Pure mathematics 1 1 Algebraic expression 代数表达式Index laws 指数定律Indices (index的复数形式) 指数Notation 注释Simplify 化简Power 指数Base 底Exponent 指数Expression 表达式Term 项Numerator 分子Expand 展开Possible 可能Fraction 分数Bracket 括号Product 乘积Multiply 乘Collecting like terms 合并同类项Linear 一次的Diagram 图形Rectangle 长方形Square 正方形Length 长度Width 宽Side length 边长Area 面积Shade 阴影Cuboid 长方体Dimension 维Show that 证明V olume 体积Given that 已知Constant 常数Value 值Factorize 因式分解Factor 因子Opposite 相反的Completely 完全地Common factor 公因式Quadratic 二次的Form 形式Real number 实数Positive 正的Negative 负的Include 包含Surd 无理数Add 加Sum 和Take out 提取Difference 差Difference of two squares 平方差Cancel 取消，相互抵消Similarly 同样的Rational 有理的Rational number 有理数Integer 整数Square root 平方根Evaluate 求…的值Substitute 代替Calculator 计算器Square number 平方数Irrational number 无理数Decimal 小数的Expansion 展开式Never-ending 无限的Never repeat 不循环的Exact 准确的Answer 答案Manipulate 操作Denominator 分母Rationalizing denominator 分母有理化Rearrange 调整Prime 质数Work out 计算Hence 然后Fully 完全地State 陈述Solve 解决Equation 方程2 Quadratics 二次方程式Quadratic equation 二次方程Solution 解Real solution 实根Set 设置Root 根Distinct 不同的Repeated root 重根Case 情况Straightforward 简单直接的Symbol 符号Plus 加，正Minus 减，负Factorization 因式分解Shape 形状Section 部分Formula 公式Reading off 读取Coefficient 系数Necessary 必要的Significant figures 有效数字Choose 选择Suitable 适当的Method 方法Trapezium 梯形Height 高Discard 丢弃Completing the square 完全平方（配方）Frequently 经常的Useful 有用的Process 过程Original 最初的Determine 决定Otherwise 另外Function 函数Mathematical 数学上的Relationship 关系Map 映射Set 集合Input 输入Output 输出Single 单一的Notation 符号Represent 代表Domain 定义域Range 值域，范围Member 成员Define 定义Minimum 最小的Occur 发生Explain 解释Consider 考虑Graph 图像Curve 曲线Parabola 抛物线Sketch 画图Identify 确定Key 关键的Feature 特征Overall 整体的Cross 交叉，横过Axis 轴Coordinate 坐标Turning point 转折点（顶点）Maximum 最大的Since 因为Symmetrical 对称的Symmetry 对称性Line of symmetry 对称轴Half-way 位于中途的Explore 探测Technology 技术Plot 绘制Scale 刻度However 但是，不管怎样Smooth 平滑的Relevant 相关的Intercept 截距Label 标记Axes (axis的复数)坐标轴Discriminant 判别式Sign 符号Check 核实Inequality 不等式Calculate 计算Match 匹配Prove 证明Algebra 代数学Diver 跳水运动员Launch 发射Springboard 跳板Meter 米Pool 水池Second 秒Model 模型High 高的Hit 撞击Reach 达到Non-zero 非零3 Equations and inequalities 方程和不等式Simultaneous 联立的Linear simultaneous equations 一次方程组Elimination 消元法Substitution 置换Quadratic simultaneous equations 二次方程组Up to 直到，多达Make sure 确保Correctly 正确地Simplest 最简的Graphically 以图表形式As 因为Satisfy 满足Intersection 相交Simultaneously 同时地Intersect 相交Once 一次Twice 两次Result 结果，导致Produce 产生Graph paper 坐标纸Accurately 准确地Verify 验证Linear inequalities 一次不等式Set notation 集合符号Number line 数轴Overlap 重叠Separately 单独地Illustrate 图解，阐明Quadratic inequalities 二次不等式Corresponding 相应的Critical 临界的Require 要求Describe 描述Interpret 解释Region 区域，范围Coordinate grid 坐标网Dotted line 虚线Solid line 实线Vertex 顶点Vertices (vertex的复数)顶点Within 在内部，之内4 Graphs and transformations 图像和转换Cubic 三次的Cubic function 三次函数Several 几个Depend on 取决于Touch 接触Coordinate axes 坐标轴Indicate 表明，显示Reciprocal 倒数的Reciprocal function 反比例函数Such as 例如Asymptote 渐近线Approach 接近Reach 到达Quadrant 象限Point of intersection 交点Steeper 更陡峭的Eventually 最后，终于Reason 理由，原因Appropriate 恰当的Number 数量Translate 平移Transform 改变Alter 改动Subtract 减Outside 在外面Vertically 竖直地Translation 平移Vector 矢量Horizontally 水平地Direction 方向In terms of 用…来表示Slide 滑动Stretch 伸缩Scale factor 比例系数Double 两倍Halve 减半，对分Inside 在里面Triple 三倍的Reflection 反射(镜面对称) Alternatively 二选一Parallel 平行Lie on 坐落在Pass through 穿过Apply 应用Unfamiliar 陌生的，不熟悉的Specific 特殊的Origin 原点Position 位置Image 像Suggest 提议Mark 标记5 Straight line graphs 直线图像Gradient 斜率Straight line 直线Join 连接Distance 距离Formula 公式Collinear 共线的Intercept 截距Define 定义Either 两者中的任一个Condition 条件Triangle 三角形General equation 一般式Parallel 平行Perpendicular 垂直Whether 是否Quadrilateral 四边形Trapezium 梯形Right angle 直角Congruent 全等的Neither 两者都不Hypotenuse 直角三角形斜边Line segment 线段Scalene 不等边的Respectively 分别地Go through 通过6 Trigonometric ratios 三角比Cosine rule 余弦定理Miss 缺失Version 版本Exchange 交换Standard 标准Prove 证明Opposite 对边Adjacent 邻边Pythagoras’ theorem 勾股定理Letter 字母Round 四舍五入Final 最终的Coastguard 海岸警卫队Station 驻地Bearing 方位Away from 远离Appropriate 适当的Mark 标记Airport 机场Due north 正北Due east 正东Due west 正西Due south 正南Sail 航行Helicopter 直升飞机Tee 球座Flag 旗Particular 特定的Hole 孔，洞Golf course 高尔夫球场Yard 码（1码=3英尺）Tee shot 发球台Land 着陆Largest 最大的Farmer 农场Field 场地Fence 栅栏Cargo 货物Plane 平面Kilometer 千米Sine rule 正弦定理Refer to 涉及Data 数据Remain 剩余Located on 坐落于Zookeeper 动物管理员Enclosure 围场Llama 骆驼Diagonal 对角线Surveyor 检验员Measure 测量Elevation 高程，仰角Apart 相距Assumption 假设Mathematical 数学的Model 模型Obtuse 钝角Acute 锐角Isosceles 等腰的Circle 圆Radius 半径Centre 圆心Least 最小的Instead 代替Crane 吊车Anchored 固定Wreck 破坏Suspend 悬挂Cable 缆绳Rotate 旋转Level 对准Proof 证明Triangular plot 三角图Involve 涉及Trigonometry 三角函数Encounter 遇到Decide 决定Mast 桅杆In order that 为了Interfere 干扰Efficient 有效的Hiker 徒步旅行者Radar 雷达Perimeter 周长Tangent 正切Periodic 周期性的Repeat 重复的Certain 确定的Interval 间距Period 周期Undefined 无意义的Knowledge 知识Periodicity 周期性Verify 证明Variation 变化Rock pool 潮汐潭Midday 中午During 在…期间Non-exact 非精准的Significant figure 有效数字Windmill 风车Sail 帆Tower 塔Deduce 推导Dune 沙丘Realistic 现实的7 Radians 弧度Radian 弧度So far 到目前为止Probably 大概，可能Degree 度Revolution 循环Around 围绕Circle 圆Subtend 朝着Arc 圆弧Circumference 周长Convert 转换Without 没有Multiple 倍数Arc length 弧长Sector 扇形Radius 半径Contain 包含Perimeter 周长Border 边界Pond 池塘Consist 由…组成Edge 边缘Minor arc 劣弧Major arc 优弧Chord 弦Diameter 直径Template 模板Brooch 胸针Ferris wheel 摩天轮Pod 蚕茧，豆荚Estimate 估计Speed 速率Patio 露台Lawn 草坪Design 设计Earring 耳环Nearest 最近点（精确到）Segment 弓形Radii (radius的复数形式) A plot of …的一块Erect 建造Along 沿着Subtract 减Tangent 切线Ratio 比例Bound 关，围入Decimal place 小数Midpoint 中点Semicircular 半圆Drawer 抽屉Handle 把手Difference 差Badge 徽章Equilateral 等边的Railway 铁路Track 轨迹Prism 三棱镜Attempt 尝试Mistake 错误8 Differentiation 微分Gradient 斜率Constantly 不断地Although 然而Comment on 对…评论Copy 抄写，复制Complete 完成Table 表格Hypothesis 假设Derivative 导数Principle 原理Detail 细节Account 解释Originate 起源Formalize 确定，形成Approach 方式，方法Limit 极限Tend to 趋向Gradient function 斜率函数Evaluate 求…的值Fixed value 定值Limiting value 定值Definition 定义One-at-a-time 一次一个Turning point 转折点（顶点）Slope 斜率Disappear 消失Polynomial 多项式Normal 切线First order derivative 一阶导数Second order derivative 二阶导数Rate of change 变化率Respect to 关于Displacement 位移Acceleration 加速度Local 局部的9 Integration 积分Reverse 相反的Differ 不同Integrate 求积分Integral 积分Indefinite 不确定的Indefinite integral 不定积分Elongated 拉长的，伸长的Arrow 箭Fire 射击Castle 城堡Drop off 下降Cliff 悬崖Cyclist 骑行者Pure mathematics 2 1Algebraic methods 代数方法Division 除法Dividing polynomial 多项式除法Finite 有限的Whole number 整数Long division 长除法Quotient 商Remainder 余数Factor