A CONNECTION BETWEEN ORDINARY PARTITIONS AND TILINGS WITH DOMINOES AND SQUARES

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高二英语哲学讨论单选题30题

高二英语哲学讨论单选题30题1. In the philosophical debate, the term "metaphysics" refers to the study of _____.A. the nature of realityB. human behaviorC. social systemsD. language structure答案：A。

“metaphysics”意为形而上学，主要研究现实的本质。

选项B“human behavior”指人类行为；选项C“social systems”指社会系统；选项D“language structure”指语言结构。

在哲学讨论中，“metaphysics”通常指对现实本质的研究，故选A。

2. When discussing philosophy, the phrase "epistemology" is concerned with _____.A. moral valuesB. knowledge and beliefC. artistic expressionD. economic systems答案：B。

“epistemology”指认识论，主要涉及知识和信念。

选项A“moral values”是道德价值观；选项C“artistic expression”是艺术表达；选项D“economic systems”是经济系统。

哲学中“epistemology”侧重于知识和信念方面，所以选B。

3. In a philosophical context, "ontology" is the branch of philosophythat examines _____.A. beauty and aestheticsB. the nature of beingC. political theoriesD. logical reasoning答案：B。

2.-第二章课后习题及答案

2.-第二章课后习题及答案LT第二章1. (Q2) For a communication session betweena pair of processes, which process is theclient and which is the server?Answer: The process which initiates the communication is the client; the process that waits to be contacted is the server. .2. (Q3) What is the difference between network architecture and application architecture?Answer: Network architecture refers to the organization of the communication process into layers (e.g., the five-layer Internet architecture). Application architecture, on the other hand, is designed by an application developer and dictates the broad structure of the application (e.g., client-server or P2P)3. (Q4) What information is used by a processrunning on one host to identify a process running on another host?Answer: The IP address of the destination host and the port number of the destination socket.4. (Q6) Referring to Figure 2.4, we see thatnone of the application listed in Figure2.4 requires both no data loss and timing.Can you conceive of an application that requires no data loss and that is also highly time-sensitive?Answer: There are no good example of an application that requires no data loss and timing. If you know of one, send an e-mail to the authors5. (Q9) Why do HTTP, FTP, SMTP, and POP3 run on top of TCP rather than on UDP?Answer: The applications associated with those protocols require that all application data be received in the correct order and without gaps. TCP provides this service whereas UDP does not.6. (Q11) What is meant by a handshaking protocol?Answer: A protocol uses handshaking if the two communicating entities first exchange control packets before sending data to each other. SMTP uses handshaking at the application layer whereas HTTP does not.7. (Q13) Telnet into a Web server and senda multiline request message. Include inthe request message the If-modified-since:header line to force a response message with the 304 Not Modified status code.Answer: Issued the following command (in Windows command prompt) followed by the HTTP GET message to the “” web server:> telnet 80Since the index.html page in this web server was not modified since Fri, 18 May 2007 09:23:34 GMT, the following output was displayed when the above commands were issued on Sat, 19 May 2007. Note that the first 4 lines are the GET message and header lines input by the user and the next 4 lines (starting from HTTP/1.1 304 Not Modified) is the response from the web server.8. (Q14) Consider an e-commerce site thatwants to keep a purchase record for each of its customers. Describe how this can be done with cookies.Answer: When the user first visits the site, the site returns a cookie number.This cookie number is stored on the user’s host and is managed by the browser.During each subsequent visit (and purchase), the browser sends the cookie number back to the site. Thus the site knows when this user (more precisely, this browser) is visiting the site.9. (Q15) Suppose Alice, with a Web-basede-mail account (such as Hotmail or gmail), sends a message to Bob, who accesses his mail from his mail server using POP3.Discuss how the message gets from Alice’s host t o Bob’s host. Be sure to list theseries of application-layer protocols that are used to move the message between the two hosts.Answer: Message is sent from Alice’s host to her mail server over HTTP. Alice’s mail server then sends the message to Bob’s mail server over SMTP. Bob then transfers the message from his mail server to his host over POP3.10. (Q10) Recall that TCP can be enhancedwith SSL to provide process-to-process security services, including encryption.Does SSL operate at the transport layer or the application layer? If the application developer wants TCP to be enhanced with SSL, what does the developer have to do?Answer: SSL operates at the application layer. The SSL socket takes unencrypteddata from the application layer, encrypts it and then passes it to the TCP socket. If the application developer wants TCP to be enhanced with SSL, she has to include the SSL code in the application.11. (Q16) Print out the header of an e-mailmessage you have recently received. How many Received: header lines are there?Analyze each of the header lines in the message.Answer: from 65.54.246.203 (EHLO ) Received：(65.54.246.203) bywith SMTP; Sat, 19 May 200716:53:51 -0700from ([65.55.135.106]) by Received: with MicrosoftSMTPSVC(6.0.3790.2668); Sat, 19 May 2007 16:52:42 -0700Received: from mail pickup service by with MicrosoftSMTPSVC; Sat,19 May 200716:52:41 -0700Message-ID:<BAY130-F26D9E35BF59E0D18A819AFB9310@p hx.gbl>Received: from 65.55.135.123 byby130fd.bay130.hotmail.msn.com with HTTP; Sat, 19 May 200723:52:36 GMTFrom: "prithula dhungel"<prithuladhungel@>To: prithula@Bcc:Subject: Test mailDate: Sat, 19 May 2007 23:52:36 +0000Mime-Version:1.0Content-Type: Text/html; format=flowedReturn-Path: prithuladhungel@Figure: A sample mail message headerReceived: This header field indicates the sequence in which the SMTP servers send and receive the mail message including the respective timestamps.In this example there are 4 “Received:”header lines. This means the mail message passed through 5 different SMTP servers before being delivered to the receiver’s mail box. The last (forth) “Received:” header indicates the mail message flow from the SMTP server of the sender to the second SMTP server in the chain of servers. The sender’s SMTP server is at address 65.55.135.123 and the second SMTP server in the chain is . The third “Received:” header indicates the mail message flow from the second SMTPserver in the chain to the third server, and so on.Finally, the first “Received:” he ader indicates the flow of the mail message from the forth SMTP server to the last SMTP server (i.e. the receiver’s mail server) in the chain.Message-id: The message has been given this numberBAY130-F26D9E35BF59E0D18A819AFB9310@ph x.gbl(by. Message-id is a unique string assigned by the mail system when the message is first created.From: This indicates the email address of the sender of the mail. In the given example, the sender is prithuladhungel@To: This field indicates the email address of the receiver of the mail. In the example, the receiver is prithula@Subject: This gives the subject of the mail (if any specified by the sender). In the example, the subject specified by the sender is “Test mail”Date: The date and time when the mail was sent by the sender. In the example, the sender sent the mail on 19th May 2007, at time 23:52:36 GMT.Mime-version: MIME version used for the mail. In the example, it is 1.0.Content-type: The type of content in the body of the mail message. In the example, it is “text/html”.Return-Path: This specifies the emailaddress to which the mail will be sent if thereceiver of this mail wants to reply to the sender. This is also used by the sender’s mail server for bouncing back undeliverable mail messages of mailer-daemonerror messages. In the example, the return path is“prithuladhungel@”.12. (Q18) Is it possible for anorganization’s Web server and mail server to have exactly the same alias fora hostname (for example, )? Whatwould be the type for the RR that contains the hostname of the mail server?Answer: Yes an organization’s mail server and Web server can have the same alias for a host name. The MX record is used to map the mail server’s host name to its IP address.13. (Q19) Why is it said that FTP sends control information “out-of-band”?Answer: FTP uses two parallel TCP connections, one connection for sending control information (such as a request to transfer a file) and another connection for actually transferring the file. Because the control information is not sent over the same connection that the file is sent over, FTP sends control information out of band.14. (P6) Consider an HTTP client that wantsto retrieve a Web document at a given URL.The IP address of the HTTP server is initially unknown. What transport and application-layer protocols besides HTTP are needed in this scenario?Answer:Application layer protocols: DNS and HTTPTransport layer protocols: UDP for DNS;TCP for HTTP15. (P9) Consider Figure2.12, for whichthere is an institutional network connected to the Internet. Suppose that the average object size is 900,000 bits and that the average request rate from the institution’s browsers to the origin servers is 10 requests per second.Also suppose that the amount of time it takes from when the router on the Internet side of the access link forwards an HTTP request until it receives the response is two seconds on average (see Section 2.2.5). Model the total average response times as the sum of the averageaccess delay (that is, the delay from Internet router to institution router) and the average Internet delay. For the average access delay, use △/(1-△β), where △ is the average time required to send an object over the access link and β is the arrival rate of objects to the access link.a. Find the total average response time.b. Now suppose a cache is installed in theinstitutional LAN. Suppose the hit rate is 0.6. Find the total response time.Answer:a.T he time to transmit an object of sizeL over a link or rate R is L/R. The average time is the average size of the object divided by R:Δ= (900,000 bits)/(1,500,000 bits/sec) = 0.6 secThe traffic intensity on the link is (1.5requests/sec)(0.6 sec/request) = 0.9. Thus, the average access delay is (0.6 sec)/(1 - 0.9) = 6 seconds. The total average response time is therefore 6 sec + 2 sec = 8 sec.b.T he traffic intensity on the access linkis reduced by 40% since the 40% of the requests are satisfied within the institutional network. Thus the average access delay is (0.6 sec)/[1 –(0.6)(0.9)] = 1.2 seconds. The responsetime is approximately zero if the request is satisfied by the cache (which happens with probability 0.4); the average response time is 1.2 sec + 2 sec = 3.2 sec for cache misses (which happens 60% of the time). So the average response time is (0.4)(0 sec) +(0.6)(3.2 sec) = 1.92 seconds. Thus theaverage response time is reduced from 8 sec to 1.92 sec.10 100 1000200 Kbps 10240 51200 512000u 600 Kbps 10240 51200 512000 1Mbps 10240 51200 512000Peer to Peer:N10 100 1000200 Kbps 10240 25904.3 47559.33 U 600 Kbps 10240 13029.6 16899.641 Mbps 10240 10240 10240。

