lecture7(ch7)
LEC02_PT1_CH04-round-offandtruncationerrors
LECTURE 2 -1MAE3100Prof. D.E. SmithLECTURE 2Round-Off and Truncation ErrorsMotivation:Understanding the concept of error and how it develops in numerical methods is important to the effective use of computer techniques.This study focuses on two major forms of numerical error: Round-offError and Truncation Error.Reading Assignment:Chapra Chapter 4 (required)Chapra and Canale Section 4.1 (optional)LECTURE 2 -2MAE3100Prof. D.E. SmithLECTURE 2 OBJECTIVESThe primary objective of this lecture is to provide a basicunderstanding of computational errors introduced bynumerical methods. More specifically, this lecture will:•Expose potential sources of computational errors.•Compare accuracy and precision.•Review numerical precision associated with digitalcomputing.•Provide specific calculations for evaluating error estimates.•Provide a means for estimating truncation error using theTaylor series.•Explore finite difference approximations for first and secondderivatives.MAE3100Prof. D.E. SmithLECTURE 2 -3You’ve Got A Problem•The numerical methods solution to the bungee jumper problem inChapter 1 employed an approximation to the derivative as•What is known?–Numerical error is introduced byapproximation–Approximation error depends on t–Computers have limited precision•What is needed?– A basic understanding of errors associated with computercalculations– A method for assessing the amount of error introduced withthe approximations used by numerical methodsii i i t t t v t v t v dt dv 11)()(MAE3100Prof. D.E. SmithLECTURE 2 -4Sources of Error•Errors in mathematical modelingResult from simplifying assumptions and approximations madewhen representing physical systems by mathematical equations.•BlundersResult from mathematical modeling errors and/or programmingerrors.•Errors in inputBEWARE: garbage in –garbage out•Machine errorsResult from rounding, chopping, underflow and overflow•Truncation errorsResult from simplifying assumptions and approximations madein the numerical procedureOccurs when truncating an infinite series or numericalevaluation of an improper integral. E.g.,!4!3!21432x x x x e xMAE3100Prof. D.E. SmithLECTURE 2 -5Accuracy and Precisiondata scatterdefinesimprecisionoruncertaintysystematic deviation defines inaccuracy or bias inaccurateandimpreciseaccurateandprecise MAE3100Prof. D.E. SmithLECTURE 2 -6Significant Figures•The significant digits of a number are those that can be used withconfidence.•What is the speed?–48 or 49?–48.8 or 48.9?–48.8642138?–#sig-figs = 3•What is the mileage?–87324.4 or 87324.5?–87324.46?–#sig-figs = 7•All results in MAE3100 must display appropriate units and Sig-Figs–Use no less than 3 sig-figs, 4 is preferred–Use the greatest accuracy possible during calculations–Report result with sig-figs consistent with inputMAE3100Prof. D.E. SmithLECTURE 2 -7Error Definitions•True (Absolute) ErrorNote: Issues arise when working with different orders-of-magnitude•True Percent Relative Error•Approximate Percent Relative Error (true value not always known)• A specified percent tolerance s may be used as a stopping criteria:I.e., stop with n decimal place accuracy when ionapproximat value true t E (100%) value true ionapproximat - value true (100%) value true error true t %)100(ion approximat current ionapproximat previous -ion approximat current (100%)ion approximat errore approximat a )%105.0(2n s a MAE3100Prof. D.E. SmithLECTURE 2 -8Round-Off Error•Recall that numbers are stored in binary format–16 bit integer representationRange: -32,768 to 32,767Shown: -173–Floating point representation•Single precision (32 bit)24 bit mantissa7-8 sig-figs Range: 10-38to 1039•Double precision (64 bit)15-16 sig-figsRange: 10-308to 10308Representation used by MATLAB (223210)272625242330292831….sMAE3100Prof. D.E. SmithLECTURE 2 -9Working with Computer Numbers•Computers work in base 2 making it impossible to accuratelyrepresent numbers of interest, e.g.,•MATLAB commands related to machine precision include realmax ,realmin , eps•Round-off errors can accumulate in large computations.•Loss of significant figures occurs when subtracting numbers ofsimilar magnitude:•Small numbers can be lost when added to large numbers using finitemachine precision 333100001.0107641.0107642.0...,7,,,1.0etc e 4444104000.010*******.010*******.0104000.0chopped MAE3100Prof. D.E. SmithLECTURE 2 -10Truncation Error•Taylor theorem : Any smooth function can be written as a polynomial.•Definition: The Taylor Series expansion of f (x )about x = a iswhere the remainder is•The n -th order Taylor Series with h = x –a becomes:• A Maclaurin Series is a Taylor Series expanded about a = 0 (h = x )nk nk k R a x a f k x f 0)()()(!1)(n -th order Taylor Series approximation f n (x )remainder))(()()()!1(111)1(n n n n a x O a x f n R x a nn n hn a f h a f h a f h a f a f h f !)(!3)(!2)()()()()(3)3(2 nn n xn f x f x f x f f x f !)0(!3)0(!2)0()0()0()()(3)3(2 error is ‘on the order of’(x -a )n +1a x XI (ks-eye)MAE3100Prof. D.E. SmithLECTURE 2 -11Truncation Error (cont.)•Accuracy increases as more terms are added to the Taylor Series expansionconstant)a (i.e., 0a function)linear a (i.e., 10h a a )polynomial order 2nd a (i.e.,2210h a h a a MAE3100Prof. D.E. SmithLECTURE 2 -12Taylor Series ExampleFrom Chapra Figure 4.2, pg. 68:Where) (i.e., 0about Expanded 2.125.05.015.01.0)(234x a x h a x x x x x f 0.1)0(25.0)0(2.1)0(f f f xx f 25.02.1)(1225.025.02.1)(x x x f 2.1)(0x fMAE3100Prof. D.E. SmithLECTURE 2 -13Taylor Series -ExampleDetermine the 4-th order Taylor Series of y (x ) = ln(1+x )about x = a = 0By successive differentiation we obtainThe Taylor Series for |x |≤ 1becomes:Note: The error is proportional to x 5: i.e., when x is reduced by afactor of 2, R 4decreases by a factor of 25= 32)1ln()(x x y 0)0(y x x y 11)(1)0(y 2)1(1)(x x y 1)0(y 3)3()1(2)(x x y 2)0()3(y 4)4()1(6)(x x y 6)0()4(y 4324413121)()(x x x x x y x y )()1(51120)(5555)5(4x O x x y R with 5)5()1(24)(y MAE3100Prof. D.E. SmithLECTURE 2 -14Defining the RemainderRecall that the remainder R n is defined in terms the variable asConsider a zero-order (n = 0)Taylor Seriesthen 1)1()()!1()(n n n a x n f R ha a where )()()(0a f x f x f hR f h f R 00)()(= a = x = a = x)(f xa a+hMAE3100Prof. D.E. SmithLECTURE 2 -15Defining the Remainder (cont)Recall our example y (x ) = ln(1+x )with the 4-th order Taylor Series aboutx = 0The remainder becomesCombining these equations givesFor x = 1, we obtainthen or which satisfies the condition 4432413121)(R x x x x x y 55432)1(151413121)1ln(x x x x x x 555554)1(151)0())1(ln(!51x x x dx d R x 12739.058333.0413121)(69315.0)(4324x x x x x y x y 105544)1()1(15110981.058333.069315.0)1()1(y y R MAE3100Prof. D.E. SmithLECTURE 2 -16Defining the Remainder (cont)NOTE:•Determining the number of terms required for a Taylor series torepresent a function of interest is based on the remainder.•Unfortunately, ξis not known exactly but merely lies somewherebetween a and x = a + h (or x i and x i+1).•Also, R n requires derivatives of f (x ),which are not generally known.•Despite this, R n is still useful for gaining insight into truncationerrors.