數(shù)學建模美國賽論文常用句式

1、The expression of . can be expanded as: . 的表達式可擴展為 .A is exponentially smaller than B,so it can be neglected.A 對 B 來說呈指數(shù)級減小,所以可以忽略不計。Equation (1 is reduced to:方程(1化簡為:Substitute the values into equation (3, we get .把這些值代入方程 3,我們得到 .According to our first assumption on Page 1,根據(jù)我們第一頁的第一個假設(shè),Thus we ar

2、rive at the conclusion:因此我們得到結(jié)論:From the model of . ,we find that theoretically, it is almost true that .由 . 模型,我們從理論上證明了 . 是真實可信的。That is the theoretical basis for . in many application areas.這是 . 在很多領(lǐng)域應用的理論基礎(chǔ)。To quantitatively analyze the different requirements of the two applications, we introduc

3、e two measures:為了定量的分析這兩種應用的不同要求,我們介紹來兩個量度標準。We give the criterion that .我們給出了 . 的判別標準According to the criterion of.根據(jù) . 的標準So its expression can be derived from equation (3 with small change.所以它的表達式可以由方程 3做微小改動而推出。Suppose that .refers to .假設(shè) . 指的是 .We can get the distribution of.我們可以得到 . 的分布along x

4、 and y axes沿著 x 和 y 軸For a further discussion of this model, please see Appendix A. 參見附錄 A(detailed in Appendix I(詳見附錄一. is fitted to the normal distribution, with the mean at 0 and variance of =1.342. 符合均值為 0,方差為 1.342的正態(tài)分布。conform to符合Fig.4 shows .圖 4表明 .Thus, if . is given, .is determined.因此,如果給定

5、 . , . 就也確定了。For a given r, we can calculate .對于給定的 r, 我們可以算出 .The two distributions are independent.這兩個分布是相互獨立的。By calculation we obtain.通過計算,我們得到 .So it is expressed as below:所以它可以表示為:. is ultimately determined by . 最終由 . 決定We fix A and examine the change of B with respect to C.我們固定 A 然后觀測 B 隨 C 的

6、變化。the logarithm values of . 的對數(shù)值That explains why the value of A decreases as B increases.這就解釋了為什么 A 的值隨 B 的增加而減少。If r increases, p(r increases accordingly.如果 r 增長, p(r也相應地增長。due to由于A is the length of . in unit of .A 是 . 的長度,以 . 為單位。We can see a "valley" between two curved faces which de

7、noted the points where A=B. 我們可以看到在兩個曲面之間有一個低谷,表示 A=B的那些點。A and B always change in opposite direction.A 和 B 總是呈相反變化。So when seeking the minimum of., we should consider how to balance A and B. 所以當尋求 . 的最小值時,我們應該考慮如何平衡 A 和 B 。So we set the optimal function as:所以我們列出最優(yōu)方程如下:However, putting equal weight

8、 on A and B is not always desirable.然而,給 A 和 B 相同的權(quán)數(shù)并不總是令人滿意的。In some situations, we must favor one over the other.在一些情況下,我們必須偏重一方。input the initialization輸入初值The program solves the optimal function and output a,b,c and d.程序求最優(yōu)解 , 并輸出 a,b,c 和 d 的值 .In consideration of考慮到 .We apply this strategy to f

9、our typical situations and list the results here.我們將這種方案應用于四種典型情況,并列出結(jié)果如下。the probability of occurrence發(fā)生的概率Theoretically, recognization can always be successful.理論上說,識別應該總是成功的。the expectation value of . 的期望值We let a=b我們令 a=bnumerical results 數(shù)值解We write a program (Appendix II in VC + to obtain the

10、result.我們用 vc+寫了一個程序來求解。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 以上結(jié)果說明 ., 也就是說 .So we arrive at (或者用 come tothe conclusion that (+句子 因此 , 我們得到結(jié)論 .Moreover, from the aspect of .,而且,從 . 方面來看 ,On the contrary ,正相反,sensitivity analsis靈敏性分析robustness穩(wěn)健

11、性alter m by 5%將 m 改變 5%They are very close.這兩個值非常接近。This is consistent with the phenomenon shown in the Fig.4.這和圖 4所示是一致的。inversely related負相關(guān)in terms of .根據(jù) . ;在 . 方面equality 等式We can rewrite the first inequality as follows:我們可以改寫第一個不等式如下:We develop a model to design.我們建立了一個模型用來設(shè)計 .The model is bas

