1、The expression of . can be expanded as: .的表達(dá)式可擴(kuò)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 arri

2、ve 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(yīng)用的理論基礎(chǔ)。To quantitatively analyze the different requirements of the two applications, we introduce two m

3、easures:為了定量的分析這兩種應(yīng)用的不同要求，我們介紹來兩個量度標(biāo)準(zhǔn)。We give the criterion that .我們給出了.的判別標(biāo)準(zhǔn)According to the criterion of.根據(jù).的標(biāo)準(zhǔn)So its expression can be derived from equation (3) with small change.所以它的表達(dá)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 and y axes沿著x和y

4、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.，.就也確定了。For a given r,

5、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的變化。the logarithm values of .的對數(shù)值That ex

6、plains 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(yīng)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 denoted 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

7、=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(dāng)尋求.的最小值時，我們應(yīng)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 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

8、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 four typical situations and list the results here.我們將這種方案應(yīng)用于四種典型情況，并列出結(jié)果如

9、下。the probability of occurrence發(fā)生的概率Theoretically, recognization can always be successful.理論上說，識別應(yīng)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 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 t

10、hat (+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 to)the 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 phenom

11、enon shown in the Fig.4.這和圖4所示是一致的。inversely related負(fù)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 based 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(jìn)一步

12、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(zhǔn)確數(shù)據(jù)Our primary aim is to .我們的主要目標(biāo)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 Algorithms,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indiv

13、idual基因庫gene pool編碼coding解碼decoding量綱dimensions隨機(jī)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 . 在確保這個之后，我們要將.最小化be far from optimal in practice在實踐中遠(yuǎn)不是最優(yōu)implement 貫徹實行The underlying idea is fairly simple.下面的想法很簡單。t

14、he 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 . , from 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 test

15、s 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 evidence.在穩(wěn)健性測試中我們發(fā)現(xiàn)，我們的模型預(yù)測值能夠很好的與經(jīng)驗值相適應(yīng)。improve efficiency by 36% on average 效率平均提高了36%contend with 對付 disposal處置n.higher

16、 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(xì)列單說明登機(jī)下機(jī)次序call for 要求degrade customers' perception of quality降低顧客對質(zhì)量的認(rèn)可度significant stochastic variability 顯著的隨機(jī)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 nece

17、ssary to notice that 注意.是十分必要的stochastic approach 隨機(jī)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 將其數(shù)值積分generate random number sets生成隨機(jī)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(dá)plot out data 將數(shù)據(jù)以圖輸出customize th

18、em to your particular problem 使其服務(wù)于你的特殊的問題periodically 周期性地, 定時性地the primary objective 主要目標(biāo)as a secondary objective 作為第二目標(biāo)be rated by 由什么定價This can be interpreted as 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

19、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(yīng)price per box 每個箱子的價格where a is .其中(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(jìn)一步推導(dǎo))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)The

20、refore 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 . 相反如果我們認(rèn)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 chang

21、e 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It 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

22、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 effect is shown in Fig. 6. far too complex to medel accurately 太復(fù)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t

23、wo 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 possibility 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 wit

24、h . 忽略和誰的進(jìn)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 effect

25、s 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、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 h

26、ere to avoid . 這里我們?nèi)∽畲笾担员苊?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This 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

27、equation to calculate .stability and sensitivity analsisas a function of time the discrete wayHypothesis 假設(shè)The results indicate that 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(dǎo)致 result from 產(chǎn)生cause a minimal effect on 引起最小限度的

28、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(bǔ)充方法We tabulate 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 th

29、at 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" 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(xué)符合這種趨勢It is apparently that. 很顯然generality 一般性Through trial and

30、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, 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(biāo), thereby reducing the a

31、mount 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 下部的兩條曲線We agree very well with 1 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

32、 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optimum 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(xué)歸納法exponential model 冪函數(shù)模型equilibrium poi

33、nt 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 denotes 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 t

34、he curve y = x + 2 is dy/dx 如何引出導(dǎo)數(shù).the dominant controllable factor affecting. .是影響。主要因素where is the density of 。 密度是數(shù)學(xué)專業(yè)英語詞匯英漢對照Tag： 數(shù)學(xué) 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 covarianc

35、e 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 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 grav

36、ity 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 analysis 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(fù)合的confidence interval 置信區(qū)間consistency 一致性constant 常數(shù)continuous variable 連續(xù)變

37、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critical 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(rèn)的definition 定義deleted residual 剔除殘差density function 密度函數(shù)dependent variable 因變

38、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(yīng)efficiency 有效性eigenvalue 特征值equal s

39、ize 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 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

40、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 design 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

41、差齊性hypothesis 假設(shè)hypothesis test 假設(shè)檢驗Iindependence 獨立independent variable 自變量independent-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

42、 峰度Llarge sample problem 大樣本問題layer 層least-significant difference 最小顯著差數(shù)least-square 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

43、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logarithms 對數(shù)logistic 邏輯的lost function 損失函數(shù)Mmain effect 主效應(yīng)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 valu

44、es 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multicollinearity 多元共線性multiple comparison 多重比較multiple correlation 多重相關(guān)multiple correlation coefficient 復(fù)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

45、multiple response 多響應(yīng)multivariate analysis 多元分析Nnegative relationship 負(fù)相關(guān)nonadditively 不可加性nonlinear 非線性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op

46、timal 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Ppaired 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?jǐn)?shù)percentiles 百分

47、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 regression 多項式回歸polynomials 多項式positive relationship 正相關(guān)power 冪P-P plot P-P概率圖predict 預(yù)測predicted value 預(yù)測值prediction intervals 預(yù)測區(qū)間principal component analysis 主成分分析proability 概率probability density function 概率

48、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，度量的quartiles 四分位數(shù)Rrandom 隨機(jī)的random number 隨機(jī)數(shù)random number 隨機(jī)數(shù)random sampling 隨機(jī)取樣random seed 隨機(jī)數(shù)種子random variable 隨機(jī)變量randomization 隨機(jī)化range 極差rank 秩rank correlation 秩相關(guān)rank stati

49、stic 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relationship 關(guān)系reliability 可靠性repeated 重復(fù)的report 報告，報表residual 殘差residual sum of squares 剩余平方和response 響應(yīng)risk function 風(fēng)險函數(shù)robustness 穩(wěn)健性root mean square 標(biāo)準(zhǔn)差row 行run 游程run test 游程檢驗Ssample 樣本s

50、ample 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sign 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

51、smooth 平滑sort 排序soruces of variation 方差來源space 空間spread 擴(kuò)展square 平方standard deviation 標(biāo)準(zhǔn)離差standard error of mean 均值的標(biāo)準(zhǔn)誤差standardization 標(biāo)準(zhǔn)化standardize 標(biāo)準(zhǔn)化statistic 統(tǒng)計量statistical quality control 統(tǒng)計質(zhì)量控制std. residual 標(biāo)準(zhǔn)殘差stepwise regression analysis 逐步回歸stimulus 刺激strong assumption 強(qiáng)假設(shè)stud. deleted re

52、sidual 學(xué)生化剔除殘差stud. residual 學(xué)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，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)

53、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 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?jǐn)?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(qiáng)制性的argument 變量attainment factor 達(dá)到因子Bbandwidth 帶寬be equivale