Two Kinds of Series Involving the Reciprocals of Binomial Coefficients

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会计英语期末试题及答案

会计英语期末试题及答案一、选择题（每题2分，共20分）1. Which of the following is NOT a financial statement?A. Balance SheetB. Income StatementB. Cash Flow StatementD. Budget Report2. What is the term used to describe the process of recording financial transactions in a company's books?A. AuditingB. BookkeepingC. Financial AnalysisD. Forecasting3. The process of determining the value of an asset orliability is known as:A. ValuationB. AmortizationC. DepreciationD. Accrual4. What does the abbreviation GAAP stand for?A. Generally Accepted Accounting PrinciplesB. Global Accounting and Auditing PracticesC. Government Accounting and Auditing PoliciesD. Good Accounting and Auditing Practices5. The term "revenue recognition" refers to the process of:A. Recording expenses when they are incurredB. Recording revenues when they are earnedC. Allocating costs to products or servicesD. Matching revenues with their related expenses6. Which of the following is a non-current asset?A. InventoryB. Accounts ReceivableC. LandD. Prepaid Expenses7. The matching principle in accounting requires that:A. All expenses must be recorded in the same period as the revenues they generateB. All assets must be listed on the balance sheetC. All liabilities must be paid off within one yearD. All revenues must be recognized in the period they are received8. What is the purpose of adjusting entries?A. To increase the company's reported profitsB. To ensure that financial statements reflect the current financial position of the companyC. To prepare the company for an auditD. To reduce the company's tax liability9. The accounting equation is:A. Assets = Liabilities + EquityB. Liabilities = Assets - EquityC. Equity = Assets - LiabilitiesD. All of the above10. Which of the following is a type of depreciation method?A. FIFOB. LIFOC. Straight-lineD. FIFO and LIFO are both inventory valuation methods答案：1. D2. B3. A4. A5. B6. C7. A8. B9. D10. C二、填空题（每空1分，共10分）11. The primary financial statements include the ______,______, and ______.12. The accounting cycle consists of several steps, including journalizing, ______, posting, and preparing financial statements.13. In accounting, the term "double-entry" refers to the practice of recording each transaction in ______ accounts. 14. The accounting equation shows the relationship between assets, liabilities, and ______.15. The accrual basis of accounting records revenues andexpenses when they are ______, not necessarily when cash is received or paid.答案：11. Balance Sheet, Income Statement, Cash Flow Statement12. footing13. two14. equity15. earned or incurred三、简答题（每题5分，共20分）16. 简述会计信息的四个主要特征。

two-stage stochastic programming

two-stage stochastic programmingTwo-stage stochastic programming is a mathematical optimization approach used to solve decision-making problems under uncertainty. It is commonly applied in various fields such as operations research, finance, energy planning, and supply chain management. In this approach, decisions are made in two stages: the first stage involves decisions made before uncertainty is realized, and the second stage involves decisions made after observing the uncertain events.In two-stage stochastic programming, the decision-maker aims to optimize their decisions by considering both the expected value and the risk associated with different outcomes. The problem is typically formulated as a mathematical program with constraints and objective functions that capture the decision variables, uncertain parameters, and their probabilistic distributions.The first stage decisions are typically made with theknowledge of the uncertain parameters, but without knowing their actual realization. These decisions are usually strategic and long-term in nature, such as investment decisions, capacity planning, or resource allocation. The objective in the first stage is to minimize the expected cost or maximize the expected profit.The second stage decisions are made after observing the actual realization of the uncertain events. These decisions are typically tactical or operational in nature, such as production planning, inventory management, or scheduling. The objective in the second stage is to minimize the cost or maximize the profit given the realized values of the uncertain parameters.To solve two-stage stochastic programming problems, various solution methods can be employed. One common approach is to use scenario-based methods, where a set of scenarios representing different realizations of the uncertain events is generated. Each scenario is associated with a probability weight, and the problem is then transformed into a deterministic equivalent problem byreplacing the uncertain parameters with their corresponding scenario values. The deterministic problem can be solved using traditional optimization techniques such as linear programming or mixed-integer programming.Another approach is to use sample average approximation, where the expected value in the objective function is approximated by averaging the objective function valuesover a large number of randomly generated scenarios. This method can be computationally efficient but may introduce some approximation errors.Furthermore, there are also robust optimization techniques that aim to find solutions that are robust against the uncertainty, regardless of the actualrealization of the uncertain events. These methods focus on minimizing the worst-case cost or maximizing the worst-case profit.In summary, two-stage stochastic programming is a powerful approach for decision-making under uncertainty. It allows decision-makers to consider both the expected valueand the risk associated with uncertain events. By formulating the problem as a mathematical program and employing various solution methods, optimal or near-optimal solutions can be obtained to guide decision-making in a wide range of applications.。

Organization Theory and Methodology

II. Positive and Normative Theory and Decision Making

In the period prior to the mid-1970s accounting theory was predominantly normative. Normative questions take the form: “How should price level changes be reflected in the accounting statements?” Positive questions take the form: “How does GPLA affect the value of the firm?” Answers to normative questions always depend on the choice of the criterion or objective function which is a matter of values. Therefore, normative propositions are never refutable by evidence. Answers to positive questions, on the other hand, involve discovery of some aspect of how the world behaves and are always potentially refutable by contradictory evidence.

the relation between positive and normative theories, the importance to the research effort of the choice of tautologies and definitions, the nature of evidence, the role of mathematics.

Fractal and Multifractal Time Series

$Fractal and Multifractal Time Series$

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• Self-aﬃne system: Generalization of a fractal system, where diﬀerent magniﬁcations s and s = sH have to be used for diﬀerent directions in order to obtain a statistically equivalent magniﬁcation. The exponent H is called Hurst exponent. Self-aﬃne time series and time series becoming self-aﬃne upon integration are commonly denoted as fractal using a less strict terminology. • Multifractal system: A system characterised by scaling laws with an inﬁnite number of diﬀerent fractal exponents. The scaling laws must be valid for the same range of the scale parameter. • Crossover: Change point in a scaling law, where one scaling exponent applies for small scale parameters and another scaling exponent applies for large scale parameters. The center of the crossover is denoted by its characteristic scale parameter s× in this article. • Persistence: In a persistent time series, a large value is usually (i. e., with high statistical preference) followed by a large value and a small value is followed by a small value. A fractal scaling law holds at least for a limited range of scales. • Short-term correlations: Correlations that decay suﬃciently fast that they can be described by a characteristic correlation time scale; e. g., exponentially decaying correlations. A crossover to uncorrelated behaviour is observed on larger scales. • Long-term correlations: Correlations that decay suﬃciently slow that a characteristic correlation time scale cannot be deﬁned; e. g., power-law correlations with an exponent between 0 and 1. Power-law scaling is observed on large time scales and asymptotically. The term long-range correlations should be used if the data is not a time series. • Non-stationarities: If the mean or the standard deviation of the data values change with time, the weak deﬁnition of stationarity is violated. The strong deﬁnition of stationarity requires that all moments remain constant, i. e., the distribution density of the values does not change with time. Non-stationarities like monotonous, periodic, or step-like trends are often caused by external eﬀects. In a more general sense, changes in the dynamics of the system also represent non-stationarities.

九年级英语科研技术单选题50题

九年级英语科研技术单选题50题1. In the field of artificial intelligence research, the term "algorithm" refers to _.A. a set of computational steps and rules for performing a specific taskB. a physical device used for data storageC. a type of software for graphic designD. a chemical substance for experiments答案：A。

解析：“algorithm”（算法）的定义就是执行特定任务的一组计算步骤和规则。

选项B，用于数据存储的物理设备是硬盘、U 盘等，不是算法的含义。

选项C，用于图形设计的软件有Photoshop 等，和算法概念不同。

选项D，算法与化学实验物质毫无关系。

2. When scientists conduct genetic research, they often study "DNA replication". "Replication" here means _.A. the process of making an exact copy of DNAB. the destruction of DNA structureC. the separation of different DNA segmentsD. the combination of DNA with other substances答案：A。

解析：“replication”在“DNA replication”DNA复制）中的意思就是制造DNA精确副本的过程。

选项B，破坏DNA结构不是“replication”的含义。

国际财务管理(英文版)课后习题答案2

CHAPTER 1 GLOBALIZATION AND THE MULTINATIONAL FIRMSUGGESTED ANSWERS TO END—OF-CHAPTER QUESTIONS QUESTIONS1。

Why is it important to study international financial management？Answer: We are now living in a world where all the major economic functions, i.e.，consumption，production, and investment，are highly globalized. It is thus essential for financial managers to fully understand vital international dimensions of financial management. This global shift is in marked contrast to a situation that existed when the authors of this book were learning finance some twenty years ago. At that time, most professors customarily (and safely, to some extent) ignored international aspects of finance。

This mode of operation has become untenable since then.2. How is international financial management different from domestic financial management？Answer：There are three major dimensions that set apart international finance from domestic finance。