12、ed on conservation of energy.這個模型的建立基于能量守恒We further classify . into three components: .我們進一步將 . 分成三部分:.To validate our model為了驗證我們的模型Due to the lack of accurate data for .由于缺少 . 方面的準確數(shù)據(jù)Our primary aim is to .我們的主要目標是 .and . are regarded as one system. 和 . 被看成是一個系統(tǒng)。notation 符號遺傳算法 (Genetic Algorithm

13、s,GA并行遺傳算法 Paralleling Genetic Algorithm,PGA數(shù)據(jù)結(jié)構(gòu) Data Structures自然選擇 natural selection種群 population個體 individual基因庫 gene pool編碼 coding解碼 decoding量綱 dimensions隨機過程 random processesflow chart 流程圖constraint condition 約束條件maximize customer enjoyment最大化顧客的愉悅Having ensured this, we should minimize . 在確保這個

14、之后,我們要將 . 最小化be far from optimal in practice在實踐中遠不是最優(yōu)implement 貫徹實行The underlying idea is fairly simple.下面的想法很簡單。the appeal of these systems to amusement parks is two-fold: 這些系統(tǒng)對游樂園的吸引力有 兩個方面:address these issues 致力于這些問題Hence, . has come into question. 因此 ,. 開始成為問題。Apart from consideration of . , fr

15、om the .'s point of view, .除去考慮 . ,從 . 的角度考慮, .integrate 積分Markov chain model 馬爾科夫鏈模型We validated our model using tests for rigor in both robustness and sensitivity.通過對穩(wěn)健性和靈敏性的測試,我們驗證了我們模型。We find that in robustness test cases that our model makes predictions that correlate well with empirical e

16、vidence.在穩(wěn)健性測試中我們發(fā)現(xiàn),我們的模型預測值能夠很好的與經(jīng)驗值相適應。improve efficiency by 36% on average 效率平均提高了 36%contend with 對付 disposal 處置 n.higher productivity and greater customer satisfaction 更高的生產(chǎn)率和更高的顧客滿意度 specify the boarding and deplaning sequence 詳細列單說明登機下機次序call for 要求degrade customers' perception of quality

17、降低顧客對質(zhì)量的認可度significant stochastic variability 顯著的隨機可變性be proportional to 和什么成比例theorem 定理 , 法則corollary 推論proposition 命題it is necessary to notice that 注意 . 是十分必要的stochastic approach 隨機方法numerical solution 數(shù)值解differential equations 微分方程partial differential equations 偏微分方程numerically integrate them 將其

18、數(shù)值積分generate random number sets生成隨機數(shù)序列formulate 用公式表示 /display顯示 / show顯示 / describe描述 /phrase 用短語表達 plot out data 將數(shù)據(jù)以圖輸出customize them to your particular problem 使其服務于你的特殊的問題periodically 周期性地 , 定時性地the primary objective 主要目標as a secondary objective 作為第二目標be rated by 由什么定價This can be interpreted as

19、 這個已被理解為 .Note that 注意the diagonal length of the face 表面的對角線的長度be approximately equal to 約等于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 軸方向Eq.1方程 1187 Joules 187焦耳correspond to 相應price per box 每個箱子的價格where a is .其中 (

20、往往用在公式后用于說明符號的含義 a 是 .thus 因此 (常用于公式后的進一步推導 safely withstand 在安全的情況下經(jīng)受住r is given by +公式 r 由 . 公式給出let r be .令 r 等于 .as a function of time 作為時間的函數(shù)Therefore we arrive at: . 因此我們得到d bounded by 234 d 限制在 234Given . 給定 .require at least 需要至少come to rest 變?yōu)殪o止Conversely, if we instead have an idea of . 相反

21、如果我們認為We can easily compute that 我們很容易計算得到the calculation for . . 的計算dissipate the energy 消耗能量, i.e. #$%& 也就是 #$%&the kinetic energy 動能the change in energy 能量變化量regardless of 不考慮We calculate sth. by solving the folllowing differential equation 我們計算 sth. 通過下列微分 方程first order equations 一階微分方程I

22、t would be unwise to ignore aie resistance 忽略空氣阻力是不明智的incorporate . into . 將什么合并入什么Ideally r should be zero, but small variations may occur. 理想情況 . ,但會小的偏差發(fā)生 uncertain initial condition 不確定的初始條件We assume the following uncertainties 我們假設(shè)如下不確定性These are shown in Fig. 5. 這些在圖 5中顯示A illustration of this

