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统计软件词汇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。
理工英文考试题及答案解析一、选择题（每题2分，共20分）1. The term "mechanical engineering" refers to the application of physics and materials science for the design, analysis, manufacturing, and maintenance of mechanical systems.A. TrueB. False答案解析： A. True. 机械工程是指应用物理和材料科学来设计、分析、制造和维护机械系统。
2. Which of the following is not a type of renewable energy?A. SolarB. WindC. NuclearD. Hydro答案解析： C. Nuclear. 核能不是可再生能源的一种，因为它依赖于有限的铀或其他放射性元素。
3. In computer science, what does "API" stand for?A. Automated Programming InterfaceB. Application Programming InterfaceC. Advanced Programming InterfaceD. Artificial Programming Interface答案解析： B. Application Programming Interface. API 是应用程序编程接口的缩写。
4. The formula for calculating the area of a circle is A = πr², where "r" represents:A. The diameter of the circleB. The circumference of the circleC. The radius of the circleD. The area of the circle答案解析： C. The radius of the circle. 圆的面积公式 A =πr²中的 "r" 表示圆的半径。
User experience and productivity The system-wide changes to the NX ®software user interface offer key benefits for the CAM Express user.The redesigned menus and input dialogs clearly communicate required input and command steps and this is consistent with the other elements of the NX product line.The re-use of common elements to enhance operational consistency and discoverability is particularly important in CAM.For example,in noncutting moves the user interaction has been rationalized across all CAM functions.The enhanced use of role-specific user interfaces is also very important in the CAM area.This enables companies to present commands appropriate to the user’s function and level of expertise,enabling first-dayproductivity for novice users and flexibility to adapt to more functionality as their needs andproficiency grow.In CAM Express the system is delivered with the optional Express and Expert Rolesas out-of-the-box roles.The Express role sets the user interface into a level that is ideal for the newuser.It also activates a series of predefined templates that configure the system for one of a numberof key machining functions such as turning,mold and die machining or mill-turn machining.Acomplementary set of built-in tutorials linked to the Express role guide the new user though a pre-setlearning experience inside the live software.What’s new in CAM Express version 5BenefitsStreamlined operation cuts smoothly and leaves a beautiful finishEasier than ever to learn and useAvailable machine tool kits make for fast implementationFaster cutting with shorter tools in deep cavitiesMore realistic machine simulationAreas of enhancements•User experience –ease of use and user productivity•Free Flow Machining ™–a new technology for toolpath creation•Machine tool support kits –out-of-the-box content for advanced post processors and machine tool simulation sets SummaryCAM Express software is the full function,CAD-neutral numerical control (NC)programming application in the Velocity Series ™portfolio.Version 5contains the latest improvements that help manufacturers increase the value of their machine tools by tailoring the programming system to the needs of the shop,the machine tool and the NC programmer.fact sheetSiemens PLM Software /plm/camexpressVelocity Seriesflowing toolpaths with far increased tool life andbasis for the new Streamlineclean up the material that would be leftpatterns once this gets to within aa tool’sfor all identified machining features.Thistrack the progress of each feature.make it faster than ever to apply the best ContactSiemens PLM SoftwareAmericas8008072200Europe44(0)1202243455Asia-Pacific852********/plm©2008Siemens Product Lifecycle Management Software Inc.All rights reserved.Siemens and the Siemens logo are registered trademarks of Siemens AG.T eamcenter,NX,Solid Edge,T ecnomatix,Parasolid,Femap,I-deas,JT,Velocity Series and Geolus are trademarks or registered trademarks of Siemens Product Lifecycle Management Software Inc.or its subsidiaries in the United States and in other countries.All other logos,trademarks,registered trademarks or service marks used herein are the property of their respective holders.5/08。
数字查找树digital search tree树的遍历traversal of tree先序遍历preorder traversal中序遍历inorder traversal后序遍历postorder traversal图graph子图subgraph有向图digraph(directed graph)无向图undigraph(undirected graph)完全图complete graph连通图connected graph非连通图unconnected graph强连通图strongly connected graph弱连通图weakly connected graph加权图weighted graph有向无环图directed acyclic graph稀疏图spares graph稠密图dense graph重连通图biconnected graph二部图bipartite graph边edge顶点vertex弧arc路径path回路（环）cycle弧头head弧尾tail源点source终点destination汇点sink权weight连接点articulation point初始结点initial node终端结点terminal node相邻边ad」acent edge相邻顶点adjacent vertex关联边incident edge入度indegree出度outdegree最短路径shortest path有序对ordered pair无序对unordered pair简单路径simple path简单回路simple cycle连通分温connected component邻接矩阵adjacency matrix邻接表adjacency list邻按多重表adjacency multilist历图traversing graph生成树spanning tree最小（代价）生成树minimum(cost)spanning tree 生成森林spanning forest拓扑排序topological sort偏序partical order拓扑有序topological orderAOV网activity on vertex networkAOE网activity on edge network关键路径criticaI