exam12s经典教材《金融时间序列分析》Ruey S. Tsay 英文第三版2012年试题及答案高清版

Booth School of Business,University of ChicagoBusiness41202,Spring Quarter2012,Mr.Ruey S.TsaySolutions to MidtermProblem A:(34pts)Answer brieﬂy the following questions.Each question has two points.1.Describe two improvements of the EGARCH model over the GARCHvolatility model.Answer:(1)allows for asymmetric response to past positive or negative returns,i.e.leverage eﬀect,(2)uses log volatility to relax parameter constraint.2.Describe two methods that can be used to infer the existence of ARCHeﬀects in a return series,i.e.,volatility is not constant over time.Answer:(1)The sample ACF(or PACF)of the squared residuals of the mean equation,(2)use the Ljung-Box statistics on the squared residuals.3.Consider the IGARCH(1,1)volatility model:a t=σt t withσ2t =α0+β1σ2t−1+(1−β1)a2t−1.Often one pre-ﬁxesα0=0.Why?Also,suppose thatα0=0and the1-step ahead volatility prediction at the forecast origin h is16.2%(annualized),i.e.,σh(1)=σh+1=16.2for the percentage log return.What is the10-step ahead volatility prediction?That is,what isσh(10)?Answer:(1)Fixingα0=0based on the prior knowledge that volatility is mean reverting.(2)σh(10)=16.2.4.(Questions4to8)Consider the daily log returns of Amazon stockfrom January3,2007to April27,2012.Some summary statistics of the returns are given in the attached R output.Is the expected(mean) return of the stock zero?Why?Answer:The data does not provide suﬃcient evidence to suggest that the mean return is not zero,because the95%conﬁdence interval con-tains zero.5.Let k be the excess kurtosis.Test H0:k=0versus H a:k=0.Writedown the test statistic and draw the conclusion.1Answer:t-ratio =9.875√24/1340=73.79,which is highly signiﬁcant com-pared with χ21distribution.6.Are there serial correlations in the log returns?Why?Answer:No,the Ljung-Box statistic Q (10)=10.69with p-value 0.38.7.Are there ARCH eﬀects in the log return series?Why?Answer:Yes,the Ljung-Box statist of squared residuals gives Q (10)=39.24with p-value less than 0.05.8.Based on the summary statistics provided,what is the 22-step ahead point forecast of the log return at the forecast origin April 27,2012?Why?Answer:The point forecast r T (22)=0because the mean is not signif-icantly diﬀerent from zero.[Give students 1point if they use sample mean.]9.Give two reasons that explain the existence of serial correlations in ob-served asset returns even if the true returns are not serially correlated.Answer:Any two of (1)bid-ask bounce,(2)nonsynchronous trading,(3)dynamic dependence of volaitlity via risk premuim.10.Give two reasons that may lead to using moving-average models inanalyzing asset returns.Answer:(1)Smoothing (or manipulation),(2)bid-ask bounce in high frequency returns.11.Describe two methods that can be used to compare diﬀerent modelsfor a given time series.Answer:(1)Information criteria such as AIC or BIC,(2)backtesting or out-of-sample forecasting.12.(Questions 12to 14)Let r t be the daily log returns of Stock A.Assume that r t =0.004+a t ,where a t =σt t with t being iid N(0,1)random variates and σ2t =0.017+0.15a 2t −1.What is the unconditionalvariance of a t ?Answer:Var(a t )=0.0171−0.15=0.02.13.Suppose that the log price at t =100is 3.912.Also,at the forecastorigin t =100,we have a 100=−0.03and σ100=pute the21-step ahead forecast of the log price (not log return)and its volatility for Stock A at the forecast origin t =100.Answer:r 100(1)=0.004so that p 100(1)=3.912+0.004=3.916.Thevolatility forecast is σ2100(1)= 0.017+0.15(−0.03)2=pute the 30-step ahead forecast of the log price and its volatilityof Stock A at the forecast origin t =100.Answer:p 100(30)=3.912+0.004×30=4.032and the voaltility is the unconditional stantard error √0.02=0.141.15.Asset volatility has many applications in ﬁnance.Describe two suchapplications.Answer:Any two of (1)pricing derivative,(2)risk management,(3)asset allocation.16.Suppose the log return r t of Stock A follows the model r t =a t ,a t =σt t ,and σ2t =α0+α1a 2t −1+β1σ2t −1,where t are iid N(0,1).Under whatcondition that the kurtosis of r t is 3?That is,state the condition under which the GARCH dynamics fail to generate any additional kurtosis over that of t .Answer:α1=0.17.What is the main consequence in using a linear regression analysis whenthe serial correlations of the residuals are overlooked?Answer:The t -ratios of coeﬃcient estimates are not reliable.Problem B .(30pts)Consider the daily log returns of Amazon stock from January 3,2007to April 27,2012.Several volatility models are ﬁtted to the data and the relevant R output is attached.Answer the following questions.1.(2points)A volatility model,called m1in R,is entertained.Write down the ﬁtted model,including the mean equation.Is the model adequate?Why?Answer:ARCH(1)model.r t =0.0018+a t ,a t =σt t with t being iidN(0,1)and σ2t =7.577×10−4+0.188a 2t −1.The model is inadequatebecause the normality assumption is clearly rejected.2.(3points)Another volatility model,called m2in R,is ﬁtted to the returns.Write down the model,including all estimated parameters.3Answer:ARCH(1)model.r t=4.907×10−4+a t,a t=σt t,where t∼t∗3.56with t∗vdenoting standardized Student-t distribution with v degreesof freedom.The volatility equation isσ2t =7.463×10−4+0.203a2t−1.3.(2points)Based on theﬁtted model m2,test H0:ν=5versus H a:ν=5,whereνdenotes the degrees of freedom of Student-t distribution.Perform the test and draw a conclusion.Answer:t-ratio=3.562−50.366=−3.93,which compared with1.96is highlysigniﬁcant.If you compute the p-value,it is8.53×10−5.Therefore, v=5is rejected.4.(3points)A third model,called m3in R,is also entertained.Writedown the model,including the distributional parameters.Is the model adequate?Why?Answer:Another ARCH(1)model.r t=0.0012+a t,a t=σt t,where t are iid and follow a skew standardized Student-t distribution with skew parameter1.065and degrees of freedom3.591.The volatility equationisσ2t =7.418×10−4+0.208a2t−1.Ecept for the insigicant mean value,theﬁtted ARCH(1)model appears to be adequate based on the model checking statistics shown.5.(2points)Letξbe the skew parameter in model m3.Does the estimateofξconﬁrm that the distribution of the log returns is skewed?Why?Perform the test to support your answer.Answer:The t-ratio is1.065−10.039=1.67,which is smaller than1.96.Thus,the null hypothesis of symmetric innovations cannot be rejected at the 5%level.6.(3points)A fourth model,called m4in R,is alsoﬁtted.Write downtheﬁtted model,including the distribution of the innovations.Answer:a GARCH(1,1)model.r t=0.0017+a t,a t=σt t,where t are iid and follow a skew standardized Student-t distribution with skew parameter1.101and degrees of freedom3.71.The volatility equationisσ2t =1.066×10−5+0.0414a2t−1+0.950σ2t−1.7.(2points)Based on model m4,is the distribution of the log returnsskewed?Why?Perform a test to support your answer.Answer:The t-ratio is1.101−10.043=2.349,which is greater than1.96.Thus,the distribution is skew at the5%level.48.(2points)Among models m1,m2,m3,m4,which model is preferred?State the criterion used in your choice.Answer:Model4is preferred as it has a smaller AIC value.9.(2points)Since the estimatesˆα1+ˆβ1is very close to1,we consideran IGARCH(1,1)model.Write down theﬁtted IGARCH(1,1)model, called m5.Answer:r t=a t,a t=σt t,whereσ2t =3.859×10−5+0.85σ2t−1+0.15a2t−1.10.(2points)Use the IGARCH(1,1)model and the information providedto obtain1-step and2-step ahead predictions for the volatility of the log returns at the forecast origin t=1340.Answer:From the outputσ21340(1)=σ21341=3.859×10−5+0.85×(0.02108)2+0.15(.146)2=0.00361.Therefore,σ21340(2)=3.859×10−5+σ2 1340(1)=0.00365.The volatility forecasts are then0.0601and0.0604,respectively.11.(2points)A GARCH-M model is entertained for the percentage logreturns,called m6in the R output.Based on theﬁtted model,is the risk premium statistical signiﬁcant?Why?Answer:The risk premium parameter is−0.112with t-ratio−0.560, which is less than1.96in modulus.Thus,the risk premium is not statistical signiﬁcant at the5%level.12.(3points)Finally,a GJR-type model is entertained,called m7.Writedown theﬁtted model,including all parameters.Answer:This is an APARCH model.The model is r t=0.0014+a t,a t=σt t,where t are iid and follow a skew standardized Student-tdistribution with skew parameter1.098and degrees of freedom3.846.The volatility equation isσ2 t =7.583×10−6+0.0362(|a t−1|−0.478a t−1)2+0.953σ2t−1.13.(2points)Based on theﬁtted GJR-type of model,is the leverage eﬀectsigniﬁcant?Why?Answer:Yes,the leverage parameterγ1is signﬁicantly diﬀerent from zero so that there is leverage eﬀect in the log returns.5Problem C.(14pts)Consider the quarterly earnings per share of Abbott Laboratories(ABT)stock from1984.III to2011.III for110observations.We analyzed the logarithms of the earnings.That is,x t=ln(y t),where y t is the quarterly earnings per share.Two models are entertained.1.(3points)Write down the model m1in R,including residual variance.Answer:Let r t be the log earnings per share.Theﬁtted model is=0.00161.(1−B)(1−B4)r t=(1−0.565B)(1−0.183B4)a t,σ2a2.(2points)Is the model adequate?Why?Answer:No,the Ljung-Box statistics of the residuals give Q(12)=25.76with p-value0.012.3.(3points)Write down theﬁtted model m2in R,including residualvariance.Answer:Theﬁtted model is=0.00144.(1−B)(1−B4)r t=(1−0.470B−0.312B3)a t,σ2a4.(2points)Model checking of theﬁtted model m2is given in Figure1.Is the model adequate?Why?Answer:Yes,the model checking statistics look reasonable.5.(2points)Compare the twoﬁtted model models.Which model ispreferred?Why?Answer:Model2is preferred.It passes model checking and has a smaller AIC value.6.(2points)Compute95%interval forecasts of1-step and2-step aheadlog-earnings at the forecast origin t=110.Answer:1-step ahead prediction:0.375±1.96×0.038,and2-step ahead prediction:0.0188±1.96×0.043.(Some students may use2-step ahead prediction due to the forecast origin confusion.)Problem D.(22pts)Consider the growth rate of the U.S.weekly regular gasoline price from January06,1997to September27,2010.Here growth rate is obtained by diﬀerencing the log gasoline price and denoted by gt in R output.The growth rate of weekly crude oil from January03,1997to September24,2010is also obtained and is denoted by pt in R output.Note that the crude oil price was known3days prior to the gasoline price.61.(2points)First,a pure time series model is entertained for the gasolineseries.An AR(5)model is selected.Why?Also,is the mean of the gtseries signiﬁcantly diﬀerent from zero?Why?Answer:An AR(5)is selected via the AIC criterion.The mean of g tis not signiﬁcantly diﬀerent from zero based on the one-sample t-test.The p-value is0.19.2.(2points)Write down theﬁtted AR(5)model,called m2,includingresidual variance.Answer:Theﬁtted model is=0.000326.(1−0.507B−0.079B2−0.136B3+0.036B4+0.086B5)g t=a t,σ2a3.(2points)Since not all estimates of model m2are statistically signiﬁ-cant,we reﬁne the model.Write down the reﬁned model,called m3.Answer:Theﬁtted model is=0.000327.(1−0.504B−0.074B2−0.122B3+0.101B5)g t=a t,σ2a4.(2points)Is the reﬁned AR(5)model adequate?Why?Answer:Yes,the Ljung-Box statistics of the residuals give Q(14)=10.27with p-value0.74,indicating that there are no serial correlationsin the residuals.5.(2points)Does the gasoline price show certain business-cycle behavior?Why?Answer:Yes,theﬁtted AR(5)polynomial contains compplex solutions.6.(3points)Next,consider using the information of crude oil price.Writedown the linear regression model,called m4,including R2and residualstandard error.Answer:Theﬁtted linear regression model isg t=0.287p t+ t,σ =0.0184,and the R2of the regression is33.66%.7.(2points)Is theﬁtted linear regression model adequate?Why?Answer:No,because the residuals t are serially correlated based onthe Ljung-Box test.78.(3points)A linear regression model with time series errors is enter-tained and insigniﬁcant parameters removed.Write down theﬁnalmodel,including allﬁtted parameters.Answer:The model is(1−0.404B−0.164B2−0.096B3+0.101B5)(g t−0.191p t)=a t,σ2=0.000253.a9.(2points)Model checking shows that theﬁttedﬁnal model has noresidual serial correlations.Based on the model,is crude oil pricehelpful in predicting the gasoline price?Why?Answer:Yes,because theﬁtted coeﬃcient of p t is signﬁcantly diﬀerentfrom zero.10.(2points)Compare the pure time series model and the regression modelwith time-series errors.Which model is preferred?Why?Answer:The regression model with time series error is preferred as ithas a smaller AIC criterion.8。