•Recall that we do have control over h and can therefore assess whathappens as we change h , i.e.,1)1(1)1()!1()()()!1()(n n nn n h n f a x n f R )())((11n n n h O a x O R xa a+h hMAE3100Prof. D.E. SmithLECTURE 2 -17Using the Remainder R n1)Establish order of error (from definition)2)Verify order of error estimate*> at h = 0.5 > at h = 1.03) Provide error estimate when h is increased or reduced*at h = 0.5, we computed R 4= 0.00442344then at h = 1.0 (doubled), we estimate R 4(0.00442344)(25) = 0.141550))(()()!1()(11)1(n n n n a x O a x n f R 0.109814)1()1(44y y R 0.00442344)5.0()5.0(44y y R 2X ~25X note: 25= 32X*For y (x ) = ln(1+x )about x = 0MAE3100Prof. D.E. SmithLECTURE 2 -18Using the Remainder R n (cont)4)Calculate value of ξwhen exact function value is known*Recall for h = 1and 5)Establish upper or lower bound on error*Recall that when h = 1, we obtain and Then the upper bound of the error may becalculated as the maximum R 4over the validrange of ξas 0.109814)1()1(44y y R *For y (x ) = ln(1+x )about x = 0554)1()1(151R Equating andsolving for ξgives12739.01054)1(151R 51)1(151)1(15110max 055max 4R maxξR 4MAE3100Prof. D.E. SmithLECTURE 2 -19Numerical DifferentiationDerivatives may be evaluated numerically withthe Finite (Divided) Difference method.1.Forward Difference (error is O (h ))2.Backward Difference (error is O (h ))3.Central Difference (error is O (h 2))hx f h x f x f )()()(hh x f x f x f )()()(hh x f h x f x f 2)()()(MAE3100Prof. D.E. SmithLECTURE 2 -20Remainder w/ Finite DifferenceConsider the 1st order Taylor Series and Remainder for f (x )expandedabout a = x (note h = x )which can be rearranged to give forward differenceExample problem: consider f (x ) = sin(x ) at x = /4exact derivative:forward finite difference:error bounded by remainder:2!2)()()()(xf x x f x f x x f R 1xf x x f x x f x f 2)()()()(O (x )7071067811.0)cos()(4/x x x f 6706029729.01.0)4/sin()1.04/sin()(x f (with x = 0.1)error = 0.0370781.04/at 0.0387084/at 0.035355)(2)sin(2)(x x f。
lecture7-memory
部分报告法实验
• 实验结果表明，在全部报告法实验中，被 试看到的或能记住的字母确实要比被被试 报告出来的多。
• Sperling（1960）证实了感觉记忆的存在， 这样两种记忆说得以发展，出现了多存贮 模型，或说信息三级加工模型。
2、证明图像记忆的特性实验（了解）
• 1、sperling（1960）改变声音信号延迟的 时距p76 • 2、Erikson&Collins（1967）点模式实验 p77
• 3、动物实验——老鼠电休克
2、自由回忆实验（Free recall ）
• Murdock（1962）让被试听一个由30个词构成的 词表，每次呈现一个词，每次1秒，然后进行自由 回忆，根据结果得到一条系列位置曲线。
•
结论
• 系列位置曲线（the serial position curve）。 • 系列位置曲线可以分为3 个部分： – 近因效应（recenty effect） – 首因效应（primary effect） – 渐进线（asymptote）
Cognitive Psychology Memory
ZHOU HENG
记忆关注的问题
• • • • • 我们的记忆是怎么发生的？ 记忆的不同阶段分别是什么，有什么作用？ 哪些因素影响我们成功创建新的记忆？ 记忆的遗忘是如何发生的？ 记忆为什么会说谎？
本章关键名词
• • • • • 两种记忆说 多贮存说 全部报告法和部分报告法 系列位置效应 感觉记忆
思考题
• 1、 两种记忆说的基本内容是什么？
• 2、 你认为应如何解释系列位置效应？ • 3、 感觉记忆有什么特性（特点）？
• 4、 多存贮模型的基本思想是什么？
总结
lecture_7_Geant4_2
除了轻子、玻色子还包括： G4MesonConstructor G4BaryonConstructor G4IonConstructor G4ShortlivedConstructor 如果对过程中可能需要的粒 子不确定，可以用这种办法 把所有粒子都构造出来。
void ExN01PhysicsList::ConstructParticle() { ConstructLeptons();//构造轻子 ConstructBosons(); //构造玻色子 ... }
2012-4-12 13
G4ParticleGun
//参数n_particle表示一次发射的粒子数目 G4ParticleGun* particleGun = new G4ParticleGun(n_particle); G4ParticleGun有很多设置函数，如： SetParticleDefinition(G4ParticleDefinition*); //粒子类型 SetParticleMomentumDirection(G4ThreeVector); //动量方向 SetParticleEnergy(G4double); //能量 SetParticlePosition(G4ThreeVector); //发射位置 ... 粒子枪的属性设置好之后，才调用generatePrimaryVertex()函数，产生 事例的主顶点。 粒子枪本身不提供随机性，发射的粒子都是指定的。如果需要按照某分布随 即发射粒子，需要在调用generatePrimaryVertex()之前，利用Geant4提 供的随机数产生子自己写出需要的分布。 参见ExN01PrimaryGeneratorAction::generatePrimaries(G4Event*) 函数
作业3_203906719
Principles of Economics I (Fall 2010)Homework #3(Lecture 7-8, Due on Nov. 24, 2010, submitted in class)Section 1: Textbook Exercises(All numbers refer to “Problems and Application” part in each chapter, the 5th international student edition of the textbook)Ch7: 2, 7, 5, 1, 6, 9, 10(Erratum: In problem 5, “Bert from problem 4” and “Ernie from problem 5” should be “Bert from problem 2” and “Ernie from problem 7”.)Ch8: 1, 2, 5, 6, 9, 10, 11Ch9: 1, 2, 5, 7, 9, 10, 12, 13Section 2: Supplemental Questions(Multiple choice question if marked with a-d, otherwise True/False questions.)(For Chapter 7)1. Economists tend to see ticket scalping asa. a way for a few to profit without producing anything of value.b. an inequitable interference in the orderly process of ticket distribution.c. a way of increasing the efficiency of ticket distribution.d. an unproductive activity which should be made illegal everywhere.(For Chapter 8)2. The deadweight loss of a tax rises even more rapidly than the size of the tax.(For Chapter 9)3. If Canada were to subsidize the production of wool blankets, and sell them in the U.S. at artificially low prices, the U.S. economy would be worse off.Section 3: Extra Supplements第三部分：其他补充题目排队、价格与效率（2006年春季双学位班期中测验题，对应教材第7章）小镇上生活着1万名居民，每个周末都会到镇里唯一的公园去休息娱乐。
抗遗忘英语单词速记-初级版-(6-10)
抗遗忘英语单词速记-初级版-(6-10)6ighteight/eit/nom.八，八个right/rait/n.右；a右边的，对的[八个人(r)在右边] bright/brait/a.明亮的，鲜艳的右边的玻(b)璃是明亮的，鲜艳的light/lait/n.光a.轻的，轻微的八条线(l)是光线，很轻的lighting/ laiti☠/n.照明，点火light+ing (名词后缀)[光出现—照明]中文串联：八个右边的玻璃是明亮的，光出现照明照亮fright/frait/n.惊吓f (夫人)+right (右)[夫人在右边受到惊吓] frighten/ frait☯n/v.吓唬fright+en (名词后缀)frightened/ frait☯nd/a.受惊吓的frighten+ed (形容词后缀)flight/flait/n.飞行fly(动词：飞行)+t(停)[停下来变成名词]fight/fait/v.打仗，战斗，打架中文串联：这次飞行是扔掉棍子(l)去打仗，去打架eightstraight/streit/a直的，笔直的；ad.直地stra+ight中文串联：八条笔直的路通向远方ilemile/mail/n.英里smile/smail/n.v.微笑s+mile while/hwail/conj.n.当---时候，一会中文串联：当她微笑的时候，一英里的路成s形ill/il/a.生病的kill/kil/v.杀k(形刀)+ill--杀till/til/prep.wnj.直到…为止t(停)+ill [直到生病为止才停下来]still/stil/ad.还，仍旧s(蛇)+till [直到春天为止，蛇还仍旧未醒]中文串联：生病的直到被杀为止，还没倒下will/wil/v.aux.将；会；愿；n.意志w+ill [胃病将会由人的意志治好]bill/bil/n.钞票，帐单b+ill [钞票账单的弊病是让人金钱万能]hill/hil/n.小山h+ill [嘿，疾病，爬上小山就能征服你]fill/fil/v.装满，充满f+ill [废掉疾病，充满理想]film/film/n.影片，电影fill—film(音：满) [箱子里装满了影片电影] village/ vilid✞/n.村庄v+ill+age为(v)疾病而衰老(age年龄)的村庄中文串联：将钞票，装满小山拍成电影到村庄放映ink/i☠k/n.墨水drink/dri☠k/v.喝，饮酒谐音：酌饮墨水--喝，饮think/ i☠k/v.想，认为谐音：思想墨水--想，认为中文串联：他思想让墨水做成饮料，再喝掉ice/ais/n.冰notice/ ⏹☯◆♦♓♦/v.注意；n.通知not(不)+ice [不是冰，是水--大家注意]twice/twais/n.两次tw+ice [它(t)的波浪(w)，被冰两次打翻] voice/v is/n.声音，嗓子vo(喂噢)+ice[喂噢--对着冰练嗓子]中文串联：冰已注意到，有两次春天的声音在呼唤advice/☯d vais/n.劝告，忠告service/ ♦☯vis/n.服务，公用事业中文串联：劝告大家服务要好office/ fis/n.办公室提示：电脑里装的办公软件-- office软件officer/ fis☯/n.官员，办事员offic(e)+er(人) [办公室的人--官员，办事员] ice/ais/n.冰nice/nais/a.使人高兴的，好的n+ice [夏天炎热，门里放块冰--使人高兴的] rice/rais/n.稻，米，饭r+ice[草(r)上长出冰一样白的稻米来]juice/♎✞◆s/n.果汁ju+ice[橘(ju)加冰--果汁]中文串联：使人高兴的稻米饭还放着水果ickpick/pik/v.拾，摘披(p)着雨衣去拾菜摘豆角kick/kik/v.踢鸭(k鸭嘴)在跳踢踏舞sick/sik/a.有病的；n.病人蛇(s)形就是有病的中文串联：又拾又摘还踢--有病的人quick/ kwik/a.快的，迅速的通过发kwik音--快的(来联系)quickly/ kwikli/ad.快quick+ly(副词后缀)thick/ ik/a.厚的，浓的湿( )的雾--厚的，浓的stick/stik/n.短棍病人(sick)拿着伞(t)当短棍ticket/ tikit/n.票，券t+icke+t [首尾都是特(t)等票]chick/t☞ik/n.小鸡chicken/ t☞iken/n.鸡/肉/，小鸡a.鸡肉的，鸡味的ifelife/laif/n.生活，生命[拉(l)住生命]wife/waif/n.妻子[娃(w)他妈--妻子]knife/naïf/n.小刀[k(刀形)+那(n)里有刀]中文串联：生活中的妻子用刀切菜indwind/wind/n.风window/ wind☯u/n.窗户[风(wind)噢(ow)一声吹开了窗户]wild/waild/a.野性的；n.荒野风(wind)推开门(n)带着棍子(l)野性的在荒野上中文串联：风吹开窗户，带着荒野，野性的味儿indfind/faind/v.找到，发现[fa--发现--找到]mind/maind/v.介意，留心；n. 思想[ma马儿在留心地上的草]kind/kaind/a.和蔼的，仁慈的；n.种类[ka客气--和蔼的] kindness/ kaindnis/n.仁慈，好意kind+ness (名词后缀)behind/bi haind/prep.在---后面be(是)+hind(后面的) [是后面的--在…后面]中文串联：在仁慈的后面发现恶意，要介意留心assist/☯sist/v.帮助，协助sister / ˈsɪstə/(姐妹)assistant/☯sist☯nt/n.助手，助理assist+ant (名词后缀)中文串联：姐妹一起帮助他，成为他得力的助手between/bi twi n/prep.在/两者/之间be(是)+tween(two二) [是在二者之间]clerk/kl☯k/n.职员，办事员clock/kl k/n.钟表[每个职员的办公桌上都放着钟表]cloth/kl /n.布clothes/kl☯◆❆/n.衣服cloth+es [用布做的衣服]coffee/ k fi/n.