模型来解决实际问题的一种手段。
在这个过程中，会涉及到一系列的常用术语，理解这些术语对于成功进行数学建模至关重要。
首先要提到的是“变量”。
变量是数学建模中的核心概念之一，它是可以变化的量，可以是数值、向量或者更复杂的数据结构。
例如，在研究物体运动时，时间和位置就是常见的变量。
变量分为自变量和因变量，自变量是主动变化的因素，因变量则是随着自变量的变化而变化的结果。
“参数”也是常见的术语。
参数通常是固定不变的量，用于描述模型的特征或限制条件。
比如在一个抛物线方程中，二次项系数就是一个参数，它决定了抛物线的开口方向和宽窄程度。
“函数”在数学建模中起着关键作用。
它描述了变量之间的关系，将输入（自变量）与输出（因变量）联系起来。
例如，在经济学中，成本函数可以表示成本与产量之间的关系。
“约束条件”是对模型的限制和规定。
比如在资源分配问题中，资源的总量就是一种约束条件，确保分配方案不会超出可用资源的范围。
“目标函数”用于定义模型要优化或最大化、最小化的目标。
例如，在生产计划中，目标可能是使成本最小化或利润最大化，相应的成本函数或利润函数就是目标函数。
“模型假设”是建立数学模型的重要步骤之一。
为了简化问题，我们会做出一些合理的假设。
但需要注意的是，假设不能过于简化以至于失去问题的本质特征。
比如在研究车辆行驶问题时，可能会假设道路是平坦的、风速为零等。
“模型求解”是运用数学方法和工具来找出满足模型条件的解。
这可能涉及到代数运算、微积分、线性规划等多种数学技术。
“灵敏度分析”用于研究模型中参数的变化对结果的影响程度。
通过这种分析，可以了解模型的稳定性和可靠性。
“误差分析”则是评估模型预测结果与实际情况之间的差异。
这有助于我们判断模型的准确性，并在必要时对模型进行改进。
“模拟”是通过计算机程序或其他手段来模拟模型的运行过程，以观察不同情况下的结果。
“验证”是将模型的结果与实际数据进行比较，以检验模型的有效性。
数模美国赛总结部分英文
数模美国赛总结部分英文第一篇：数模美国赛总结部分英文Conclusions1、As 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、The 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。
美赛数学建模比赛论文模板
The Keep-Right-Except-To-Pass RuleSummaryAs 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 controlContentContent (2)1. Introduction (3)2. Analysis of the problem (3)3. Assumption (3)4. Symbol Definition (3)5. Models (4)5.1 Building of the Cellular automaton model (4)5.1.1 Verify the effectiveness of the keep right except to pass rule (4)5.1.2 Numerical simulation results and discussion (5)5.1.3 Conclusion (8)5.2 The solving of second question (8)5.2.1 The building of the stochastic multi-lane traffic model (9)5.2.2 Conclusion (9)5.3 Taking the an intelligent vehicle system into a account (9)5.3.1 Introduction of the Intelligent Vehicle Highway Systems (9)5.3.2 Control problem (9)5.3.3 Results and analysis (9)5.3.4 The comprehensive analysis of the result (10)6. Improvement of the model (11)6.1 strength and weakness (11)6.1.1 Strength (11)6.1.2 Weakness (11)6.2 Improvement of the model (11)7. Reference (13)1. IntroductionAs is known to all, it’s essential for us to drive automobiles, thus the driving rules is crucial important. In many countries like USA, China, drivers obey the rules which called “The Keep-Right-Except-To-Pass (that is, when driving automobiles, the rule requires drivers to drive in the right-most unless theyare passing another vehicle)”.2. Analysis of the problemFor the first question, we decide to use the Cellular automaton to build models,then analyze the performance of this rule in light and heavy traffic. Firstly,we mainly use the vehicle density to distinguish the light and heavy traffic; secondly, we consider the traffic flow and safe as the represent variable which denotes the light or heavy traffic; thirdly, we build and analyze a Cellular automaton model; finally, we judge the rule through two different driving rules,and then draw conclusions.3. AssumptionIn order to streamline our model we have made several key assumptions●The highway of double row three lanes that we study can representmulti-lane freeways.●The data that we refer to has certain representativeness and descriptive●Operation condition of the highway not be influenced by blizzard oraccidental factors●Ignore the driver's own abnormal factors, such as drunk driving andfatigue driving●The operation form of highway intelligent system that our analysis canreflect intelligent system●In the intelligent vehicle system, the result of the sampling data hashigh accuracy.4. Symbol Definitioni The number of vehiclest The time5. ModelsBy analyzing the problem, we decided to propose a solution with building a cellular automaton model.5.1 Building of the Cellular automaton modelThanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years. Let )(t x i be the position of vehicle i at time t , )(t v i be the speed of vehicle i at time t , p be the random slowing down probability, and R be the proportion of trucks and buses, the distance between vehicle i and the front vehicle at time t is:1)()(1--=-t x t x gap i i i , if the front vehicle is a small vehicle.3)()(1--=-t x t x gap i i i , if the front vehicle is a truck or bus.5.1.1 Verify the effectiveness of the keep right except to pass ruleIn addition, according to the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow:There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120–100km/h (including 100 km/h)；the speed of the second lane (the middle lane) is 100–80km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right.● Lane changing rules based lane speed controlIf vehicle on the high-speed lane meets control v v <, ),1)(min()(max v t v t gap i f i +≥, safe b i gap t gap ≥)(, the vehicle will turn into the adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where control v is the minimum speed of the corresponding lane.● The application of the Nasch model evolutionLet d P be the lane changing probability (taking into account the actual situation that some drivers like driving in a certain lane, and will not takethe initiative to change lanes), )(t gap f i indicates the distance between the vehicle and the nearest front vehicle, )(t gap b i indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane changing equals to the maximum speed of the following vehicle in the adjacent lanes.Lane changing rules based on keeping right except to passIn general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), interacting process (interacting between the two flows), and merging process (the two flows merging into one) [4].Fig.5.1.1 Control plan of overtaking process(1) If vehicle on the first lane (passing lane) meets ),1)(min()(max v t v t gap i f i +≥ and safe b i gap t gap ≥)(, the vehicle will turn into the second lane, the speed of the vehicle after lane changing remains unchanged.5.1.2 Numerical simulation results and discussionIn order to facilitate the subsequent discussions, we define the space occupation rate as L N N p truck CAR ⨯⨯+=3/)3(, where CAR N indicates the number ofsmall vehicles on the driveway,truck N indicates the number of trucks and buses on the driveway, and L indicates the total length of the road. The vehicle flow volume Q is the number of vehicles passing a fixed point per unit time,T N Q T /=, where T N is the number of vehicles observed in time duration T .The average speed ∑∑⨯=T it i a v T N V 11)/1(, t i v is the speed of vehicle i at time t . Take overtaking ratio f p as the evaluation indicator of the safety of traffic flow, which is the ratio of the total number of overtaking and the number of vehicles observed. After 20,000 evolution steps, and averaging the last 2000 steps based on time, we have obtained the following experimental results. In order to eliminate the effect of randomicity, we take the systemic average of 20 samples [5].Overtaking ratio of different control rule conditionsBecause different control conditions of road will produce different overtaking ratio, so we first observe relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.(a) Based on passing lane control (b) Based on speed control Fig.5.1.3Fig.5.1.3 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.It can be seen from Fig. 5.1.3:(1) when the vehicle density is less than 0.05, the overtaking ratio will continue to rise with the increase of vehicle density; when the vehicle density is larger than 0.05, the overtaking ratio will decrease with the increase of vehicle density; when density is greater than 0.12, due to the crowding, it willbecome difficult to overtake, so the overtaking ratio is almost 0.(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with the increase of large vehicles; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than 0.5, the overtaking ratio will decrease with the increase of large vehicles, especially under lane-based control condition s the decline is very clear.● Concrete impact of under different control rules on overtaking ratioFig.5.1.4Fig.5.1.4 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions. (Figures in left-hand indicate the passing lane control, figures in right-hand indicate the speed control. 1f P is the overtaking ratio of small vehicles over large vehicles, 2f P is the overtaking ratio of small vehicles over small vehicles, 3f P is the overtaking ratio of large vehicles over small vehicles, 4f P is the overtaking ratio of large vehicles over large vehicles.). It can be seen from Fig. 5.1.4:(1) The overtaking ratio of small vehicles over large vehicles under passing lane control is much higher than that under speed control condition, which is because, under passing lane control condition, high-speed small vehicles have to surpass low-speed large vehicles by the passing lane, while under speed control condition, small vehicles are designed to travel on the high-speed lane, there is no low- speed vehicle in front, thus there is no need to overtake. ● Impact of different control rules on vehicle speedFig. 5.1.5 Relationships among vehicle density, proportion of large vehicles and average speed under different control conditions. (Figures in left-hand indicates passing lane control, figures in right-hand indicates speed control.a X is the average speed of all the vehicles, 1a X is the average speed of all the small vehicles, 2a X is the average speed of all the buses and trucks.).It can be seen from Fig. 5.1.5:(1) The average speed will reduce with the increase of vehicle density and proportion of large vehicles.