theorem 因式定理Remainder theorem 余数定理Logical 逻辑的Structured 有组织的Argument 论据Statement 命题Conjecture 猜想Previously 预先Establish 建立Deduction 推导Desired 想要的Conclusion 结论Odd number 奇数Demonstration 示范，演示Even number 偶数Identical 完全相等的Identity 恒等式Parallelogram 平行四边形Rhombus 菱形Congruent 全等的Exhaustion 穷举法Consecutive 连续的Square number 平方数Break into 拆分Is suited to 适合于Disprove 反驳Counter-example 反例Sufficient 充分的Prime number 质数Divisible 可整除的Either … or…二者择一的Cube number 立方数Hold 有效Claim 宣称Opposite edge 对边Hexagon 六边形Regular hexagon 正六边形Side length 边长Reason 原因2Coordinate geometry in the (x,y) plane 解析几何Bisector 二等分线Perpendicular bisector 中垂线Averaging 求平均值Endpoint 端点Circumcentre 外心Equidistant 等距的Fixed point 定点Vector 向量Property 性质Unique 独一无二的Circumcircle 外接圆3Exponentials and logarithms 指数和对数Exponential 指数的Decrease 减小Increase 增加Smooth 光滑的，平滑的Increasing function 增函数Decreasing function 减函数Justify 证明Logarithms 对数Specific 特定的Button 按钮Typically 典型的Natural logarithms 自然对数Instance 实例Multiplication law 乘法定律Division law 除法定律Power law 指数定律Recognize 识别Attention 注意Condition 条件Complicated 复杂的Whenever 无论何时Convenient 方便的Suppose 假设Notice 注意Particular 特别的4The binomial expansion 二项式展开Binomial 二项式Pascal’s triangle 杨辉三角（帕斯卡三角形）Immediately 直接地Pattern 图案Adjacent 相邻的Investment 投资Interest rate 利率Annum 年，岁Approximation 近似值Ignore 忽略Factorial notation 阶乘Combination 组合Superscript 上标Subscript 下标Probability 可能性Toss 投Likelihood 可能性Ascending powers 升幂Individual 个别的Estimation 估值Engineering 工程学Science 科学Percentage error 百分误差Microchip 微型集成电路片Faulty 有缺点的Chip 芯片Restrict 限制Achieve 达到School fair 学校园游会Prize 奖赏Digit 数字Display 显示5Sequences and series 数列和级数Arithmetic sequence 等差数列Arithmetic progression 等差数列Common difference 公差Arithmetic series 等差级数（等差数列前n 项求和）Exceed 超过Inclusive 包含的Stick 棒子Pentagon 五角形Geometric sequences 等比数列Geometric progression 等比数列Common ratio 公比Converge 收敛Alternating sequence 交错数列Million 百万Geometric series 等比级数（等比数列前n项求和）Sum to infinity 无限项求和Divergent 发散的Convergent 收敛的Recurring 循环的Sigma notation 求和符号Capital 首都，大写字母Signify 表示Recurrence relations 递推关系Previous term 前一项First term 初项Generate 生成，产生Periodic sequence 周期数列Period 周期Salary 薪水Profit 利润Predict 预言Annual 年度的Business 商业Financial 金融的Advisor 顾问Fold 折叠Thickness 厚度Unrealistic 不切实际的Investor 投资人Account 账户Thereafter 以后Deposit 存款，定金Wage 工资Rise 上升Gear 齿轮Successive 连续的Intermediate 中间的Valuable 有价值的Commission 佣金Insurance 保险Policy 政策Prospector 勘探者Drill 钻孔Subsequent 随后的Available 可获得的Payment 报酬Virus 病毒Infect 传染Diagnose 诊断Overfish 过度捕捞Chess 象棋Chessboard 棋盘Sponsored 赞助的Polygon 多边形Appointment 约会，任命6Trigonometric identities and equations 三角恒等式和方程Unit circle 单位圆Anticlockwise 逆时针Quadrant 象限Equivalent 相等的Equilateral triangle 等边三角形Isosceles right-angled triangle 等腰直角三角形Identity 恒等式Reflex 优角(大于180度，在第三、四象限)Principal value 主值Inverse trigonometric function 反三角函数Justification 理由7Differentiation 微分Strictly 严格地Interval 区间Stationary point 驻点Local maximum 局部最大Greatest value 最大值Local minimum 局部最小Least value 最小值Point of inflection 拐点，反曲点Immediate 最接近的Vicinity 邻近，附近Second derivative 二次求导Rate of change 改变的快慢Convex 凸Concave 凹Establish 建立，证实Liter 升Instant 瞬间Tank 水槽Cuboid 长方体的Sheet 薄片Metal 金属Sphere 球体Displacement 位移Cylinder 圆柱体Perimeter 周长Semicircular 半圆的Semicircle 半圆Frame 框架Split 分离，分开Motion 运动Damped 阻尼Spring 弹簧Bent 弯的Biscuit 饼干Tin 罐头Close-fitting 紧贴的Lid 盖子Thin 薄的，瘦的Wastage 损耗Obtain 获得Percentage 百分比Store 储存Capacity 容量Container 容器Calculus 微积分学8Integration 积分Definite integral 定积分Indefinite integral 不定积分Whereas 反之，然而Upper limit 上限Lower limit 下限Square bracket 中括号Magnitude 大小Negligible 可忽略的Straddle 跨坐Unless 除非Complicated 复杂的Trapezium 梯形Trapezium rule 梯形法则Beneath 在…下面Strip 条，带Boundary 边界Adjacent 相邻的Improve 改善Accuracy 精确度Approximation 近似值Underestimate 低估Overestimate 高估Compare 比较Pure mathematics 3 Common multiple 公倍数Improper fraction 假分数Partial fractions 部分分数Degree 次数Modulus function 模函数Absolute value 绝对值Argument 辐角Set notation 集合符号Piecewise-defined function 分段函数Composite function 复合函数Inverse function 反函数Secant 正割Cosecant 余割Cotangent 余切Interval 区间Symmetry 对称性Symmetrical 对称的Chord 弦Inverse trigonometric function 反三角函数Addition formulae 加法公式Compound-angle formulae 复合角公式Double-angle formulae 二倍角公式Round 四舍五入Exponential function 指数函数Natural logarithms 自然对数Trend 趋势Outlier 极值Chain rule 链式法则Product rule 乘法法则Quotient rule 除法法则Continuous 连续的Fixed point iteration 定点迭代Successive 连续的Converge 收敛Staircase diagram 梯形图Cobweb diagram 网状图Diverge 发散Pure mathematics 4 Contradiction 反驳Assert 主张Falsehood 虚假Negation 反论Prime number 质数Split 分解Separate 独立的Parametric equation 参数方程Variable 变量Parameter 参数Revolution 循环Plot 绘图Valid 有效的As long as 只要Condition 条件Accurate 精确的Ascending 上升的Approximation 近似值Implicit differentiation 隐函数微分Explicitly 明确的Implicit 隐含的Rate of change 变化率Hemisphere 半球Cylindrical 圆柱形的Conical 圆锥形的Concave 凹Convex 凸Integrand 被积函数Integration by substitution 换元积分法Integration by part 分部积分法Polynomial 多项式Separating the variables 分离变量General solution 通解Boundary condition 边界条件Directed line segment 有向线段Parallelogram 平行四边形Unit vector 单位向量Column vector 列向量Position vector 位置矢量Scalene 不等边的21Clockwise 顺时针Anticlockwise 逆时针Coplanar 共面的Parallelepiped 平行六面体Trisect 三等分Hexagon 六边形Regular hexagon 正六边形Direction vector 方向向量Anchor 固定Dot product 点乘22。
iEffectiveness of Personalized Ventilation as a Control Measure forRespiratory Disease Transmission during Close ContactByJingcui XUA Thesis Submitted toThe Hong Kong University of Science and Technologyin Partial Fulfillment of the Requirements forthe Degree of Doctor of Philosophyin Mechanical EngineeringAugust 2020, Hong KongKUST Library eproduction is prohibited without the author’s prior written consentAcknowledgementsI would like to express my sincerest thanks to my supervisor, Prof. Christopher Yu Hang Chao, for giving me the opportunity to study for my PhD degree at The Hong Kong University of Science and Technology. During my PhD study, he gave me lots of academic suggestions and support in my research and presentation. His confidence and enthusiasm impressed and inspired me deeply.I would like to express my deep thanks to Prof. Huihe Qiu for serving as my co-supervisor in the last two years of my study.I would like to show my appreciation to the members of Prof. Chao’s research team. Dr. Sau Chung Fu gave me many useful suggestions and patiently taught me to express ideas during my study. Dr. Chan, Dr. Leung and Dr. Tso also gave me much useful advice about the research and improvement of writing. Their advice has