path匹配matching最大匹配maximum matching增广路径augmenting path增广路径图augmenting path graph查找searching线性查找（顺序查找）linear search (sequential search) 二分查找binary search分块查找block search散列查找hash search平均查找长度average search length散列表hash table散列函数hash funticion且接定址法immediately allocating method数字分析法digital analysis method平方取中法m吐square method折叠法folding method除法division method随机数法random number method排序sort内部排序internal sort外部排序external sort插入排序insertion sort随小增量排序diminishing increment sort选择排序selection sort堆排序heap sort快速排序quick sort归并排序merge sort基数排序radix sort外部排序external sort平衡归并排序balance merging sort二路平衡归并排序balance two-way merging sort多步归并排序ployphase merging sort置换选择排序replacement selection sort件file主文件master file顺序文件sequential file索引文件indexed file索引顺序文件indexed sequential file索引非顺序文件indexed non-sequential file直接存取文件direct access file多重链表文件multilist file倒排文件inverted file目录结构directory structure树型索引tree index。
2011年CUDA校园编程竞赛指定题目−最短路径问题最短路径问题(Shortest Path Problem)是经典图论问题之一，具有重大研究价值和工程意义。
从学术角度来说，图灵奖得主EdsgerDijkstra针对该问题的一系列工作是现代算法研究的起点之一，以他的名字命名的Dijkstra最短路径算法成为计算机科学家武器库中的基本装备。
从工程意义上讲，最短路径问题是对大量工程问题的直观抽象。
最典型的例子当然是导航，我们在谷歌地图上寻找驾车路径时，显然就是要找到一条物理距离最短或者行驶时间最短的路线。
此外，机器人路径规划、集成电路布线、计算机网络路由等应用都需要寻找最短路径。
因此，今年我们选择该问题作为CUDA校园编程竞赛指定题目。
最短路径问题是在图(graph)的概念上定义的。
这里的“图”服从图论中的定义，但是不需要学习图论也可以理解其概念。
一个图由节点(vertex或者node)集合和边(edge或者arc)集合组成，图1是一个例子。
其中，标有数字的圆圈是节点，分别具有编号0到5，即节点0到节点5一共六个。
两个节点之间可以由一条边连接，由相应节点标志，例如图1中连接节点0和1的边可以记作(0,1)。
边可以有方向或无方向，本次竞赛中只考虑有方向的边，因此图1中的边都有箭头。
这时可以一条边(i,j)是由节点i指向节点j，当然反过来也行，相应的图被称为有向图。
每条边上一般可以有一个权重，表示某种属性，图1里面每条边旁边的数字就是相应权重。
对本次竞赛而言，可以把权重理解为相应节点之间的真实物理距离，因此权重是大于0的实数。
图1. 图及其节点和边在一个图里面，从某一节点i开始，经由一系列边可以到达某个节点k，则i→k称为一条路径(path)，该路径的长度是所有经过的边上的权重之和。
如果从某一节点出发，能够找到至少一条去往其它任何节点的路径，则该图是连通的，本次竞赛只考虑连通图。
连通图中的任意两个节点i和j之间一般来说存在多条路径，最短路径问题就是找到其中最短的一条。
统计学专业名词·中英对照我大学毕业已经多年，这些年来，越发感到外刊的重要性。
读懂外刊要有不错的英语功底，同时，还需要掌握一定的专业词汇。
掌握足够的专业词汇，在国内外期刊的阅读和写作中会游刃有余。
在此小结，按首字母顺序排列。
这些词汇的来源，一是专业书籍，二是网上查找，再一个是比较重要的期刊。
当然，这些仅是常用专业词汇的一部分，并且由于个人精力、文献查阅的限制，难免有不足和错误之处，希望读者批评指出。
Aabscissa 横坐标absence rate 缺勤率Absolute deviation 绝对离差Absolute number 绝对数absolute value 绝对值Absolute residuals 绝对残差accident error 偶然误差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Accumulated frequency 累积频数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 factori ng 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 data 分析资料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Arithmetic weighted mean 加权算术均数Arrhenius relation 艾恩尼斯关系Assessing fit 拟合的评估Associative laws 结合律Assumed mean 假定均数Asymmetric distribution 非对称分布Asymmetry coefficient 偏度系数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 deviation 平均差Average growth rate 平均增长率BBar chart/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Biometrics 生物统计学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Box plot 箱线图/箱尾图Breakdown bound 崩溃界/崩溃点CCanonical correlation 典型相关Caption 纵标目Cartogram 统计图Case fatality rate 病死率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census 普查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-sguare(X2) test 卡方检验卡方检验/χ2 检验Choleskey decomposition 乔洛斯基分解Circle chart 圆图Class interval 组距Classification 分组、分类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 correlation 相关系数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Collection of data 资料收集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Combined standard deviation 合并标准差Combined variance 合并方差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Complete survey 全面调查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 level 可信水平，置信水平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Constituent ratio 构成比，结构相对数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Continuity 连续性Contingency table 列联表Contour 边界线Contribution rate 贡献率Control 对照质量控制图Control group 对照组Controlled experiments 对照实验Conventional depth 常规深度Convolution 卷积Coordinate 坐标Corrected factor 校正因子Corrected mean 校正均值Correction coefficient 校正系数Correction for continuity 连续性校正Correction for grouping 归组校正Correction number 校正数Correction value 校正值Correctness 正确性Correlation 相关，联系Correlation analysis 相关分析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 frequency 累积频率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DD test D 检验data 资料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 confidence 可信度，置信度degree of dispersion 离散程度Degree of precision 精密度Degree of reliability 可靠性程度degree of variation 变异度Degression 递减Density function 密度函数Density of data points 数据点的密度Dependent variableDepth 深度Derivative matrix 导数矩阵Derivative-free methods 无导数方法Design 设计design of experiment 实验设计Determinacy 确定性Determinant 行列式Determinant 决定因素Deviation 离差Deviation from average 离均差diagnose accordance rate 诊断符合率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EError Bar 均值相关区间图Effect 实验效应Effective rate 有效率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Equation of linear regression 线性回归方程Equivariance 同变性Error 误差/错误Error of estimate 估计误差Error of replication 重复误差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Experiment design 实验设计Experiment error 实验误差Experimental group 实验组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FF 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Freguency distribution 频数分布Frequency polygon 频数多边图Frontier point 界限点Function relationship 泛函关系GGamma 