(2) When vehicle density is less than 0.15,a X ,1a X and 2a X are almost the same under both control conditions.Effect of different control conditions on traffic flowFig.5.1.6Fig. 5.1.6 Relationships among vehicle density, proportion of large vehicles and traffic flow under different control conditions. (Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b indicates the traffic flow difference between the two conditions.It can be seen from Fig. 5.1.6：(1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0.4 to 1, the traffic flow of the two control conditions are basically the same.(2) Except that, the traffic flow under passing lane control condition is slightly larger than that of speed control condition.5.1.3 ConclusionIn this paper, we have established three-lane model of different control conditions, studied the overtaking ratio, speed and traffic flow under different control conditions, vehicle density and proportion of large vehicles.5.2 The solving of second question5.2.1 The building of the stochastic multi-lane traffic model5.2.2 ConclusionOn one hand, from the analysis of the model, in the case the stress is positive, we also consider the jam situation while making the decision. More specifically, if a driver is in a jam situation, applying ))(,2(x P B R results with a tendency of moving to the right lane for this driver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process )7.0,2(B where the probability of moving to the right is 0.7and to the left otherwise, and the conclusion is under the rule of keep left except to pass, So, the fundamental reason is the formation of the driving habit.5.3 Taking the an intelligent vehicle system into a accountFor the third question, if vehicle transportation on the same roadway was fully under the control of an intelligent system, we make some improvements for the solution proposed by us to perfect the performance of the freeway by lots of analysis.5.3.1 Introduction of the Intelligent Vehicle Highway SystemsWe will use the microscopic traffic simulator model for traffic simulation purposes. The MPC traffic controller that is implemented in the Matlab needs a traffic model to predict the states when the speed limits are applied in Fig.5.3.1. We implement a METANET model for prediction purpose[14].5.3.2 Control problemAs a constraint, the dynamic speed limits are given a maximum and minimum allowed value. The upper bound for the speed limits is 120 km/h, and the lower bound value is 40 km/h. For the calculation of the optimal control values, all speed limits are constrained to this range. When the optimal values are found, they are rounded to a multiplicity of 10 km/h, since this is more clear for human drivers, and also technically feasible without large investments.5.3.3 Results and analysisWhen the density is high, it is more difficult to control the traffic, since the mean speed might already be below the control speed. Therefore, simulations are done using densities at which the shock wave can dissolve without using control, and at densities where the shock wave remains. For each scenario, five simulations for three different cases are done, each with a duration of one hour. The results of the simulations are reported in Table 5.1, 5.2, 5.3.●Enforced speed limits●Intelligent speed adaptationFor the ISA scenario, the desired free-flow speed is about 100% of the speed limit. The desired free-flow speed is modeled as a Gaussian distribution, with a mean value of 100% of the speed limit, and a standard deviation of 5% of the speed limit. Based on this percentage, the influence of the dynamic speed limits is expected to be good[19].5.3.4 The comprehensive analysis of the resultFrom the analysis above, we indicate that adopting the intelligent speed control system can effectively decrease the travel times under the control of an intelligent system, in other words, the measures of dynamic speed control can improve the traffic flow.Evidently, under the intelligent speed control system, the effect of the dynamic speed control measure is better than that under the lane speed control mentioned in the first problem. Because of the application of the intelligent speed control system, it can provide the optimal speed limit in time. In addition, it can guarantee the safe condition with all kinds of detection device and the sensor under the intelligent speed system.On the whole, taking all the analysis from the first problem to the end into a account, when it is in light traffic, we can neglect the factor of safe with the help of the intelligent speed control system.Thus, under the state of the light traffic, we propose a new conclusion different from that in the first problem: the rule of keep right except to pass is more effective than that of lane speed control.And when it is in the heavy traffic, for sparing no effort to improve the operation efficiency of the freeway, we combine the dynamical speed control measure with the rule of keep right except to pass, drawing a conclusion that the application of the dynamical speed control can improve the performance of the freeway.What we should highlight is that we can make some different speed limit as for different section of road or different size of vehicle with the application of the Intelligent Vehicle Highway Systems.In fact, that how the freeway traffic operate is extremely complex, thereby,with the application of the Intelligent Vehicle Highway Systems, by adjusting our solution originally, we make it still effective to freeway traffic.6. Improvement of the model6.1 strength and weakness6.1.1 Strength●it is easy for computer simulating and can be modified flexibly to consideractual traffic conditions ,moreover a large number of images make the model more visual.●The result is effectively achieved all of the goals we set initially, meantimethe conclusion is more persuasive because of we used the Bernoulli equation.●We can get more accurate result as we apply Matlab.6.1.2 Weakness●The relationship between traffic flow and safety is not comprehensivelyanalysis.●Due to there are many traffic factors, we are only studied some of the factors,thus our model need further improved.6.2 Improvement of the modelWhile we compare models under two kinds of traffic rules, thereby we come to the efficiency of driving on the right to improve traffic flow in some circumstance. Due to the rules of comparing is too less, the conclusion is inadequate. In order to improve the accuracy, We further put forward a kinds of traffic rules: speed limit on different type of cars.The possibility of happening traffic accident for some vehicles is larger, and it also brings hidden safe troubles. So we need to consider separately about different or specific vehicle types from the angle of the speed limiting in order to reduce the occurrence of traffic accidents, the highway speed limit signs is in Fig.6.1.Fig .6.1Advantages of the improving model are that it is useful to improve the running condition safety of specific type of vehicle while considering the difference of different types of vehicles. However, we found that the rules may be reduce the road traffic flow through the analysis. In the implementation it should be at the 85V speed of each model as the main reference basis. In recent years, the85V of some researchers for the typical countries from Table 6.1[ 21]:Author Country ModelOttesen and Krammes2000 AmericaLC DC L DC V C ⨯---=01.0012.057.144.10285Andueza2000Venezuela ].[308.9486.7)/894()/2795(25.9885curve horizontal L DC Ra R V T++--=].[tan 819.27)/3032(69.10085gent L R V T +-= Jessen2001America][00239.0614.0279.080.86185LSD ADT G V V P --+=][00212.0432.010.7285NLSD ADT V V P -+=Donnell2001 America22)2(8500724.040.10140.04.78T L G R V --+=22)3(85008369.048.10176.01.75T L G R V --+=22)4(8500810.069.10176.05.74T L G R V --+=22)5(8500934.008.21.83T L G V --=BucchiA.BiasuzziK. And SimoneA.2005Italy DCV 124.0164.6685-= DCE V 4.046.3366.5585--=2855.035.1119.0745.65DC E DC V ---=FitzpatrickAmericaKV 98.17507.11185-= Meanwhile, there are other vehicles driving rules such as speed limit in adverseweather conditions. This rule can improve the safety factor of the vehicle to some extent. At the same time, it limits the speed at the different levels.7. Reference[1] M. Rickert, K. Nagel, M. Schreckenberg, A. Latour, Two lane trafficsimulations using cellular automata, Physica A 231 (1996) 534–550.[20] J.T. Fokkema, Lakshmi Dhevi, Tamil Nadu Traffi c Management and Control inIntelligent Vehicle Highway Systems,18(2009).[21] Yang Li, New Variable Speed Control Approach for Freeway. (2011) 1-66。
美国大学生数学建模竞赛MCM写作模板（各个部分）
美国⼤学⽣数学建模竞赛MCM写作模板（各个部分）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。
美赛数学建模英文写作
第二部分 怎样写作论文主体项目
标题（Title)
基本功能：概括全文；吸引读者；便于检索 语言特点：一般不用完整的句子；多用名词 词组或动名词，如: Database Logic,
Conference Interpreting and Its Effect Evaluation, Nonlinear Waves in Elastic Rods， Introducing Management into…
复合句多 科学技术是研究外界事物的发展变化规律 极其应用的学问。为了十分准确地反映事 物内在联系，就需要严密的逻辑思维，而 这种思维内容反映在语言的形式上，就必 然是并列关系和多种主从关系的长句。如:
An electric current which reverses its direction at regular intervals, and which is constantly changing in magnitude is called an alternating current, which is usually abbreviated to a.c. …
“Investigation on …”, “Observation on …”, “The Method of …”, “Some thought on…”, “A research on…”等冗余套语 。