been very helpful to improve my research and the quality of my study.I would also like to thank the communication tutors, Graham Young and Mark Ellwood. The quality of my thesis and papers was much better following their comments. Besides, Mr. Young helped me a lot to improve my spoken English. In addition, I would like to thank technicians and staff from the Department of Mechanical and Aerospace Engineering for helping me so much.I express my sincere thanks to my family for their support of my study and life. I would like to thank my friends, for sharing my pleasure and sorrow. Especially, thanks to Cunteng Wang, who helped me a lot.This work has been supported by ITS/410/16FP and CRF C7025-16G.ivTable of ContentsTitle Page (i)Authorization Page (ii)Signature Page (iii)Acknowledgements (iv)Table of Contents (v)List of Figures (x)List of Tables (xiv)Nomenclature (xv)Abstract (xviii)Chapter 1 Introduction (1)1.1 Background (1)1.2 Literature review (4)1.2.1 Disease transmission during close contact (4)1.2.1.1 The Short-range airborne route (4)1.2.1.2 The large-droplet route (5)1.2.1.3 The fomite route (6)1.2.2 Dilution strategy of total volume ventilation for airborne droplets (7)1.2.3 The development of personalized ventilation (9)1.2.3.1 Performance of Personalized ventilation in thermal comfort and energy saving (9)1.2.3.2 Dynamic airflow for personalized ventilation (10)1.2.3.3 Performance of Personalized ventilation in the control of airborne diseasetransmission (11)1.2.4 Head angle and relative orientations between the healthy person and infected persons (14)1.2.5 Effect of wearing face masks (15)v1.2.6 Infection risk assessment for respiratory disease transmission (16)1.3 Objectives (19)Chapter 2 Performance of airflow distance from personalized ventilation on personal exposure to airborne droplets from different orientations (20)2.1 Introduction (20)2.1.1 Objectives (20)2.2 Experimental Instruments and Methods (20)2.3 Results and discussion (30)2.3.1 Size distribution of droplets generated (30)2.3.2 Personal exposure and exposure reduction (31)2.3.2.1 PV at a distance of 0.2 m from the HP (31)2.3.2.2 PV at a distance of 0.5 m from the HP (34)2.3.2.3 Personal exposure with constant PV flow with different velocities (38)Chapter 3 Short-range bioaerosol deposition and inhalation of cough droplets and performance of personalized ventilation (41)3.1 Introduction (41)3.1.1 Objectives (41)3.2 Experimental Instruments and Methods (42)3.2.1 Bioaerosol generation (42)3.2.2 Experimental setup (45)3.2.3 Measurement of bioaerosol deposition on the HP manikin (46)3.2.4 Measurement of inhalation of bioaerosol (48)3.2.5 Measurement of personal exposure (49)3.2.6 Velocity of cough cloud jet (50)3.3 Results (51)3.3.1 Short-range bioaerosol exposure (51)vi3.3.1.1 Short-range bioaerosol deposition on the HP without PV (51)3.3.1.2 Personal exposure of the HP (55)3.3.1.3 Inhalation of bioaerosol by the HP (58)3.3.2 Effect of PV (59)3.3.2.1 Bioaerosol deposition on the HP with PV (59)3.3.2.2 Inhalation of bacteria by the HP with PV (64)3.3.2.3 Personal exposure of the HP with PV (64)3.3.1 Deposition density on the HP’s surfaces (65)3.4 Discussion (68)Chapter 4 The effect of head orientation and personalized ventilation on short-range bioaerosol deposition of cough droplets (70)4.1 Introduction (70)4.1.1 Objectives (70)4.2 Experimental Instruments and Methods (71)4.2.1 Bioaerosol generation (71)4.2.2 Experimental setup (73)4.2.3 Measurement of bioaerosol deposition on the HP manikin (76)4.2.4 Measurement of personal exposure (78)4.3 Results (79)4.3.1 Short-range bioaerosol exposure (79)4.3.1.1 Deposition on the HP without PV (79)4.3.1.2 Personal exposure without PV (86)4.3.2 Effect of PV (88)4.3.2.1 Deposition on the HP with PV (88)4.3.2.2 Personal exposure with PV (98)vii4.4 Discussion (99)Chapter 5 Infection risk assessment of the fomite route during close contact (101)5.1 Introduction (101)5.1.1 Objectives (101)5.2 Calculation of exposure via fomite route (101)5.2.1 A Markov Chain model (101)5.2.2 The Markov matrix (103)5.2.3 Rates and probabilities (104)5.3 Dose-infection response model (105)5.4 Case: Bacteriophage experiment (106)5.4.1 Model parameterization (106)5.4.1.1 Pathogen loads (106)5.4.1.2 Rates of transfer to the hands and mucous membranes (106)5.4.1.3 The dose by the fomite route (108)5.4.2 Effect of a face mask (109)5.4.3 Effect of different touch frequency (110)5.4.4 Results and discussion (111)5.4.4.1 Effect of PV flow, head orientation and wearing a face mask (111)5.4.4.2 Effect of different touch frequency (112)Chapter 6 Conclusions and suggestions for future study (114)6.1 Conclusion (114)6.1.1 Performance of airflow distance from personalized ventilation on personal exposure toairborne droplets from different orientations (114)6.1.2 Short-range bioaerosol deposition and inhalation of cough droplets and performance ofpersonalized ventilation (115)viii6.1.3 The effect of head orientation and personalized ventilation on short-range bioaerosoldeposition of cough Droplets (116)6.1.4 Infection risk assessment of the fomite route during close contact (116)6.2 Suggestions for future work (117)6.2.1 The effect of diameter of PV terminal (117)6.2.2 Comparison of pathogens deposited on the healthy person and inhaled by the healthyperson caused by coughing, talking and sneezing (117)6.2.3 Rotation of the infected person’s head (117)6.2.4 Correlation between exhaled droplets and personalized ventilation airflow (118)References (119)Publication list (134)ixList of FiguresFigure 2.1 Schematic of the personalized ventilation system (23)Figure 2.2 Examples of dynamic PV airflow of period of (a)1s and (b) 5 s measured at the PV outlet (24)Figure 2.3 (a) The schematic setup for the PIV measurement; (b) the experimental setup for the PIV measurement (26)Figure 2.4 (a) Experimental design in the environmental chamber. The IP (Infected Person) facing the HP at different orientations of π/8, 2π/8, 4π/8, 6π/8 and π; (b) Schematic of the experimental set-up in the environmental chamber at π orientation; (c) Illustration of the experimental setup with the IP at the orientations of 4 π/8 and π under PV at a distance of 0.5 m from the HP (29)Figure 2.5 Size distribution of droplets generated by the Collison nebulizer. In the vertical axis, df = dN/N, where dN means the number concentration (#/cm3) in each