Experimental and numerical investigation of the hydrodynamic loads ...s

population 母体sample 样本census 普查sampling 抽样quantitative 量的qualitative/categorical质的discrete 离散的continuous 连续的population parameters 母体参数sample statistics 样本统计量descriptive statistics 叙述统计学inferential/inductive statistics 推论... 抽样调查（sampliing survey单纯随机抽样（simple random sampling 系统抽样（systematic sampling分层抽样（stratified sampling整群抽样（cluster sampling多级抽样（multistage sampling常态分配(Parametric Statistics)无母数统计学(Nonparametric Statistics) 实验设计(Design of Experiment)参数(Parameter)Data analysis 资料分析Statistical table 统计表Statistical chart 统计图Pie chart 圆饼图Stem-and-leaf display 茎叶图Box plot 盒须图Histogram 直方图Bar Chart 长条图Polygon 次数多边图Ogive 肩形图Descriptive statistics 叙述统计学Expectation 期望值Mode 众数Mean 平均数Variance 变异数Standard deviation 标准差Standard error 标准误Covariance matrix 共变异数矩阵Inferential statistics 推论统计学Point estimation 点估计Interval estimation 区间估计Confidence interval 信赖区间Confidence coefficient 信赖系数Testing statistical hypothesis 统计假设检定Regression analysis 回归分析Analysis of variance 变异数分析Correlation coefficient 相关系数Sampling survey 抽样调查Census 普查Sampling 抽样Reliability 信度Validity 效度Sampling error 抽样误差Non-sampling error 非抽样误差Random sampling 随机抽样Simple random sampling 简单随机抽样法Stratified sampling 分层抽样法Cluster sampling 群集抽样法Systematic sampling 系统抽样法Two-stage random sampling 两段随机抽样法Convenience sampling 便利抽样Quota sampling 配额抽样Snowball sampling 雪球抽样Nonparametric statistics 无母数统计The sign test 等级检定Wilcoxon signed rank tests 魏克森讯号等级检定Wilcoxon rank sum tests 魏克森等级和检定Run test 连检定法Discrete uniform densities 离散的均匀密度Binomial densities 二项密度Hypergeometric densities 超几何密度Poisson densities 卜松密度Geometric densities 几何密度Negative binomial densities 负二项密度Continuous uniform densities 连续均匀密度Normal densities 常态密度Exponential densities 指数密度Gamma densities 伽玛密度Beta densities 贝他密度Multivariate analysis 多变量分析Principal components 主因子分析Discrimination analysis 区别分析Cluster analysis 群集分析Factor analysis 因素分析Survival analysis 存活分析Time series analysis 时间序列分析Linear models 线性模式Quality engineering 品质工程Probability theory 机率论Statistical computing 统计计算Statistical inference 统计推论Stochastic processes 随机过程Decision theory 决策理论Discrete analysis 离散分析Mathematical statistics 数理统计统计学: Statistics母体: Population样本: Sample资料分析: Data analysis统计表: Statistical table统计图: Statistical chart圆饼图: Pie chart茎叶图: Stem-and-leaf display 盒须图: Box plot直方图: Histogram长条图: Bar Chart次数多边图: Polygon肩形图: Ogive叙述统计学: Descriptive statistics 期望值: Expectation众数: Mode平均数: Mean变异数: Variance标准差: Standard deviation标准误: Standard error共变异数矩阵: Covariance matrix 推论统计学: Inferential statistics 点估计: Point estimation区间估计: Interval estimation信赖区间: Confidence interval信赖系数: Confidence coefficient统计假设检定: Testing statistical hypothesis回归分析: Regression analysis变异数分析: Analysis of variance相关系数: Correlation coefficient抽样调查: Sampling survey普查: Census抽样: Sampling信度: Reliability效度: Validity抽样误差: Sampling error非抽样误差: Non-sampling error随机抽样: Random sampling简单随机抽样法: Simple random sampling分层抽样法: Stratified sampling群集抽样法: Cluster sampling系统抽样法: Systematic sampling两段随机抽样法: Two-stage random sampling 便利抽样: Convenience sampling配额抽样: Quota sampling雪球抽样: Snowball sampling无母数统计: Nonparametric statistics等级检定: The sign test魏克森讯号等级检定: Wilcoxon signed rank tests 魏克森等级和检定: Wilcoxon rank sum tests连检定法: Run test离散的均匀密度: Discrete uniform densities二项密度: Binomial densities超几何密度: Hypergeometric densities卜松密度: Poisson densities几何密度: Geometric densities负二项密度: Negative binomial densities连续均匀密度: Continuous uniform densities常态密度: Normal densities指数密度: Exponential densities伽玛密度: Gamma densities贝他密度: Beta densities多变量分析: Multivariate analysis主因子分析: Principal components区别分析: Discrimination analysis群集分析: Cluster analysis因素分析: Factor analysis存活分析: Survival analysis时间序列分析: Time series analysis线性模式: Linear models品质工程: Quality engineering机率论: Probability theory统计计算: Statistical computing统计推论: Statistical inference随机过程: Stochastic processes决策理论: Decision theory离散分析: Discrete analysis数理统计: Mathematical statistics统计名词市调辞典众数(Mode) 普查(census)指数(Index) 问卷(Questionnaire)中位数(Median) 信度(Reliability)百分比(Percentage) 母群体(Population)信赖水准(Confidence level) 观察法(Observational Survey)假设检定(Hypothesis Testing) 综合法(Integrated Survey)卡方检定(Chi-square Test) 雪球抽样(Snowball Sampling)差距量表(Interval Scale) 序列偏差(Series Bias)类别量表(Nominal Scale) 次级资料(Secondary Data)顺序量表(Ordinal Scale) 抽样架构(Sampling frame)比率量表(Ratio Scale) 集群抽样(Cluster Sampling)连检定法(Run Test) 便利抽样(Convenience Sampling)符号检定(Sign Test) 抽样调查(Sampling Sur)算术平均数(Arithmetic Mean) 非抽样误差(non-sampling error) 展示会法(Display Survey)调查名词准确效度(Criterion-Related Validity)元素(Element) 邮寄问卷法(Mail Interview)样本(Sample) 信抽样误差(Sampling error)效度(Validity) 封闭式问题(Close Question)精确度(Precision) 电话访问法(Telephone Interview)准确度(Validity) 随机抽样法(Random Sampling)实验法(Experiment Survey)抽样单位(Sampling unit) 资讯名词市场调查(Marketing Research) 决策树(Decision Trees)容忍误差(Tolerated erro) 资料采矿(Data Mining)初级资料(Primary Data) 时间序列(Time-Series Forecasting) 目标母体(Target Population) 回归分析(Regression)抽样偏差(Sampling Bias) 趋势分析(Trend Analysis)抽样误差(sampling error) 罗吉斯回归(Logistic Regression)架构效度(Construct Validity) 类神经网络(Neural Network)配额抽样(Quota Sampling) 无母数统计检定方法(Non-Parametric Test) 人员访问法(Interview) 判别分析法(Discriminant Analysis)集群分析法(cluster analysis) 规则归纳法(Rules Induction)内容效度(Content Validity) 判断抽样(Judgment Sampling)开放式问题(Open Question) OLAP(Online Analytical Process)分层随机抽样(Stratified Random sampling) 资料仓储(Data Warehouse) 非随机抽样法(Nonrandom Sampling) 知识发现(Knowledge Discovery Absolute deviation, 绝对离差Absolute number, 绝对数Absolute residuals, 绝对残差Acceleration array, 加速度立体阵Acceleration in an arbitrary direction, 任意方向上的加速度Acceleration normal, 法向加速度Acceleration space dimension, 加速度空间的维数Acceleration tangential, 切向加速度Acceleration vector, 加速度向量Acceptable hypothesis, 可接受假设Accumulation, 累积Accuracy, 准确度Actual frequency, 实际频数Adaptive estimator, 自适应估计量Addition, 相加Addition theorem, 加法定理Additive Noise, 加性噪声Additivity, 可加性Adjusted rate, 调整率Adjusted value, 校正值Admissible error, 容许误差Aggregation, 聚集性Alpha factoring,α因子法Alternative hypothesis, 备择假设Among groups, 组间Amounts, 总量Analysis of correlation, 相关分析Analysis of covariance, 协方差分析Analysis Of Effects, 效应分析Analysis Of Variance, 方差分析Analysis of regression, 回归分析Analysis of time series, 时间序列分析Analysis of variance, 方差分析Angular transformation, 角转换ANOVA （analysis of variance）, 方差分析ANOVA Models, 方差分析模型ANOVA table and eta, 分组计算方差分析Arcing, 弧/弧旋Arcsine transformation, 反正弦变换Area 区域图Area under the curve, 曲线面积AREG , 评估从一个时间点到下一个时间点回归相关时的误差ARIMA, 季节和非季节性单变量模型的极大似然估计Arithmetic grid paper, 算术格纸Arithmetic mean, 算术平均数Arrhenius relation, 艾恩尼斯关系Assessing fit, 拟合的评估Associative laws, 结合律Asymmetric distribution, 非对称分布Asymptotic bias, 渐近偏倚Asymptotic efficiency, 渐近效率Asymptotic variance, 渐近方差Attributable risk, 归因危险度Attribute data, 属性资料Attribution, 属性Autocorrelation, 自相关Autocorrelation of residuals, 残差的自相关Average, 平均数Average confidence interval length, 平均置信区间长度Average growth rate, 平均增长率Bar chart, 条形图Bar graph, 条形图Base period, 基期Bayes' theorem , Bayes定理Bell-shaped curve, 钟形曲线Bernoulli distribution, 伯努力分布Best-trim estimator, 最好切尾估计量Bias, 偏性Binary logistic regression, 二元逻辑斯蒂回归Binomial distribution, 二项分布Bisquare, 双平方Bivariate Correlate, 二变量相关Bivariate normal distribution, 双变量正态分布Bivariate normal population, 双变量正态总体Biweight interval, 双权区间Biweight M-estimator, 双权M估计量Block, 区组/配伍组BMDP(Biomedical computer programs), BMDP统计软件包Boxplots, 箱线图/箱尾图Breakdown bound, 崩溃界/崩溃点Canonical correlation, 典型相关Caption, 纵标目Case-control study, 病例对照研究Categorical variable, 分类变量Catenary, 悬链线Cauchy distribution, 柯西分布Cause-and-effect relationship, 因果关系Cell, 单元Censoring, 终检Center of symmetry, 对称中心Centering and scaling, 中心化和定标Central tendency, 集中趋势Central value, 中心值CHAID -χ2 Automatic Interaction Detector, 卡方自动交互检测Chance, 机遇Chance error, 随机误差Chance variable, 随机变量Characteristic equation, 特征方程Characteristic root, 特征根Characteristic vector, 特征向量Chebshev criterion of fit, 拟合的切比雪夫准则Chernoff faces, 切尔诺夫脸谱图Chi-square test, 卡方检验/χ2检验Choleskey decomposition, 乔洛斯基分解Circle chart, 圆图Class interval, 组距Class mid-value, 组中值Class upper limit, 组上限Classified variable, 分类变量Cluster analysis, 聚类分析Cluster sampling, 整群抽样Code, 代码Coded data, 编码数据Coding, 编码Coefficient of contingency, 列联系数Coefficient of determination, 决定系数Coefficient of multiple correlation, 多重相关系数Coefficient of partial correlation, 偏相关系数Coefficient of production-moment correlation, 积差相关系数Coefficient of rank correlation, 等级相关系数Coefficient of regression, 回归系数Coefficient of skewness, 偏度系数Coefficient of variation, 变异系数Cohort study, 队列研究Collinearity, 共线性Column, 列Column effect, 列效应Column factor, 列因素Combination pool, 合并Combinative table, 组合表Common factor, 共性因子Common regression coefficient, 公共回归系数Common value, 共同值Common variance, 公共方差Common variation, 公共变异Communality variance, 共性方差Comparability, 可比性Comparison of bathes, 批比较Comparison value, 比较值Compartment model, 分部模型Compassion, 伸缩Complement of an event, 补事件Complete association, 完全正相关Complete dissociation, 完全不相关Complete statistics, 完备统计量Completely randomized design, 完全随机化设计Composite event, 联合事件Composite events, 复合事件Concavity, 凹性Conditional expectation, 条件期望Conditional likelihood, 条件似然Conditional probability, 条件概率Conditionally linear, 依条件线性Confidence interval, 置信区间Confidence limit, 置信限Confidence lower limit, 置信下限Confidence upper limit, 置信上限Confirmatory Factor Analysis , 验证性因子分析Confirmatory research, 证实性实验研究Confounding factor, 混杂因素Conjoint, 联合分析Consistency, 相合性Consistency check, 一致性检验Consistent asymptotically normal estimate, 相合渐近正态估计Consistent estimate, 相合估计Constrained nonlinear regression, 受约束非线性回归Constraint, 约束Contaminated distribution, 污染分布Contaminated Gausssian, 污染高斯分布Contaminated normal distribution, 污染正态分布Contamination, 污染Contamination model, 污染模型Contingency table, 列联表Contour, 边界线Contribution rate, 贡献率Control, 对照, 质量控制图Controlled experiments, 对照实验Conventional depth, 常规深度Convolution, 卷积Corrected factor, 校正因子Corrected mean, 校正均值Correction coefficient, 校正系数Correctness, 正确性Correlation coefficient, 相关系数Correlation, 相关性Correlation index, 相关指数Correspondence, 对应Counting, 计数Counts, 计数/频数Covariance, 协方差Covariant, 共变Cox Regression, Cox回归Criteria for fitting, 拟合准则Criteria of least squares, 最小二乘准则Critical ratio, 临界比Critical region, 拒绝域Critical value, 临界值Cross-over design, 交叉设计Cross-section analysis, 横断面分析Cross-section survey, 横断面调查Crosstabs , 交叉表Crosstabs 列联表分析Cross-tabulation table, 复合表Cube root, 立方根Cumulative distribution function, 分布函数Cumulative probability, 累计概率Curvature, 曲率/弯曲Curvature, 曲率Curve Estimation, 曲线拟合Curve fit , 曲线拟和Curve fitting, 曲线拟合Curvilinear regression, 曲线回归Curvilinear relation, 曲线关系Cut-and-try method, 尝试法Cycle, 周期Cyclist, 周期性D test, D检验Data acquisition, 资料收集Data bank, 数据库Data capacity, 数据容量Data deficiencies, 数据缺乏Data handling, 数据处理Data manipulation, 数据处理Data processing, 数据处理Data reduction, 数据缩减Data set, 数据集Data sources, 数据来源Data transformation, 数据变换Data validity, 数据有效性Data-in, 数据输入Data-out, 数据输出Dead time, 停滞期Degree of freedom, 自由度Degree of precision, 精密度Degree of reliability, 可靠性程度Degression, 递减Density function, 密度函数Density of data points, 数据点的密度Dependent variable, 应变量/依变量/因变量Dependent variable, 因变量Depth, 深度Derivative matrix, 导数矩阵Derivative-free methods, 无导数方法Design, 设计Determinacy, 确定性Determinant, 行列式Determinant, 决定因素Deviation, 离差Deviation from average, 离均差Diagnostic plot, 诊断图Dichotomous variable, 二分变量Differential equation, 微分方程Direct standardization, 直接标准化法Direct Oblimin, 斜交旋转Discrete variable, 离散型变量DISCRIMINANT, 判断Discriminant analysis, 判别分析Discriminant coefficient, 判别系数Discriminant function, 判别值Dispersion, 散布/分散度Disproportional, 不成比例的Disproportionate sub-class numbers, 不成比例次级组含量Distribution free, 分布无关性/免分布Distribution shape, 分布形状Distribution-free method, 任意分布法Distributive laws, 分配律Disturbance, 随机扰动项Dose response curve, 剂量反应曲线Double blind method, 双盲法Double blind trial, 双盲试验Double exponential distribution, 双指数分布Double logarithmic, 双对数Downward rank, 降秩Dual-space plot, 对偶空间图DUD, 无导数方法Duncan's new multiple range method, 新复极差法/Duncan新法Error Bar, 均值相关区间图Effect, 实验效应Eigenvalue, 特征值Eigenvector, 特征向量Ellipse, 椭圆Empirical distribution, 经验分布Empirical probability, 经验概率单位Enumeration data, 计数资料Equal sun-class number, 相等次级组含量Equally likely, 等可能Equivariance, 同变性Error, 误差/错误Error of estimate, 估计误差Error type I, 第一类错误Error type II, 第二类错误Estimand, 被估量Estimated