Aggressiveness and survival of overconFIdent traders

*E-mail:benos @hec.frJournal of Financial Markets 1(1998)353—383Aggressiveness and survival of overconﬁdent tradersAlexandros V.Benos *Department of Finance,HEC School of Management,F-78351Jouy-en-Josas Cedex,France AbstractThis paper explicitly models investor behaviour in ﬁnancial markets allowing for traits linked to a notion of imperfect rationality.We study an extreme form of posterior overconﬁdence where some risk neutral investors overestimate the precision of their private information.They compete in market orders with another group of informed traders who have rational expectations.The participation of overconﬁdent traders in the market leads to higher transactions volume,larger depth,more volatile and more informative prices.More importantly,such traders may make higher expected proﬁts than rational ones and may even earn more than if they switched to rational behaviour.Their unconscious commitment to aggressive trading oﬀers them a ‘ﬁrst mover advant-age’.I consider an extension with risk averse market makers and ﬁnd that the nature of results depends on whether exogenous noise trading exists. 1998Elsevier ScienceB.V.All rights reserved.JEL classi ﬁcation:G14;D84;D82Keywords:Overconﬁdence;Strategic substitutes;Precommitment0.IntroductionSome fascinating events in ﬁnancial markets,such as wide price movements with no apparent reason (‘runs on the Street’),short-term proﬁt taking and aggressive trading,have rarely been explicitly studied in theoretical ﬁnance,perhaps for the simple reason they seem dangerously close to behavioural traits of irrational traders.Some other aspects of markets which have recently been captured in the rational paradigm,(for example,trading volume and technical analysis (Blume et al.,1994;Grundy and McNichols,1989;Brown and Jennings,1989),leave the behavioural side out.In this paper,we try to address directly the 0304-405X/98/$—see front matter 1998Elsevier Science B.V.All rights reserved.PII S 1386-4181(97)00010-4354 A.V.Benos/Journal of Financial Markets1(1998)353—383implications onﬁnancial markets of speciﬁc human behaviour,such as overcon-ﬁdence or persistent errors.In a behavioural approach to investing,two stories are often proposed.In the ﬁrst one,investors lacking important pieces of information,either natural or strategic,try to forecast them.They form probability judgments about events, about the judgments formed by other agents and so on(cf.‘beauty contest’in Keynes,1964).The complexity of following this iteration ad inﬁnitum causes the agents to stop at a certain level corresponding to their innate ability,the computational equipment at hand,the signal or action to be predicted,etc.At the higher levels of this iteration,they are,however,more likely to treat their judgments as being better than they actually are,and,in the limit,as being precisely correct.Jaﬀe and Winkler(1976)and Figlewski(1978)are two early examples of modeling imperfect forecasting ability in aﬁnancial economics model.In the second story,investors receive imperfect information on asset charac-teristics.Some treat these signals cautiously,recognizing they contain irrelevant noise.Others think signals are perfect,thereby overestimating their precision.In the extreme case,they may consider the noisy signal received as the realization of the unknown random variable itself.The sources of such overconﬁdence can be indirect,like computational constraints or frictions which,in theﬁrst story,diminish the marginal beneﬁts of additional iterations in judgments. The second story lends itself more easily to a diﬀerent ad hoc cognition and decision process.For example,the trader may think he can interpret the information better than he really does(cf.‘rational beliefs’in Kurz(1994)).Stated diﬀerently,he may exhibit overconﬁdence in his own interpretation of information.A possible reason is a non-Bayesian non-additive probability model like the one in Gilboa and Schmeidler(1993).But, whatever the source of overconﬁdence,the essential point is that posterior beliefs are overoptimistic.In both stories,investors put more value on their judgments or signals than they should correctly do.Under such circumstances, we show these traders may very well survive inﬁnancial markets under some conditions.This fallacy of excessive subjective certainty is widely documented in cognitive psychology and in the calibration literature(see Lichtenstein et al.,1982for an excellent review).Alpert and Raiﬀa(1982)notice people tend to be overconﬁdent and take on more risk than expected in many experimental contexts.Attention factors and the insensitivity of risk taking to probability estimates are also ersky and Kahneman(1974)describe anchoring behaviour in the assessment of subjective probability distributions.March and Shapira See,for example,Canning(1988)and Rubinstein(1986)on rational optimization under memory constraints.A.V.Benos/Journal of Financial Markets1(1998)353—383355 (1987)argue that managers tend to reject estimates of risk as given to them and try to revise them.Selection and survivorship biases may also be sources of overconﬁdence.Successful traders usually overestimate their own contribution to their success,confusing‘brains with a bull market’,against the old Wall Street adage. This paper explicitly introduces such behavioural biases in the modeling ofﬁnancial markets and examines their eﬀects.The latter will,of course,depend on how the market is organized and on which participants are overconﬁdent. The setup draws heavily on Benos(1993).We use Kyle’s(1985)one shot call auction market with many informed traders,some of which are overconﬁdent. By construction,traders do not have common priors on asset value distribution but know about the beliefs of all their opponents.We can say they agree to disagree over priors but not over how these priors are distributed in the population.We investigate eﬀects of overconﬁdence in comparison to the‘all rational traders’benchmark.Though it is hard to conceive of a market entirely comprised of overconﬁdent traders,we can also easily accommodate an‘all overconﬁdent traders’case for comparison purposes.Market makers compete(a la Bertrand)to service the total orderﬂow and set a price schedule,conditional on the information they have about the orderﬂow and conditional on their beliefs about the signals of the insiders.Exogenous liquidity traders are still necessary because,though overconﬁdent traders behave erroneously,they still possess better information than the market maker who will not wish to deal only with traders better informed than herself.We obtain many new and interesting results on market characteristics and traders’survival.First,under a risk neutral market maker,market depth,trading volume,price volatility and price informativeness increase when there are over-conﬁdent informed investors participating in the market.Since they put more weight on their signal than they should rationally do,they submit larger orders. This increases price volatility and informativeness since it reveals a larger part of the private signals to the public.The market maker,realizing that a part of the total orderﬂow is due to aggressive behaviour,increases market depth. Overconﬁdent informed traders closely resemble Black’s(1986)idea of noise trading deﬁned as‘2trading on noise as if it were information’.Indeed,weﬁnd most of his conjectures come true.Prices become more variable and markets more liquid but,contrary to Black,more eﬃcient as well,because of risk neutrality.He notes,however,in the same paper(p.532,footnote7),that‘In Kyle’s2model,having more noise traders can make markets more eﬃcient’. Some argue professional investors are not likely to do such suboptimal judgments,and that,in any case,compensation schemes align incentives with optimal decisions.Contrary to that,Griﬃn and Tversky(1992)show that experts may even be more overconﬁdent than amateurs when the environment is hard to predict(like theﬁnancial market).Moreover,this‘compensation’argument has never been formalized and,worse,it is even some times blamed for exactly this kind of overconﬁdence and short-termism by portfolio managers.356 A.V.Benos/Journal of Financial Markets1(1998)353—383More importantly,individual proﬁts of overconﬁdent traders may be positive and even higher than those of their rational opponents.Since rational traders fear pushing the price too much in one or the other direction,they are forced to scale down their own demands,when confronted to aggressive traders. Overconﬁdence becomes,therefore,an(unconscious)ﬁrst-mover advantage, similar to that enjoyed by the leader in a market entry game.Aggressive trading is here analogous to overinvestment by the leader in order to reduce the follower’s scale of entry(but still accommodate him).It is a barrier to mobility in the market(Dixit,1979).We also show that it is not in the rational traders’interest to mimic the overconﬁdent behaviour.At an individual level,it goes against the optimality result of their Nash equilibrium strategy.But,even if we assume that everybody proﬁting from deviating actually mimics the overconﬁdent aggressive trading style,such a‘group change of behaviour’is proﬁtable only if the rational group is relatively small in size.As their number rises,the expected individual proﬁt from deviating falls and they prefer sticking to their original Nash equilibrium strategy.This result is close to‘bandwagon behaviour’and is linked to a unim-odality result on total expected proﬁts of rational traders.We show these increase with the size of the rational group,for small values of this size,but they decrease for large group sizes.A larger number of rational traders engage in intense competition among themselves and shrink the pie which they will share. Overconﬁdent traders as a group beneﬁt from such competition.Two comments are necessary at this point.First,ourﬁndings depend on the conjectures trader groups hold,not only about the distribution of uncertain-ty but also about each other’s rationality and about the market maker’s information.A Nash equilibrium can be built only if both groups have the same beliefs about the market maker’s pricing schedule and about each other’s strategy.Second,this paper is quite diﬀerent from the DeLong et al.(1990) approach where noise traders also make positive proﬁts.As stated in the abstract of their paper,‘the disproportionate amount of risk[noise traders] themselves create enables[them]to earn a higher expected return than rational investors’.In this paper,there are no such eﬀects since all traders are risk neutral.Irrational investors overestimate just the precision of the signal they receive.They do not imagine asset returns following a distribution when they do not.Our result comes from aﬁrst-mover advantage,not from excessive risk taking.We also analyze the case where the market maker is risk averse.Two equilibria are now possible depending on whether we keep exogenous unin-formed liquidity traders in the model or not.If we dispense with those traders altogether,leaving the irrational,overconﬁdent traders playing the role of‘noise traders’,the latter lose money on average to the rational traders and the equilibrium changes radically.Market depth may now fall as the number of overconﬁdent traders increases.On the other hand,we may keep traditionalA.V.Benos/Journal of Financial Markets1(1998)353—383357 noise traders in the model.We thenﬁnd all of the comparative statics results with a risk neutral market maker are still valid.To resume,risk aversion of the market maker changes results on expected proﬁts of informed traders,depend-ing on whether exogenous noise traders exist in the market or not.Risk aversion does not change results concerning depth,volume or price variability unless it is accompanied by a radical change of the market structure,such as eliminating uninformed traders altogether.A few other papers deal explicitly with mistaken beliefs about risky payoﬀs. Odean(1996)presents three diﬀerent market structures,two of which examine price-taking overconﬁdent informed traders(like in Grossman and Stiglitz, 1980)and one which looks at a Kyle(1985)setting.His results depend a lot on the speciﬁc assumptions about risk preferences of agents and competition.In his ‘Model II’,which most closely resembles our market structure,results are similar with the exception of expected proﬁts.This diﬀerence is due to the lack of competition in his model,since there is only one informed trader in the market. We can easily show the same result in the extreme case of a single overconﬁdent insider.Caballe and Sa kovics(1994)treat the question of overconﬁdence in a more complex setting.They assume a player’s degree of overconﬁdence is not known to the others.So,in order to let players maintain their possibly inconsist-ent beliefs,they revise the solution concept of the game closer to a conjectural equilibrium.They tooﬁnd higher trading volume,higher price volatility and more informative st but not least,Kyle and Wang(1997)have indepen-dently developed a similar(but more complicated)modeling of overconﬁdence with only two informed traders,arriving at most of our results with a risk neutral market maker.They arrive at the same result as this paper,namely that overconﬁdent traders can make greater expected proﬁts than rational ones, using the‘commitment to trade more aggressively’argument.Their approach, however,does not capture the competition eﬀect between traders with diﬀerent beliefs since they do not consider multiple informed traders.In this paper,we study extensively the eﬀects of an exogenous or endogenous changes in the number of informed traders and,more speciﬁcally,we study what happens if we add more overconﬁdent ones in the market.Weﬁnd,for example,that more overconﬁdent traders facing a market with a given number of rational traders increase market depth,trading volume and price variance.Moreover,we extend the model to a risk averse market makerﬁnding that risk preferences do not change qualitatively the equilibrium.The plan of the paper is as follows.In the following Section,we present the set-up of beliefs in detail.Then the trading game with both types of beliefs coexisting in the market is discussed and a unique Nash equilibrium with a risk neutral market maker is deﬁned,shown to exist and characterized.In Section3, comparisons of market depth,price volatility,trading volume and price in-formativeness with the two benchmark cases are presented.Section4discusses the survival of overconﬁdent traders in the market.Section5extends the modelThis ‘truth plus noise’parameterization is chosen for its tractability and captures the second story described above.It is nevertheless,observationally equivalent to the ﬁrst one,with the ‘forecasts’.Consider the simple case with two insiders and let the underlying value F be the sum of two uncorrelated parts s G ,each received by one insider.These signals form the strictly private information of the traders.Then,each trader forms a forecast of the signal he does not possess.Let us denote such forecast of agent i by f H "s H #e G (j O i )with e G his personalised prediction error.To summarise,each trader i observes a signal s G and forms an estimate f H about the signal his rival received.Trader 1’s best estimate for F is then E (F )"s #f "s #s #e "F #e .Clearly,this is equal to the simpler ‘truth plus noise’formulation,given the white noise garbling form used for the forecast f H.to the case of a risk averse market maker.Section 6concludes the paper.Proofs,when necessary,are contained in the Appendix.1.The trading modelConsider a market for a risky asset with an ex-post liquidation value of F .There are three kinds of traders:a number of risk neutral insiders with unique access to a personalised signal s G about F ;uninformed liquidity traders submit-ting a total random order u ;and a competitive market maker setting a price schedule p ( )and servicing the total order ﬂow ,given her beliefs about the type of insiders.The total number of informed traders is exogenous and their type decomposition (how many rational and how many overconﬁdent types)is common knowledge.It is also commonly known that s G "F #e G where F and e G are both normally distributed with means zero (for expositional reasons)and variances and respectively. Errors e G are uncorrelated to all other random variables in the model.Liquidity demand has mean zero and variance of S and is also normally distributed.Trading is done in two steps.First,the exogenous values of s G and u are realized.Then,investors form expectations of random variables in the model,such as F ;they use belief functions G G (x )giving,for any random variable x ,the expectation of x given i ’s information.To remind us of conditional expectations,we will write these belief functions as G G (x "s G ).We will call an insider rational if he accounts for the non-zero variance of the noise in his signal,e G ,and takes the correct mathematical conditional expectation of any random variable x .In this case,we can writeG G (x "s G )"E(x "s G "s G )(1)We will call an investor overconﬁdent if he takes the variance of e G as being equal to zero and uses the forecast as the actual realization of the unknown value of 358 A.V.Benos /Journal of Financial Markets 1(1998)353—383This may be extreme but it is very useful in showing clearly the eﬀects of such behaviour in ﬁnancial markets.A more natural approach would be overconﬁdent traders only underestimating slightly the error variance but this would not change the qualitative results of the paper.the stock. The overconﬁdent investor treats his forecasts as more reliable information than they really are.His belief function can be written asG G (x "s G )"E(x "F "s G)(2)The market maker does not diﬀer from other players in the model since she similarly forms beliefs about the distribution of her signal which is the total order ﬂow .She may,for example,think (mistakenly)all traders are rational.In that case,she will be overpricing the order ﬂow by extracting too much information from it.On the other hand,she may (correctly)take into account that some traders are overconﬁdent.She will then price the order ﬂow optimally but less than she would if she believed (or knew)all agents were rational.In what follows,we assume the market maker knows the type and number of traders and behaves optimally.We allow both groups of rational and overconﬁdent investors to compete against each other in quantities.This makes best responses of traders strategic substitutes of each other.If one trader increases the quantity of his market order,the best response of the others is,ceteris paribus,to lower their own.This plays a major role,both in the survival of overconﬁdent traders and in market properties,as we will show in Sections 3and 4.We can then check whether rationality proves to be a ‘ﬁtter’strategy.Although such veriﬁcation has seldom been formally made (for notable exceptions,see Schaﬀer (1989),Blume and Easley (1992),Palomino (1996)),the ‘ﬁttest strategy’argument in support of rationality is casually used in most of ﬁnance and economics.Both groups are aware of the presence of the other;rational traders know there are some aggressive players in the market and overconﬁdent ones realize there are some cautious agents on the ﬂoor with them.So they diﬀer not only in their belief about the quality of their own signal but also on their beliefs about the other group’s belief.Rational traders know that s G is a noisy version of the payoﬀF and believe that the overconﬁdent group has received a signal of similar quality as them but treats it as the actual payoﬀitself.They are aware of the overconﬁdence of their rivals.Overconﬁdent traders,on the other hand,believe their rivals underestimate the precision of their signal.They think s H is the realization of the payoﬀF ,so they believe the other group treats it mistakenly as a noisy version of the payoﬀ.In a sense,they are aware of the cautiousness of their rivals.This overconﬁdence is common knowledge contrary to the (ﬁrst-order)beliefs about the distribution of the signal which are not.We can think of this setup not as prior overoptimistic beliefs by speculators but as evidence of A.V.Benos /Journal of Financial Markets 1(1998)353—383359Kurz (1994)postulates economic agents do not have any structural knowledge on the underlying variables but only a large set of past data which they use to learn.Their interpretation of the same data can therefore diﬀer vastly.This is an additional hint to the absurdity of the clairvoyance concept of Nash equilibrium.Otherwise irrational agents have consistent conjectures about the types of their rivals but an unconscious precommitment to aggressive trading;rational agents respond to such precommitment but are not selected even though they exist.posterior overconﬁdence .Traders think they can interpret the signal better than they really do.Since signals are not known,the game considered is a Bayesian one but without the uncertainty of types.It is common knowledge that there exists a ﬁnite number of players,M of them overconﬁdent and N rational.Each player entertains trivial beliefs about the ‘types’of other players.For example,the probability a player assigns to the eventthatis the actual proﬁle of types for the other players,is 1if he is overconﬁdent and 0,otherwise.This is necessary for precommitment to produce beneﬁts for the player who has precomitted.On the contrary,such an assumption is not necessary in Schaﬀer (1989)since,in that model,rational agents do not modify their strategies based on the knowledge that they are playing against irrational agents.In that paper,irrational players end up obtaining higher expected utility than rational ones because they hurt rational players more than they hurt themselves (evolutionary spite).In our approach,rational agents are ‘more rational’than Schaﬀer’s (1989)proﬁt maximisers.For each player k ,the set of possible strategy proﬁles X I :s I |R ,is the set of real functions from his signal to the order he submits.Purchases (sales)are positive (negative)and there are no indivisibilities.Risk neutrality and imperfect competition causes their payoﬀfunction to equal realized proﬁts I (X I ,X I ),X I (s I )[F !p (X I ,X \I )].The (Bayesian)Nash equilibrium is de-ﬁned in the usual way as the payoﬀmaximising strategy choice.Note that even though there may be disagreement among traders about the precision of the signal,each group forms the same ﬁrst-order conjectures about the pricing schedule p ())set by the market maker.Otherwise,the Nash equilib-rium concept cannot be used.Caballe and Sa kovics (1994)use a diﬀerent concept in their approach to overconﬁdence.They consider a model with only overconﬁ-dent traders thinking they are not overconﬁdent even when they believe every-one else is.They consider this behaviour to be ‘one of the most important characteristics’of such traders.They hence have diﬃculties with incorrect beliefs about strategies in equilibrium and do not use the Nash construction.In 360 A.V.Benos /Journal of Financial Markets 1(1998)353—383A.V.Benos/Journal of Financial Markets1(1998)353—383361 response,they develop a solution called‘Mirage’equilibrium.Players maintain possibly inconsistent beliefs but maximise against strategies which they consider to be best responses according to the beliefs they attribute to other players,and to the beliefs they think other players have about their own conﬁdence.Aﬁnal point about common knowledge and Nash equilibrium is in order before we proceed.We need to assume that if an agent decides to change his behaviour,the other agents somehow know of the change.Such an assumption is objectionable in a static,simultaneous move game.It is,moreover,not clear that assuming consistent conjectures is a strong point when modeling irrational-ity.One could even interpret our result on higher overconﬁdent expected returns as a reduction to absurdity of the Nash equilibrium concept itself.Our choice is,however,a deliberate choice of methodology.We think that,before undertaking adventurous expeditions into the lands of Nash reﬁnements,we should be absolutely clear of the possible results of overconﬁdence under the most basic solution concept of Nash equilibrium.2.Equilibrium with a risk neutral market makerEach of the N rational insiders submits a quantity x G and each of the M overconﬁdent ones,submits a quantity y H,for a total of x and y respectively. As most literature based on Kyle(1985),we characterize the unique linear Nash equilibrium.Writing x G" s G and y H" s H as the individual optimal demand functions of rational and overconﬁdent agents respectively,each trader esti-mates his rivals’total demand when maximising his subjective expected proﬁts. Rational traders use y" +H s H as the total demand submitted by overconﬁ-dent speculators and the latter,in turn,do the corresponding estimation. Consistency is guaranteed by the assumption of common knowledge of over-conﬁdence.The market maker is assumed to be smart(so she prices the orderﬂow optimally given what she knows)and risk neutral(until Section5).She,there-fore,sets prices such that she expects to earn zero proﬁts conditional on her observing the net orderﬂow:p( )"E(F" )" (3) where1/ is the usual measure of market depth.Price linearity follows from the normality of distributions and the assumed linearity of trading strategies. Note the market maker will choose to close the market if there are no liquidity traders.Though the overconﬁdent traders can be thought as‘noise’traders in the sense of DeLong et al.(1991)—they‘falsely believe they have special information about the future price of the risky asset’—they still know more about the risky asset than the market maker.She will therefore lose money to both groups of insiders if there are no liquidity traders around.Given the linear demands and the price schedule,traders solve the usual proﬁt maximisation program.Rational trader i calculatesE(F "s G )" s G,(4)whereas overconﬁdent trader k letsG I (F "s I )"s I.(5)Rational traders maximize expected proﬁts for individual demands ofx G "12 # s G !(N !1)E(x H "s G )2!E(y "s G )2,i O j ,(6)while overconﬁdent traders maximize ‘perceived’proﬁts for individual demands ofy I "s I 2 !(M !1)G (y J "s I )2!G (x "s I )2,k O l .(7)We need to evaluate the beliefs G ())of trader k for other individual overconﬁdent orders y J as well as his beliefs over the total demand x submitted by rational traders.In both cases,the main ingredient is k ’s belief about the other trader’s signal,G I (s J "s I ),which is equal to k ’s signal.In other words,the best estimate of a rival’s signal for an overconﬁdent trader is his own information,since he considers it to be perfect.Substituting in Eqs.(6)and (7),we get the following system:# M (N #1) #2 "1 (N #1) #2 ,N M #1 # "1 1M #1.(8)Solving the above system,we have:¸emma 1.For a given liquidity parameter ,the order submitted by rational trader i is s G and that submitted by overconﬁdent trader k is s I,where "1 (M #N #1) #2(M #1),(9) "1 #2 (M #N #1) #2(M #1) .(10)First,note that,for all values of market depth,overconﬁdent speculators are using their signal more aggressively when trading.It is clear traders must have consistent conjectures (a)about the pricing parameter ,and (b)about each other’s chosen strategy.The former implies one group maximizes assuming the 362 A.V.Benos /Journal of Financial Markets 1(1998)353—383。