咖啡谐音：咖啡office/ fis/n.办公室[办公室里放着咖啡] college/ k lid✞/n./综合性大学中的/学院col+leg(腿)+e 烤着火腿进学院colour/ k✈●☯/n.颜色col+our(我们的) 烤成我们喜欢的颜色first/f☯st/n.第一thirst/ ☯st/n.渴，口渴；v.渴望thirsty/ ☯sti/a.口渴的中文串联：在沙漠里，第一要解决的是口渴一事row/r☯u/n./一/列，/一/排throw/ r☯u/v.扔，投，掷th(音：四)+row(排) [他把铅球投掷到了四排房] tide/taid/n.潮汐tidy/ taidi/a.整洁的中文串联：潮汐退后，留下整洁的沙滩little/ litl/a.小的，幼小的lit+tle title/ taitl/n.标题，书名ti+tle [小小的标题，书名]time/taim/n.时间timid/ timid/a.胆怯的，羞怯的中文串联：有些时候，人是胆怯的，羞怯的raw/r /a.生的，未煮的，原始的draw/dr /v.画d+raw [他在画一幅原始的生活景象]old/ /a.老的，旧的elder/ eld☯/a.年龄较大的，年长的eld+er (形容词后缀)element/ elim☯nt/n.要素，元素elementary/ eli m☯nt☯ri/a.基本的，初级的element+ary (形容词后缀)[要素，元素是构成物质基本的，初级的形式] enemy/ enimi/n.敌人ene+my (我的) [ene是我的敌人]7igbig/bi♈/a.大的dig/di♈/v.挖[地里挖]pig/oi♈/n.猪[呸--猪(骂人)]中文串联：地里挖到一头大的猪just/d✞✈st/ad.正好，恰好谐音：讲师团--正好来这儿讲课adjust/☯d✞✈st/v.调节，调整ad(阿弟)+just中文串联：正好需要阿弟调节jojob/d✞b/n.工作，零活谐音：就不--工作joy/ d✞i/n.欢喜，高兴join/ d✞in/v.参加，加入中文串联：我参加工作，干点零活，这次欢喜和高兴是特别lalab/l✌b/n.实验室谐音：兰博在实验室law/l /n.法律，法规谐音：狼--需法律裁制lay/lei/v.放置，铺设，生/蛋/中文串联：法律规定实验室不能放置，铺设生鸡蛋lidslide/slaid/n.滑，幻灯v.滑动谐音：老师拉儿子--滑(冰)--就像一个幻灯滑动solid/ ♦lid/n.固体a.坚硬的谐音：耸立的--固体--坚硬的lectcollect/k☯lekt/v.收集，采集electric/i lektrik/a.电的lecture/ lekt☞☯/n.讲演，讲座中文串联：收集电的讲座，你去听吗？littlittle/ litl/a.小，少量litt+lelitter/ lit☯/n.废物，垃圾；v.乱丢litt+er中文串联：小而少量的废物垃圾不要乱丢lot/l t/n.许多谐音：老头--许多(公园里有许多老头) plot/pl t/n.小块地，图，阴谋；v.密谋p+lot在小块地皮(p)上有许多图，阴谋pilot/ pail☯t/n.飞行员小块地上飞行员(i)在练习飞行中文串联：许多小块地上飞行员在练习飞行pollute/p☯lu t/v.污染，弄脏谐音：俘虏它--它污染弄脏了环境pollution/ p☯lu ☞☯⏹/n.污染pollut(e)+ion(名称后缀)solution/s☯lu ☞☯⏹/n.解决(方法)，解答中文串联：污染的问题要解决low/l☯u/a.低的，矮的blow/bl☯u/v.吹，风吹；吹风b(不)+low [不住低的怕风吹进来] below/bi l☯u/prep.ad.在…下面be(是)+low [是在低的下面]slow/sl☯u/a.慢的s+low [蛇在低的地方慢的爬]中文串联：在低的下面风慢的吹进来flow/fl☯u/v.流动，流f(风)+low [风在低的地方流动]flower/ flau☯/n.花flow+er(人) [流动的人儿是我的花儿]allow/☯●♋◆/v.允许，准许al+low [一(a)根棍(l)在低的地方允许生根发芽] follow/ f ●☯◆/v.跟随，接着，听从fo+llow [允许fo跟随]left/left/a.左边的n.左lift/lift/n.电梯i(形：人)人乘电梯中文串联：左边的电梯关闭了love/l✈v/v.n.爱lovely/l✈vli/a.可爱的，好看的，美好的love+ly(形容词后缀)lalady/ leidi/n.女士lazy/ leizi/a.懒惰的中文串联：女士是懒惰的mamatter/ ❍✌♦☯/n.物质，麻烦事，事情谐音：馒头[物质的，因为馒头惹了许多麻烦事，事情] master/ ma st☯/n.主人v.精通中文串联：馒头这种物质，惹了许多麻烦事，主人还是(s)精通处理的monmoney/ ❍✈⏹♓/n.钱，货币monkey/ ❍✈☠♓/n.猴子ki(声音)[猴子的叫声]中文串联：用钱贩猴子是违法的movmove/mu v/v.移动，摇动谐音：幕--在移动movie/ ❍◆❖♓/n.电影i(形：人)幕里面人在移动--电影mount/maunt/v.登上amount/☯maunt/n.数量，总数a(一)+mount(登上)一登上山，就看人的数量总数到齐没有mountain/ mauntin/n.大山mount+ain [登上顶(tin)--大山]中文串联：登上大山，看看人的数量总数对不对model// ❍♎l/n.模型，模特modern/ ❍♎☯⏹/a.现代化的，现代化谐音：摩登中文串联：模特是现代的产物now/nau/ad.现在no(不)--不，现在就做know/n☯u/v.知道k+now [老k现在就来--知道了]snow/sn☯u/v.下雪n.雪s+now [现在下着蛇形的雪]中文串联：现在知道下雪，还来得及赶路nounce/nauns/ ＝to report（报告）announce/☯nauns/v. 宣布，声称an+nounceannouncer/☯nauns☯/n.广播员announc(e)+er(人) [宣布的人--广播员]pronounce/pr☯nauns/v.发音，宣告中文串联：广播员宣布，他发音宣告结束nneltunnel/ ♦✈⏹●/n.地道，隧道tu(途)+nnel [途径两个门洞--地道隧道]nn:象隧道的两个门洞channel/ ♦☞✌⏹☯●/n.(电视)频道，海峡，航道ch(插)+nnel [线路插进两个洞里(电视)频道]中文串联：(电视)频道是联系海峡两岸的航道或地道隧道osenose/n☯uz/n.鼻子n象鼻子的样子lose/lu z/v.丢失，失去失去了一根棍(l) close/kl☯uz/a.靠近的v.关闭，结束cl(音:卡拉)一声靠近的，关闭了中文串联：鼻子丢失了，靠近的嘴也卡拉一声关闭了，结束了oatgoat/♈☯◆♦/n.山羊g(音:狗) [狗和山羊呆在一起]coat/k☯◆♦/n.外衣，上衣c(音:扣) [扣子与外衣，上衣联系在一起]raincoat/ reink☯◆♦/n.雨衣rain(雨)+coat(外衣)--雨衣中文串联：下雨时，山羊的外衣也当雨衣使ocklock/l k/v.锁上n.锁形似词:look(看)有句俗话:门缝里看人，现在是门锁眼里看人locker/ l k☯/n.抽屉，小柜[c象一把锁]lock(锁上)+er(名词后缀) [锁什么呢？抽屉，小柜]clock/kl k/n.钟c(音:刻)+lock(锁) [表针刻在了锁上成了钟表]knock/n k/n.v.敲门声，敲clock -- knock [钟的敲门(n)声]中文串联：锁上抽屉的钟表发出了嗒嗒的敲门声pocket/ p kit/n.衣袋p+ock+et stocking/ ♦♦♓☠/n.长统袜st+ock+ing stock/♦♦/ (贮存)+ing [贮存的长筒袜]中文串联：衣袋里装着长筒袜old/☯◆●♎/a.年老的，---岁的cold/k☯◆●♎/a.冷的，n.感冒c可[外面可冷的，老人小心感冒]gold/♈☯◆●♎/n.黄金g哥[哥哥老了有黄金] hold/h☯◆●♎/v.抓住，握住h河[河水大，年老的要抓住，握住船杆]soldier/ s☯◆●♎✞☯/a.士兵，军人s(死)+old(年老的)+ier(人)—死掉年老的人士兵，军人中，年轻人才能生存中文串联：年老的人，可冷呢，小心感冒士兵抓住了哥老会的黄金ostpost/p☯ust/n.邮政v.邮寄p(跑)+ost [跑--邮政]cost/k st/v.花费，值...钱；n.费用邮政的花费是c级的most/m☯ust/a.最多的，ad.最花费最多的是malmost/ m☯ust/ad.几乎，差不多al(噢)+most [噢，最多的--几乎全是我们的] 中文串联：邮政的花费最多的几乎都是我们的olehole/h☯ul/n.洞h(形:洞)+olepole/p☯ul/n.极/点/南极臭氧层破(p)了个洞whole/h☯ul/a.整个的，全部的w (形:锯)+hole (洞) [锯开整个的洞]中文串联：整个的南极，臭氧层破了个洞onglong/●☠/a.长的v.渴望谐音：拉--长的--渴望belong/bi ●☠/v.属于，附属be(是)+long [是长长的渴望--属于你祖国！] along/☯●☠/prep.沿着a(一)+long [一条长长的路--沿着--走下去] among/☯m✈☠/prep.在...之中与along差一字母m在一生之中，沿着母(m)亲的路走下去中文串联：是长长的渴望，属于你祖国！在一生之中，沿着母亲的路走下去...oordoor/dɔː/ n.门谐音：捣--门doormat/ˈdɔːmæt/ n.门垫door+mat/mæt/(垫)-- 门垫poor/puə/ a.可怜的, 贫穷的谐音:破[穿得破旧--可怜的，贫穷的]中文串联：贫穷的人家门里没有门垫8ootfoot/fu t/n.英尺，脚root/ru t/n.根v.生根[脚下的草(r)生根了] food/fu d/n.食物(猪)脚成了他的(d)食物了wood/wud/n.木头[锯(w)木头当碗来盛食物] wooden/ wudn/a.木(制)的wood+en (形容词后缀)中文串联：脚下生根，脚当食物，木头来盛oomoon/mu n/n.月亮，月光母(m)亲的两个月亮(00)挂上了门(n)noon/nu n/n.中午中午，两个门中间升起两个太阳(o)soon/su n/ad.不久，很快月亮出来了，蛇(s)不久很快出动了hoop/hu p/n.环，圈谐音：琥珀--项链--环，圈中文串联：中午的月亮不久变成了环，圈ordword/w☯♎/n.单词，词谐音：我的--单词order/ d☯/n.次序v.命令中文串联：学单词要有次序ordinary/ ♎☯⏹☯❒♓/a.普通的，平常的record/ri k ♎/n.记录，唱片，录音带recorder/ri k ♎☯/n.录音机record+er(名词后缀)中文串联：普通的记录，唱片用录音机放就可以了oughcough/k f/n.v.咳嗽c(音：咳)+ough -- 咳嗽enough/i n✈f/a.足够的en+ough 治咳嗽需要足够的药plough/plau/v.n.犁pl(音：曝)+ough [农民在暴晒下犁地]中文串联：足够的咳嗽能犁地though/❆☯◆/conj.虽然，尽管th+ough through/ ❒◆/prep.通过，尽管th+r(形：人)+ough [人虽然通过了，但...]throughout/ ❒◆aut/prep.遍及，贯穿through+out(在...外面) [通过外面--遍及一切]中文串联：人虽然通过了，遍及外面的羊群被鬼子扣留了oundsound/saund/v.听起来；n.声音，语音s--(沙)的声音--听起来wound/wu nd/n.创伤，伤w(捂)住创伤wounded/ wu ndid/a.受伤的wound+ed (形容词后缀)中文串联：沙---听起来象捂住创伤的受伤的声音our/au☯/prop.我们的flour/ flau☯/n.面粉fl(福了)+our [福了牌是我们的面粉]floor/fl /n.地板与(flour面粉)差一字母(o)[面粉掉在地板上污(u)染了一圈(o)]中文串联：我们的福了牌面粉污染了地板一圈four/f /num.四[F4--我们的偶像]hour/au☯/n.小时新闻发布会，F4坐椅子(h)-回答了好几个-小时tour/tu☯/n.旅游；v.旅行，周游F4打雨伞(t)去旅游周游世界tourist/ tu☯rist/n.游客tour+ist(名词后缀) [旅游的人--游客]中文串联：F4坐椅子几个小时接受采访，然后打雨伞去旅游，成为游客own/☯un/v.拥有；a.自己的owner/ ☯un☯/n.拥有者，物主own+er(名词后缀) [拥有的人--拥有者]town/taun/n.城镇t(音：他)+own [他拥有--城镇]down/daun/ad.向下d(形：高尔夫球杆)+own[高尔夫球拥有者打球是，头--向下]中文串联：拥有自己的人就是物主，他才拥有城镇和向下的球杆over/ ☯uv☯/prep.在...之上；ad.结束cover/ k✈v☯/n.盖；v.覆盖c(形：盖子)+over [盖在之上--覆盖]discover/dis k✈v☯/v.发现，看出dis(音：的士)+cover [的士揭开盖--发现，看出]中文串联：在汽车盖之上，的士发现了蛛丝马迹oytoy/t i/n.玩具t(音：淘气)--孩童--玩具joy/d✞i/n.欢乐，高兴j(音：叫)--高声叫着--欢乐，高兴enjoy/in d✞i/v.喜欢，享受en(前缀：使...)+joy [使欢乐--喜欢，享受]boy/b i/n.男孩子b(音：宝) [宝贝--男孩子] schoolboy/ sku lb i/n.男学生school(学校)+boy [学校男孩--男学生]中文串联：男孩喜欢玩具，到了学校，成为男学生就失去了欢乐oudloud/laud/a.响的，大声的l(音：啦)+oud [卡啦一雷声--响的，大声的]proud/praud/a.自豪的，骄傲的p(形：旗)+r(人)+oud[生在红旗下的人是--自豪的，骄傲的]cloud/klaud/n.白云c(云的形状)+loud [在响亮的雷声中飘着一朵--白云]中文串联：自豪的，骄傲的白云能酝酿出响的，大声的雷电orchporch/☐♦☞/n.门廊，走廊p(音：跑)+orch [能跑的地方--门廊，走廊] torch/t ♦☞/n火把，手筒t(形：伞把)+orch [伞把着火--火把--手电筒]中文串联：走廊里跑出一个人拿着火把，打着手电筒泡湿了门廊，湿透了火把pro--essprocess/ ☐❒☯◆♦♏♦/v.处理，加工；n.过程，程序pro+c+essprogress/ ☐❒☯◆♑❒♏♦/n.进步，进展pro+g+ress中文串联：处理加工的过程，在于进步的技术革新priprice/prais/n.价格pri+ce pride/praid/n.骄傲，自豪；v.以---自豪pri+de prize/praiz/m.奖品pri+ze 这组单词正确处理后两个字母的发音不同的字母依次是：c.d.z中文串联：cd价格值得骄傲自豪的是可以当2(z)个奖品来买pop/p p/a.大众的，流行的；n.流行音乐popular/ p p ◆●☯/a.大众的，流行的pot/pot/n.锅，罐top/top/n.顶部，顶点[锅(pot)反过来就是(top)顶部，顶点]中文串联：大众的流行音乐是在锅罐的顶部敲击publipublic/ p✈blik/a.公众的，公共的；n.公众谐音：怕不理(克)--公众publish/ p✈bli☞/v.出版谐音：怕不理诗(诗歌)--出版中文串联：这诗出版后，公众怕不理(克)呢planplan/pl✌n/n.计划，打算plant/pla nt/v.种植；n.植物plan(计划)+t [计划特别的种植]plane/plein/n.飞行plan+e(鹅) [计划象鹅一样--飞行]planet/ pl✌nit/n.行星plane(飞行)+t(特) [飞行特别的东西--行星]中文串联：我计划种植特别的植物，让它象鹅一样飞行成为行星parespare/sp☪/a.多余人v.提供s+p+are(是) [死皮是多余的，不需提供]prepare/pri p☪/v.准备pre+pare compare/k☯m p☪/v.比较，比作com+pare中文串联：多余的准备要比较一下present/ preznt/n.礼物，现在；a.出席的presence/ prezns/n.出席presen+ce(名词后缀)中文串联：带着礼物的出席是有脸面的port/p t/n.港口sport/sp t/n.运动s(蛇)+port [蛇在港口--运动]report/ri p t/v.报告；n.报告，成绩单re(人)+port [人在港口--报告(发现敌情)]中文串联：蛇在港口运动，人在港口报告import/im p t/n.重要性，进口im+port(港口的重要性)important/im p t☯⏹♦/a.