Lecture 18

合集下载

离散数学 可数集与不可数集

离散数学  可数集与不可数集

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则f是[0,1]到(0,1]上的双射。 令g: (0,1] → {x|x∈R且x≥0},g(x)=-logx,则g是双射,因而gf是[0,1] 到{x|x∈R且x≥0}的双射。故它具有基数。
1 1 4 3
1 2
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2004-11-29
离散数学-lecture18
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(3) f: [0,1] →(0,1],同(2), 再令g: (0,1] →{<x,y>|x,y∈R且x2+y2=1} g(x)=<cos2x, sin2x> 则g是双射,因而gf是[0,1]到{<x,y>|x,y∈R且x2+y2=1}的双射,因而 它具有基数。
2004-11-29 离散数学-lecture18 19
习题
(1) (a) A={<p,q>|p、q都是整数} 因为f:N→I,使得f(x)=(-1/2)x,当x为偶数;f(x)=(1/2)(n+1),当x为奇数, 则f是双射,所以K(I)=0。 作g:N×N→I×I,使得g(<m,n>)=<f(m),f(n)>,则g是双射,所以 K[N×N]=K[I×I]=K[A],即K[A]= 0 。

所以 f(m,n)-f(0,n)=mn+m(m+3)/2 因 f(0,n)=n(n+1)/2 经整理得: f(m,n)=(1/2)(m+n)(m+n+1)+m 其中m,n∈N。 (A) b) 若给出f(m,n) ∈N,可由(A)式唯一确定序偶<m,n>。 因 f(m,n)=(1/2)(m+n)(m+n+1)+m 其中m,n∈N。 令 =f(m,n),则≥ (1/2)(m+n)(m+n+1) < (1/2)(m+n)(m+n+1)+(m+n)+1= (1/2)(m+n)(m+n+3)+1 令m+n=A,则(1/2)A(A+1) ≤ < (1/2)A(A+3) +1 即A2+A-2 ≤0, A2+3A-2(-1)>0

Writing Handout Lecture 18-19衔接与连贯

Writing Handout Lecture 18-19衔接与连贯

Lecture 18-19 Cohesion & Coherence1. 指称 (Reference) & 替代 (Substitution)1.1. Definition :指称主要使用代词代替文章中重复出现的词,避免单调啰嗦的问题。

替代指用一些特定的词语来指代某一类事务,这些词可以是名词,也可以是动词或一个分句。

1.2 Sample AnalysisThe New Englanders were better prepared to meet hardship. Not only were the New Englander's migrations longer and better organized than those of the individual travelers, the individual travelers made the individual travelers ’ way to the Chesopeake area, but the New Englanders ’ theology helped make the explicable the trails the new Englanders faced.2 省略 (Omission)省略也是一种简化行文的方式。

只要在上下文中能够被理解,就可以把一些部分省略掉。

e.g.His task is to clean the room of the master, of the children, and even of the servants.Reading makes a full man; confidence a ready man; and writing an exact man.Exercise (Independent Work )Translate the following sentences into Chinese with substitution or/and omission.1. 细娃盼过年,大人盼开春。

berkley 半导体工艺讲义18--平坦化

berkley 半导体工艺讲义18--平坦化

EE143 F05
Lecture 18
Polyimides
Polymers: excellent thermal stability (up to 450oC)
good dielectric properties (εr=3.3, ρ=1016 -cm) superior chemical resistance
1
ILD = Inter-Level Dielectric
2 3
5
4
6
Professor N Cheung, U.C. Berkeley
EE143 F05
Lecture 18
Dual Damascene Cu Metallization with Diffusion Barrier
Cu
Professor N Cheung, U.C. Berkeley
function of film hardness, Young’s modulus, slurry, pad composition and structure
Professor N Cheung, U.C. Berkeley
EE143 F05
Lecture 18
CMP Selectivity
CMP of SiO2 poly-Si W Al Selectivity to Si3N4 6:1 280:1 75:1 40:1
Planarization Techniques
1. Spin-on glass or polyimide 2. Deposit and Etchback 3. Chemical-Mechanical Polishing (CMP)
Professor N Cheung, U.C. Berkeley