size range and N is the total number concentration of droplets in the range of 0.3-10 μm. (31)Figure 2.6 HP’s exposure with standard deviation and (b) exposure reduction with the PV at a distance of 0.2 m from the HP (34)Figure 2.7 Illustrative diagram of PV flow as a free jet flow (34)Figure 2.8 (a) HP’s exposure with standard deviation and (b) exposure reduction with the PV at a distance of 0.5 m from the HP (36)Figure 2.9 Droplet motions and the correlated velocity magnitude contour in the inhalation zone influenced by (a) constant PV flow and (b) 1s-period PV airflow at orientation of π/8 orientation. Droplets were released from the Collison nebulizer at time zero. (37)Figure 2.10 Exposure influenced by different PV velocities in the inhalation zone with (a) the IP at the orient ation of π/8 and (b) the IP at the orientation of 2π/8 (40)Figure 3.1 Preperation of E. coli resuspended in the simulated saliva solution (43)Figure 3.2 Schematic diagram of the cough generator: (a) air and liquid control system; (b-c) the nozzle in the infected person’s mouth (45)Figure 3.3 The schematic of the experimental setup in the chamber (46)Figure 3.4 Sampling measurements (a) at the HP’s face and (b) body surfaces (47)Figure 3.5 The cultivation method for E. coli (47)Figure 3.6 Schematic showing the measurement of bioaerosol inhalation by SKC Biosampler . 49xFigure 3.7 Schematic of velocity measurement of the cough air jet (51)Figure 3.8 (a) Total number of bacteria deposited on the HP (the face and body surfaces) (b) Number of bacteria deposited on the HP’s face and body surfaces at diff erent distances from the IP (54)Figure 3.9 Number of bacteria deposited on individual parts of the HP’s face and body surfaces at different distances from the IP (55)Figure 3.10 Average aerosol concentration time profiles of the HP exposed to the cough droplets from the IP at a distance of (a) 0.5 m, (b) 0.8 m and (c) 1.2 m under the cases without PV 57 Figure 3.11 Personal exposure of the HP influenced by the IP at a distance of 0.5 m, 0.8 m, and1.2 m without PV (58)Figure 3.12 Inhalation of bacteria of the HP measured by SKC Biosampler at different distances from the IP (58)Figure 3.13 Total number of bacteria deposited on the HP including face and body surfaces with and without PV at different distances from the IP (61)Figure 3.14 Number of bacteria deposited on the HP’s face and body surfaces with and without PV at a distance of (a) 0.5 m, (b) 0.8 m, and (c) 1.2 m from the IP (62)Figure 3.15 Number of bacteria deposited on individual parts of the HP’s face and body surfaces with and without PV at a distance of (a) 0.5 m, (b) 0.8 m, and (c) 1.2 m from the IP (63)Figure 3.16 Inhalation of bacteria of the HP with and without PV measured by SKC Biosampler at different distances from the IP (64)Figure 3.17 Personal exposure of the HP influenced by the IP at a distance of 0.5 m, 0.8 m, and1.2 m with and without PV (65)Figure 3.18 Deposition density on the HP’s (a) body and (b) face surfaces with and without PV at different distances from the IP (66)Figure 3.19 Deposition density on the HP’s individual part with the IP at a distance of (a) 0.5 m,(b) 0.8 m and (c) 1.2 m (68)Figure 4.1 The cultivation method of the host E. coli (72)Figure 4.2 The preparation of bacteriophage titration solution (73)Figure 4.3 The schematic of experimental setup in the chamber (75)Figure 4.4 The diagram of the cases of L12 and L24 for illustration (75)xiFigure 4.5 The sampling location (a) on the HP’s face and body, (b) the detail information on the face (76)Figure 4.6 The cultivation method for bacteriophage T3 (77)Figure 4.7 The number of viable bacteriophage deposited on the HP’s (a) body and (b) face under cases of L24-H24, on the HP’s (c) body and (d) face under cases of H0-R24 (83)Figure 4.8 The number of viable bacteriophage deposited on the individual parts of the HP without PV under cases of (a) L24-H24 and (b) H0-R24 (84)Figure 4.9 The number of bacteriophage deposited on the mucous membranes (eyes, nose and mouth) without PV flow under cases of (a) L24-H24, and (b) H0-R24 (85)Figure 4.10 The total number of bacteriophage deposited on the HP without PV flow under cases of (a) L24-H24, and (b) H0-R24 (86)Figure 4.11 Personal exposure of the HP without PV under cases of (a) L24-H24, and (b) H0-R24 (87)Fi gure 4.12 The number of bacteriophage deposited on the HP’s (a) body and (b) face under cases of L24-H24; and on the HP’s (c) body and (d) face under cases of H0-R24 with and without PV flow (91)Figure 4.13 The number of bacteriophage deposited on the individual parts of the HP under the cases of (a) L24, (b) L12, (c) H0, (d) H12, (e) H24, and (f) R12 with and without PV (94)Figure 4.14 The number of bacteriophage deposited on the mucous membranes (eyes, nose and mouth) under cases of (a) L24-H24, and (b) H0-R12 with and without PV (96)Figure 4.15 The total number of bacteriophage deposited on the HP under cases of (a) L24-H24, and (b) H0-R12 with and without PV (97)Figure 4.16 Personal exposure of the HP under cases of (a) L24-H24, and (b) H0-R24 with and without PV (99)Figure 5.1 A diagram of the Markov chain model of fomite transmission. The directional arrow indicates the direction of transfer from Item i to Item j. λij is the first-order (exponential) rate of transfer from Item i to Item j. (103)Figure 5.2 Infection risk of the fomite route under different factors of a surgical mask, PV and the infected person’s head orientation; ‘H0’ means the infected person and the healthy person has an upright face-to-face situation; ‘Orientation-L24’ means the infected person lower the head at 24° in a face-to-face situation with the healthy person; ‘H0-PV’ means infected person andxiithe healthy person has an upright face-to-face situation and the healthy person uses PV; ‘H0-mask’ means the infected person and healthy person in an upright face-to-face situation while the healthy person wears a surgical mask. (112)Figure 5.3 Infection risk of the fomite route influenced by different touch frequency on the mucous membranes (113)xiiiList of TablesTable 2.1 Summary of velocity and turbulence intensity of constant and dynamic PV flows (24)Table 3.1 The velocity of cough cloud around the face, chest, left shoulder and right shoulder on the HP without PV (53)Table 5.1 Model inputs for calculation of infection risk (108)Table 5.2 Literature data used for infection risk assessment [151] (109)xivNomenclatureLetterA Surface area cm2 A sampling Surface area of the silicone sheets cm2 C0Average background concentration #/cm3 C s(t) Real-time concentration #/cm3 dN Number concentration in each size range #/cm3D m The dose for the fomite route #E body Total Pathogens on the HP’s clothes#/hour E face Total Pathogens on the HP’s face#/hour E(t1, t1+T) Personal exposure from t1 to t1 + T (#/cm3)*s E off Exposure without PV (#/cm3)*s E on Exposure with PV (#/cm3)*s IR Infection risk - N Total number concentration of droplets (#/cm3) N2The steady-state value of pathogens on the HP’s face# N3The steady-state value of pathogens on the HP’s clothes#Total number of deposited viable E. coli/bacteriophage CFU (Numberdeposition)samplingn Time steps - P Matrix - P(n)P multiplied by itself n times -xv(n)Probability of a pathogen from Item i to Item j after n× Δt- Pijtime steps.