目录2-1随机过程:随机游动与鞅1 Lecture2 日期:2011-03-23作者:杨广宇 摘要 目录 1随机游动、例子2-2 2输光问题2-3 3首达时2-5 4反射原理、反正弦律及对偶2-9 5Wald等式2-15 6附注2-18 6.1鞅停止定理......................................2-18 6.2稳定律的一个例子..................................2-19
1随机游动、例子2-2 1随机游动、例子 随机游动是最简单的随机过程，它同Brown运动、马氏过程、鞅以及L′e vy过程都有紧密的联系，并且在金融、物理、化学和生物信息学中都有广泛和深入的应用。我们这里仅介绍随机游动的一些基本性质。 定义1设{ξn,n≥1}是独立同分布的随机变量序列，其分布函数为F。x∈Z，令 S0=x,S n=x+ n ∑ i=1 ξi,n≥1.(1) 称随机过程{S n,n≥0}为从x出发，具有步长分布F的随机游动。无说明情况下，总取x=0。 习题2随机游动{S n,n≥0}也可以表示为S0=0，S n=S n?1+ξn,n≥1。也即可将S n解释为粒子在时刻n的位置，每个时刻粒子以同样的分布随机的选择一个步长，并跳转到位置S n?1+ξn。试证明S2n?S n与S n相互独立并具有相同的分布。 例3(简单随机游动)若步长随机变量ξ1和?ξ1的分布相同，则说随机游动{S n}是对称随机游动。特别的，若P(ξ1=1)=P(ξ=?1)=1/2，称{S n}为Z上简单(对称)随机游动。若P(ξ1=1)=1?P(ξ=?1)=p=1/2，称{S n}为有偏紧邻随机游动。自然可以考虑Z d上的简单随机游动和有偏紧邻随机游动。 例4(Gauss随机游动)若步长随机变量ξ1取值空间为R，并且ξ1服从标准正态分布N(0,1)，则说随机游动{S n}为Gauss随机游动。易知S n服从均值为0，方差为n的正态分布。 习题5由正态分布的可加性知：S n～N(0,n)。试证明n?1S n a.s.??→0。 例6(重尾随机游动)若步长随机变量ξ1是具有重尾分布1的随机变量，则说随机游动{S n}为重尾随机游动。譬如，令ξ1为具有密度函数 f(x)={ α 2 ·1|x|α+1,若|x|≥1; 0,其它. 1重尾随机变量：设X为非负随机变量，若任意的λ>0，EeλX=∞，则称X是重尾的，否则，若存在λ 0使得对任意的0<λ<λ0，EeλX<∞，称随机变量X是轻尾的。用分布来说，若任意的s≥0，lim t→∞[1?F(t+ s)]/[1?F(t)]=1，则说F为重尾分布。关于“重尾”有多种不同形式的定义，直观上，若密度函数依幂指衰减到0，则该分布为重尾分布；若密度函数依指数衰减0，则该分布为轻尾分布。常说的重尾分布一般为幂律分布。
Lecture2Diction Part1Varieties of English 1.1Variation in English 1.2Style&Register(P14) Formal spoken Address at Gettysburg,1863 Fourscore and seven years ago our fathers brought forth on this continent a new nation,conceived in liberty and dedicated to the proposition that all men are created equal.Now we are engaged in a great civil war,testing whether that nation,or any nation so conceived and so dedicated,can long endure…. ...It is rather for us to be here dedicated to the great task remaining before us—that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion;that we here highly resolve that these dead shall not have died in vain;that this nation,under God,shall have a new birth of freedom;and that government of the people,by the people,for the people,shall not perish from the earth. 1.3Spoken&written(1a—6b,P14) Spoken:More informal,More personal,Less concise,Less organized Active voice,Simple connectors,wordy Written:More formal,More impersonal,More precise,Economical in the use of words,Passive voice,Complex connectors,concise More example: (a)Cleared,the site would be very valuable. (b)If it were cleared,the site would be very valuable.(written) 1.4Formal&Informal Word choice (a)The concert concluded with a performance of Beethoven’s5th symphony.(formal) (b)They ended the concert with Beethoven’s5th symphony. Grammar use (a)Bill speaks French more fluently than I.(formal) (b)Bill speaks French more fluently than me. 1.5General English A middle course between formal and informal levels Usually the best choice for college or business writing Formal general informal Automobile car wheels Visage face mug Odious offensive gross Attire clothes threads Spectacles glasses specs In your dictionary,you may find special usage labels for words or particular definitions of words that differ from the general English vocabulary.
1/62 建工学院土木系Dept. of Civil Engineering Autumn 2008 Solution to Lecture 2 Dr. Shao Weiyun Dept. of Civil Engineering Email:shaowy@https://www.doczj.com/doc/812205673.html, 2/62 建工学院土木系Dept. of Civil Engineering Autumn 2008 2.10 The basic elements of a hydraulic press are shown in Fig. P2.10.The plunger has an area of 1 in.2, and a force, F 1, can be applied to the plunger through a lever mechanism having a mechanical advantage of 8 to 1. If the large piston has an area of 150 in.2, what load, F 2, can be raised by a force of 30 lb applied to the lever? Neglect the hydrostatic pressure variation.
