1、数学建模美国赛论文常用句式总结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
2、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 i
3、ntroduce 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 a
4、nd 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 =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。F
5、or 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 o
6、f .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
7、示A=B的那些点。A and B 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。I
8、n 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
9、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
10、 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 analsis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 phen
11、omenon 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
12、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ind
13、ividual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
14、。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 f
15、or 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。We find that in robustness test cases that our model makes predictions that correlate well with empirical evidence.在稳健性测试中我们发现，我们的模型预测值能够很好的与经验值相适应。improve efficiency by 36% on average 效率平均提高了36%contend with 对付 disposal处置n.higher pr
16、oductivity and greater customer satisfaction 更高的生产率和更高的顾客满意度specify the boarding and deplaning sequence 详细列单说明登机下机次序call for 要求degrade customers perception of quality降低顾客对质量的认可度significant stochastic variability 显著的随机可变性be proportional to 和什么成比例theorem定理,法则corollary 推论proposition命题it is necessary to
17、 notice that 注意.是十分必要的stochastic approach 随机方法numerical solution 数值解differential equations 微分方程partial differential equations 偏微分方程numerically integrate them 将其数值积分generate random number sets生成随机数序列formulate 用公式表示/display显示 / show显示 / describe描述 /phrase 用短语表达plot out data 将数据以图输出customize them to yo
18、ur particular problem 使其服务于你的特殊的问题periodically 周期性地, 定时性地the primary objective 主要目标as a secondary objective 作为第二目标be rated by 由什么定价This can be interpreted as 这个已被理解为.Note that 注意the diagonal length of the face 表面的对角线的长度be approximately equal to 约等于sth. of dimension a*b*c /sth. in dimensions a*b*c .的
19、尺寸是a*b*c4 meters high, 4 meters wide, 4 meters longin the z-direction 在z轴方向Eq.1方程1187 Joules 187焦耳correspond to 相应price per box 每个箱子的价格where a is .其中(往往用在公式后用于说明符号的含义)a是.thus 因此 (常用于公式后的进一步推导)safely withstand 在安全的情况下经受住r is given by +公式 r由.公式给出 let r be .令r等于.as a function of time 作为时间的函数Therefore w
20、e arrive at: . 因此我们得到d bounded by 234 d限制在234Given . 给定 .require at least 需要至少come to rest 变为静止Conversely, if we instead have an idea of . 相反如果我们认为We can easily compute that 我们很容易计算得到the calculation for . .的计算dissipate the energy 消耗能量, i.e. #$%& 也就是#$%& the kinetic energy 动能the change in energy 能量变化
21、量regardless of 不考虑We calculate sth. by solving the folllowing differential equation 我们计算sth.通过下列微分方程first order equations 一阶微分方程It would be unwise to ignore aie resistance 忽略空气阻力是不明智的incorporate . into . 将什么合并入什么Ideally r should be zero, but small variations may occur. 理想情况.，但会小的偏差发生uncertain initia
22、l condition 不确定的初始条件We assume the following uncertainties 我们假设如下不确定性These are shown in Fig. 5. 这些在图5中显示A illustration of this effect is shown in Fig. 6. far too complex to medel accurately 太复杂以致不能精确模拟make the following assumptions to approximate and simplify the problem做以下假设，来近似简化问题two dimensional s
23、pace二维空间We restrict our attention to 我们集中精力在There is no reason for . 什么是没有理由的Making this simplification does affect the possibility of 做这个简化，确实影响到什么的概率However, we will later show that these effects are negligible in most cases.然而，稍后我们将证明这个影响在大多数情况下是可以忽略的ignore further interaction with . 忽略和谁的进一步交互作用
24、The velocity magnitude is reduced but the direction is unchanged.速度的大小减小了 但方向未改变a uniform level 相同的水平. is represented by . 什么有什么来代表 代替We modify . according to . 我们根据什么调整什么sth. described in the following section (see Eq. 2) .在下部分被描述的(参见方程2)We use this process to account for the effects of friction. 我
25、们用这个过程来计算解释摩擦的作用horizontal 水平 vertical 竖直The vertical compoment of the velocity is set to zero. 速度的竖直分量被置为0rectangle 长方形、矩形 triangle 三角形slow his descent 降低他的降落速度This is a good approximation in the average of a large number of collisions.这是一个很好的近似，在大量撞击的平均水平We are taking the maximum here to avoid . 这
26、里我们取最大值，以避免.To show that sth. are negligible, we vary . 为了证明什么是可忽略的，我们改变.step size 步长no distinguishable change 没有显著改变This verifies that sth. is highly insensitive to. 这证实了sth. 对.高度不敏感conservation of energy 能量守恒conservation of momentum 动量守恒the change in his velocity 速度的变化量We use this equation to calc
27、ulate .stability and sensitivity analsisas a function of time the discrete wayHypothesis 假设The results indicate that type (1) is optimal.figure out 计算出be shown in detail in Fig. 2final recommendationrumor 瘤 humor幽默 rumor流言谣言result in 导致 result from 产生cause a minimal effect on 引起最小限度的影响10 seconds up
28、to a couple hoursunder various conditionsbe fairly independent of . 与什么无关two complementary measures 两个补充方法We tabulate the relationship between and 我们将 列成表格be proportional to the square of velocity 和速度的平方成比例the above considerations lead us to formulate .This is precisely the effect that we wish to ca
29、pture.modified poisson process 改良的泊松过程 test and demonstrate our algorithm 测试和证明我们的算法The defination of simple is up to you.be implemented in 在某处实施It also shows that Duke is not alone in this trend. 这也显示了不仅杜克大学符合这种趋势It is apparently that. 很显然generality 一般性Through trial and error we determined a possib
30、le coefficient of 0.2.figure out / calculate /compute 计算 formulate用公式表明in terms of根据, 按照, 用.的话, 在.方面For this reason, class size is not directly involved in the model.be reflected in . 反映在某方面tend toward 趋向the most extreme caseas long as 只要index 指数指标, thereby reducing the amount of time taken to select a treatment plan 因此three dimensional image 三维图像fitting data 拟合数据the bottom two curves 下部的两条曲线We agree very well with 1 cubic millimeter