- p ii Probability for the pathogen remaining in Item i after timeΔtp ij Probability for the pathogen to move from Item i to Item j-after time Δtr Fitting parameter - Δt Time interval s AbbreviationADS Albumin-Dextrose-Saline - ATCC American Type Culture Collection - CCD Charge-Coupled Device - CFD Computational Fluid Dynamics - CFU Colony Forming Unit - DnV Downward Ventilation - DV Displacement Ventilation - E. coli Escherichia coli - HP Healthy Person - IAQ Indoor Air Quality - ID50Median Infective Dose - IP Infected Person - MV Mixing Ventilation -xviOPS Optical Particle Sizer - PE Personalized Exhaust - PFU Plaque Forming Unit - PIV Particle Image Velocimetry - PV Personalized Ventilation - RMP Round Movable Panel - SARS Severe Acute Respiratory Syndrome - TCID50Median Tissue Culture Infective Dose - TSB Tryptone Soya Broth - UFAD Under-Floor Air Distribution - VDG Vertical Desk Grille -Greek symbolsεExposure reduction -minute-1λij The first-order (exponential) rate of transfer from Item i toItem j.λi Sum of the probability that a pathogen leaves Item i. minute-1xviiEffectiveness of Personalized Ventilation as a Control Measure for Respiratory DiseaseTransmission during Close ContactBy Jingcui XUDepartment of Mechanical and Aerospace EngineeringThe Hong Kong University of Science and TechnologyAbstractDue to outbreaks of respiratory disease, the control and prevention strategy of respiratory disease transmission has become a global issue and concern. In indoor environments, a healthy person (HP) has a high possibility of being infected when facing expiratory droplets from an infected person (IP) during close contacts. This work investigated experimentally bioaerosol deposition and inhalation by the HP and the control of disease transmission by using personalized ventilation (PV) during close contact. Two thermal manikins were used to represent the HP and IP. A PV system was designed and built. Benign Escherichia coli and bacteriophage were used to represent the bacterial and viral pathogens in expiratory droplets, respectively. Firstly, the effect of distance between the PV and the HP on exposure of the HP to airborne droplets from the IP in different orientations was studied. With a short distance between the HP and the PV, both constant and dynamic PV airflow patterns can effectively reduce personal exposure of the HP. Secondly, bioaerosol deposition and inhalation by the HP and the effect of PV on the HP were investigated. By optimizing the velocity of PV flow with respect to the distance between the HP and IP, the bioaerosol deposited on the HP’s face and body, and then inhaled, can be reduced by around 98%, 85% and 100%, respectively. Thirdly, the effect of head orientations of the IP and the performance of PV on bioaerosol deposition on the HP during close contact was studied. Different orientations of the IP's head result in significantly different effects on deposition on the HP. PV flow reduced the bioaerosol deposition on the HP for most cases, and the reduction was between 51.7% andxviii94.5% compared to each case without PV. The results show that during close contact PV is an effective method to control the droplet spray on the mucous membranes, droplet deposition, and inhalation by the exposed person.xixChapter 1Introduction1.1BackgroundDue to the outbreaks of severe acute respiratory syndrome (SARS), H1N1 influenza, Meningitis, Pertussis, Diphtheria, and recent COVID-19 pandemic, the control and prevention strategy of respiratory disease transmission has become a global issue and concern [1, 2]. Normally, people spend most of their time in indoor environments where exposed persons have a high possibility of being infected when facing expiratory activities (breathing, talking, coughing, and sneezing) from infected persons. Many pathogen-laden droplets, as the major source of disease transmission, are generated by infected persons [3-5]. For coughing and sneezing, the higher initial velocity and droplet concentration poses a bigger threat for exposed persons. Despite breathing and talking with a lower initial velocity and lower concentration of pathogen-laden droplets, their frequency is higher.These respiratory activities from infected persons pose a high threat for exposed persons as some exhaled droplets directly spray on their mucous membrane over a short distance, called large-droplet route [6]; some are inhaled by susceptible persons via short-range or long-range airborne transmission [7]; some droplets deposit on the exposed persons or environmental surfaces. Then, they may be transferred to people’s mucous membranes of eyes, mouth and nose via hand touching. This is called fomite transmission [8]. In addition, the distance of 1-2 m between exposed persons and infected persons distinguishes the short-range route and long-range route. In the long-range route (beyond 2 m), the exhaled droplet nuclei influenced by the background ventilation are dispersed in the indoor environment. The exposed persons can be infected by the long-range airborne route and distant fomite route. During the short-range route (within 1-2 m), the exposed person has much higher infection risk due to the high concentration of the droplets during close contact, which is defined as any full of partial face-to-face interaction of two people at a distance of no more than 1.5 m [9]. In a close contact situation, an exposed person could be infected by the short-range airborne