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HHalf-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IImage 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JJacobian 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KK-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LLack 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 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MMain 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NNatural 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OObjective 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PPaired 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（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QQR 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RRadix 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SSample 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TTags 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UUMVU 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VVague concept 模糊概念Validity 有效性V ARCOMP (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V olume of distribution 容积WW 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X此组的词汇还没找到YYouden's index 尤登指数ZZ test Z 检验Zero correlation 零相关Z-transformation Z 变换。
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土力学词汇英汉对照编写人：邵俐审核人: 刘松玉、张克恭东南大学交通学院二00五年三月Aabsorbed water 吸着水accumulation sedimentation method累积沉淀法active earth pressure主动土压力E aactivity index 活性指数Aadamic earth,red soil 红粘土additional stress(pressure）of subsoil地基附加应力（压力)zadverse geologic phenomena 不良地质现象aeolian soils 风积土aeolotropic soil 各向异性土air dried soils 风干土allowable subsoil bearing capacity地基容许承载力［0］allowable settlement 容许沉降alluvial soil 冲积土angle between failure plane and major principal plane破坏面与大主平面的夹角angle of internal，external (wall） friction 内摩擦角、外（墙背)摩擦角angular gravel，angular pebble 角砾anisotropic soil 各向异性土aquifer 含水层aquifuge，impermeabler layer 不透水层area of foundation base 基础底面面积Aartesian water head 承压水头artificial fills 人工填土artificial foundation 人工地基Atterberg Limits 阿太堡界限attitude 产状average consolidation pressure平均固结压力average heaving ratio of frozen soil layer 冻土层的平均冻胀率average pressure ,additional pressure of foundation base基底平均压力、平均附加压力p、p0Bbase tilt factor of foundation基础倾斜系数b c、b q、bbase tilt factors基底倾斜系数b c、b q、b bearing capacity 承载力bearing capacity factors承载力系数N c,、N q，、N[California]Bearing Ratio [CBR] 承载比bearing stratum 持力层bedrock，original rock 基岩beginning hydraulic gradient起始水力梯度（坡降）i oBiot consolidation theory 比奥固结理论Bishop’s slice method 比肖普条分法（完整）土力学词汇英文翻译bound water 结合水（束缚水)boulder 漂石Boussinesq theory 布辛奈斯克理论bridge 桥梁bridge pier 桥墩broken stone，crushed stone 碎石bulk modulus 体积模量buried depth of foundation 基础埋置深度d buoyant density 浮密度buoyant gravity density(unit weight)浮重度（容重）’CCalifornia Bearing Ratio（CBR)加州承载比capillary rise 毛细水上升高度capillary water 毛细（管）水categorization of geotechnical projects岩土工程分级cementation 胶结作用central load 中心荷载(轴心荷载)characteristic value of subsoil bearing capacity 地基承载力特征值f akchemical grouting 化学灌浆circular footing圆形基础clay 粘土clay content 粘粒含量clay minerals 粘土矿物clayey silt 粘质粉土clayey soils ,clayly soils 粘性土coarse aggregate 粗骨料coarse-grained soils 粗粒土coarse sand 粗砂cobble 卵石Code for design of building foundation建筑地基基础设计规范coefficient of active earth pressure主动土压力系数K acoefficient of passive earth pressure被动土压力系数K Pcoefficient of collapsibility 湿陷系数s coefficient of compressibility 压缩系数a coefficient of curvature 曲率系数C c coefficient of earth pressure at rest 静止土压力系数Kcoefficient of lateral pressure侧压力系数K0coefficient of permeability 渗透系数k coefficient of secondary consolidation次固结系数coefficient of uniformity 不均匀系数coefficient of vertical consolidation竖向固结(压密)系数c v。
Curvature-Constrained Shortest Paths in a Convex Polygon(Extended Abstract)Pankaj K.Agarwal Therese Biedl Sylvain LazardSteve Robbins Subhash Suri Sue WhitesidesAbstractLet be a point robot moving in the plane,whose path is con-strained to have curvature at most,and let be a convex polygonwith vertices.We study the collision-free,optimal path-planningproblem for moving between two configurations inside(a con-figuration specifies both a location and a direction of travel).Wepresent an time algorithm for determining whether acollision-free path exists for between two given configurations.Ifsuch a path exists,the algorithm returns a shortest one.We providea detailed classification of curvature-constrained shortest paths in-side a convex polygon and prove several properties of them,whichare interesting in their own right.Some of the properties are quitegeneral and shed some light on curvature-constrained shortest pathsamid obstacles.curvature-constrained shortest path inside a convex polygon.We establish several new properties of shortest paths in-side a convex polygon and use these properties to charac-terize shortest ing these properties of shortest paths and some results in computational geometry[2,8],we presentan efficient algorithm that,given initial and desiredfinal con-figurations and in the polygon,determines whether a curvature-constrained path from to exists,and if so,computes a shortest one.1.1Previous resultsDubins[10]was perhaps thefirst to study curvature-constrainedshortest paths.He proved that,in