error mean squares, 估计误差均方Estimated error sum of squares, 估计误差平方和Euclidean distance, 欧式距离Event, 事件Event, 事件Exceptional data point, 异常数据点Expectation plane, 期望平面Expectation surface, 期望曲面Expected values, 期望值Experiment, 实验Experimental sampling, 试验抽样Experimental unit, 试验单位Explained variance （已说明方差）Explanatory variable, 说明变量Exploratory data analysis, 探索性数据分析Explore Summarize, 探索-摘要Exponential curve, 指数曲线Exponential growth, 指数式增长EXSMOOTH, 指数平滑方法Extended fit, 扩充拟合Extra parameter, 附加参数Extrapolation, 外推法Extreme observation, 末端观测值Extremes, 极端值/极值F distribution, F分布F test, F检验Factor, 因素/因子Factor analysis, 因子分析Factor Analysis, 因子分析Factor score, 因子得分Factorial, 阶乘Factorial design, 析因试验设计False negative, 假阴性False negative error, 假阴性错误Family of distributions, 分布族Family of estimators, 估计量族Fanning, 扇面Fatality rate, 病死率Field investigation, 现场调查Field survey, 现场调查Finite population, 有限总体Finite-sample, 有限样本First derivative, 一阶导数First principal component, 第一主成分First quartile, 第一四分位数Fisher information, 费雪信息量Fitted value, 拟合值Fitting a curve, 曲线拟合Fixed base, 定基Fluctuation, 随机起伏Forecast, 预测Four fold table, 四格表Fourth, 四分点Fraction blow, 左侧比率Fractional error, 相对误差Frequency, 频率Frequency polygon, 频数多边图Frontier point, 界限点Function relationship, 泛函关系Gamma distribution, 伽玛分布Gauss increment, 高斯增量Gaussian distribution, 高斯分布/正态分布Gauss-Newton increment, 高斯-牛顿增量General census, 全面普查Generalized least squares, 综合最小平方法GENLOG (Generalized liner models), 广义线性模型Geometric mean, 几何平均数Gini's mean difference, 基尼均差GLM (General liner models), 通用线性模型Goodness of fit, 拟和优度/配合度Gradient of determinant, 行列式的梯度Graeco-Latin square, 希腊拉丁方Grand mean, 总均值Gross errors, 重大错误Gross-error sensitivity, 大错敏感度Group averages, 分组平均Grouped data, 分组资料Guessed mean, 假定平均数Half-life, 半衰期Hampel M-estimators, 汉佩尔M估计量Happenstance, 偶然事件Harmonic mean, 调和均数Hazard function, 风险均数Hazard rate, 风险率Heading, 标目Heavy-tailed distribution, 重尾分布Hessian array, 海森立体阵Heterogeneity, 不同质Heterogeneity of variance, 方差不齐Hierarchical classification, 组内分组Hierarchical clustering method, 系统聚类法High-leverage point, 高杠杆率点High-Low, 低区域图Higher Order Interaction Effects，高阶交互作用HILOGLINEAR, 多维列联表的层次对数线性模型Hinge, 折叶点Histogram, 直方图Historical cohort study, 历史性队列研究Holes, 空洞HOMALS, 多重响应分析Homogeneity of variance, 方差齐性Homogeneity test, 齐性检验Huber M-estimators, 休伯M估计量Hyperbola, 双曲线Hypothesis testing, 假设检验Hypothetical universe, 假设总体Image factoring,, 多元回归法Impossible event, 不可能事件Independence, 独立性Independent variable, 自变量Index, 指标/指数Indirect standardization, 间接标准化法Individual, 个体Inference band, 推断带Infinite population, 无限总体Infinitely great, 无穷大Infinitely small, 无穷小Influence curve, 影响曲线Information capacity, 信息容量Initial condition, 初始条件Initial estimate, 初始估计值Initial level, 最初水平Interaction, 交互作用Interaction terms, 交互作用项Intercept, 截距Interpolation, 内插法Interquartile range, 四分位距Interval estimation, 区间估计Intervals of equal probability, 等概率区间Intrinsic curvature, 固有曲率Invariance, 不变性Inverse matrix, 逆矩阵Inverse probability, 逆概率Inverse sine transformation, 反正弦变换Iteration, 迭代Jacobian determinant, 雅可比行列式Joint distribution function, 分布函数Joint probability, 联合概率Joint probability distribution, 联合概率分布K-Means Cluster逐步聚类分析K means method, 逐步聚类法Kaplan-Meier, 评估事件的时间长度Kaplan-Merier chart, Kaplan-Merier图Kendall's rank correlation, Kendall等级相关Kinetic, 动力学Kolmogorov-Smirnove test, 柯尔莫哥洛夫-斯米尔诺夫检验Kruskal and Wallis test, Kruskal及Wallis检验/多样本的秩和检验/H检验Kurtosis, 峰度Lack of fit, 失拟Ladder of powers, 幂阶梯Lag, 滞后Large sample, 大样本Large sample test, 大样本检验Latin square, 拉丁方Latin square design, 拉丁方设计Leakage, 泄漏Least favorable configuration, 最不利构形Least favorable distribution, 最不利分布Least significant difference, 最小显著差法Least square method, 最小二乘法Least Squared Criterion，最小二乘方准则Least-absolute-residuals estimates, 最小绝对残差估计Least-absolute-residuals fit, 最小绝对残差拟合Least-absolute-residuals line, 最小绝对残差线Legend, 图例L-estimator, L估计量L-estimator of location, 位置L估计量L-estimator of scale, 尺度L估计量Level, 水平Leveage Correction，杠杆率校正Life expectance, 预期期望寿命Life table, 寿命表Life table method, 生命表法Light-tailed distribution, 轻尾分布Likelihood function, 似然函数Likelihood ratio, 似然比line graph, 线图Linear correlation, 直线相关Linear equation, 线性方程Linear programming, 线性规划Linear regression, 直线回归Linear Regression, 线性回归Linear trend, 线性趋势Loading, 载荷Location and scale equivariance, 位置尺度同变性Location equivariance, 位置同变性Location invariance, 位置不变性Location scale family, 位置尺度族Log rank test, 时序检验Logarithmic curve, 对数曲线Logarithmic normal distribution, 对数正态分布Logarithmic scale, 对数尺度Logarithmic transformation, 对数变换Logic check, 逻辑检查Logistic distribution, 逻辑斯特分布Logit transformation, Logit转换LOGLINEAR, 多维列联表通用模型Lognormal distribution, 对数正态分布Lost function, 损失函数Low correlation, 低度相关Lower limit, 下限Lowest-attained variance, 最小可达方差LSD, 最小显著差法的简称Lurking variable, 潜在变量Main effect, 主效应Major heading, 主辞标目Marginal density function, 边缘密度函数Marginal probability, 边缘概率Marginal probability distribution, 边缘概率分布Matched data, 配对资料Matched distribution, 匹配过分布Matching of distribution, 分布的匹配Matching of transformation, 变换的匹配Mathematical expectation, 数学期望Mathematical model, 数学模型Maximum L-estimator, 极大极小L 估计量Maximum likelihood method, 最大似然法Mean, 均数Mean squares between groups, 组间均方Mean squares within group, 组内均方Means (Compare means), 均值-均值比较Median, 中位数Median effective dose, 半数效量Median lethal dose, 半数致死量Median polish, 中位数平滑Median test, 中位数检验Minimal sufficient statistic, 最小充分统计量Minimum distance estimation, 最小距离估计Minimum effective dose, 最小有效量Minimum lethal dose, 最小致死量Minimum variance estimator, 最小方差估计量MINITAB, 统计软件包Minor heading, 宾词标目Missing data, 缺失值Model specification, 模型的确定Modeling Statistics , 模型统计Models for outliers, 离群值模型Modifying the model, 模型的修正Modulus of continuity, 连续性模Morbidity, 发病率Most favorable configuration, 最有利构形MSC（多元散射校正）Multidimensional Scaling (ASCAL), 多维尺度/多维标度Multinomial Logistic Regression , 多项逻辑斯蒂回归Multiple comparison, 多重比较Multiple correlation , 复相关Multiple covariance, 多元协方差Multiple linear regression, 多元线性回归Multiple response , 多重选项Multiple solutions, 多解Multiplication theorem, 乘法定理Multiresponse, 多元响应Multi-stage sampling, 多阶段抽样Multivariate T distribution, 多元T分布Mutual exclusive, 互不相容Mutual independence, 互相独立Natural boundary, 自然边界Natural dead, 自然死亡Natural zero, 自然零Negative correlation, 负相关Negative linear correlation, 负线性相关Negatively skewed, 负偏Newman-Keuls method, q检验NK method, q检验No statistical significance, 无统计意义Nominal variable, 名义变量Nonconstancy of variability, 变异的非定常性Nonlinear regression, 非线性相关Nonparametric statistics, 非参数统计Nonparametric test, 非参数检验Nonparametric tests, 非参数检验Normal deviate, 正态离差Normal distribution, 正态分布Normal equation, 正规方程组Normal P-P, 正态概率分布图Normal Q-Q, 正态概率单位分布图Normal ranges, 正常范围Normal value, 正常值Normalization 归一化Nuisance parameter, 多余参数/讨厌参数Null hypothesis, 无效假设Numerical variable, 数值变量Objective function, 目标函数Observation unit, 观察单位Observed value, 观察值One sided test, 单侧检验One-way analysis of variance, 单因素方差分析Oneway ANOVA , 单因素方差分析Open sequential trial, 开放型序贯设计Optrim, 优切尾Optrim efficiency, 优切尾效率Order statistics, 顺序统计量Ordered categories, 有序分类Ordinal logistic regression , 序数逻辑斯蒂回归Ordinal variable, 有序变量Orthogonal basis, 正交基Orthogonal design, 正交试验设计Orthogonality conditions, 正交条件ORTHOPLAN, 正交设计Outlier cutoffs, 离群值截断点Outliers, 极端值OVERALS , 多组变量的非线性正规相关Overshoot, 迭代过度Paired design, 配对设计Paired sample, 配对样本Pairwise slopes, 成对斜率Parabola, 抛物线Parallel tests, 平行试验Parameter, 参数Parametric statistics, 参数统计Parametric test, 参数检验Pareto, 直条构成线图（又称佩尔托图）Partial correlation, 偏相关Partial regression, 偏回归Partial sorting, 偏排序Partials residuals, 偏残差Pattern, 模式PCA（主成分分析）Pearson curves, 皮尔逊曲线Peeling, 退层Percent bar graph, 百分条形图Percentage, 百分比Percentile, 百分位数Percentile curves, 百分位曲线Periodicity, 周期性Permutation, 排列P-estimator, P估计量Pie graph, 构成图,饼图Pitman estimator, 皮特曼估计量Pivot, 枢轴量Planar, 平坦Planar assumption, 平面的假设PLANCARDS, 生成试验的计划卡PLS（偏最小二乘法）Point estimation, 点估计Poisson distribution, 泊松分布Polishing, 平滑Polled standard deviation, 合并标准差Polled variance, 合并方差Polygon, 多边图Polynomial, 多项式Polynomial curve, 多项式曲线Population, 总体Population attributable risk, 人群归因危险度Positive correlation, 正相关Positively skewed, 正偏Posterior distribution, 后验分布Power of a test, 检验效能Precision, 精密度Predicted value, 预测值Preliminary analysis, 预备性分析Principal axis factoring,主轴因子法Principal component analysis, 主成分分析Prior distribution, 先验分布Prior probability, 先验概率Probabilistic model, 概率模型probability, 概率Probability density, 概率密度Product moment, 乘积矩/协方差Profile trace, 截面迹图Proportion, 比/构成比Proportion allocation in stratified random sampling, 按比例分层随机抽样Proportionate, 成比例Proportionate sub-class numbers, 成比例次级组含量Prospective study, 前瞻性调查Proximities, 亲近性Pseudo F test, 近似F检验Pseudo model, 近似模型Pseudosigma, 伪标准差Purposive sampling, 有目的抽样QR decomposition, QR分解Quadratic approximation, 二次近似Qualitative classification, 属性分类Qualitative method, 定性方法Quantile-quantile plot, 分位数-分位数图/Q-Q图Quantitative analysis, 定量分析Quartile, 四分位数Quick Cluster, 快速聚类Radix sort, 基数排序Random allocation, 随机化分组Random blocks design, 随机区组设计Random event, 随机事件Randomization, 随机化Range, 极差/全距Rank correlation, 等级相关Rank sum test, 秩和检验Rank test, 秩检验Ranked data, 等级资料Rate, 比率Ratio, 比例Raw data, 原始资料Raw residual, 原始残差Rayleigh's test, 雷氏检验Rayleigh's Z, 雷氏Z值Reciprocal, 倒数Reciprocal transformation, 倒数变换Recording, 记录Redescending estimators, 回降估计量Reducing dimensions, 降维Re-expression, 重新表达Reference set, 标准组Region of acceptance, 接受域Regression coefficient, 回归系数Regression sum of square, 回归平方和Rejection point, 拒绝点Relative dispersion, 相对离散度Relative number, 相对数Reliability, 可靠性Reparametrization, 重新设置参数Replication, 重复Report Summaries, 报告摘要Residual sum of square, 剩余平方和residual variance (剩余方差)Resistance, 耐抗性Resistant line, 耐抗线Resistant technique, 耐抗技术R-estimator of location, 位置R估计量R-estimator of scale, 尺度R估计量Retrospective study, 回顾性调查Ridge trace, 岭迹Ridit analysis, Ridit分析Rotation, 旋转Rounding, 舍入Row, 行Row effects, 行效应Row factor, 行因素RXC table, RXC表Sample, 样本Sample regression coefficient, 样本回归系数Sample size, 样本量Sample standard deviation, 样本标准差Sampling error, 抽样误差SAS(Statistical analysis system ), SAS统计软件包Scale, 尺度/量表Scatter diagram, 散点图Schematic plot, 示意图/简图Score test, 计分检验Screening, 筛检SEASON, 季节分析Second derivative, 二阶导数Second principal component, 第二主成分SEM (Structural equation modeling), 结构化方程模型Semi-logarithmic graph, 半对数图Semi-logarithmic paper, 半对数格纸Sensitivity curve, 敏感度曲线Sequential analysis, 贯序分析Sequence, 普通序列图Sequential data set, 顺序数据集Sequential design, 贯序设计Sequential method, 贯序法Sequential test, 贯序检验法Serial tests, 系列试验Short-cut method, 简捷法Sigmoid curve, S形曲线Sign function, 正负号函数Sign test, 符号检验Signed rank, 符号秩Significant Level, 显著水平Significance test, 显著性检验Significant figure, 有效数字Simple cluster sampling, 简单整群抽样Simple correlation, 简单相关Simple random sampling, 简单随机抽样Simple regression, 简单回归simple table, 简单表Sine estimator, 正弦估计量Single-valued estimate, 单值估计Singular matrix, 奇异矩阵Skewed distribution, 偏斜分布Skewness, 偏度Slash distribution, 斜线分布Slope, 斜率Smirnov test, 斯米尔诺夫检验Source of variation, 变异来源Spearman rank correlation, 斯皮尔曼等级相关Specific factor, 特殊因子Specific factor variance, 特殊因子方差Spectra , 频谱Spherical distribution, 球型正态分布Spread, 展布SPSS(Statistical package for the social science), SPSS统计软件包Spurious correlation, 假性相关Square root transformation, 平方根变换Stabilizing variance, 稳定方差Standard deviation, 标准差Standard error, 标准误Standard error of difference, 差别的标准误Standard error of estimate, 标准估计误差Standard error of rate, 率的标准误Standard normal distribution, 标准正态分布Standardization, 标准化Starting value, 起始值Statistic, 统计量Statistical control, 统计控制Statistical graph, 统计图Statistical inference, 统计推断Statistical table, 统计表Steepest descent, 最速下降法Stem and leaf display, 茎叶图Step factor, 步长因子Stepwise regression, 逐步回归Storage, 存Strata, 层（复数）Stratified sampling, 分层抽样Stratified sampling, 分层抽样Strength, 强度Stringency, 严密性Structural relationship, 结构关系Studentized residual, 学生化残差/t化残差Sub-class numbers, 次级组含量Subdividing, 分割Sufficient statistic, 充分统计量Sum of products, 积和Sum of squares, 离差平方和Sum of squares about regression, 回归平方和Sum of squares between groups, 组间平方和Sum of squares of partial regression, 偏回归平方和Sure event, 必然事件Survey, 调查Survival, 生存分析Survival rate, 生存率Suspended root gram, 悬吊根图Symmetry, 对称Systematic error, 系统误差Systematic sampling, 系统抽样Tags, 标签Tail area, 尾部面积Tail length, 尾长Tail weight, 尾重Tangent line, 切线Target distribution, 目标分布Taylor series, 泰勒级数Test(检验)Test of linearity, 线性检验Tendency of dispersion, 离散趋势。