route, large-droplet route and fomite route [7, 10].1Many respiratory diseases are believed to be transmitted during close contact [11, 12] where exposure of the nearby persons to airborne droplets is substantially increased when the infected person is at a distance within 1-2 m. The inhaled airborne droplets are able to penetrated the lower respiratory tract [13, 14], probably resulting in lower respiratory tract infection. Within the short distance, there is also a high possibility that large droplets can directly deposit on the mucous membranes and cause infection. Attention also needs to be paid to the deposited pathogens on the clothing and body of the exposed persons, which are likely to be transmitted to mucous membranes via hand touching. The frequency of touching his/her own clothes or body surfaces is higher than other environmental surfaces [15, 16]. Moreover, the pathogens deposited on the surfaces can survive from a few hours to several weeks [17, 18]. This means that the transmission via touching the clothes and body would last for a long period if there is no proactive surface disinfection. Meanwhile, the relevant studies about the deposition on the exposed person are still limited.The exhaled pathogen-laden droplets are the major source of respiratory infection. The velocity direction of exhaled pathogen-laden droplets is mainly determined by the orientation of the head. In reality, there is a high probability for people to move their heads in different orientations at any time. Different directions of exhalation result in a variation of inhalation and deposition for the exposed person. It is important to find out how the head orientation affects the deposition and inhalation quantitatively during close contact.Personalized ventilation (PV) system is suggested to be a potentially effective method to reduce the infection risk of airborne infectious transmission [19]. PV can supply fresh and clean air directly to the inhalation zone of users to make a clean microenvironment. It was found that a desk-based PV can reduce the 41%-99% intake fraction of cough droplets for the exposed person [20]. It can also reduce the peak aerosol concentration and shorten the exposure time [21]. Lipczynska et al. [22] showed that the system of PV combined with a chilled ceiling could substantially reduce the concentration of contamination and improve indoor air quality at workstations, while satisfying the requirement of thermal comfort. However, some studies [23, 24]showed that there was a possibility for the PV performance to be influenced by background2ventilation systems and indicated that PV could worsen the air quality in the inhalation zone in some test cases. Although it is suggested that PV can supplement the traditional ventilation system, most works focus on the performance of PV flow on the long-range airborne transmission, and few researchers have investigated the performance of PV flow on the user exposed to an infected person during close contact.31.2Literature review1.2.1Disease transmission during close contact1.2.1.1The Short-range airborne routeAirborne disease transmission is prevalent in public transport [25-29], airplanes [30], and other indoor environments [31-33]. The disease transmission route can be divided into the short-range airborne route and long-range airborne route based on the distance between an infected person and an exposed person. For the long-range airborne route, the exhaled airborne droplet nuclei in indoor environments can remain in the air for a long time and are strongly affected by the ventilation flow, thermal plume of a human being, and respiratory flow [34, 35]. In contrast to the long-range airborne route, for the short-range airborne route, the exhaled fine droplets (< 10 μm in diameter) from the infected persons can be directly inhaled by the exposed persons. The inhaled airborne droplets of such a small size are easy to penetrate into the lower respiratory tract [13, 14] and probably cause lower respiratory infection. Larger droplets can also be inhaled and possibly deposited on the upper respiratory tract. Thesis is a substantial increase in exposure for the exposed persons when the infected persons are within a distance of 1-2 m.Exposure caused by the short-range airborne route is much higher than that of the long-range airborne route. Liu et al. [36] investigated the exposure of an exposed person to airborne droplets from an infected person at a distance from 0.5 m to 3.0 m. Results showed a substantial increase in exposure to airborne droplets exhaled by the infected person when the exposed person is within a distance of 1.5 m. Chen et al. [37] indicated that, over a short distance, exposure caused by the short-range airborne route is higher than that of a large-droplets route and a long-range airborne route.41.2.1.2The large-droplet routeIn the large-droplet route, pathogen-laden droplets directly deposit on the mucous membranes of eyes, nose and mouth of an exposed person within a distance of 1-2 m from the infected person. The velocity of breathing, talking, coughing, and sneezing is around 1-4.74 m/s [35, 38-41], 3.6-4.6 m/s [42], 6-52 m/s [42-46], and 4.5-104.6 m/s [40, 47, 48], respectively. The distance travelled by the exhaled droplets is determined by the exhalation velocity. The high velocity results in the droplet impingement on the mucous membranes of exposed persons because of the high inertia. Some studies indicated that the large-droplet route has been considered as a primary transmission route for some respiratory infectious diseases, such as influenza [49], SARS [50], and MERS [51]. Brankston et al. [49] indicated that the large-droplet route and direct physical contact are the primary factors resulting in influenza transmission. By analysing the infection risk probability using a mathematical model in an aircraft cabin, Lei et al. [52] demonstrated that the large-droplet route is one of the significant routes for transmission of influenza and SARS.However, there is a controversy about the dominant role of large-droplet route on respiratory disease transmission. Chen et al. [37] demonstrated that the short-range airborne route was more important than the large-droplet route. Lindsley et al. [5] indicated that there is a higher concentration of pathogens in small droplets than that in large droplets. This means that there are more pathogens via the short-range airborne route than the large-droplet route. Even though Atkinson et al. [53] indicated that the infection probability caused by large-droplet route is significant for sneezing, in reality, the low frequency of sneezing linked with the downward exhaled direction make it difficult for droplets to deposit on the mucous membranes. Furthermore, the projected surface area of mucous membranes is 10-20 cm2, which only accounts for 0.86-1.72% of the surface area of the head with an approximate value of 0.116 m2 [54]. Thus, more studies are needed to investigate and compare the importance of the short-range airborne route and large-droplet route.5。