4. 少用问题性标题 5. 避免名词与动名词混杂使用 如:标题是 “The Treatment of Heating and Eutechticum of Steel” 宜改为 “Heating and Eutechticuming of Steel” 6. 避免使用非标准化的缩略语 论文标题要 求简洁,但一般不使用缩略语 ,更不能使用 非标准化的缩略语 。
美国大学生数学建模MCM 数学专用名词
美国大学生数学建模MCM 数学专用名词augmented matrix增广矩阵asymptotic渐进的asymptote渐进线asymmetrical非对称的associative law结合律ascending上升的arrangement排列arithmetic算术argument幅角，幅度，自变量，论证area面积arc length弧长apothem边心距apex顶点aperiodic非周期的antisymmetric反对称的antiderivative原函数anticlockwise逆时针的annihilator零化子angular velocity角速度angle of rotation旋转角angle of incidence入射角angle of elevation仰角angle of depression俯角angle of circumference圆周角analytic space复空间analytic geometry解析几何analytic function解析函数analytic extension解析开拓amplitude幅角，振幅alternative互斥的alternate series交错级数almost everywhere几乎处处algebraic topology代数拓扑algebraic expression代数式algebraic代数的affine仿射(几何学)的admissible error容许误差admissible容许的adjugate伴随转置的adjoint operator伴随算子adjoint伴随的adjacency邻接additive加法，加性acute angle锐角accumulation point聚点accidential error偶然误差accessible point可达点abstract space抽象空间abstract algebra抽象代数absolute value绝对值absolute integrable绝对可积absolute convergent绝对收敛Abelian阿贝尔的，交换的balance equation平衡方程bandwidth带宽barycenter重心base基base vectors基向量biased error有偏误差biased statistic有偏统计量bilinear双线性的bijective双射的bilateral shift双侧位移的binomial二项式bisector二等分线，平分线boundary边界的，边界bounded有界的broken line折线bundle丛，把，卷calculus微积分calculus of variations变分法cancellation消去canonical典型的，标准的canonical form标准型cap交，求交运算capacity容量cardinal number基数Cartesian coordinates笛卡尔坐标category范畴，类型cell单元，方格，胞腔cell complex胞腔复形character特征标characterization特征circuit环路，线路，回路circular ring圆环circulating decimal循环小数clockwise顺时针方向的closed ball闭球closure闭包cluster point聚点coefficient系数cofinal共尾的cohomology上同调coincidence重合，叠和collinear共线的collective集体的columnar rank列秩combinatorial theory组合理论common tangent公切线commutative交换的compact紧的compact operator紧算子compatibility相容性compatible events相容事件complementary余的，补的complete完全的，完备的complex analysis复变函数论complex potential复位势composite复合的concave function凹函数concentric circles同心圆concurrent共点conditional number条件数confidence interval置信区间conformal共形的conic圆锥的conjugate共轭的connected连通的connected domain连通域consistence相容，一致constrained约束的continuable可延拓的continuity连续性contour周线，回路，轮廓线convergence收敛性convexity凸形convolution对和，卷积coordinate坐标coprime互质的，互素的correspondence对应coset陪集countable可数的counterexample反例covariance协方差covariant共变的covering覆盖critical临界的cubic root立方根cup并，求并运算curl旋度curvature曲率curve曲线cyclic循环的decade十进制的decagon十边形decimal小数的，十进制的decision theory决策论decomposable可分解的decreasing递减的decrement减量deduction推论，归纳法defect亏量，缺陷deficiency亏格definition定义definite integral定积分deflation压缩deflection挠度，挠率，变位degenerate退化的deleted neighborhood去心邻域denominator分母density稠密性，密度density function密度函数denumerable可数的departure偏差，偏离dependent相关的dependent variable因变量derangement重排derivation求导derivative导数descent下降determinant行列式diagram图，图表diameter直径diamond菱形dichotomy二分法diffeomorphism微分同胚differentiable可微的differential微分differential geometry微分几何difference差，差分digit数字dimension维数directed graph有向图directed set有向集direct prodect直积direct sum直和direction angle方向角directional derivative方向导数disc圆盘disconnected不连通的discontinuous不连续的discrete离散的discriminant判别式disjoint不相交的disorder混乱，无序dissection剖分dissipation损耗distribution分布，广义函数divergent发散的divisor因子，除数division除法domain区域，定义域dot product点积double integral二重积分dual对偶dynamic model动态模型dynamic programming动态规划dynamic system动力系统eccentricity离心率econometrics计量经济学edge棱，边eigenvalue特征值eigenvector特征向量eigenspace特征空间element元素ellipse椭圆embed嵌入empirical equation经验公式empirical assumption经验假设endomorphism自同态end point端点entropy熵entire function整函数envelope包络epimorphism满同态equiangular等角equilateral等边的equicontinuous等度连续的equilibrium平衡equivalence等价error estimate误差估计estimator估计量evaluation赋值，值的计算even number偶数exact sequence正合序列exact solution精确解excenter外心excision切割，分割exclusive events互斥事件exhaustive穷举的expansion展开，展开式expectation期望experimental error实验误差explicit function显函数exponent指数extension扩张，外延face面factor因子factorial阶乘fallacy谬误fiducial置信field域，场field theory域论figure图形，数字finite有限的finite group有限群finite iteration有限迭代finite rank有限秩finitely covered有限覆盖fitting拟合fixed point不动点flag标志flat space平旦空间formula公式fraction分数，分式frame架，标架free boundary自由边界frequency频数，频率front side正面function函数functional泛函functor函子，算符fundamental group基本群fuzzy模糊的gain增益，放大率game对策gap间断，间隙general topology一般拓扑学general term通项generalized普遍的，推广的generalized inverse广义逆generalization归纳，普遍化generating line母线genus亏格geodesic测地线geometrical几何的geometric series几何级数golden section黄金分割graph图形，网格half plane半平面harmonic调和的hexagon六边形hereditary可传的holomorphic全纯的homeomorphism同胚homogeneous齐次的homology同调homotopy同伦hyperbola双曲线hyperplane超平面hypothesis假设ideal理想idempotent幂等的identical恒等，恒同identity恒等式，单位元ill-condition病态image像点，像imaginary axis虚轴imbedding嵌入imitation模仿，模拟immersion浸入impulse function脉冲函数inclination斜角，倾角inclined plane斜面inclusion包含incomparable不可比的incompatible不相容的，互斥的inconsistent不成立的indefinite integral不定积分independence无关（性），独立（性）index指数，指标indivisible除不尽的inductive归纳的inductive definition归纳定义induced诱导的inequality不等式inertia law惯性律inference推理，推论infimum下确界infinite无穷大的infinite decimal无穷小数infinite series无穷级数infinitesimal无穷小的inflection point拐点information theory信息论inhomogeneous非齐次的injection内射inner point内点instability不稳定integer整数integrable可积的integrand被积函数integral积分intermediate value介值intersection交，相交interval区间intrinsic内在的，内蕴的invariant不变的inverse circular funct反三角函数inverse image逆像，原像inversion反演invertible可逆的involution对合irrational无理的，无理数irreducible不可约的isolated point孤立点isometric等距的isomorphic同构的iteration迭代joint distribution联合分布kernel核keyword关键词knot纽结known已知的large sample大样本last term末项lateral area侧面积lattice格子lattice point格点law of identity同一律leading coefficient首项系数leaf蔓叶线least squares solution最小二乘解lemma引理Lie algebra李代数lifting提升likelihood似然的limit极限linear combination线性组合linear filter线性滤波linear fraction transf线性分linear filter线性滤波式变换式变换linear functional线性泛函linear operator线性算子linearly dependent线性相关linearly independent线性无关local coordinates局部坐标locus(pl.loci)轨迹logarithm对数lower bound下界logic逻辑lozenge菱形lunar新月型main diagonal主对角线manifold流形mantissa尾数many-valued function多值函数map into映入map onto映到mapping映射marginal边缘master equation主方程mathermatical analysis数学分析mathematical expectati数学期望matrix(pl. matrices)矩阵maximal极大的，最大的maximum norm最大模mean平均，中数measurable可测的measure测度mesh网络metric space距离空间midpoint中点minus减minimal极小的，最小的model模型modulus模，模数moment矩monomorphism单一同态multi-analysis多元分析multiplication乘法multipole多极mutual相互的mutually disjoint互不相交natural boundary自然边界natural equivalence自然等价natural number自然数natural period固有周期negative负的，否定的neighborhood邻域nil-factor零因子nilpotent幂零的nodal节点的noncommutative非交换的nondense疏的，无处稠密的nonempty非空的noncountable不可数的nonlinear非线性的nonsingular非奇异的norm范数normal正规的，法线normal derivative法向导数normal direction法方向normal distribution正态分布normal family正规族normal operator正规算子normal set良序集normed赋范的n-tuple integral重积分number theory数论numerical analysis数值分析null空，零obtuse angle钝角octagon八边形octant卦限odd number奇数odevity奇偶性off-centre偏心的one-side单侧的open ball开球operations reserach运筹学optimality最优性optimization最优化optimum最佳条件orbit轨道order阶，级，次序order-preserving保序的order-type序型ordinal次序的ordinary寻常的，正常的ordinate纵坐标orient定方向orientable可定向的origin原点original state初始状态orthogonal正交的orthonormal规范化正交的outer product外积oval卵形线overdetermined超定的overlaping重叠，交迭pairity奇偶性pairwise两两的parabola抛物线parallel平行parallel lines平行线parallelogram平行四边形parameter参数parent population母体partial偏的，部分的partial ordering偏序partial sum部分和particle质点partition划分，分类path space道路空间perfect differential全微分period周期periodic decimal循环小数peripheral周界的，外表的periphery边界permissible容许的permutable可交换的perpendicular垂直perturbation扰动，摄动phase相，位相piecewise分段的planar平面的plane curve平面曲线plane domain平面区域plane pencil平面束plus加point of intersection交点pointwise逐点的polar coordinates极坐标pole极，极点polygon多边形polygonal line折线polynomial多项式positive正的，肯定的potency势，基数potential位势prime素的primitive本原的principal minor主子式prism棱柱proof theory证明论probability概率projective射影的，投影proportion比例pure纯的pyramid棱锥，棱锥体quadrant像限quadratic二次的quadric surface二次曲面quantity量，数量quasi-group拟群quasi-norm拟范数quasi-normal拟正规queuing theory排队论quotient商radial径向radical sign根号radication开方radian弧度radius半径ramified分歧的random随机randomize随机化range值域，区域，范围rank秩rational有理的raw data原始数据real function实函数reciprocal倒数的，互反的reciprocal basis对偶基reciprocity互反性rectangle长方形，矩形rectifiable可求长的recurring decimal循环小数reduce简化，化简reflection反射reflexive自反的region区域regular正则regular ring正则环related function相关函数remanent剩余的repeated root重根residue留数，残数resolution分解resolvent预解式right angle直角rotation旋转roundoff舍入row rank行秩ruled surface直纹曲面runs游程，取遍saddle point鞍点sample样本sampling取样scalar field标量场scalar product数量积，内积scale标尺，尺度scattering散射，扩散sectorial扇形self-adjoint自伴的semicircle半圆semi-definite半定的semigroup半群semisimple半单纯的separable可分的sequence序列sequential相继的，序列的serial序列的sheaf层side face侧面similar相似的simple curve简单曲线simplex单纯形singular values奇异值skeleton骨架skewness偏斜度slackness松弛性slant斜的slope斜率small sample小样本smooth manifold光滑流形solid figure立体形solid geometry立体几何solid of rotation旋转体solution解solvable可解的sparse稀疏的spectral theory谱论spectrum谱sphere球面，球形spiral螺线spline function样条函数splitting分裂的statistics统计，统计学statistic统计量stochastic随机的straight angle平角straight line直线stream-line流线subadditive次可加的subinterval子区间submanifold子流形subset子集subtraction减法sum和summable可加的summand被加数supremum上确界surjective满射的symmetric对称的tabular表格式的tabulation列表，造表tangent正切，切线tangent space切空间tangent vector切向量tensor张量term项terminal row末行termwise逐项的tetrahedroid四面体topological拓扑的torsion挠率totally ordered set全序集trace迹trajectory轨道transcendental超越的transfer改变，传transfinite超限的transformation变换式transitive可传递的translation平移transpose转置transverse横截、trapezoid梯形treble三倍，三重trend趋势triad三元组triaxial三轴的，三维的trigon三角形trigonometric三角学的tripod三面角tubular管状的twist挠曲，扭转type类型，型，序型unbiased无偏的unbiased estimate无偏估计unbounded无界的uncertainty不定性unconditional无条件的unequal不等的uniform一致的uniform boundness一致有界uniformly bounded一致有界的uniformly continuous一致连续uniformly convergent一致收敛unilateral单侧的union并，并集unit单位unit circle单位圆unitary matrix酉矩阵universal泛的，通用的upper bound上界unrounded不舍入的unstable不稳定的valuation赋值value值variation变分，变差variety簇vector向量vector bundle向量丛vertex顶点vertical angle对顶角volume体积，容积wave波wave form波形wave function波函数wave equation波动方程weak convergence弱收敛weak derivatives弱导数weight权重，重量well-ordered良序的well-posed适定的zero零zero divisor零因子zeros零点zone域，带</Words>。