重要的import+ant(形容词后缀)importance/im p t☯⏹s/n.重要性import+ance(名词后缀)pen/pen/n.笔，钢笔open/ ☯up☯n/v.打开；a.开着的，营业的谐音：噢，打开笔opening/ ☯◆☐☯⏹♓☠/n.孔，穴，口子open+ing(名词后缀) [打开个--孔，穴，口子] peeny/ peni/n.便士pee+ny [钢笔是ny个便士]spend/spend/v.用钱，花费；度过s+p+end[小斯(s)的钢笔-用钱，花费是很高的(d)] expense/ik spens/n.费用，花费expen+seexpensive/ik spensiv/a.昂贵的expen+sive(形容词后缀)中文串联：费用花费是昂贵的happen/ h✌☐☯⏹/v.(偶然)发生，碰巧hap(/h✌☐/n.机会)+pen中文串联：polipolice/p☯●♓♦/n.警察，警方(警察的总称) policeman/ p☯●♓♦m☯⏹/n.警察，警员police+man(男人) [警方里的男人--警察，警员] polite/ p☯●ait/a.有礼貌的与police差一字母[警察是有礼貌的]politics/ p litiks/n.政治polit(e)+ics [有礼貌的，讲政治的]中文串联：警察是有礼貌的，讲政治的paint/peint/v.绘画，油漆painter/ peint☯/n.画家paint+er(名词后缀，表人) [绘画的人--画家，油漆] painting/ peinti☠/n.画，油画，水彩画paint+ing(名词后缀，表物)中文串联：绘画的结果--画，油画，水彩画pain/pein/v.n.痛paint(绘画) [绘画时间长了,身上很痛,去掉t好一点] point/p int/v.指，指出；n.点，小数点形似：paint(绘画)中文串联：指出了绘画中的一(a)个点(o)是错误的ququiet/ kwai☯t/a.安静的quite/ kwait/ad.相当，完全，十分[这个地方是相当安静的]queen/ kwi n/n.女王queue/kju /n.队列，长队中文串联：女王的队列排着长队raise/reiz/v.举起，使升高r(形：草) [草在生长--举起，是升高] praise/preiz/v.n.赞扬，表扬p(形：镰刀，斧头)+raise[镰刀的红旗举起在阵地上][胜利啦--受到了，赞扬，表扬]read/ri d/v.读，阅读reading/ ri di☠/n.阅读，读物read+ing(名词后缀)ready/ redi/a.准备好的read+y(形容词后缀) y形：一瓶花中文串联：他在阅读读物是有个习惯，花(y)要准备好的放在身边bread/ bred/n.面包b(音：包)+read [看书前要吃面包]spread/spred/v.传开，展开sp+read [阅读活动全面展开传开了]already/ ●redi/ad.已经al(噢)+ready [噢，阅读已经开始了]中文串联：看书前吃面包，这一活动传开后，已经展开了rock/rɔk/ n.岩石rocket/ˈrɔkɪt/n.火箭rock+et中文串联：岩石被载到火箭上round/raund/a.圆的；prep.围(绕)着around/☯raund/prep.在...周围，环绕a(一)+round [一个圆的-在...周围]ground/♈raund/n.地面g(音：搁)+round [把圆的搁在地面]playground/ plei♈raund/n.操场play (玩)+ground(地面) [玩的地面--操场]中文串联：在操场周围，环绕着圆的地面跑步ridgebridge/brid✞/n.桥b(音：波)--水--桥fridge/frid✞/n.电冰箱f(福瑞)--福瑞牌--冰箱中文串联：在水波上面架了座桥，桥上面一个福瑞牌冰箱rise/raiz/v.升起，上升，起立high-rise/ hai raiz/.高层建筑high(高的)+rise [高的在升起--高层建筑]surprise/s☯praiz/v.使惊奇surp(音：舍扑)+rise[舍扑(相扑的一种)突然升起来--使惊奇]中文串联：突然升起了高层建筑，使人惊奇rive/raiv/v.撕裂，劈开drive/draiv/v.驾驶d(音：道)+rive [道路被撕裂--驾驶]driver/draiv☜/n.驾驶员，司机driv(e)+er(名词后缀，人)--司机river/ riv☜/n.江，河rive+r(草) [劈开了草原流下来的是--江河]arrive/☜raiv/v.到达ar(一个)+rive [一人撕裂开了荆棘—到达目的地]中文串联：司机驾驶汽车劈开了草原来到了江河，翻了车，一人撕裂了路旁的荆棘终于到达了彼岸rob/r b/v.抢劫谐音：肉搏一战--抢劫robbery/ r b☜ri/n.抢劫(案)rob+b+ery(名词后缀)robot/ r☯◆♌♦/n.机器人rob+ot(oT) [抢劫OT是机器人干的]中文串联：在这次抢劫OT的抢劫案中，机器人参与了肉搏rrowtomorrow/t☯❍❒☯◆/ad.明天tomo+rrow borrow/ b ❒☯◆/v.借bo(音：宝)+rrow [宝要借明天]narrow/⏹✌❒☯◆/a.狭窄的na(难)+rrow [在这狭窄的空间很难到明天]中文串联：很难呆在狭窄的空间，宝要借明天9rycry/krai/v.叫，喊，哭c(象一个张开的嘴)-- 叫，喊，哭dry/drai/a.干的，干燥的哭得(d)眼都是干的，干燥的try/trai/v.尝试，试图，努力她(t)尝试着努力，从头再来中文串联：失败了，就张开嘴哭啊，喊啊，叫啊，哭得眼都是干的，然后，她尝试努力从头再来sorry/ s ri/a.抱歉的worry/ w✈ri/v./使/担心w(音：忘) [忘掉抱歉，不用再--担心了]carry/ k✌ri/v.携带，传送car(汽车) [汽车在携带，传送]hurry/ h✈ri/n.赶紧，匆忙hu(呼呼喘气) [赶紧，匆忙]中文串联：汽车呼呼喘气赶紧匆忙携带传送货物ring/ri☠/v.打电话；n.环，戒指bring/bri☠/v.带来b(音：爸)+ring [爸爸打电话让人带来了戒指]boring/ b ri☠/a.烦人的bo(音：抱--怨)+ring [抱怨老打电话是烦人的]during/ dju☯ri☠/prep.在---期间du(拼音：都)+ring [在休息期间，都来打电话]中文串联：在休息期间，都来打电话，带来了烦人的结果，抱怨四起ropdrop/dr p/n.滴；v.使下滴，落下d(滴)+ropcrop/kr p/n.农作物c(形谷穗)+rop [谷穗压弯了腰—农作物]中文串联：雨滴落下，滋润着农作物run/r✈n/v.跑runner/ r✈n☯/n.跑步的人run+n+er(名词后缀，表人)[跑步穿过一个门的人]-- 跑步的人rub/r✈b/v.搓，擦中文串联：跑步时不(b)要和其他人发生搓，擦star/sta /n.星星stay/stei/v.停留；暂住y--(形状树杈)中文串联：星星啊，请你停留在树杈上steasteal/sti l/v.偷谐音：偷与(l)可联系steam/sti m/n.蒸汽谐音：m--冒--蒸气中文串联：你说，这事情怪不怪，居然有人偷蒸气s—eetstreet/stri t/n.街，街道谐音：翠--翠绿的--街道sweet/swi t/a.甜的谐音：味--味道--甜的中文串联：翠绿的街道飘来甜甜的味道sa--esafe/seif/a.安全的谐音：谁服--安全的--药品save/seiv/v.节省，储蓄，搭救谐音：谁无--节省，储蓄，搭救--的概念中文串联：谁服安全的药品，谁无节省的念头station/ stei☞☯⏹/n.车站谐音：湿忒深--湿的太深了--车站--被水淹了stationery/ stei☞☯⏹☯ri/n.文具station+ery [车站里卖文具]中文串联：发大水了，从湿得太深的车站了抢运出一批文具来servserve/s☯v/v.为---服务谐音：舍无--舍掉无产阶级你--为(谁)服务service/ s☯vis/n.服务；公用事业serv(e)+ice(名词后缀)deserve/di z☯v/v.值得，应受de+serve [他的(de)为人民服务--值得应受--表扬]中文串联：服务公共事业是为无产阶级服务，值得(de)表扬st--pstop/st p/n.停车站，停止；v.停止step/step/n. /脚/步中文串联：请停止你犯罪的脚步skin/skin/n.皮肤谐音：丝巾--皮肤象丝巾skip/skip/v.跳绳p(皮)--跳皮筋--跳绳slip/slip/v.滑跤，失足li--里--往里--滑跤，失足中文串联：她在跳绳时往里滑了一跤，划破丝巾一样的皮肤set/set/v.放，设置；树立，创造（记录）谐音：散(赛)特商场—放着，设置，创记录的东西upset/✈☐set/v.使心烦，弄翻；a.心烦的up(向上)+set [向上放--放心不下--使心烦，心烦的]settle/ setl/v.安放，定居，解决set+tle [把家放在某地--安放，定居]中文串联：把家安放好，定居了使心烦的事情解决了son/s✈n/n.儿子soon/su n/ad.不久，很快song/s ☠/n.歌曲中文串联：儿子不尽创作的歌曲获奖了lesson/ lesn/n.课谐音：les懒儿子懒的上课去person/ p☯sn/n.人per+sonreason/ ri zn/n.理由，原因rea+sonseason/ si zn/n季节sea(海)+son [海是儿子的--季节]中文串联：儿子懒得上课去，这个人是有理由的，海才是儿子的季节sea/si /n.海，海洋see(看) 看海去season/ si zn/n.季节sea+son 海是儿子的季节seaside/ si said/n.a.海边，海滨sea+side(边) [海边，海滨]中文串联：海洋是儿子的季节，夏季都是来到海边short/☞♦/a.短的，矮的谐音：少的--短的，矮的shout/☞aut/v.喊，叫喊sh(杀)+out(在外面) [杀声阵阵在外面--喊，叫喊]中文串联：少的，短的，矮的在外面叫喊store/st /n.商店；v.储存story/ st ri/n.故事，小说storm/st m/n.暴，雨(雪)中文串联：商店里储存着故事和小说:一个暴风雨雪的晚上shop/ /n.商店shoe/☞u /n.鞋show/☞☜◆/v.显示，展现；n.展览，演出shopping/ ☞pi☠/n.购物shop(商店)+p+ing(名词后缀) [商店平价--购物]中文串联：商店里的平价购物，鞋显示展现出其魅力tire/tai☜/v.劳累形似词:fire火，消防员灭火时特(t)劳累tired/tai☜d/a.累的，疲劳的tir(e)+ed (形容词后缀)retired/ri tai☜d/a.退休的re(前缀:再)+tired [再劳累就退休吧]中文串联：老消防员灭火时特劳累，累的，疲劳的，再(re)也不能干下去了，到退休的时候了torystory/ st ri/n.故事，小说history/ hist☜ri/n.历史his(他的)+story [他的故事编进了历史]victory/ vikt☜ri/n.胜利v(手指动作)vi+ctory [胜利成了故事编成了小说，(注意c)]中文串联：他的动人故事写进了历史，写成了小说，叙述着胜利的喜悦tectprotect/pr☜tekt/v.保护pro+tect detect/di tekt/v.民现，察觉de+tect detective/di tektiv/a.侦察的；n.侦探detect+ive（形容词后缀）中文串联：被保护人发现察觉了侦探侦侦察的跟踪temple/templ/n.庙宇，寺院temperature/ tempr☜♦☞☜/n.温度temp+er+ature(名词后缀)中文串联：庙宇寺院由于烧香温度很高type/taip/n.类型，类v.打字tape/teip/n.磁带中文串联：商场上，各种类型的磁带琳琅满目ten/ten/num.十tennis/ tenis/n.网球ten+nis(十个网球) tent/tent/n.帐篷ten+t [十个特(t)别的帐篷]中文串联：在十个特别的帐篷中放着十个网球team/ti m/n.队，组谐音：替补--队，组term/t☜m/n.学期谐音：特务--培训需几个--学期中文串联：替补队.组的特务培训还要几个学期table/teibl/n.表格，课桌表格放在课桌上timetable/ taimteibl/n.时刻表time(时间)+table [时间表格--时刻表]vegetable/ ved✞♓♦☯♌●/n.蔬菜vege(音：万只)+table [万只课桌上长起了--蔬菜]中文串联：课桌上刻着时刻表，生长着万只蔬菜sure/☞◆☜/a.ad.确信，当然，有把握cure/kju☜/v.治愈，治疗中文串联：医生确信有把握治愈治疗好这种病ubetube/tju b/n.管子谐音：挑拨--这个--管子cube/kju b/n.立方体，立方谐音：Qb--阿Q不懂--立方体，立方中文串联：挑拨管子摆成立方，立方体，阿Q不懂urnburn/b☜n/v.燃烧，发热turn/t☜n/v.转动，转变；n.轮到中文串联：煤燃烧，发热，转动机器转变为电能ullbull/bul/n.公牛谐音：b--捕dull/d✈l/a.乏味的，迟钝的谐音：d--当pull/pul/v.拉，拖谐音：p--铺中文串联：捕捉这头公牛是件相当乏味的，令人迟钝的事，铺平路才能拉，拖回来use/ju s/v.用谐音：有--用useful/ ju sful/a.有用的use+ful(形容词后缀) museum/mju zi☜m/n.博物馆m+use+u+m--门+用+无+门门里有用无用皆有--博物馆amuse/☜❍◆/v.娱乐，消遣am+use [俺们有--娱乐，消遣]ushpush/pu☞/v.推谐音：扑--倒--是被--推rush/❒✈☞/v.冲，奔谐音：入啊--冲啊--冲，奔brush/b❒✈☞/n.刷子b(不)+rush [不去冲洗--刷子]中文串联：把他推上前线，冲奔上阵，还真是把刷子uckduck/d✈k/n.鸭luck/l✈k/n.幸运，运气lucky/ l✈ki/a.幸运的luck+y(形容词后缀) luckily/ l✈kili/ad.幸运地，侥幸地lucki+ly(副词后缀) unlucky/ ✈⏹l✈ki/a.不吉祥的un(前缀:不)+lucky(幸运的) [不是幸运的--不吉利的]中文串联：鸭子是幸运的,侥幸的逃过了不吉祥的命运umpjump/dʒʌmp/v.跳pump/pʌmp/v.用抽水机抽p(嘭)+um+p(嘭) [用抽水机抽时两端发出的声音]中文串联：用抽水机抽时，水泵跳了起来。
2019高中英语新教材必修一 Welcome Unit单词详解
2019高中英语新教材必修一Welcome Unit单词详解（全）思可为Thinkwell原创发布---------------------------------------------------------------------------------------------------------------------- 1. exchange/ɪks'tʃeɪdʒ/n.交换；交流vt.交换；交流；交易；兑换ex- 向外。
change改变，变换，交换。
exchange交换出去，交易出去。
exchange A for B把A交易出去，把B换回来。
2. lecture/'lektʃə(r)/n.讲座；讲课；教训vi.(开)讲座；讲课vt.训斥lect-天选，选择—说话，如“急不择言”，急得来不及选择词语，形容说话十分急迫或紧张。
-ure名词后缀，如creature生物。
3. registration /redʒi'streiʃ(ə)n/n.登记；注册；挂号re-回。
gistr-携带，拿，来自PIE root *ag- "to drive, draw out or forth, move"驱使，移动，挪动。
-ation名词后缀。
register的意思是“拿回信息”，即记录信息、登记信息、注册信息。
4. register/'redʒɪstə(r)/vt.& vi.登记；注册register的意思是“拿回信息”，即记录信息、登记信息、注册信息。
5. sex/seks/n.性别sex是一个拟声词，（S）K的音就是咔咔咔地砍，引申为分开——区分开——区别——性别。
所谓男女有别，“别”右边是把刀，左边是“另外”的“另”，意思是用刀分开。
看来中英文语义逻辑差不多。
这里存在语音通转：C=G=K=CH=KH=X，都是“砍、割、刻”的声音。
6. female /'fiːmeɪl/ adj. 女性的；雌性的n. 女性；雌性动（植）物fe-的词根是PIE root *dhe(i)- "to suck"，dh进入拉丁语是变成了f，进而*dhe(i)- 进入英语变成了fe-（原始印欧语dh=希腊语th=拉丁语f/d）。
英语新北师大版(2019)选择性必修第一册 UNIT 3 Period1TopicTalk