英语六级历年阅读题及答案

2010年6月阅读Section BDirections: There are 2 passages in this section. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A), B), C) and D). You should decide on the best choice and mark the corresponding letter on Answer Sheet2 with a single line through the centre.Passage OneQuestions 51 to 56 are based on the following passage.Only two countries in the advanced world provide no guarantee for paid leave from work to care for a newborn child. Last spring one of the two, Australia, gave up the dubious distinction by establishing paid family leave starting in 2011. I wasn't surprised when this didn't make the news here in the United States—we're now the only wealthy country without such a policy.The United States does have one explicit family policy, the Family and Medical Leave Act, passed in 1993. It entitles workers to as much as 12 weeks' unpaid leave for care of a newborn or dealing with a family medical problem. Despite the modesty of the benefit, the Chamber of Commerce and other business groups fought it bitterly, describing it as "government-run personnel management" and a "dangerous precedent". In fact, every step of the way, as (usually) Democratic leaders have triedto introduce work-family balance measures into the law, business groups have been strongly opposed.As Yale law professor Anne Alstott argues, justifying parental support depends on defining the family as a social good that, in some sense, society must pay for. In her book No Exit: What Parents Owe Their Children and What Society Owes Parents, she argues that parents are burdened in many ways in their lives: there is "no exit" when it comes to children. "Society expects—and needs—parents to provide their children with continuity of care, meaning the intensive, intimate care that human beings need to develop their intellectual, emotional and moral capabilities. And society expects—and needs—parents to persist in their roles for 18 years, or longer if needed."While most parents do this out of love, there are public penalties for not providing care. What parents do, in other words, is of deep concern to the state, for the obvious reason that caring for children is not only morally urgent but essential for the future of society. The state recognizes this in the large body of family laws that govern children' welfare, yet parents receive little help in meeting the life-changing obligations society imposes. To classify parenting as a personal choice for which there is no collective responsibility is not merely to ignore the social benefits of good parenting; really, it is to steal those benefits because they accrue (不断积累) to the whole of society as today's children become tomorrow'sproductive citizenry (公民). In fact, by some estimates, the value of parental investments in children, investments of time and money (including lost wages), is equal to 20-30% of gross domestic product. If these investments generate huge social benefits—as they clearly do—the benefits of providing more social support for the family should be that much clearer.注意：此部分试题请在答题卡2上作答。

根本原因分析-阿波罗法-(RCA-Chinese)

Root Cause Analysis Apollo Methodology
根本原因分析阿波罗法
Why RCA ?????……..Prevailing most common industrial situation
为何RCA？？？？？………广泛适用
2
WHY RCA ??…为何应用RCA？？…
Everything that happens is the
result of causes set in motion所
有事件都是一系列因连续作用的
结果
Caused
Effect果 By
Cause 因
Condition条件
Each time we ask why, look for
Actions & Conditions to identify causes每次产生疑问时，从行为和条件两方面去发现原因
continuum因果是无限连续统一体的一部分
3rd
-
Each effect has at least two causes in
the form of actions and conditions，一果至少两因，分
别以行为和条件形式存在。
4th
-
An effect exist only if its causes exist at
-
Categorical thinking绝对性思维
6
ROOT CAUSE ANALYSIS根本原因分析
EFFECTIVE PROBLEM SOLVING DEFINED 有效问题解决方式
o Appreciative understanding有价值的理解
-
Diversity of thought is valuable多样性思维最具价值

20101212（练习答案汇总）

20101212（练习答案汇总）Unit 1 Mathematics1. Match the Chinese in the left column with the English in the right column.迭代函数iterative function优先权之争priority battle分形特征fractal properties有意义make sense以越来越小的规模重复同一模式patterns repeat themselves at smaller and smaller scales混沌理论chaos theory季刊a quarterly journal数学界the mathematics community波纹线crisp lines会议公报proceedings of a conference3. Translate the sentences into Chinese.1) He is best known for coining the term fractal to describe phenomena (such as coastlines, snowflakes,mountains and trees) whose patterns repeat themselves at smaller and smaller scales.他主要是因为用分形这个概念来描述（海岸线，雪花，山脉和树木）等不规则形状等现象而闻名于世，这些不规则形状在越来越小的规模上不断重复同一模式。

2) A closer look reveals that the borders of the set do not form crisp lines but seem to shimmer like flames.如果再仔细观察，就可以发现集的边界并没有呈波纹线，而是像火焰一样闪光。

3) Krantz introduced a new element into the debate, however, by stating that the Mandelbrot set "was notinvented by Mandelbrot but occurs explicitly in the literature a couple of years before the term 'Mandelbrot set' was coined."但是，克朗兹在这场辩论中引入了一个新东西，他说曼德布洛特集不是曼德布洛特发明的，而是早在“曼德布洛特集”这个术语出现几年以前就已经明确地在数学文献中出现了。

复变函数论(英文版)

z zz¯ |z|2
We also have the following important relationships between a complex number and its conjugate:
1. A REVIEW OF COMPLEX NUMBERS
3
Proposition 1.5. Suppose that z = x + iy is a complex number.
2101 Complex Analysis Autumn 2010
Alexander V. Sobolev
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT
E-mail address: A.Sobolev@
Proof. (1) Write |z|2 = x2 + y2, z = x + iy. (2) Let us prove the triangle inequality:
|z + w|2 = (z + w)(z¯ + w¯) = zz¯ + ww¯ + (wz¯ + zw¯)
= |z|2 + |w|2 + 2 Re(wz¯)
Definition 1.3. The complex conjugate of a complex number z = x + iy is deﬁned to be the complex number z = x − iy.
Graphically, (meaning represented on the Argand plane) z is the reﬂection of z in the real axis.