数学论文常用语句经典句式
数学论⽂常⽤语句经典句式常数C：the specific value of C is not required but should be clear from the surrounding context.C may denote different constants in what follows.Note the the value of the constants C will change during the proof.We denote by C the generic constant which is independent of... but may change line by line.We may use C and its variations, such as C_j, C_j^i, etc., to represent some generic smooth function(s) within... whose particular definition may change/(be changed) line by line.由于epsilon取值的任意性，我们可以得出结论...since epsilon is taken arbitrarily, we can conlude...我们暂时混⽤⼀些符号with (a slight)/some/an abuse of notationwith slight ambiguity我们假设f充分光滑：We assume that f is sufficiently smooth, so that we can take x-derivatives necessary times.XXX is the smallest possible extension in which differentiation is always possible.合理的(有依据的)假设：under a reasonable assumption on...取消假设：drop the assumption主要是理论上的重要性：is primarily of theoretical interest它本⾝也是个有意思的主题：It is of interest in its own right.想法/灵感来⾃于：The idea of this work/This derivation is motivated by抽出⼀个⼦列：after passing to a subsequence类似前⾯的⽅法：by arguments similar to the ones used in xxx, we have xxx.为了保持⾏⽂流畅To keep the context flowing这随后的内容中，就会清楚。
数学建模美赛论文中可以用到的短语
MCM论文写作常用句型（长文，建议收藏）The expression of ... can be expanded as: ......的表达式可扩展为...A is exponentially smaller than B, so it can be neglected.A对B来说呈指数级减小，所以可以忽略不计。
Equation (1) is reduced to:方程（1）化简为：Substitute the values into equation (3), we get...把这些值代入方程3，我们得到...According to our first assumption on Page 1,根据我们第一页的第一个假设，Thus we arrive at the conclusion：因此我们得到结论：From the model of ..., we find that theoretically, it is almost true that ...由...模型，我们从理论上证明了... 是真实可信的。
That is the theoretical basis for ... in many application areas.这是...在很多领域应用的理论基础。
To quantitatively analyze the different requirements of the two applications, we intro duce two measures:为了定量的分析这两种应用的不同要求，我们介绍来两个量度标准。
We give the criterion that...我们给出了...的判别标准According to the criterion of...根据...的标准So its expression can be derived from equation (3) with small change.所以它的表达式可以由方程3做微小改动而推出。
美赛数学建模比赛论文实用模板
The Keep-Right-Except-To-Pass RuleSummaryAs 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 controlContentContent (2)1. Introduction (3)2. Analysis of the problem (3)3. Assumption (3)4. Symbol Definition (3)5. Models (4)5.1 Building of the Cellular automaton model (4)5.1.1 Verify the effectiveness of the keep right except to pass rule (4)5.1.2 Numerical simulation results and discussion (5)5.1.3 Conclusion (8)5.2 The solving of second question (8)5.2.1 The building of the stochastic multi-lane traffic model (9)5.2.2 Conclusion (9)5.3 Taking the an intelligent vehicle system into a account (9)5.3.1 Introduction of the Intelligent Vehicle Highway Systems (9)5.3.2 Control problem (9)5.3.3 Results and analysis (9)5.3.4 The comprehensive analysis of the result (10)6. Improvement of the model (11)6.1 strength and weakness (11)6.1.1 Strength (11)6.1.2 Weakness (11)6.2 Improvement of the model (11)7. Reference (13)1. IntroductionAs is known to all, it’s essential for us to drive automobiles, thus the driving rules is crucial important. In many countries like USA, China, drivers obey the rules which called “The Keep-Right-Except-To-Pass (that is, when driving automobiles, the rule requires drivers to drive in the right-most unless theyare passing another vehicle)”.2. Analysis of the problemFor the first question, we decide to use the Cellular automaton to build models,then analyze the performance of this rule in light and heavy traffic. Firstly,we mainly use the vehicle density to distinguish the light and heavy traffic; secondly, we consider the traffic flow and safe as the represent variable which denotes the light or heavy traffic; thirdly, we build and analyze a Cellular automaton model; finally, we judge the rule through two different driving rules,and then draw conclusions.3. AssumptionIn order to streamline our model we have made several key assumptions●The highway of double row three lanes that we study can representmulti-lane freeways.●The data that we refer to has certain representativeness and descriptive●Operation condition of the highway not be influenced by blizzard oraccidental factors●Ignore the driver's own abnormal factors, such as drunk driving andfatigue driving●The operation form of highway intelligent system that our analysis canreflect intelligent system●In the intelligent vehicle system, the result of the sampling data hashigh accuracy.4. Symbol Definitioni The number of vehiclest The time5. ModelsBy analyzing the problem, we decided to propose a solution with building a cellular automaton model.5.1 Building of the Cellular automaton modelThanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years. Let )(t x i be the position of vehicle i at time t , )(t v i be the speed of vehicle i at time t , p be the random slowing down probability, and R be the proportion of trucks and buses, the distance between vehicle i and the front vehicle at time t is:1)()(1--=-t x t x gap i i i , if the front vehicle is a small vehicle.3)()(1--=-t x t x gap i i i , if the front vehicle is a truck or bus.5.1.1 Verify the effectiveness of the keep right except to pass ruleIn addition, according to the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow:There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120–100km/h (including 100 km/h)；the speed of the second lane (the middle lane) is 100–80km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right.● Lane changing rules based lane speed controlIf vehicle on the high-speed lane meets control v v <, ),1)(min()(max v t v t gap i f i +≥, safe b i gap t gap ≥)(, the vehicle will turn into the adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where control v is the minimum speed of the corresponding lane.● The application of the Nasch model evolutionLet d P be the lane changing probability (taking into account the actual situation that some drivers like driving in a certain lane, and will not takethe initiative to change lanes), )(t gap f i indicates the distance between the vehicle and the nearest front vehicle, )(t gap b i indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane changing equals to the maximum speed of the following vehicle in the adjacent lanes.Lane changing rules based on keeping right except to passIn general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), interacting process (interacting between the two flows), and merging process (the two flows merging into one) [4].Fig.5.1.1 Control plan of overtaking process(1) If vehicle on the first lane (passing lane) meets ),1)(min()(max v t v t gap i f i +≥ and safe b i gap t gap ≥)(, the vehicle will turn into the second lane, the speed of the vehicle after lane changing remains unchanged.5.1.2 Numerical simulation results and discussionIn order to facilitate the subsequent discussions, we define the space occupation rate as L N N p truck CAR ⨯⨯+=3/)3(, where CAR N indicates the number ofsmall vehicles on the driveway,truck N indicates the number of trucks and buses on the driveway, and L indicates the total length of the road. The vehicle flow volume Q is the number of vehicles passing a fixed point per unit time,T N Q T /=, where T N is the number of vehicles observed in time duration T .The average speed ∑∑⨯=T it i a v T N V 11)/1(, t i v is the speed of vehicle i at time t . Take overtaking ratio f p as the evaluation indicator of the safety of traffic flow, which is the ratio of the total number of overtaking and the number of vehicles observed. After 20,000 evolution steps, and averaging the last 2000 steps based on time, we have obtained the following experimental results. In order to eliminate the effect of randomicity, we take the systemic average of 20 samples [5].Overtaking ratio of different control rule conditionsBecause different control conditions of road will produce different overtaking ratio, so we first observe relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.(a) Based on passing lane control (b) Based on speed control Fig.5.1.3Fig.5.1.3 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.It can be seen from Fig. 5.1.3:(1) when the vehicle density is less than 0.05, the overtaking ratio will continue to rise with the increase of vehicle density; when the vehicle density is larger than 0.05, the overtaking ratio will decrease with the increase of vehicle density; when density is greater than 0.12, due to the crowding, it willbecome difficult to overtake, so the overtaking ratio is almost 0.(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with the increase of large vehicles; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than 0.5, the overtaking ratio will decrease with the increase of large vehicles, especially under lane-based control condition s the decline is very clear.