2022年大学生英语四级考试答案（完整版）转瞬间20xx年年底我们又迎来了一次惊慌的四六级考试了，不知对于20xx年最终一次的四六级考试你们是否很惊慌呢?以下是我为大家打算了20xx年大学生英语四级考试答案(完整版)，欢送参阅。

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Proceedings ofASME TURBO EXPO 2001June 4-7, 2001, New Orleans, Louisiana, USA2001-GT-0328 A NUMERICAL INVESTIGATION ON THE VOLUTE/IMPELLER STEADY-STATEINTERACTION DUE TO CIRCUMFERENTIAL DISTORTIONFahua Gu Turbomachinery Lab Michigan State University East Lansing, MI 48824Abraham Engeda Turbomachinery Lab Michigan State University East Lansing, MI 48824ABSTRACTTo understand the volute/impeller interaction at off-design conditions, the steady-state interaction between volute and impeller is investigated in this paper using CFX-TASCflow’s frozen rotor model. This model is applicable to the compressor flow where the acoustic Strouhal number is close to zero. The gentle circumferential pressure distortion is confirmed at the exit of the vaneless diffuser; but the radical pressure distortion is found around the tongue, resulting from the incidence to the tongue. The circumferential pressure distortion, which is lagged in phase to the total pressure distortion, is predicted to propagate upstream over the vaneless diffuser without significant decay. It is found that the impeller exit flow pattern depends on the slope of the circumferential variation of the static pressure at exit. This explains why the impeller efficiency is reduced at off-design conditions. Therefore, this study suggests that the undersized volute is beneficial to the impeller. INTRODUCTIONThe study of volute flows in centrifugal compressors is highlighted by the fact that the circumferential distortion occurs inside the volutes and vaneless/vaned diffusers at off-design conditions. This distortion propagates upstream and causes flow fluctuation in impellers. The efficiency drop of a centrifugal compressor at off-design conditions can be attributed to many factors, but the flow distortion caused by volute is definitely among them.The circumferential pressure distortion in the volute has attracted much attention recently. Van den Braembussche and Hande (1990) reported and explained the pressure distortion at the vaneless diffuser exit of a straight model at off-design conditions. At lower/higher mass flow, the flow inside the volute is decelerated/accelerated according to continuity, resulting in pressure increasing/decreasing according to the conservation of momentum. Ayder et al. (1993) confirmed that the vaneless diffuser exit flow was distorted in a centrifugal compressor with a volute of elliptic cross sections.The interaction between volute and vaneless diffuser can be in both axial and circumferential directions. The axial interaction is indicated by the dependence of the volute flow structure on the diffuser inflow (Gu, et al., 2000). The circumferential interaction is suggested by the static and total pressure distortion at the diffuser exit. The phase lag between the static and total pressure distortions has been observed by Ayder et al. (1993) and Hagelstein et al. (1999), respectively. At high mass flow, Ayder observed a maximum total pressure region around 70o downstream the tongue, which is about 30o lag of the maximum static pressure. It was explained that due to the mass flow variation along the circumference of the impeller, blades are operating at different conditions. At lower mass flow, Hagelstein noted that the total pressure is seen to increase due to the increase in the throttling effect circumferentially, and the minimum value of the total temperature and (total) pressure is found at about θ=120o, which corresponds to a position behind the tongue. It is explained that the phase shift is due to the impeller response to the perturbation of the tongue, which is transmitted along a streamline to the diffuser exit.The volute/impeller interaction essentially is an unsteady phenomenon. Fatsis et al. (1997) suggested using the acoustic Strouhal number to quantify the relative effects of the rotation and pressure wave propagation. The acoustic Strouhal number was defined ascfLSr=where L is normally defined as the length of a blade passage, and f is the rotation frequency times the number of perturbation waves around the circumference. For the impeller discussed in this paper, the Strouhal number is around 0.133 when f isreplaced by rotation frequency since the volute only has one tongue. It indicates that the pressure wave propagation is much faster than the rotation of the impeller. That is, the pressure perturbation finishes traveling over the passage at almost the same time as when the impeller rotates to a new position. Therefore, the “frozen rotor model” provided by CFX-TASCflow (1999) can be used to study the pressure distortion due to the volute.In this paper, the flow fields of a centrifugal compressor stage are simulated at three mass flow points using the frozen rotor model. Tongue flow field is investigated to explain the circumferential pressure distortion at the vaneless diffuser exit. The pressure distortion due to the volute is observed to cause each impeller passage to work at different exit pressure, therefore with different mass flow, at off-design conditions. NOMENCLATUREC p specific heat at constant pressurec soundspeedc p pressure recoveryD diameterF forcef frequencyL blade passage lengthm mass flow ratep pressureQ volume flow rateR radialRo Rossby numberSr Strouhal numberT temperaturet time,totalU blade speedV absolute velocityW relative velocityZ axial directionαabsolute flow angle from radialβrelative flow angle from radialΦ flow coefficientη efficiencyθangle of volute sectionρ densityωtotal pressure loss coefficient, impeller rotate speedΨisentropic head coefficientSubscriptsisen isentropicr radialref reference (design) conditiontip tip of the impeller0 stagnation, inlet flange1 inlet of impeller2 exit of impeller3 inlet of diffuser4 impeller/diffuser grid interface5 diffuser exit7 critical surface, θ=08 exit flange of the compressorCFD MODELA single stage pipeline centrifugal compressor is studied to investigate the circumferential pressure distortion due to the volute. It has a total-to-total pressure ratio of 1.4 with a high flow coefficient. The impeller has 11 backward swept blades of 52o from radial. The machine tip Mach number at the design point is 0.65 and the diffuser ratio25DD is 1.9. The impeller grid of a single passage was generated by a commercial code. A self-written code then read in the single passage grid and sweeps to 360o in such a way that the impeller has a uniform pitch. The volute grid is generated by a self-written code. A butterfly section is used to reduce the grid skewness. The size of the model is 096,18131687=××points for one passage of the impeller and 145,535 for the volute, and the number of total points is 344,591. Fig.1 shows the grid for this study. The convention of the compressor is shown in Fig.2.The commercially available CFD software, CFX-TASCflow, is employed for this study. The validation of this code for the configuration of centrifugal compressors can be found, for example, in the work of Flathers et al. (1994, 1999). The code solves the Reynolds averaged Navier-Stokes equations in the primitive variable form. The effects of turbulence are modeled using the standard k-ε turbulent model. To make the simulation timely economical, a wall function is used to resolve the wall flows. This explains why the grid in this study is relatively coarse.To investigate the pressure distortion due to the volute, the impeller and volute must be solved as a coupled system. TASCflow provides a simulation model, referred to as Steady-State Multiple Frame of Reference (MFR) analysis. A slidinginterface was established between the two components. Numerical details of this methodology were outlined in Galpin et al. (1995). The frozen rotor model achieves a frame change across the interface without a relative position change over time and without any interface averaging. Therefore, all the impeller passages have to be modeled. Local flow features are allowed to transport across the interface; thus, pressure nonuniformities in the volute are allowed to propagate upstream to the impeller, which results in different exit flow conditions for each impeller passage. This model is an exact representation of the case Sr=0 in which either the sound speed is infinite or the rotation speed is zero and is an approximation when the Strouhal number is small enough as in this case. Flathers and Bache (1999) used this model to predict the radial force of impeller.Fig.2 Compressor conventionThe inflow boundary condition was assigned upstream of the impeller at station 0-0, which is about one chord upstream of the impeller, in order to capture the flow distortion at the impeller leading edge. Uniform total temperature, total pressure and flow angles are assigned on this station. Mass flow rate was imposed on the exit of the cone as the outflow boundary condition. At off-design points, only the assigned exit mass flow rate was changed. On the sliding interface between the volute and impeller, the frozen rotor model is employed as discussed above.The code was run at three mass flow rates: one being design mass flow, one being 75% design mass flow, and one being 125% design mass flow. It took about 48 hours to iterate 400 steps to reduce the maximum residual to 1e-4 at the design point on a Sun Workstation 450 using one of its processors. At lower mass flow, the computer time was doubled.RESULTS AND DISCUSSIONAs will be shown, the predicted performance of the compressor is too close to the experimental one at lower mass flow. The fact is that the CFD model didn’t incorporate the leakage loss in the cavity and the disc friction loss; the predicted performance should be better than the experimental one. This motivated the authors to investigate the steady-state interaction to understand 1) the propagation mechanism of the perturbation with lower acoustic Strouhal numbers and 2) the characteristic of the numerical model. The performance of the compressor is therefore presented first. Contributions to the performance variation are then explored, which include the flow in the diffuser, tongue flow, and the flow in the impeller passages.Compressor performance The experiment was run at 10901 rpm, while the CFD study was conducted at 10530 rpm. The overall performance is therefore compared in terms of non-dimensional parameters as shown in Fig. 3. The inlet flow coefficient and isentropic head coefficient are defined as421tiptipUDQ××=Φπ (1)()2,01082tipttisenpUTTC−−=Ψη (2) .0.30.50.70.91.11.30.500.75 1.00 1.25 1.501.75Inlet flow coefficientΦ/ΦrefIsentropicheadcoefficientΨ/ΨrefFig.3 Compressor performanceIt can be seen that the predicted compressor performance from the frozen rotor model shows a different tendency; the isentropic head drops faster as the operation points shift left. The comparison of the impeller performance between stage model (Gu, et al., 2000) and frozen rotor one indicates that the frozen rotor model predicted less isentropic head at lower mass flow and higher head at higher mass flow. The difference between the curves at impeller discharge and the cone discharge represents the losses in the vaneless diffuser and volute. It can be seen that the losses in the volute and veneless diffuser are predicted higher at lower mass and lower at higher mass flow, compared to the stage model. The essential difference between stage model and frozen rotor one is their responses to the pressure perturbations of different Strouhal numbers. In the stage model, the pressure perturbation from the tongue dies out at the mixing plane, preventing impellers from any disturbance. The frozen rotor model assumes that the perturbation propagates into the impeller at an infinite speed, which is a good approximation for low frequency perturbations. Therefore, the generation and propagation of the pressure perturbations will be investigated.Perturbation Generation The generation of the pressure perturbation has been clearly stated by Van den Braembussche and Hande (1990). At off-design conditions, the pressure begins a gently circumferential increase or decrease downstream of the tongue and ends up with a maximum or minimum around the tongue. The tongue region therefore is the location where the radical pressure distortion occurs. The circumferential position of the extreme varies with the flow rate. Fig.4 shows the static pressure distortion on the surface in the mid of the vaneless diffuser at lower mass flow. The impeller passage is numbered from 0 to 10 for later use.Fig.4 Pressure distortion on a z-surface at 75% mass flow(a) 75% mass flow(b) 125% mass flowFig.5 Pressure contours on the y-planeThe pressure contours are plotted in Fig.5a on a y-plane surface of 1.9 r tip to the z-axis. This plane cuts the tongue. It can be seen that at lower mass flow, the pressure distribution is rather uniform at the beginning of the conical diffuser. Radical flow expansion happens around the tongue in the volute passage of smaller area. Flow is strongly accelerated due to this pressure gradient, resulting in flow deflection from the conical diffuser passage to the volute passage of smaller area as shown in Fig.6a. The beneficial effect of the mass immigration to the volute passage is that the deflected mass increases the total mass flow inside the volute; the circumferential pressure distortion is therefore smoothed. The detrimental effect is that additional losses will be generated due to the friction associated with the longer path of the fluid particles and the thickened boundary layers on the volute wall due to the incidence to thetongue.(a) 75% mass flow(b) 125% mass flow Fig.6 Vectors on the y-planeAt higher mass flow (Fig.5b), a maximum pressure zone is seen at the beginning of the conical diffuser passage, indicating that the acceleration process in the volute passage stops before the flow reaches the tongue. This is in agreement with the observation of Hagelstein et al. (1999) that the minimum pressure at higher mass flow is located upstream of the tongue. One surprising observation is that an acceleration process begins in the conical diffuser inlet! The tongue separates the flow passage upstream of the tongue into the exit cone passageand the volute passage of small area. When the flow deflectsinto the exit cone before the tongue (Fig. 6b), it is goingthrough a converged passage. Contrary to the small mass flow,the flow deflecting into the diffuser passage reduces the totalmass flow in the volute. The flow deflection also causes a tongue incidence, resulting in thickened boundary layers on the other side of the volute wall. The vector plot also shows that the twin vortex structure at higher mass flow (Gu, et al., 2000) happens downstream away from the tongue. It indicates that the twin vortex structure is primarily created by the non-uniformness in the axial direction. Propagation in the Vaneless Diffuser It is commonly assumed that the circumferential distortion is transmitted in the vaneless diffuser passage, even though the interactions among streamlines can exist. Therefore, Stanitz ’s equations (1952) were employed to transmit the distortion (Van den Braembussche, et al., 1999). However, the phase lag between total pressure and static pressure circumferential distortion indicates that the streamline interaction is not negligible. The distortion propagation in the vaneless diffuser is tracked by the mass averaged static and total pressures distribution at the three surfaces as shown in Fig.7. The surfaces of 85.1=tip r r and 06.1=tip r r are the end and beginning of the vaneless diffuser, respectively. The surface of 25.1=tipr r liesin between.The static pressure (Fig.7a) at the lower mass flow increases downstream of the tongue and reaches the maximum upstream of the tongue, resulting in an abrupt favorable circumferential pressure gradient around the tongue. This favorable pressure gradient prevents the generation of the twin vortices (Gu, et al., 2000). The same tendency of pressure distortion is observed inside the vaneless diffuser and at the exit of the impeller. An opposite case occurs at the higher mass flow rate where the maximum pressure occurs downstream of the tongue. A weaker adverse circumferential pressure gradient is built around the tongue. In both cases, the radical pressure distortion occurs and propagates inwards to the axis in the region between -30o and 60o around the tongue at all the three radial locations. Fig.7b shows that the total pressure circumferential variation is similar to that of the static pressure at the beginning of the vaneless diffuser; the locations of the total pressure extremes are identical to these of the static pressure. The lowest total pressure point at lower mass flow and the highest total pressure point at higher mass flow are convected downstream along the streamlines. This explains why there is a phase lag between static and total pressure distortion at the diffuser exit.The phase difference between the distortions of static pressure and that of total pressure can be described as 1) at the impeller exit there are no significant phase differences between static pressure and total pressure; 2) at the diffuser exit, the radical distortions in total pressure happen downstream of the static pressure distortion; 3) the radical static pressure distortion happens at the same circumferential position, which is aroundP /P r e f-180-120-60060120180θP /P r e f-180-120-60060120180θP 0/P r e f-180-120-60060120180θP 0/P r e f(b)Total pressure variation in circumferential directionFig.7 Perturbation in the vaneless diffuserThe phenomenon reported by Hagelstein et al. (1997) and Sorokes et al. (1998) was not observed that the pressure distortion at diffuser inlet is ½ of that at the diffuser exit. This discrepancy could possibly result from the frozen rotor model because this model lacks the capability to simulate the response of the impeller to the higher frequency perturbations of acoustic Strouhal numbers above zero. The other possibility is that the diffusers studied by Hagelstein and Sorokes are pinched.Exit Flow of the Impeller Impeller exit flow can be either of jet/wake two-zone or of a single zone. Johnson and Moore (1980) pointed out that the size and location of the wake are mainly determined by the Rossby number,n R W Ro ω=. Krain ’s (1988) experimental study revealed that the classical jet/wake exit flow was replaced by a single zone flow in his impeller with backward swept blades, even though swirling flow happened inside the impeller passage. However, it is not fully understood how the impeller responds to the distorted exit pressure.The impeller in this paper has 52o degree backward swept blades. Figure 8 shows the relative total pressure contour at the impeller exit. As shown in Fig.4, passage 3 and 4 are located upstream and downstream of the tongue, respectively. Passages 7 and 8 are located further downstream of the tongue. At all mass flow rates, the periodicity between passage 7 and 8 indicates that the effect of the pressure distortion away from the tongue can be neglected. At design (Fig.8c, d) and high mass flow rates (Fig.8e, f), the fluids with low relative total pressure concentrate in the suction/shroud corner, showing the classicaljet/wake pattern. No significant difference can be seen between the passages around tongue and these away from tongue. It indicates that at design and higher mass flow rates, the circumferential pressure distortion has very limited impact on the impeller flow. It could be due to the fact that at higher mass flow, the pressure distortion is relatively weak compared with that at lower mass flow as shown in Fig.7a. The other reason is that the pressure circumferential variation has different slopes at(75% flow: a, b; design flow: c, d; 125% flow: e, f)At lower mass flow, however, the flow pattern around the tongue is obviously different from that away from the tongue (figure 4a,b). In passages 7 and 8, the pitch-wise relative total pressure gradient dominants the exit flow. A higher loss region (label less than 10) occupying almost half of the passage indicates higher losses happened in these passages. On the contrary, the flow around the tongue shows a similar pattern as in design and higher mass flows. It suggests that the flow in the passage around the tongue is closer to the design flow than the flows in other passages.In summary, the pressure distortion makes each passage of the impeller work at different operation conditions. However, the exit flow pattern does not depend on the level of the exit pressure exclusively. Instead, it is determined to some degree bythe slope of the pressure variation. This is especially true atlower mass flow. Passages 3 and 4 have different exit pressure levels from these at the design points but have same tendency of slopes. The exit flow patterns therefore are the same. At higher mass flow, the pressure slightly increases around the tongue, so no significant flow pattern changes can be observed.Flow in the Impeller Because the circumferential pressure distortion exists at the impeller exit, each passage of Fig.9a shows the pressure variation in each passage at the Passage NumberPassage Number(a) Pressure distortion (b) PerformancePassage NumberM a s s f l o w m 1/m r e fPassage Number(c) Mass flow (d) relative flow angle Fig.9 Flow in each passage of the impellerIt seems plausible to analog the flow in each passage predicted by the frozen rotor model to the flow in an impeller at different operation points. For example, as the total mass flow increases, the average exit pressure (Fig.9a) and isentropic head coefficient (Fig.9b) are reduced. This analogy also holds true for passage 4, which is closest to the tongue downstream. At low mass flow, the exit (also inlet) static pressure of passage 4 is the lowest, so the mass flow in this passage (Fig.9c) is the highest. However, the variations of mass flow in passage 2 and 3 contradict this analogy at lower mass flow. In these two passages, the exit pressure is above the average; so is the mass flow! The only explanation for this phenomenon is that flow in these two passages must be of different structures. Fig.9d shows that negative incident angles exist in passages 2 and 3, whilepositive ones exist in all other passages away from the tongue. Fig. 10 shows that the positive incidence causes severe flow separations on the suction-side/shroud corner in passage 5, typical for passages away from the tongue, resulting in higher blockage. It also shows that the separations in passages 2 and 3 are less severe than in passage 5. This explains why more mass flow goes through passage 2 and 3, but the inlet pressure of these passages is still higher than average. The flow structure changes also can be observed at the exit of the impeller. In fact, Fig.8 has shown that at lower mass flow, the relative total pressure contours at the exit of passage 3 are similar to that at design and higher mass flows, but passages 7 and 8, as well asother passages, are different.5234Fig.10 Surface vectors near shroud surfaceBy comparing the circumferential pressure variations among passages at the impeller exit (06.1=tip r r ) for the lower mass flow in Fig.7a, it can be seen that the flow pattern changes in passages 2 and 3 upstream of the tongue are caused by the pressure slope at the impeller exit. The pressure is seen decreasing in passages 2-4 as the impeller rotates, while the pressure is seen increasing in the other passages. The effect of pressure variation on the flow structure can be studied by force analysis on a balanced flow particle, as shown in Fig.11. The equation of motion for the relative flow, assuming an inviscid flow without body force, is given by (Di Liberti 1998)ρωωpU W Dt W D ∇−=×−×+r r r r2 (3) In this equation, the first term represents the relative acceleration, and the second and third the forces due to Coriolis and centrifugal acceleration, respectively. In a streamline coordinate system, the projection of the equation of the motion in the normal direction isnp U W R W n ∂∂=+−ρβωω1sin 22(4) The forces are plotted in Fig.11. Their sum is balanced by the force due to the pressure gradient. It can be seen that the purpose of blade back sweeping is to introduce the normalcomponent of centrifugal force βωsin U and the centrifugal force n R W 2 due to streamline curvature to counteract the Coriolis force. The circumferential pressure gradient is therefore reduced, resulting in more uniform exit flows.passage At the design point, the blade was back swept in such a way that the balance of the force in the normal direction is zero, so the pressure is tangentially uniform. At lower mass flow, the pressure on the pressure side is higher than on the suction side for passages 2-4. It indicates that the normal component of centrifugal force βωsin U and centrifugal force n R W 2are reduced. Possible mechanisms to reduce these two forces are smaller flow angle β and larger streamline curvature radius R n . That is, the exit flows in these two passages are more radial. The pressure gradients in the other passages are reversed; higher pressure exists on the suction side, which totally violates the basic design philosophy. Contrary to passage 2-4, the streamline curvature radius must be smaller. The exit flow, therefore, must be more tangential, which severely deteriorates the flow on the suction side. Therefore, these passages with higher exit pressure on the suction side show lower efficiency (Fig.9b).In summary, the deterioration of the impellerperformance at lower mass flow is not caused by the radical pressure variation around the tongue but by the gently increased pressure in the circumferential direction. At higher mass flow, the impeller performance is not reduced significantly because only a few passages downstream of the tongue face the circumferentially increased pressure. It should be noted that the frozen rotor model failed to predict the decay of the pressure distortion. The actual pressure distortion at the impeller exit therefore is less severe, resulting in smoother flow variation in a passage over one rotation period. This explains why the frozen rotor model did not accurately predict the compressor performance at off-design conditions.CONCLUSIONSThe steady-state volute/impeller interaction is numerically studied using the frozen rotor model provided by the commercially available CFD software, CFX-TASCflow. The pressure distortion due to the volute at off-design conditions is traced from the tongue to the impeller inlet. The following conclusions have been reached:• The frozen rotor model is applicable to the compressor flow where the acoustic Strouhal number is close to zero. Itcannot predict the response of the impeller to pressure perturbation of higher frequency.• The pressure gently increases circumferentially at lower mass flow, and gently decreases at high mass flow. The radical pressure variation around the tongue is caused bythe incidence to the tongue at off-design conditions.• The frozen rotor model failed to predict the decay of the pressure perturbation when it propagates upstream from thevaneless diffuser exit to the inlet.• The performance drop of the compressor at off-design conditions is primarily due to the performance drop of theimpeller. The circumferentially increased pressure at the impeller exit is detrimental to the impeller flow. Therefore,at higher mass flow, the impeller efficiency deterioration comes from these passages upstream of the tongue in therange of about 150o. At lower mass flow, all the passagesbut the two around tongue are responsible for the lower impeller efficiency.• A design idea from this analysis is that the undersized volute is beneficial to the impeller due to the fact that theimpeller is experiencing the exit pressure of negative slopes.REFERENCESAyder, E., Van den Braembussche, R. and Brasz, J. J. 1993, “Experimental and Theoretical Analysis of the Flow in a Centrifugal Compressor V olute,” ASME Journal of Turbomachinery, V ol. 115, pp. 582-589.Di Liberti, Jean-Luc, 1998, “Design and Development of Low-Flow Coefficient Centrifugal Compressors for Industrial Application,” Ph.D. dissertation of Michigan State University.Fatsis, A., Pierret, S. and Van den Braembussche, R., 1997, “Three-Dimensional Unsteady Flow and Forces in Centrifugal Impellers with Circumferential Distortion of the Outlet Static Pressure,” ASME Journal of Turbomachinery, V ol. 119, pp. 94-102.Flathers, M. B., Bache, G. E., and Rautensberger, R., 1994, “An Experimental and Computational Investigation of Flow In a Radial Inlet of An Industrial Pipeline Centrifugal Compressor,”ASME Paper No. 94-GT-134Flathers, M. B., Bache, G. E., 1999, “Aerodynamically Induced Radial Forces in a Centrifugal Gas Compressor: Part 2 – Computational Investigation,” ASME Journal of Engineering for Gas Turbines and Power, V ol. 121, pp. 725-734.Galpin, P. F., Broberg, R. B., and Hutchinson, B. R., 1995, “Three-Dimensional Navier Stokes Predictions of Steady State Rotor/Stator Interaction with pitch Change,” CFD 95 – CFD Society of Canada, Banff, Alberta, Canada.Gu, F., Engeda, A., Cave, M. and Di Liberti, J., 2000, “A Numerical Investigation on the V olute/Diffuser Interaction due to the axial Distortion at the Impeller Exit,” The 2000 ASME International Mechanical Engineering Congress and Exposition, Nov. 5-10, Orlando, FL.Hagelstein, D., Van den Braembussche, R. A., Keiper, R. and Rautenberg M., 1997, “Experimental Investigation of the circumferential static pressure distortion in centrifugal gas compressor stages,” ASME Paper No. 97-GT-50.Hagelstein, D., Hillewaert, K, Van den Braembussche, R.A., Engeda, A., Keiper, R. and Rautenberg M., 1999, “Experimental and Numerical Investigation of the Flow in a Centrifugal Compressor V olute,” ASME 99-GT-79.Hillewaert, K. and Van den Braembussche, R. A., 1999, “Numerical Simulation of Impeller-V olute Interaction in Centrifugal Compressors,” ASME Journal of Turbomachinery, V ol. 121, pp. 603-608.Johnson, M. W. and Moore, J., 1980, “The Development of Wake Flow in a Centrifugal Impeller,” ASME Journal of Engineering for Power, V ol. 102, pp. 383-390.Krain H., 1988, “Swirling Impeller Flow,” ASME Journal of Turbomachinery, V ol. 110, pp.122-128.Sorokes, J. M., Borokes, C. and Koch, J. M., 1998, “Investigation of the Circumferential Static Pressure Non-Uniformity Caused by a Centrifugal Compressor discharge V olute,” ASME Paper No. 98-GT-326.Stanitz, J. D., 1952, “One-dimensional Compressible Flow in Vaneless Diffusers of Radial or Mixed-flow Centrifugal Compressors, Including Effects of Friction, Heat Transfer and Area Change,” NACA TN 2610.TASCflow Version 2.9 Users Manual, 1999, Advanced Engineering Computing.Van den Braembussche, R. A. and Hande, B. M., 1990, “Experimental and Theoretical Study of the Swirling Flow in Centrifugal Compressor V olutes,” ASME Journal of Turbomachinery, V ol. 112, pp. 38-43.。