美国研究生入学考试题库GRE真题三_真题无答案-交互

美国研究生入学考试题库（GRE）真题三(总分156, 做题时间150分钟)SECTION 1There are five questions below，Five participants at an international conference are plan-ning to take a car trip together. Two persons― the driver and one passenger― will sit in the front seat of the car, and three persons will sit in the back seat. The names of the five participants and all of the languages that each of them speaks are as follows:Mohsen: Farsi and HebrewOrlando: Italian and RussianShelly: Hebrew and RussianTheo: German and ItalianUrsula: Farsi, German, and HebrewThe participants must be seated in the car according to the following restrictions: The driver must be Orlando or else Shelly. Two persons can be seated side by side only if at least one of the languages they speak is the same.SSS_SINGLE_SELWhich of the following is an acceptable seating arrangement, with the driver listed first under “Front Seat” and the passengers in the back seat listed from one side to the other side?Front Seat Back SeatA Mohsen, Ursula Theo, Orlando, ShellyB Orlando, Mohsen Shelly, Theo, UrsulaC Orlando, Shelly Mohsen, Ursula, TheoD Shelly, Mohsen Ursula, Orlando, TheoE Shelly, Orlando Theo, Mohsen, UrsulaA B C D ESSS_SINGLE_SELIf Mohsen sits in the front seat, which of the following can be true?AOrlando will be the driver.BOrlando will sit next to Ursula.CShelly will sit in the middle position in the backDShelly will be the driver.EUrsula will sit in the middle position in the backSSS_SINGLE_SELIf Theo sits in the front seat, which of the following must be true?AMohsen and Shelly will sit side by side.BMohsen and Ursula will sit side by side.COrlando and Theo will sit side by side.DOrlando and Ursula will sit side by side.EShelly and Ursula will sit side by side.SSS_SINGLE_SELIf both persons sitting in the front seat speak Hebrew, then it must be true thatAexactly one person sitting in the back seat speaks RussianBneither speaker of Farsi is sitting in the front seatCno one sitting in the front seat speaks RussianDno one sitting in the back seat speaks HebrewEa speaker of Russian is sitting in the middle position in the back seatSSS_SINGLE_SELWhich of the following must be true if Orlando is the driver?AIf Shelly sits in the front seat, Ursula will sit in the middle position in the back seatBIf Shelly sits in the back seat, she will sit next to UrsulaCIf Theo sits in the front seat, Ursula will sit in the middleposition in the back seat.DIf Theo sits in the back seat, he will sit between Mohsen and Ursula.EIf Ursula sits in the back seat, she will sit in the middle position in the back seat.seat.There are two questions below，SSS_SINGLE_SELAThe termination of a governmental subsidy to the publictransportation system that serves both the city and its suburbs caused a sub- stantial increase in fares.BMany new trains and buses were put into service in the public transportation system both within the city and between the city and its suburbsCSecurity was improved in the passenger waiting areas and on thepublic trains and buses used within the city as well as on those used between the city and its suburbs.DLegislation was passed that increased the fre- quency of public transportation service within the city as well as between the city and its suburbs.The number of points served by the public trans- portation system both within the city and between the city and its suburbs was increased substantially by adding new routes.SSS_SINGLE_SELAThe price per gallon for gasoline declined by five percent.BThe cost of using public transportation, per mile traveled, increased.CThe number of people **muted to work via public transportation from points in or near downtown Allentia increasedDThe frequency of public transportation service between the city and its suburbs decreased.EThe cost per mile of getting to and from work by car tripled.8.A new and more aggressive form of the fungus that caused the Irish potato famine of the nineteenth century has recently arisen. However, since this new form of the fungus can be killed by increased application of currently used fungicides, it is unlikely that the fungus will cause widespread food shortages in countries that currently rely on potatoes for sustenance.Which of the following, if true, most calls into question the con- clusion in the argument above?SSS_SINGLE_SELAThough potatoes are an important staple crop in many parts of the world, people in most countries rely primarily on wheat or rice for sustenanceBPotato farmers in many countries to which the new form of the fungus has spread cannot afford to increase their spending on fungicidesCThe new form of the fungus first began to spread when contaminated potato seeds were inadvertently exported from a major potato-exporting country.Potato farmers in most countries use several insecticides on their crops in addition to fungicides of the sort that kill the new form of the fungus.EMost governments have funds set aside that can be used to alleviate the effects of large-scale disasters such as severe food shortages and floodsThere are eight questions below，The organizers of a music festival are scheduling exactly six master classes, one class per day for six consecutive days. Three of the classes will be given by violinists and three by pianists. The only musicians who can teach the classes are the violinists F, G, H, and J, and the pianists R, S, T, W, and Z. The festival's organizers must observe the following constraints:No musician will teach more than one class. F will not teach unless the first three classes are taught by violinists. If J teaches a class, it will be the sixth. R will teach only if T teaches the first class. No pianist will teach on a day that immediately pre- cedes or immediately follows a day on which W teachesSSS_SINGLE_SELWhich of the following can be the musicians scheduled to teach the master classes, in the order in which they will teach, from first to sixth?AF, J, G, T, Z, SBF, W, H, T, G, ZCG, F, H, T, S, ZDS, G, W, H, R, JET, G, W, H, R, SSSS_SINGLE_SELIf R is scheduled to teach the second class, which of the following could be scheduled to teach the third class?AFBGCJDTEWSSS_SINGLE_SELWhich of the following must be true about the schedule of master classes?AJ is not scheduled to teach if R is scheduled to teach.BJ is not scheduled to teach if T is scheduled to teachCJ is not scheduled to teach if W is scheduled to teach.DW is not scheduled to teach if F is scheduled to teachEZ is not scheduled to teach if W is scheduled to teach.SSS_SINGLE_SELIf pianists are scheduled to teach the fourth, fifth, and sixth classes, which of the following must be true?AF is scheduled to teach the first classBG is scheduled to teach the first classCH is scheduled to teach an earlier class than the class Z is scheduled to teach.DR is scheduled to teach an earlier class than the class T is scheduled to teach.ES is scheduled to teach an earlier class than the class T is scheduled to teach.SSS_SINGLE_SELWhich of the following must be true about the schedule of the master classes?AIf F is scheduled to teach a class, then H is also scheduled to teach a classBIf J is scheduled to teach a class, then R is also scheduled to teach a class.CIf J is scheduled to teach a class, then S is also scheduled to teach a classDIf T is scheduled to teach a class, then R is also scheduled to teach a class.EIf W is scheduled to teach a class, then Z is also scheduled to teach a class.SSS_SINGLE_SELIf classes are scheduled so that the classes taught by pianists and the classes taught by violinists alternate with one another, which of the following can be true?AF is scheduled to teach the fourth classBG is scheduled to teach the first class.CH is scheduled to teach the third class.DR is scheduled to teach the fifth class.EW is scheduled to teach the second class.SSS_SINGLE_SELIf a violinist is scheduled to teach the first class and another violinist is scheduled to teach the sixth class, which of the following can be true?AF is scheduled to teach the second class.BH is scheduled to teach the sixth class.CR is scheduled to teach the fourth classDT is scheduled to teach the second class.EW is scheduled to teach the third class.SSS_SINGLE_SELWhich of the following CANNOT be true about the schedule of the master classes?AF is scheduled to teach the third class.BG is scheduled to teach the first class.CT is scheduled to teach the sixth class.DW is scheduled to teach the sixth class.EZ is scheduled to teach the fifth class.There are five questions below，In a small office suite, six offices are arranged in a straight line, one after another, and are consecutively num- bered 1 through 6.E xactly six people― P, Q, R, S, T and U― are to be assigned to these six offices, exactly one person to an office, according to the following conditions:P must be assigned to an office immediately adjacent to the office to which T is assigned.Q cannot be assigned to an office immediately adja- cent to theoffice to which S is assigned.R must be assigned either to office 1 or to office 6.S must be assigned to a lower-numbered office than the office to which U is assigned.SSS_SINGLE_SELWhich of the following can be the list of the six people in the order of their offices, from office 1 through office 6?AQ, U, S, T, P, RBR, P, T, S, U, QCR, S, Q, U, P, TDS, T, Q, P, U, RET, P, S, R, Q, USSS_SINGLE_SELIf T is assigned to office 6. then U must be assigned to officeA1B2C3D4E5SSS_SINGLE_SELIf Q is assigned to office 2, then the person assigned to office 6 must beAPBRCSDTEUSSS_SINGLE_SELIf Q is assigned to office 1, which of the following CANNOT be true?AP is assigned to office 3.BP is assigned to office 4.CS is assigned to office 4.DT is assigned to office 2.ET is assigned to office 3.SSS_SINGLE_SELIf U is assigned to office 3, then Q must be assigned to officeA1 or 2B1 or 6C2 or 5D4 or 5E4 or 6SSS_SINGLE_SELIf S is assigned to office 2, which of the following can be true?AP is assigned to office 1.BQ is assigned to office 3.CR is assigned to office 6.DT is assigned to office 5.EU is assigned to office 4.23.As government agencies, faced with budget difficulties, reduce their funding for scientific research, a greater amount of such research is being funded by private foundations. This shift means that research projects likely to produce controversial results will almost **prise a smaller proportion of all funded research projects, since private foundations, concerned about their public image, tend to avoid controversy.Which of the following is an assumption on which the argument depends?SSS_SINGLE_SELAOnly research that is conducted without concern for the possibility of generating controversy is likely to produce scientifically valid results.BPrivate foundations that fund scientific research projects usually recognize that controversial results from those projects cannot always be avoided.CScientists who conduct research projects funded by private foundations are unlikely to allow the concerns of the funding organizations to influence the manner in which they conduct the research.DMany government agencies are more concerned about their public image than are most private foundations.EGovernment agencies are more willing than are private foundations to fund research projects that are likely to produce controversial results24.Juries in criminal trials do not base verdicts on uncorroborated testimony given by any one witness. Rightly so, because it is usually prudent to be highly skeptical of unsubstantiated claims made by any one person. But then, to be consistent, juries should end an **mon practice: convicting defendants on the basis of an uncorroboratedfull confession.Which of the following, if true, most strengthens the argument above?SSS_SINGLE_SELAJuries often acquit in cases in which a defendant retracts a full confession made before trialBThe process of jury selection is designed to screen out people who have a firm opinion about the defendant's guilt in advance of thetrialCDefendants sometimes make full confessions when they did in fact do what they are accused of doing and **e to believe that the prose- cutor **pelling proof of this.DHighly suggestible people who are accused of wrongdoing sometimes become so unsure of their own recollection of the past that they **e to accept the accusations made against them.EMany people believe that juries should not con- vict defendants who have not made a full confession.25.Although spinach is rich in calcium, it also contains large amounts of oxalic acid, a substance that greatly impedes calcium absorption by the body. Therefore, other calcium-containing foods must be eaten either instead of or in addition to spinach if a person is to be sure of getting enough calcium.Which of the following, if true, most seriously weakens the argu-ment above?SSS_SINGLE_SELARice, which does not contain calcium, counteracts the effects of oxalic acid on calcium absorption.BDairy products, which contain even more calcium than spinach does, are often eaten by people who eat spinach on a regularbasis.CNeither the calcium nor the oxalic acid in spinach is destroyed when spinach is cooked.DMany leafy green vegetables other than spinach that are rich in calcium also contain high concentrations of oxalic acid.EOxalic acid has little effect on the body's ability to absorb nutrients other than calcium.SECTION 226.Of the following, which is the closest approximation toSSS_SINGLE_SELA400B120C100D40E1027.If (x - 1) 2 = (x - 2) 2 , then x=SSS_SINGLE_SELAB2/3C4/3D2/3E5/228.In the figure above, the areas of square regions X and Y are 1 and 4, respectively. What is the area of the triangular region?SSS_SINGLE_SELA2B1C3/4D1/2E1/429.If erasers cost $0.25 each, at most how many erasers can be purchased for n dollars, where n is an integer?SSS_SINGLE_SELAn/25Bn/4C4nDE25n/430.Three salespeople are **missions in proportion to the amount of their sales, which total $25, 000, $40, 000, and $60, 000, respectively. If a total of $20, 000 is allocated for these **missions, what is the amount of the **mission paid?SSS_SINGLE_SELA$8, 000B$8, 400C$9, 600D$10, 000E$12, 000There are three questions below，For a cash advance, a certain credit **pany charges a transaction fee equal to a percent of the total amount of the cash advance, according to the graph below.SSS_SINGLE_SELA$5 moreB$10 moreCthe sameD$5 less$10 lessSSS_SINGLE_SELFor which of the following cash advance amounts is the transaction fee approximately $4?A$190B$420C$750D$1, 200E$1, 580SSS_SINGLE_SELFor a total of $1, 500 that is advanced in separate cash amounts, for which of the following is the total of the transaction fees the LEAST?ATwo cash advances of $750BThree cash advances of $500CSix cash advances of $250DTwo cash advances, one of $1, 100 and one of $400ETwo cash advances, one of $1, 250 and one of $250There are two questions below，SSS_SINGLE_SELWhat is the median nighttime charge for 360 minutes of calling?$63.84B$71.40C$72.50D$87.92E$113.29SSS_SINGLE_SELThe daytime charge for 360 minutes of calling for phone service T is approximately what percent more than the nighttime charge?A7%B14%C28%D33%E40%36.A square dart board has four dark circular regions of radius 3 inches as shown in the design above. Each point on the dart board is equally likely to be hit by a dart that hits the board. What is the probability that a dart that hits the board will his one of the circular regions?SSS_SINGLE_SELAπ/16Bπ/48π/64D1/3E1/437.If x increased by 50 percent is equal to 20, then x =SSS_SINGLE_SELA40/3B10C20/3D5E3/438.In the rectangular coordinate plane, point A has coordinates (-4, 0), point B has coordinates (0, 4), point C has coordinates (4, 0), and point D has coordinates (0, -4). What is the area of quadrilateral ABCD?SSS_SINGLE_SELA8B16C24D32E6439.An experiment has three possible outcomes, l, J, and K. The probabilities of the outcomes are 0.25, 0.35, and 0.40, respectively. If the experiment is to be performed twice and the successive outcomes are independent, what is the probability that K will not be an outcome either time?SSS_SINGLE_SELA**B**C**D**E**40.If the inside diameter of a cylindrical garden hose is 1 inch, whatis the length, in inches, of a straight hose that can hold a maximum of 1 gallon of water? (1 gallon = 231 cubic inches)SSS_SINGLE_SELA231πB231/πC924D924πE924/πSECTION 341.It is assumed that scientists will avoid making ---- claims about the results of their experiments because of the likelihood that they will be exposed when other researchers cannot ---- their findings.SSS_SINGLE_SELAhypothetical.. evaluateBfraudulent.. duplicateCverifiable.. contradictDradical.. contestEextravagant.. dispute42.As long as the nuclear family is ---- a larger kinship group through contiguous residence on undivided land, the pressure to ---- and thus to get along with relatives is strong.SSS_SINGLE_SELAnurtured among.. abstainBexcluded from.. compromiseCembedded in .. shareDscattered throughout.. rejectEaccepted by .. lead43.In contrast to the substantial muscular activity required for inhalation, exhalation is usually a ---- process.SSS_SINGLE_SELAslowBpassiveCpreciseDcomplexEconscious44.The documentary film about high school life was so realistic and ---- that feelings of nostalgia flooded over the college-age audience.SSS_SINGLE_SELAlogicalBpitifulCevocativeDcriticalEclinical45.Although Georgia O'Keeffe is best known for her affinity with the desert landscape, her paintings of urban subjects ---- her longtime residency in New York City.SSS_SINGLE_SELAcondemnBobfuscateCattest toDconflict withEcontend with46.Even though the survey was designated as an inter- disciplinary course, it involved no real ---- of subject matter.SSS_SINGLE_SELAencapsulationBorganizationCsynthesisDdiscussionEverification47.The failure of many psychotherapists to ---- the results of pioneering research could be due in part to the specialized nature of such findings: even ---- findings may not be useful.SSS_SINGLE_SELAunderstand.. bafflingBenvision.. accessibleCutilize.. momentousDreproduce.. duplicatedEaffirm.. controversial48.EARPLUG: NOISE::SSS_SINGLE_SELAsaw: woodBdetonation: explosionCclothes: coveringDliquid: flaskEshield: impact49.REVISE: MANUSCRIPT::SSS_SINGLE_SELAretouch: pictureBreplicate: experimentCrepair: hammerDreplace: bookErestore: masterpiece50.DAREDEVIL: AUDACITY::SSS_SINGLE_SELAmalcontent: dissatisfactionBperfectionist: patienceCcynic: indiscretionDmelancholic: bitternessEhedonist: ambition51.CALCIUM: MINERAL::SSS_SINGLE_SELAsugar: carbohydrateBsalt: solutionCenzyme: foodDmilk: cheeseEcalorie: diet52.DIRGE: GRIEF::SSS_SINGLE_SELAdiatribe: uneasinessBparody: crueltyCpaean: praiseDtestimonial: veracityEanthem: seriousness53.ABANDON: INHIBITION::SSS_SINGLE_SELAascendancy: effortBprickliness: sensationCsurrender: resignationDreversal: instigationEtran quillity: agitation 54.INAUGURATION: OFFICIAL::SSS_SINGLE_SELAinstruction: lecturerBelection: politicianCpilgrimage: devoteeDdispute: arbitratorEmatriculation: student 55.SCORN: REJECT::SSS_SINGLE_SELAadulate: flatterBconjecture: forecastCpledge: renegeDallege: declareEdisparage: ignore56.PROFLIGATE: SOLVENT::SSS_SINGLE_SELAmercurial: committedBcaustic: rationalCindecisive: confusedDcautious: uncertainEpractical: seemlyThere are seven questions below，As people age, their cells become less efficient and less able to replace **ponents. At the same time their tissues stiffen. For example, the lungs and the heart muscle expand less successfully, the blood vessels become increasingly rigid, and the ligaments and tendons tighten .Few investigators would attribute such diverse effects to a single cause. Nevertheless, researchers have discov- ered that a process long known to discolor and toughen foods may also contribute to age- related impairment of both cells and tissues. That process is nonenzymatic glycosylation, whereby glucose becomes attached to proteins without the aid of enzymes. When enzymes attach glucose to proteins (enzymatic glycosylation), they do so at a specific site on a specific protein molecule for a specific purpose. In contrast, the nonenzymatic process adds glucose haphazardly to any of several sites along any available peptide chain within a protein molecule.This nonenzymatic glycosylation )has been understood by food chemists for decades, although few biologists recognized until recently that the same steps could take place in the body. Nonenzymatic glycosylation begins when an aldehyde group (CHO) of glucose and an amino group (NH2) of a protein are attracted to each other. The **bine, forming what is called a Schiff base within the protein. **- bination is unstable and quickly rearranges itself into a stabler, but still reversible, substance known as an Amadori product.If a given protein persists in the body for months or years, some of its Amadori products slowly dehydrate and rearrange themselves yet again, into new glucose-derived structures. These **bine with various kinds of mol- ecules to form irreversible structures namedadvanced glycosylation end products (AGE's). Most AGE's are yellowish brown and fluorescent and have specific spectrographic properties. More important for the body, many are also able to cross-link adjacent proteins, particularly ones that give structure to tissues and organs. Although no one has yet satisfactorily described the origin of all such bridges between proteins, many investigators agree that extensive cross-linking of proteins probably contrib- utes to the stiffening and loss of elasticity characteristic of aging tissues.In an attempt to link this process with the develop- ment of cataracts (the browning and clouding of the lens of the eye as people age), researchers studied the effect of glucose on solutions of purified crystallin, the major protein in the lens of the eye. Glucose-free solutions remained clear, but solutions with glucose caused the proteins to form clusters, suggesting that the molecules had become cross-linked. The clusters diffracted light, making the solution opaque. The researchers also discovered that the pigmented cross-links in human cataracts have the brownish color and fluorescence characteristic of AGE's. These data suggest that nonenzymatic glycosylation of lens crystallins may contributeto cataract formation.SSS_SINGLE_SELWith which of the following statements concerning the stiffening of aging tissues would the author most likely agree?AIt is caused to a large degree by an increased rate of cell multiplication.BIt paradoxically both helps and hinders the longevity of proteins in the human bodyCIt can be counteracted in part by increased ingestion of glucose-free foods.DIt is exacerbated by increased enzymatic glycosylation.EIt probably involves the nonenzymatic glycosylation of proteins.SSS_SINGLE_SELAccording to the passage, which of the following statements is true of the process that discolors and toughens foods?AIt takes place more slowly than glycosylation in the human bodyBIt requires a higher ratio of glucose to protein than glycosylation requires in the human body.CIt does not require the aid of enzymes to attach glucose to protein.DIt proceeds more quickly when the food proteins have a molecular structure similar to that of crystallin proteins.EIts effectiveness depends heavily on the amount of environmental moistureSSS_SINGLE_SELAccording to the passage, which of the following is characteristic of enzymatic glycosylation of proteins?AAGE's are formed after a period of months or years.BProteins affected by the process are made unstable.CGlucose attachment impairs and stiffens tissues.DGlucose is attached to proteins for specific purposes.EAmino **bine with aldehyde groups to form Schiff bases.SSS_SINGLE_SELAccording to the passage, which of the following statements is true of Amadori products in proteins?AThey are more plentiful in a dehydrated environment.BThey are created through enzymatic glycosylation.CThey **posed entirely of glucose molecules.DThey are derived from Schiff bases.EThey are derived from AGE's.SSS_SINGLE_SELWhich of the following best describes the function of the third paragraph of the passage (lines 19-29)?AIt offers evidence that contradicts the findings described in thefirst two paragraphsBIt presents a specific example of the process discussed in the first two paragraphsCIt explains a problem that the researchers mentioned in the second paragraph have yet to solve.DIt evaluates the research discoveries described in the previous paragraph.EIt begins a detailed description of the process introduced in the previous two paragraphs.SSS_SINGLE_SELThe passage suggests that which of the following would be LEAST important in determining whether nonenzymatic glycosylation is likely to have taken place in the proteins of a particular tissue?AThe likelihood that the tissue has been exposed to free glucoseBThe color and spectrographic properties of structures within the tissueCThe amount of time that the proteins in the tissue have persisted in the bodyDThe number of amino groups within the proteins in the tissueEThe degree of elasticity that the tissue exhibitsSSS_SINGLE_SELIf the hypothesis stated in lines 56-58 is true, it can be inferred that the crystallin proteins in the lenses of peopleAhave increased elasticityB。

Inverting Sampled Traffic

Network traﬃc measurement is essential for traﬃc engineering (e.g. link upgrades or traﬃc re-routing) and traﬃc accounting (e.g. usage based pricing). Routers oﬀer tools such as Cisco’s Netﬂow [1] or Inmon’s sFlow [2] that give information about the ﬂows of packets that traverse them. However the generation of detailed traﬃc statistics does not scale well with link speed. This is why packet sampling techniques are increasingly being used in routers [3] to export the statistics of a portion of the traﬃc only. The problem that then immediately arises is how to deal with such partial measurements. One can think of this as a two step process: ﬁrst recover the statistics of the full traﬃc from the retained sampled data through some inversion procedure, and second, take appropriate decisions based on the characteristics of the full traﬃc. While the second step is left to traﬃc engineers and managers, the ﬁrst corresponds to an interesting and important task which has only recently been attracting attention. Our aim is to provide theoretical results for the problem of recovering statistics beyond ﬁrst order from sampled traﬃc, and to see how successfully such results can be applied in practice with real traﬃc. We focus mainly on two statistics: the spectral density of the packet arrival process, and the distribution of the number of packets per ﬂow. This implies that we limit ourselves to portions of traﬃc that can be considered stationary. It also means that we do not try to recover sample values, such as actual number of packets in ﬂows on the measured link, but rather the distribution from which these samples were drawn. Traﬃc statistics commonly considered vary widely depending on user requirements and the capabilities of the collection mechanism. In this paper we ﬁrst place ourselves in a general framework whereby any raw statistics of the sampled data that we may need are considered to be available, as we focus primarily on the feasibility of the inversion problem. In some cases these statistics may not be readily available in today’s routers, or they may be close to impossible to provide because of real-time constraints. For example few routers can export packet level statistics such as sizes and timestamps of individual packets. In addition, currently high-end routers use switched instead of shared backplanes, and therefore not all packets are seen at any single point of the backplane [4]. Purpose built link monitoring boxes however, or dedicated passive measurement infrastructures supporting oﬄine studies based on sampled traﬃc, will be capable of much ﬁner grained storage and processing.