高三英语学术文章单选题50题

高三英语学术文章单选题50题1. In the scientific research paper, the term "hypothesis" is closest in meaning to _.A. theoryB. experimentC. conclusionD. assumption答案：D。

解析：“hypothesis”的意思是假设，假定。

“assumption”也表示假定，假设，在学术语境中，当提出一个假设来进行研究时，这两个词意思相近。

“theory”指理论，是经过大量研究和论证后的成果；“experiment”是实验，是验证假设或理论的手段；“conclusion”是结论，是研究之后得出的结果，所以选D。

2. The historical article mentioned "feudal system", which refers to _.A. democratic systemB. hierarchical social systemC. capitalist systemD. modern political system答案：B。

解析：“feudal system”是封建制度，它是一种等级森严的社会制度。

“democratic system”是民主制度；“capitalist system”是资本主义制度；“modern political system”是现代政治制度，与封建制度完全不同概念，所以选B。

3. In a literary review, "metaphor" is a figure of speech that _.A. gives human qualities to non - human thingsB. compares two different things without using "like" or "as"C. uses exaggeration to emphasize a pointD. repeats the same sound at the beginning of words答案：B。

Handbook of economic finance(MIT Stephen A.Ross)

Arbitrage,State Prices and Portfolio Theory Handbook of the Economics of FinancePhilip Dybvig Washington University in Saint Louis Stephen A.RossMITFirst draft:September,2001 This draft:September19,2002AbstractNeoclassicalﬁnancial models provide the foundation for our understanding of ﬁnance.This chapter introduces the main ideas of neoclassicalﬁnance in a single-period context that avoids the technical difﬁculties of continuous-time models,but preserves the principal intuitions of the subject.The starting point of the analysis is the formulation of standard portfolio choice problems.A central conceptual result is the Fundamental Theorem of Asset Pricing,which asserts the equivalence of absence of arbitrage,the existence of a positive linear pricing rule,and the existence of an optimum for some agent who prefers more to less.A related conceptual result is the Pricing Rule Representation Theorem, which asserts that a positive linear pricing rule can be represented as using state prices,risk-neutral expectations,or a state-price density.Different equivalent rep-resentations are useful in different contexts.Many applied results can be derived from theﬁrst-order conditions of the portfolio choice problem.Theﬁrst-order conditions say that marginal utility in each state is proportional to a consistent state-price density,where the constant of proportion-ality is determined by the budget constaint.If markets are complete,the implicit state-price density is uniquely determined by investment opportunities and must be the same as viewed by all agents,thus simplifying the choice problem.Solv-ingﬁrst-order conditions for quantities gives us optimal portfolio choice,solving them for prices gives us asset pricing models,solving them for utilities gives us preferences,and solving them for for probabilities gives us beliefs.We look at two popular asset pricing models,the CAPM and the APT,as well as complete-markets pricing.In the case of the CAPM,theﬁrst-order conditions link nicely to the traditional measures of portfolio performance.Further conceptual results include aggregation and mutual fund separation theory, both of which are useful for understanding equilibrium and asset pricing.The modern quantitative approach toﬁnance has its original roots in neoclassicaleconomics.Neoclassical economics studies an idealized world in which marketswork smoothly without impediments such as transaction costs,taxes,asymme-try of information,or indivisibilities.This chapter considers what we learn fromsingle-period neoclassical models inﬁnance.While dynamic models are becom-ing more and more common,single-period models contain a surprisingly largeamount of the intuition and intellectual content of modernﬁnance,and are alsocommonly used by investment practitioners for the construction of optimal port-folios and communication of investment results.Focusing on a single period isalso consistent with an important theme.While general equilibrium theory seeksgreat generality and abstraction,ﬁnance has work to be done and seeks speciﬁcmodels with strong assumptions and deﬁnite implications that can be tested andimplemented in practice.1Portfolio ProblemsIn our analysis,there are two points of time,0and1,with an interval of time inbetween during which nothing happens.At time zero,our champion(the agent)is making decisions that will affect the allocation of consumption between non-random consumption,c0,at time0,and random consumption cωacross statesω12Ωrevealed at time1.At time0and in each state at time1,there is a single consumption good,and therefore consumption at time0or in a state attime1is a real number.This abstraction of a single good is obviously not“true”in any literal sense,but this is not a problem,and indeed any useful theoreticalmodel is much simpler than reality.The abstraction does,however face us withthe question of how to interpret our simple model(in this case with a single good)in a practical context that is more complex(has multiple goods).In using a single-good model,there are two usual practices:either use nominal values and measureconsumption in dollars,or use real values and measure consumption in inﬂation-adjusted dollars.Depending on the context,one or the other can make the mostsense.In this article,we will normally think of the consumption units as beingthe numeraire,so that“cashﬂows”or“claims to consumption”have the samemeaning.Following the usual practice from general equilibrium theory of thinking of units2of consumption at various times and in different states of nature as different goods, a typical consumption vector is C c0c1cΩ,where the real number c0de-notes consumption of the single good at time zero,and the vector c c1cΩof real numbers c1cΩdenotes random consumption of the single good in each state1Ωat time1.If this were a typical exercise in general equilibrium theory,we would have a price vector for consumption across goods.For example,we might have the following choice problem,which is named after two great pioneers of general equilibrium theory,Kenneth Arrow and Gerard Debreu:Problem1Arrow-Debreu ProblemChoose consumptions C c0c1cΩtomaximize utility of consumption U C subject tothe budget constraintc0Ω∑ω1pωcωW(1)Here,U is the utility function that represents preferences,p is the price vector, and W is wealth,which might be replaced by the market value of an endowment. We are taking consumption at time0to be the numeraire,and pωis the price of the Arrow-Debreu security which is a claim to one unit of consumption at time1 in stateω.Theﬁrst-order condition for Problem1is the existence of a positive Lagrangian multiplierλ(the marginal utility of wealth)such that U0c0λ,and for allω1Ω,UωcωλpωThis is the usual result from neoclassical economics that the gradient of the util-ity function is proportional to prices.Specializing to the leading case inﬁnance of time-separable von Neumann-Morgenstern preferences,named after John von Neumann and Oscar Morgenstern,two great pioneers of utility theory,we have that U C v c0∑Ωω1πωu cω.We will take v and u to be differentiable, strictly increasing(more is preferred to less),and strictly concave(risk averse).3Here,πωis the probability of stateω.In this case,theﬁrst-order condition is the existence ofλsuch that(2)v c0λand for allω12n,(3)πωu cωλpωor equivalently(4)u cωλρωwhereρωpωπωis the state-price density(also called the stochastic discount factor or pricing kernel),which is a measure of priced relative scarcity in state of natureω.Therefore,the marginal utility of consumption in a state is pro-portional to the relative scarcity.There is a solution if the problem is feasible, prices and probabilities are positive,the von Neumann-Morgenstern utility func-tion is increasing and strictly concave,and there is satisﬁed the Inada condition lim c∞u c0.1There are different motivations of von Neumann-Morgenstern preferences in the literature and the probabilities may be objective or subjective. What is important for us that the von Neumann-Morgenstern utility function rep-resents preferences in the sense that expected utility is higher for more preferred consumption patterns.2Using von Neumann-Morganstern preferences has been popular in part because of axiomatic derivations of the theory(see,for example,Herstein and Milnor [1953]or Luce and Raiffa[1957],chapter2).There is also a large literature on alternatives and extensions to von Neumann-Morgenstern preferences.Forsingle-period models,see Knight[1921],Bewley[1988],Machina[1982],Blume, Brandenburger,and Dekel[1991],and Fishburn[1988].There is an even richer set of models in multiple periods,for example,time-separable von Neumann-Morgenstern(the traditional standard),habit formation(e.g.Duesenberry[1949], Pollak[1970],Abel[1990],Constantinides[1991],and Dybvig[1995]),local substitutability over time(Hindy and Huang[1992]),interpersonal dependence (Duesenberry[1949]and Abel[1990]),preference for resolution of uncertainty (Kreps and Porteus[1978]),time preference dependent on consumption(Bergman [1985]),and general recursive utility(Epstein and Zin[1989]).Recently,there have also been some attempts to revive the age-old idea of study-ingﬁnancial situations using psychological theories(like prospect theory,Kahne-man and Tversky[1979]).Unfortunately,these models do not translate well to ﬁnancial markets.For example,in prospect theory framing matters,that is,the observed phenomenon of an agent making different