the absence of obstacles, a curvature-constrained shortest path from any start config-uration to anyfinal configuration consists of at most three segments,each of which is either a straight line or an arc ofa circle of unit radius,assuming that the maximum curvatureof the path is bounded by.Reeds and Shepp[23]extended this obstacle-free characterization to robots that are allowedto make reversals,that is,to back ing ideas from con-trol theory,Boissonnat,C´e r´e zo and Leblond[4]gave an al-ternative proof for both cases,and recently Sussmann[29]was able to extend the characterization to the-dimensional case.In the presence of obstacles,Fortune and Wilfong[11]gave a-time algorithm,where is the total num-ber of vertices in the polygons defining the obstacles andis the number of bits of precision with which all points arespecified;their algorithm only decides whether a path ex-ists,without necessarilyfinding one.Jacobs and Canny[13], Wang and Agarwal[30],and Sellen[27,28]gave approx-imation algorithms for computing an-robust path.(Infor-mally,a path is-robust if-perturbations of certain pointsalong the path do not violate the feasibility of the path.)For the restricted case of pairwise disjoint moderate obsta-cles,i.e.,convex obstacles whose boundaries have curvaturebounded by,Agarwal,Raghavan and Tamaki[1]gave effi-cient approximation algorithms.Boissonnat and Lazard[5] gave an-time algorithm for computing the exact shortest paths for the case when the edges of the pairwise disjoint moderate obstacles are circular arcs of unit radius orline segments.Their algorithm works even if the obstaclesintersect each other,and thus inside a convex polygon,but the running time is then.Wilfong[31]studied a re-stricted problem in which the robot must stay on one ofline segments(thought of as“lanes”),except to turn between lanes.For a scene with obstacle vertices,his algorithm preprocesses the scene in time,follow-ing which queries are answered in time.There has also been work on computing curvature-constrained paths when is allowed to make reversals[3,19,21].Other, more general,dynamic constraints have been considered in [6,7,9,22].1.2Our model and resultsLet be a point robot and a closed convex polygon withvertices.For simplicity we assume that the edges of are in general position:no two edges are parallel and no unit-radius circle is tangent to three edges of.A configuration for is a pair LOC,where LOC is a point in the plane representing the location of the robot and is anangle between and representing its orientation.When the meaning is clear,we often write instead of LOC.The image of a differentiable functionis called a path.We denote both the function and the path it defines by.We regard a path as oriented fromto.We assume a path is parameterized by its arclength,and denotes its length.We say that is a path from a configuration to another configuration ifLOC,LOC,and the oriented angles(with re-spect to the positive-axis)of and are and ,respectively.A path is called moderate if its average curvature is at most in every positive-length interval.1This implies that the curvature is at most whenever it is defined.Any curve that lies entirely within the closed polygonis called free.A path is feasible if it is moderate and free.A feasible path from a configuration to another configura-tion is optimal if its length is minimum among all feasible paths from to(it can be shown that whenever a feasi-ble path from to exists,then an optimal such path also exists[13]).Main Results.Let be a convex polygon in the plane with vertices,and let and be two configurations inside.(i)We prove that an optimal path from to consists of atmost eight maximal segments,each of which is either aline segment or a circular arc of unit radius.(ii)We give an-time algorithm to determine whether a feasible path from to exists.If such a pathexists,then the algorithm returns an optimal path fromto.If there are only edges of within distancefrom and,then the running time of our algorithmcan be improved to,Our algorithm is significantly faster than the algorithmby Boissonnat and Lazard[5],whose running time was. Our paper is organized as follows.In Section2,we present basic definitions,notation,and useful known results.In Sec-tion3,we give a classification of the optimal path.In Sec-tions4and5,we describe our algorithms.Section6con-cludes.2Geometric PreliminariesGiven a configuration,the oriented line passing through LOC with orientation is denoted.A configura-tion belongs to an oriented path(or curve)if LOCand is the oriented tangent line to at LOC.Note that a configuration belongs to two oriented unit-radius circles.We will use(resp.)to denote the two circles of unit radius,oriented counterclockwise(resp.clockwise) to which the configuration belongs.If and are two points on a simple closed curve, then(resp.)denotes the portion of from to in the counterclockwise(resp.clockwise)di-rection,including and;we will useto denote portions excluding.Similarly,for a path and two configurations,we will use to denote the portion of from to.Segments and Dubins paths.Let be a feasible path.We call a nonempty subpath of a-segment(resp.