● Concrete impact of under different control rules on overtaking ratioFig.5.1.4Fig.5.1.4 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions. (Figures in left-hand indicate the passing lane control, figures in right-hand indicate the speed control. 1f P is the overtaking ratio of small vehicles over large vehicles, 2f P is the overtaking ratio of small vehicles over small vehicles, 3f P is the overtaking ratio of large vehicles over small vehicles, 4f P is the overtaking ratio of large vehicles over large vehicles.). It can be seen from Fig. 5.1.4:(1) The overtaking ratio of small vehicles over large vehicles under passing lane control is much higher than that under speed control condition, which is because, under passing lane control condition, high-speed small vehicles have to surpass low-speed large vehicles by the passing lane, while under speed control condition, small vehicles are designed to travel on the high-speed lane, there is no low- speed vehicle in front, thus there is no need to overtake.● Impact of different control rules on vehicle speedFig. 5.1.5 Relationships among vehicle density, proportion of large vehicles and average speed under different control conditions. (Figures in left-hand indicates passing lane control, figures in right-hand indicates speed control.a X is the average speed of all the vehicles, 1a X is the average speed of all the small vehicles, 2a X is the average speed of all the buses and trucks.).It can be seen from Fig. 5.1.5:(1) The average speed will reduce with the increase of vehicle density and proportion of large vehicles.(2) When vehicle density is less than 0.15,a X ,1a X and 2a X are almost the same under both control conditions.Effect of different control conditions on traffic flowFig.5.1.6Fig. 5.1.6 Relationships among vehicle density, proportion of large vehicles and traffic flow under different control conditions. (Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b indicates the traffic flow difference between the two conditions.It can be seen from Fig. 5.1.6：(1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0.4 to 1, the traffic flow of the two control conditions are basically the same.(2) Except that, the traffic flow under passing lane control condition is slightly larger than that of speed control condition.5.1.3 ConclusionIn this paper, we have established three-lane model of different control conditions, studied the overtaking ratio, speed and traffic flow under different control conditions, vehicle density and proportion of large vehicles.5.2 The solving of second question5.2.1 The building of the stochastic multi-lane traffic model5.2.2 ConclusionOn one hand, from the analysis of the model, in the case the stress is positive, we also consider the jam situation while making the decision. More specifically, if a driver is in a jam situation, applying ))(,2(x P B R results with a tendency of moving to the right lane for this driver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process )7.0,2(B where the probability of moving to the right is 0.7and to the left otherwise, and the conclusion is under the rule of keep left except to pass, So, the fundamental reason is the formation of the driving habit.5.3 Taking the an intelligent vehicle system into a accountFor the third question, if vehicle transportation on the same roadway was fully under the control of an intelligent system, we make some improvements for the solution proposed by us to perfect the performance of the freeway by lots of analysis.5.3.1 Introduction of the Intelligent Vehicle Highway SystemsWe will use the microscopic traffic simulator model for traffic simulation purposes. The MPC traffic controller that is implemented in the Matlab needs a traffic model to predict the states when the speed limits are applied in Fig.5.3.1. We implement a METANET model for prediction purpose[14].5.3.2 Control problemAs a constraint, the dynamic speed limits are given a maximum and minimum allowed value. The upper bound for the speed limits is 120 km/h, and the lower bound value is 40 km/h. For the calculation of the optimal control values, all speed limits are constrained to this range. When the optimal values are found, they are rounded to a multiplicity of 10 km/h, since this is more clear for human drivers, and also technically feasible without large investments.5.3.3 Results and analysisWhen the density is high, it is more difficult to control the traffic, since the mean speed might already be below the control speed. Therefore, simulations are done using densities at which the shock wave can dissolve without using control, and at densities where the shock wave remains. For each scenario, five simulations for three different cases are done, each with a duration of one hour. The results of the simulations are reported in Table 5.1, 5.2, 5.3. Table.5.1 measured results for the unenforced speed limit scenariodem q case#1 #2 #3 #4 #5 TTS:mean(std ) TPN 4700no shock 494.7452.1435.9414.8428.3445.21(6.9%) 5:4wave 3 5 8 8 0 14700nocontrolled520.42517.48536.13475.98539.58517.92(4.9%)6:364700 controlled 513.45488.43521.35479.75-486.5500.75(4.0%)6:244700 no shockwave493.9472.6492.78521.1489.43493.96(3.5%)6:034700 uncontrolled635.1584.92643.72571.85588.63604.84(5.3%)7:244700 controlled 575.3654.12589.77572.15586.46597.84(6.4%)7:19●Enforced speed limits●Intelligent speed adaptationFor the ISA scenario, the desired free-flow speed is about 100% of the speed limit. The desired free-flow speed is modeled as a Gaussian distribution, with a mean value of 100% of the speed limit, and a standard deviation of 5% of the speed limit. Based on this percentage, the influence of the dynamic speed limits is expected to be good[19].5.3.4 The comprehensive analysis of the resultFrom the analysis above, we indicate that adopting the intelligent speed control system can effectively decrease the travel times under the control of an intelligent system, in other words, the measures of dynamic speed control can improve the traffic flow.Evidently, under the intelligent speed control system, the effect of the dynamic speed control measure is better than that under the lane speed control mentioned in the first problem. Because of the application of the intelligent speed control system, it can provide the optimal speed limit in time. In addition, it can guarantee the safe condition with all kinds of detection device and the sensor under the intelligent speed system.On the whole, taking all the analysis from the first problem to the end into a account, when it is in light traffic, we can neglect the factor of safe with the help of the intelligent speed control system.Thus, under the state of the light traffic, we propose a new conclusion different from that in the first problem: the rule of keep right except to pass is more effective than that of lane speed control.And when it is in the heavy traffic, for sparing no effort to improve the operation efficiency of the freeway, we combine the dynamical speed control measure with the rule of keep right except to pass, drawing a conclusion that the application of the dynamical speed control can improve the performance ofthe freeway.What we should highlight is that we can make some different speed limit as for different section of road or different size of vehicle with the application of the Intelligent Vehicle Highway Systems.In fact, that how the freeway traffic operate is extremely complex, thereby, with the application of the Intelligent Vehicle Highway Systems, by adjusting our solution originally, we make it still effective to freeway traffic.6. Improvement of the model6.1 strength and weakness6.1.1 Strength●it is easy for computer simulating and can be modified flexibly to consideractual traffic conditions ,moreover a large number of images make the model more visual.●The result is effectively achieved all of the goals we set initially, meantimethe conclusion is more persuasive because of we used the Bernoulli equation.●We can get more accurate result as we apply Matlab.6.1.2 Weakness●The relationship between traffic flow and safety is not comprehensivelyanalysis.●Due to there are many traffic factors, we are only studied some of the factors,thus our model need further improved.6.2 Improvement of the modelWhile we compare models under two kinds of traffic rules, thereby we come to the efficiency of driving on the right to improve traffic flow in some circumstance. Due to the rules of comparing is too less, the conclusion is inadequate. In order to improve the accuracy, We further put forward a kinds of traffic rules: speed limit on different type of cars.The possibility of happening traffic accident for some vehicles is larger, and it also brings hidden safe troubles. So we need to consider separately about different or specific vehicle types from the angle of the speed limiting in order to reduce the occurrence of traffic accidents, the highway speed limit signs is in Fig.6.1.Fig .6.1Advantages of the improving model are that it is useful to improve the running condition safety of specific type of vehicle while considering the difference of different types of vehicles. However, we found that the rules may be reduce the road traffic flow through the analysis. In the implementation it should be at the 85V speed of each model as the main reference basis. In recent years, the 85V of some researchers for the typical countries from Table 6.1[ 21]: Table 6.1 Operating speed prediction modeAuthorCountry Model Ottesen andKrammes2000America LC DC L DC V C ⨯---=01.0012.057.144.10285Andueza2000Venezuel a ].