关于实验数据回归的书-回复以下是一些关于实验数据回归的书籍推荐：1. "Linear Regression Analysis" by Douglas C. Montgomery - 这本书详细介绍了线性回归分析的理论和应用，包括实验设计和数据分析。

2. "Applied Linear Regression" by Michael H. Kutner, Christopher J. Nachtsheim, and John Neter - 这本书涵盖了线性回归模型的各个方面，包括模型选择、假设检验、预测和结果解释。

3. "Regression Analysis by Example" by Samprit Chatterjee and Ali S. Hadi - 这本书通过实例讲解了回归分析的方法和技巧，包括简单和多元回归、残差分析和模型诊断。

4. "The Elements of Statistical Learning: Data Mining, Inference, and Prediction" by Trevor Hastie, Robert Tibshirani, and Jerome Friedman - 虽然这本书主要关注机器学习和统计学习，但它也包含了大量的回归分析内容，包括岭回归、套索回归和弹性网络等现代回归方法。

5. "Experimental Design and Analysis for Engineers and Scientists" by Gary O. Hutchinson - 这本书专门针对工程师和科学家的需求，介绍了实验设计和数据分析的方法，包括回归分析和其他统计技术。

以上书籍都是关于实验数据回归的经典著作，可以帮助读者深入理解回归分析的理论和实践。

Introduction to probability theory andmathematical statisticsThe theory of probability and the mathematical statistic are carries on deductive and the induction science to the stochastic phenomenon statistical rule, from the quantity side research stochastic phenomenon statistical regular foundation mathematics discipline, the theory of probability and the mathematical statistic may divide into the theory of probability and the mathematical statistic two branches. The probability uses for the possible size quantity which portrays the random event to occur. Theory of probability main content including classical generally computation, random variable distribution and characteristic numeral and limit theorem and so on. The mathematical statistic is one of mathematics Zhonglian department actually most directly most widespread branches, it introduced an estimate (rectangular method estimate, enormousestimate), the parameter supposition examination, the non-parameter supposition examination, the variance analysis and the multiple regression analysis, the fail-safe analysis and so on the elementary knowledge and the principle, enable the student to have a profound understanding tostatistics principle function. Through this curriculum study, enables the student comprehensively to understand, to grasp the theory of probability and the mathematical statistic thought and the method, grasps basic and the commonly used analysis and the computational method, and can studies in the solution economy and the management practice question using the theory of probability and the mathematical statistic viewpoint and the method.Random phenomenonFrom random phenomenon, in the nature and real life, some things are interrelated and continuous development. In the relationship between each other and developing, according to whether there is a causal relationship, very different can be divided into two categories: one is deterministic phenomenon. This kind of phenomenon is under certain conditions, will lead to certain results. For example, under normal atmospheric pressure, water heated to 100 degrees Celsius, is bound to a boil. This link is belong to the inevitability between things. Usually in natural science is interdisciplinary studies and know the inevitability, seeking this kind of inevitable phenomenon.Another kind is the phenomenon of uncertainty. This kind of phenomenon is under certain conditions, the resultis uncertain. The same workers on the same machine tools, for example, processing a number of the same kind of parts, they are the size of the there will always be a little difference. As another example, under the same conditions, artificial accelerating germination test of wheat varieties, each tree seed germination is also different, there is strength and sooner or later, respectively, and so on. Why in the same situation, will appear this kind of uncertain results? This is because, we say "same conditions" refers to some of the main conditions, in addition to these main conditions, there are many minor conditions and the accidental factor is people can't in advance one by one to grasp. Because of this, in this kind of phenomenon, we can't use the inevitability of cause and effect, the results of individual phenomenon in advance to make sure of the answer. The relationship between things is belong to accidental, this phenomenon is called accidental phenomenon, or a random phenomenon.In nature, in the production, life, random phenomenon is very common, that is to say, there is a lot of random phenomenon. Issue such as: sports lottery of the winning Numbers, the same production line production, the life of the bulb, etc., is a random phenomenon. So we say: randomphenomenon is: under the same conditions, many times the same test or survey the same phenomenon, the results are not identical, and unable to accurately predict the results of the next. Random phenomena in the uncertainties of the results, it is because of some minor, caused by the accidental factors.Random phenomenon on the surface, seems to be messy, there is no regular phenomenon. But practice has proved that if the same kind of a large number of repeated random phenomenon, its overall present certain regularity. A large number of similar random phenomena of this kind of regularity, as we observed increase in the number of the number of times and more obvious. Flip a coin, for example, each throw is difficult to judge on that side, but if repeated many times of toss the coin, it will be more and more clearly find them up is approximately the same number.We call this presented by a large number of similar random phenomena of collective regularity, is called the statistical regularity. Probability theory and mathematical statistics is the study of a large number of similar random phenomena statistical regularity of the mathematical disciplines.The emergence and development of probability theoryProbability theory was created in the 17th century, it is by the development of insurance business, but from the gambler's request, is that mathematicians thought the source of problem in probability theory.As early as in 1654, there was a gambler may tired to the mathematician PASCAL proposes a question troubling him for a long time: "meet two gamblers betting on a number of bureau, who will win the first m innings wins, all bets will be who. But when one of them wins a (a < m), the other won b (b < m) bureau, gambling aborted. Q: how should bets points method is only reasonable?" Who in 1642 invented the world's first mechanical addition of computer.Three years later, in 1657, the Dutch famous astronomy, physics, and a mathematician huygens is trying to solve this problem, the results into a book concerning the calculation of a game of chance, this is the earliest probability theory works.In recent decades, with the vigorous development of science and technology, the application of probability theory to the national economy, industrial and agricultural production and interdisciplinary field. Many of applied mathematics, such as information theory, game theory, queuing theory, cybernetics, etc., are based on the theory of probability.Probability theory and mathematical statistics is a branch of mathematics, random they similar disciplines are closely linked. But should point out that the theory of probability and mathematical statistics, statistical methods are each have their own contain different content.Probability theory, is based on a large number of similar random phenomena statistical regularity, the possibility that a result of random phenomenon to make an objective and scientific judgment, the possibility of its occurrence for this size to make quantitative description; Compare the size of these possibilities, study the contact between them, thus forming a set of mathematical theories and methods.Mathematical statistics - is the application of probability theory to study the phenomenon of large number of random regularity; To through the scientific arrangement of a number of experiments, the statistical method given strict theoretical proof; And determining various methods applied conditions and reliability of the method, the formula, the conclusion and limitations. We can from a set of samples to decide whether can with quite large probability to ensure that a judgment is correct, and can control the probability of error.- is a statistical method provides methods are used in avariety of specific issues, it does not pay attention to the method according to the theory, mathematical reasoning.Should point out that the probability and statistics on the research method has its particularity, and other mathematical subject of the main differences are:First, because the random phenomena statistical regularity is a collective rule, must to present in a large number of similar random phenomena, therefore, observation, experiment, research is the cornerstone of the subject research methods of probability and statistics. But, as a branch of mathematics, it still has the definition of this discipline, axioms, theorems, the definitions and axioms, theorems are derived from the random rule of nature, but these definitions and axioms, theorems is certain, there is no randomness.Second, in the study of probability statistics, using the "by part concluded all" methods of statistical inference. This is because it the object of the research - the range of random phenomenon is very big, at the time of experiment, observation, not all may be unnecessary. But by this part of the data obtained from some conclusions, concluded that the reliability of the conclusion to all the scope.Third, the randomness of the random phenomenon, refers to the experiment, investigation before speaking. After the real results for each test, it can only get the results of the uncertainty of a certain result. When we study this phenomenon, it should be noted before the test can find itself inherent law of this phenomenon.The content of the theory of probabilityProbability theory as a branch of mathematics, it studies the content general include the probability of random events, the regularity of statistical independence and deeper administrative levels.Probability is a quantitative index of the possibility of random events. In independent random events, if an event frequency in all events, in a larger range of stable around a fixed constant. You can think the probability of the incident to the constant. For any event probability value must be between 0 and 1.There is a certain type of random events, it has two characteristics: first, only a finite number of possible results; Second, the results the possibility of the same. Have the characteristics of the two random phenomenon called"classical subscheme".In the objective world, there are a large number of random phenomena, the result of a random phenomenon poses a random event. If the variable is used to describe each random phenomenon as a result, is known as random variables.Random variable has a finite and the infinite, and according to the variable values is usually divided into discrete random variables and the discrete random variable. List all possible values can be according to certain order, such a random variable is called a discrete random variable; If possible values with an interval, unable to make the order list, the random variable is called a discrete random variable.The content of the mathematical statisticsIncluding sampling, optimum line problem of mathematical statistics, hypothesis testing, analysis of variance, correlation analysis, etc. Sampling inspection is to pair through sample investigation, to infer the overall situation. Exactly how much sampling, this is a very important problem, therefore, is produced in the sampling inspection "small sample theory", this is in the case of the sample is small, the analysis judgment theory.Also called curve fitting and optimal line problem. Some problems need to be according to the experience data to find a theoretical distribution curve, so that the whole problem get understanding. But according to what principles and theoretical curve? How to compare out of several different curve in the same issue? Selecting good curve, is how to determine their error? ...... Is belong to the scope of the optimum line issues of mathematical statistics.Hypothesis testing is only at the time of inspection products with mathematical statistical method, first make a hypothesis, according to the result of sampling in reliable to a certain extent, to judge the null hypothesis.Also called deviation analysis, variance analysis is to use the concept of variance to analyze by a handful of experiment can make the judgment.Due to the random phenomenon is abundant in human practical activities, probability and statistics with the development of modern industry and agriculture, modern science and technology and continuous development, which formed many important branch. Such as stochastic process, information theory, experimental design, limit theory, multivariate analysis, etc.译文：概率论和数理统计简介概率论与数理统计是对随机现象的统计规律进行演绎和归纳的科学，从数量侧面研究随机现象的统计规律性的基础数学学科，概率论与数理统计又可分为概率论和数理统计两个分支。