-segment) if it is a circular arc of unit radius(resp.line segment)and maximal.A segment is either a-segment or an-segment. While referring to a-segments on a path,we will call it a-segment(resp.-segment)if it is counterclockwise (resp.clockwise)oriented along.Suppose consists of a-segment,an-segment,and a-segment;then we will say that is of type,or if we want to distin-guish between the two-segments;superscripts andwill be used to specify the orientations of-segments of. Abusing the notation slightly,we will also use to de-note the-segments and to denote the-segment of. The above notation can be generalized to an arbitrarily long sequence.Dubins[10]proved the following result.Lemma2.1(Dubins[10])In an obstacle-free environment, an optimal path between any two configurations is of type or,or a substringthereof.Figure1.Different types of Dubins paths.We will refer to paths of type or or sub-strings thereof as Dubins paths.In the presence of obsta-cles,Jacobs and Canny[13]observed that any subpath of an optimal path that does not touch any obstacle except at the endpoints is a Dubins path.In particular,they proved the following.Lemma2.2(Jacobs and Canny[13])Let be a closed polyg-onal environment,an initial configuration,and afinal configuration.Then an optimal path from to in con-sists of a sequence of feasible paths,where each is a Dubins path from a configuration to a configu-ration,such that,,and,for, LOC.The above lemma implies that an optimal path in a closed polygonal environment consists of-and-segments.In the following,we will consider only those paths that are formed by-and-segments.We will refer to circles and circular arcs of unit radius simply as circles and circular arcs. Notationally,we differentiate between a-segment and its supporting circle by using calligraphic font for the latter. Terminal and nonterminal segments.A segment of a fea-sible path is called terminal if it is thefirst or the last seg-ment of;otherwise it is called nonterminal.We apply the adjectives terminal and nonterminal to subpaths as well.If thefirst or last segment in is a-segment,we will refer to it as a-segment or a-segment,respectively.,, ,and are called terminal circles(see Figure2).The following lemmas state some basic known properties of optimal paths;see[1,10,13].Lemma2.3In an optimal path inside,(i)any nonterminal C-segment has length greater than, (ii)any nonterminal C-segment is tangent to or to a terminal circle in at least one point,and(iii)no nonterminal subpath has type.Lemma2.4Let be an optimal path of type in-side.Let be the common endpoint of the-and -segments,and let be the last tangent point of the-segment with along.Then the length of the-segment between and is greater than,i.e.,.Anchored segments.A-segment or circle is called an-chored if it is tangent to or to terminal circles at two points.The terminal circles are not considered anchored. An anchored-segment is denoted by.By our general-position assumption on,there are afinite number of an-chored circles.A-segment tangent to in at least one point is denoted by.An anchored-segment or circle is-anchored if it is tangent to at two points and-anchored if it is tangent to at one point and tangent to a terminal circle at another point;see Figure2.A circular arc is called long if its length is greater than; else it is called short.A-anchored-segment is called strongly-anchored if it contains the long arc defined by the tangent points of its supporting circle with(see Fig-ure3(b)).Similarly,a-anchored-segment is called strongly-anchored if it contains the long arc defined by two tangent points of its supporting circle with and with a terminal circle(see Figure4(a)).Pockets.Let be a circle intersecting at two or more points,and let be two consecutive intersection points of with so that the short arc of joining and lies inside.If is the short arc and the turning angle2Figure2.-anchored()and-anchored()circles.of is less than,then the closed region bounded by and is called a pocket if(see Fig-ure3),and is denoted by.We define similarly the pocket when is the shorter arc.We will mostly be interested in pockets for which is tangent toat.(a)(b)Figure3.Pockets.It can be verified that the condition on the turning angle implies that a pocket does not have enough room to contain a unit ing this simple observation,we can prove the following lemma,which will be crucial for characterizing the optimal paths containing a strongly anchored-segment.In particular,the lemma implies that if a feasible path enters the interior of a pocket,then it cannot escape the pocket(see Figure3).Lemma2.5Let be a circle tangent to at that defines a pocket.If a feasible path from to enters (resp.escapes)at,then either contains the small arc of joining and,or(resp.).3Classification of Optimal PathsThe goal of this section is to prove thefirst of our main re-sults,namely a detailed characterization of optimal paths in convex polygons.We show that any optimal path is of typeor a subsequence of this form.However, not every subsequence of the above sequence can form an optimal path.The following theorem gives a more refined description of optimal path types.Recall that a segment has non-zero length by definition.In the following,we use to denote a subpath of zero length.Theorem3.1An optimal path inside is a Dubins path or has one of the types listed below.Except in case(B.i),all the-segments labeled are strongly anchored.