数学建模美国赛论文常用句式

1、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 ar

2、rive 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 introduc

3、e 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

4、 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 =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

5、 . , . 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

6、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 de

7、noted 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 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

8、 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 f

9、our 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

10、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 tothe 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

11、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 bas

12、ed 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 Algorithm

13、s,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

14、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 . , fr

15、om 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。We find that in robustness test cases that our model makes predictions that correlate well with empirical e

16、vidence.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 productivity 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

17、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 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

18、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 your 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

19、 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 (

20、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 we 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

21、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I

22、t 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 initial 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

23、 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 space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 possib

24、ility 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

25、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、

26、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T

27、his 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 calculate .stability and sensitivity analsisas a function of timethe discrete wayHypothesis 假设The results indicate tha

28、t 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 to a couple hoursunder various conditionsbe fairly independent of . 与什么无关two complementary measures 两个补充方法We tabul

29、ate 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 capture.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&

30、quot; 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 possible 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 ,

31、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

32、线We agree very well with1 cubic millimeter 一立方毫米This algorithm makes use of . to . 利用be similar to 相似The end result is that.with regard to /with respect to 关于in the range of 7.1 to 7.5自己总结 :centre of gravity 重心centre of mass 质心check digit 校验位delivery cost,petrol 油料运输费用minimum cost solution 最底费用解opti

33、mum solution 最优解non-conforming samples 不合格抽样potential energy 势能weighting factors 加权因子differential equations 微分方程mathematical induction 数学归纳法exponential model 幂函数模型equilibrium point 平衡点We can verify that p = 5,000 is an equilibrium point numerically by computing *; D(p = c*5000 - 500 p ,where p denot

34、es price and c is constant 其中 p 是指价格 p1 = 20 ppm. The abbreviation ppm stands for parts per million.宿写的 ppm 代表 . the amount * depends more directly on * than on *The derivative of the curve y = x + 2 is dy/dx 如何引出导数.the dominant controllable factor affecting. . 是影响。 。 。主要因素where is the density of 。

35、。 。 。 。 。 密度是数学专业英语词汇英汉对照Tag :数学 专业 英语 词汇 英汉1 概率论与数理统计词汇英汉对照表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

36、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 ana

37、lysis 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crit

38、ical 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

39、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

40、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Ffactor 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 de

41、sign 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 independ

42、ent-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-squa

43、re 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logarit

44、hms 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

45、multicollinearity 多元共线性multiple comparison 多重比较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

46、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Ppai

47、red 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 regressio

48、n 多项式回归 polynomials 多项式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

49、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relationshi

50、p 关系reliability 可靠性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Ssample 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s

51、ign 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

52、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,

53、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

54、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