Theory of the proximity effect in junctions with unconventional superconductors
边沁论效用原理(英汉对照)
VIII. When an action, or in particular a measure of government, is supposed by a man to be conformable to the principle of utility, it may be convenient, for the purposes of discourse, to imagine a kind of law or dictate, called a law or dictate of utility: and to speak of the action in question, as being conformable to such law or dictate.
IV.共同体的利益是有关道德的用语中最笼统的词语，难怪它常常失去意义。当它有意义时，它的意思要以如下方式理解：共同体是一个虚构体，由个人组成，这些个人被看作它的成员(The community is a fictitiousbody,composed of the individual persons who are considered as constituting as it were itsmembers.)。那么，共同体的利益是什么呢？是组成它的若干成员的利益的和。
V. It is in vain to talk of the interest of the community, without understanding what is the interest of the individual.*8A thing is said to promote the interest, or to beforthe interest, of an individual, when it tends to add to the sum total of his pleasures: or, what comes to the same thing, to diminish the sum total of his Nhomakorabeapains.
利益相关者理论的分析---原创
第一章
1.1
我国改革开放以来，随着经济的迅猛发展，房地产市场得以全面启动，使得土地使用制度和住房分配制度下的另一产物——物业管理应运而生。中国的物业管理始于八十年代初的经济特区深圳，伴随我国城市化进程加剧，住房制度的改革和房管制度的革新，以及中国房地产业的迅猛发展，新建商品房住宅的数量日益增多，而且越来越呈现出住宅小区规模大型化、功能综合化的特点。传统的房屋管理方式已经不能适应住宅产业迅速发展的需要。大量住宅小区投入使用，带来了管理工作的变化，除了对房屋进行维修外，还必须对附属物、设备、场地、环卫、绿化、道路、治安进行专业化管理，以保持住宅小区的完好，发挥其整体功能和综合效益。物业管理作为一种新型的管理方式越来越受到开发商的重视和业主的欢迎，它对促进房地产业的良性运转，推动我国经济发展，改善人民生活条件以及提高城市现代文明都起了重要的作用。在今后相当长一段时期内，随着住宅建设的持续快速发展以及旧住宅区物业管理覆盖面的不断扩大，将保持快速发展。在《国民经济和社会发展第十二个五年规划》中提出“在全面发展城市社区建设，把社区建设成为管理有序、服务完善、文明祥和的社会生活共同体中需要充分发挥物业管理机构的积极作用”。
Combing the stakeholder theory system, this paper explain the evolution process of stakeholder theory and the important factors, such as literature analysis, case analysis research method, on the basis of combining the theory of strategic management as well as in the actual matrix model of stakeholder analysis, focusreflects the property company, government, owner and the benefit analysis and behavioral effects between real estate developers.Finally, combining with the actual situation of zhuji city, zhuji city, put forward in accordance with property overall strategy implementation suggestion for the development of the company.Zhuji city, at the same time, the government to help property management at the same time, also puts forward the relevant policy recommendations, zhuji city, expect this research can advance the progress on the property management company governance.