[308.9486.7)/894()/2795(25.9885curve horizontal L DC Ra R V T ++--= ].[tan 819.27)/3032(69.10085gent L R V T +-= Jessen2001 America ][00239.0614.0279.080.86185LSD ADT G V V P --+=][00212.0432.010.7285NLSD ADT V V P -+=Donnell2001 America 22)2(8500724.040.10140.04.78T L G R V --+=22)3(85008369.048.10176.01.75T L G R V --+= 22)4(8500810.069.10176.05.74T L G R V --+=22)5(8500934.008.21.83T L G V --=BucchiA.BiasuzziK.And SimoneA.2005Italy DC V 124.0164.6685-= DC E V 4.046.3366.5585--= 2855.035.1119.0745.65DC E DC V ---= Fitzpatrick America KV 98.17507.11185-= Meanwhile, there are other vehicles driving rules such as speed limit in adverseweather conditions. This rule can improve the safety factor of the vehicle to some extent. At the same time, it limits the speed at the different levels.7. Reference[1] M. Rickert, K. Nagel, M. Schreckenberg, A. Latour, Two lane traffi csimulations using cellular automata, Physica A 231 (1996) 534–550.[20] J.T. Fokkema, Lakshmi Dhevi, Tamil Nadu Traffi c Management and Control inIntelligent Vehicle Highway Systems,18(2009).[21] Yang Li, New Variable Speed Control Approach for Freeway. (2011) 1-66。
数学建模术语
angle 相角
ans 最新表达式的运算结果
any 有非零元则为真
area 面域图
asec 反正割
asech 反双曲正割
asin 反正弦
asinh 反双曲正弦
atan 反正切
atan2 四象限反正切
atanh 反双曲正切
autumn 红、黄浓淡色
EraseMode 图形对象属性
error 显示错误信息
排列(permutation):P
组合(combination):C
..2/3 as many A as B: A=2/3*B
...twice as many... A as B: A=2*B
power 次方 （2^5=the fifth power of 2）
reciprocal 倒数 （x的倒数为1/x）
per capita 每人
mid point 中点
median of an trangle 三角形的中线
median 中数 <MEDIUM ADJ.>
length
width
height=altitude
in terms of 用...表达
be contained in 位于...上
-hedron -面体
hexahedron六面体
quadrihedron四面体=三角锥
cone圆锥（体积=1/3PI*R*R*H）
pyramid 角锥、棱椎, 金字塔, 叠罗汉
volume体积
cube立方数/立方体
cylinder圆柱体
sphere球体
美赛数学建模常用方法
美赛数学建模常用方法Mathematical modeling is an essential tool in the field of applied mathematics and is widely used in the modeling and analysis of real-world problems. 数学建模是应用数学领域中的一种重要工具，广泛应用于对现实世界问题的建模和分析。
There are several commonly used methods in mathematical modeling, including but not limited to differential equations, optimization, statistical analysis, and simulation. 在数学建模中有几种常用的方法，包括但不限于微分方程、优化、统计分析和模拟。
Differential equations are often used to describe how quantities change over time. 微分方程经常用于描述数量随时间的变化。
Optimization involves finding the best solution from a set of possible solutions, based on specific criteria or constraints. 优化涉及在一组可能的解决方案中找到基于特定标准或约束条件的最佳解决方案。
Statistical analysis is used to make inferences and predictions about data, using techniques such as regression analysis, hypothesis testing,and data visualization. 统计分析用于使用回归分析、假设检验和数据可视化等技术对数据进行推断和预测。
数模美赛论文常用词汇
exclusively专门undobtedly毫无疑问的notable 值得注意的tremedous/significant极大的notion概念definition定义——defineInterpret……as…… 理解……为invoke(+模型援引，引用equation方程式，等式function 因变量——提示符号的含义matrix矩阵，模型constant 常数，常量It requires I t o be a constant for …to be truealgorithm演算方法——a general algorithm 通用算法simplify the algorithm 简化算法we have produced a general algrrithm to solve this tpye of problems.derivative微分，倒数antiderivative 不定积分optimal results 最优结果invesgate the problem from different point of view调查问题——investgation调查survey 调查subproblem 子问题，次要问题——major problem 主要问题metric 度量标准，指标digit 数字delete some digitselement /component 元素解题思路seek/explore——explore different ideas探索不同的想法we seek to device a new model for solving the problem by exploring the new direction suggested by their investigations.解决方案design/device ——develop/establish/conductBased on our analysis, we design a model for the problem using integral linear programming(线性积分). We then devise a polynominal-time apprximation algorithm to produce near optimal ing integral linear programming.We then device a polynominal-time approximation toWe conduct sensitivity analysis on…to find…xxx analysis is also performed.解决结果tackle/solveWe tackle the problem using the new technique we developed in the previous section.While it is difficult to solve the problem completely, we are able to solve a major subproblem.计划与打算approach/proposeWe approach the problem using the proposed method.We propose a new approach to tackling the problem.词组Based on…以……为基础According to根据Devide …into…——subdivide into细分…is applied to…使用了……模型来……——we apply our model into将我们的模型运用于Model proves to be efficient in other sports.模型被证明在其他方面有效….,which indicates that………反映了…,which led to the change of…导致了……的变化We…..only to find that..我们……只是发现了……… doesn’t matter ……是无关的Take…as example/as a case study 举例formulate and justify the assumptions 阐述并证明假说design/establish a model设计模型devise an algorithm 设计一个运算法/计算程序carry out numerical simulations 进行数学模拟for our problem a relationship exists that(… 我们的问题中存在一个关系式，使……we will assume/suppose that…我们假设……compare with different approaches 与不同的措施相比较There are at least two notions of where the sweet spot should be—an impact location on the bat that either· minimizesthe discomfort to the hands, or· maximizes the outgoing velocity Of the ball.We focus exclusively on the second definition我们专注于第二种定义We interpret the error of +2 as a normal distribution,.一with standard deviation of 1。
数模美赛论文常常使用辞汇
exclusively专门undobtedly毫无疑问的notable 值得注意的tremedous/significant极大的notion概念definition概念——defineInterpret……as…… 理解……为invoke(+模型援引，引用equation方程式，等式function 因变量——提示符号的含义matrix矩阵，模型constant 常数，常量It requires I t o be a constant for …to be truealgorithm演算方式——a general algorithm 通用算法simplify the algorithm 简化算法we have produced a general algrrithm to solve this tpye of problems.derivative微分，倒数antiderivative 不定积分optimal results 最优结果invesgate the problem from different point of view调查问题——investgation调查survey 调查subproblem 子问题，次要问题——major problem 主要问题metric 气宇标准，指标digit 数字delete some digitselement /component 元素解题思路seek/explore——explore different ideas探索不同的想法we seek to device a new model for solving the problem by exploring the new direction suggested by their investigations.解决方案design/device ——develop/establish/conductBased on our analysis, we design a model for the problem using integral linear programming(线性积分). We then devise a polynominal-time apprximation algorithm to produce near optimal integral linear then device a polynominal-time approximation toWe conduct sensitivity analysis on…to find…xxx analysis is also performed.解决结果tackle/solveWe tackle the problem using the new technique we developed in the previous it is difficult to solve the problem completely, we are able to solve a major subproblem.计划与打算approach/proposeWe approach the problem using the proposed method.We propose a new approach to tackling the problem.词组Based on…以……为基础According to按照Devide …into…——subdivide into细分…is applied to…利用了……模型来……——we apply our model into将咱们的模型运用于Model proves to be efficient in other sports.模型被证明在其他方面有效….,which indicates that………反映了…,which led to the change of…致使了……的转变We…..only to find that..咱们……只是发现了……… doesn’t matter ……是无关的Take…as example/as a case study 举例formulate and justify the assumptions 论述并证明假说design/establish a model设计模型devise an algorithm 设计一个运算法/计算程序carry out numerical simulations 进行数学模拟for our problem a relationship exists that(… 咱们的问题中存在一个关系式，使……we will assume/suppose that…咱们假设……compare with different approaches 与不同的办法相较较There are at least two notions of where the sweet spot should be—an impact location on the bat that either· minimizesthe discomfort to the hands, or· maximizes the outgoing velocity Of the ball.We focus exclusively on the second definition咱们专注于第二种概念We interpret the error of +2 as a normal distribution,.一with standard deviation of 1。
[DOC]-数学建模美赛论文标准格式参考--中英文对照
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[DOC]-数学建模美赛论文标准格式参考--中英文对照数学建模美赛论文标准格式参考--中英文对照Your Paper's Title Starts Here: Please Centeruse Helvetica (Arial) 14论文的题目从这里开始:用Helvetica (Arial)14号FULL First Author1, a, FULL Second Author2,b and Last Author3,c 第一第二第三作者的全名1Full address of first author, including country第一作者的地址全名，包括国家2Full address of second author, including country第二作者的地址全名，包括国家3List all distinct addresses in the same way第三作者同上aemail, bemail, cemail第一第二第三作者的邮箱地址Keywords: List the keywords covered in your paper. These keywords will also be used by the publisher to produce a keyword index.关键字: 列出你论文中的关键词。
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For the rest of the paper, please use Times Roman (Times New Roman) 12论文的其他部分请用Times Roman (Times New Roman) 12号字Abstract. This template explains and demonstrates how to prepareyour camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.Please make the page settings of your word processor to A4 format(21 x 29,7 cm or 8 x 11 inches); with the margins: bottom 1.5 cm (0.59 in) and top 2.5 cm (0.98 in), right/left margins must be 2 cm (0.78 in).摘要:这个模板解释和示范供稿技术刊物有限公司时，如何准备你的供相机使用文件。
数学建模名言名句
数学建模名言名句
1.数学建模是连接现实世界与数学世界的桥梁。
2.数学建模是一种艺术，它需要精确的技巧和深厚的理解。
3.数学建模是对现实问题的抽象和概括，它让我们更好地理解世界。
4.数学建模是思维的体操，它可以锻炼我们的思维能力和创造力。
5.数学建模是一种科学方法，它可以帮助我们探索未知的世界。
6.数学建模是一种语言，它可以帮助我们与世界进行交流。
7.数学建模是一种工具，它可以帮助我们解决现实世界中的问题。
8.数学建模是一种哲学，它可以帮助我们理解世界的本质。
9.数学建模是一种文化，它可以帮助我们传承和发扬数学的精神。
10.数学建模是一种智慧，它可以帮助我们认识和理解世界的复杂性。
11.数学建模是一种力量，它可以帮助我们改变世界。
12.数学建模是一种艺术，它可以帮助我们创造美。