【语言提升】 switch to切换到，变成 To keep fit, you can switch to morning or lunchtime exercise. 为了保持健康，你可以转变到早上或午间锻炼。 Please switch to the news channel. I’d like to watch the news program. 请转换到新闻频道。我想看看新闻。
【针对练习】 单句语法填空 (1)Please ________ the radio to listen to news and the weather forecast. (2)Be sure to ________ the light when you leave the office.
(3)We’d better take the train into the city center, then a bus, ________ the tram(有轨电车), then maybe a taxi.
My uncle hasn’t been able to quit smoking, but at least he has cut down.
我叔叔还未能戒烟，但至少他已经少抽了。 We need to cut the article down to 1,000 words. 我们得把这篇文章压缩到1 000词。
【针对练习】 单句语法填空 (1)Wildlife has been greatly ________(threat) in the modern age. (2)Our neighbor threatened ________(call) the police if we didn’t stop the noise.
高斯讲座Lecture 07
The spin state of the molecule must also be specified when inputting an electronic structure calculation. •For closed shell systems, the spin state is a singlet (s=0) •For a system with a single dangling bond, the charge state is usually a doublet (s=1/2) •For a system with multiple unpaired electrons, the charge state is not often obvious.
QC Practical Issues
Lecture 7 Page 7
Methylene example
Methylene: Neutral molecule. Singlet or triplet? 2 CH bonds CH ~ 1.09Å 2 mirror planes. (C2V symmetry, like water).
3 Nodes
QC Practical Issues
Lecture 7 Page 2
Molecular Orbitals from SALC of Atomic Orbitals
We can make combinations of SALC of atomic orbitals to form molecular orbitals:
QC Practical Issues
Lecture 7 Page 6
Ethylene example
大学英语课本答案
Unit oneword s in actio nExercise one:1. N owaday s pe ople pre fe r to commu nicate withone anothe rby e-mai l.2. Bein g tall gav e him a(n) advantage over the ot her player s.3. He b ased his a rticle onthe rele va nt informa tion he hadgathered.4. Sometim es s he eat s a lo t an d someti me s nothingat all; shejust goesfr om one e xtre me tothe ot her.5. It i sassumed th at the Inter net is anef ficientmean s of c ommuni cati on.Exer ci se 3:1. I t is not tha t I don'tli ke thissing er. Th e fact isthat I'mn ot very fo nd of countr y music.2.The cost isdirect ly rel ated to theam ount of ti me spent onthe projec t.3. We a re p aid ac cordin g to how muc hwork we do.4. To a ce rtain exte nt, it was myfaultthat w e lo st the m at ch.5. Gir ls may bring their boyf riends t o th e part y andvice versa.6. He is alw ays ready to help othe rs; no dou bt h e'll b e will ingto helpyo u , too.7. Y ou must p ay $2000;or else, y ou w ill ha ve togo t o prison.8. cleared up 9. or e lse 10. a tall cost s 11. sur e enou gh12. He ca nn ot ride abicycle, let alone a m ot orbike.13.What h e talk ed a bout inye sterday'slecture is b ased on wh at he says inthe ar ticle.14. It's nou se worryin g about Jim; he is noww ith hisaunt who l oves h im a nd willno doubt tak e good careof him.15.He wants toimprov e hisEngl ish by r ea ding dicti onaries, but in my vie wit is no t an effec tive m etho d of lea rn ing.16. I called Lind a last nig ht and ask ed h er ifthe ex hibi tion ofCh inese pain ting in heruniversityw as worth see ing.T ransla tion from Ch in es to engl ish:1. 这个婴儿还不会爬,更不要说走了.(let alo ne)The ba by can't e ven craw lyet, let a lone walk!2. 威尔声称谋杀案发生时,他正在与一群朋友吃饭,但是我认为他在说谎.(c laim, in one's opinion)Will claimed he was di ni ng witha gr oup of frien ds a t the ti me of the mu rder, but in my opinio nhe tolda li e.3.一定程度阅读速度与阅读技巧密切相关.有了阅读技巧,你就可以更好地应对课外阅读了.(t o a certai nextent,rela te ...to..., cop e with)To a certain extent thespeed of r ea ding isclos ely re latedto r eading s ki lls; and w ith readingskills youc an copewith outsi de cla ss r eading b et ter.4. 根据规则他俩都可以参加比赛.(accordingt o)Accor ding to th e regu lati on/rule,t hey both c an play thegame .5.有些人想当然地认为日语中的每一个词在汉语中都有对应的词语.(assume,eq uivalent)Some peopleassume tha tthere is a C hinese equiv alen t for ev er y Japanese word.6. 我们已将所有的相关信息告知了警方.(rele vant)We h ave pa ssed all rel ev ant inform antion on to the polic e.7. 关于那件事你问我再多的问题也没有,因为我是不会回答你的.(it'sno use)It is no useasking mean y more q uest ions a bout t hatmatter b ec ause i won't answer.8. 事先没有仔细阅读合同就签了名是吉姆的错误.(on one's par t)I t was ami stake on J im's part to sign theco ntract w itho ut rea ding i t ca refully.9. 他们拒绝向我们提供所需要的全部信息.(p rovide...w it h...)Th ey r efused to pr ovid e us wit hall the in formation we need.10.这起事故与三年前发生的一起事故极为相似.(simi larto)Thisa ccident is very simila r to the o ne that ha ppen ed thr ee yea rs a go.11.这部影片是根据莎士比亚的戏剧改编的.(baseon)This f il m is bas ed o n a pl ay byShak espeare.12. 如果你的英语和电脑技能都掌握得好,那么你在谋职时就一定比别人更有优势.(hav e ad vantag e over)If you hav ea good com mand of Engl ish and co mp uter ski lls,you w ill su rely have ana dvantage o ver others i n findingajob.13.然而大量的教学活动建立在行为主义心理学基础之上。
纺织专业英语课件
Lecture 1—Classification of fibers
Espol--PTT纤维
ESPOL (SDY): 50/24, 50/48, 75/36, 75/72, 100/48, 150/96 规格
ESPOL (DTY): 50/24, 75/24, 75/36, 75/72, 150/48 150/72, 150/144
solution spinning=＞wet spinning
Lecture 1-- Classification of fibers
Rayon—R：人造丝 Rayon stable －人造丝短纤维 泛指以天然纤维素为基本原料，以Viscose法或者 Cuprammonium 法生产的化学纤维，习惯指长丝
Natural fiber-Vegetable fiber Color cotton —green, brown
Lecture 1-- Classification of fibers
Kapok--木棉
Lecture 1-- Classification of fibers
bast fiber: ramie—Ram：苎麻 flax—F：亚麻
Lecture 1- Classification of fibers
Regenerated fibers Viscose --Vis：粘胶
天然纤维素，经碱化、老化、黄化等工序制成
可溶性纤维素黄酸酯
再溶于稀碱液=＞纺丝=＞凝固浴
Spinning method: solution spinning
bamboo original fiber--竹原纤维
Anti-bacterial fiber--抗菌 odor resistant fiber--除臭 ultraviolet resistant fiber --抗紫外线 Emit negative ions --发射负氧离子
lecture7
第七讲 载流子的漂移和扩散（续）9月16，2001内容：1.漂移2.扩散3.传输时间阅读作业del Alamo Ch. 4，§4.2-4.4主要问题●在电场中，载流子如何移动？漂移速度主要由什么决定？●能带图如何表示一个电场的存在？●浓度梯度如何影响载流子？●平均起来，一个载流子通过漂移或扩散从半导体的一个区域移动另一个区域要花多长时间？⒈ 漂移存在电场时载流子发生移动：□ 漂移速度－电场：ε－加在电子上的电场力：q ε−－碰撞间的加速度：ceq m ε∗−－在时间ce τ获得的速度：drift cee ce q m ετυ∗=−或 drift ee υµε=− e µ电子迁移率[2/cm V s ]迁移率表明载流子响应ε的容易程度。
drift e e υµε=−drift h h υµε=−迁移率取决于掺杂水平以及是多数载流子还是少数载流子类型。
Si 在300K 时：●在低的N时：由声子散射所限制●在高的N时：由离化杂质散射所限制□ 速度饱和隐含的假定：准平衡，也就是说，散射率不太受平衡的影响。
drift drift thυευυ:=只在对高的ε：载流子从ε许多能量→光子发射显著增强→散射率1/ε:→漂移速度饱和sat υ;对Si 在300K 时，710/sat cm s υ;漂移速度与电场的关系由下式很好的表示： 1drift satµευµευ=+m 速度饱和时所要求的电场： satsat υεµ=在现代器件中速度饱和是至关重要的：如果2500/cm V s µ=，4210/sat V cm ε=（1m µ上2V ）因为µ取决于掺杂，sat ε也取决于掺杂。
□ 粒子流和电流密度粒子流#粒子通过单位的表面（与流动方向正交）每单位时间[21cm s −−]电流密度电荷通过单位的表面（与流动方向正交）每单位时间[21cm s −−]e e J qF =−e e e n dt F n dt υυ==那么e e J qn υ=− h hJ qn υ=−漂移电流（低电场）e e J q n µε=h h J q n µε=总的为：()e h J q n p εµµε=+电导率[()1cm −Ω]：()e h q n p σµµ=+电阻率[cm Ω]：()1e h q n p ρµµ=+检查符号：()1e h q n p ρµµ=+ρ强烈的依赖于掺杂经常被硅片供应商用来表明衬底的掺杂水平 -对n 型：1n e D q N ρµ; -对p 型：1p h A q N ρµ;Si 在300K 时：漂移电流（高电场）：esat esatJ qn υ= hsat hsatJ qn υ=得到更大电流的唯一方法是增加载流子浓度。
《创新设计》高中英语外研版选修7(课标通用)配套课件-1-1电子教案
martokpe-dclafossr vmaortiiovuatsiobnall games
4．________adj.of very good quality or a very high
standard
6．_va_r_io_u_s___adj.different 7 ．tal_en_t_e_d____adj.having a natural ability to do
[，例是句现仿在写分] 词作状语，其逻辑主语是主句的主语。
穿着11号球衣，姚明在火箭队打了几个
赛W季ea。ring
his number 11
shirt
________ ________ ________ ________
________ ， Yao Ming played several seasons in
5．But there is no doubt that he deserves the title “outstanding player of his generation”． [信息提取] there is no doubt that毫无疑问 [例句仿写] 毫不怀疑，汤姆会准时来。 __T_h_e_re___ __i_s _____ _no______do_u_b_t ___th_a_t_ ________ Tom will come on time.