dynamic foreclosure theory
dynamic foreclosure theoryDynamic Foreclosure Theory: Exploring the Interplay of Market Power and InnovationDynamic foreclosure theory is a relatively new economic concept that aims to explain how market power and innovation interact to shape the competitive landscape of an industry. Foreclosure refers to the ability of a dominant firm to limit the access of rivals to critical inputs or distribution channels, thereby reducing their ability to compete effectively.In traditional economic models, foreclosure is viewed as a static event - a one-time action by a dominant firm that permanently limits the ability of rivals to compete. However, dynamic foreclosure theory takes a more nuanced view, recognizing that the effects of foreclosure can vary depending on the level of innovation in the industry.In dynamic foreclosure theory, innovation is seen as a key driver of competition. A firm that is able to innovate and create new products or services can disrupt the existing competitive order, potentially overcoming the advantages of a dominant firm. However, if the dominant firm is able to use its market power to limit the access of rivals to critical inputsor distribution channels, it can slow down or even stifle innovation, ultimately harming consumers and reducing overall economic welfare.A key insight of dynamic foreclosure theory is that the effects of foreclosure are not static, but rather dynamic and evolving over time. As the level of innovation increases, the ability of a dominant firm to maintain its market power through foreclosure may diminish. Conversely, as innovation slows down, the power of a dominant firm to engage in foreclosure may increase.This dynamic interplay between market power and innovation has important implications for antitrust policy. Static measures of market concentration may not capture the evolving nature of competition in dynamic industries, where innovation and foreclosure are in constant flux. Therefore, policymakers may need to adopt more dynamic approaches to antitrust enforcement, taking into account the changing nature of the competitive landscape over time.Overall, dynamic foreclosure theory offers a valuable framework for understanding the complex interplay between market power and innovation in dynamic industries. By recognizing the dynamic nature of competition, policymakerscan better design antitrust policies that promote innovation, protect consumers, and enhance overall economic welfare.。
伍德里奇计量经济学导论第四版
15CHAPTER 3TEACHING NOTESFor undergraduates, I do not work through most of the derivations in this chapter, at least not in detail. Rather, I focus on interpreting the assumptions, which mostly concern the population. Other than random sampling, the only assumption that involves more than populationconsiderations is the assumption about no perfect collinearity, where the possibility of perfect collinearity in the sample (even if it does not occur in the population should be touched on. The more important issue is perfect collinearity in the population, but this is fairly easy to dispense with via examples. These come from my experiences with the kinds of model specification issues that beginners have trouble with.The comparison of simple and multiple regression estimates – based on the particular sample at hand, as opposed to their statistical properties – usually makes a strong impression. Sometimes I do not bother with the “partialling out” interpretation of multiple regression.As far as statistical properties, notice how I treat the problem of including an irrelevant variable: no separate derivation is needed, as the result follows form Theorem 3.1.I do like to derive the omitted variable bias in the simple case. This is not much more difficult than showing unbiasedness of OLS in the simple regression case under the first four Gauss-Markov assumptions. It is important to get the students thinking aboutthis problem early on, and before too many additional (unnecessary assumptions have been introduced.I have intentionally kept the discussion of multicollinearity to a minimum. This partly indicates my bias, but it also reflects reality. It is, of course, very important for students to understand the potential consequences of having highly correlated independent variables. But this is often beyond our control, except that we can ask less of our multiple regression analysis. If two or more explanatory variables are highly correlated in the sample, we should not expect to precisely estimate their ceteris paribus effects in the