Lecture 18 – GMMIV, Nonlinear Models

Lecture 18 – GMMIV, Nonlinear Models

Lecture 18 – GMM:IV, Nonlinear ModelsLet g(Z t,β) be an rx1 function of a kx1 parameter vector β, r > k, and a random vector Z t , such that the r population moment conditions (also called estimating equations)E(g(Z t,β0)) = 0hold for all t, where β0 is the true value of β.For example, in the linear case we considered earlier, Z t = [y t x t’ w t’]’ and g(Z t,β) = w t*(y t-x t’β), where r is equal to the dimensionality of w t.Another example – nonlinear regression model y t = f(x t,β0) + εtE(w tεt) = 0In this case,Z t = [y t x t’ w t’]’ and g(Z t,β) = w t*(y t-f(x t,β))Yet another example –Hansen and Singleton (Econometrica , 1982)In the consumption-based asset pricing model developed by Lucas (Econometrica , 1978), therepresentative household chooses a consumption plan in period t to maximize expected discounted utility subject to a sequence of budget constraints. In addition to purchasing a consumption good (the numeraire good), the agent can purchase N assets which differ according to the number of periods until maturity (1,2,…,N). These providing the future income that support future consumption.With a constant relative risk aversion utility function, this optimization problem turns out to produce the following Euler equations for the agent’s o ptimal consumption path –01])/)(/([1,,00=--++t t m t t j m t j m I c c p r E j j j γδfor j = 1,…,N, where c t is period t consumption, j m t j r +,is the period t+m j payoff from a unit of asset j purchased in period t, and p j ,t is the period t price of a unit of asset j. δ0 an d γ0 are the parameters of the model (δ0 = the discount rate, γ0 = the parameter thatspecifies the particular CRRA utility function). I t denotes the agent’s information set in period t.We are interested in estimating the parameters δ and γ.We can rewrite the Euler equations as0]1)/)(/([1,,00=--++t t m t t j m t j m I c c p r E j j j γδand, applying the law of iterated expections,0]1)/)(/([1,,00=--++t t m t t j m t j m w c c p r E j j jγδwhere w t is an n-dimensional vector contained in I t . (E.g., j m t t j m t j t j c c p r --/,/,,, or any othermacroeconomic and/or financial variables that might be in I t .)It follows that the following n moment conditions must hold for all t:0)]1)/)(/(([1,,00=--++γδt m t t j m t j m t c c p r w E j j jwhich is of the form E(g(Z t ,β0)) = 0What is the alternative to GMM to estimate this model? MLE. But MLE requires specifying the sequence of joint conditional distributions for (t m t t j m t j c c p r j j /,/,,++) then maximizing the log likelihood function subject to the sequence of Euler equations. Except in special cases (e.g., lognormal distribution), this is a very messy problemcomputationally. [However, subject to the correct specification of the relevant distributions, the MLE will be more efficient asymptotically than GMM. GMM is semiparametrically efficient but the MLE is a fully parametric estimator and is more efficient than GMM.]The CAPM example and other economic examples which give rise to moment conditions of this form are provided in Chapter 1 of Hall’s GMM textbookThe sample analogues of the r population momentsE(g(Z t ,β0))are the r sample moments∑=Tt T Z g T g 1),(1)(ββThe (efficient) GMM estimator of β is:)()'(min arg ˆββββT T T GMM g Q g T =where Q T is the weighting matrix∑--=T T T t t T g g g g T Q 11''])~()~()/1[(ββ where β~ is any consistent estimator of β.Notes –1. This estimator will generally have to be calculated numerically. (See Ch. 3 of Hall’s GMM book for more discussion of this.)2. To obtain a preliminary consistent estimator of β we can appl y “inefficient GMM.” That is, apply GMM with any p.d. Q T, e.g., Q T = I T. An iterative version of this estimator may work better in applications although there will be no asymptotic gain to iterating.Under suitable regularity conditions))'(,0()ˆ(11--Ω→-G G N T DGMM ββwhere)())('('t t t g g E and g E G =Ω∂∂=ββConsistent estimators of G and Ω:∑∑=Ω∂∂=T T GMM t GMM t GMM t g g T and g T G 11')ˆ()ˆ(1ˆ)ˆ('1ˆββββOveridentification Test – (Assume r > k)Under H 0: E(g t ) = 0,)(2k r J D-X →whereT T T GMM g Q g T J J ')ˆ(==β(Note that T g and Q T are evaluated here at .ˆGMM β)Testing (Linear and/or Nonlinear) Restrictions on β –Consider a set of q linear and/or nonlinear restrictions on β. LetJ T = J statistic from the unrestricted GMMregressionJ T,R = J statistic from the restricted GMMs.t. the same Q matrix used in forming J T is also used in forming J T,R .Then under the null hypothesis (that the q restrictions are correct))(2,q J J DT R T X →-。