23、 effect is shown in Fig. 6.far too complex to medel accurately 太復雜以致不能精確模擬make the following assumptions to approximate and simplify the problem做以下假設(shè),來近似簡化問題two dimensional space二維空間We restrict our attention to 我們集中精力在There is no reason for . 什么是沒有理由的Making this simplification does affect the possib

24、ility of 做這個簡化,確實影響到什么的概 率However, we will later show that these effects are negligible in most cases.然而,稍后我們將證明這個影響在大多數(shù)情況下是可以忽略的ignore further interaction with . 忽略和誰的進一步交互作用The velocity magnitude is reduced but the direction is unchanged.速度的大小減小了 但方向未改變a uniform level 相同的水平. is represented by . 什么

25、有什么來代表 代替We modify . according to . 我們根據(jù)什么調(diào)整什么sth. described in the following section (see Eq. 2 . 在下部分被描述的 (參見方程 2 We use this process to account for the effects of friction. 我們用這個過程來計算解釋摩擦 的作用horizontal 水平 vertical 豎直The vertical compoment of the velocity is set to zero. 速度的豎直分量被置為 0rectangle 長方形、

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.這是一個很好的近似,在大量撞擊的平均水平We are taking the maximum here to avoid . 這里我們?nèi)∽畲笾?以避免 .To show that sth. are negligible, we vary . 為了證明什么是可忽略的,我們改變 . step size 步長no distinguishable change 沒有顯著改變T

27、his verifies that sth. is highly insensitive to. 這證實了 sth. 對 . 高度不敏感 conservation of energy 能量守恒conservation of momentum 動量守恒the change in his velocity 速度的變化量We use this equation to calculate .stability and sensitivity analsisas a function of timethe discrete wayHypothesis 假設(shè)The results indicate tha

28、t type (1 is optimal.figure out 計算出be shown in detail in Fig. 2final recommendationrumor 瘤 humor 幽默 rumor 流言謠言result in 導致 result from 產(chǎn)生cause a minimal effect on 引起最小限度的影響10 seconds up to a couple hoursunder various conditionsbe fairly independent of . 與什么無關(guān)two complementary measures 兩個補充方法We tabul

29、ate the relationship between and 我們將 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 改良的泊松過程test and demonstrate our algorithm 測試和證明我們的算法The defination of "simple&

30、quot; is up to you.be implemented in 在某處實施It also shows that Duke is not alone in this trend. 這也顯示了不僅杜克大學符合這種趨勢 It is apparently that. 很顯然generality 一般性Through trial and error we determined a possible coefficient of 0.2.figure out / calculate /compute 計算 formulate 用公式表明in terms of根據(jù) , 按照 , 用 . 的話 ,

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 趨向the most extreme caseas long as 只要index 指數(shù)指標, thereby reducing the amount of time taken to select a treatment plan 因此three dimensional image 三維圖像fitting data 擬合數(shù)據(jù)the bottom two curves 下部的兩條曲

32、線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 關(guān)于in the range of 7.1 to 7.5自己總結(jié) :centre of gravity 重心centre of mass 質(zhì)心check digit 校驗位delivery cost,petrol 油料運輸費用minimum cost solution 最底費用解opti

33、mum solution 最優(yōu)解non-conforming samples 不合格抽樣potential energy 勢能weighting factors 加權(quán)因子differential equations 微分方程mathematical induction 數(shù)學歸納法exponential model 冪函數(shù)模型equilibrium point 平衡點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 是指價格 p1 = 20 ppm. The abbreviation ppm stands for parts per million.宿寫的 ppm 代表 . the amount * depends more directly on * than on *The derivative of the curve y = x + 2 is dy/dx 如何引出導數(shù).the dominant controllable factor affecting. . 是影響。 。 。主要因素where is the density of 。

35、。 。 。 。 。 密度是數(shù)學專業(yè)英語詞匯英漢對照Tag :數(shù)學 專業(yè) 英語 詞匯 英漢1 概率論與數(shù)理統(tǒng)計詞匯英漢對照表Aabsolute value 絕對值accept 接受acceptable region 接受域additivity 可加性adjusted 調(diào)整的alternative hypothesis 對立假設(shè) analysis 分析analysis of covariance 協(xié)方差分析 analysis of variance 方差分析 arithmetic mean 算術(shù)平均值 association 相關(guān)性assumption 假設(shè)assumption checking