population.I find extensive treatments of multicollinearity, where one “tests” or somehow “solves” the multicollinearity problem, to be misleading, at best. Even the organization of some texts gives the impression that imperfect multicollinearity is somehow a violation of the Gauss-Markovassumptions: they include multicollinearity in a chapter or part of the book devoted to “violation of the basic assumptions,” or something like that. I have noticed that master’s students who have had some undergraduate econometrics are often confused on the multicollinearity issue. It is very important that students not confuse multicollinearity among the included explanatory variables in a regression model with the bias caused by omitting an important variable.I do not prove the Gauss-Markov theorem. Instead, I emphasize its implications. Sometimes, and certainly for advanced beginners, I put a special case of Problem 3.12 on a midterm exam, where I make a particular choice for the function g (x . Rather than have the students directly 课后答案网ww w.kh d aw .c om16compare the variances, they should appeal to the Gauss-Markov theorem for the superiority of OLS over any other linear, unbiased estimator.SOLUTIONS TO PROBLEMS3.1 (i Yes. Because of budget constraints, it makes sense that, the more siblings there are in a family, the less education any one child in the family has. To find the increase in the number of siblings that reduces predicted education by one year, we solve 1 = .094(Δsibs , so Δsibs = 1/.094 ≈ 10.6.(ii Holding sibs and feduc fixed, one more year of mother’s education implies .131 years more of predicted education. So if a mother has four more years of education, her son is predicted to have about a half a year (.524 more years of education. (iii Since the number of siblings is the same, but meduc and feduc are both different, the coefficientson meduc and feduc both need to be accounted for. The predicted difference in education between B and A is .131(4 + .210(4 = 1.364.3.2 (i hsperc is defined so that the smaller it is, the lower the student’s standing in high school. Everything else equal, the worse the student’s standing in high school, the lower is his/her expected college GPA. (ii Just plug these values into the equation:n colgpa= 1.392 − .0135(20 + .00148(1050 = 2.676.(iii The difference between A and B is simply 140 times the coefficient on sat , because hsperc is the same for both students. So A is predicted to have ascore .00148(140 ≈ .207 higher.(iv With hsperc fixed, n colgpaΔ = .00148Δsat . Now, we want to find Δsat such that n colgpaΔ = .5, so .5 = .00148(Δsat or Δsat = .5/(.00148 ≈ 338. Perhaps not surprisingly, a large ceteris paribus difference in SAT score – almost two and one-half standard deviations – is needed to obtain a predicted difference in college GPA or a half a point.3.3 (i A larger rank for a law school means that the school has less prestige; this lowers starting salaries. For example, a rank of 100 means there are 99 schools thought to be better.课后答案网ww w.kh d aw .c om17(ii 1β > 0, 2β > 0. Both LSAT and GPA are measures of the quality of the entering class. No matter where better students attend law school, we expect them to earn more, on average. 3β, 4β > 0. The numbe r of volumes in the law library and the tuition cost are both measures of the school quality. (Cost is less obvious than library volumes, but should reflect quality of the faculty, physical plant, and so on. (iii This is just the coefficient on GPA , multiplied by 100: 24.8%. (iv This is an elasticity: a one percent increase in library volumes implies a .095% increase in predicted median starting salary, other things equal. (v It is definitely better to attend a law school with a lower rank. If law school A has a ranking 20 less than law school B, the predicted difference in starting salary is 100(.0033(20 = 6.6% higher for law school A.3.4 (i If adults trade off sleep for work, more work implies less sleep (other things equal, so 1β < 0. (ii The signs of 2β and 3β are not obvious, at least to me. One could argue that more educated people like to get more out of life, and so, other things equal,they sleep less (2β < 0. The relationship between sleeping and age is more complicated than this model suggests, and economists are not in the best position to judge such things.