大一数学知识点英文Mathematical Concepts in Freshman YearMathematics is an essential subject that plays a significant role in various fields. It provides a logical and systematic approach to problem-solving. In this article, we will explore some important mathematical concepts that are typically covered in a freshman year curriculum.1. Number SystemsNumber systems form the foundation of mathematics. In freshman year, students learn about different types of numbers, such as natural numbers, whole numbers, integers, rational numbers, and real numbers. Understanding the properties and relationships between these numbers is crucial for further mathematical study.2. Algebraic ExpressionsAlgebraic expressions involve variables, constants, and operations. Students in their freshman year learn how to simplify and evaluate expressions, solve equations, and manipulate algebraic expressions using various techniques like factoring, expanding, and solving linear and quadratic equations.3. Functions and GraphsFunctions describe relationships between inputs and outputs. Freshman students are introduced to different types of functions, such as linear, quadratic, exponential, and logarithmic functions. They learn to graph functions on a coordinate plane and analyze their properties, including domain, range, intercepts, and transformations.4. TrigonometryTrigonometry deals with the relationships between angles and sides of triangles. Freshman students learn about trigonometric ratios (sine, cosine, and tangent) and their applications in solving right-angled triangles. They explore concepts like trigonometric identities, equations, and the unit circle.5. DifferentiationFreshman year introduces the concept of differentiation, which is a fundamental tool in calculus. Students learn how to find derivatives of functions using differentiation rules, including power rule, product rule, quotient rule, and chain rule. They apply these principles to analyze rates of change and solve optimization problems.6. IntegrationIntegration is the reverse process of differentiation and is also a key concept in calculus. Students learn various integration techniques, such as substitution, integration by parts, and partial fractions. They apply integration to find areas, volumes, and evaluate definite integrals.7. Probability and StatisticsProbability and statistics play a crucial role in many real-life applications. Freshman students learn the basics of probability, including calculating probabilities of events, understanding permutations and combinations, and exploring concepts like expected value and standard deviation. They also study data analysis, including data representation, measures of central tendency, and dispersion.8. Matrices and Systems of EquationsMatrices are rectangular arrays of numbers, and they have applications in various fields, including engineering and computer science. Freshman students learn about matrix operations, determinants, and inverse matrices. They also study systems of linear equations and solve them using matrix methods, such as Gaussian elimination.These are just a few examples of the mathematical concepts typically covered in a freshman year. Building a strong foundation in these concepts is essential for further advancements in mathematics and related disciplines. By understanding and applying these concepts, students develop critical thinking skills and enhance their problem-solving abilities.。
数学专业英语词汇代数局部1. 有关数*算add，plus 加" subtract 减"difference 差"multiply, times 乘"product 积"divide 除"divisible 可被整除的"divided evenly被整除"dividend 被除数，红利"divisor 因子，除数"quotient 商"remainder余数"factorial 阶乘"power 乘方"radical sign, root sign 根号"round to四舍五入"to the nearest 四舍五入2. 有关集合union 并集"proper subset 真子集"solution set 解集"3.有关代数式、方程和不等式algebraic term 代数项"like terms, similar terms同类项"numerical coefficient 数字系数"literal coefficient 字母系数"inequality 不等式"triangle inequality 三角不等式"range 值域"original equation 原方程"equivalent equation 同解方程，等价方程" linear equation 线性方程(e.g. 5"*"+6=22)"4.有关分数和小数proper fraction真分数" improper fraction 假分数"mi*ed number 带分数"vulgar fraction，mon fraction 普通分数" simple fraction简分数"ple* fraction繁分数"numerator 分子"denominator 分母"(least) mon denominator〔最小〕公分母" quarter 四分之一"decimal fraction 纯小数"infinite decimal 无穷小数recurring decimal循环小数"tenths unit 十分位"5. 根本数学概念arithmetic mean 算术平均值"weighted average 加权平均值"geometric mean 几何平均数"e*ponent 指数，幂"base 乘幂的底数,底边"cube 立方数，立方体"square root平方根"cube root 立方根"mon logarithm 常用对数"digit 数字"constant 常数"variable 变量"inverse function反函数"plementary function 余函数"linear 一次的，线性的"factorization 因式分解"absolute value绝对值，e.g.｜-32｜=32" round off四舍五入" 6.有关数论natural number 自然数" positive number 正数"negative number 负数"odd integer, odd number 奇数"even integer, even number 偶数"integer, whole number 整数"positive whole number 正整数"negative whole number 负整数" consecutive number 连续整数"real number, rational number 实数,有理数" irrational〔number〕无理数"inverse 倒数"posite number 合数 e.g. 4,6,8,9,10,12,14,15……"prime number 质数e.g. 2,3,5,7,11,13,15……注意：所有的质数(2除外)都是奇数，但奇数不一定是质数reciprocal 倒数"mon divisor 公约数"multiple 倍数"(least)mon multiple (最小)公倍数" (prime) factor (质)因子"mon factor 公因子"ordinary scale, decimal scale 十进制"nonnegative 非负的"tens 十位"units 个位"mode众数"median 中数"mon ratio 公比"7.数列arithmetic progression(sequence) 等差数列"geometric progression(sequence) 等比数列"appro*imate 近似"(anti)clockwise (逆) 顺时针方向"cardinal 基数"ordinal 序数"direct proportion 正比"distinct 不同的"estimation 估计，近似"parentheses 括号"proportion 比例"permutation 排列"bination 组合" table 表格"trigonometric function 三角函数"unit 单位,位"几何局部1. 所有的角alternate angle 错角" corresponding angle 同位角"vertical angle对顶角"central angle圆心角"interior angle 角"e*terior angle 外角"supplementary angles补角"plementary angle余角"adjacent angle 邻角"acute angle 锐角"obtuse angle 钝角"right angle 直角"round angle周角"straight angle 平角"included angle夹角"2.