lecture的意思用法大全

lecture的意思用法大全

lecture的意思用法大全lecture有演讲,训斥,教训的意思。

那你们想知道lecture的用法吗?今日我给大家带来了lecture的用法,盼望能够关心到大家,一起来学习吧。

lecture的意思n. 演讲,训斥,教训vi. 作演讲vt. 给…作演讲,教训(通常是长篇大论的)变形:过去式: lectured; 现在分词:lecturing; 过去分词:lectured;lecture用法lecture可以用作名词lecture主要指教育性或学术性“演讲”,引申可指“冗长的训斥或责备”。

lecture是可数名词,其后接介词on或about ,意为“关于…的演讲”“就…做演讲”“因…训斥或责备某人”。

lecture作“讲演,讲课”解时,是不及物动词。

说“讲授某课程”时常与介词on连用,说“在某地讲演”时常与介词at〔in〕连用。

lecture用作名词的用法例句She ran over her notes before giving the lecture.她讲课前把讲稿匆忙看了一遍。

His lecture covered various aspects of language.他的讲课涉及到语言诸方面的问题。

They could not follow the lecture.他们听不懂这次演讲。

lecture可以用作动词lecture作“讲演,讲课”解时,是不及物动词。

说“讲授某课程”时常与介词on连用,说“在某地讲演”时常与介词at〔in〕连用。

lecture也可用作及物动词,意思是“向…讲演,给…讲课”,接名词或代词作宾语。

lecture还可作“责怪”“教训”“训斥”解,用作及物动词,接名词或代词作宾语。

“因…而受到训斥”可说lecture sb for n./v -ing。

lecture用作动词的用法例句It was a shame for me to be lectured in front of the whole class.当着整个班级的面被训斥了一顿,真让我感到羞辱。

C#LectureNotes_第18章

C#LectureNotes_第18章
来自 18.3 多线程编程的基本步骤(2)
第二个步骤是启动刚定义的线程thread1,代码为: thread1.Start( ); 接着,根据具体情况,可以悬挂该线程,可以重启该线程,也可以 让该线程休眠等。 最后,该线程执行完以后自动撤销。如果在线程执行完以前希望终 止它,则可以调用Abort( )方法。注意,终止一个线程可能造成数据 的不完整等问题,因此调用该函数要特别当心。
ou ck Gr


B调用wait( ), Join( ) A调用sleep( ) WaitSleepJoin B调用Interrupt( )
线 程 完 成 StoppedRequested Stopped
图18.1 线程的生命周期示意图
18.3 多线程编程的基本步骤(1)
第一个步骤是定义Thread对象。Thread类是一个sealed类,不能被继 承,可以创建Thread类的实例。每个线程指代一个方法,称为线程 方法或线程函数,该方法无参数,且返回值类型为void。若需要传 递相关的参数,可以使用对象的成员变量或方法。生成Thread实例 时,首先定义一个指代,然后定义一个Thread对象,调用Thread类 的构造方法生成该实例。例如,下列代码生成一个Thread实例: public delegate void ThreadStart ( ); Thread thread1 = new Thread( new ThreadStart( obj.myThreadFun ) ); private void myThreadFun ( ) { ……; }
第18章 多线程
主要内容
本章主要讲解多线程的编程,学习的目标包括:理解多线程 的概念;了解多线程提高程序性能的方式;掌握线程的创建、 控制和同步;理解线程的生命周期、优先级和调度;理解线 程的安全性;掌握线程的实现方式。

MIT基础数学讲义(计算机系)lecture18

MIT基础数学讲义(计算机系)lecture18
Yet some people felt that the probability of disaster was su ciently high that they staged vigorous protests and led suit in federal court to prevent the launch. How could there be such intense dispute about a probability question? Part of the problem is that probability is a tricky subject. In principle, probability boils down to a few simple rules. The di culty is that these rules often produce highly counterintuitive results \common sense" often leads to the wrong answer! We will see two examples of this today.
1 The Monty Hall Problem
In the 1970's, there was a game show called Let's Make a Deal, hosted by Monty Hall and his assistant Carol Merryl. At one stage of the game, a contestant is shown three doors. The contestant knows there is a prize behind one door and that there are goats behind the other two. The contestant picks a door. To build suspense, Carol always opens a di erent door, revealing a goat. The contestant can then stick with his original door or switch to the other unopened door. He wins the prize only if he now picks the correct door. Should the contestant \stick" with his original door, \switch" to the other door, or does it not matter? We will analyze the probability that the contestant wins with the \switch" strategy that is, the contestant chooses a random door initially and then always switches after Carol reveals a goat behind one door. The analysis can be broken down into four steps.