③As you can see，Michael Jordan is someone who is worth recognition. He is someone who I look up to when it comes to the game.Jordan has accomplished a lot，and it wasn't all fun and games，it took a lot of hard work ， practice and effort to be one of the greatest basketball players of all times.Now do you see why everyone wants to be like Mike? Everyone wants the fame，the fortune and the just plain and simply the life that Michael Jordan lives.Jordan is an example that whatever you dream to become，it is possible to become just that.And whatever your goal is，you can reach it ， with a little hard work ， effort ， and
ch7RiskandRatesofReturn(solutions_nss_nc_8)
Chapter 8Risk and Rates of ReturnLearning ObjectivesAfter reading this chapter, students should be able to:◆Define risk and calculate the expected rate of return, standard deviation, and coefficient of variation fora probability distribution.◆Specify how risk aversion influences required rates of return.◆Graph diversifiable risk and market risk; explain which of these is relevant to a well-diversified investor.◆State the basic proposition of the Capital Asset Pricing Model (CAPM) and explain how and why aportfolio’s risk may be reduced.◆Explain the significance of a stock’s beta coefficient, and use the Security Market Line to calculate astock’s required rate of return.◆List changes in the market or within a firm that would cause the required rat e of return on a firm’sstock to change.◆Identify concerns about beta and the CAPM.◆Explain the implications of risk and return for corporate managers and investors.179Lecture SuggestionsRisk analysis is an important topic, but it is difficult to teach at the introductory level. We just try to give students an intuitive overview of how risk can be defined and measured, and leave a technical treatment to advanced courses. Our primary goals are to be sure students understand (1) that investment risk is the uncertainty about returns on an asset, (2) the concept of portfolio risk, and (3) the effects of risk on required rates of return.What we cover, and the way we cover it, can be seen by scanning the slides and Integrated Case solution for Chapter 8, which appears at the end of this chapter solution. For other suggestions about the lecture, please see the “Lecture Suggestions” in Chapter 2, where we describe how we conduct our classes.DAYS ON CHAPTER: 3 OF 58 DAYS (50-minute periods)180Answers to End-of-Chapter Questions8-1 a.No, it is not riskless. The portfolio would be free of default risk and liquidity risk, but inflation could erode the portfolio’s purchasing power. If the actual inflation rate is greater than thatexpected, interest rates in general will rise to incorporate a larger inflation premium (IP) and—as we saw in Chapter 7—the value of the portfolio would decline.b.No, you would be subject to reinvestment rate risk. You might expect to “roll over” theTreasury bills at a constant (or even increasing) rate of interest, but if interest rates fall, yourinvestment income will decrease.c. A U.S. government-backed bond that provided interest with constant purchasing power (that is,an indexed bond) would be close to riskless. The . Treasury currently issues indexed bonds.8-2 a.The probability distribution for complete certainty is a vertical line.b.The probability distribution for total uncertainty is the X-axis from -∞ to +∞.8-3 a.The expected return on a life insurance policy is calculated just as for a common stock. Each outcome is multiplied by its probability of occurrence, and then these products are summed.For example, suppose a 1-year term policy pays $10,000 at death, and the probability of thepolicyholder’s death in that year is 2%. Then, there is a 98% probability of zero return and a2% probability of $10,000:Expected return = ($0) + ($10,000) = $200.This expected return could be compared to the premium paid. Generally, the premium will be larger because of sales and administrative costs, and insurance company profits, indicating anegative expected rate of return on the investment in the policy.b.There is a perfect negative correlation between the returns on the life insurance policy and thereturns on the policy holder’s human capital. In fact, these events (death and future lifetimeearnings capacity) are mutually exclusive. The prices of goods and services must cover theircosts. Costs include labor, materials, and capital. Capital costs to a borrower include a returnto the saver who supplied the capital, plus a mark-up (called a “spread”) for the financialintermediary that brings the saver and the borrower together. The more efficient the financialsystem, the lower the costs of intermediation, the lower the costs to the borrower, and, hence,the lower the prices of goods and services to consumers.c.People are generally risk averse. Therefore, they are willing to pay a premium to decrease theuncertainty of their future cash flows. A life insurance policy guarantees an income (the facevalue of the policy) to the policyholder’s beneficiaries when the policy holder’s future earningscapacity drops to zero.8-4Yes, if the portfolio’s beta is equal to zero. In practice, however, it may be imp ossible to find individual stocks that have a nonpositive beta. In this case it would also be impossible to have a stock portfolio with a zero beta. Even if such a portfolio could be constructed, investors would probably be better off just purchasing Treasury bills, or other zero beta investments.1818-5Security A is less risky if held in a diversified portfolio because of its negative correlation with other stocks. In a single-asset portfolio, Security A would be more risky because σA > σB and CV A > CV B. 8-6No. For a stock to have a negative beta, its returns would have to logically be expected to go up inthe future when other stocks’ returns were falling. Just because in one year the stock’s return increases when the market declined doesn’t mean the s tock has a negative beta. A stock in a given year may move counter to the overall market, even though the stock’s beta is positive.8-7The risk premium on a high-beta stock would increase more than that on a low-beta stock.RP j = Risk Premium for Stock j = (r M– r RF)b j.If risk aversion increases, the slope of the SML will increase, and so will the market risk premium (r M– r RF). The product (r M– r RF)b j is the risk premium of the j th stock. If b j is low (say, , then the product will be small; RP j will increase by only half the increase in RP M. However, if b j is large (say, , then its risk premium will rise by twice the increase in RP M.8-8According to the Security Market Line (SML) equation, an increase in beta will increase a company’s expected return by an amount equal to the market risk premium times the change in beta. For example, assume that the risk-free rate is 6%, and the market risk premium is 5%. If the company’s beta doubles from to its expected return increases from 10% to 14%. There fore, in general, a company’s expected return will not double when its beta doubles.8-9 a. A decrease in risk aversion will decrease the return an investor will require on stocks. Thus, prices on stocks will increase because the cost of equity will decline.b.With a decline in risk aversion, the risk premium will decline as compared to the historicaldifference between returns on stocks and bonds.c.The implication of using the SML equation with historical risk premiums (which would be higherthan the “current” risk premium) is that the CAPM estimated required return would actually behigher than what would be reflected if the more current risk premium were used.182183Solutions to End-of-Chapter Problems7-1r ˆ = (-50%) + (-5%) + (16%) + (25%) + (60%) = %.σ2 = (-50% – %)2 + (-5% – %)2 + (16% – %)2+ (25% – %)2 + (60% – %)2σ2 = ; σ = %.CV =11.40%26.69% = .7-2 Investment Beta $35,00040,000Total $75,000b p = ($35,000/$75,000) + ($40,000/$75,000) = .7-3 r RF = 8%; r M = 12%; b = ; r = ?r = r RF + (r M – r RF )b = 8% + (12% – 8%)= %.7-4 r RF = %; RP M = %; r M = ?r M = % + %)1 = 12%.r when b = = ?r = % + % = %.7-5a. r = 11%; r RF = 7%; RP M = 4%.r = r RF + (r M – r RF )b 11% = 7% + 4%b4% = 4%b b = 1.184b. r RF = 7%; RP M = 6%; b = 1.r = r RF + (r M – r RF )b= 7% + (6%)1 = 13%.7-6a. ∑==N 1i i i r P r ˆ.Y r ˆ = (-35%) + (0%) + (20%) + (25%) + (45%)= 14% versus 12% for X.b. σ =∑=-N 1i i 2i P )r ˆr (.2X σ = (-10% – 12%)2 + (2% – 12%)2 + (12% – 12%)2 + (20% – 12%)2 + (38% – 12%)2 = %.