(A)If has no nonterminal subpath,then has oneof the following types:(A.i)where,and(see Figure3(b))(A.ii)where,and(see Figure4(a))(B)If has a nonterminal subpath,then has one ofthe following types:(B.i)or(B.ii)or where,and(B.iii)where,and(see Figures4(b),(c))(c)Figure4.Examples of shortest paths.Proposition3.2The type,consisting of eight segments,does occur as an optimal path type.Proof(Sketch):Figure4(c)shows an instance of and ini-tial andfinal configurations in which a feasible path has eight segments.We can argue that no paths of the other types de-scribed in Theorem3.1are feasible,which implies that the optimal path is of the given type.The proof of Theorem3.1is based on the following lem-mas.Lemma3.3(Agarwal,Raghavan and Tamaki[1])An optimal path has at most one nonterminal subpath.Moreover,any nonterminal C-segment that precedes(resp.follows)a subpath is oriented the same way as(resp.).Next,we state a lemma,which can be proved using geo-metric perturbations similar to the ones used in[1,5].Lemma3.4(i)If an optimal path has a subpath of type ,then the-segment in that subpath is strongly-anchored.(ii)If an optimal path has a subpath of type(or )so that the-segment does not touch, then is strongly-anchored.We next characterize the optimal paths that contain a strongly-anchored-segment.Lemma3.5If an optimal path contains a strongly-anchored-segment,then is of type,, ,or a substring thereof(containing).Proof(Sketch):By assumption,.is strongly -anchored;hence its supporting circle,,has two or more intersections with.Let denote thefirst tangent pointof with along.Let be thefirst point from on —moving in the opposite sense of’s orientation—which intersects(see Figure5).It is easy to prove that such a exists,and that defines a pocket.Lemma2.5 implies that the path up to,i.e.and perhaps part of,is contained in the pocket.We can also prove that con-sists of at most two segments,so is either,,ora substring thereof.Likewise,is,,or a sub-string thereof.The result follows by noting that paths of typeare ruled out by Lemma2.3(iii).Figure5.For the proof of Lemma3.5.An optimal path containing a strongly-anchored-segment must start and end in a pocket.We state now another lemma which will be useful for the algorithm.The proof is similar to that of Lemma3.5.Lemma3.6If an optimal path contains a strongly-anchored-segment whose supporting circle is not free, then is of type,,,, or a substring thereof(containing).We now prove Theorem3.1.Proof of Theorem3.1:The proof proceeds by considering how a nonterminal-segment may appear in.If there is no nonterminal-segment in,then is of typeor a substring thereof,i.e.,is a Dubins path.Assume now that there is a nonterminal-segment in. Then such a segment belongs to a subpath of of type either or.Suppose contains a subpath of type. By Lemma3.4,the-segment in must be strongly -anchored.Thus,by Lemma3.5,is of type, or substrings(containing)thereof.In other words,is of type(A.i).If contains a nonterminal-segment but not a subpath of type,we know it must contain a subpath of type .There are two cases to consider,depending on whether the subpath is terminal.Case1:does not contain any nonterminal subpath of type.Thus,one of the-segments in any sub-path must be a terminal segment.Either is of type,(i.e.,a Dubins path),or any nonterminal-segment is also adjacent to an-segment.must then be of type ,or any substring thereof containing and a ter-minal.By Lemma2.4,the nonterminal-segments are strongly anchored.All these types of paths are covered by type(A.ii).Case2:contains a nonterminal subpath of type. By Lemma3.3,it is the only nonterminal subpath in. Thus has the form.A nonterminal-segment in must be followed by an-segment,otherwise there will be a nonterminal subpath in(Lemma2.3(iii)). Furthermore,since we have no subpath in,a nonter-minal segment must be preceded by a terminal-segment. This means or a subsequence of it.The subse-quence cannot not be empty,for otherwise the middle subpath would be terminal;nor can it be simply,as noted above.Thus,.Similarly,.If or,then the nonterminal -segment in or is strongly anchored by Lemma2.4.If both and contain an-segment,then the non-terminal subpath in is preceded and followed by an -segment.Thus,both-segments of the nonterminal subpath in touch.Indeed,otherwise contains a sub-path of type or that does not touch,which contradicts Lemma2.2.Hence,if both and contain an,is of type(B.iii).Suppose that neither nor contains an-segment. Then,the path is of type.One of the nontermi-nal-segments must touch by Lemma2.2.This-segment is also tangent to a terminal circle and is therefore-anchored.Thus the path is of type(B.i).Note that if both nonterminal-segments touch,then the path is of type which can be considered as type(B.i)or(B.iii).The last case to consider is when exactly one of or contains an-segment.Say and. The path has form where starts with an-segment.We know that must touch by Lemma2.3(ii). If also touches,then the path is of type(B.iii). Otherwise,if does not touch,then by Lemma3.4(ii), must be