Lecture 18 心理测量中文版.

Lecture 18 心理测量中文版.
• 每次你去一个医生的办公室, 他们就会 称体重,说你体重有140磅了。 • 你测量的140磅来自一个测试吗? 为什 么是,或者为什么不是?
评价
• 定义1:根据测量目的,做出对测量结果的判 断过程。
• 定义2:获取信息(数据)的过程,并用它来 做出判断,这反过来又用于决策。
参与评估的步骤
1. 2. 3. 4. 5. 定义测试的任务和目的。 测量性能或管理测试。 查找或开发一个标准。 将一个人的表现与标准进行比较。 做出评价,并以最恰当的方式对结果 进行讨论和发布。
• 所有儿童都是相同的指令和格式
• 标准化样本
• 通过一个孩子可以与其他的孩子相比,建立规范 的绩效
44
心理学历史:智力测试
• Alfred Binet
• 标准化样本
• 50个3-11岁正常孩子 • “一些”智力迟钝的儿童和成年人
• 1908 Binet-Simon 测量
• 更多项目(更大的可靠性) • 更标准化的样本 (300明正常孩子) • 心理年龄的介绍
12
测试类型
• 个人测试 vs. 小组测试
• 个人测试:测试管理员给单个人做一次 测试
• e.g. WAIS-III, MMPI-2
• 小组测试:单个考官给了一组人的测试
• e.g. SAT, GRE
13
测试类型
• (人类) 能力测试
• 成就测试
• 评估一个人所学到的 • 测量先前活动
• 能力倾向测试
• 这种差异往往只受精密度的限制
10
心理测试基础
• 测试
• 测量装置或技术,用于量化行为,有助于对 行为的理解和预测 • 心理测试 • 一套用来衡量人类特点的统筹项目 • 行为

lecture18

lecture18
35
Converging Lens
All rays parallel to principal axis pass through focal point F. Double Convex
Preflight 18.6
P.A.
F F
A beacon in a lighthouse produces a parallel beam of light. The beacon consists of a bulb and a converging lens. Where should the bulb be placed?
27% • block more light 62% • block more glare
9%
1%
• are safer for your eyes • are cheaper
When glare is around qB, it’s mostly horiz. polarized!
Polarizing sunglasses (when worn by someone standing up) work by absorbing light polarized in which direction?
n2
normal
n1 sin q1 n2 sin q2
q
2
48
Preflight 18.1
Can the person standing on the edge of the pool be prevented from seeing the light by total internal reflection ?
23
Rainbow:
Preflight 18.5

机器学习课件 Lecture18 Sparse Optimization

机器学习课件 Lecture18 Sparse Optimization
sparseoptimization2750shanghaitechlassoregressionfirstordermethodsforgenericconvexregularizersgrouplassowhy?1and?0yieldssparsitythesimplestproblemwith?1regularizationx?argminx12x?y2xsy?????y?ygt
j=1
▶ ▶ ▶

Hence, have a “path” of solutions indexed by t No shrinkage if t = ... Often, the path of solutions is indexed by a fraction of shrinkage factor of t
Group lasso
LARS - illustration for 2-dimensional cases
Lecture 18: Sparse Optimization
14 / 50
ShanghaiTech
LASSO Regression
First-order methods for generic convex regularizers
Group lasso
LARS - illustration for 2-dimensional cases
Lecture 18: Sparse Optimization
12 / 50
ShanghaiTech
LASSO Regression
First-order methods for generic convex regularizers
Lecture 18: Sparse Optimization