3/62 建工学院土木系 Dept. of Civil Engineering Autumn 2008 2.16A U-tube manometer is connected to a closed tank as shown in Fig. P2.16. The air pressure in the tank is 0.50 psi and the liquid in the tank is oil (γ= 54.0 lb/ft3). The pressure at point A is 2.00 psi. Determine: (a) the depth of oil, z , and (b) the differential reading, h , on the manometer. 4/62 建工学院土木系 Dept. of Civil Engineering Autumn 2008 2.21?The inverted U-tube manometer of Fig. P2.21 contains oil (SG = 0.9) and water as shown. The pressure differential between pipes A and B , pA ?pB , is ?5 kPa. Determine the differential reading, h .
Unit 1 Practice During Gap Year Lecture 2 My Gap Year Hello！I’m Selena. Nice to see you again! Last class, we just talked about the colorful activities of young people. However, besides joy and excitements, the lives of young people are also full of puzzles and confusions, and restless hearts. Young people need some time to figure out their goals for the future and be prepared. Taking a Gap Year is a typical way of seeking self-realization. In the UK, after graduating from high school, young people often ask each other: ‘ Which country would you like to travel to?’ Of course, this is not a holiday trip in our usual sense. In the UK, students are allowed to travel around the world for a year to experience life before they enter college. This year is called Gap Year. It is not a new concept. In the 17th century, young British nobles traveled to Europe to experience the knowledge that was previously learned in the classroom. This “Grand Tour” is the ancestor of the gap year. How did Gap Year become a trend in modern times? Let’s learn its development through a short film. Recent years, there are more and more people choose to take a gap year, like the five members of the Beatles, Steve Jobs( the founder of
Lecture Two A Contrastive Study of Chinese and English 只赢得：几杵疏钟，半江渔 火，两行秋雁，一枕清霜。 There left behind are bronze bells heard occasionallyand fishing boats with flickering lamps seen in the middle of the lake, wild geese leaving in a hurry in two files in autumn, and only frosted snow all over the terrains in winter. What remains is only sparse bells ringing in cold hills, fishermen ' s lantern lights by riverside, two rows of wild geese flying in autumn sky and a dreary dream of hoary winter frost. 知己知彼，百战不殆；不知彼而知己，一胜一负；不知彼不知己，每战必殆。 You can fight a hundred battles without defeat if you know the enemy as well as yourself. You will win one battle and lose another if you know yourself but leave yourself in the dark about the enemy. You will lose every battle if you leave both the enemy and yourself in the dark. From Structure 1. 英语有形态变化 ,汉语没有严格意义的形态变化 . English : gender, number, case, tense, voice, mood, degree of comparison, person and parts of speech. 汉语 : 数量助词 ,动态助词 ,结构助词 He is a professional. He is a loose man. He served as a call boy when he was 19. She is a professional. She is a loose woman. She served as a call girl when she was 19. 2. 英语经常使用定冠词和不定冠词 I have lived here for more than a year. I have lived here fore more than one year. It isn ' t going to rain today, is it? Just think it over. All right, let ' s make it tomorrow. Let 's go. 打吧 ,打不下去 ;跑吧 ,跑不了 ,敌人只好投降 . Unable to fight on or to escape, the enemy were forced to surrender. 3. 英语常用介词 ,汉语则少用介词 . What is he at? 他正在干什么 ? John voted with the Tories. John 投票支持保守党 . He is a man above vulgar interests. 他是一个脱离了低级趣味的人 It looks as if we are in for a storm. 看来我们免不了要碰上一场暴风雨了 . If a man couldn ' t walk into a room and tell who was for him and who was against him, then he wasn ' t much of a politic 。要是一个人不能一上任就看出谁支持他 , 谁反对他 ,那他就不配搞政治 From Intonation 1. 英语是语调语言 ,语音表意手段主要是语调和重音 . You said he would COME. YOU said he would come. You said HE would come. out of question out of the question 2.汉语有丰 富多彩的助词 吧 今天不会下雨吧 你好好想想吧 ! 明天就明天吧 . 咱们走吧 . take a chair take the chair