13.数学建模是一种精神，它可以帮助我们追求卓越。
14.数学建模是一种勇气，它可以帮助我们面对挑战。
15.数学建模是一种乐趣，它可以帮助我们享受学习的过程。
16.数学建模是一种使命，它可以帮助我们实现自己的价值。
17.数学建模是一种责任，它可以帮助我们为社会做出贡献。
18.数学建模是一种信仰，它可以帮助我们坚持自己的理念。
19.数学建模是一种追求，它可以帮助我们实现自己的梦想。
20.数学建模是一种精神，它可以帮助我们超越自我。
数学专业词汇-美赛-数模-中英对照100页word文档
数学专业词汇 (1)代数英语： (7)数学专业词汇Aabsolute value 绝对值 accept 接受 acceptable region 接受域additivity 可加性 adjusted 调整的 alternative hypothesis 对立假设analysis 分析 analysis of covariance 协方差分析 analysis of variance 方差分析 arithmetic mean 算术平均值 association 相关性 assumption 假设 assumption checking 假设检验 availability 有效度average 均值Bbalanced 平衡的 band 带宽 bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验Ccalculate 计算 case 个案 category 类别 center of gravity 重心 central tendency 中心趋势 chi-square distribution 卡方分布 chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较 comparison 对照 components 构成，分量 compound 复合的confidence interval 置信区间consistency 一致性constant 常数continuous variable 连续变量 control charts 控制图 correlation 相关covariance 协方差 covariance matrix 协方差矩阵 critical point 临界点critical value 临界值 crosstab 列联表cubic 三次的，立方的 cubic term 三次项 cumulative distribution function 累加分布函数 curve estimation 曲线估计Ddata 数据 default 默认的 definition 定义 deleted residual 剔除残差density function 密度函数 dependent variable 因变量 description 描述design of experiment 试验设计 deviations 差异 df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离 distribution 分布D-optimal design D-优化设计Eeaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值 equal size 等含量 equation 方程 error 误差 estimate 估计 estimation of parameters 参数估计 estimations 估计量 evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的 exponential distributon 指数分布 extreme value 极值 F factor 因素，因子 factor analysis 因子分析 factor score 因子得分factorial designs 析因设计factorial experiment 析因试验fit 拟合fitted line 拟合线 fitted value 拟合值 fixed model 固定模型 fixed variable 固定变量 fractional factorial design 部分析因设计 frequency频数 F-test F检验 full factorial design 完全析因设计function 函数Ggamma distribution 伽玛分布 geometric mean 几何均值 group 组Hharmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设hypothesis test 假设检验Iindependence 独立 independent variable 自变量independent-samples 独立样本 index 指数 index of correlation 相关指数 interaction 交互作用interclass correlation 组内相关 interval estimate 区间估计 intraclass correlation 组间相关 inverse 倒数的iterate 迭代Kkernal 核 Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验 kurtosis 峰度Llarge sample problem 大样本问题 layer 层least-significant difference 最小显著差数 least-square estimation 最小二乘估计 least-square method 最小二乘法 level 水平 level of significance 显著性水平 leverage value 中心化杠杆值 life 寿命 life test 寿命试验 likelihood function 似然函数likelihood ratio test 似然比检验 linear 线性的 linear estimator 线性估计linear model 线性模型 linear regression 线性回归 linear relation 线性关系 linear term 线性项 logarithmic 对数的 logarithms 对数 logistic 逻辑的 lost function 损失函数Mmain effect 主效应matrix 矩阵maximum 最大值maximum likelihood estimation 极大似然估计 mean squared deviation(MSD) 均方差 mean sum of square 均方和 measure 衡量 media 中位数 M-estimator M估计minimum 最小值 missing values 缺失值 mixed model 混合模型 mode 众数model 模型Monte Carle method 蒙特卡罗法moving average 移动平均值multicollinearity 多元共线性multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析multiple regression equation 多元回归方程multiple response 多响应 multivariate analysis 多元分析Nnegative relationship 负相关 nonadditively 不可加性 nonlinear 非线性nonlinear regression 非线性回归 noparametric tests 非参数检验 normal distribution 正态分布 null hypothesis 零假设 number of cases 个案数Oone-sample 单样本 one-tailed test 单侧检验 one-way ANOVA 单向方差分析one-way classification 单向分类 optimal 优化的optimum allocation 最优配制 order 排序order statistics 次序统计量 origin 原点orthogonal 正交的 outliers 异常值Ppaired observations 成对观测数据 paired-sample 成对样本 parameter 参数parameter estimation 参数估计 partial correlation 偏相关partial correlation coefficient 偏相关系数 partial regression coefficient 偏回归系数percent 百分数percentiles 百分位数pie chart 饼图point estimate 点估计 poisson distribution 泊松分布 polynomial curve 多项式曲线polynomial regression 多项式回归polynomials 多项式positive relationship 正相关 power 幂P-P plot P-P概率图 predict 预测 predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析 proability 概率 probability density function 概率密度函数 probit analysis 概率分析 proportion 比例Qqadratic 二次的Q-Q plot Q-Q概率图quadratic term 二次项 quality control 质量控制 quantitative 数量的，度量的 quartiles 四分位数Rrandom 随机的random number 随机数random number 随机数random sampling 随机取样 random seed 随机数种子 random variable 随机变量randomization 随机化 range 极差 rank 秩 rank correlation 秩相关 rank statistic 秩统计量 regression analysis 回归分析 regression coefficient 回归系数 regression line 回归线 reject 拒绝 rejection region 拒绝域relationship 关系 reliability 可*性 repeated 重复的 report 报告，报表residual 残差 residual sum of squares 剩余平方和 response 响应 risk function 风险函数 robustness 稳健性 root mean square 标准差 row 行 run 游程 run test 游程检验Sample 样本 sample size 样本容量 sample space 样本空间 sampling 取样sampling inspection 抽样检验 scatter chart 散点图 S-curve S形曲线separately 单独地 sets 集合 sign test 符号检验 significance 显著性significance level 显著性水平significance testing 显著性检验significant 显著的，有效的significant digits 有效数字skewed distribution 偏态分布 skewness 偏度 small sample problem 小样本问题smooth 平滑 sort 排序 soruces of variation 方差来源 space 空间 spread 扩展 square 平方 standard deviation 标准离差 standard error of mean 均值的标准误差 standardization 标准化 standardize 标准化 statistic 统计量 statistical quality control 统计质量控制 std. residual 标准残差stepwise regression analysis 逐步回归 stimulus 刺激 strong assumption 强假设 stud. deleted residual 学生化剔除残差 stud. residual 学生化残差subsamples 次级样本sufficient statistic 充分统计量 sum 和 sum of squares 平方和 summary 概括，综述Ttable 表 t-distribution t分布 test 检验 test criterion 检验判据 test for linearity 线性检验 test of goodness of fit 拟合优度检验 test of homogeneity 齐性检验 test of independence 独立性检验 test rules 检验法则 test statistics 检验统计量 testing function 检验函数 time series 时间序列tolerance limits 容许限total 总共，和 transformation 转换treatment 处理 trimmed mean 截尾均值 true value 真值 t-test t检验two-tailed test 双侧检验Uunbalanced 不平衡的 unbiased estimation 无偏估计 unbiasedness 无偏性uniform distribution 均匀分布Vvalue of estimator 估计值variable 变量variance 方差variance components 方差分量 variance ratio 方差比 various 不同的 vector 向量Wweight 加权，权重 weighted average 加权平均值 within groups 组内的ZZ score Z分数2. 最优化方法词汇英汉对照表Aactive constraint 活动约束 active set method 活动集法 analytic gradient 解析梯度 approximate 近似 arbitrary 强制性的 argument 变量 attainment factor 达到因子Bbandwidth 带宽 be equivalent to 等价于 best-fit 最佳拟合 bound 边界Ccoefficient 系数 complex-value 复数值 component 分量 constant 常数constrained 有约束的constraint 约束constraint function 约束函数continuous 连续的 converge 收敛 cubic polynomial interpolation method 三次多项式插值法 curve-fitting 曲线拟合Ddata-fitting 数据拟合 default 默认的，默认的 define 定义 diagonal 对角的direct search method 直接搜索法direction of search 搜索方向discontinuous 不连续Eeigenvalue 特征值 empty matrix 空矩阵 equality 等式 exceeded 溢出的Ffeasible 可行的 feasible solution 可行解 finite-difference 有限差分first-order 一阶GGauss-Newton method 高斯-牛顿法 goal attainment problem 目标达到问题gradient 梯度 gradient method 梯度法Hhandle 句柄 Hessian matrix 海色矩阵Independent variables 独立变量 inequality 不等式 infeasibility 不可行性 infeasible 不可行的 initial feasible solution 初始可行解 initialize 初始化 inverse 逆 invoke 激活 iteration 迭代 iteration 迭代JJacobian 雅可比矩阵LLagrange multiplier 拉格朗日乘子 large-scale 大型的 least square 最小二乘 least squares sense 最小二乘意义上的 Levenberg-Marquardt method 列文伯格-马夸尔特法 line search 一维搜索 linear 线性的 linear equality constraints 线性等式约束 linear programming problem 线性规划问题 local solution 局部解M medium-scale 中型的 minimize 最小化 mixed quadratic and cubic polynomial interpolation and extrapolation method 混合二次、三次多项式内插、外插法 multiobjective 多目标的Nnonlinear 非线性的 norm 范数Oobjective function 目标函数observed data 测量数据optimization routine 优化过程optimize 优化optimizer 求解器over-determined system 超定系统Pparameter 参数partial derivatives 偏导数polynomial interpolation method 多项式插值法Qquadratic 二次的 quadratic interpolation method 二次内插法 quadratic programming 二次规划Rreal-value 实数值 residuals 残差 robust 稳健的 robustness 稳健性，鲁棒性S scalar 标量 semi-infinitely problem 半无限问题 Sequential Quadratic Programming method 序列二次规划法simplex search method 单纯形法solution 解 sparse matrix 稀疏矩阵 sparsity pattern 稀疏模式 sparsity structure 稀疏结构 starting point 初始点 step length 步长 subspace trust region method 子空间置信域法 sum-of-squares 平方和 symmetric matrix 对称矩阵Ttermination message 终止信息 termination tolerance 终止容限 the exit condition 退出条件 the method of steepest descent 最速下降法 transpose 转置Uunconstrained 无约束的 under-determined system 负定系统Vvariable 变量 vector 矢量Wweighting matrix 加权矩阵3 样条词汇英汉对照表Aapproximation 逼近 array 数组 a spline in b-form/b-spline b样条 aspline of polynomial piece /ppform spline 分段多项式样条Bbivariate spline function 二元样条函数 break/breaks 断点Ccoefficient/coefficients 系数 cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式 cubic smoothing spline 三次平滑样条 cubic spline 三次样条 cubic spline interpolation 三次样条插值/三次样条内插curve 曲线Ddegree of freedom 自由度 dimension 维数Eend conditions 约束条件 input argument 输入参数 interpolation 插值/内插 interval 取值区间Kknot/knots 节点Lleast-squares approximation 最小二乘拟合Mmultiplicity 重次 multivariate function 多元函数Ooptional argument 可选参数 order 阶次 output argument 输出参数P point/points 数据点Rrational spline 有理样条 rounding error 舍入误差（相对误差）Sscalar 标量 sequence 数列（数组） spline 样条 spline approximation 样条逼近/样条拟合spline function 样条函数 spline curve 样条曲线 spline interpolation 样条插值/样条内插spline surface 样条曲面 smoothing spline 平滑样条Ttolerance 允许精度Uunivariate function 一元函数Vvector 向量Wweight/weights 权重4 偏微分方程数值解词汇英汉对照表Aabsolute error 绝对误差 absolute tolerance 绝对容限 adaptive mesh 适应性网格Bboundary condition 边界条件Ccontour plot 等值线图 converge 收敛 coordinate 坐标系Ddecomposed 分解的 decomposed geometry matrix 分解几何矩阵 diagonal matrix 对角矩阵 Dirichlet boundary conditions Dirichlet边界条件Eeigenvalue 特征值 elliptic 椭圆形的error estimate 误差估计 exact solution 精确解Ggeneralized Neumann boundary condition 推广的Neumann边界条件 geometry 几何形状 geometry description matrix 几何描述矩阵 geometry matrix 几何矩阵 graphical user interface（GUI）图形用户界面Hhyperbolic 双曲线的Iinitial mesh 初始网格Jjiggle 微调LLagrange multipliers 拉格朗日乘子 Laplace equation 拉普拉斯方程 linear interpolation 线性插值 loop 循环Mmachine precision 机器精度 mixed boundary condition 混合边界条件NNeuman boundary condition Neuman边界条件 node point 节点 nonlinear solver 非线性求解器 normal vector 法向量PParabolic 抛物线型的 partial differential equation 偏微分方程 plane strain 平面应变plane stress 平面应力Poisson's equation 泊松方程polygon 多边形 positive definite 正定Qquality 质量Rrefined triangular mesh 加密的三角形网格 relative tolerance 相对容限relative tolerance 相对容限 residual 残差 residual norm 残差范数Ssingular 奇异的代数英语：(0,2) 插值||(0,2) interpolation0#||zero-sharp; 读作零井或零开。