PhysRevA.55.2290

Nonperturbative decay of an atomic system in a cavityB.M.GarrawayOptics Section,The Blackett Laboratory,Imperial College,Prince Consort Road,London SW72BZ,United Kingdom͑Received24July1996͒Atoms can nowadays be placed in increasingly exotic environments such as microscopic cavities andmaterials with photonic band gaps.High-Q cavities can now easily result in a strong coupling between an atomand its environment where perturbation theory should no longer be appropriate.The purpose of this paper is todescribe the dynamics of a multilevel V-type atomic system͑including the case of a two-level system͒whichinteracts with a reservoir modeled by a generalized density of states.A theoretical construct,the pseudomode,is utilized to develop general methods for solution.Without using perturbation theory the equivalent masterequation is developed and the relationship between the master equation,the pseudomodes,and the generalizeddensity of states function is explored with examples.Utilizing a straightforward deﬁnition of the pseudomode,it is found that many functions for the density of states lead to problematic non-Lindblad master equations.Several examples are given,and it is shown how to convert the non-Lindblad master equations into a Lindbladform in these cases.The examples include a non-Lorentzian resonance and a simple model of a photonic bandgap.͓S1050-2947͑97͒04102-4͔PACS number͑s͒:42.50.Md,31.70.Hq,42.50.LcI.INTRODUCTIONThe decay of excited atomic systems has been of interestsince the time of the pioneering work of Weisskopf andWigner͓1͔.It has long been known that the decay of an atomis not an intrinsic property of that atom,but depends stronglyon the nature of the environment of that atom͓2͔.Recently,this has been of much interest͑see,for example,Refs.͓3–16͔͒in part because of the development of microlasers͑see,for example,͓17–19͔͒.The nonperturbative features ofthe interaction between an atom and its environment are es-pecially apparent if there is such a strong coupling that en-ergy leaving the atom can later return͓20,21͔.Changing theenvironment often means placing the atom in a cavity ofsome kind,but nowadays the atom may instead be an exci-ton,and the environment that of a quantum well.For brevitywe will refer to a cavity throughout most of this paper.The dynamics of the atom-environment interactions havelong been described by master equations derived from per-turbation theory͓22,23͔,which is an approach that workswell in two regimes:it works in the low-Q cavity,where thecavityﬁeld can be eliminated in favor of atomic dynamics,and it works in the high-Q regime where we consider theatomic system coupled to a damped cavity mode.A central purpose of this paper is to provide a generaldescription of the atom-environment interaction which doesnot rely on perturbation theory at all.Furthermore,one of thetasks is to compose the appropriate master equation to de-scribe the decay of the atomic system for a given type ofenvironment.In achieving this a particular difﬁculty isexposed—that a direct approach generates pathological mas-ter equations which do not have an acceptable physical in-terpretation.However,examples are given in this paper of aprocedure to correct this problem and return to an acceptableform for the master equation.The acceptable form is theLindblad form͓24͔d dt ␳ˆϭϪi͓H0,␳ˆ͔Ϫ͚lͩ12Lˆl†Lˆl␳ˆϪLˆl␳ˆLˆl†ϩ12␳ˆLˆl†Lˆlͪ,͑1͒where the Lindblad operators are the Lˆl,H0is the systemHamiltonian,and␳ˆis the density matrix.This form of mas-ter equation arises very naturally from time-dependent per-turbation theory applied to the interaction of the system witha zero-temperature heat bath.The Lindblad terms then origi-nate from the double commutator of the system-bath interac-tion evaluated to second order͓22,23͔.However,when thecoupling of the system to the environment is very strong,perturbation theory cannot be expected to yield the correctresult.In this paper we will see that for many decayingcavity-atom systems a form of the Lindblad master equation͑1͒is still appropriate.In Sec.II we will formulate the problem.Then in Sec.IIIwe will see how the time evolution can be solved in terms ofaﬁnite set of coupled differential equations,and how thoseequations can be formulated in terms of a nonperturbativemaster equation.Some straightforward examples are thengiven in Sec.IV.In Sec.V we identify some problems withsome of the master equations that would be generated by themethods of Sec.III.A procedure for correcting the defect isshown and then the more general master equation is found inSec.VI.Examples of this type of master equation are thengiven in Sec.VII.The Laplace transform method of solutionis summarized in Sec.VIII.Some concluding remarks arethen provided in Sec.IX.II.MATHEMATICAL DESCRIPTIONIn this paper we consider multilevel V-type atomic sys-tems,including systems with only two levels,as illustrated inFig.1.Thus the atomic system comprises a single ground-state level,labeled0,coupled to a number of excited stateswhich have the labels i͑or j)for i(j)ϭ1,2,3,...and anenergy difference͑measured from the ground state͒of␻i.The labels i and j will be used for only the atomic system.The number of excited levels is not speciﬁed,but may be oneor more.The multilevel system is coupled to a bath of oscil-lators and the creation and annihilation operators for eachPHYSICAL REVIEW A MARCH1997VOLUME55,NUMBER3551050-2947/97/55͑3͒/2290͑14͒/$10.002290©1997The American Physical Societyoscillator are a ␭†and a ␭,where the oscillator,which has frequency ␻␭,is labeled here by the index ␭.Then,within the rotating wave approximation and with only dipole inter-actions,the Hamiltonian for the system can be written asH ϭ͚␭␻␭a ␭†a ␭ϩ͚i␻i ͉i ͘aa ͗i ͉ϩ͚i ,␭g ␭͑i ͒͑a ␭†͉0͘aa ͗i ͉ϩa ␭͉i ͘aa ͗0͉͒,͑2͒where g ␭(i )is the frequency-dependent coupling between the transition i Ϫ0and the mode labeled ␭.For speciﬁc cavity-atom geometries,these couplings will be taken to include all the necessary spatial factors.For convenience in later parts of this paper,the basis for the states is chosen so that thecouplings g ␭(i )are real.The sum over modes ␭is taken to include polarizations,and in the limit of a continuous distribution this sum can be converted into an integral by including the density of states ␳␭,͚␭→͵d ␻␭␳␭.͑3͒For the development in the next sections of this paper we will not have to assume any speciﬁc form for the density of states function,but ultimately the form plays an important role.To reﬂect this,we can extract the shape of the density of states function into a normalized density of states D (␻␭)such that␳␭͑g ␭͑i ͒͒2ϭ⍀i 22␲D ͑␻␭͒͑4͒so each transition couples to the same density of states func-tion,but with different strengths ⍀i .The function D (␻␭)is then a generalized density of states which contains the frequency-dependent elements of both the density of states and the couplings.In the continuous limit,and with ␻␭→␻,the normalization of D (␻)is given by͵Ϫϱϱd ␻D ͑␻͒ϭ2␲,͑5͒which is a normalization in terms of natural,rather than an-gular,frequency.This choice is simply for convenience.The extension of the integral to Ϫϱis very useful to the physical interpretation,though not essential.The main requirement is that the integral over the density of states and the frequency-dependent couplings should be a good approximation in the region of interest.This is true for optical cavities,though we note that for other physical systems it may not be true and we can then obtain ‘‘threshold’’effects ͓25͔.The strengths ⍀i are deﬁned from the weight of the density of states,⍀i 2ϭ͚␭͑g ␭͑i ͒͒2,͑6͒and we will deﬁne a total strength for all the transitions as⍀02ϭ͚i⍀i 2.͑7͒We may split the Hamiltonian Eq.͑2͒into two pieces comprising the interacting part and the noninteracting ͑bare ͒part so that H ϭH B ϩH I ,H B ϭ͚␭␻␭a ␭†a ␭ϩ͚i␻i ͉i ͘aa ͗i ͉,H I ϭ͚␭,ig ␭͑i ͒͑a ␭†͉0͘aa ͗i ͉ϩa ␭͉i ͘aa ͗0͉͒.͑8͒The interaction Hamiltonian H I will only connect certain combinations of atomic states and ﬁeld states.For a single excitation of the total system these states are␺i ϭ͉i ͘a ͉000......000͘,␺␭ϭ͉0͘a ͉000......010......000͘,͑9͒where the ket ͉000......000͘indicates the ﬁeld statewhere all the radiation modes are in a vacuum state,and the ket ͉000......010......000͘in Eq.͑9͒indicates a state of the radiation ﬁeld where all of the modes are in a vacuum state apart from mode ␭which is in the ﬁrst excited state.The unexcited state␺0ϭ͉0͘a ͉000......000͑͘10͒is not coupled to any otherstate.FIG.1.The type of multilevel atomic system considered in this paper.The ground state 0is coupled to the upper states 1,2,3,...by transitions with frequencies ␻1,␻2,␻3,....The examples in the text are given for a two-level system,when only levels 0and 1are present.552291NONPERTURBATIVE DECAY OF AN ATOMIC SYSTEM ...Now for the noninteracting part of the Hamiltonian we will trivially obtainH B␺iϭ␻i␺i,H B␺␭ϭ␻␭␺␭,͑11͒while for the interacting part of the HamiltonianH I␺iϭ͚␭g␭͑i͒␺␭,H I␺␭ϭ͚i g␭͑i͒␺i.͑12͒It is clear from these equations that we have a closed system of equations for the time evolution.We will now expand a general state vector of the system as⌿͑t͒ϭc0␺0ϩ͚i c i͑t͒␺iϩ͚␭c␭͑t͒␺␭͑13͒in terms of the states͑9͒and insert this into the Schro¨dinger equation i(d/dt)⌿ϭH⌿to obtain the following͑inﬁnite͒set of coupled equations:i ddtc iϭ␻i c iϩ͚␭g␭͑i͒c␭,id dt c␭ϭ␻␭c␭ϩ͚i g␭͑i͒c i.͑14͒The coefﬁcient c0is constant in time.It is convenient to move to an interaction representation by means of the fol-lowing time-dependent transformations:c˜i͑t͒ϭe i␻i t c i͑t͒,c˜␭͑t͒ϭe i␻␭t c␭͑t͒,͑15͒so that we obtain the following coupled equations:i ddtc˜iϭ͚␭g␭͑i͒eϪi⌬␭i t c˜␭,͑16͒iddtc˜␭ϭ͚i g␭͑i͒e i⌬␭i t c˜i,͑17͒with the detunings from the mode␭deﬁned by⌬␭iϭ␻␭Ϫ␻i.͑18͒Now we can eliminate the coefﬁcients c˜␭by integrating Eq.͑17͒͑in time͒and substituting the resulting expression for c˜␭into Eq.͑16͒.The integration of Eq.͑17͒yieldsc˜␭͑t͒ϭϪi͵0t dtЈ͚i g␭͑i͒e i⌬␭i tЈc˜i͑tЈ͒,͑19͒where the initial condition assumed isc˜␭͑0͒ϭc␭͑0͒ϭ0,͑20͒which simply means that there are no photons in the external bath͑or cavity͒.We thus obtain aﬁnite set of coupled integro-differential equationsddtc˜i͑t͒ϭϪ͵0t dtЈ͚j G˜i j͑t,tЈ͒c˜j͑tЈ͒,͑21͒where the functions G˜i j(t,tЈ)are deﬁned byG˜i j͑t,tЈ͒ϭ͚␭g␭͑i͒g␭͑j͒exp͓i͑⌬␭j tЈϪ⌬␭i t͔͒͑22͒for a pair of transitions i,j.In writing down Eq.͑21͒we have exchanged the order of summation over␭and integration over time.This then allows us to write down the expressions͑22͒which can be evaluated analytically for a speciﬁc ex-pression of the coupling given in Eq.͑4͒.If we transfer the equations͑21͒back into the original basis we obtainddtc i͑t͒ϭϪi␻i c i͑t͒Ϫ͵0t dtЈ͚j G i j͑tϪtЈ͒c j͑tЈ͒,͑23͒where the difference kernel G i j(tϪtЈ)isG i j͑tϪtЈ͒ϭexp͑Ϫi␻i tϩi␻j tЈ͒G˜i j͑t,tЈ͒ϭ͚␭g␭͑i͒g␭͑j͒exp͓Ϫi␻␭͑tϪtЈ͔͒.͑24͒Then when the sum over␭becomes a continuous integral we obtain the kernels as integrals,which can be regarded as Fourier transforms of D(␻),G i j͑tϪtЈ͒ϭ⍀i⍀j2͵Ϫϱϱd␻D͑␻͒eϪi␻͑tϪtЈ͒͑25͒ϭ⍀i⍀jͱ2␲D¯͑tϪtЈ͒.͑26͒In the following sections we will examine some of the ways we can solve the integrodifferential equations͑23͒for differ-ent forms of D(␻).III.METHOD OF POLESA.PseudomodesIt proves very useful to be able to calculate the integral ͑25͒from a contour in the complex␻plane.In this case the function D(␻)should be analytic and the poles of that func-tion will correspond to resonances.The contour is closed in the lower half plane,where the exponential part of Eq.͑25͒causes the integrand to vanish͓because tуtЈin Eq.͑21͔͒. There are functions D(␻)which cannot have contours closed in the lower half plane,and then other methods have to be used.An example of an alternative approach is given in Sec.VIII.So we take a contour in the lower half plane and we will assume that the contribution to the contour integral from the semicircle is negligible.Then we will haveG i j͑tϪtЈ͒ϭϪ⍀i⍀j2ͶC dzD͑z͒eϪiz͑tϪtЈ͒.͑27͒Now we will suppose that the function D(z)has poles in the lower half plane at zϭz1,z2,...,z l,....͑The index l will be reserved for the positions of poles hereafter.͒And we will denote the residues of D(z)at these poles by r l.Then by the theorem of residues,229255B.M.GARRAWAYG i j͑tϪtЈ͒ϭϪi⍀i⍀j͚l r l eϪiz l͑tϪtЈ͒.͑28͒We note that this is now the case of a separable kernel and we have excluded any possibility of interfering branch cuts in the lower half plane.However,we do not need to have only simple poles.With this result inserted into Eq.͑23͒we willﬁnd thati ddtc i͑t͒ϭ␻i c i͑t͒Ϫ͚l⍀i r l͚j⍀j eϪiz l t͵0t dtЈe iz l tЈc j͑tЈ͒.͑29͒On the basis of Eq.͑29͒we can now deﬁne aﬁctionalpseudomode amplitude as͓16͔b l͑t͒ϭϪi͚i⍀iͱϪir l eϪiz l t͵0t dtЈe iz l tЈc i͑tЈ͒.͑30͒This pseudomode amplitude is chosen to be associated with the pole at z l so that Eqs.͑23͒becomei ddtc i͑t͒ϭ␻i c i͑t͒ϩ͚l g il b l͑t͒,͑31͒i ddtb l͑t͒ϭz l b l͑t͒ϩ͚i g ilc i͑t͒,͑32͒where Eq.͑32͒follows from the differentiation of Eq.͑30͒. Note that we now have aﬁnite set of coupled differential equations instead of the inﬁnite set found in Eq.͑14͒.The coupling between the pseudomode l and the atomic level i isg ilϭ⍀iͱϪir l,͑33͒which is,in general,a complex quantity.Note that g il ap-pears in both Eq.͑31͒and Eq.͑32͒rather than g il and its complex conjugate.The ramiﬁcations of this will be dis-cussed further in Sec.V.To proceed we will assume here that the couplings g il are real.Indeed,we note that this is the case for Lorentzian resonances.In the general case the resi-dues r l all sum to i and have no net real part.This is because of the normalization͑5͒which means that G i j(0)ϭ⍀i⍀j, and thus from Eq.͑28͒we always have͚l͑Ϫir l͒ϭ1.͑34͒The case of a two-level system interacting with a simple Lorentzian resonance is considered further in Sec.IV A.If we now review the problem in hand we note that we have converted the original problem,which consisted of an inﬁnite set of ordinary differential equations͓Eq.