σX = % versus % for Y.CV X = σX /r ˆX = %/12% = , whileCV Y = %/14% = .If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.7-8 Portfolio beta =$4,000,000$400,000 + $4,000,000$600,000 + $4,000,000$1,000,000 + $4,000,000$2,000,000b p = + + += – + + = .r p = r RF + (r M – r RF )(b p ) = 6% + (14% – 6%) = %.Alternative solution: First, calculate the return for each stock using the CAPM equation [r RF + (r M – r RF )b], and then calculate the weighted average of these returns.r RF = 6% and (r M – r RF ) = 8%.Stock Investment Beta r = r RF + (r M – r RF )b Weight A $ 400,000 18%B 600,000 2C 1,000,000 16D 2,000,000 12 Total $4,000,000r p = 18% + 2% + 16% + 12% = %.7-9In equilibrium:r J =rˆ = %.Jr J = r RF + (r M– r RF)b% = % + % – %)bb = .7-10We know that b R = , b S = , r M = 13%, r RF = 7%.r i = r RF + (r M– r RF)b i = 7% + (13% – 7%)b i.r R = 7% + 6% = %r S = 7% + 6% =%7-11An index fund will have a beta of . If r M is % (given in the problem) and the risk-free rate is 5%, you can calculate the market risk premium (RP M) calculated as r M– r RF as follows:r = r RF + (RP M)b% = 5% + (RP M)% = RP M.Now, you can use the RP M, the r RF, and the two stocks’ betas to calculate their required re turns.Bradford:r B= r RF + (RP M)b= 5% + %)= 5% + %= %.Farley:r F= r RF + (RP M)b= 5% + %)= 5% + %= %.The difference in their required returns is:% – % = %.7-12r RF = r* + IP = % + % = 6%.r s = 6% + %) = %.1851867-13a. r i = r RF + (r M – r RF )b i = 9% + (14% – 9%) = %.b. 1. r RF increases to 10%:r M increases by 1 percentage point, from 14% to 15%.r i = r RF + (r M – r RF )b i = 10% + (15% – 10%) = %.2. r RF decreases to 8%:r M decreases by 1%, from 14% to 13%.r i = r RF + (r M – r RF )b i = 8% + (13% – 8%) = %.c. 1. r M increases to 16%:r i = r RF + (r M – r RF )b i = 9% + (16% – 9%) = %.2. r M decreases to 13%:r i = r RF + (r M – r RF )b i = 9% + (13% – 9%) = %.7-15 Using Stock X (or any stock):9% = r RF + (r M – r RF )b X9% = % + (r M – r RF ) (r M – r RF ) = %.7-16 Old portfolio beta =$150,000$142,500(b) + $150,000$7,500 = +== b.New portfolio beta = + = ≈ .Alternative solutions:1. Old portfolio beta == b 1 + b 2 + ... + b 20= ∑)b (i ∑i b = = .New portfolio beta = – + = ≈ .2. ∑i b excluding the stock with the beta equal to is – = , so the beta of the portfolioexcluding this stock is b = 19 = . The beta of the new portfolio is:+ = ≈ .1877-17 b HRI = ; b LRI = . No changes occur. r RF = 6%. Decreases by % to %. r M = 13%. Falls to %. Now SML: r i = r RF + (r M – r RF )b i . r HRI = % + % – %) = % + 6% = % r LRI = % + % – %) = % + 6% = % Difference %7-18 Step 1: Determine the market risk premium from the CAPM:= + (r M – r RF ) (r M – r RF ) = .Step 2: Calculate the beta of the new portfolio:($500,000/$5,500,000) + ($5,000,000/$5,500,000) = .Step 3:Calculate the required return on the new portfolio:% + %) = %.7-19 After additional investments are made, for the entire fund to have an expected return of 13%, the portfolio must have a beta of as shown below:13% = % + %)b b = . Since the fund’s beta i s a weighted average of the betas of all the individual investments, we can calculate the required beta on the additional investment as follows:= 000,000,25$)5.1)(000,000,20($ + 000,000,25$X 000,000,5$ = +=X = .7-20a. ($1 million) + ($0) = $ million.b. You would probably take the sure $ million.c. Risk averter.d. 1. ($ million) + ($0) = $575,000, or an expected profit of $75,000.2. $75,000/$500,000 = 15%.3. This depends on the individual’s degree of risk aversion.4. Again, this depends on the individual.5. The situation would be unchanged if the stocks’ returns were perfectly positively correlated.Otherwise, the stock portfolio would have the same expected return as the single stock(15%) but a lower standard deviation. If the correlation coefficient between each pair ofstocks was a negative one, the portfolio would be virtually riskless. Since ρ for stocks isgenerally in the range of +, investing in a portfolio of stocks would definitely be animprovement over investing in the single stock.7-21rˆ = 10%; b X = ; σX = 35%.Xrˆ = %; b Y = ; σY = 25%.Yr RF = 6%; RP M = 5%.a.CV X = 35%/10% = . CV Y = 25%/% = .b.For diversified investors the relevant risk is measured by beta. Therefore, the stock with thehigher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X.c.r X = 6% + 5%= %.r Y = 6% + 5%= 12%.d.r X = %;rˆ = 10%.Xr Y = 12%;rˆ = %.YStock Y would be most attractive to a diversified investor since its expected return of % isgreater than its required return of 12%.e.b p= ($7,500/$10,000) + ($2,500/$10,000)= += .r p = 6% + 5%= %.f.If RP M increases from 5% to 6%, the stock with the highest beta will have the largest increasein its required return. Therefore, Stock Y will have the greatest increase.Check:r X= 6% + 6%= %. Increase % to %.r Y= 6% + 6%= %. Increase 12% to %.188百度文库 - 让每个人平等地提升自我1897-22 The answers to a, b, c, and d are given below:r Ar BPortfolio 2001 %) %) %) 2002 2003 2004 2005Mean Std. Dev.Coef. Var.e. A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since theportfolio offers the same expected return but with less risk. This result occurs because returns on A and B are not perfectly positively correlated (r AB = .7-23 a. M r ˆ = (7%) + (9%) + (11%) + (13%) + (15%) = 11%.r RF = 6%. (given)Therefore, the SML equation is:r i = r RF + (r M – r RF )b i = 6% + (11% – 6%)b i = 6% + (5%)b i .b. First, determine the fund’s beta, b F . The weights are the percentage of funds invested in eachstock:A = $160/$500 = .B = $120/$500 = .C = $80/$500 = .D = $80/$500 = .E = $60/$500 = .b F = + + + + = + + + + = .Next, use b F = in the SML determined in Part a:F r ˆ = 6% + (11% – 6%) = 6% + 9% = 15%.c. r N = Required rate of return on new stock = 6% + (5%) = 16%.An expected return of 15% on the new stock is below the 16% required rate of return on aninvestment with a risk of b = . Since r N = 16% > N r ˆ= 15%, the new stock should not be purchased. The expected rate of return that would make the fund indifferent to purchasing the stock is 16%.。
字母发音规律
（１）、字母Bb的发音规律1。
字母 b一般读/b/，如：bike，bus, bag， boot，2。
但位于m后或t前,这时b不发音。
如：climb,comb，tomb，debt,doubt如果不在同一个音节里,不受影响。
如：December， Nove mber.试读下列单词：big, bed， break, bomb， tomb， lamb (2)字母Cc的发音规律1. 字母c 在胖元音（a， o， u)和辅音字母之前读/k/，例如：cap， cold， cut, picture2.在瘦元音(e, i/y）之前读/s/，例如: centre, city， cycle3。
在ia之前读/∫/,如：special， social。
试读下列单词：cat， clinic, clothes, cute, circle， cemetery, cent （3)字母Dd的发音规律1. 字母d或—ed在清辅音之后读/t/,例如： work-worked2. 在浊辅音和元音之后读/d/,例如:move-moved, , offer—offered。
3. 在t和d之后读/id/。
例如：want—wanted， guide-guided,试读下列单词：live-lived， reach-reached， smile-sm iled， wish—wished， improve—improved， destro y—destroyed(４）、字母Gg的发音规律1。
字母g在胖元音（a， o, u）和辅音字母之前通常读/ g /, 2。
在瘦元音（e, i/y）之前读/dʒ/.例如： gesture， giant, gym,。
(get, give， gift， forget, begin, forgive， gear， girl， a nger, hunger等词例外).试读下列单词：gather， general， gem, god， gymnast (５)、字母Nn的发音规律1.字母n通常读/n/，2. 词尾是mn时，n一般不发音,例如：autumn,column；3字母n在/k/、/ g / 音前或ng组合中读/ŋ /，例如：thank，language，bank,anxious.试读下列单词： fine, cent, uncle, hungry， young， si ng（６）、字母Ss的发音规律1. 字母s 在音节开头或清辅音前读/s/,例如：sit, sleep, desk2. 在元音字母间或浊辅音前读/z/，例如： music, husband；3. 在名词变复数或动词变为单数第三人称形式时，位于清辅音之后读/s/,例如：book-books, work-works; 位于浊辅音和元音之后读/z/，例如:radio-radios， apple —apples;如果这个名词或动词的结尾读音为/s/或/z/，加—s后应读/i z/,例如：place—places, house-houses；在以s, x， ch， sh结尾的词加—es, 读/iz/,例如:class-classes, box-boxes， watch-watches， b rush-brushes。
Lecture 24 Degenerate Fermi Gas (Ch 7) - Department of 讲座24退化的费米气体系
empty states
EF
0
conduction band
valence band
electron states in an isolated
atom
electron states in metal
The electrons are prevented from escaping from the metal by the net Coulomb attraction to the positive ions; the energy required for an electron to escape (the work function) is typically a few eV. The model assumes that the electrons for an ideal Fermi gas confined within impenetrable walls.
expkBT1
The most important degenerate Fermi gas is the electron gas in metals and in white dwarf stars. Another case is the neutron star, whose density is so high that the neutron gas is degenerate.
EF2m 2 32n2/38hm 23n2/3
the Fermi energy ( of an ideal Fermi gas at T=0)
= EF
E F 8 h m 2 3 n 2 /3 6 8 .6 9 1 1 3 3 0 0 2 4 1 1 120 2 9 /3J 1 1 10 J 8 6 eV
流平剂(2)
Ａ
一一：竺恐·：Ｚ鼍黧ｊ耋要紫ｉ雩擘髦竺黧乙酯 氧系粉末涂料中作为流平助剂的专利ｕｓ ４０１ ７４４７，明确相
莴蒜器子磊
对分子质量为５ ｏＯＯ～１ ５ ０００之间的液态１ ＯＯ名Ｓ聚丙烯酸
甲基丙烯酸月桂酯
Ｂ
黧
莴磊蒜
马来酸单丁酯
ｃ
鬻凝誓
甲釜莴蒜鑫；：曩莴酯
甲基丙烯酸２一羟乙酯
乙酯。 一Ｂａｙｅｒｌ ９７６年公布了ＵＳ ３９４７５２８直指Ｈｏｄａｆｌ。ｗ，认
号很多。
讪一羞啦Ｈ妾坩斟挚 蚕黧翥禚纛罴醮篓
Ｈ。十ｃＨ２，ｒ１１０‘【ｃＨ矗ｒｌ｝。一ｃＨ２一ｓ“ｃＨ３＇『。千ｓ“ｃＨ３圩。七ｒｓｉ（ｃＨ３＇ｒｃＨ２一。＿ｔｌ十ｃＨ２）ｒ。ｔｌ十ｃＨ２）ｒ。Ｈ 式。。４，
一伽小一计响２）５一ｌｊ＿州ｃＨ２）３叫（ｃＨ３沪。十溯３）２０榔耥卜唧咖一１矿㈣㈣ｔｌ一出～搠。，
万方数据
涂拳斗讲坛
‘｛。“舭。
Ｃｏａｔｉｎｇｓ Ｌｅｃｔｕｒｅ
…一阱 ｓｉ—Ｏ—
Ｉ
ｌ
Ｉ
０（ｃＨ赴ｃ暑Ｆ１７
＾怔婀№ｋ—ｒ一恒啦叫 ｃＨ３ ｆｃＨ
：Ｈ２）２ｃ８Ｆｌ，
聚酯或聚醚的（甲基）丙烯酸酯见！ ￡３２。
一
Ｒ１一
ｃＨ ２一ｃ一 一×
，、ＩＨ２ｃ矿“导“、Ｒ２卜—ｉ＿～
０正Ｃ
诵～一ｅ世一１ 阱｝…。秘轰，Ｌ
显然，Ａ是丙烯酸酯为主，Ｂ是羧基单体，Ｃ是羟基 单体。上述共聚物能够作为各种工业涂料的流平助剂，且 能帮助消除··鱼眼”。
根据上述聚丙烯酸酯流平助剂的变迁，可以理解的 是：
（１）丙烯酸的烷基酯起着提供基本表面活性的作用。 （２）一ｃ００Ｈ、一０Ｈ、一ＮＲ，能帮助上面的结构调整相容 性，以适用于各种不同的体系。 （３）相对分子质量大小与最终的展布性能直接有关， Ｔｅｇｏ的非硅型流平剂资料中列出了相容性要求，见图７。 具有临界的相容性以及聚丙烯酸酯的链构型都是成为合 适流平剂的必要条件。其可能的流平机理主要表现在后期 的流动控制阶段，见图８。
Lecture联立方程内生性问题Crosssectionandpanel
Lecture 12 (Ch16)
Simultaneous Equations Models (SEMs)
©
1
Introducdtion
We have learned two “sources” of endogeneity. 1. Omitted variables 2. Errn, the exgoneous variables in SEM are exogenous in ‘econometric sense’ as well.
In addition, the two structural errors, u1 & u2, are assumed to be uncorrelated with each other.
These two equations constitute a simultaneous equations model (SEM). These two equations are called the structural equations. α1,β1, α2, β2 are called the structural parameters. 7
In SEM framework, hi and wi are endogenous variables because they are determined by the equilibrium between the two equations.
In the same way, zi1 and zi2 are exogenous variables because they are determined outside of the model.