(iii Since totwrk is in minutes, we must convert five hours into minutes: Δtotwrk = 5(60 = 300. Then sleep is predicted to fall by .148(300 = 44.4 minutes. For a week, 45 minutes less sleep is not an overwhelming change. (iv More education implies less predicted time sleeping, but the effect is quite small. If we assume the difference between college and high school is four years, the college graduate sleeps about 45 minutes less per week, other things equal. (v Not surprisingly, the three explanatory variables explain only about 11.3% of the variation in sleep . One important factor in the error term is general health. Another is marital status, and whether the person has children. Health (however we measure that, marital status, and number and ages of children would generally be correlated with totwrk . (For example, less healthy people would tend to work less.3.5 Conditioning on the outcomes of the explanatory variables, we have 1E(θ =E(1ˆβ + 2ˆβ = E(1ˆβ+ E(2ˆβ = β1 + β2 = 1θ.3.6 (i No. By definition, study + sleep + work + leisure = 168. Therefore, if we change study , we must change at least one of the other categories so that the sum is still 168. 课后答案网ww w.kh d aw .c om18(ii From part (i, we can write, say, study as a perfect linear function of the otherindependent variables: study = 168 − sleep − work − leisure . This holds for every observation, so MLR.3 violated. (iii Simply drop one of the independent variables, say leisure :GPA = 0β + 1βstudy + 2βsleep + 3βwork + u .Now, for example, 1β is interpreted as the change in GPA when study increases by one hour, where sleep , work , and u are all held fixed. If we are holding sleep and work fixed but increasing study by one hour, then we must be reducing leisure by one hour. The other slope parameters have a similar interpretation.3.7 We can use Table 3.2. By definition, 2β > 0, and by assumption, Corr(x 1,x 2 < 0.Therefore, there is a negative bias in 1β: E(1β < 1β. This means that, on average across different random samples, the simple regression estimator underestimates the effect of thetraining program. It is even possible that E(1β is negative even though 1β > 0.3.8 Only (ii, omitting an important variable, can cause bias, and this is true only when the omitted variable is correlated with the included explanatory variables. The homoskedasticity assumption, MLR.5, played no role in showing that the OLS estimators are unbiased.(Homoskedasticity was used to o btain the usual variance formulas for the ˆjβ. Further, the degree of collinearity between the explanatory variables in the sample, even if it is reflected in a correlation as high as .95, does not affect the Gauss-Markov assumptions. Only if there is a perfect linear relationship among two or more explanatory variables is MLR.3 violated.3.9 (i Because 1x is highly correlated with 2x and 3x , and these latter variables have largepartial effects on y , the simple and multiple regression coefficients on 1x can differ by largeamounts. We have not done this case explicitly, but given equation (3.46 and the discussion with a single omitted variable, the intuition is pretty straightforward.(ii Here we would expect 1β and 1ˆβ to be similar (subject, of course, to what we mean by “almost uncorrelated”. The amount of correlation between 2x and 3x does not directly effect the multiple regression estimate on 1x if 1x is essentially uncorrelated with 2x and 3x .(iii In this case we are (unnecessarily introducing multicollinearity into the regression: 2x and 3x have small partial effects on y and yet 2x and 3x are highly correlated with 1x . Adding2x and 3x like increases the standard error of the coefficient on 1x substantially, so se(1ˆβis likely to be much larger than se(1β . 课后答案网ww w.kh d aw .c om19(iv In this case, adding 2x and 3x will decrease the residual variance without causingmuch collinearity (because 1x is almost uncorrelated with 2x and 3x , so we should see se(1ˆβ smaller than se(1β. The amount of correlation between 2x and 3x does not directly affect se(1ˆβ.3.10 From equation (3.22 we have111211ˆ,ˆni ii ni i r yr β===∑∑where the 1ˆi rare defined in the problem. As usual, we must plug in the true model for y i : 1011223311211ˆ(.ˆni i i i ii ni i r x x x u r βββββ==++++=∑∑The numerator of this expression simplifies because 11ˆni i r=∑ = 0, 121ˆni i i r x =∑ = 0, and 111ˆni i i r x =∑ = 211ˆni i r =∑. These all follow from the fact that the 1ˆi rare the residuals from the regression of 1i x on 2i x : the 1ˆi rhave zero sample average and are uncorrelated in sample with 2i x . So the numerator of 1βcan be expressed as2113131111ˆˆˆ.n n ni i i i i i i i rr x r u ββ===++∑∑∑Putting these back over the denominator gives 13111113221111ˆˆ.