2012年美国大学生数学建模竞赛B题特等奖文章翻译要点
2012年美赛B题题目翻译：到Big Long River（225英里）游玩的游客可以享受那里的风景和振奋人心的急流。
远足者没法到达这条河，唯一去的办法是漂流过去。
这需要几天的露营。
河流旅行始于First Launch，在Final Exit结束，共225英里的顺流。
旅客可以选择依靠船桨来前进的橡皮筏，它的速度是4英里每小时，或者选择8英里每小时的摩托船。
旅行从开始到结束包括大约6到18个晚上的河中的露营。
负责管理这条河的政府部门希望让每次旅行都能尽情享受野外经历，同时能尽量少的与河中其他的船只相遇。
当前，每年经过Big Long河的游客有X组，这些漂流都在一个为期6个月时期内进行，一年中的其他月份非常冷，不会有漂流。
在Big Long上有Y处露营地点，平均分布于河廊。
随着漂流人数的增加，管理者被要求应该允许让更多的船只漂流。
他们要决定如何来安排最优的方案：包括旅行时间（以在河上的夜晚数计算）、选择哪种船（摩托还是桨船），从而能够最好地利用河中的露营地。
换句话说，Big Long River在漂流季节还能增加多少漂流旅行数？管理者希望你能给他们最好的建议，告诉他们如何决定河流的容纳量，记住任两组旅行队都不能同时占据河中的露营地。
此外，在你的摘要表一页，准备一页给管理者的备忘录，用来描述你的关键发现。
沿着大朗河露营摘要我们开发了一个模型来安排沿大河的行程。
我们的目标是为了优化乘船旅行的时间，从而使6个月的旅游旺季出游人数最大化。
我们模拟团体从营地到营地旅行的过程。
根据给定的约束条件，我们的算法输出了每组沿河旅行最佳的日程安排。
通过研究算法的长期反应，我们可以计算出旅行的最大数量，我们定义为河流的承载能力。
我们的算法适应于科罗多拉大峡谷的个案分析，该问题的性质与大长河问题有许多共同之处。
最后，我们考察当改变推进方法，旅程时间分布，河上的露营地数量时承载能力的变化的敏感性。
我们解决了使沿大朗河出游人数最大化的休闲旅行计划。
美国数学建模MCM_ICM论文常用词汇
如何写论文摘要论文摘要的写法不象数学术语的定义和数学定理的叙述那样，有一定的格式可循，但对于初学者来说，仍有一些常见的句子可以摹仿。
现略举一些这样的句子，并附上一些论文摘要作为例子，供读者参考。
需要指出的是，这里所举的例句对普遍的文章均适合，比较抽象，具体的论文摘要除了可上下面某些句子外，必须有具体内容，更确切地说摘要中要包含一些key words 以说明该文涉及的内容，但一般不要在摘要中引用文献。
1．开门见山，说明文章内容，可用下面的句子起句：The aim(or object, purpose) of this paper(or note)The aim(or object, purpose) of this paper(or note)The aim(or object, purpose) of this paper(or note)The aim(or object, purpose) of this paper(or note)The aim(or object, purpose) of this paper(or note)The aim(or object, purpose) of this paper(or note)It is the purpose of this paper to prove…It is the purpose of this paper to show…It is the purpose of this paper to present…It is the purpose of this paper to develop…It is the purpose of this paper to generalize…It is the purpose of this paper to investigate…This paper is concerned with…This paper deals with…In this paper we prove…n this paper we present…In this paper we propose to show…2．如果需要简略回顾历史，然后再说明自己文章的内容，则可参考采用下面的句子：is to prove…is to show…is to present…is to develop…is to generalize…is to investigate…The problem…was first treated by…and later…improved by….The purpose of this paper ………….is to prove that it holds in a more general case. . …first raised the problem which was later partly solved by … .We now solve this problem in the case of …3．如果文章推广了别人的结果，或减弱了别人结果中的条件，则可参考采用下面的句子：The purpose of this paper is to generalize the results obtained by …to a more general case, i. e. , … . .In this paper we shall prove several theorems which are generalizations to the results given by …This paper intends to remove some unnecessary assumptions(e. g. , regularity) fromthe . . paper on……This paper deals with generalizations of the following problem……This paper improves the result of …on…by weakening the conditions………例：It is the purpose of the present paper to point out that certain basic aspects of information-processing systems possess dynamical analogy, and to show that these analogies can be exploited to obtain deeper insights into the behaviour of complex systems.We present a general comparision principle for systems of employ this result boundary value problems and for proving existence and uniqueness of solutions, stability and existence of periodic solutions for non-linear boundary value problems.We proved a theorem for generalized non-expansive mapping in locally convex spaces and extend the results of results of Brouder.This paper is concerned with the existence of multiple solutions of for the non-linear differential equation of the form…This paper is concerned with the question of local multiplicity not greater than 2.The object of this paper is to investigate the behaviour at the boundary of solutions to the uniformly semi-linear equation…uniqueness of solutions of Cauchy boundary problems Kirk and Kaun. We also obtain a theorem which generalizes the . Problem for elliptic partial differential equations with characteristics of The aim of this paper is to try to minimize the functional over the class F of all absolutely continuous functions f(x) which satisfy the boundary conditions社论——写自己的比赛论文导言今年的ICM 出现了一些瑕疵，两支队伍被取消了资格。
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MCM论文写作常用句型（长文，建议收藏）The expression of ... can be expanded as: ......的表达式可扩展为...A is exponentially smaller than B, so it can be neglected.A对B来说呈指数级减小，所以可以忽略不计。
Equation (1) is reduced to:方程（1）化简为：Substitute the values into equation (3), we get...把这些值代入方程3，我们得到...According to our first assumption on Page 1,根据我们第一页的第一个假设，Thus we arrive at the conclusion：因此我们得到结论：From the model of ..., we find that theoretically, it is almost true that ...由...模型，我们从理论上证明了... 是真实可信的。
That is the theoretical basis for ... in many application areas.这是...在很多领域应用的理论基础。
To quantitatively analyze the different requirements of the two applications, we intro duce two measures:为了定量的分析这两种应用的不同要求，我们介绍来两个量度标准。
We give the criterion that...我们给出了...的判别标准According to the criterion of...根据...的标准So its expression can be derived from equation (3) with small change.所以它的表达式可以由方程3做微小改动而推出。
Suppose that ...refers to...假设...指的是...We can get the distribution of...我们可以得到...的分布Along x and y axes沿着x和y轴For a further discussion of this model, please see Appendix A. 参见附录A (Detailed in Appendix I)（详见附录一）... is fitted to the normal distribution，with the mean at 0 and variance of σ=1.342. ...符合均值为0，方差为1.342的正态分布。
conform to符合Fig.4 shows...图4表明...Thus, if ... is given,is determined.因此，如果给定...，...就也确定了。
For a given r, we can calculate...对于给定的r, 我们可以算出...The two distributions are independent.这两个分布是相互独立的。
By calculation we obtain...通过计算，我们得到...So it is expressed as below:所以它可以表示为：... is ultimately determined by ...... 最终由...决定We fix A and examine the change of B with respect to C.我们固定A然后观测B随C的变化。
the logarithm values of ......的对数值That explains why the value of A decreases as B increases.这就解释了为什么A的值随B的增加而减少。
If r increases, p(r) increases accordingly.如果r增长，p(r)也相应地增长。
due to由于A is the length of ... in unit of ...A是...的长度，以...为单位。
We can see a "valley" between two curved faces which denoted the points where A =B.我们可以看到在两个曲面之间有一个低谷，表示A=B的那些点。
A andB always change in opposite direction.A和B总是呈相反变化。
So when seeking the minimum of..., we should consider how to balance A and B. 所以当寻求...的最小值时，我们应该考虑如何平衡A和B。
So we set the optimal function as:所以我们列出最优方程如下：However, putting equal weight on A and B is not always desirable.然而，给A和B相同的权数并不总是令人满意的。
In some situations, we must favor one over the other.在一些情况下，我们必须偏重一方。
input the initialization输入初值The program solves the optimal function and output a, b, c and d.程序求最优解,并输出a,b,c和d的值.In consideration of考虑到...We apply this strategy to four typical situations and list the results here.我们将这种方案应用于四种典型情况，并列出结果如下。
the probability of occurrence发生的概率Theoretically, recognization can always be successful.理论上说，识别应该总是成功的。
the expectation value of ......的期望值We let a=b我们令a=bnumerical results数值解We write a program (Appendix II) in VC ++ to obtain the result.我们用vc++写了一个程序来求解。
As shown in Tab. 4,如表4所示,The above results show that (+句子) ,which means (或者用that is ), (+句子) 以上结果说明...,也就是说...So we arrive at (或者用come to)the conclusion that (+句子)因此,我们得到结论...Moreover, from the aspect of ...,而且，从...方面来看,On the contrary,正相反，sensitivity analysis灵敏性分析robustness稳健性alter m by 5%将m改变5%They are very close.这两个值非常接近。
This is consistent with the phenomenon shown in the Fig.4. 这和图4所示是一致的。
inversely related负相关in terms of ...根据...；在...方面Equation/equality等式We can rewrite the first inequality as follows：我们可以改写第一个不等式如下：We develop a model to design....我们建立了一个模型用来设计...The model is based on conservation of energy.这个模型的建立基于能量守恒We further classify ... into three components: ...我们进一步将...分成三部分：...To validate our model为了验证我们的模型Due to the lack of accurate data for...由于缺少...方面的准确数据Our primary aim is to...我们的主要目标是......and ... are regarded as one system....和...被看成是一个系统。
notation符号遗传算法(Genetic Algorithms,GA)并行遗传算法Paralleling Genetic Algorithm,PGA数据结构Data Structures自然选择natural selection种群population个体individual基因库gene pool编码coding解码decoding量纲dimensions随机过程random processesflow chart 流程图constraint condition 约束条件maximize customer enjoyment最大化顾客的愉悦Having ensured this, we should minimize ... 在确保这个之后，我们要将...最小化be far from optimal in practice在实践中远不是最优implement 贯彻实行The underlying idea is fairly simple.下面的想法很简单。
the appeal of these systems to amusement parks is two-fold: 这些系统对游乐园的吸引力有两个方面：address these issues 致力于这些问题Hence … has come into question. 因此,...开始成为问题。
Apart from consideration of ..., from the ...'s point of view...除去考虑...，从...的角度考虑，...integrate 积分Markov chain model 马尔科夫链模型We validated our model using tests for rigor in both robustness and sensitivity.通过对稳健性和灵敏性的测试，我们验证了我们模型。