decisions when facing identi-cal decision problems described differently.However,this is an alien concept for ﬁnancial economists and when they proxy for it in models they substitute some-thing more familiar(for example,some history dependence as in Barberis,Huang, and Santos[2001]).Another problem with the psychological theories is that they tend to be isolated stories rather than a general speciﬁcation,and they are often hard to generalize.For example,prospect theory says that agents put extra weight on very unlikely outcomes,but it is not at all clear what this means in a model with a continuum of states.This literature also has problems with using ex post explanations(positive correlations of returns are underreaction and negative cor-relations are overreactions)and a lack of clarity of how much is going on that cannot be explained by traditional models(and much of it can).In actualﬁnancial markets,Arrow-Debreu securities do not trade directly,even if they can be constructed indirectly using a portfolio of securities.A security is characterized by its cashﬂows.This description would not be adequate for analysis of taxes,since different sources of cashﬂow might have very different tax treatment,but we are looking at models without taxes.For an asset like a common stock or a bond,the cashﬂow might be negative at time0,from payment of the price,and positive or zero in each state at time1,the positive amount coming from any repayment of principal,dividends,coupons,or proceeds from sale of the asset.For a futures contract,the cashﬂow would be0at time0,and the cashﬂow in different states at time1could be positive,negative,or zero, depending on news about the value of the underlying commodity.In general,we5think of the negative of the initial cashﬂow as the price of a security.We denote by P P1P N the vector of prices of the N securities1N,and we denote by X the payoff matrix.We have that P n is the price we pay for one unit of security n and Xωn is the payoff per unit of security n at time1in the single state of nature ω.With the choice of a portfolio of assets,our choice problem might becomeProblem2First Portfolio Choice ProblemChoose portfolio holdingsΘΘ1Θn and consumptions C c0cΩto maximize utility of consumption U C subject toportfolio payoffs c c1cωXΘandbudget constraint c0PΘW.Here,Θis the vector of portfolio weights.Time0consumption is the numeraire, and wealth W is now chosen in time0consumption units and the entire endow-ment is received at time0.In the budget constraint,the term PΘis the cost of the portfolio holding,which is the sum across securities n of the price P n times the number of shares or other unitΘn.The matrix product XΘsays that the consump-tion in stateωis cω∑n XωnΘn,i.e.the sum across securities n of the payoff Xωn of security n in stateω,times the number of shares or other unitsΘn of security n our champion is holding.Theﬁrst-order condition for Problem2is the existence of a vector of shadow prices p and a Lagrangian multiplierλsuch that(5)πωu cωλpωwhere(6)P pXTheﬁrst equation is the same as in the Arrow-Debreu model,with an implicit shadow price vector in place of the given Arrow-Debreu prices.The second equa-tion is a pricing equation that says the prices of all assets must be consistent with6the shadow prices of the states.For the Arrow-Debreu model itself,the state-space tableau X is I,the identity matrix,and the price vector P is p,the vector of Arrow-Debreu state prices.For the Arrow-Debreu model,the pricing equation determines the shadow prices as equal to the state prices.Even if the assets are not the Arrow-Debreu securities,Problem2may be essen-tially equivalent to the Arrow-Debreu model in Problem1.In economic terms, the important feature of the Arrow-Debreu problem is that all payoff patterns are spanned,i.e.,each potential payoff pattern can be generated at some price by some portolio of assets.Linear algebra tells us that all payoff patterns can be generated if the payoff matrix X has full row rank.If X has full row rank,p is determined(or over-determined)by(6).If p is uniquely determined by the pricing equation(and therefore also all Arrow-Debreu assets can be purchased as portfolios of assets in the economy),we say that markets are complete,and for all practical purposes we are in an Arrow-Debreu world.For the choice problem to have a solution for any agent who prefers more to less, we also need for the price of each payoff pattern to be unique(the“law of one price”)and positive,or else there would be arbitrage(i.e.,a“money pump”or a “free lunch”).If there is no arbitrage,then there is at least one vector of positive state prices p solving the pricing equation(6).There is an arbitrage if the vector of state prices is overdetermined or if all consistent vectors of state prices assign a negative or zero price to some state.The notion of absence of arbitrage is a central concept inﬁnance,and we develop its implications more fully in the section on preference-free results.So far,we have been stating portfolio problems in prices and quantities,as we would in general equilibrium theory.However,it is also common to describe assets in terms of rates of return,which are relative price changes(often expressed as percentages).The return to security n,which is the relative change in total value (including any dividends,splits,warrant issues,coupons,stock issues,and the like as well as change in the price).There is not an absolute standard of what is meant by return,in different contexts this can be the rate of rate of return,one plus the rate of return,or the difference between two rates of return.It is necessary to ﬁgure which is intended by asking or from ing the notation above,the rate of return in stateωis rωn=Xωn P n P n.3Often,consumption at the outsetis suppressed,and we specialize to von Neumann-Morgenstern expected utility. In this case,we have the following common form of portfolio problem. Problem3Portfolio Problem using ReturnsChoose portfolio proportionsθθ1θn and consumptions c c1cΩtomaximize expected utility of consumption∑Ωω1πθu cωsubject tothe consumption equation c Wθ1r and the budget constraintθ11.Here,ππ1πΩis a vector of state probabilities,u is the von Neumann-Morgenstern utility function,and1is a vector of1’s.The dimensionality of1is determined implicitly from the context,here the dimensionality is the number of assets.Theﬁrst-order condition for an optimum is the existence of shadow state price density vectorρand shadow marginal utility of wealthλsuch that(7)u cωλρωand(8)1E1rρThese equations say that the state-price density is consistent with the marginal valuation by the agent and with pricing in the market.As ourﬁnal typical problem,let us consider a mean-variance optimization.This optimization is predicated on the assumption that investors care only about mean and variance(typically preferring more mean and less variance),so we have a utility function V m v in mean m and variance v.For this problem,suppose there is a risk-free asset paying a return r(although the market-level implications of mean-variance analysis can also be derived in a general model without a riskyasset).In this case,portfolio proportions in the risky assets are unconstrained (need not sum to1)because the slack can be taken up by the risk-free asset.We denote byµthe vector of mean risky asset returns and byσthe covariance matrix of risky returns.Then our champion solves the following choice problem. Problem4Mean-variance optimizationChoose portfolio proportionsθθ1θn tomaximize the mean-variance utility function V rµr1θθΣθ.Theﬁrst-order condition for the problem is(9)µr1λΣθwhereλis twice the marginal rate of substitution V v m v V m m v,evaluated at m rµr1θand vθΣθ,whereθis the optimal choice of portfolio pro-portions.Theﬁrst-order condition(9)says that mean excess return for each asset is proportional to the marginal contribution of volatility to the agent’s optimal portfolio.We have seen a few of the typical types of portfolio problem.There are a lot of variations.The problem might be stated in terms of excess returns(rate of return less a risk-free rate)or total return(one plus the rate of return).Or,we might constrain portfolio holdings to be positive(no short sales)or we might require consumption to be nonnegative(limited liability).Many other variations adapt the basic portfolio problem to handle institutional features not present in a neoclassical formulation,such as transaction costs,bid-ask spreads,or taxes. These extensions are very interesting,but beyond the scope of what we are doing here,which is to explore the neoclassical foundations.2Absence of Arbitrage and Preference-free ResultsBefore considering speciﬁc solutions and applications,let us consider some gen-eral results that are useful for thinking about portfolio choice.These results are9preference-free in the sense that they do not depend on any speciﬁc assumptions about preferences but only depend on an assumption that agents prefer more to less.Central to this section is the notion of an arbitrage,which is a“money pump”or a“free lunch”.If there is arbitrage,linearity of the neoclassical problem im-plies that any candidate optimum can be dominated by adding the arbitrage.As a result,no agent who prefers more to less would have an optimum if there ex-ists arbitrage.Furthermore,this seemingly weak assumption is enough to obtain two useful theorems.The