ˆˆnni i ii i nni i i i r x rur r βββ=====++∑∑∑∑课后答案网ww w.kh d aw .c om20Conditional on all sample values on x 1, x 2, and x 3, only the last term is random due to its dependence on u i . But E(u i = 0, and so131113211ˆE(=+,ˆni i i ni i r xr βββ==∑∑which is what we wanted to show. Notice that the term multiplying 3β is the regressioncoefficient from the simple regression of x i 3 on 1ˆi r.3.11 (i 1β < 0 because more pollution can be expected to lower housing values; note that 1β isthe elasticity of price with respect to nox . 2β is probably positive because rooms roughlymeasures the size of a house. (However, it does not allow us to distinguish homes where each room is large from homes where each room is small. (ii If we assume that rooms increases with quality of the home, then log(nox and rooms are negatively correlated when poorer neighborhoods have more pollution, something that is often true. We can use Ta ble 3.2 to determine the direction of the bias. If 2β > 0 andCorr(x 1,x 2 < 0, the simple regression estimator 1βhas a downward bias. But because 1β < 0, this means that the simple regression, on average, overstates the importance of pollution. [E(1β is more negative than 1β.] (iii This is what we expect from the typical sample based on our analysis in part (ii. The simple regression estimate, −1.043, is more negative (larger in magnitude than the multiple regression estimate, −.718. As those estimates are only for one sample, we can never know which is closer to 1β. But if this is a “typical” sample, 1β is closer to −.718.3.12 (i For notational simplicity, define s zx = 1(;ni i i z z x =−∑ this is not quite the samplecovariance between z and x because we do not divide by n – 1, but we are only using it tosimplify notation. Then we can write 1β as11(.niii zxz z ys β=−=∑This is clearly a linear function of the y i : take the weights to be w i = (z i −z /s zx . To show unbiasedness, as usual we plug y i = 0β + 1βx i + u i into this equation, and simplify: 课后答案网w w w .k h d aw .c o m21 11 1 011 111(( (((n ii i i zxnni zx i ii i zxniii zxz z x u s z z s z z u s zz u s ββββββ====−++=−++−=−=+∑∑∑∑where we use the fact that 1(ni i z z =−∑ = 0 always. Now s zx is a function of the z i and x i and theexpected value of each u i is zero conditional on all z i and x i in the sample. Therefore, conditional on these values,1111(E(E(niii zxz z u s βββ=−=+=∑because E(u i = 0 for all i . (ii From the fourth equation in part (i we have (again conditional on the z i and x i in the sample,2111222212Var ((Var(Var((n ni i i i i i zx zxnii zxz z u z z u s s z z s βσ===⎡⎤−−⎢⎥⎣⎦==−=∑∑∑because of the homoskedasticit y assumption [Var(u i = σ2 for all i ]. Given the definition of s zx , this is what we wanted to show.课后答案网ww w.kh d aw .c om22(iii We know that Var(1ˆβ = σ2/21[(].ni i x x =−∑ Now we can rearrange the inequality in the hint, drop x from the sample covariance, and cancel n -1everywhere, to get 221[(]/ni zx i z z s =−∑ ≥211/[(].ni i x x =−∑ When we multiply through by σ2 we get Var(1β ≥ Var(1ˆβ, which is what we wanted to show.3.13 (i The shares, by definition, add to one. If we do not omit one of the shares then the equation would suffer from perfect multicollinearity. The parameters would not have a ceteris paribus interpretation, as it is impossible to change one share while holding all of the other shares fixed. (ii Because each share is a proportion (and can be at most one, when all other shares are zero, it makes little sense to increase share p by one unit. If share p increases by .01 – which is equivalent to a one percentage point increase in the share of property taxes in total revenue – holding share I , share S , and the other factorsfixed, then growth increases by 1β(.01. With the other shares fixed, the excluded share, share F , must fall by .01 when share p increases by .01.SOLUTIONS TO COMPUTER EXERCISESC3.1 (i Prob ably 2β > 0, as more income typically means better nutrition for the mother and better prenatal care. (ii On the one hand, an increase in income generally increases the consumption of a good, and cigs and faminc could be positively correlated. On the other, family incomes are also higher for families with more education, and more education and cigarette smoking tend to benegatively correlated. The sample correlation between cigs and faminc is about −.173, indicating a negative correlation.