今天，环球托福为备考托福听力的考友们带来托福TPO听力文本翻译Lecture2 Computer Science（下），请看环球托福分享的托福TPO听力文本： Lecture2 Computer Science There are two projects that I worked on a couple of years ago. One, which I’ll call Project Split, well, the testing and development teams did not work well together. And the other, I’ll call Project Unity, during which both teams worked very well together. Now, during Project Split, we had defect meetings where the developers and the testers met together, eh... eh... to discuss various problems and how they should be fixed. And you could sense the conflict just by walking into the room. Literally, the testers and the developers sat on opposite sides on the table. Um... and ... and the developers were very defensive about the feedback. 托福TPO听力文本翻译 几年之前我干过两个项目。第一个，我把它叫做“扯皮项目”，嗯，测试和开发团队之间合作得不好。另一个，我叫它“团结项目”，双方合作愉快。干“扯皮项目”的时候，我们经常召开产品缺陷会议，开发人员和测试人员一起……呃……讨论各种毛病，以及如何修复它们。那时候你一走进会议室就能闻到冲突味儿。测试人员和开发人员坐在会议桌的两边，立场分明，嗯，而且，开发人员对测试反馈完全持一种抵抗和防卫的态度。 Student Well, if bugs are being pointed out they wouldn’t be too happy since it’s their work. 托福TPO听力文本翻译 嗯，如果发现了虫子，他们肯定不太高兴嘛，毕竟那是他们的工作成果。 Professor Exactly. Now, ‘because the two teams weren’t working well together, the fixes were coming very slowly. And you know, a lot of times when you fix bugs you introduce new bugs, or you discover bugs and other areas that only come to light because something has been changed, so fixing all those new additional bugs was also being delayed. Um... the test process went on much longer than expected and we ended up having to put the product on the market with known bugs in it, which was obviously not ideal. 托福TPO听力文本翻译 对。由于两个团队合作得不好，修复工作进行得很慢。你知道，很多时候你对问题的修复会导致新的问题，或者因为情形的变化而发现或暴露了新问题。结果，对这些新出现的问题的解决也被耽搁了。额，测试过程因此拖得很久、完全超出了预期，最终我们只好把这些毛病尚存的产品推向市场，这显然是不理想的。 Student Ok and what about Project Unity? How was it different? 托福TPO听力文本翻译 那“团结项目”呢？有何不同？
Lecture2 Sales and promotion
What are the repeating words in our text? We all know that department stores and super-markets use various techniques to persuade us to buy more than we plan to. For customers, these techniques are like a siren song. You can outsmart them, however, if you’re a little more prepared. Let’s go through a few examples of these techniques, and brainstorm ways to resist them. Technique: Time-limited offers, sales and discounts It is one of the most obvious and tricky techniques. When a store uses this technique, you often get excited. Suddenly, you’re convincing yourself that passing up this deal would be a mistake you’ll regret for the rest of your life. Response: Stick to your list Before you go into the store, mentally prepare yourself for these types of offers. Tell yourself in advance that you will only buy the things on your list and nothing else. Technique: Candies and magazines at the checkout counter Store managers place them at the point just before you pay — knowing that you will have a desire to purchase them. Why candies and magazines? Because they are irresistible, and we feel that we deserve a reward after completing our shopping.
Lecture 教师：薛蕴雯级别：1级课次：第二次 1-10分钟上节课词汇、词组、语法复习 10-20分钟导入news用3分钟，可以用图片视频等 7分钟讲单词、词组 20-25分钟阅读前先让学生主动讲故事 25-40分钟课文，拓展词组和用法，拓展句子。 Once upon a time see sb doing sth A plot of be impatient with Seedling hit upon Every / each 的区别by / to 增长了/到 Wait to do / for sth be+感情+to do 40-45分钟让学生复述故事，看谁讲得好。一季度评出一个讲故事大王45-55分钟训练学生怎么描述一个人，从外表，性格，爱好等方面，拓展一些描述性格的词汇。 55-65分钟课堂活动：你来描述我来猜，我会在ppt上备好名人或者他们感兴趣的图片，让学生两人一组进行游戏。全称只能说英语。说 汉语要扣分。最后赢了的两个人每人拿到一分。 65-70分钟放一段这俩人拍的电影—The Last Lions导入 70-75分钟讲生词以及语法点 As while Play an important role
70-75分钟教大家一些body language，可以边演边教。 课本里的让学生演。 75-80分钟拓词 Get in touch with draw the attention of Swing out of control Start/ light a fire clockwise Message received 80-90分钟两人一组编对话，放听力原文进行对比 Shadowing 练习，激发学生听力听英语兴趣 90-100分钟课堂活动：找一段视频，不给字幕，分组进行字幕翻译，看哪个组的神翻译较多一个季度可以评出一个神翻译字幕组100-100分钟language points 将来时表达方式 Will be+doing Be+going to do simple present tense 110-120分钟程度副词 Extremely-totally-completely-absolutely-incredibly Really-pretty- so-fairly 频率副词 Always-often-frequently-seldom-scarcely-never 120-140分钟联系星座讲性格 140—180分钟讲writing
CMOS RF IC Design (Radio Frequency Integrated Circuit) 2005-6Institute of Microelectronics1
Contents: z Introduction z Transmission Line Theory z Smith Chart z Impedance Matching z Inductor z Varactor z Active Device z System requirement z LNA design z Mixer design z VCO design z PA design 2005-6Institute of Microelectronics
Lecture 2: Smith Chart & impedance transformation 2005-6Institute of Microelectronics3
No Kirchhoff’s voltage and current laws in RF circuit 2005-6Institute of Microelectronics
The Smith Chart z The Smith Chart was developed in 1939 by Philip Smith at the Bell Telephone Laboratories z The Smith chart is a plot of the reflection coefficient, Γ, in the complex plane z It can be used to convert reflection coefficients (Γ) to normalized impedance (z=Z/Z0) and admittances (y=Y/Y0), and vice versa. z Nearly all computer aided design programs utilize the Smith Chart for the analyses of high frequency circuits. 2005-6Institute of Microelectronics