电化学课件-纯英文7Ultramicroelectrodes
EQCM - Principles of Operation
• Solution exerts a dampening effect:
– Under potential control – XPS, SEM, etc. not in situ
• Very sensitive
– Good for complex matrices
• Physiological fluids
• Detection limit
– pmole - fmole
ele–ctr2odeelectrodes sandwiching quartz (piezoelectric)
Quartz cry• sotaslcillating E surface of quartz wafer • oscillation at characteristic frequency (2 - 20 MHz)
• Stray capacitance
– Impurities
• Maintenance
– Cost – Fragile construction
UME’s - Applications
• Determine [analyte] • Study reactions
– at low temperatures = frozen glasses
• Biological systems
– Single cells – organelles
• Fast kinetics • Development of analytical tools for
英语音标对应字母(经典打印版)
英语音标极其对应字母1.辅音(1) [p] pen pear play pig pour pull push(2) [b] book big boot bike bread break(3) [t] tree two ten ton town twenty city(4) [d] door dull desk dose do dog dictionary(5) [k] king kite key look cook book kitchen sky (发音字母k)card cat cream correct climb come account accept (发音字母c)fox box oxygen x-ray (发音字母x)school schedule schema (字母组合ch)(6) [g] girl good goal goat grade long language(7) [m] man make moon morning move come comb(8) [n] pen ten nine fine night noon moon clean(9) [ŋ] uncle bank English think thank junksing king morning evening(10) [l] long land lend lord fly flag blackworld cold could goal soul(11) [r] read red right run room write(12) [f] five fly fine flag frog fog roof knife life wifecough laugh rough physic photo phone(13) [v] very evening even every voice vest(14) [s] six sit student same seat kiss miss case scarf (发音字母s)license city cease cedar ceiling celebrate (发音字母c)licence piece juice science lance space ace (字母组合ce) (15) [z] zoo zebra zero zapclose nose hose suppose pause those whose(16) [θ] think thank three thirty tooth mouth(17) [ð] that this those these though(18) [ʃ] sheep shoulder ship shoe she brush washnation attention stationsocial specialsure(19) [ʃə] pleasure(20) [h] hot hop home house horse how who(21) [w] when what where window wind wood(22) [j] yes year yell you your yolk yellow(23) [tʃ] child chicken china chair lunch ouch catch teach (字母组合ch）catch watch match （字母组合tch)(24) [dʒ] age language cabbage vegetable stage bridgejoy enjoy join July June junk(25) [tr] tree country try treat track trunk(26) [dr] dry dream drop drive drink(27) [ts] students boots boats goats nuts(28) [dz] goods woods moods hoods2.容易混淆的辅音(1) [v] [w]vest-west vet-wet vine-wine very-well(2) [s] [θ]sink-think mass-math miss-myth sort-sought(3) [z] [ð]close-cloth breeze-breathe(4) [n] [ŋ]thin-thing sin-sing ran-rang ban-bang win-wing3. 元音:(1) [i:] 字母组合:ee ea e ie ei (eo ey i)three tree green sheep meet beef see seekeat tea meat leave lead teacher team mean speak clean pleasehe she mepiece receive ceiling(2) [i] 发音字母i y e ui u asit picture it is list six mix fix fit pig big build miss myth many twenty happy dictionarydefect decide delicious(3) [æ]发音字母abag hand and ant happy hat map mad bad black back glad flag shall man(4) [e]字母组合ea e ahead bread pleasureelephant electric remember sell shell lesson better bed desk hotel yesmany any(5) [ə:] 字母组合ir ur ear er orgirl shirt skirt thirty thirteen third birdturn burn murder nurse turtle Thursday burgerlearn earn earth heardterm her nerd servework worm work world(6) [ə]字母组合er or ou ar o a e uteacher leader remember player speaker farmer powder doctor actor mayor author tractordelicious gracious pleasurefamiliar collar dollartogether tomorrow today shallop lesson Washington control polite around account ago elephant manta banana Canada Japan chinamen listenfamulus Saturday(7) [a:] 字母组合ar acar farm card arm gardenfast class last glass plant aunt calm(8) [ʌ]发音字母u o ou ooup supper lunch fun gun hunt cup buscome mother dose brother love abovetrouble rough flourishblood flood(9) [ɔ:]字母组合al or au our arsmall wall talk tall hall ball call walkshort more lord horse for forty sport door floor store author caught autumn four mourn court boughtwarm quarrel quarter draw saw flaw(10) [ɒ] / [ɔ]发音字母o a ouhot lost lot fox box mop hop loss collar notwant wash(11) [u:]字母组合oo o ufood moon room gloom broom doom goose toothshoe do two true truth blue full(12) [u] 字母组合oo ou u olook good foot book woodshould couldput full bull pull pushwomen whose wolf(13) [ei] 发音字母a ay ea ai eyname cake late gate plane Aprilplay say may waygreat breakrain paint plainthey grey(14) [ai] 发音字母i ybike fine find die nine light night highmy try fly eye(15) [au] 字母组合ou owhouse out flour ground account count sound loud around mouseflower down now cow how town(16) [əu] 发音字母o ow oahome cold go no phone host ghostknow low below grow blow show flowboat coat goal(17) [ɔɪ] 字母组合oy oiboy toy joyoil soil voice choice(18) [iə] 字母组合eer earbeer deerear near idea here fierce(19) [eə] 字母组合ear air erepear bearchair air faircarethere where(20) [uə]字母组合our owertour hourpoorflower shower4.容易混淆的元音(读音先后按音标顺序)(1) [æ] [e]bad-bed hand-head man-men land-lend pan-pen sad-said (2) [i] [ei]real-rail greet-great mean-main read-raid(3) [e] [ai]bet-bite red-write said-side head-hide(4) [au] [ɔ:]house-horse loud-lord south-sauce cloud-clause now-nor count-corn (5) [au] [ʌ]found-fond down-done gown-gone town-ton5.字母，组合音节发音规律(1) a[ei] late private grade bake grape nation station page [æ] active hand bank fan parent family glad flag[ə ] accept about above formative machine cinema [a:] fast last glass class past father[ɔ:] wash what watch want(2) e[i:] appreciate extremely secret she me he[e] letter left message generate pebble[i ] decide pretty previous result restore[ə] problem prosperous student confident[不发音] active table late wife store lecture(3) i[ai] high price library ice cream wife size line[i ] fist pick chicken piano fiance city unit(4) o[əu] lode host cold note okay old home[u:] lose do who whose prove[ʌ ] love some other mother honey company[ə] today tomorrow t ogether control collect[ɔ] lost hot mock office soft honest(5) u[ju] university refuse unique universe huge[u ] put push pull full bull[ʌ ] but brush bucket duck bubble[ə ] support suggest(6) c[k] country camp camera courage cable[s] city ceiling celebrate cell cease(7) g[g ] girl grade glass glade bag flag[dʒ] village vegetable bridge gentleman gym[ŋ ] long song sing morning evening(8) l[l] 读音不同listen learn anguage collect English gorilla world cold soil tall sell cool animal(9)n[n] moon night noodle number[ŋ] uncle hungry angry young(10) r[r] right read write grade progress[ɔ:] (美语发音)card board door floor form north (11) y[j] yellow year yell young yolk[i] university country pretty happy[ai] dyke dying fly buy by my(12)ar[a:] farm card garden mark[ə ] dollar[ɔ:] warm quarrel quarter(13) ea[i:] cease season breathe feature meat please[e] bread breast breath meadow weather[ei] great break[iə] idea realize(14) ear[ə:] learn earth earn heard[iə] hear near clear ear fear(15) er[ə:] deserve serve her person[ ə] teacher driver anger singer[iə] serious experience mysterious fierce(16) ere[iə] here mere fere sere[εə] there(17)ir[ə:] shirt girl skirt[ai] admire desire(18) oo[u:] room tool cool moon noon goof food[u] good foot stood wood wool cook wood book [ʌ] blood flood[ɔ:] door floor(19) or[ɔ:] short form corn born for[ə:] work world worm word worst[ə] tractor doctor actor sector senior senator (20) oor[ɔ:] door floor[uə] moor poor boor(21) our[uə] hour tour flour bourn lour[ɔ:] pour court four mourn(22) ou[au] house mouth mouse sound found[ʌ ] enough trouble touch[ə ] delicious gracious prosperous(23) ow[əu] window meadow know show low[au]now town how down cow(24) se[z] nose suppose gose lose pose rose[s] mouse house(25) th[θ]thank think thought cloth[ð] clothes that this then than(26) sion[ʃə n] Propulsion tension progression passion[ʒə n] protrusion provision conclusion television (27) tion[ʃə n] station nation translation attention[tʃə n] (不常见)question6.开音节:(1)辅音+元音+辅音+不发音e kite cake name bike make take home plane shine(2)辅音+元音he hi go no do be tree three hello8.闭音节:(1)辅音+元音+辅音sit bed bad bag hot hop let mad map head(2)元音+辅音it is of in on up out ant。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
7- 3
Cash Flow vs. Accounting Income
Discount actual cash flows Using accounting income, rather than cash flow, could lead to erroneous decisions. Example A project costs $2,000 and is expected to last 2 years, producing cash income of $1,500 and $500 respectively. The cost of the project can be depreciated at $1,000 per year. Given a 10% required return, compare the NPV using cash flow to the NPV using accounting income.
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc.,2001
7- 4
Cash Flow vs. Accounting Income
Cash Income Depreciation Accounting Income Year 1 Year 2 $1500 $ 500 - $1000 - $1000 + 500 - 500
1+ nominal interest rate 1 + real interest rate = 1+inflation rate
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
7- 10
Inflation
Example - nominal figures
- 2000 1500 500 Cash NPV = + + = −$223.14 2 3 1.10 (110) . (110) .
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
7- 6
Incremental Cash Flows
Discount incremental cash flows Include All Indirect Effects Forget Sunk Costs Include Opportunity Costs Recognize the Investment in Working Capital Beware of Allocated Overhead Costs
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
7- 12
Separation of Investment & Financing Decisions
When valuing a project, ignore how the project is financed. Following the logic from incremental analysis ask yourself the following question: Is the project existence dependent on the financing? If no, you must separate financing and investment decisions.
500 − 500 Accounting NPV = + = $41.32 2 1.10 (110) .
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
7- 5
Cash Flow vs. Accounting Income
Today Cash Income Project Cost Free Cash Flow - 2000 - 2000 Year 1 Year 2 $1500 $ 500 +1500 + 500
CF from Op Net Cash Flow -11,500
NPV @ 12% = $3,564,000
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc.,2001
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
7- 2
Topics Covered
Discounted Cash Flows, NetProfits Incremental Cash Flows Treatment of Inflation Separation of Investment & Financing Decisions Example: Blooper Industries
IMPORTANT Ask yourself this question Would the cash flow still exist if the project does not exist? If yes, do not include it in your analysis. If no, include it.
7- 1
Fundamentals of Corporate Finance
Third Edition
Chapter 7
Using Discounted Cash Flow Analysis to Make Investment Decisions
Brealey Myers Marcus
slides by Matthew Will
Cash Flow = 7766.99 = 7766.99 = 7766.99 = 7766.99
7766.99 1.068 7766.99 1.0682 7766.99 1.0683 7766.99 1.0684
PV@6.7961% = 7272.73 = 6809.92 = 6376.56 = 5970.78 = $26,429.99
$26,429.99
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc.,2001
7- 11
Inflation
Example - real figures
Year 1 2 3 4
8000 1.03 8240 1.032 8487.20 1.033 8741.82 1.034
Year Cash Flow 1 2 3 4 8000 8000x1.03 = 8240 8000x1.032 = 8240 8000x1.03 = 8487.20
3
PV @ 10%
8000 1.10
= 7272.73 = 6809.92 = 6376.56 = 5970.78
8240 1.102 8487 .20 1.103 8741.82 1.104
Year 0 Cap Invest Change in WC -10,000 -1,500
1 - 2,575 3,950 1,375
2 - 204 4,113 3,909
3 - 214 4,283 4,069
4 - 2329
6 3,039 3,039
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc.,2001
7- 8
Inflation
INFLATION RULE Be consistent in how you handle inflation!! Use nominal interest rates to discount nominal cash flows. Use real interest rates to discount real cash flows. You will get the same results, whether you use nominal or real figures
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
7- 13
Blooper Industries
Year 0 Cap Invest WC Change in WC Revenues Expenses Depreciation Pretax Profit .Tax (35%) Profit 10,000 1,500 1,500 1 4,075 2,575 15,000 10,000 2,000 3,000 1,050 1,950 2 4,279 204 15,750 10,500 2,000 3,250 1137 , 2,113 3 4,493 214 16,538 11,025 2,000 3,513 1,230 2,283 4 4,717 225 17,364 11,576 2,000 3,788 1,326 2,462 5 3,039 − 1,678 18,233 12,155 2,000 4,078 1,427 2,651 6 0 − 3,039
Incremental Cash Flow
=
cash flow with project
-
cash flow without project
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
7- 7
Incremental Cash Flows
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc.,2001