计量经济学中英文对照词汇(总21页)-CAL-FENGHAI.-(YICAI)-Company One1-CAL-本页仅作为文档封面，使用请直接删除计量经济学中英对照词汇Absolute deviation, 绝对离差Absolute number, 绝对数Absolute residuals, 绝对残差Acceleration array, 加速度立体阵Acceleration in an arbitrary direction, 任意方向上的加速度Acceleration normal, 法向加速度Acceleration space dimension, 加速度空间的维数Acceleration tangential, 切向加速度Acceleration vector, 加速度向量Acceptable hypothesis, 可接受假设Accumulation, 累积Accuracy, 准确度Actual frequency, 实际频数Adaptive estimator, 自适应估计量Addition, 相加Addition theorem, 加法定理Additive Noise, 加性噪声Additivity, 可加性Adjusted rate, 调整率Adjusted value, 校正值Admissible error, 容许误差Aggregation, 聚集性Alpha factoring,α因子法Alternative hypothesis, 备择假设Among groups, 组间Amounts, 总量Analysis of correlation, 相关分析Analysis of covariance, 协方差分析Analysis Of Effects, 效应分析Analysis Of Variance, 方差分析Analysis of regression, 回归分析Analysis of time series, 时间序列分析Analysis of variance, 方差分析Angular transformation, 角转换ANOVA （analysis of variance）, 方差分析ANOVA Models, 方差分析模型ANOVA table and eta, 分组计算方差分析Arcing, 弧/弧旋Arcsine transformation, 反正弦变换Area 区域图Area under the curve, 曲线面积AREG , 评估从一个时间点到下一个时间点回归相关时的误差ARIMA, 季节和非季节性单变量模型的极大似然估计Arithmetic grid paper, 算术格纸Arithmetic mean, 算术平均数Arrhenius relation, 艾恩尼斯关系Assessing fit, 拟合的评估Associative laws, 结合律Asymmetric distribution, 非对称分布Asymptotic bias, 渐近偏倚Asymptotic efficiency, 渐近效率Asymptotic variance, 渐近方差Attributable risk, 归因危险度Attribute data, 属性资料Attribution, 属性Autocorrelation, 自相关Autocorrelation of residuals, 残差的自相关Average, 平均数Average confidence interval length, 平均置信区间长度Average growth rate, 平均增长率Bar chart, 条形图Bar graph, 条形图Base period, 基期Bayes' theorem , Bayes定理Bell-shaped curve, 钟形曲线Bernoulli distribution, 伯努力分布Best-trim estimator, 最好切尾估计量Bias, 偏性Binary logistic regression, 二元逻辑斯蒂回归Binomial distribution, 二项分布Bisquare, 双平方Bivariate Correlate, 二变量相关Bivariate normal distribution, 双变量正态分布Bivariate normal population, 双变量正态总体Biweight interval, 双权区间Biweight M-estimator, 双权M估计量Block, 区组/配伍组BMDP(Biomedical computer programs), BMDP统计软件包Boxplots, 箱线图/箱尾图Breakdown bound, 崩溃界/崩溃点Canonical correlation, 典型相关Caption, 纵标目Case-control study, 病例对照研究Categorical variable, 分类变量Catenary, 悬链线Cauchy distribution, 柯西分布Cause-and-effect relationship, 因果关系Cell, 单元Censoring, 终检Center of symmetry, 对称中心Centering and scaling, 中心化和定标Central tendency, 集中趋势Central value, 中心值CHAID -χ2 Automatic Interaction Detector, 卡方自动交互检测Chance, 机遇Chance error, 随机误差Chance variable, 随机变量Characteristic equation, 特征方程Characteristic root, 特征根Characteristic vector, 特征向量Chebshev criterion of fit, 拟合的切比雪夫准则Chernoff faces, 切尔诺夫脸谱图Chi-square test, 卡方检验/χ2检验Choleskey decomposition, 乔洛斯基分解Circle chart, 圆图Class interval, 组距Class mid-value, 组中值Class upper limit, 组上限Classified variable, 分类变量Cluster analysis, 聚类分析Cluster sampling, 整群抽样Code, 代码Coded data, 编码数据Coding, 编码Coefficient of contingency, 列联系数Coefficient of determination, 决定系数Coefficient of multiple correlation, 多重相关系数Coefficient of partial correlation, 偏相关系数Coefficient of production-moment correlation, 积差相关系数Coefficient of rank correlation, 等级相关系数Coefficient of regression, 回归系数Coefficient of skewness, 偏度系数Coefficient of variation, 变异系数Cohort study, 队列研究Collinearity, 共线性Column, 列Column effect, 列效应Column factor, 列因素Combination pool, 合并Combinative table, 组合表Common factor, 共性因子Common regression coefficient, 公共回归系数Common value, 共同值Common variance, 公共方差Common variation, 公共变异Communality variance, 共性方差Comparability, 可比性Comparison of bathes, 批比较Comparison value, 比较值Compartment model, 分部模型Compassion, 伸缩Complement of an event, 补事件Complete association, 完全正相关Complete dissociation, 完全不相关Complete statistics, 完备统计量Completely randomized design, 完全随机化设计Composite event, 联合事件Composite events, 复合事件Concavity, 凹性Conditional expectation, 条件期望Conditional likelihood, 条件似然Conditional probability, 条件概率Conditionally linear, 依条件线性Confidence interval, 置信区间Confidence limit, 置信限Confidence lower limit, 置信下限Confidence upper limit, 置信上限Confirmatory Factor Analysis , 验证性因子分析Confirmatory research, 证实性实验研究Confounding factor, 混杂因素Conjoint, 联合分析Consistency, 相合性Consistency check, 一致性检验Consistent asymptotically normal estimate, 相合渐近正态估计Consistent estimate, 相合估计Constrained nonlinear regression, 受约束非线性回归Constraint, 约束Contaminated distribution, 污染分布Contaminated Gausssian, 污染高斯分布Contaminated normal distribution, 污染正态分布Contamination, 污染Contamination model, 污染模型Contingency table, 列联表Contour, 边界线Contribution rate, 贡献率Control, 对照, 质量控制图Controlled experiments, 对照实验Conventional depth, 常规深度Convolution, 卷积Corrected factor, 校正因子Corrected mean, 校正均值Correction coefficient, 校正系数Correctness, 正确性Correlation coefficient, 相关系数Correlation, 相关性Correlation index, 相关指数Correspondence, 对应Counting, 计数Counts, 计数/频数Covariance, 协方差Covariant, 共变Cox Regression, Cox回归Criteria for fitting, 拟合准则Criteria of least squares, 最小二乘准则Critical ratio, 临界比Critical region, 拒绝域Critical value, 临界值Cross-over design, 交叉设计Cross-section analysis, 横断面分析Cross-section survey, 横断面调查Crosstabs , 交叉表Crosstabs 列联表分析Cross-tabulation table, 复合表Cube root, 立方根Cumulative distribution function, 分布函数Cumulative probability, 累计概率Curvature, 曲率/弯曲Curvature, 曲率Curve Estimation, 曲线拟合Curve fit , 曲线拟和Curve fitting, 曲线拟合Curvilinear regression, 曲线回归Curvilinear relation, 曲线关系Cut-and-try method, 尝试法Cycle, 周期Cyclist, 周期性D test, D检验Data acquisition, 资料收集Data bank, 数据库Data capacity, 数据容量Data deficiencies, 数据缺乏Data handling, 数据处理Data manipulation, 数据处理Data processing, 数据处理Data reduction, 数据缩减Data set, 数据集Data sources, 数据来源Data transformation, 数据变换Data validity, 数据有效性Data-in, 数据输入Data-out, 数据输出Dead time, 停滞期Degree of freedom, 自由度Degree of precision, 精密度Degree of reliability, 可靠性程度Degression, 递减Density function, 密度函数Density of data points, 数据点的密度Dependent variable, 应变量/依变量/因变量Dependent variable, 因变量Depth, 深度Derivative matrix, 导数矩阵Derivative-free methods, 无导数方法Design, 设计Determinacy, 确定性Determinant, 行列式Determinant, 决定因素Deviation, 离差Deviation from average, 离均差Diagnostic plot, 诊断图Dichotomous variable, 二分变量Differential equation, 微分方程Direct standardization, 直接标准化法Direct Oblimin, 斜交旋转Discrete variable, 离散型变量DISCRIMINANT, 判断Discriminant analysis, 判别分析Discriminant coefficient, 判别系数Discriminant function, 判别值Dispersion, 散布/分散度Disproportional, 不成比例的Disproportionate sub-class numbers, 不成比例次级组含量Distribution free, 分布无关性/免分布Distribution shape, 分布形状Distribution-free method, 任意分布法Distributive laws, 分配律Disturbance, 随机扰动项Dose response curve, 剂量反应曲线Double blind method, 双盲法Double blind trial, 双盲试验Double exponential distribution, 双指数分布Double logarithmic, 双对数Downward rank, 降秩Dual-space plot, 对偶空间图DUD, 无导数方法Duncan's new multiple range method, 新复极差法/Duncan新法Error Bar, 均值相关区间图Effect, 实验效应Eigenvalue, 特征值Eigenvector, 特征向量Ellipse, 椭圆Empirical distribution, 经验分布Empirical probability, 经验概率单位Enumeration data, 计数资料Equal sun-class number, 相等次级组含量Equally likely, 等可能Equivariance, 同变性Error, 误差/错误Error of estimate, 估计误差Error type I, 第一类错误Error type II, 第二类错误Estimand, 被估量Estimated error mean squares, 估计误差均方Estimated error sum of squares, 估计误差平方和Euclidean distance, 欧式距离Event, 事件Event, 事件Exceptional data point, 异常数据点Expectation plane, 期望平面Expectation surface, 期望曲面Expected values, 期望值Experiment, 实验Experimental sampling, 试验抽样Experimental unit, 试验单位Explained variance （已说明方差）Explanatory variable, 说明变量Exploratory data analysis, 探索性数据分析Explore Summarize, 探索-摘要Exponential curve, 指数曲线Exponential growth, 指数式增长EXSMOOTH, 指数平滑方法Extended fit, 扩充拟合Extra parameter, 附加参数Extrapolation, 外推法Extreme observation, 末端观测值Extremes, 极端值/极值F distribution, F分布F test, F检验Factor, 因素/因子Factor analysis, 因子分析Factor Analysis, 因子分析Factor score, 因子得分Factorial, 阶乘Factorial design, 析因试验设计False negative, 假阴性False negative error, 假阴性错误Family of distributions, 分布族Family of estimators, 估计量族Fanning, 扇面Fatality rate, 病死率Field investigation, 现场调查Field survey, 现场调查Finite population, 有限总体Finite-sample, 有限样本First derivative, 一阶导数First principal component, 第一主成分First quartile, 第一四分位数Fisher information, 费雪信息量Fitted value, 拟合值Fitting a curve, 曲线拟合Fixed base, 定基Fluctuation, 随机起伏Forecast, 预测Four fold table, 四格表Fourth, 四分点Fraction blow, 左侧比率Fractional error, 相对误差Frequency, 频率Frequency polygon, 频数多边图Frontier point, 界限点Function relationship, 泛函关系Gamma distribution, 伽玛分布Gauss increment, 高斯增量Gaussian distribution, 高斯分布/正态分布Gauss-Newton increment, 高斯-牛顿增量General census, 全面普查Generalized least squares, 综合最小平方法GENLOG (Generalized liner models), 广义线性模型Geometric mean, 几何平均数Gini's mean difference, 基尼均差GLM (General liner models), 通用线性模型Goodness of fit, 拟和优度/配合度Gradient of determinant, 行列式的梯度Graeco-Latin square, 希腊拉丁方Grand mean, 总均值Gross errors, 重大错误Gross-error sensitivity, 大错敏感度Group averages, 分组平均Grouped data, 分组资料Guessed mean, 假定平均数Half-life, 半衰期Hampel M-estimators, 汉佩尔M估计量Happenstance, 偶然事件Harmonic mean, 调和均数Hazard function, 风险均数Hazard rate, 风险率Heading, 标目Heavy-tailed distribution, 重尾分布Hessian array, 海森立体阵Heterogeneity, 不同质Heterogeneity of variance, 方差不齐Hierarchical classification, 组内分组Hierarchical clustering method, 系统聚类法High-leverage point, 高杠杆率点High-Low, 低区域图Higher Order Interaction Effects，高阶交互作用HILOGLINEAR, 多维列联表的层次对数线性模型Hinge, 折叶点Histogram, 直方图Historical cohort study, 历史性队列研究Holes, 空洞HOMALS, 多重响应分析Homogeneity of variance, 方差齐性Homogeneity test, 齐性检验Huber M-estimators, 休伯M估计量Hyperbola, 双曲线Hypothesis testing, 假设检验Hypothetical universe, 假设总体Image factoring,, 多元回归法Impossible event, 不可能事件Independence, 独立性Independent variable, 自变量Index, 指标/指数Indirect standardization, 间接标准化法Individual, 个体Inference band, 推断带Infinite population, 无限总体Infinitely great, 无穷大Infinitely small, 无穷小Influence curve, 影响曲线Information capacity, 信息容量Initial condition, 初始条件Initial estimate, 初始估计值Initial level, 最初水平Interaction, 交互作用Interaction terms, 交互作用项Intercept, 截距Interpolation, 内插法Interquartile range, 四分位距Interval estimation, 区间估计Intervals of equal probability, 等概率区间Intrinsic curvature, 固有曲率Invariance, 不变性Inverse matrix, 逆矩阵Inverse probability, 逆概率Inverse sine transformation, 反正弦变换Iteration, 迭代Jacobian determinant, 雅可比行列式Joint distribution function, 分布函数Joint probability, 联合概率Joint probability distribution, 联合概率分布K-Means Cluster逐步聚类分析K means method, 逐步聚类法Kaplan-Meier, 评估事件的时间长度Kaplan-Merier chart, Kaplan-Merier图Kendall's rank correlation, Kendall等级相关Kinetic, 动力学Kolmogorov-Smirnove test, 柯尔莫哥洛夫-斯米尔诺夫检验Kruskal and Wallis test, Kruskal及Wallis检验/多样本的秩和检验/H检验Kurtosis, 峰度Lack of fit, 失拟Ladder of powers, 幂阶梯Lag, 滞后Large sample, 大样本Large sample test, 大样本检验Latin square, 拉丁方Latin