所有的三角形equilateral triangle 等边三角形"scalene triangle不等边三角形"isosceles triangle等腰三角形"right triangle 直角三角形"oblique 斜三角形"inscribed triangle 接三角形"3.有关收敛的平面图形，除三角形外semicircle 半圆"concentric circles 同心圆"quadrilateral四边形"pentagon 五边形"he*agon 六边形"heptagon 七边形"octagon 八边形"nonagon 九边形"decagon 十边形"polygon多边形"parallelogram 平行四边形"equilateral 等边形"plane 平面"square 形，平方"rectangle 长方形"regular polygon 正多边形"rhombus 菱形" trapezoid梯形"4.其它平面图形arc 弧"line, straight line 直线"line segment 线段"parallel lines 平行线"segment of a circle 弧形"5.有关立体图形cube 立方体，立方数" rectangular solid 长方体"regular solid/regular polyhedron 正多面体" circular cylinder 圆柱体"cone圆锥"sphere 球体"solid 立体的"6.有关图形上的附属物altitude 高" depth 深度"side 边长"circumference, perimeter 周长"radian弧度"surface area 外表积"volume 体积"arm 直角三角形的股"cross section 横截面"center of a circle 圆心"chord 弦"radius 半径"angle bisector 角平分线"diagonal 对角线"diameter 直径"edge 棱"face of a solid 立体的面"hypotenuse 斜边"included side夹边"leg三角形的直角边"median of a triangle 三角形的中线"base 底边，底数〔e.g. 2的5次方，2就是底数〕"opposite直角三角形中的对边"midpoint 中点"endpoint 端点"verte* (复数形式vertices)顶点"tangent 切线的"transversal截线"intercept 截距" 7.有关坐标coordinate system 坐标系" rectangular coordinate 直角坐标系" origin 原点"abscissa横坐标"ordinate纵坐标"number line 数轴"quadrant 象限"slope斜率"ple* plane 复平面"8.其它plane geometry 平面几何" trigonometry 三角学"bisect 平分"circumscribe 外切"inscribe 切"intersect相交"perpendicular 垂直"pythagorean theorem勾股定理" congruent 全等的"multilateral 多边的"-1.单位类cent 美分"penny 一美分硬币"nickel 5美分硬币"dime 一角硬币"dozen 打〔12个〕"score 廿(20个)"Centigrade 摄氏"Fahrenheit 华氏"quart 夸脱"gallon 加仑(1 gallon = 4 quart)"yard 码"meter 米"micron 微米"inch 英寸"foot 英尺"minute 分(角度的度量单位，60分=1度)" square measure 平方单位制"cubic meter 立方米"pint 品脱(干量或液量的单位)" 2.有关文字表达题，主要是有关商业intercalary year(leap year) 闰年(366天)"mon year 平年(365天)"depreciation 折旧"down payment 直接付款"discount 打折"margin 利润"profit 利润"interest 利息"simple interest 单利"pounded interest 复利"dividend 红利"decrease to 减少到"decrease by 减少了"increase to 增加到"increase by 增加了"denote 表示"list price 标价"markup 涨价"per capita 每人"ratio 比率"retail price 零售价"tie 打Chapter onefunction notation方程符号函数符号quadratic functions 二次函数quadratic equations 二次方程式二次等式chapter twoEquivalent algebraic e*pressions 等价代数表达式rational e*pression 有理式有理表达式horizontal and vertical translation of functions 函数的水平和垂直的平移reflections of functions 函数的倒映映射chapter threeE*ponential functions 指数函数e*ponential decay 指数式衰减e*ponent 指数properties of e*ponential functions 指数函数的特性chapter fourTrigonometry 三角学Reciprocal trigonometric ratios 倒数三角函数比Trigonometric functions 三角函数Discrete functions 离散函数数学mathematics, maths(BrE), math(AmE) 公理a*iom定理theorem计算calculation运算operation证明prove假设hypothesis, hypotheses(pl.)命题proposition算术arithmetic加plus(prep.), add(v.), addition(n.)被加数augend, summand加数addend和sum减minus(prep.), subtract(v.), subtraction(n.) 被减数minuend减数subtrahend差remainder乘times(prep.), multiply(v.), multiplication(n.) 被乘数multiplicand, faciend乘数multiplicator积product除divided by(prep.), divide(v.), division(n.) 被除数dividend除数divisor商quotient等于equals, is equal to, is equivalent to 大于is greater than小于is lesser than大于等于is equal or greater than小于等于is equal or lesser than运算符operator数字digit数number自然数natural number整数integer小数decimal小数点decimal point分数fraction分子numerator分母denominator比ratio正positive负negative零null, zero, nought, nil十进制decimal system二进制binary system 十六进制he*adecimal system权weight, significance进位carry截尾truncation四舍五入round下舍入round down上舍入round up有效数字significant digit无效数字insignificant digit代数algebra公式formula, formulae(pl.)单项式monomial多项式polynomial, multinomial系数coefficient未知数unknown, *-factor, y-factor, z-factor 等式，方程式equation一次方程simple equation二次方程quadratic equation三次方程cubic equation四次方程quartic equation不等式inequation阶乘factorial对数logarithm-指数，幂e*ponent乘方power二次方，平方square三次方，立方cube四次方the power of four, the fourth power n次方the power of n, the nth power开方evolution, e*traction二次方根，平方根square root三次方根，立方根cube root四次方根the root of four, the fourth root n次方根the root of n, the nth root集合aggregate元素element空集void子集subset交集intersection并集union补集plement映射mapping函数function定义域domain, field of definition值域range常量constant 变量variable单调性monotonicity奇偶性parity周期性periodicity图象image数列，级数series微积分calculus微分differential导数derivative极限limit无穷大infinite(a.) infinity(n.) 无穷小infinitesimal积分integral定积分definite integral不定积分indefinite integral 有理数rational number无理数irrational number实数real number虚数imaginary number复数ple* number矩阵matri*行列式determinant几何geometry-点point线line面plane体solid线段segment射线radial平行parallel相交intersect角angle角度degree弧度radian锐角acute angle直角right angle钝角obtuse angle平角straight angle周角perigon底base边side高height三角形triangle锐角三角形acute triangle 直角三角形right triangle 直角边leg 斜边hypotenuse勾股定理Pythagorean theorem钝角三角形obtuse triangle不等边三角形scalene triangle等腰三角形isosceles triangle等边三角形equilateral triangle四边形quadrilateral平行四边形parallelogram矩形rectangle长length宽width菱形rhomb, rhombus, rhombi(pl.), diamond 形square梯形trapezoid直角梯形right trapezoid等腰梯形isosceles trapezoid五边形pentagon六边形he*agon七边形heptagon八边形octagon九边形enneagon十边形decagon十一边形hendecagon十二边形dodecagon多边形polygon正多边形equilateral polygon 圆circle圆心centre(BrE), center(AmE) 半径radius直径diameter圆周率pi弧arc半圆semicircle扇形sector环ring椭圆ellipse圆周circumference周长perimeter面积area轨迹locus, loca(pl.)相似similar全等congruent四面体tetrahedron五面体pentahedron六面体he*ahedron平行六面体parallelepiped 立方体cube七面体heptahedron八面体octahedron九面体enneahedron十面体decahedron十一面体hendecahedron 十二面体dodecahedron 二十面体icosahedron 多面体polyhedron棱锥pyramid棱柱prism棱台frustum of a prism 旋转rotation轴a*is圆锥cone圆柱cylinder圆台frustum of a cone 球sphere半球hemisphere底面undersurface外表积surface area体积volume空间space坐标系coordinates坐标轴*-a*is, y-a*is, z-a*is 横坐标*-coordinate纵坐标y-coordinate原点origin双曲线hyperbola抛物线parabola三角trigonometry正弦sine余弦cosine正切tangent余切cotangent正割secant余割cosecant反正弦arc sine反余弦arc cosine反正切arc tangent反余切arc cotangent反正割arc secant反余割arc cosecant相位phase周期period振幅amplitude 心incentre(BrE), incenter(AmE)外心e*centre(BrE), e*center(AmE)旁心escentre(BrE), escenter(AmE)垂心orthocentre(BrE), orthocenter(AmE)重心barycentre(BrE), barycenter(AmE)切圆inscribed circle外切圆circumcircle统计statistics平均数average加权平均数weighted average方差variance标准差root-mean-square deviation, standard deviation比例propotion百分比percent百分点percentage百分位数percentile排列permutation组合bination概率，或然率probability分布distribution正态分布normal distribution非正态分布abnormal distribution-图表graph条形统计图bar graph柱形统计图histogram折线统计图broken line graph曲线统计图curve diagram扇形统计图pie diagram。