36、假設(shè)檢驗 availability 有效度average 均值Bbalanced 平衡的band 帶寬bar chart 條形圖beta-distribution 貝塔分布 between groups 組間的bias 偏倚binomial distribution 二項分布 binomial test 二項檢驗Ccalculate 計算case 個案category 類別center of gravity 重心central tendency 中心趨勢chi-square distribution 卡方分布 chi-square test 卡方檢驗classify 分類cluster ana

37、lysis 聚類分析 coefficient 系數(shù)coefficient of correlation 相關(guān)系數(shù) collinearity 共線性column 列compare 比較comparison 對照components 構(gòu)成,分量 compound 復合的confidence interval 置信區(qū)間 consistency 一致性constant 常數(shù)continuous variable 連續(xù)變量 control charts 控制圖correlation 相關(guān)covariance 協(xié)方差covariance matrix 協(xié)方差矩陣critical point 臨界點crit

38、ical value 臨界值crosstab 列聯(lián)表cubic 三次的,立方的cubic term 三次項cumulative distribution function 累加分布函數(shù) curve estimation 曲線估計Ddata 數(shù)據(jù)default 默認的definition 定義deleted residual 剔除殘差density function 密度函數(shù)dependent variable 因變量description 描述design of experiment 試驗設(shè)計deviations 差異df.(degree of freedom 自由度diagnostic 診斷

39、dimension 維discrete variable 離散變量discriminant function 判別函數(shù) discriminatory analysis 判別分析distance 距離distribution 分布D-optimal design D-優(yōu)化設(shè)計Eeaqual 相等effects of interaction 交互效應efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 誤差estimate 估計estimation of parameters 參數(shù)估計 estimations 估計量evaluate

40、衡量exact value 精確值expectation 期望expected value 期望值exponential 指數(shù)的exponential distributon 指數(shù)分布extreme value 極值Ffactor 因素,因子factor analysis 因子分析factor score 因子得分factorial designs 析因設(shè)計factorial experiment 析因試驗fit 擬合fitted line 擬合線fitted value 擬合值fixed model 固定模型fixed variable 固定變量fractional factorial de

41、sign 部分析因設(shè)計 frequency 頻數(shù)F-test F檢驗full factorial design 完全析因設(shè)計 function 函數(shù)Ggamma distribution 伽瑪分布 geometric mean 幾何均值group 組Hharmomic mean 調(diào)和均值 heterogeneity 不齊性histogram 直方圖homogeneity 齊性homogeneity of variance 方差齊性 hypothesis 假設(shè)hypothesis test 假設(shè)檢驗Iindependence 獨立independent variable 自變量 independ

42、ent-samples 獨立樣本index 指數(shù)index of correlation 相關(guān)指數(shù) interaction 交互作用interclass correlation 組內(nèi)相關(guān)interval estimate 區(qū)間估計intraclass correlation 組間相關(guān)inverse 倒數(shù)的iterate 迭代Kkernal 核Kolmogorov-Smirnov test柯爾莫哥洛夫 -斯米諾夫檢驗kurtosis 峰度Llarge sample problem 大樣本問題layer 層least-significant difference 最小顯著差數(shù) least-squa

43、re estimation 最小二乘估計least-square method 最小二乘法level 水平level of significance 顯著性水平leverage value 中心化杠桿值life 壽命life test 壽命試驗likelihood function 似然函數(shù)likelihood ratio test 似然比檢驗linear 線性的linear estimator 線性估計linear model 線性模型linear regression 線性回歸linear relation 線性關(guān)系linear term 線性項logarithmic 對數(shù)的logarit

44、hms 對數(shù)logistic 邏輯的lost function 損失函數(shù)Mmain effect 主效應matrix 矩陣maximum 最大值maximum likelihood estimation 極大似然估計 mean squared deviation(MSD 均方差mean sum of square 均方和measure 衡量media 中位數(shù)M-estimator M估計minimum 最小值missing values 缺失值mixed model 混合模型mode 眾數(shù)model 模型Monte Carle method 蒙特卡羅法moving average 移動平均值

45、multicollinearity 多元共線性multiple comparison 多重比較multiple correlation coefficient 復相關(guān)系數(shù) multiple correlation coefficient 多元相關(guān)系數(shù) multiple regression analysis 多元回歸分析 multiple regression equation 多元回歸方程 multiple response 多響應multivariate analysis 多元分析Nnegative relationship 負相關(guān)nonadditively 不可加性nonlinear 非