square design, 拉丁方设计Leakage, 泄漏Least favorable configuration, 最不利构形Least favorable distribution, 最不利分布Least significant difference, 最小显著差法Least square method, 最小二乘法Least Squared Criterion，最小二乘方准则Least-absolute-residuals estimates, 最小绝对残差估计Least-absolute-residuals fit, 最小绝对残差拟合Least-absolute-residuals line, 最小绝对残差线Legend, 图例L-estimator, L估计量L-estimator of location, 位置L估计量L-estimator of scale, 尺度L估计量Level, 水平Leveage Correction，杠杆率校正Life expectance, 预期期望寿命Life table, 寿命表Life table method, 生命表法Light-tailed distribution, 轻尾分布Likelihood function, 似然函数Likelihood ratio, 似然比line graph, 线图Linear correlation, 直线相关Linear equation, 线性方程Linear programming, 线性规划Linear regression, 直线回归Linear Regression, 线性回归Linear trend, 线性趋势Loading, 载荷Location and scale equivariance, 位置尺度同变性Location equivariance, 位置同变性Location invariance, 位置不变性Location scale family, 位置尺度族Log rank test, 时序检验Logarithmic curve, 对数曲线Logarithmic normal distribution, 对数正态分布Logarithmic scale, 对数尺度Logarithmic transformation, 对数变换Logic check, 逻辑检查Logistic distribution, 逻辑斯特分布Logit transformation, Logit转换LOGLINEAR, 多维列联表通用模型Lognormal distribution, 对数正态分布Lost function, 损失函数Low correlation, 低度相关Lower limit, 下限Lowest-attained variance, 最小可达方差LSD, 最小显著差法的简称Lurking variable, 潜在变量Main effect, 主效应Major heading, 主辞标目Marginal density function, 边缘密度函数Marginal probability, 边缘概率Marginal probability distribution, 边缘概率分布Matched data, 配对资料Matched distribution, 匹配过分布Matching of distribution, 分布的匹配Matching of transformation, 变换的匹配Mathematical expectation, 数学期望Mathematical model, 数学模型Maximum L-estimator, 极大极小L 估计量Maximum likelihood method, 最大似然法Mean, 均数Mean squares between groups, 组间均方Mean squares within group, 组内均方Means (Compare means), 均值-均值比较Median, 中位数Median effective dose, 半数效量Median lethal dose, 半数致死量Median polish, 中位数平滑Median test, 中位数检验Minimal sufficient statistic, 最小充分统计量Minimum distance estimation, 最小距离估计Minimum effective dose, 最小有效量Minimum lethal dose, 最小致死量Minimum variance estimator, 最小方差估计量MINITAB, 统计软件包Minor heading, 宾词标目Missing data, 缺失值Model specification, 模型的确定Modeling Statistics , 模型统计Models for outliers, 离群值模型Modifying the model, 模型的修正Modulus of continuity, 连续性模Morbidity, 发病率Most favorable configuration, 最有利构形MSC（多元散射校正）Multidimensional Scaling (ASCAL), 多维尺度/多维标度Multinomial Logistic Regression , 多项逻辑斯蒂回归Multiple comparison, 多重比较Multiple correlation , 复相关Multiple covariance, 多元协方差Multiple linear regression, 多元线性回归Multiple response , 多重选项Multiple solutions, 多解Multiplication theorem, 乘法定理Multiresponse, 多元响应Multi-stage sampling, 多阶段抽样Multivariate T distribution, 多元T分布Mutual exclusive, 互不相容Mutual independence, 互相独立Natural boundary, 自然边界Natural dead, 自然死亡Natural zero, 自然零Negative correlation, 负相关Negative linear correlation, 负线性相关Negatively skewed, 负偏Newman-Keuls method, q检验NK method, q检验No statistical significance, 无统计意义Nominal variable, 名义变量Nonconstancy of variability, 变异的非定常性Nonlinear regression, 非线性相关Nonparametric statistics, 非参数统计Nonparametric test, 非参数检验Nonparametric tests, 非参数检验Normal deviate, 正态离差Normal distribution, 正态分布Normal equation, 正规方程组Normal P-P, 正态概率分布图Normal Q-Q, 正态概率单位分布图Normal ranges, 正常范围Normal value, 正常值Normalization 归一化Nuisance parameter, 多余参数/讨厌参数Null hypothesis, 无效假设Numerical variable, 数值变量Objective function, 目标函数Observation unit, 观察单位Observed value, 观察值One sided test, 单侧检验One-way analysis of variance, 单因素方差分析Oneway ANOVA , 单因素方差分析Open sequential trial, 开放型序贯设计Optrim, 优切尾Optrim efficiency, 优切尾效率Order statistics, 顺序统计量Ordered categories, 有序分类Ordinal logistic regression , 序数逻辑斯蒂回归Ordinal variable, 有序变量Orthogonal basis, 正交基Orthogonal design, 正交试验设计Orthogonality conditions, 正交条件ORTHOPLAN, 正交设计Outlier cutoffs, 离群值截断点Outliers, 极端值OVERALS , 多组变量的非线性正规相关Overshoot, 迭代过度Paired design, 配对设计Paired sample, 配对样本Pairwise slopes, 成对斜率Parabola, 抛物线Parallel tests, 平行试验Parameter, 参数Parametric statistics, 参数统计Parametric test, 参数检验Pareto, 直条构成线图（又称佩尔托图）Partial correlation, 偏相关Partial regression, 偏回归Partial sorting, 偏排序Partials residuals, 偏残差Pattern, 模式PCA（主成分分析）Pearson curves, 皮尔逊曲线Peeling, 退层Percent bar graph, 百分条形图Percentage, 百分比Percentile, 百分位数Percentile curves, 百分位曲线Periodicity, 周期性Permutation, 排列P-estimator, P估计量Pie graph, 构成图,饼图Pitman estimator, 皮特曼估计量Pivot, 枢轴量Planar, 平坦Planar assumption, 平面的假设PLANCARDS, 生成试验的计划卡PLS（偏最小二乘法）Point estimation, 点估计Poisson distribution, 泊松分布Polishing, 平滑Polled standard deviation, 合并标准差Polled variance, 合并方差Polygon, 多边图Polynomial, 多项式Polynomial curve, 多项式曲线Population, 总体Population attributable risk, 人群归因危险度Positive correlation, 正相关Positively skewed, 正偏Posterior distribution, 后验分布Power of a test, 检验效能Precision, 精密度Predicted value, 预测值Preliminary analysis, 预备性分析Principal axis factoring,主轴因子法Principal component analysis, 主成分分析Prior distribution, 先验分布Prior probability, 先验概率Probabilistic model, 概率模型probability, 概率Probability density, 概率密度Product moment, 乘积矩/协方差Profile trace, 截面迹图Proportion, 比/构成比Proportion allocation in stratified random sampling, 按比例分层随机抽样Proportionate, 成比例Proportionate sub-class numbers, 成比例次级组含量Prospective study, 前瞻性调查Proximities, 亲近性Pseudo F test, 近似F检验Pseudo model, 近似模型Pseudosigma, 伪标准差Purposive sampling, 有目的抽样QR decomposition, QR分解Quadratic approximation, 二次近似Qualitative classification, 属性分类Qualitative method, 定性方法Quantile-quantile plot, 分位数-分位数图/Q-Q图Quantitative analysis, 定量分析Quartile, 四分位数Quick Cluster, 快速聚类Radix sort, 基数排序Random allocation, 随机化分组Random blocks design, 随机区组设计Random event, 随机事件Randomization, 随机化Range, 极差/全距Rank correlation, 等级相关Rank sum test, 秩和检验Rank test, 秩检验Ranked data, 等级资料Rate, 比率Ratio, 比例Raw data, 原始资料Raw residual, 原始残差Rayleigh's test, 雷氏检验Rayleigh's Z, 雷氏Z值Reciprocal, 倒数Reciprocal transformation, 倒数变换Recording, 记录Redescending estimators, 回降估计量Reducing dimensions, 降维Re-expression, 重新表达Reference set, 标准组Region of acceptance, 接受域Regression coefficient, 回归系数Regression sum of square, 回归平方和Rejection point, 拒绝点Relative dispersion, 相对离散度Relative number, 相对数Reliability, 可靠性Reparametrization, 重新设置参数Replication, 重复Report Summaries, 报告摘要Residual sum of square, 剩余平方和residual variance (剩余方差)Resistance, 耐抗性Resistant line, 耐抗线Resistant technique, 耐抗技术R-estimator of location, 位置R估计量R-estimator of scale, 尺度R估计量Retrospective study, 回顾性调查Ridge trace, 岭迹Ridit analysis, Ridit分析Rotation, 旋转Rounding, 舍入Row, 行Row effects, 行效应Row factor, 行因素RXC table, RXC表Sample, 样本Sample regression coefficient, 样本回归系数Sample size, 样本量Sample standard deviation, 样本标准差Sampling error, 抽样误差SAS(Statistical analysis system ), SAS统计软件包Scale, 尺度/量表Scatter diagram, 散点图Schematic plot, 示意图/简图Score test, 计分检验Screening, 筛检SEASON, 季节分析Second derivative, 二阶导数Second principal component, 第二主成分SEM (Structural equation modeling), 结构化方程模型Semi-logarithmic graph, 半对数图Semi-logarithmic paper, 半对数格纸Sensitivity curve, 敏感度曲线Sequential analysis, 贯序分析Sequence, 普通序列图Sequential data set, 顺序数据集Sequential design, 贯序设计Sequential method, 贯序法Sequential test, 贯序检验法Serial tests, 系列试验Short-cut method, 简捷法Sigmoid curve, S形曲线Sign function, 正负号函数Sign test, 符号检验Signed rank, 符号秩Significant Level, 显著水平Significance test, 显著性检验Significant figure, 有效数字Simple cluster sampling, 简单整群抽样Simple correlation, 简单相关Simple random sampling, 简单随机抽样Simple regression, 简单回归simple table, 简单表Sine estimator, 正弦估计量Single-valued estimate, 单值估计Singular matrix, 奇异矩阵Skewed distribution, 偏斜分布Skewness, 偏度Slash distribution, 斜线分布Slope, 斜率Smirnov test, 斯米尔诺夫检验Source of variation, 变异来源Spearman rank correlation, 斯皮尔曼等级相关Specific factor, 特殊因子Specific factor variance, 特殊因子方差Spectra , 频谱Spherical distribution, 球型正态分布Spread, 展布SPSS(Statistical package for the social science), SPSS统计软件包Spurious correlation, 假性相关Square root transformation, 平方根变换Stabilizing variance, 稳定方差Standard deviation, 标准差Standard error, 标准误Standard error of difference, 差别的标准误Standard error of estimate, 标准估计误差Standard error of rate, 率的标准误Standard normal distribution, 标准正态分布Standardization, 标准化Starting value, 起始值Statistic, 统计量Statistical control, 统计控制Statistical graph, 统计图Statistical inference, 统计推断Statistical table, 统计表Steepest descent, 最速下降法Stem and leaf display, 茎叶图Step factor, 步长因子Stepwise regression, 逐步回归Storage, 存Strata, 层（复数）Stratified sampling, 分层抽样Stratified sampling, 分层抽样Strength, 强度Stringency, 严密性Structural relationship, 结构关系Studentized residual, 学生化残差/t化残差Sub-class numbers, 次级组含量Subdividing, 分割Sufficient statistic, 充分统计量Sum of products, 积和Sum of squares, 离差平方和Sum of squares about regression, 回归平方和Sum of squares between groups, 组间平方和Sum of squares of partial regression, 偏回归平方和Sure event, 必然事件Survey, 调查Survival, 生存分析Survival rate, 生存率Suspended root gram, 悬吊根图Symmetry, 对称Systematic error, 系统误差Systematic sampling, 系统抽样Tags, 标签Tail area, 尾部面积Tail length, 尾长Tail weight, 尾重Tangent line, 切线Target distribution, 目标分布Taylor series, 泰勒级数Test(检验)Test of linearity, 线性检验Tendency of dispersion, 离散趋势Testing of hypotheses, 假设检验Theoretical frequency, 理论频数Time series, 时间序列Tolerance interval, 容忍区间Tolerance lower limit, 容忍下限Tolerance upper limit, 容忍上限Torsion, 扰率Total sum of square, 总平方和Total variation, 总变异Transformation, 转换Treatment, 处理Trend, 趋势Trend of percentage, 百分比趋势Trial, 试验Trial and error method, 试错法Tuning constant, 细调常数Two sided test, 双向检验Two-stage least squares, 二阶最小平方Two-stage sampling, 二阶段抽样Two-tailed test, 双侧检验Two-way analysis of variance, 双因素方差分析Two-way table, 双向表Type I error, 一类错误/α错误Type II error, 二类错误/β错误UMVU, 方差一致最小无偏估计简称Unbiased estimate, 无偏估计Unconstrained nonlinear regression , 无约束非线性回归Unequal subclass number, 不等次级组含量Ungrouped data, 不分组资料Uniform coordinate, 均匀坐标Uniform distribution, 均匀分布Uniformly minimum variance unbiased estimate, 方差一致最小无偏估计Unit, 单元Unordered categories, 无序分类Unweighted least squares, 未加权最小平方法Upper limit, 上限Upward rank, 升秩Vague concept, 模糊概念Validity, 有效性VARCOMP (Variance component estimation), 方差元素估计Variability, 变异性Variable, 变量Variance, 方差Variation, 变异Varimax orthogonal rotation, 方差最大正交旋转Volume of distribution, 容积W test, W检验Weibull distribution, 威布尔分布Weight, 权数Weighted Chi-square test, 加权卡方检验/Cochran检验Weighted linear regression method, 加权直线回归Weighted mean, 加权平均数Weighted mean square, 加权平均方差Weighted sum of square, 加权平方和Weighting coefficient, 权重系数Weighting method, 加权法W-estimation, W估计量W-estimation of location, 位置W估计量Width, 宽度Wilcoxon paired test, 威斯康星配对法/配对符号秩和检验Wild point, 野点/狂点Wild value, 野值/狂值Winsorized mean, 缩尾均值Withdraw, 失访Youden's index, 尤登指数Z test, Z检验Zero correlation, 零相关Z-transformation, Z变换Z-transformation, Z变换。