Fundamental Theorem of Asset Pricing says that the following are equivalent:absence of arbitrage,existence of a consistent positive linear pricing rule,and existence of an optimum for some hypothetical agent who prefers more to less.The Pricing Rule Representation Theorem gives different equivalent forms for the consistent positive linear pricing rule,using state prices, risk-neutral probabilites(martingale valuation),state-price density(or stochastic discount factor or pricing kernel),or an abstract positive linear operator.The re-sults in this section are from Cox and Ross[1975],Ross[1976c,1978b],and Dybvig and Ross[1987].The results have been formalized in continuous time by Harrison and Kreps[1979]and Harrison and Pliska[1981].Occasionally,the theorems in this section can be applied directly to obtain an in-teresting result.For example,linearity of the pricing rule is enough to derive put-call parity without constructing the arbitrage.More often,the results in this sec-tion help to answer conceptual questions.For example,an option pricing formula that is derived using absence of arbitrage is always consistent with equilibrium, as can be seen from the Fundamental Theorem.By the Fundamental Theorem, absence of arbitrage implies there is an optimum for some hypothetical agent who prefers more to less;we can therefore construct an equilibrium in the single-agent pure exchange economy in which this agent is endowed with the optimal holding. By construction the equilibrium in this economy will have the desired pricing,and therefore any no-arbitrage pricing result is consistent with some equilibrium.In this section,we will work in the context of Problem2.An arbitrage is a change in the portfolio that makes all agents who prefer more to less better off.We make all such agents better off if we increase consumption sometime,and in some state of nature,and we never decrease consumption.By combining the two constraints in Problem2,we can write the consumption C associated with any portfolio choice10Θusing the stacked matrix equationC WPXΘTheﬁrst row,W PΘ,is consumption at time0,which is wealth W less the cost of our portfolio.The remaining rows,XΘ,give the random consumption across states at time1.Now,when we move from the portfolio choiceΘto the portfolio choiceΘη, the initial wealth term cancels and the change in consumption can now be writtenas∆CPXηThis will be an arbitrage it∆C is never negative and is positive in at least one component,which we will write as4∆C0orPXη0Some authors describe taxonomies of different types of arbitrage,having perhaps a negative price today and zero payoff tomorrow,a zero price today and a non-negative but not identically zero payoff tomorrow,or a negative price today and a positive payoff tomorrow.These are all examples of arbitrages that are sub-sumed by our general formula.The important thing is that there is an increase in consumption in some state of nature at some point of time and there is never any decrease in consumption.Fundamental Theorem of Asset PricingTheorem1Fundamental Theorem of Asset Pricing The following conditions on prices P and payoffs X are equivalent:i Absence of arbitrage:ηP Xη0.ii Existence of a consistent positive linear pricing rule(positive state prices): p0P p X.iii Some agent with strictly increasing preferences U has an optimum in Prob-lem2.P ROOF We prove the equivalence by showing i ii,ii iii,and iii i.i ii:This is the most subtle part,and it follows from a separation theorem or the duality theorem from linear programming.From the deﬁnition of absence of arbitrage,we have that the setsS1PXηηℜnandS2xℜΩ1x0must be disjoint.Therefore,there is a separating hyperplane z such that z x0for all x S1and z x0for all x S2.(See...,theorem...)Normalizing so that the ﬁrst component(the shadow price of time zero consumption)is1,we will see that p deﬁned by1p z z0is the consistent linear pricing rule we seek.Constancy of zx for x S1implies that1p P X0,which is to say that P p X,i.e. p is a consistent linear pricing rule.Furthermore,z x positive for x S2implies z0and consequently p0,and p is indeed the desired consistent positive linear pricing rule.ii iii:This part is proven by construction.Let U C1p C,thenΘ0 solves Problem2.To see this,note that the objective function U C is constant and equal to W for allΘ:U C1p C1p WPXΘW P p XΘW12(The motivation this construction is observation that the existence of the consistent linear pricing rule with state prices p implies that all feasible consumptions satisfy 1p C W.)iii i:This part is obvious,since any candidate optimum is dominated by adding the arbitrage,and therefore there can be no arbitrage if there is an optimum. More formally,adding an arbitrage implies the change of consumption∆C0, which implies an increase in U C.Pricing Rule Representation TheoremDepending on the context,there are different useful ways of representing the pric-ing rule.For some abstract applications(like proving put-call parity),it is easiestto use a general abstract representation as a linear operator L c such that c0 L c0.For asset pricing applications,it is often useful to use either the thestate-price representation we used in the Fundamental Theorem,L c∑ωpωcω,or risk-neutral probabilities,L c1r1E cω1r1∑ωπωcω.The intuition behind the risk-neutral representation(or martingale representation5)is that the price is the expected discounted value computed using a shadow risk-free rate(equal to the actual risk-free rate if there is one)and artiﬁcial risk-neutral probabilitiesπthat assign positive probability to the same states as do the true probabilities.Risk-neutral pricing says that all investments are fair gambles once we have adjusted for time preference by discounting and for risk preference by adjusting the probabilities.Theﬁnal representation using the state-price density (or stochastic discount factor)ρto write L c Eρωcω∑ωπωρωcω.The state price density simpliﬁesﬁrst-order conditions of portfolio choice problems because the state-price density measures priced scarcity of consumption.The state-price density is also handy for continuous-state models in which individual states have zero state probabilities and state prices but there exists a well-deﬁned positive ratio of the two.Theorem2Pricing Rule Representation Theorem The consistent positive lin-ear pricing rule can be represented equivalently usingi an abstract linear functional L c that is positive:c0L c0ii positive state prices p0:L c∑Ωω1pωcωiii positive risk-neutral probabilitiesπ0summing to1with associated shadow risk-free rate r:L c1r1E cω1r1∑ωπωcωiv positive state-price densitiesρ0:L c Eρc∑ωπωρωcω.P ROOF i ii:This is the known form of a linear operator inℜΩ.ii iii:Noteﬁrst that the shadow risk-free rate must price the riskless asset c1:Ω∑ω1pω11r1E1which implies(since E11)that r1p1 1.Then,matching coefﬁcients inΩ∑ω1pωcω1r1∑ωπωcωwe have thatπp1p,which sums to1as required and inherits positivity from p.iii iv:Simply letρω1r1πω(which is the same as pωπω).iv i:immediate.time s of receiving subsequent cashﬂows c s1,c s2...c t is given by t∑τs1E sρτ1r s1r s11rτ(11)Note that unless the riskfree rate is nonrandom,we cannot take the discount fac-tors out of the expectation.6This is because of the way that the law of iterated expectations works.For example,consider the value V0at time0of the cashﬂow in time2.V01r11E0V1(12)1r11E01r21E1c21r11E01r21c2Now,1r11is outside the expectation(as could be1r s11in(11)),but 1r21cannot come outside the expectation unless it is nonrandom.7So,it is best to remember that when interest rates are stochastic,discounting for risk-neutral valuation should use the rolled-over spot rate,within the expectation.3Various Analyses:Arrow-Debreu WorldThe portfolio problem is the starting point of a lot of types of analysis inﬁnance. Here are some implications that can be drawn from portfolio problems(usually through theﬁrst-order conditions):optimal portfolio choice(asset allocation or stock selection)portfolio efﬁciencyaggregation and market-level implicationsasset pricing and performance measurementpayoff distribution pricingrecovery or estimation of preferencesinference of expectationsWe can think of many of these distinctions as a question of what we are solving for when we look at theﬁrst-order conditions.In optimal portfolio choice and its aggregation,we are solving for the portfolio choice given the preferences and be-liefs about returns.In asset pricing,we are computing the prices(or restrictions on expected returns)given preferences,beliefs about payoffs,and the optimal choice (which is itself often derived using an aggregation result).In recovery,we derive preferences from beliefs and idealized observations about portfolio choice,e.g.at all wealth levels.Estimation of preferences is similar,but works with noisy obser-vations of demand at aﬁnite set of data points and uses a restriction in the func-tional form or smoothing in the statistical procedure to identify preferences.And, inference of expectations derives probability beliefs from preferences,prices,and the(observed)optimal demand.In this section,we illustrate the various analyses in the case of an Arrow-Debreu world.Analysis of the complete-markets model has been developed by many people over a period of time.Some of the more important works include some of the origi-nal work on competitive equilibrium such as Arrow and Debreu[1954],Debreu17。