strongly-anchored.Lemma3.5then restricts the path to be of type(B.ii).Similarly,if and ,the path is of type(B.ii).4A Simple AlgorithmTheorem3.1can be used to obtain the following simple al-gorithm for computing an optimal path inside.We enu-merate all possible paths of types described in Theorem3.1 (however paths of type(B.iii)are handled specially).For each such path,we check whether it is feasible,compute the length if so,and then we return the shortest feasible path.In order to determine whether a path is feasible,we rely on the circle-shooting data structure by Agarwal and Sharir[2] that preprocesses in time into a data struc-ture that makes it possible to determine in time whether a given circular arc intersects.If the radius of all query circles is the same,then using fractional cas-cading[8],the data structure may be modified without af-fecting the preprocessing time,so that a query is answered in time.This immediately implies the following lemma.Lemma4.1can be preprocessed in time into a data structure that enables us to determine intime whether a given path consisting of-and-segments is feasible.To bound the running time of this simple algorithm,we must count the number of candidate paths to check.We note that once a path type is given,and the supporting cir-cles for-segments are known,there are candidate paths.These are determined by the choices of the orienta-tions for the-segments.Hence we are interested in the number of possible supporting circles for each path type. Note that there may be-anchored circles and -anchored circles.There are Dubins path candidates.For paths of type(A.i)and(B.ii),once the-anchored circle is chosen,there are choices for other support-ing circles,and hence candidate paths.Since there are-anchored circles,there are candidate paths for these two path types.For type(A.ii),the path may have up to two-anchored segments.Once their supporting circles are chosen,there are path candidates.There are potential-anchored circles.If both anchored segments are present,we have paths to check;otherwise,we have only.Paths of type(B.i)are also determined by a-anchored circle;hence there are of them as well.Paths of type(B.iii),i.e.of type, present a special problem.If we know the supporting cir-cles of the subpath,the rest of the path is determined by a pair of-anchored circles,for which there arepossibilities.Unfortunately,there is an infinite family of supporting circles for the subpath.The following re-sult by Boissonnat and Lazard[5]allows us to consider only afinite set of subpaths.Lemma4.2(Boissonnat and Lazard[5])Given two config-urations and,and two edges,of,we can com-pute3in time afinite set of paths from to of type ,where and are tangent to edges and ,respectively.This set contains all optimal paths fromto of type.Given a pair of edges and a pair of-anchored circles,tangent to and,respectively,we choose to be the configuration determined by the intersection of and and to be the configuration determined by and.Now by the above lemma,we can compute intime a constant number of candidate paths for this pair of edges and anchored circles.Doing this for all possible pairs of edges,and pairs of,we determinepath candidates of type(B.iii)in time.In summary,the simple algorithm examines can-didate paths,and for each,spends time checking feasibility,by Lemma4.1with.Therefore,the over-all running time is.5An Efficient AlgorithmIn this section we prove additional properties of optimal paths that drastically reduce the number of candidates to examine. We have already shown that we need to consider only Dubins paths and candidates for paths of type(B.i). We will show that it suffices to consider only candidate paths of type(A.i)and(B.ii),candidate paths of type (A.ii),and candidate paths of type(B.iii). Computing paths of type(A.i)and(B.ii).The paths of types(A.i)and(B.ii)contain a strongly-anchored-segment.The circle supporting defines one or two pockets that contain a point of tangency of with(see Figures3(b)and5).By Lemma2.5,we know that and must belong to these pockets.The following lemma states that there exists at most one circle with these properties. Lemma5.1For afixed pair of configurations,there exists at most one-anchored circle so that the long arc defined by the tangent points of with is free and so that and belong to the pocket(s)defined by and its tangent points with.This circle can be computed in time.By the lemma,we can compute,in time,a set ofcandidate paths of types(A.i)and(B.ii).The candi-date paths may be checked for feasibility in time. Therefore,an optimal path of type(A.i)or(B.ii)can be com-puted in time.A monotonicity property of paths.Subpaths of type occur in both(A.ii)and(B.iii)path types.In this subsection,we ignore the polygon,and study paths from to of type,with specified orientations on the-segments.Then the circles and supporting and,respectively,arefixed.Circle is determined by,its tangent point with.For each,there is at most one path of type with the specified orientations on-segments.For certain positions of,one of the segments may vanish.These positions of are called singular points.The following lemma is proved by calculus. Lemma5.2As moves along the oriented circle, increases