金融博士书目经济学、金融学博士书目（A：数学分析微分方程矩阵代数）微观金融学包括金融市场及金融机构研究、投资学金融工程学金融经济学、公司金融财务管理等方面，宏观金融学包括货币经济学货币银行学、国际金融学等方面，实证和数量方法包括数理金融学、金融计量经济学等方面，以下书目侧重数学基础、经济理论和数理金融学部分。

◎函数与分析《什么是数学》，牛津丛书●集合论Paul R. Halmos，Naive Set Theory 朴素集合论（美）哈莫斯（好书，深入浅出但过简洁）集合论(英文版)Thomas Jech（有深度）Moschovakis，Notes on Set Theory集合论基础（英文版）——图灵原版数学·统计学系列（美）恩德滕●数学分析○微积分Tom M. Apostol, Calculus vol Ⅰ&Ⅱ（数学家写的经典高等微积分教材/参考书，写法严谨，40年未再版，致力于更深刻的理解，去除微积分和数学分析间隔，衔接分析学、微分方程、线性代数、微分几何和概率论等的学习，学实分析的前奏，线性代数应用最好的多元微积分书，练习很棒，对初学者会难读难懂，但具有其他教材无法具备的优点。

Stewart 的书范围相同，也较简单。

）Carol and Robert Ash，The Calculus Tutoring Book（不错的微积分辅导教材）R. Courant, F. John, Introduction to Calculus and Analysis vol Ⅰ&Ⅱ（适合工科，物理和应用多）Morris Kline，Calculus, an intuitive approachRon LarsonCalculus (With Analytic Geometry（微积分入门教材，难得的清晰简化，与Stewart同为流行教材）《高等微积分》Lynn H.Loomis / Shlomo StermbergMorris Kline，Calculus: An Intuitive and Physical Approach （解释清晰的辅导教材）Richard Silverman，Modern Calculus with Analytic GeometryMichael，Spivak，Calculus（有趣味，适合数学系，读完它或者Stewart的就可以读Rudin 的Principles of Mathematical Analysis 或者Marsden的Elementary Classical Analysis，然后读Royden的Real Analysis学勒贝格积分和测度论或者Rudin的Functional Analysis 学习巴拿赫和希尔伯特空间上的算子和谱理论）James Stewart，Calculus（流行教材，适合理科及数学系，可以用Larson书补充，但解释比它略好，如果觉得难就用Larson的吧）Earl W. Swokowski，Cengage Advantage Books: Calculus: The Classic Edition（适合工科）Silvanus P. Thompson，Calculus Made Easy（适合微积分初学者，易读易懂）○实分析（数学本科实变分析水平）（比较静态分析）Understanding Analysis，Stephen Abbott，（实分析入门好书，虽然不面面俱到但清晰简明，Rudin, Bartle, Browder等人毕竟不擅于写入门书，多维讲得少）T. M. Apostol, Mathematical AnalysisProblems in Real Analysis 实分析习题集(美)阿里普兰斯，（美）伯金肖《数学分析》方企勤，北大胡适耕，实变函数《分析学》Elliott H. Lieb / Michael LossH. L. Royden, Real AnalysisW. Rudin, Principles of Mathematical AnalysisElias M.Stein，Rami Shakarchi, Real Analysis：MeasureTheory，Integration and Hilbert Spaces，实分析(英文版) 《数学分析八讲》辛钦《数学分析新讲》张筑生，北大社周民强，实变函数论，北大周民强《数学分析》上海科技社○测度论（与实变分析有重叠）概率与测度论（英文版）（美）阿什（Ash.R.B.），(美)多朗-戴德（Doleans-Dade,C.A.）?Halmos，Measure Theory，测度论(英文版)（德）霍尔姆斯○傅里叶分析（实变分析和小波分析各有一半）小波分析导论（美）崔锦泰H. Davis, Fourier Series and Orthogonal FunctionsFolland，Real Analysis：Modern Techniques and Their ApplicationsFolland，Fourier Analysis and its Applications，数学物理方程：傅里叶分析及其应用（英文版）——时代教育.国外高校优秀教材精选（美）傅兰德傅里叶分析（英文版）——时代教育·国外高校优秀教材精选（美）格拉法科斯B. B. Hubbard, The World According to Wavelets: The Story of a Mathematical Technique in the MakingKatanelson，An Introduction to Harmonic AnalysisR. T. Seeley, An Introduction to Fourier Series and IntegralsStein，Shakarchi，Fourier Analysis：An Introduction○复分析（数学本科复变函数水平）L. V. Ahlfors, Complex Analysis ，复分析——华章数学译丛，（美）阿尔福斯（Ahlfors,L.V.）Brown，Churchill，Complex Variables and Applications Convey, Functions of One Complex Variable Ⅰ&Ⅱ《简明复分析》龚升, 北大社Greene，Krantz，Function Theory of One Complex VariableMarsden，Hoffman，Basic Complex AnalysisPalka，An Introduction to Complex Function TheoryW. Rudin, Real and Complex Analysis 《实分析与复分析》鲁丁（公认标准教材，最好有测度论基础）Siegels，Complex VariablesStein，Shakarchi，Complex Analysis 《复变函数》庄坼泰●泛函分析（资产组合的价值）○基础泛函分析（实变函数、算子理论和小波分析）实变函数与泛函分析基础，程其衰，高教社Friedman，Foundations of Modern Analysis《实变与泛函》胡适耕《泛函分析引论及其应用》克里兹格泛函分析习题集（印）克里希南Problems and methods in analysis，Krysicki夏道行，泛函分析第二教程，高教社夏道行，实变函数与泛函分析《数学分析习题集》谢惠民，高教社泛函分析·第6版（英文版） K.Yosida《泛函分析讲义》张恭庆，北大社○高级泛函分析（算子理论）J.B.Conway, A Course in Functional Analysis，泛函分析教程(英文版)Lax，Functional AnalysisRudin，Functional Analysis，泛函分析（英文版）[美]鲁丁（分布和傅立叶变换经典，要有拓扑基础）Zimmer，Essential Results of Functional Analysis○小波分析Daubeches，Ten Lectures on WaveletsFrazier，An Introduction to Wavelets Throughout Linear Algebra Hernandez，《时间序列的小波方法》PercivalPinsky，Introduction to Fourier Analysis and WaveletsWeiss，A First Course on WaveletsWojtaszczyk，An Mathematical Introduction to Wavelets Analysis●微分方程（期权定价、动态分析）○常微分方程和偏微分方程（微分方程稳定性，最优消费组合）V. I. Arnold, Ordinary Differential Equations，常微分方程（英文版）（现代化，较难）W. F. Boyce, R. C. Diprima, Elementary Differential Equations and Boundary Value Problems《数学物理方程》陈恕行，复旦E. A. Coddington, Theory of ordinary differential equationsA. A. Dezin, Partial differential equationsL. C. Evans, Partial Differential Equations丁同仁《常微分方程教程》高教《常微分方程习题集》菲利波夫，上海科技社G. B. Folland, Introduction to Partial Differential EquationsFritz John, Partial Differential Equations《常微分方程》李勇The Laplace Transform: Theory and Applications，Joel L. Schiff（适合自学）G. Simmons, Differntial Equations With Applications and Historecal Notes索托梅约尔《微分方程定义的曲线》《常微分方程》王高雄，中山大学社《微分方程与边界值问题》Zill○偏微分方程的有限差分方法（期权定价）福西斯，偏微分方程的有限差分方法Kwok，Mathematical Models of Financial Derivatives（有限差分方法美式期权定价）?Wilmott，Dewynne，Howison，The Mathematics of Financial Derivatives （有限差分方法美式期权定价）○统计模拟方法、蒙特卡洛方法Monte Carlo method in finance （美式期权定价）D. Dacunha-Castelle, M. Duflo，Probabilités et Statistiques IIFisherman，Monte Carlo Glasserman，Monte Carlo Mathods in Financial Engineering （金融蒙特卡洛方法的经典书，汇集了各类金融产品）Peter Jaeckel，Monte Carlo Methods in Finance（金融数学好，没Glasserman的好）?D. P. Heyman and M. J. Sobel, editors，Stochastic Models, volume 2 of Handbooks in O. R. and M. S., pages 331-434. Elsevier Science Publishers B.V. (North Holland) Jouini，Option Pricing，Interest Rates and Risk ManagementD. Lamberton, B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance （连续时间）N. Newton，Variance reduction methods for diffusion process :H. Niederreiter，Random Number Generation and Quasi-Monte Carlo Methods. CBMS-NSF Regional Conference Series in Appl. Math. SIAMW.H. Press and al.，Numerical recepies.B.D. Ripley. Stochastic SimulationL.C.G. Rogers et D. Talay, editors，Numerical Methods in Finance. Publicationsof the Newton Institute.D.V. Stroock, S.R.S. Varadhan，Multidimensional diffusion processesD. Talay，Simulation and numerical analysis of stochastic differential systems, a review. In P. Krée and W. Wedig, editors,Probabilistic Methods in Applied Physics, volume 451 of Lecture Notes in Physics, chapter 3, pages 54-96.P.Wilmott and al.，Option Pricing (Mathematical models and computation). Benninga，Czaczkes，Financial Modeling ○数值方法、数值实现方法Numerical Linear Algebra and Its Applications，科学社K. E. Atkinson, An Introduction to Numerical AnalysisR. Burden, J. Faires, Numerical Methods《逼近论教程》CheneyP. Ciarlet, Introduction to Numerical Linear Algebra and Optimisation, Cambridge Texts in Applied MathematicsA. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge Texts in Applied Mathematics 《数值逼近》蒋尔雄《数值分析》李庆杨，清华《数值计算方法》林成森J. Stoer, R. Bulirsch, An Introduction to Numerical AnalysisJ. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations L. Trefethen, D. Bau, Numerical Linear Algebra《数值线性代数》徐树芳，北大其他（不必）《数学建模》Giordano《离散数学及其应用》Rosen《组合数学教程》Van Lint◎几何学和拓扑学（凸集、凹集）●拓扑学○点集拓扑学Munkres，Topology：A First Course《拓扑学》James R.MunkresSpivak，Calculus on Manifolds◎代数学（深于数学系高等代数）（静态均衡分析）○线性代数、矩阵论（资产组合的价值）M. Artin，AlgebraAxler, Linear Algebra Done RightCurtis，Linear Algeria：An Introductory ApproachW. Fleming, Functions of Several VariablesFriedberg, Linear Algebra Hoffman & Kunz, Linear AlgebraP.R. Halmos，Finite-Dimensional Vector Spaces（经典教材，数学专业的线性代数，注意它讲抽象代数结构而不是矩阵计算，难读）J. Hubbard, B. Hubbard, Vector Calculus, Linear Algebra, and Differential Forms: A Unified ApproachN. Jacobson，Basic Algebra Ⅰ&ⅡJain《线性代数》Lang，Undergraduate AlgeriaPeter D. Lax，Linear Algebra and Its Applications（适合数学系）G. Strang, Linear Algebra and its Applications（适合理工科，线性代数最清晰教材，应用讲得很多，他的网上讲座很重要）●经济最优化Dixit，Optimization in Economic Theory●一般均衡Debreu，Theory of Value●分离定理Hildenbrand，Kirman，Equilibrium Analysis（均衡问题一般处理）Magill，Quinzii，Theory of Incomplete Markets（非完备市场的均衡）Mas-Dollel，Whinston，Microeconomic Theory（均衡问题一般处理）Stokey，Lucas，Recursive Methods in Economic Dynamics （一般宏观均衡）经济学、金融学博士书目（B：概率论、数理统计、随机）◎概率统计●概率论（金融产品收益估计、不确定条件下的决策、期权定价）○基础概率理论（数学系概率论水平）《概率论》（三册）复旦Davidson，Stochastic Limit TheoryDurrett，The Essential of Probability，概率论第3版（英文版）W. Feller，An Introduction to Probability Theory and its Applications概率论及其应用（第3版）——图灵数学·统计学丛书《概率论基础》李贤平，高教G. R. Grimmett, D. R. Stirzaker, Probability and Random ProcessesRoss，S. A first couse in probability，中国统计影印版；概率论基础教程（第7版）——图灵数学·统计学丛书（例子多）《概率论》汪仁官，北大王寿仁，概率论基础和随机过程，科学社《概率论》杨振明，南开，科学社○基于测度论的概率论测度论与概率论基础，程式宏，北大D. L. Cohn, Measure TheoryDudley，Real Analysis and ProbabilityDurrett，Probability：Theory and ExamplesJacod，Protter，Probability Essentials Resnick，A Probability PathShirayev，Probability严加安，测度论讲义，科学社钟开莱，A Course in Probability Theory○随机过程微积分Introduction of diffusion processes (期权定价)K. L. Chung, Elementary Probability Theory with Stochastic ProcessesCox，Miller，The Theory of StochasticR. Durrett, Stochastic calculus黄志远，随机分析入门黄志远《随机分析学基础》科学社姜礼尚，期权定价的数学模型和方法，高教社《随机过程导论》KaoKarlin，Taylor，A First Course in Stochastic Prosses（适合硕士生）Karlin，Taylor，A Second Course in Stochastic Prosses（适合硕士生）随机过程，劳斯，中国统计J. R. Norris，Markov Chains（需要一定基础）Bernt Oksendal, Stochastic differential equations（绝佳随机微分方程入门书，专注于布朗运动，比Karatsas和Shreve的书简短好读，最好有概率论基础，看完该书能看懂金融学术文献，金融部分没有Shreve的好）Protter，Stochastic Integration and Differential Equations （文笔优美）D. Revuz, M. Yor, Continuous martingales and Brownian motion（连续鞅）Ross，Introduction to probability model（适合入门）Steel，Stochastic Calculus and Financial Application（与Oksendal的水平相当，侧重金融，叙述有趣味而削弱了学术性，随机微分、鞅）《随机过程通论》王梓坤，北师大○概率论、随机微积分应用（连续时间金融）Arnold，Stochastic Differential Equations《概率论及其在投资、保险、工程中的应用》BeanDamien Lamberton,Bernard Lapeyre. Introduction to stochastic calculus applied t o finance.David Freedman.Browian motion and diffusion.Dykin E. B. Markov Processes.Gihman I.I., Skorohod A. V.The theory of Stochastic processes 基赫曼，随机过程论，科学Lipster R. ,Shiryaev A.N. Statistics of random processes.Malliaris，Brock，Stochastic Methods in Economics and FinanceMerton，Continuous-time FinanceSalih N. Neftci，Introduction to the Mathematics of Financial DerivativesSteven E. Shreve ，Stochastic Calculus for Finance I: The Binomial Asset Pric ing Model；II: Continuous-Time Models（最佳的随机微积分金融（定价理论）入门书，易读的金融工程书，没有测度论基础最初几章会难些，离散时间模型，比Naftci的清晰，S hreve的网上教程也很优秀）Sheryayev A. N. Ottimal stopping rules.Wilmott p., J.Dewynne,S. Howison. Option Pricing: Mathematical Models and Compu tations.Stokey，Lucas，Recursive Methods in Economic Dynamics Wentzell A. D. A Course in the Theory of Stochastic Processes.Ziemba，Vickson，Stochastic Optimization Models in Finance○概率论、随机微积分应用（高级）Nielsen，Pricing and Hedging of Derivative SecuritiesRoss，《数理金融初步》An Introduction to Mathematical Finance：Options and othe r TopicsShimko，Finance in Continuous Time：A Primer○概率论、鞅论P. Billingsley，Probability and MeasureK. L. Chung & R. J. Williams，Introduction to Stochastic IntegrationDoob，Stochastic Processes严加安，随机分析选讲，科学○概率论、鞅论Stochastic processes and derivative products （高级）J. Cox et M. Rubinstein : Options MarketIoannis Karatzas and Steven E. Shreve，Brownian Motion and Stochastic Calculu s（难读的重要的高级随机过程教材，若没有相当数学功底，还是先读Oksendal的吧，结合Rogers & Williams的书读会好些，期权定价，鞅）M. Musiela - M. Rutkowski : (1998) Martingales Methods in Financial Modelling ?Rogers & Williams，Diffusions, Markov Processes, and Martingales: Volume 1, F oundations；Volume 2, Ito Calculus （深入浅出，要会实复分析、马尔可夫链、拉普拉斯转换，特别要读第1卷）David Williams，Probability with Martingales（易读，测度论的鞅论方法入门书，概率论高级教材）○鞅论、随机过程应用Duffie，Rahi，Financial Market Innovation and Security Design：An Introduction，Journal of Economic Theory Kallianpur，Karandikar，Introduction to Option Pricing TheoryDothan，Prices in Financial Markets （离散时间模型）Hunt，Kennedy，Financial Derivatives in Theory and Practice何声武，汪家冈，严加安，半鞅与随机分析，科学社Ingersoll，Theory of Financial Decision MakingElliott Kopp，Mathematics of Financial Markets（连续时间）Marek Musiela，Rutkowski，Martingale Methods in Financial Modeling（资产定价的鞅论方法最佳入门书，读完Hull书后的首选，先读Rogers & Williams、Karatzas and Sh reve以及Bjork打好基础）○弱收敛与随机过程收敛Billingsley，Convergence of Probability MeasureDavidson，Stochastic Limit TheoremEthier，Kurtz，Markov Process：Characterization and Convergence Hall，Marting ale Limit TheoremsJocod，Shereve，Limited Theorems for Stochastic Process Van der Vart，Weller，Weak Convergence and Empirical Process◎运筹学●最优化、博弈论、数学规划○随机控制、最优控制（资产组合构建）Borkar，Optimal control of diffusion processesBensoussan，Lions，Controle Impulsionnel et Inequations Variationnelles Chiang，Elements of Dynamic Optimization Dixit，Pindyck，Investment under UncertaintyFleming，Rishel，Deterministic and Stochastic Optimal ControlHarrison，Brownian Motion and Stochastic Flow SystemsKamien，Schwartz，Dynamic OptimizationKrylov，Controlled diffusion processes○控制论（最优化问题）●数理统计（资产组合决策、风险管理）○基础数理统计（非基于测度论）R. L. Berger, Cassell, Statistical InferenceBickel，Dokosum，Mathematical Stasistics：Basic Ideas andSelected TopicsBirrens，Introdution to the Mathematical and Statistical Foundation of Econom etrics数理统计学讲义，陈家鼎，高教Gallant，An Introduction to Econometric TheoryR. Larsen, M. Mars, An Introduction to Mathematical Statistics《概率论及数理统计》李贤平，复旦社Papoulis，Probability，random vaiables，and stochastic processStone，《概率统计》《概率论及数理统计》中山大学统计系，高教社○基于测度论的数理统计(计量理论研究)Berger，Statistical Decision Theory and Bayesian Analysis陈希儒，高等数理统计Shao Jun，Mathematical StatisticsLehmann，Casella，Theory of Piont EstimationLehmann，Romano，Testing Statistical Hypotheses《数理统计与数据分析》Rice○渐近统计Van der Vart，Asymptotic Statistics○现代统计理论、参数估计方法、非参数统计方法参数计量经济学、半参数计量经济学、自助法计量经济学、经验似然经济学、金融学博士书目（C：计量经济学、数理金融）统计学基础部分1、《统计学》《探索性数据分析》 David Freedman等，中国统计（统计思想讲得好）2、Mind on statistics 机械工业（只需高中数学水平）3、Mathematical Statistics and Data Analysis 机械工业（这本书理念很好，讲了很多新东西）4、Business Statistics a decision making approach 中国统计（实用）5、Understanding Statistics in the behavioral science 中国统计回归部分1、《应用线性回归》中国统计（蓝皮书系列，有一定的深度，非常精彩）2、Regression Analysis by example，（吸引人，推导少）3、《Logistics回归模型——方法与应用》王济川郭志刚高教（不多的国内经典统计教材）多元1、《应用多元分析》王学民上海财大（国内很好的多元统计教材）2、Analyzing Multivariate Data，Lattin等机械工业（直观，对数学要求不高）3、Applied Multivariate Statistical Analysis，Johnson & Wichem，中国统计（评价很高）《应用回归分析和其他多元方法》Kleinbaum《多元数据分析》Lattin时间序列1、《商务和经济预测中的时间序列模型》弗朗西斯著（侧重应用，经典）2、Forecasting and Time Series an applied approach，Bowerman & Connell（主讲Box-Jenkins(ARIMA)方法，附上了SAS和Minitab程序）3、《时间序列分析：预测与控制》 Box，Jenkins 中国统计《预测与时间序列》Bowerman抽样1、《抽样技术》科克伦著（该领域权威，经典的书。