Lecture18 - Multiview stereo

Lecture18 - Multiview stereo

3. General Case
• Space carving [Kutulakos & Seitz 98]
> For more info:
/homes/seitz/papers/kutu-ijcv00.pdf
Space Carving Algorithm
Complexity and computability
Discretized Scene Volume N voxels C colors
3
True Scene
N ) All Scenes ( C Photo-Consistent Scenes
3
Issues
Theoretical Questions
Dinosaur Reconstruction
72 K voxels colored 7.6 M voxels tested 7 min. to compute on a 250MHz SGI
Flower Reconstruction
70 K voxels colored 7.6 M voxels tested 7 min. to compute on a 250MHz SGI
1. Choose voxel 2. Project and correlate 3. Color if consistent
(standard deviation of pixel colors below threshold)
Visibility Problem:
in which images is each voxel visible?
Discrete formulation: Voxel Coloring
Discretized Scene Volume

lecture18_76404660

lecture18_76404660

7-1 质系动量定理7-2 质系对定点的动量矩定理7-3 质系对动点及质心的动量矩定理7-4 质系动能定理及动力学普遍定理得综合应用7-5 碰撞问题(1)碰撞及积分形式的动量(矩)定理(2)刚体碰撞及恢复系数7-6 达朗贝尔原理与动静法第七章质点系动力学(1)碰撞及积分形式的动量(矩)定理碰撞:物体相互接触并伴有速度突然变化的力学过程。

1.在极短时间内(10-4~s),物体之间发生有限量的动量传递,伴随极大的碰撞力(一般力的几百~上千倍)。

2.机械能之间、机械能与其它形式的能量之间产生急剧转化。

机械能不守恒!质系动量定理的积分形式: 质系动量在一段时间内的增量等于外力的主矢在这段时间的冲量。

sin )S αj (/1)cos sin Ox Oy S mal J S S S αα=-⎧⎪⎨=⎪⎩=0)α力控制球的转动。

保证球在碰撞后的快速、低角度弹出。

1v'2v'1v 2v n分别为碰撞前后时刻的系统动能。

(2)刚体碰撞及碰撞恢复系数讨论:打铁与打桩的动量传递与能量变化分析分析:恢复系数是e 的两物体正碰动能损失假设e = 0,v 2=0。

112(1/)T T m m ∆=+211121v m T =22121212()(1)2()m m T v v e m m ∆=--+打铁: 小锤打大铁转化为有用功。

12m m <<1T T ∆≈打桩: 大锤打小桩,桩在碰撞后获得攻入速度,。

12m m >>0T ∆≈21v v '≈碰撞后时刻心速度和角速度。

eI 解:碰撞前板平动→碰撞后板平面运动。

Cxv 碰撞前时刻a ab b内激励的作用等()]t τ-,。

单自由度振动系统任意激励下的强迫响应的Duhamel 积分任意激励下的强迫响应:Duhamel 积分)(t F kx xc x m =++ m c n 2=mk n /2=ω0F kx x m =+例:无阻尼振子零初始条件的阶跃响应:001()sin[()]t n n x t t d F m ωττω=-⎰)cos 1(20t m F n n ωω-=)cos 1(0t kFn ω-=解:解毕!阶跃响应注:无阻尼振子的阶跃响应幅值是静位移的两倍。

lecture 18

lecture 18

Lecture 17英汉语句子结构与思维方式The Study of Sentence Structure and the mode of thinkingin both Chinese and EnglishIn intercultural communication, the difference in the structure of sentences in both English and Chinese often becomes a barrier. 在汉英翻译和跨文化交际中,汉英句子结构的差异常常成为不小的障碍。

We should study the rules of these differences and try to find effective answers. 王还先生说得好:“任何人学外语最自然、最容易做的事就是把自己母语mother tongue的习惯套在外语上,有时套对了,有时就套错了。

那些母语和外语不同的地方就一定要套错。

”这里的“习惯”主要是思维方式the mode of thinking, ie. to understand and organize sentences of a foreign language from the mode of thinking of a mother tongue one is accustomed to,(即用习以为常的母语思维方式去理解或组织外语句子)。

language is the carrier of thought and also the representation of it. The mode of thinking restricts sentence structure and in different cultures, the modes of thinking may have similarities and differences. (语言既是思维的主要载体,也是思维的主要表现形式,思维方式制约句子结构不同文化之间思维方式有同有异。