语言学辽宁慕课习题整理chapter1-7

语言学辽宁慕课习题整理chapter1-7Chapter 1 Invitations to linguistics1introduction to linguistics选择题1、Which of the following statements is NOT true?A Language consists of the systems of sounds and grammar.B Language is instrumental.C Language is social and conventional.D Language is a system of symbols.2、The scope of linguistic study may be generally divided into ______________.A interlinguistic study and extralinguistic studyB sociolinguistics and psycholinguisticsC descriptive linguistics and prescriptive linguisticsD phonetics and phonology3、Saussure made the distinction between _______________.A Langue and paroleB theoretical linguistics and applied linguisticsC comparative linguistics and historical linguisticsD competence and performance4、Chomsky made the distinction between _______________.A diachronic linguistics and synchronic linguisticsB Langue and paroleC competence and performanceD comparative linguistics and historical linguistics5、As modern linguistics aims to describe and analyze the language people actually use, and not to lay down rules for “correct” linguistic behavior, it is said to be ___________.A prescriptiveB descriptiveC sociolinguisticD psycholinguistic判断题6、Language consists of the systems of sounds and grammar.7、The actual production and comprehension of the speech by speakers of a language is called performance.8、English is an intonation language.9、The fact that children can speak before they can read or write shows that language is arbitrary.10、According to Chomsky, a language user’s underlying knowledge about the system of rules is called his linguistic competence.答案：AAACB X√√X√2design features of language选择题1、Which of the following is NOT a frequently discussed design feature of language?A DualityB ConventionC DisplacementD Arbitrariness.2、“I can refer to Confucius even though he died 2000 years ago.” This shows that language has the design feature of __________.A dualityB creativityC arbitrarinessD displacement3、The design feature of __________ refers to the property ofhaving two levels of structures, such that units of the primary level are composed of elements of the secondary level.A arbitrarinessB creativityC displacementD duality4、One of the properties of language is that a language user can understand and produce sentences he/she has never heard before. This property of language is called ________.A productivityB dualityC displacementD arbitrariness5、In broad terms, linguists agree to define language as a system of ____vocal symbols used for human communication.A arbitraryB conventionalC motivatedD dual答案：BDDAA3origins of language选择题1、There are some well-known theories about the origin of language, the natural response theory, also called .A the sing-song theoryB the pooh-pooh theoryC the Ding-Dong theoryD the yo-he-ho theory2、Ding-Dong theory is put forward by German scholar .A M. MULLerB HallidayC SaussureD Malinowski3、holds that language develops from primitive ritual songs of praise.A the yo-he-ho theoryB The sing-song theoryC the pooh-pooh theoryD the Ding-Dong theory4、holds that language originated from people’s imitations of animal cries and other sounds heard in nature.A The bow-wow theoryB the pooh-pooh theoryC the yo-he-ho theoryD the Ding-Dong theory判断题5、The bow-wow theory is a theory on the origin of language.6、Now linguists have known the specific origin of language.7、The yo-he-ho theory explains that language originated from the cries uttered during strain of work.答案：CABA √X√4functions of language选择题1、When people use language to express attitudes, feelings and emotions, people are using the ____________function of language.A creativeB phaticC emotiveD metalingual2、The social functions of language do NOT include_______________.A interrogative functionB phatic functionC metacognitive functionD informative function3、Which of the following is NOT a metafunction of language proposed by Halliday?A IdeationalB ConventionalC InterpersonalD Textual4、The social functions of language do NOT include_______________.A interrogative functionB informative functionC metacognitive functionD phatic function5、The ______ function refers to the fact that language can be used for establishing a favorable atmosphere or maintaining social contact rather than for exchanging information or ideas.A phaticB evocativeC directiveD performative判断题6、“Language operates by rules” is a fu ndamental view about language.7、When people use language to indulge in itself for its ownsake, people are using the creative function of language.8、According to Halliday’s theory of metafunctions of language, interpersonal function enacts social relationship.9、According to Halliday, a theory of metafunctions of language, that is , language has ideational, interpersonal and textual function.10、When people use language to indulge in itself for its own sake, people are using the poetic function of language.答案：CCBCA √X√√√Chapter 1 主观题1、名词解释：Diachronic linguisticsDiachronic linguistics is the study of a language through the course of its history.2、名词解释：Synchronic linguisticsA synchronic description takes a fixed instant (usually, but not necessarily, the present) as its point of observation.3、名词解释：PsycholinguisticsPsycholinguistics is the study of psychological aspects of language; it usually studies the psychological states and mental activity associated with the use of language. Most problems in psycholinguistics are more concrete, involving the study of language acquisition especially in children and linguistic performance such as producing and comprehending utterances or sentences among adults.4、名词解释：DualityBy Duality is meant the property of having two levels of structures, such that units of the primary level are composed of elements of the secondary level and each of the two levels has its own principles of organization. The property of duality only exists in such a system, namely, with both elements and units.Besides, the language is hierarchical.5、名词解释：DisplacementDisplacement means that human languages enable their users to symbolize objects, events and concepts which are not present (in time and space) at the moment of communication. Displacement benefits human beings by giving them the power to handle generalizations and abstractions. In a word, the intellectual benefits of displacement to us is that it makes it possible for us to talk and think in abstract terms.6、Do you think that onomatopoeia indicates a non-arbitrary relationship between form and meaning? Why or why not?No matter whether you say “Yes” or “No”, you cannot deny that onomatopoeia needsarbitrariness. Before we feel a word is onomatopoeic we should first know which sound the word imitates. In order to imitate the noise of flying mosquitoes, there are many choices like “murmurous” and “murderous”. They both bear more or less resemblance to the genuine natural sound, but “murmurous” is fortunately chosen to mean the noise while “murderous” is chose n to mean something quite different. They are arbitrary as signifiers.（参考答案）No, I don't think so. There exists the arbitrary relationship between the sound of a morpheme and its meaning. Also, in English, totally different words are used to describe the sound. In fact, arbitrariness and onomatopoeic effect may work at the same time. For example, Widdowson cites a line from Keats' Ode to a Nightingale to illustrate. The murmurous haunt of flies on summer eves. To test this, just think of using the similar sounding word murderous to substitute murmurous, and no connectionwhatsover will be established between the sounds and the little noises of the flying flies. "It's only when you know the meaning that you infer that the form is appropriate." （我的答案）7、Illustrate the origins of language you have known.The sing-song theory: it holds that language develops from primitive ritual songs of praise.The Ding-Dong theory: the natural response theory postulates that language began with vocal expressions being assigned to objects found in the environment.The pooh-pooh theory: the theory traces language back to interjections which expresses the speakers’ emotions.The yo-he-ho theory: it explains that language originated form the cries uttered during strain of work.The bow-wow theory: it holds that language originated from people’s imitations of animal cries and other sounds heard in nature.Ta-Ta theory: it believes that body movement preceded language. language began as an unconscious vocal imitation of these movements.8、Language is generally defined as a system of arbitrary vocal symbols used for human communication. Explain it in detail.Language is a means of verbal communication. It is instrumental in that communicating by speaking or writing is a purposeful act. It is social and conventional in that language is a social semiotic and communication can only take place effectively if all the users share a broad understanding of human interaction including such associated factors as nonverbal cues, motivation, and socio-cultural roles.Chapter 2 Phonetics5phonetics选择题1、Pair ___________ doesn’t form a minimal pair.A cat and actB tip and dipC gap and capD pat and pad2、The study of the production of speech sounds is closely connected with ____________.A articulatory phoneticsB auditory phoneticsC acoustic phoneticsD arbitrary phonetics3、The study of the physical properties of speech sounds is closely connected with ____________.A acoustic phoneticsB articulatory phoneticsC auditory phoneticsD arbitrary phonetics4、The study of the perception of speech sounds is closely connected with .A acoustic phoneticsB articulatory phoneticsC auditory phoneticsD arbitrary phonetics5、Pair ________is not in complementary distribution.A spot and potB stop and topC light and gladD school and cool判断题1、A single phoneme always represents a single morpheme.2、When the vocal folds are apart, the air can pass through easily and the sound produced is said to be voiced.3、Cave and shave forms a minimal pair.4、Phonetics studies how speech sounds are produced, transmitted, and perceived.5、The tongue is divided into five parts: the tip, the blade, the front, the back and the root.主观题1、Please describe what is phoneme.The speech sound segments that can distinguish or contrast words in sound and meaning are phonemes. (A phoneme is the minimal or smallest distinctive linguistic unit in a language.)2、Please describe what is complementary distribution.The different allophones of the same phoneme never occur in the same phonetic context. When two or more allophones of one phoneme never occur in the same linguistic environment they are said to be in complementary distribution.答案：AAACC ××√√√6English Consonan t选择题1、The classification and description of English consonants are based on ___________________.A narrow and broad transcriptionB the shape of vocal tractC the place and manner of articulationD the position of the tongue2、According to the manner of articulation, [m] is a ___________.A nasalB plosiveC bilabialD lateral3、In terms of the place of articulation, the following sounds [t], [n], [z] share the feature of ____________.A alveolarB velarC palatalD bilabial4、Which of the following sounds is a bilabial?A [ t ]B [ b ]C [ g ]D [ d ]5、Which of the following sounds is an alveolar?A [ d ]B [ m ]C [ g ]D [ b ]判断题1、The difference between vowels and consonants lies in the obstruction of the airstream.2、According to the manner of articulation, [s] is a fricative.3、English consonants can be classified in terms of place of articulation and the part of the tongue that is raised the highest.4、According to the manner of articulation, some of the types into which the consonants can be classified are stops, fricatives, bilabial and alveolar.5、/d/ is a voiced alveolar stop.主观题Please describe what are consonants.Consonants are sounds produced by constricting or obstructing the vocal tract at some place to divert, impede or completely shut off the flow of the air in the oral cavity.答案：CAABA √√××√7English Vowels1、The classification and description of English vowels are based on ___________________.A the position of the tongueB the shape of the lipsC the shape of vocal tractD all of the above2、The difference between vowels and consonants lies in ___________________.A the intonation of the soundsB the obstruction of the airstreamC the place and manner of articulationD the aspiration of the sounds3、A ____ vowel is one that is produced with the front part of the tongue maintaining the highest position.A centralB frontC middleD back3、can be differentiated by a number of factors: the position of tongue in the mouth, the openness of the mouth, the shape of the lips, and the length of the vowels.A Consonant soundsB Voicing soundsC Vowel soundsD devoicing sounds主观题1、Please describe what are vowels.V owels are sounds produced without obstruction, so no turbulence or a total stopping of the a ir can be perceived.2、What are the criteria that a linguist uses in classifying vowels?1. V owels may be distinguished as front, central and back in terms of the position of the tongue in the mouth.2. According to how wide our mouth is opened, we classify the vowels into four groups: close vowels, semiclose vowels, semi-open vowels, and open vowels.3. According to the shape of the lips, vowels are divided into rounded vowels and unrounded vowels.4. The English vowels can also be classified into long vowels and short vowels according to the length of the sound.