(iii The regressions without and with faminc aren 119.77.514bwghtcigs =−21,388,.023n R ==and n 116.97.463.093bwghtcigs faminc =−+21,388,.030.n R ==课后答案网ww w.kh d aw .c om23The effect of cigarette smoking is slightly smaller when faminc is added to the regression, but the difference is not great. This is due to the fact that cigs and faminc are not very correlated, and the coefficient on faminc is practically small. (The variable faminc is measured in thousands, so $10,000 more in 1988 income increases predicted birth weight by only .93 ounces.C3.2 (i The estimated equation isn 19.32.12815.20price sqrft bdrms =−++288,.632n R ==(ii Holding square footage constant, n price Δ = 15.20 ,bdrms Δ and so n price increases by 15.20, which means $15,200.(iii Now n price Δ = .128sqrft Δ + 15.20bdrms Δ = .128(140 + 15.20 = 33.12, or $33,120. Because the size of the house is increasing, this is a much larger effect than in (ii. (iv About 63.2%. (v The predicted price is –19.32 + .128(2,438 + 15.20(4 = 353.544, or $353,544. (vi From part (v, the estimated value of the home based only on square footage and number of bedrooms is $353,544. The actual selling price was $300,000, which suggests the buyer underpaid by some margin. But, of course, there are many other features of a house (some that we cannot even measure that affect price, and we have not controlled for these.C3.3 (i The constant elasticity equation isn log( 4.62.162log(.107log(salary sales mktval =++ 2177,.299.n R ==(ii We cannot include profits in logarithmic form because profits are negative for nine of the companies in the sample. When we add it in levels form we getn log( 4.69.161log(.098log(.000036salary sales mktval profits =+++2177,.299.n R ==The coefficient on profits is very small. Here, profits are measured in millions, so if profits increase by $1 billion, which means profits Δ = 1,000 – a huge change – predicted salaryincreases by about only 3.6%. However, remember that we are holding sales and market value fixed.课后答案网ww w.kh d aw .c om24Together, these variables (and we could drop profits without losing anything explain almost 30% of the sample variation in log(salary . This is certainly not “most” of the variation.(iii Adding ceoten to the equation givesn log( 4.56.162log(.102log(.000029.012salary sales mktval profits ceoten =++++2177,.318.n R ==This means that one more year as CEO increases predicted salary by about 1.2%. (iv The sample correlation between log(mktval and profits is about .78, which is fairly high. As we know, this causes no bias in the OLS estimators, although it can cause their variances to be large. Given the fairly substantial correlation between market value andfirm profits, it is not too surprising that the latter adds nothing to explaining CEO salaries. Also, profits is a short term measure of how the firm is doing while mktval is based on past, current, and expected future profitability.C3.4 (i The minimum, maximum, and average values for these three variables are given in the table below:Variable Average Minimum Maximum atndrte priGPA ACT 81.71 2.59 22.516.25 .86131003.93 32(ii The estimated equation isn 75.7017.26 1.72atndrtepriGPA ACT =+− n = 680, R 2 = .291.The intercept means that, for a student whose prior GPA is zero and ACT score is zero, the predicted attendance rate is 75.7%. But this is clearly not an interesting segment of thepopulation. (In fact, there are no students in the college population with priGPA = 0 and ACT = 0, or with values even close to zero. (iii The coefficient on priGPA means that, if a student’s prior GPA is one point higher (say, from 2.0 to 3.0, the attendance rate is about 17.3 percentage points higher. This holds ACT fixed. The negative coefficient on ACT is, perhaps initially a bit surprising. Five more points on the ACT is predicted to lower attendance by 8.6 percentage points at a given level of priGPA . As priGPAmeasures performance in college (and, at least partially, could reflect, past attendance rates, while ACT is a measure of potential in college, it appears that students that had more promise (which could mean more innate ability think they can get by with missing lectures. 课后答案网ww w.kh d aw .c om(iv We have atndrte = 75.70 + 17.267(3.65 –1.72(20 ≈ 104.3. Of course, a student cannot have higher than a 100% attendance rate. Getting predictions like this is always possible when using regression methods for dependent variables with natural upper or lower bounds. In practice, we would predict a 100% attendance rate for this student. (In fact, this student had an actual attendance rate of 87.5%. (v The difference in predicted attendance rates for A and B is 17.26(3.1 − 2.1 − (21 − 26 = 25.86. C3.5 The regression of educ on exper and tenure yields n = 526, R2 = .101. ˆ Now, when we regres s log(wage on r1 we obtain ˆ log( wage = 1.62 + .092 r1 n = 526, R2 = .207. (ii The slope coefficientfrom log(wage on educ is β1 = .05984. ˆ ˆ (iv We have β1 + δ 1 β 2 = .03912 +3.53383(.00586 ≈ .05983, which is very close to .05984; the small difference is due to rounding error. C3.7 (i The results of the regression are math10 = −20.36 + 6.23log(expend − .305 lnchprg 课 (iii The slope coefficients from log(wage on educ and IQ are ˆ = .03912 and β = .00586, respectively. ˆ β1 2 后答案 C3.6 (i The slope coefficient from the regression IQ on educ is (rounded to five decimal places δ1 = 3.53383. n = 408, R2 = .180. 