绘制流网的数值计算方法水利水运科学研究1994年6月tan一是一或d—dx一0式中口为与轴的夹角,和分别为在和轴向的分量.(2)式为描述流线的流线方程,对二维渗流场都适用.在地下水(假定为不可压缩)的渗流问题中,有渗流连续性方程+:0drdV故流线方程(2)式则为全微分方程(=』z(1)(2)(4)或d妇,)一d+d=Vdy—dx(5)得渗流速度与流函数的关系为y一1:型}J由Darcy定律fa一一到薹}㈣【J及(6)式可得'+雾一(—k)啬+k(耄一雾)(8)式中,,及为Darcy渗透系数;,)为水头函数.可见,当渗流域为各向同性域时(一,一=O),流函数,)满足Laplace微分方程;当域中介质为各向异性体时≠,一≠O),流函数不满足Laplace方程.再由(6)和(7)式可得(k警+b)+(k箬+)一o(9)因此,当渗流域由各向同性体组成时,有+等=o㈣,.av.…或V?V一0(11)表明流网中流线与等水头线互为正交,流网为一正交型曲线网络图.反之,在各向异性庠渗流场中,(10)或(n)式均不等于0.即流网流线与等水头线不正交,流网为一斜交型曲线网第1,z期朱岳明等t绘制流同的数值计算方法络图.三,流网的数值计算在渗流域S内,(6)式的两边分别对y及徽分,整理得流函数的Passion型徽分方程+等+警一=o0.0.…再沿面域S的边界曲线r对(6)式分别乘以和n,相加得(12)式解的Neumaun边界条件+=一(13)式中n和,为边界曲线r的外法线方向余弦i渗流速度和,是水头函数的梯度函数,可用有限元法先计算出水头函数在域中的分布,再求得和.如引入单元内水头函数,y)的有限元法插值式,)一∑Ⅳ.(14)则有一一∑∑k警+b警警+警(15)式中,M和m分别为单元结点的水头值,插值基函数和单元结点数固已有水头函数的有限元离散解,和V只是位置坐标的函数.根据变分原理,由(12)和(13)式构成的流函数的解为下述泛函Ⅱ()的驻值点一盯[吉c丢cc警一一f'一nV,)dP(16)因有V=dPⅡ主(VDdS及一JJV,)dS(16)式.q-简化为)一盯[丢(-f-W¨-+,一(17)把(15)式代/k(17)式并在单元内引入流函数的有限元插值(18)式,);∑Ⅳj(18)则在计算域S内,对(17)式进行有限元法的离散运算及单元传导矩阵和左,右端项的集合组装后,可得标准型有限元法线性支配方程水利水运科学研究1994年6月I-K2{}一{Q)(19)式中的{}为流函数的未知结点值向量.~(18)am(19)式,每个单元对系数矩阵[]和右端项{Q}中相应元素的作用分别为b:盯(警警+警警jacz.:=Ⅱ{警[耋ckiaN,+b警]～警[喜ck警+]cz式中为单元的面域}f,j=1.2'..?,m.(19)式的解就为流函数(z,y)的有限元解.有了水头函数,y)和流函数(z,y)的有限元数值解,再经过有限元解后处理子程序的计算,整理后,即可得绘制流网所需的所有技术数据或直接在计算机上绘制出高精度的流网.事实上,(13)式把渗流场中流函数的强制性第一类边界条件(,)一(,y)转化成了第二类自然边界条件,避开了渗出面上流函数事先不易确定的问题,使流网的数值计算大为简化.为了消除系数矩阵[]的奇异性并使解唯一性,在解(19)式前,可根据问题的性质及其物理意义,对某些结点直接引入已知值,如位于浸润线上结点的值为0.0;位于计算域底部不透水面上结点的值为总渗流量q(或取相对值100).四,算例(一)土提中无压渗流场的流网计算'图2为一均质各向同性土堤中无压Fi.P要誊ed印渗流场流网的计算结果,流线与荨水头"ow.ughhomo~eneoandisotop线互为正交,计算域为ABCDEA,上,下游水头分别为6.0和2.0.在求解水头函数的分布及确定浸润线位置时,采用结点虚流量法[3}在求解流函数(,y)的分布时,令浸润线AD上所有结点的值为0.0.劫一盟赴-rdlD第l,2期朱岳明等绘制谎同的数值计算方法(二)闸坝下成层各向异性地基中流网的计算图3为某一水闸下非均质成层各向异性体地基中流网的计算结果.在计算域中,视闸体混凝土为不透水体,厚 2.0rn,深40.0m的棍凝土防渗板桩也为相对不透水体,约40m深的强透水砂砾覆盖层为均质各向异性透水体,其Dare),渗透张量为吡=(m/d)r2.320,01一lo.o1.16J如/s)覆盖层下为水平向层状岩体,其渗透张量为嘲,一[c…m闸坝上,下游水头分别为20.0m和5.0m,计算中令位于闸底板面上结点的=0.0,位于z一一100.0m,z一150.0m和=一100.0m的边界面上的结点满足=舢(为总渗流量). 图3非均质各向异性闸基域中的斜交型流网F.3Tiltedflowztetofeon|inedseepageflowthrou暮hinhomogeneousandanlsotroplc foundationof8sluice如图3所示,在一一40.0m的地基材料分界面上,因受渗流越流量连续性条件的约束,流线与等势线均发生折射;又因材料均为各向异性体,尽管渗透方向与整体坐标和Y轴同向(==O),流线斜交于等水头线,流网为斜交网络图.这种流网难以用徒手勾画, 也不便由模型试验中得到.124水刺水运科学研究1994年6月(三)非均质土石坝中流网的计算图4为一壤土质宽心墙非均质各向同性体土石坝中渗流流网的计算结果.该坝高30.0m,底宽160.Om,心墙底宽96.Om,坝上,下游水头分别为148.Om和130.Om.整个渗流计算域主要由四种透水性不同的材料组成t一区为壤土质宽心墙体,其渗透系数h;1.16×10一m/s}二区为上,下游坝坡区的粗砂砾填筑区,其岛一L16×10～m/s{三区为深选50.Om的细砂砾覆盖层,其=1.16X10-5m/s;四区为覆盖层下的砂质岩层,其h= 1.16×10一m,s.":,\\汹l—?.'.....'..一1160—————————卜—一l伽———图4壤土质宽心墙土石坝中的流网F.4Flowtofseepagethroughanearthdam该坝虽在各子区域内介质为各向同性体,流线与等水头线正交,但在一70.0m和一120.Om等不同透水体的分界面上流线和等水头线均发生折射,使得流网的形态复杂化.显然,流网也不宜用徒手勾画.五,结语(一)本文介绍的方法适用于各种非均质,各向异性域中复杂流网的绘制工作.与传统的几种方法相比,尤其适用于材料分界面处流线和等水头线均折射及各向异性域中斜交流网的绘制.(二)求解漉函数(z,)时.虽基于已求解得水头函数z,)的基础上,但采用的是饲一种网格.(三)在非均质域中,困在相邻材料区的分界线上流线和等水头线均要发生折射,为了提高流网的计算及绘制精度,对这些分界线区单元,应布置得相对密一些.同理?在水力梯度变化较大的有关阻水及排水区,单元也应布置得小些.∞+占●上第l,2期朱岳明等:绘制浇两的数值箅方法12j参考文献1HarrME.GroundwaterandSeepage.LondonlMCGraw—HillBookCompany.19622AahoJ.Finiteelementseepageflownets.IntJforNumericalaMAnalysis MethodsinGeomechanlcs,1984l8t297—3033ZhuYueming,WangRuyun,XuHongbo.Someadaptivetechnlquesfor solutionoffreesurfaceseepageflowthrougharchdamabutments.In±Procof theIntSymposiumonArchDams,1992 NumericalmethodfordrawingflownetofseepageZhuYuemlng(HohaiUniversity)HeJian(ZheiiangProvinceWaterConservancy,~[anagement)ShaoJingdong(ChenduHydroelectricInvestigation,DesignandResearchInstituteofMOE,M~VR) AbstractAtthefirst.thefundamentaltheoryandcharacteristicoftheflownetsof2-D.DarcyS seepageflowproblemareintroduced.Basedonthevariationalprincipleandfiniteelementmethod,thenumericalmethodandthecorrespondingcalculationexpressionsarepresented indetail.Threeillustrativeexamplesaboutthenumerlzationanddrawingoftheflownets ofseepagesthroughembankmentandsluicefoundationaresuccessfullygiven.Themethod hasfoundamentlysolutedtheproblemthatallofthecomplicatedflownetsingeoengineer—ingmaybenumericallydrawnwithquickandhighprecision.Keywords:seepage,flownet,finiteelementmethod,numericalcalculation,tWO,dimensionaIflOW。