答案：DBBCChapter 3 Phonology8phonology选择题1、Of all the speech organs, the _______ is/are the most flexible.A lipsB tongueC mouthD vocal cords2、A(n) ___________ is a unit that is of distinctive value. It is an abstract unit, a collection of distinctive phonetic features.A soundB phoneC phonemeD allophone3、The different phones which can represent a phoneme in different phonetic environments are called the ____ of that phoneme.A phonesB soundsC allophonesD phonemes4、Since /p/ and /b/ are phonetically similar, occur in the same environments and they can distinguish meaning, they are said to be ___________.A in phonemic contrastB the allophonesC in complementary distributionD minimal pair5、The assimilation rule assimilates one sound to another by “copying”a feature of a sequential phoneme, thus making the two phones ____________.A sameB identicalC exactly alikeD similar判断题1、Phonetics is different from phonology in that the latter studies the combinations of the sounds to convey meaning in communication.2、Phonology is concerned with how the sounds can be classified into different categories.3、The rules governing the phonological patterning arelanguage specific.4、Distinctive features of sound segments can be found running over a sequence of two or more phonemic segments.5、When two different forms are identical in every way except for one sound segment which occurs in the same place in the strings, the two words are said to form a phonemic contrast.主观题What are the major differences between phonology and phonetics?1．They differ in their approach and focus.2．Phonetics is of a general nature; it is interested in all the speech sounds used in all human languages: how they are produced, how they differ from each other, what phonetic features they p ossess, how they can be classified.3．Phonology, on the other hand, is interested in the system of sounds of a particular languag e; it aims to discover how speech sounds in a language form patterns and how these sounds are use d to convey meaning in linguistic communication.答案：BCCA D √×√√×9coarticulation选择题1、When such simultaneous or overlapping articulation are involved, we call the process .A coarticulationB aspirationC nasalizationD epenthesis2、In producing a nasal the soft palate is lowered to allow airflow through the .A nasal tractB vocal foldsC vocal cordsD larynx3、The fact that the vowel in lamb has some quality of the following nasal is a phenomenon we call .A devoicingB velarizationC nasalizationD aspiration4、In coarticulation, if the sound becomes more like the following sound, as in lamb, it is known as .A perseverative coarticulationB aspirationC nasalizationD anticipatory coarticulation5、When we use a simple set of symbols in our transcription, it is called a .A aspirationB narrow transcriptionC nasalizationD broad transcription判断题1、In English, the distinction between aspirated [p?] and unaspirated [p] is not phonemic.2、In the word peak, /p/ is unaspirated, phonetically transcribed as [p]3、Aspiration is a distinctive feature in English.4、In phonetic terms, phonemic transcriptions represent the “narrow” transcription.5、Speech is a continuous process, so the vocal organs donot move from one sound segment to thenext in a series of separate steps.主观题名词解释：CoarticulationCoarticulation：Simultaneous or overlapping articulations, as when the nasal quality of a nasal sound affects the preceding or following sound so that the latter becomes nasalized. If the affected sound becomes more like the following sound, it is known as anticipatory coarticulation; if the sound shows the influence of the preceding sound, it is perseverative coarticulation.答案：AACDD √×××√10suprasegmentals选择题1、Which of the following is NOT a Suprasegmental feature?A toneB intonationC syllableD stress2、In a syllable, a vowel often serves as ____________.A onsetB sequenceC peak or nucleusD coda3、The word “digitalization” consists of _______ syllables, and _________ morphemes.A six/ threeB five/ threeC six/ fourD five /five4、The word “digitalization” consists of _______ syllables, and _________ morphemes.A six/ threeB six/ fourC five /fiveD five/ three5、Distinctive features can be found running over a sequence of two or more phonemic segments. The phonemic features that occur above the level of the segments are called _______.A immediate constituentsB phonetic componentsC suprasegmental featuresD semantic features主观题1、名词解释：suprasegmental featuresThe features that occur above the level of the segments and can distinguish meaning are called suprasegmental features, which include syllable structure, stress, tone and intonation.2、名词解释： intonationWhen pitch, stress and sound length are tied to the sentence rather than the word in isolation,they are collectively known as intonation.3、Illustrate with examples how suprasegmental features can affect meaning.1. The location of stress in English distinguishes meaning, such as `import and im`port. The similar alternation of stress also occurs between a compound noun and a phrase consisting of the same elements. A phonological feature of the English compounds, is that the stress of the word always falls on the firstelement and the second element receives secondary stress, for example: `blackbird is a particular kind of bird, which is not necessarily black, but a black `bird is a bird that is black.2. The more important words such as nouns, verbs adjectives, adverbs, etc. are pronounced with greater force and made more prominent. But to give special emphasis to a certain notion, a word in sentence that is usually unstressed can be stressed to achieve different effect. Take the sentence “He is driving my car.” for example. To emphasize the fact that the car he is driving is not his, or yours, but mine, the speaker can stress the possessive pronoun my, which under normal circumstances is not stressed.3. English has four basic types of intonation, known as the four tones: When spoken in different tones, the same sequence of words may have different meanings. Generally speaking, the falling tone indicates that what is said is a straight-forward, matter-of-fact statement, the rising tone often makes a question of what is said, and the fall-rise tone often indicates that there is an implied message in what is said.答案：CCCBCChapter 4 Morphology11morphology选择题1.Derivational affixes are bound morphemes added to existing form to construct new words. English derivational affixes are divided into ________and _______.A prefixes, infixesB suffixes and infixesC prefixes, suffixesD morphemes, allomorphs2.In the word “unavailability”, ______________ is the root.A unB availableC availD ability3.In today’s grammar we normally say that English does not have a “future tense”. This is because in English ________________.A the future can be expressed in many waysB the future is not expressed by morphological changeC the future is expressed by modal verbsD the future belongs to the category of “aspect”4.The morpheme “vision” in the word “television” is a(n)____________.A inflectional morphemeB bound formC free morphemeD bound morpheme5.Which of the following words is made up of bound morphemes only?A televisioB happinessC ecologyD teacher6.Morpheme is the minimal unit of meanin7.–ing is an “inflectional suffix”8.Stems in English can be classified into derivational morphemes and inflectional morphemes.9.The bound morpheme in “apples” is inflectional morpheme.10.Although is an open-class word.主观题11..名词解释：RootRoot: Root refers to the base form of a word that cannot be further analyzed without loss of identity. That is to say, it is that part of the word that is left when all the affixes are removed. And roots can be further classified into free root morpheme and bound root morpheme.12.名词解释：AllomorphAllomorph: A morpheme, like a phoneme, is a linguistic abstraction, which must be realized as certain phonetic forms or variants in different phonetic environments. Each of the phonetic for ms or variants is a morph. A single morpheme may be phonetically realized as two or more morph s. The different morphs that represent or which are derived from one morpheme is called the allom orphs of that morpheme答案：CCBCC √√×√×12word formation选择题1._________can best describe the following group of words: table--tables, influenza--flu.A Inflection and derivationB Derivation and blendingC Inflection and abbreviationD Compound and derivation2.Which of the following ways of word-formation does not change the grammatical class of the stem?A inflectionB compoundC derivationD coinage3._________can best describe the word formation rules of thefollowing group of words: to burgle (from burglar), Eurodollar (from European + dollar).A Back-formation and blendingB Inflection and derivationC Derivation and blendingD Compound and derivation4._________can best describe the following group of words: table—tables, day + break—daybreak.A Inflection and derivationB Derivation and blending.C Compound and derivation.D Inflection and compound5.__________can be best describe the following group of words: advertisement—ad, bicycle—bike.A abbreviationB compoundC derivationD coinage6.“Invention” is a form of compounding, in which two words are blended by joining the initial par t of the first word and the final part of the second word, or by joining the initial parts of the two w ords.7.Blending is a relatively complex form of compounding.8.Derivation does not change the grammatical class of the stem.9.Derivation can be further divided into two sub-types: the derivational type and the compositional type.10.Inflection shows a relationship between roots and affixes.主观题11.What is the distinction between inflectional affixes andderivational affixes?1.When an affix, usually a suffix in English, indicates the tense of a verb, the plurality of a counta ble noun, or the comparative/superlative degree of an adjective, it is termed as inflectional morphe me. For example, '-ed' in 'worked', '-ing' in 'studying', '-s' in 'books' or 'er' in 'shorter' and 'est' in 'lo ngest' are all inflectional morphemes. Usually, the inflectional morpheme will not change the part of speech of a word to which it is attached.2.But a derivational morpheme usually changes the part of speech of a word to which it is attached . When we attach '-al' to the word 'nation' to form 'national', the part of speech of the word 'nation', i.e. a noun, has been changed into an adjective. As we can see, the concept of derivational morphe me is related to a kind of word formation called derivation.答案：CAADA ×√×√×Chapter 5 Syntax13concept of grammar选择题1.A sentence is considered ____ when it does not conform to the grammatical knowledge in the mi nd of native speakers.A wrongB ungrammaticalC rightD grammatical2. A __________ in the embedded clause refers to the introductory word that introduces the embedded clause.A particleB prepositionC subordinatorD coordinator3. Phrase structure rules have ____ properties.A recursiveB grammaticalC socialD functional4. Phrase structure rules allow us to better understand _____________.A All of the above.B how words and phrases form sentences.C what constitutes the grammaticality of strings of wordsD how people produce and recognize possible sentences5. The syntactic rules of any language are ____ in number.A smallB largeC finiteD infinite判断题6.Descriptive grammar refers to grammarian’s attempt to legislate what speakers’ grammatical rules should be, rather than what they are.7.Grammatical sentences are formed following a set of syntactic rules.8.Universally found in the grammars of all human languages, syntactic rules that comprise the system of internalized linguistic knowledge of a language speaker are known as linguistic competence9.The syntactic rules of any language are finite in number, but there is no limit to the number of sentences native speakers of that language are able to produce and comprehend.10.In a complex sentence, the two clauses hold unequal status, one subordinating the other.答案：DBDDD XX√√√主观题1. What are the basic components of a sentence?Normally, a sentence consists of at least a subject and its predicate which contains a finite verb or a verb phrase.2. What are the major types of sentences? Illustrate them with examples.①Traditionally, there are three major types of sentences. They are simple sentence, coordinate (compound) sentence, and complex sentence. A simple sentence consists of a single clause which contains a subject and a predicate and stands alone as its own sentence.For example: John reads extensively.②A coordinate sentence conta ins two clauses joined by a linking word that is calledcoordinat ing conjunction, such as “and”, “but”, “or”.For example: John is reading a linguistic book, and Mary is preparing for her history exam.A complex sentence contains two, or more, clauses, one of which is incorporated into the other. The two clauses in a complex sentence do not have equal status, one is subordinate to the other.For example: Before John gave her a lecture, Mary showed no interest in linguistics.14Cultural Approach选择题1. A __________ in the embedded clause refers to the introductory word that introduces the embedded clause.。