͑14͔͒,into aﬁnite set of ordinary differential equations,Eqs.͑31͒and ͑32͒.These equations can now be solved by well known analytic,or numerical methods.The restriction on D(␻)is that it is analytic in the lower half plane,and contains only poles there.The number of coupled differential equations is the number of poles added to the number of upper atomic levels.If there are an inﬁnite number of poles,then we do again obtain an inﬁnite number of coupled differential equa-tions,though with discrete frequencies corresponding to the positions of the poles.B.Equivalent master equationWe have seen that if we know the positions and residues of the poles of D(z)we can compute the time evolution of the atomic system from the straightforward equations͑31͒and͑32͒.However,it is possible to gain insight into the atom-ﬁeld dynamics by examining the equations of motion of a specially constructed density matrix.This takes the form of a master equation.The equations are more complex,but they provide more convincing evidence that the amplitudes b l are connected to the amplitude of a mode.We start by constructing a state vector and a basis for a system comprising the pseudomode and the atom.The͑un-normalized͒state vector is͉␺˜͑t͒͘ϭc0͉0͘a͟l͉0͘lϩc1͑t͉͒1͘a͟l͉0͘lϩc2͑t͉͒2͘a͟l͉0͘lϩ•••ϩb1͑t͉͒0͘a͉1͘1͟l 1͉0͘lϩb2͑t͉͒0͘a͉1͘2͟l 2͉0͘lϩb3͑t͉͒0͘a͉1͘3͟l 3͉0͘l ϩ•••,͑35͒where͉i͘a are the basis states of the atomic system͓as in Eq.͑2͔͒and͉n l͘l͑where n lϭ0,1)are the newly introduced states for the pseudomode l.The fact that the state vector͉␺˜(t)͘is not normalized is emphasized by the tilde.We will refer to the set of states͉0͘a͉0͘1͉0͘2͉0͘3...,͉1͘a͉0͘1͉0͘2͉0͘3...,͉2͘a͉0͘1͉0͘2͉0͘3...,Ӈ͉0͘a͉1͘1͉0͘2͉0͘3...,͉0͘a͉0͘1͉1͘2͉0͘3...,͉0͘a͉0͘1͉0͘2͉1͘3...••͑36͓͒used in Eq.͑35͒above͔as the pseudomode basis.We should stress that this basis is a mathematical construction and,strictly,does not exist physically.The lowest energy,or vacuum,state will be denoted by the symbol͉0͘so that͉0͘ϭ͉0͘a͉0͘1͉0͘2͉0͘3 (37)By using the basis͑36͒we can deﬁne an effective non-Hermitian evolution operator which replicates the equations ͑31͒and͑32͒with the unnormalized state vector͑35͒:H effϭ͚l z l aˆl†aˆlϩ͚i␻i͉i͘aa͗i͉ϩ͚il g il͑aˆl†␴ˆϪ͑i͒ϩaˆl␴ˆϩ͑i͒͒,͑38͒552293NONPERTURBATIVE DECAY OF AN ATOMIC SYSTEM...where the atomic raising and lowering operators between levels0and i are␴ˆϩ(i)ϭ͉i͘a a͗0͉and␴ˆϪ(i)ϭ͉0͘a a͗i͉.We will also have(␴ˆz(i)ϩ1)/2ϭ͉i͘a a͗i͉.The operators aˆl and aˆl†are the annihilation and creation operators for excitations of the ﬁctional mode l.For example,aˆl͉1͘lϭ͉0͘l,and ͓aˆl†,aˆm͔ϭ␦lm.Then͉␺˜(t)͘satisﬁes the equationddt͉␺˜͑t͒͘ϭϪiH eff͉␺˜͑t͒͘.͑39͒The effective Hamiltonian H eff can be split into a Hermitian part and an anti-Hermitian part in the formH effϭH0Ϫi2͚lLˆl†Lˆl,͑40͒where we have the Hermitian HamiltonianH0ϭ͚l Re͑z l͒aˆl†aˆlϩ͚i␻i͉i͘aa͗i͉ϩ͚il g il͑aˆl†␴ˆϪ͑i͒ϩaˆl␴ˆϩ͑i͒͒,͑41͒and Lindblad operators involving the pseudomode,LˆlϭͱϪ2Im z l aˆl.͑42͒The Lindblad͑42͒requires that Im(z l)Ͻ0,i.e.,we closed the contour͑27͒in the lower half plane.We see now that because we consider the poles of D(z)in the lower half complex plane the Lindblads Lˆl have real coefﬁcients.The sign of the energy of the pseudomode l depends on whether the pole at z l is to the right or left of the imaginary axis.The particular form of splitting in Eqs.͑40͒–͑42͒depends on the coefﬁcients g il being real.The complications of complex g il are considered in Secs.V and VI.Thus we may determine the dynamics of the upper atomic energy levels from Eqs.͑31͒and͑32͒or the equivalent equa-tion͑39͒.However,to obtain the dynamics of the atomic ground-state population we need more than just these differ-ential equations because there are contributions from both the initial ground-state population and from each excited ﬁeld state͑which would have the atomic system in the ground state͒.Thus there cannot be a description in terms of a pure state.If we start from the fundamental equation͑13͒and denote the atomic ground-state population by⌸0,we have⌸0ϭ͉c0͉2ϩ͚␭͉c␭͉2͑43͒in terms of the original modes of the system.Now we obtain a differential equation for the population by differentiating and using Eq.͑17͒so thatddt⌸0ϭϪ͚i d dt͉c i͉2,͑44͒which simply expresses conservation of probability.But now we use the pseudomode equations͑31͒toﬁnd thatddt⌸0ϭ͚il͑ic i*g il b lϪic i g il*b l*͒͑45͒and we compare this to the total population growth of the pseudomodes from Eq.͑32͒,͚lddt͉b l͉2ϭ2͚l Im͑z l͉͒b l͉2ϩ͚il͑ic i*g il*b lϪic i g il b l*͒͑46͒so that͑in the case that g il is real͒ddt⌸0ϭ͚l d dt͉b l͉2Ϫ2͚l Im͑z l͉͒b l͉2ϭ͚l d dt͉b l͉2ϩ͚l͗␺˜͉Lˆl†Lˆl͉␺˜͘,͑47͒where the last line follows from Eqs.͑35͒and͑42͒.Clearly, in the pseudomode system,the rise in⌸0is not given by just the increase in the pseudomode population,because the pseudomodes are lossy and lose population.We will now proceed to a density matrix description of the system by combining the results of both Eqs.͑39͒and ͑47͒in the spirit of master equation unraveling͓26͔͑though the process performed here is master equation composition͒. We know that all the atomic coherences and populations ͑with the exception of the ground-state population͒are de-scribed by␳ˆn jϭ͉␺˜͗͘␺˜͉͑48͒from Eq.͑35͒.And from Eq.͑39͒we know that␳ˆn j obeys the differential equationddt␳ˆn jϭϪi͓H eff,␳ˆn j͔.͑49͒Then to complete the density matrix we must include an additional term to account for the behavior of the ground-state population which is described by Eq.͑47͒.Thus the additional term belongs to the pseudomode vacuum state and is of the form␳ˆjϭ⌸j͑t͉͒0͗͘0͉.͑50͒Then the total population of the pseudomode vacuum com-prises two pieces:the new component from␳ˆj,and a con-tribution from␳ˆn j,the time-independent͉c0͉2.Thus⌸vac͑t͒ϭ⌸j͑t͒ϩ͉c0͉2,͑51͒where⌸vac(t)is simply the population of the pseudomode vacuum.Now by analogy with Eq.͑43͒͑for the original system͒,the atomic ground-state population will be given by the sum of population of the pseudomode vacuum and the populations of all of the pseudomodes so that⌸0ϭ⌸vacϩ͚l͉b l͉2.͑52͒Then by considering Eq.͑47͒and Eq.͑51͒we have229455B.M.GARRAWAYddt⌸jϭ͚l͗␺˜͉Lˆl†Lˆl͉␺˜͘ϭ͚l͗0͉Lˆl͉␺˜͗͘␺˜͉Lˆl†͉0͘,͑53͒where the last line follows because the action of any of the Lindblads͓Eq.͑42͔͒is to project the pseudomode system ͓Eq.͑35͔͒onto the vacuum.Then by utilizing this result in Eq.͑50͒we can write a differential equation for␳ˆj in the formddt␳ˆjϭ͚l Lˆl␳ˆn j Lˆl†.͑54͒Now,we note thatLˆl␳ˆj Lˆl†ϭ0͑55͒and that͓H eff,␳ˆj͔ϭ0͑56͒so that we can easily combine our equations for␳ˆj and␳ˆn j into an equation for the complete density matrix,ddt␳ˆϭϪi͓H eff,␳ˆ͔ϩ͚l Lˆl␳ˆLˆl†,͑57͒where␳ˆϭ␳ˆn jϩ␳ˆj͑58͒forms the complete composed density matrix.If we substi-tute Eq.͑40͒for H eff we obtain a master equation which is in the exact form of Eq.͑1͒and thus the process of constructing a master equation for the system is complete.The solution of the master equation is given by Eq.͑58͒and is clearly in the form of a statistical mixture of the vacuum state and the state vector␺˜,␳ˆ͑t͒ϭ⌸j͑t͉͒0͗͘0͉ϩ͉␺˜͑t͒͗͘␺˜͑t͉͒.͑59͒We can then use Eqs.͑47͒,͑51͒,and͑52͒,and the initial conditions for the b l and⌸j͑all zero͒to determine⌸j(t) from the integral,⌸j͑t͒ϭϪ2͚l Im͑z l͒͵0t͉b l͑tЈ͉͒2dtЈ.͑60͒IV.APPLICATIONS TO SIMPLE SYSTEMSA.Master equation for a single pseudomodeAs a simple example of a master equation generated by the nonperturbative behavior of the atom-ﬁeld coupling we consider a two-level atom,and let it interact with a density of states function D(␻)which has a single pole in the lower half plane which is located atz1ϵ␻cϪi⌫/2.͑61͒Because there is only one pole it follows from the normal-ization property͑34͒that the single pseudomode coupling is simply the real quantityg11ϭ⍀0.͑62͒Now to proceed to a master equation we simply use Eqs.͑41͒,͑42͒,and͑1͒toﬁnd thatddt␳ˆϭϪi͓H0,␳ˆ͔Ϫ⌫2͑aˆ†aˆ␳ˆϪ2aˆ␳ˆaˆ†ϩ␳ˆaˆ†aˆ͒, H0ϭ␻0͑␴ˆzϩ1͒/2ϩ␻c aˆ†aˆϩ⍀0͑aˆ†␴ˆϪϩaˆ␴ˆϩ͒.͑63͒This master equation is the well known equation for the damped Jaynes-Cummings model͓27͔describing the quan-tum coupling of a two-level atom to a damped mode.How-ever,this master equation is usually derived using perturba-tion theory.The master equation is completely independent of the function D(␻),for a single simple pole and within the re-strictions described above͑i.e.,with no branch cuts and in-tegrable through the lower half plane contour͒.This result is strongly suggestive of the wide applicability of the damped Jaynes-Cummings model,Eq.͑63͒.The most straightforward example of a single pseudo-mode is given by the Lorentzian resonance,D͑␻͒ϭ⌫͑␻Ϫ␻c͒2ϩ͑⌫/2͒2.͑64͒The coupling of this type of resonance to three-͑and two-͒level systems has been considered in detail in Ref.͓16͔,but here we noteﬁrst that for a very narrow cavity resonance,⌫→0in Eq.͑61͒,we will be able to neglect the dissipative part of Eq.͑63͒and we then simply obtain the master equa-tion for a two-level system coupled to a single mode.Sec-ondly,in the case that the cavity resonance is very broad,and the coupling strength⍀0weak,it is well known that for the master equation͑63͒we can perform an adiabatic elimina-tion of theﬁeld variable͑for simplicity we consider the case of cavity-atom resonance where aˆϷϪ2i⍀0␴Ϫ/⌫).This is done in exactly the same way as the atomic variable is elimi-nated in the semiclassical theory of the laser͑see,e.g.,Ref.͓23͔͒.This then leads to the well known low-Q master equa-tion for the atomic density matrix alone:ddt␳ˆAϭϪi͓H,␳ˆA͔Ϫ␥2͑␴ˆϩ␴ˆϪ␳ˆAϪ2␴ˆϪ␳ˆA␴ˆϩϩ␳ˆA␴ˆϩ␴ˆϪ͒,͑65͒where Hϭ␻0(␴ˆzϩ1)/2and the spontaneous emission rate ␥is␥ϭ4⍀02/⌫0.͑66͒This is,of course,exactly the peturbative result we obtain by applying Fermi’s golden rule to the system͑2͒with g␭de-termined by Eqs.͑64͒and͑4͒.The dependence of␥on 1/⌫is exactly as expected from the Purcell formula where ␥(Q)ϰQ,with Qϭ␻0/⌫0͓2͔.We can also obtain the same limiting result from the pseudomode equations͑31͒and͑32͓͒16͔.In the case of the Lorentzian resonance͑64͒,and a resonant two-level system,Eqs.͑31͒and͑32͒take the form552295NONPERTURBATIVE DECAY OF AN ATOMIC SYSTEM...i ddtc1͑t͒ϭ␻0c1͑t͒ϩ⍀0b1͑t͒,͑67͒i ddtb1͑t͒ϭ͑␻0Ϫi⌫/2͒b1͑t͒ϩ⍀0c1͑t͒,͑68͒where the only time-dependent variables are c1and b1.For the low-Q cavity,Eq.͑68͒yields b1(t)ϷϪ2i⍀0c1(t)/⌫which can be substituted back into Eq.͑67͒to yield the same low-Q,approximate,decay rate as in Eq.͑66͒.B.Example with two Lorentzian modesWe will now give a very simple example of an atomic system coupled to two pseudomodes.In this case we con-sider a density of states function which is simply a sum of two Lorentzian functions,D͑␻͒ϭW1⌫1͑␻Ϫ␻c͑1͒͒2ϩ͑⌫1/2͒2ϩW2⌫2͑␻Ϫ␻c͑2͒͒2ϩ͑⌫2/2͒2,͑69͒where the weights of the two Lorentzians are such that W1ϩW2ϭ1.The two cavity resonances are located at the different frequencies␻c(1)and␻c(2).This time the poles are located atz1ϭ␻c͑1͒Ϫi⌫1/2,z2ϭ␻c͑2͒Ϫi⌫2/2,͑70͒and the squares of the couplings(g il2ϭϪir l⍀i2)areg112ϭW1⍀02,g122ϭW2⍀02.Then if we follow the procedure of Eqs.͑41͒,͑42͒,and Eq.͑1͒we simply obtain the master equationd dt ␳ˆϭϪi͓H0,␳ˆ͔Ϫ⌫12͑aˆ1†aˆ1␳ˆϪ2aˆ1␳ˆaˆ1†ϩ␳ˆaˆ1†aˆ1͒Ϫ⌫22͑aˆ2†aˆ2␳ˆϪ2aˆ2␳ˆaˆ2†ϩ␳ˆaˆ2†aˆ2͒,͑71͒with the HamiltonianH0ϭ␻0͑␴ˆzϩ1͒/2ϩ␻c͑1͒aˆ1†aˆ1ϩ␻c͑2͒aˆ2†aˆ2ϩ⍀0ͱW1͑aˆ1†␴ˆϪϩaˆ1␴ˆϩ͒ϩ⍀0ͱW2aˆ2†␴ˆϪϩaˆ2␴ˆϩ͒.͑72͒We see that this time weﬁnd a two-mode damped Jaynes-Cummings model with the atomic system coupled to two decaying pseudomodes.This result generalizes straightfor-wardly to multiple Lorentzian resonances and multiple atomic levels of the form given in Fig.1.V.COUPLED PSEUDOMODESA.The non-Lindblad problems associated with complex g ilWhen we consider more complex functions than Lorent-zians for the generalized density of states,we can quickly run into serious difﬁculties because the couplings g il would no longer be real.͑Some examples will be given in Sec.VII.͒We can then no longer use the results given in Eqs.͑41͒,͑42͒,and͑1͒.This is a general problem which arises only ifwe consider more than one pseudomode,and when we have density of states functions which are more complex than Lorentzian functions.There are at least two types of difﬁculty.First,we can start with H eff in the form given in Eq.͑38͒and splitting g il into real and imaginary parts so thatg ilϭg il͑r͒ϩig il͑i͒͑73͒we can split H eff into Hermitian and anti-Hermitian parts as we have done in Eq.͑40͒.Then weﬁnd for the Hermitian pieceH0ϭ͚l Re͑z l͒aˆl†aˆlϩ͚i␻i͉i͘aa͗i͉ϩ͚il g il͑r͒͑aˆl†␴ˆϪ͑i͒ϩaˆl␴ˆϩ͑i͒͒,͑74͒and the anti-Hermitian piece leads to the requirement for the following sum over general Lindblad operators Lˆm:͚mLˆm†LˆmϵϪ2͚l Im͑z l͒aˆl†aˆlϪ2͚il g il͑i͒͑aˆl†␴ˆϪ͑i͒ϩaˆl␴ˆϩ͑i͒͒,͑75͒which cannot be satisﬁed.Theﬁrst sum on the right hand side is not a problem and can be treated using the Lindblads of Eq.͑42͒.The second sum cannot,apparently,be factored into the Lˆm†Lˆm form.For example,we can rewrite Eq.͑75͒in the form͚mLˆm†LˆmϵϪ2͚l Im͑z l͒aˆl†aˆlϪ2͚il g il͑i͒͑␣f aˆl†ϩ␣a␴ˆϩ͑i͒͒ϫ͑␣f aˆlϩ␣a␴ˆϪ͑i͒͒ϩ2͚il g il͑i͒␣f2aˆl†aˆlϩ2͚il g il͑i͒␣a2␴ˆϩ͑i͒␴ˆϪ͑i͒,͑76͒where␣f␣aϭ1.The right hand side of this equation is nearly in the required form,but in fact the equivalence can never be satisﬁed.The reason is that whatever choice is made over the signs of g il(i),some of the terms in the sums will have positive coefﬁcients and some will have negative coefﬁcients.The terms with negative coefﬁcients cannot sat-isfy the equivalence in Eq.͑76͒.The second difﬁculty arises over the identiﬁcation of the connection between the rate of change of the ground-state population,Eq.͑45͒,with the rate of change of the pseudo-mode populations in Eq.͑46͒.This is because the coupling g il appears with the wrong phase factors.However,we can still calculate the rate of change of⌸vac,which from Eq.͑52͒is given by the rate of change of the difference in the ground-state population and total population of the pseudo-modes.For the rate of change of the ground-state population229655B.M.GARRAWAY。