MIT6_254S10_lec18

MIT6_254S10_lec18
according to the conditional distribution p (θ −i | θ i ).
4
Game Theory: Lecture 18
Bayesian Games
Bayesian Nash Equilibria
Definition (Bayesian Nash Equilibrium) The strategy profile s (·) is a (pure strategy) Bayesian Nash equilibrium if for all i ∈ I and for all θ i ∈ Θi , we have that si (θ i ) ∈ arg max ∑ p (θ −i | θ i )ui (si� , s−i (θ −i ), θ i , θ −i ), �
Private value auctions: valuation of each agent is independent of others’ valuations; Common value auctions: the object has a potentially common value, and each individual’s signal is imperfectly correlated with this common value.
Asu Ozdaglar
MIT
April 22, 2010
1
Game Theory: Lecture 18
Introduction
Outline
Bayesian Nash Equilibria. Auctions. Extensive form games of incomplete information. Perfect Bayesian (Nash) Equilibria.
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New Media TechnologyWhen it first makes its appearance, a new industrial technology is often greeted with as much fear as welcome. The fear of course is the fear of obsolescence and replacement among those who depend on older technology for their livelihood. It's pretty clear why this happens, and I'm sure we could come up with a number of historical examples to show that this does happen. But. today I want to talk about one particular example from the world of mass media; one that I think makes a good case study.It happened with the introduction of radio as a medium of mass communication in the early 20th century. This caused a lot of anxiety in the newspaper industry. Many newspaper workers wondered what kind of impact it would have on their business and most assumed the worst. Considering the advantages radio apparently had, I guess their fears were understandable. Media experts predicted that because radio was a quick, virtually free medium that was so easy to access, it would replace the newspapers altogether. I mean, after all radio could keep large numbers of people spread over a wide area informed about events as they happened. This was something that newspapers obviously couldn't do, or at least not as well.But there were a few optimists in the newspaper industry too. They thought there might be a bright side to the situation. Their argument was built on the assumption that a brief news broadcast heard on the air would stimulate the listeners' interest in a news story; that it would, uh whet their appetite, so to speak. The way they saw things this might actually encourage people to buy a newspaper to get all of the details. Newspaper sales would go up instead of down. I shouldn't even have to ask this, but now. who was right, the optimists or the pessimists?(Student 1) Obviously, it was the optimists. Newspapers are still awfully popular today. They certainly haven't disappeared.Exactly! Today, almost a hundred years later, and despite the fact that there are radios and now televisions delivering a constant stream of news to virtually every home, newspapers are just as popular as they ever were, probably more so. The doomsayers were proved wrong. But the question for us is why? Radio and television are faster and. over the long term; they're even cheaper than newspapers. So why is there still a market for news in print? The papers must offer us something because we still buy them.Well, as it turns out. The relationship between different forms of media is not necessarily one of displacement or replacement. It's a bit more complicated than that. There is a third possibility; that is of reinforcement. We now know that the radio and the print news media are not usually in direct competition, but in fact complement and enhance each other. Each one supplies something the other can not. Newspapers supply detail and the all-important luxury of having the news when you want it and in a sequence that reflects your personal priorities. That's what has kept the papers alive. But for how much longer? Would anyone like to go out on a limb and make a prediction?(Student 2) I think papers will be around for quite a while. Sure, you can get customized news delivered over the Internet. The problem is you have to have access to a computer and anInternet connection.Okay, but you're really not risking much with that answer, are you? The question is for how long? High-speed wireless Internet access is already becoming possible from almost anywhere and over handheld devices as small as cell phones. You're no longer really tied to a computer, are you? So, what's left to attract people to traditional newspapers? Well, there is the probability that an aging population will continue to buy them out of habit, but that's a market that can't last. When alsowe consider the environmental impact of printing millions upon millions of newspapers every single day. it's pretty easy to imagine the traditional newspaper disappearing completely in the not-too-distant future, probably in less than a generation.According to the professor, what effect does the introduction of new technology often have?1.Improved efficiency in old industries.2.Concern among those who work in old industries.3.The replacement of older industries.4. A movement of workers from older to newer industries.According to the speaker, what relationship developed between the radio and the newspaper industries?1.Radio caused the downfall of the newspaper industry.2.Newspapers and radio increased each other’s audience.3.Radio drew readers away from newspapers.4.One provided what the other did not.Which of the following is supported in the lecture?1.Newspapers will gain in popularity.2.Electronic news sources are already more popular than newspapers.3.Newspapers will disappear gradually.4.Newspapers can survive if their price can be lowered.What is mentioned as a reason traditional newspapers are likely to disappear?1.Increasing subscription prices.2.The popularity of computers.3.The habits of older people.4.Environmental concerns.What does the professor imply when she says this?1.It is unlikely that the students will know the answer.2.The answer should be obvious to anyone.3.She has asked this question before.4.The students do not need to know the answer.What can be inferred about the professor when she says this?1.The student’s answer is insufficient.2.The student should have known the answer.3.The student gave too much information.4.The professor didn’t understand the student’s answer.。

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