The_Wu_Xing_Theory_and_Homeostatic_Interaction_of_

Chinese Medicine, 2010, 1, 45-48doi:10.4236/cm.2010.12009 Published Online September 2010 (/journal/cm)The Wu Xing Theory and Homeostatic Interaction ofOrgansYevgeny V. Albegov, Dmitry V. Butenko, Lyudmila N. ButenkoCAD/CAE Systems Department; Volgograd State Technical University, Volgograd, RussiaE-mail: albegov05Received June 21, 2010; revised August 9, 2010; accepted August 13, 2010AbstractIn this paper the making of homeostatic models of the bioenergetic informational acupunctural human’s sys-tem of the “Pentacube” and the “Hexagon” according to the Wu Xing rules and energy shifts dynamics is considering. The making of the meridional homeostatic model of the bioenergetic informational acupunctural human’s system based on the existing knowledges about the human body meridians is considering. Prefer-ence to choice of the homeostatic functional models of the human body organs energies interaction is sub-stantiated. The meridional control submodel of homeostatic system is defined and constructed. The descrip-tion of control submodel, perspectives of application and development are represented.Keywords:System Stability, Homeostat, Homeostatic Model, “Pentacube”, “Hexagon”, Meridional Homeo-static Model, Control Submodel, “Merkabah”1. IntroductionThe fundamental issues of any system are the problems of stability. In this paper various types of stability and models, this stability is achieved with, are considering. As a prototype, we consider how to reach stability in complex systems, which are biological organisms.For biosystems the stability issues is the problem of homeostasis [1]. As an example of this system class sta-bility, we selected the human organism and examined it based on the five-membered cycle of the Wu Xing which reflects the interaction of human organs groups.In the process of studying of organs rhythm activity of the Yin-Yang cycles, we came to the conclusion that the interaction is homeostatic in nature. Then based on this conclusion we constructed the functional homeostatic “Pentacube” model. Next, on the basis of data available to us, the sixth group of organs of the “Fire' ” element was extracted. As a result we increased the order of the system stability transforming the “Pentacube” into the “Hexagon” model.The next step of the model development was the ex-traction of regulating channels of processes and their switching centers in the homeostatic relationships. They are represented by the meridians of the human body, encephalon and spinal cord.Based on the information about the levels of the system organization processes, we have attempted to identify the implicit control structure of the meridional homeostatic system. On the basis of representation of two-dimensional discrete set of stars we have concluded that the control submodel is the “Merkabah” system.The stellated tetrahedron is an invariant of the octahe-dron, and hence, it is quite a stable structure in different coordinate systems. The “Merkabah” submodel also pro- ves the correctness of the hexagonal homeostatic model and the meridional homeostatic model: a stable system of biological type can be controlled only by a stable internal structure with the same stability level. In systems of the pentagonal type the correct stable internal model is not observed.Thus, the stability of the human body functioning can be explained in terms of homeostatic nets.2. Making of the Homeostatic Models2.1. Making of the “Pentacube”According to the Wu Xing theory, the pentagons of human organs Yang and Yin have two circular cycles. One is clockwise and stimulating in nature, the other is anticlockwise and depressive [2]. The pentagons’ sti- mulating and depressive processes can be graphically represented as a pentagram (a five-pointed star). ThisY. V. ALBEGOV ET AL. 46may be due to the interaction between two poles of homeostats. Besides, if you combine the Yin and Yang organs relating to the same element according to the Wu Xing theory, you can get a number of Yin-Yang homeostats. The homeostatic nature of this interaction is confirmed by the fact that organs interactions in these homeostats are synchronized. For example, in homeo-stat of “Metal” element (lungs—large intestine) lungs become more active from 3 till 5 in the morning, and large intestine from 5 till 7 in the morning; in homeostat of “Water” element (kidneys—urinary bladder) urinary bladder becomes more active from 15 till 17 in the af-ternoon, and kidneys from 17 till 19 in the afternoon; in homeostat of “Wood” element (liver—gall bladder) gall bladder becomes more active from 23 till 1 in the night, and liver from 1 till 3 in the night; in the homeostat of “Fire” element (small intestine—heart), the heart be-comes more active from 11 till 13 in the afternoon, and small intestine from 13 till 15 in the afternoon; in the homeostat of “Earth” element (spleen/pancreas—stom-ach) stomach becomes more active from 7 till 9 in the morning, and spleen/pancreas from 9 till 11 in the morning. So, connecting all 5 known organs of Yin and Yang horizontally and vertically, we get the homeo-static functional “Pentacube”, in the vertexes of which there are human organs, and the edges are homeostatic connections between organs (Figure 1).The direction of arrows on the figures of homeostatic models indicate “generating” (the green one) and “over-coming” (the black one) processes accepted and thor-oughly described in the Wu Xing theory.In particular, alongside with “Pentacube” model one obtains a partial fractal model of the relationships hier-archy of homeostats. At the same time, the chain of “the conglutinated” homeostats represents the homeostat of higher organizational level. The new homeostat proc-esses information in the same manner as the component homeostats do but at qualitatively superior level [3].2.2. Making of the “Hexagon”First of all, the premises for the existence of sixth groupFigure 1. Homeostatic “Pentacube” of organs were made many hundreds years ago by an-cient Chinese scholars. In parallel with the system of five Zang-Fu, they created a system of circulation of the twelve meridians (Jing-Luo), the imaginary vessel, which circulates Qi energy, usually called “vital force”. After developing the system of meridians, the ancient Chinese scholars associated each meridian with a spe-cific internal organ. Meanwhile, onto the 12 meridians only 10 of the internal organs were assigned. So, the question if two more internal organs existed arose. For the additional Zang organ, the so-called “Master of the Heart” (Xin Zhu) also known as pericardium was se-lected. Onto the place of the sixth Fu organ, the “su-per-organ” was selected. It is known as San Jiao or triple heater. This organ of Three Jiaos is involved in meta-bolic processes of the organism. Currently, one can come across the fact that in addition to five-membered ring in the Wu Xing cycle, there is another equal “member”. The “Fire” element is dual and contains 4 elements (two Zang organs and two Fu organs) in that representation. Secondly, although the element of “Fire” fills the hu-man body with vital energy, the physical-chemical me-chanism of oxidation (“internal warming”) in the “Fire” of hear t—small intestine and in the “Fire” of pericar-dium—triple heater is different.Thirdly, we turn to the stability of systems built on polygons. Hexagon has a higher symmetry axis L6 against the pentagonal L5. Structures of solids, characterized by the fifth-order axis of symmetry of the prohibited in classical crystallography, occur rarely in nature and have a prefix “quasi-”. The very nature aspires to create ob-jects of different complexity levels in the hexagonal structures. This property is manifested both at the mac-rocosm and microcosm levels.Fourthly, the interaction rhythm (by analogy with the previously described homeostats) of organs such as peri-cardium—triple heater will also be homeostatic in nature: the pericardium becomes more active from 19 to 21 in the evening, and triple heater from21 till 23 in the evening. And fifth, in a model of five-membered cycle in pathological states of excess or lack of Qi energy in the organs, logical rhythmic of activity has a probabilistic nature, and points to an extreme degree of degeneration of the pentagonal system. In the model of six-membered cycle this uncertainty states is completely eliminated. The ideas described above enable us to draw a conclu-sion that the sixth group of organs exists: triple heater— pericardium, relating to the element “Fire' ”. The proc-esses of stimulating and suppression and, accordingly, the homeostatic interactions of organs in sexangles of Yin and Yang of the homeostatic functional “Hexagon” are the same as the processes between the organs in the pentagons of “Pentacube” (Figure 2).Y. V. ALBEGOV ET AL.473. Making of the Meridional Homeostatic ModelDue to the fact, there are regulators in the compound of homeostatic bioenergetic system, then we suggest, that as channels of regulating the standard meridians are used, which have projections on the surfaces of human body. It is known, that besides 12 standard meridians, related to the definite organs of the human body, there are other subsys-tems of meridians, performing the functions of additional direct and feedback connections (“miraculous” meridians, tendinomuscular meridians, unpaired meridians, collat-erals and secondary meridians) [4]. To switching centers, transmitting control action into the unpaired posterome-dian and unpaired anteromedian pretend, to our mind, spinal cord for Yin organs and encephalon for Yang or-gans. Chief-regulator likely to represent consis- tent be-ginning of nature, pacing the works of homeostats of or-gans. Since inner homeostatic interactions between the organs in pentagon of organs are described as a five- point star (a star as a planar geometric figure is meant) and are exhaustive, so in sexangle of organs the inner homeostatic interactions will be described as a six-point star/hexagram, representing in form the projection of stellated trigonal bipyramid on the plane, and will be also exhaustive [5,6]. Consequently the conclusion can be made about the pres-ence of homeostatic connections between the homeostat of “Wood” element (liver—gall bladder) and homeostat of “Fire' ” element (pericardium—triple heater), and be-tween the homeostat of the “Fire” element (small intes-tine—heart) and the homeostat of “Earth” element (spleen/pancreas—stomach) in homeostatic “Hexagon” of the human body organs (Figure 3).The given model of interaction of human organs ener-gies represents a hierarchy meridional and homeostatic net, where the meridional net represents a tracking sys-tem with feedback connection on the wholeness of ho-meostatic net system.The preference of choosing forms of homeostatic modelsFigure 2. Homeostatic “Hexagon”.is based on “gold” polygons and polyhedrons since the structures having in its basis correct n-angles have the maximal degree of stability, information, self- organizing and a harmonicity, whether there are creations of civili-zations (the Egyptian pyramids, protective forts, calendars of ancient civilizations, the theory of “civilizing hexagon”, models of location of cities, models of classification of smells) or the very nature (structure of che- mical sub-stances (fullerenes, frame structures), of a atomic nucleus, DNA chain, a crystal lattice and nanostructures) [7]. “The golden section” and corresponding “golden” properties of edges of functional homeostatic models are based on concepts of space of variability of natural processes and homeostat (elementary homeostatic system) [8].4. Making of the Meridional Submodel “Merkabah”Proceeding from judgment that organizers and regulators of local processes in the control space of the lower level of system of correct polygons are stars (connected and not connected), it is possible to make a conclusion, that in homeostatic “Hexagon” (a polyhedron – a prism) of the meridional homeostatic system of energies interaction of human body organs such organizer-regulator of processes is a star-shaped polyhedron—Merkabah or a stellated tetrahedron.Merkabah as a member of a row of Platonic solids (oc-tahedron is an invariant to stellated trigonal bipyramid) can model dualism. Merkabah as a process is the integral stage of biosystem genesis, namely biological-energy evolution of a cell: at the third stage of the ovicell division eight cells form a stellated tetrahedron and they are ab-solutely identical to each other [7]. Static cognitive model of interaction a stellated tetrahedron reflects the basicFigure 3. Meridional homeostatic model.Y. V. ALBEGOV ET AL. 48rules of constructing of meridional biosystem and the technology of forming homeostatic connections as com-plete units. Knots in “Merkabah” system represent a brain as the switching centers of a human body. 4 knots of Yang-tetrahedron are the encephalon, and 4 knots of Yin-tetrahedron – the spinal cord. And as the switching centers encephalon and the spinal cord will be absolutely identical to character of controlling.The key rule of constructing consists of the following: the meridian represents not unidirectional structural unit (brain – body), but a contour (brain – organ – brain), or a construction of the tunnel type with "two-way traffic". The technology of formation of homeostatic units is ob-viously displayed on a stellated trigonal bipyramid: ho-meostatic couple of Yin-Yang organs is formed owing to a crossing of meridians of the corresponding Yin-Yang organs. We can notice that such approach does not con-tradict, namely proves the correctness of meridional ho-meostatic model. Having connected homeostatic couples of Yin-Yang organs by a broken line in view of their timely activity, we receive a flat figure hexanema, de-termining a timely way [9] (Figure 4).Proceeding the meridians in view of timely activity both in a stellated tetrahedron as a whole, and in Yin and Yang tetrahedrons, and consequently also a process of meridional energy circulation (signals), on the given cognitive models occurs at first clockwise, then changes its direction on counter, i.e. on an endless helix, and on a plane looks like an infinity sign.Figure 4. Meridional submodel “Merkabah”.5. ConclusionsThe system approach to the construction of functional submodel allows to observe all scope of relations of “Merkabah” elements and connections between them and to approach to understanding of dialectic “plan” of the nature in organizing and controlling the processes, to see dynamics in statics. From the point of view of the applied component of the research, the given control submodel allows to understand the essence of pathological proc-esses in a human body, as infringement of energy flow (transferring signals) in meridional system with the fur-ther disbalance of rhythms of homeostats and displace ment of homeostatic energy from optimum areas to the risky areas. The same comprehension of occurrence of disease states in turn, on the basis of knowledge of tradi-tional Chinese medicine, will lead to forming and using of algorithms of updating of biosystem and taking out from pathological conditions by methods of not classical me- dicine, but phytotherapy or acupuncture. We’d like to note that “Merkabah” as conceptual model of relations of complicated compound elements, has all preconditions to deep system complication (by all aspects of the given concept), owing to the analysis and decomposition of components.6. References[1] A. G. Teslinov, “Development of Control Systems:Methodology and Conceptual Structures,” Globus, Moscow, 1998.[2]W. Xing, 2005. /wiki/Wu_Xing[3] A. M. Stepanov, “The Fundamental Principle of theMedical Homeostatics,” MODEC, Voronezh, 1994.[4]G. Luvsan, “Traditional and Modern Aspects of OrientalAcupuncture,” Nauka, Moscow, 1991.[5]The Star (geometry), 2008. /wiki/Звезда_(геометрия)[6]The Bipyramid, 2008./wiki/Бипирамида[7] A. Stahov, A. Sluchenkova and I. Scherbakov, “The DaVinci code and Fibonacci series,” Piter, SPb, 2007.[8]Yu. M. Gorsky, A. M. Stepanov and A. G. Teslinov,“Homeostatic: Harmony in Game of Contradiction,”Reprotsentr A1, Irkutsk 1998.[9]V. Eremeev, “A Diagram of Anthropocosmos,” ASM,Moskva, 1994.。