monotonically,except at singular points.At singular points where a-segment vanishes,the path length changes by.The-segment vanishes when and have opposite orientation and are tangent.4Thus, there may be two singular points where the-segment van-ishes.If there are two,they split the circle into two arcs. Along one of the arcs,circles and properly intersect, and so is not defined there.Thus,the singular points corresponding to a vanishing-segment are the endpoints of the arc of on which the path is defined.There may be up to six singular points.See Figure6for an illustration of six singular points in a path of type.All the singular points can be computed in time.Figure6.Paths of type from to and the six singular points,,,,and on.Computing type(A.ii)paths.As mentioned in Section4, we can compute in time the feasible candidates of type(A.ii)paths with at most one-anchored segment. If the path is of type,a simple analysis givesProof:Lemma3.6directly yields that and are free. Suppose now for a contradiction that is not free.As before,we assume that the orientations are such that.Let be the tangent point be-tween and.Moving along,let be the last tan-gent point between and.Starting at and moving along,let be thefirst proper intersection point between and(see Figure??).By Lemma2.4,the length of between and is greater than,i.e..It follows that, and define a pocket(see Figure??).ByLemma2.5,this pocket contains and therefore con-tains.We know the free circle cannot be entirely in-side a pocket.The path enters the pocket at,and since is free,it is possible to escape the pocket by extend-ing segment.This contradicts Lemma2.5,establishing that is free.A symmetric argument shows that circle is free.We now introduce the following simple definition.Given a circle and a point,a point is called thefirst free point after along if and only if the circle tangent to at is free and for any,the circle tangent to at is not free(in Figure7,is thefirst free point after along).Note that could be.The circle tangent to at thefirst free point after is called thefirst free circle after along.We show that,given,,and,we can compute in time a set of candidate circles that con-tain the-segments of any optimal path from to of type.We show how to compute can-didate circles for;computing candidate circles for is similar.We identify two circles and that are the candidate circles for.Let be thefirst free circle after along. If there is no free circle after along,then and are not defined.Assume,after a possible rotation,that the line through is horizontal and is above.If the distance between and the center of is greater than,then is not defined.Otherwise,there exist two circles that are above and tangent to both and.Let be the leftmost of these two circles,and let be its tangent point with. Let be thefirst free circle after along.Note that and only depend on,,and on the line through.Figure7.Definition of and.Lemma5.4Let be an optimal path of type, and let be the line through the edge tangent to.Then is supported by or.Proof(Sketch):We prove the lemma only in the case where and properly intersect.Let be the configurationat the tangent point between and.The circle supporting the-segment is tangent to.As before,any choice of a point defines atmost one path of the form,which beginsat and ends at,and where and are tangent at.Let be the intersection point of the-and seg-ments of the optimal path.Then is a subpath ofand so it is an optimal path from to.By the mono-tonicity property(Lemma5.2),and since and are free (Lemma5.3),must be thefirst free point along aftera singular point of.Since and properly inter-sect,there are only two singular points and of,where corresponds to the vanishing of.If is thefirst free point after along,then is supported by,thefirst free circle after.If is thefirstfree point after,then we show that is supported by ,thefirst free circle after.By Lemma2.4,the arc length of from its tangent pointwith to must be at least.See Figure4(c).In otherwords,must be in the right half of(as is horizontaland is above).Therefore by definition of,the arclength of in is less than.It follows that for any point,the arclength of in is less than,so by Lemma2.3,cannot be part of the optimal path.Thus,does not belongto.So if is thefirst free point after,then it is thefirst free point after.In other words,is supported by.Lemma5.5and can be computed in time.Proof:Let be the circle of radius concentric with.Let(resp.)be the intersection point between andthe ray emanating from the center of and going through (resp.)(see Figure8).Let be the retracted polygonof with respect to a unit circle,i.e.,is the set of pointssuch that the unit circle centered at lies inside;isa convex polygonal region with at most edges,and it canbe computed in linear time.Let be thefirst intersectionpoint between and starting at and moving along.The center of is.Indeed,by definition of,the circle centered at is free,and any circle(of unit radius)centeredat a point on is not free.Similarly,the center of is thefirst intersection point between and starting atand moving ing the circle-shooting data structure by Agarwal and Sharir[2],can be preprocessedin time,so that and can be computed intime.。