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However much we may abhor it, deception comes naturally to all living things. Birds do it by feigning injury to lead hungry predators away from nesting young. Spider crabs do it by disguise: adorning themselves with strips of kelp and other debris, they pretend to be something they are not--and so escape their enemies. Nature amply rewards successful deceivers by allowing them to survive long enough to mate and reproduce. So it may come as no surprise to learn that human beings--who, according to psychologist Gerald Jellison of the University of South California, are lied to about 200 times a day, roughly one untruth every five minutes--often deceive for exactly the same reasons: to save their own skins or to get something they can't get by other means.

TPO29-2Competition

CompetitionWhen several individuals of the same species or of several different species depend on the same limited resources, a situation may arise that is referred to as competition. The existence of competition has been long known to naturalists, its effects were described by Darwin in considerable detail. Competition among individuals of the same species (intraspecies competition), one of the major mechanisms of natural selection, is the concern of evolutionary biology. Competition among the individuals of different species (intraspecies competition) is a major concern of ecology. It is one of the factors controlling the size of competing populations, and in extreme cases it may lead to the extinction of one of the competing species. This was described by Darwin fro indigenous New Zealand species of animals and plants, which died out when competing species from Europe were introduced.No serious competition exists when the major needed resources is in superabundant supply, as in most cases of the coexistence of herbivores (plant eaters). Furthermore, most species do not depend entirely on a single resource. If the major resource for a species becomes scarce resource, the competing species usually switch to different alternative resources. Competition is usually most severe among close compete for the same resource, such as seed-eating rodents and ants. The effects of such competition are graphically demonstrated when all the animals or all the plants in an ecosystem come into competition, as happened 2 million years ago at the end of Pliocene, when North and South America become joined by the Isthmus of Panama. North and South America species migrating across the Isthmus now came into competition with each other. The result was the extermination of a large fraction of the South American mammals, which were apparently unable to withstand the competition from invading North American species-although added predation was also an important factor.To what extent competition determines the composition of a community and the density of particular species has been the source of considerable controversy. The problem is that competition ordinarily cannot be observed directly but must be inferred from the spread of increase of one species and the concurrent reduction or disappearance of another species. The Russian biologist G.F Gause performed numerous two-species experiments in the laboratory, in which one of the species became extinct when only a single kind of resource was available. On the basis of these experiments and of field observations, the so-called law of competitive exclusion was formulated, according to which no two species can occupy the same niche. Numerous seeming exceptions to this law have since been found, but they can usually be explained as cases in which the two species, even though competing for a major joint resource, did not really occupy exactly the same niche.Competition among species is of considerable evolutionary importance. The physical structure of species competing for resources in the same ecological nichetends to gradually evolve in ways that allow territories no longer overlap. The evolutionary effect of competition on species has been referred to as “species selection,” however, this description is potentially misleading. Only the individuals of a species are subject to the pressure of natural selection. The effect on the well-being and existence of a species is just the result of the effects of selection on all the individuals of the species. Thus species selection is actually a result of individual selection.Competition may occur for many needed resource. In the case of animals it is usually food; in the case of forest plants it may be light; in the case of substrate inhabitants it may be space, as in many shallow-water bottom-dwelling marine organisms. Indeed, it may be for any of the factors, physical as well as biotic, that are essential for organisms. Competition is usually the more severe the denser the population. Together with predation, it is the most important density-dependent factor in regulating population growth.Competition may occur for any needed resource. ■ In the case of animals it is usually food; in the case of forest plants it may be light; in the case of substrate inhabitants it may be space, as in many shallow-water bottom-dwelling marine organisms. ■ Indeed, it may be for any of the factors, physical as well as biotic, that are essential for organisms. ■ Competition is usually the more seve r the denser the population. ■ Together with predation, it is the most important density-dependent factor in regulating population growth.Roman pottery was transported not only in large quantities but also over substantial distances. Many Roman pots, in particular amphorae and the fine wares designed for use at tables, could travel hundreds of miles—all over the Mediterranean and also further afield. But maps that show the various spots where Roman pottery of a particular type has been found tell only part of the story. What is more significant than any geographical spread is the access that different levels of society had to good-quality products. In all but remotest regions of the empire, Roman pottery of a high standard is common at the sites of humble villages and isolated farmsteads.(844 words) ********************************************************************* [paragraph 1]When several individuals of the same species or of several different species depend on the same limited resources, a situation may arise that is referred to as competition. The existence of competition has been long known to naturalists, its effects were described by Darwin in considerable detail. Competition among individuals of the same species (intraspecies competition), one of the major mechanisms of natural selection, is the concern of evolutionary biology. Competition among the individuals of different species (intraspecies competition) is a major concern of ecology. It is one of the factors controlling the size of competing populations, and in extreme cases it may lead to the extinction of one of the competing species. This was described by Darwin fro indigenous New Zealandspecies of animals and plants, which died out when competing species from Europe were introduced.Q1 The phrase “mechanisms of natural selection” in the passage is closest in meaning toA.types of natural selection.B.dangers of natural selectionC.Problems natural selection solvesD.ways natural selection works.Q2 According to paragraph 1, what is one effect of competition among individuals of different species?A.It results in the eventual elimination of the resources for which they arecompetingB.It leads to competition among individuals of the same speciesC.It encourages new species to immigrate to an areaD.It controls the number of individuals in the competing populationsQ3 The word “indigenous” in the passage is closest in meaning to:A.NativeB.rareC.MostD.NumerousQ4 In paragraph 1, why does the author mention what happened in New Zealand?A.To indicate that Darwin understood the importance of competitionB.To illustrate that competition can lead to the extinction of speciesC.To identify where the idea of competition among species first aroseD.To argue against the idea that the process of selection is a natural occurrence [paragraph 2]No serious competition exists when the major needed resources is in superabundant supply, as in most cases of the coexistence of herbivores (plant eaters). Furthermore, most species do not depend entirely on a single resource. If the major resource for a species becomes scarce resource, the competing species usually switch to different alternative resources. Competition is usually most severe among close compete for the same resource, such as seed-eating rodents and ants. The effects of such competition are graphically demonstrated when all the animals or all the plants in an ecosystem come into competition, as happened 2 million years ago at the end of Pliocene, when North and South America become joined by the Isthmus of Panama. North and South America species migrating across the Isthmus now came into competition with each other. The result was the extermination of a large fraction of the South American mammals, which were apparently unable to withstand the competition from invading North American species-although added predation was also an important factor.Q5 According to paragraph 2, competition is not usually a significant factor among the coexisting species whenA.One of the species has only recently moved into the territory of the otherB.The species are closely related to each otherC.The population of one species is much larger than that of the otherD.Both of the species are herbivoresQ6 The word “graphically” in the passage is closest in meaning toA.VividlyB.FrequentlyC.BroadlyD.TypicallyQ7 In the paragraph 2, why does the author talk about what happened as a result of North and South America becoming joined at the Isthmus of Panama> A.To make the point that predation can have as much effect on species survival ascompetition does.B.To show how the ability to switch to an alternative resource can give species acompetitive advantage.C.To account for the current species composition of North and South America.D.To provide an example of the serious effects of competition between unrelatedspecies.[Paragraph 3]To what extent competition determines the composition of a community and the density of particular species has been the source of considerable controversy. The problem is that competition ordinarily cannot be observed directly but must be inferred from the spread of increase of one species and the concurrent reduction or disappearance of another species. The Russian biologist G.F Gause performed numerous two-species experiments in the laboratory, in which one of the species became extinct when only a single kind of resource was available. On the basis of these experiments and of field observations, the so-called law of competitive exclusion was formulated, according to which no two species can occupy the same niche. Numerous seeming exceptions to this law have since been found, but they can usually be explained as cases in which the two species, even though competing for a major joint resource, did not really occupy exactly the same niche.Q8 Paragraph 3 supports the idea that Gause’s experiments were important because theyA.Provide a situation in which competition could be removed from the interactionbetween two species.B.Showed that previous ideas about the extent to which competition determines thecomposition of a community were completely mistakenC.Help establish that competition will remove all but one species from any givenecological niche.D.Offered evidence that competition between species is minimal when these is anoverabundance of a single food source.Q9 Which of the sentences below best expresses the essential information in the highlighted sentence in the passage? Incorrect choices change the meaning in important ways or leave out essential information.A.Apparent exceptions to this law usually involve cases in which two speciescompete for the same major resource but occupy slightly different niches.B.Although it may appear two species always have different niches, manyexceptions show that species compete with each other.C.Cases in which two species not only for a shared resource but also occupy similarniches are considered exceptions to this law.D.Cases in which the two species do not occupy the same niche yet still compete forthe same resource are believed to exceptions to this law.[paragraph 4]Competition among species is of considerable evolutionary importance. The physical structure of species competing for resources in the same ecological niche tends to gradually evolve in ways that allow territories no longer overlap. The evolutionary effect of competition on species has been referred to as “species selection,” however, this description is potentially misleading. Only the individuals of a species are subject to the pressure of natural selection. The effect on the well-being and existence of a species is just the result of the effects of selection on all the individuals of the species. Thus species selection is actually a result of individual selection.Q10 According to paragraph 4, how does competition affect evolution?A.It results in the evolution of physical structures that allow the species to competewith each other more effectivelyB.It results in the evolutionary extinction of all but one of the competing species.C.It results in the competing species evolving in such a way that they no longercompete for the same resources.D.It results in the competing species evolving to become so much like each otherthat the competition between them eventually of disappears.Q11 According to paragraph 4, “species selection” is a misleading term because itA.overemphasizes the role of selection pressures in species extinctionB.Suggests that selection pressures directly influence whole species.C.Does not make a distinction between species extinction and species evolutionD.Suggests that extinction always results whenever there is competition. [paragraph 5]Competition may occur for many needed resource. In the case of animals it is usually food; in the case of forest plants it may be light; in the case of substrate inhabitants it may be space, as in many shallow-water bottom-dwelling marine organisms. Indeed, it may be for any of the factors, physical as well as biotic, that are essential for organisms. Competition is usually the more severe the denser thepopulation. Together with predation, it is the most important density-dependent factor in regulating population growth.Q12 The word” regulating ” in the passage is closest in meaning toA.ControllingB.ExplainingC.ObservingD.Stopping[paragraph 6]Competition may occur for any needed resource. ■ In the case of animals it is usually food; in the case of forest plants it may be light; in the case of substrate inhabitants it may be space, as in many shallow-water bottom-dwelling marine organisms. ■ Ind eed, it may be for any of the factors, physical as well as biotic, that are essential for organisms. ■ Competition is usually the more sever the denser the population. ■ Together with predation, it is the most important density-dependent factor in regulating population growth.Q13 Look at the four squares【■】that indicate where the following sentence could be added to the passage.That is, as the density of a population increases, competition has a greater impact and leads to greater mortality.Q14 Directions: An introductory sentence for a brief summary of the passage is provided below. Complete the summary by selecting the THREE answer choices that express the most important ideas in the passage. Some sentences do not belong in the summary because they express ideas that are not presented in the passage or are minor ideas in the passage. This question is worth 2 points.When necessary resources are limited, competition can occur among individuals of the same species or of different species.A. Competition can eliminate a species , but since most species do not depend on a single resource, competition is often reduced by switching to alternative resources.B. Competition between individuals of the same species is usually for food whereas competition between species is usually for habitat.C. Investigation of the ecological role of competition is difficult because ordinary the competition cannot be observed directly and must be inferred from its presumed effects.D. Experiments and field observations have established that competition between species is strong enough to prevent two species form occupying the same ecological niche.E. Competition between a pair of species tends to lessen over time because the species tend to evolve to occupy different ecological niches and rangesF. Competition is usually strongest when the density of the competing populations is the same.Competition当同一种族或是不同种族的多个个体都依赖于同一种有限的资源生活时，就会有种被称作竞争的情况出现。