英文论文审稿意见英文版

is impossible to judge whether the algorithm is an improvement on previous work.
10、严谨度问题： MNQ is easier than the primitive PNQS, how to prove that.
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胡壮麟语言学教程笔记重点

《语言学教程》重难点学习提示第一章语言的性质语言的定义：语言的基本特征（任意性、二重性、多产性、移位、文化传递和互换性）；语言的功能（寒暄、指令、提供信息、询问、表达主观感情、唤起对方的感情和言语行为）；语言的起源（神授说，人造说，进化说）等。

第二章语言学语言学定义；研究语言的四大原则（穷尽、一致、简洁、客观）；语言学的基本概念（口语与书面语、共时与历时、语言与言学、语言能力与言行运用、语言潜势与语言行为）；普通语言学的分支（语音、音位、语法、句法、语义）；；语言学的应用（语言学与语言教学、语言与社会、语言与文字、语言与心理学、人类语言学、神经语言学、数理语言学、计算语言学）等。

第三章语音学发音器官的英文名称；英语辅音的发音部位和发音方法；语音学的定义；发音语音学；听觉语音学；声学语音学；元音及辅音的分类；严式与宽式标音等。

第四章音位学音位理论；最小对立体；自由变异；互补分布；语音的相似性；区别性特征；超语段音位学；音节；重音（词重音、句子重音、音高和语调）等。

第五章词法学词法的定义；曲折词与派生词；构词法（合成与派生）；词素的定义；词素变体；自由词素；粘着词素（词根，词缀和词干）等。

第六章词汇学词的定义；语法词与词汇词；变词与不变词；封闭词与开放词；词的辨认；习语与搭配。

第七章句法句法的定义；句法关系；结构；成分；直接成分分析法；并列结构与从属结构；句子成分；范畴（性，数，格）；一致；短语，从句，句子扩展等。

第八章语义学语义的定义；语义的有关理论；意义种类（传统、功能、语用）；里奇的语义分类；词汇意义关系（同义、反义、下义）；句子语义关系。

第九章语言变化语言的发展变化（词汇变化、语音书写文字、语法变化、语义变化）；第十章语言、思维与文化语言与文化的定义；萨丕尔-沃夫假说；语言与思维的关系；语言与文化的关系；中西文化的异同。

第十一章语用学语用学的定义；语义学与语用学的区别；语境与意义；言语行为理论（言内行为、言外行为和言后行为）；合作原则。

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INTEGERS:ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY7(2007),#A10A CONNECTION BETWEEN ORDINARY PARTITIONS AND TILINGSWITH DOMINOES AND SQUARESLouis W.KolitschDepartment of Mathematics and StatisticsUniversity of Tennessee at MartinMartin,TN38237,United Stateslkolitsc@Received:5/5/06,Revised:8/21/06,Accepted:2/8/07,Published:2/15/07AbstractIn this paper a way of representing an ordinary partition as a tiling with dominoes and squares is introduced.The generating functions associated with such tilings is developed and explained analytically and combinatorially.1.IntroductionThe results in this paper were inspired by a talk given by Arthur Benjamin at the South-eastern Section meeting of the MAA in2004and based on his new book with Jennifer Quinn [2].At this meeting Benjamin discussed tilings of a1×n rectangle with1×1squares and 1×2dominoes.The total number of such tilings of a1×n rectangle is the n th Fibonacci number and these tilings can be used to explain numerous identities involving the Fibonacci numbers.For n<5the values of p(n),the number of partitions of n,match the values of the Fibonacci sequence.The natural question that arises is“Can the partitions of n be explained in terms of tilings using squares and dominoes?.”The answer to this question is “yes”as theﬁrst theorem below explains.2.The Main TheoremBefore we state theﬁrst theorem,we introduce some notation.In a tiling,we will number the dominoes from left to right as d1,d2,...,d m.We will let s0be the number of squares preceding d1;s i for1≤i<m will be the numbers of squares between d i and d i+1;and s m will be the number of squares succeeding d m.Theorem1The number of partitions of n is the number of tilings of a1×n rectangle where the numbers of squares following successive dominoes form a nondecreasing sequence.That is,s1≤s2≤...≤s m.Theorem1follows by observing that(1)a tiling of the type described can be converted into the partition of n consisting of s0ones and the parts2+s i for1≤i≤m,and(2)aINTEGERS:ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY7(2007),#A102 partition n can be converted into a tiling of the type described by making the ones initial squares and converting each part k bigger than one into a domino followed by k−2squares.3.Some Other ResultsUnlike the Fibonacci sequence,which has a simple recursion formula,F n=F n−1+F n−2,the recursion formula for the partition function is given by Euler’s Pentagonal Number Theorem, p(n)=p(n−1)+p(n−2)−p(n−5)−p(n−7)+···= ∞k=1(−1)k+1(p(n−3k2−k)+p(n−3k2+k)). For n>5,p(n−1)+p(n−2)overestimates p(n).The next result can be used to explainthis overestimate.We present an analytical and a combinatorial proof of this theorem.Theorem2The following holds:1(q;q)∞=1+q+q2 (q;q)∞− ∞i=2q2i+1(1−q)(q i;q)∞.Analytically,this theorem follows by setting x=1in the equation for s(x,q)in identity 10on page29in[1]and then dividing by(q;q)∞.Combinatorially,we can create a tiling representation for a partition of n by placing an extra square to the left of a tiling represen-tation for a partition of n−1.This will create all partitions of n which contain a one.When we place a domino to the left of a tiling representation for a partition of n−2we will create a tiling representation of a partition of n in which the smallest part is at least two unless the partition for n−2contains m≥1ones and a part greater than1and less than m+2.The generating function for these exceptions is given by ∞m=1q2+m m+1k=2q k k∞,which is equal to the sum being subtracted on the left side of the equation in Theorem2. Note that ∞i=2q2i+1i∞enumerates the number of ways of expressing n as x1+x2+···+x r,where r≥1,x i≥2for all i,and x1>x2≤x3≤···≤x r.In other words,we almost have a partition of n into parts greater than1,since only theﬁrst part is out of order.By observing that q2kk is the generating function for partition tilings containing kdominoes we can give a tiling interpretation of the following theorem due to Euler. Theorem3The following holds:1 ∞k=0q2k k= ∞n=0p(n)q n.When k=0and there are no dominoes,the partition consists of only ones,with gener-ating function11−q.For k>0,to see that the generating function for partition tilings with kdominoes is q2k(1−q)(q;q)k ,we look at the Ferrers’graph for a partition containing k parts greaterthan one,which gives us k dominoes by using theﬁrst two nodes of each part greater than one to form the k dominoes;q2k.To the right of the dominoes we have columns containingk or fewer nodes;1(q;q)k ,and below the dominoes we have the parts that are ones;11−q.References1.Andrews,George,The Theory of Partitions,in“Encyclopedia of Mathematics and Its Applications,”Vol.2,Addison-Wesley,Reading,MA,1976.2.Benjamin,Authur and Quinn,Jennifer,Proofs that Really Count,The Mathematical Association of America,2003.。