46、線性nonlinear regression 非線性回歸 noparametric tests 非參數(shù)檢驗normal distribution 正態(tài)分布null hypothesis 零假設(shè)number of cases 個案數(shù)Oone-sample 單樣本one-tailed test 單側(cè)檢驗one-way ANOVA 單向方差分析one-way classification 單向分類optimal 優(yōu)化的optimum allocation 最優(yōu)配制order 排序order statistics 次序統(tǒng)計量origin 原點orthogonal 正交的outliers 異常值Ppai

47、red observations 成對觀測數(shù)據(jù)paired-sample 成對樣本parameter 參數(shù)parameter estimation 參數(shù)估計partial correlation 偏相關(guān)partial correlation coefficient 偏相關(guān)系數(shù) partial regression coefficient 偏回歸系數(shù) percent 百分數(shù)percentiles 百分位數(shù)pie chart 餅圖point estimate 點估計poisson distribution 泊松分布polynomial curve 多項式曲線polynomial regressio

48、n 多項式回歸 polynomials 多項式power 冪P-P plot P-P概率圖predict 預測predicted value 預測值prediction intervals 預測區(qū)間principal component analysis 主成分分析 proability 概率probability density function 概率密度函數(shù) probit analysis 概率分析proportion 比例Qqadratic 二次的Q-Q plot Q-Q概率圖quadratic term 二次項quality control 質(zhì)量控制quantitative 數(shù)量的,度

49、量的quartiles 四分位數(shù)Rrandom 隨機的random number 隨機數(shù)random number 隨機數(shù)random sampling 隨機取樣random seed 隨機數(shù)種子random variable 隨機變量 randomization 隨機化range 極差rank 秩rank correlation 秩相關(guān)rank statistic 秩統(tǒng)計量regression analysis 回歸分析regression coefficient 回歸系數(shù) regression line 回歸線reject 拒絕rejection region 拒絕域relationshi

50、p 關(guān)系reliability 可靠性repeated 重復的report 報告,報表residual 殘差residual sum of squares 剩余平方和 response 響應risk function 風險函數(shù)robustness 穩(wěn)健性root mean square 標準差row 行run 游程run test 游程檢驗Ssample 樣本sample size 樣本容量sample space 樣本空間sampling 取樣sampling inspection 抽樣檢驗scatter chart 散點圖S-curve S形曲線separately 單獨地sets 集合s

51、ign test 符號檢驗significance 顯著性significance level 顯著性水平 significance testing 顯著性檢驗 significant 顯著的,有效的significant digits 有效數(shù)字skewed distribution 偏態(tài)分布 skewness 偏度small sample problem 小樣本問題 smooth 平滑sort 排序soruces of variation 方差來源space 空間spread 擴展square 平方standard deviation 標準離差standard error of mean 均

52、值的標準誤差 standardization 標準化standardize 標準化statistic 統(tǒng)計量statistical quality control 統(tǒng)計質(zhì)量控制 std. residual 標準殘差stepwise regression analysis 逐步回歸 stimulus 刺激strong assumption 強假設(shè)stud. deleted residual 學生化剔除殘差 stud. residual 學生化殘差 subsamples 次級樣本sufficient statistic 充分統(tǒng)計量sum 和sum of squares 平方和summary 概括,

53、綜述Ttable 表t-distribution t分布test 檢驗test criterion 檢驗判據(jù)test for linearity 線性檢驗test of goodness of fit 擬合優(yōu)度檢驗 test of homogeneity 齊性檢驗 test of independence 獨立性檢驗 test rules 檢驗法則test statistics 檢驗統(tǒng)計量testing function 檢驗函數(shù)time series 時間序列tolerance limits 容許限total 總共,和transformation 轉(zhuǎn)換treatment 處理trimmed

54、mean 截尾均值true value 真值t-test t檢驗two-tailed test 雙側(cè)檢驗Uunbalanced 不平衡的unbiased estimation 無偏估計 unbiasedness 無偏性uniform distribution 均勻分布 Vvalue of estimator 估計值variable 變量variance 方差variance components 方差分量 variance ratio 方差比various 不同的vector 向量Wweight 加權(quán),權(quán)重weighted average 加權(quán)平均值 within groups 組內(nèi)的ZZ score Z分數(shù)2. 最優(yōu)化方法詞匯英漢對照表 Aactive constraint 活動約束active set method 活動集法analytic gradient 解析梯度 approximate 近似arbitrary 強制性的argument 變量attainment factor 達到因子Bbandwidth 帶寬be equivalent to 等價于best-fit 最佳擬合bound 邊界Ccoefficient 系數(shù)complex-value 復數(shù)值component 分量