25 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher. 网ˆ As expected, the coefficient on r1 in the second regression is identical to the coefficient on educ in equation (3.19. Notice that the R-squared from the above regression is below that in (3.19. ˆ In effect, the regression of log(wage on r1 explains log(wage using only the part of educ that is uncorrelated with exper and tenure; separate effects of exper and tenure are not included. ww w. kh da w. co m ˆ educ = 13.57 − .074 exper + .048 ten ure + r1 .The signs of the estimated slopes imply that more spending increases the pass rate (holding lnchprg fixed and a higher poverty rate (proxied well by lnchprg decreases the pass rate (holding spending fixed. These are what we expect. (ii As usual, the estimated intercept is the predicted value of the dependent variable when all regressors are set to zero. Setting lnchprg = 0 makes sense, as there are schools with low poverty rates. Setting log(expend = 0 does not make sense, because it is the same as setting expend = 1, and spending is measured in dollars per student. Presumably this is well outside any sensible range. Not surprisingly, the prediction of a −20 pass rate is nonsensical. (iii The simple regression results are failing to account for the poverty rate leads to an overestimate of the effect of spending. C3.8 (i The average of prpblck is .113 with standarddeviation .182; the average of income is 47,053.78 with standard deviation 13,179.29. It is evident that prpblck is a proportion and that income is measured in dollars. (ii The results from the OLS regression are psoda = .956 + .115 prpblck + .0000016 income 后 If, say, prpblck increases by .10 (ten percentage points, the price of soda is estimated toincrease by .0115 dollars, or about 1.2 cents. While this does not seem large, there are communities with no black population and others that are almost all black, in which case the difference in psoda is estimated to be almost 11.5 cents. (iii The simple regression estimate on prpblck is .065, so the simple regression estimate is actually lower. This is because prpblck and income are negatively correlated (-.43 and income has a positive coefficient in the multiple regression. (iv To get a constant elasticity, income should be in logarithmic form. I estimate the constant elasticity model: 26 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher. 课答案 n = 401, R2 = .064. 网ww ˆ (v We can use equation (3.23. Because Corr(x1,x2 < 0, which means δ1 < 0 , and β 2 < 0 , ˆ the simple regression estimate, β , is larger than the multiple regression estimate, β . Intuitively, 1 w. kh (iv The sample correl ation between lexpend and lnchprg is about −.19 , which means that, on average, high schools with poorer students spent less per student. This makes sense, especially in 1993 in Michigan, where school funding was essentially determined by local property tax collections. da w. n = 408, R2 = .030 and the estimated spending effect is larger than it was in part (i –almost double. co 1 m math10 = −69.34 + 11.16 log(expendlog( psoda = −.794 + .122 prpblck + .077 log(income n = 401, R2 = .068. If prpblck increases by .20, log(psoda is estimated to increase by .20(.122 = .0244, or about 2.44 percent. ˆ (v β prpblck falls to about .073 when prppov is added to the regression. (vi The correlation is about −.84 , which makes sense because poverty rates are determined by income (but not directly in terms of median income. (vii There is no argument that they are highly correlated, but we are using them simply as controls to determine if the is price discrimination against blacks. In order to isolate the pure discrimination effect, we need to control for as many measures of income as we can; including both variables makes sense. C3.9 (i The estimated equation is (iv The estimated equation is gift = −7.33 + 1.20 mailsyear − .261 giftlast + 16.20 propresp + .527 avggift Aft er controlling for the average past gift level, the effect of mailings becomes even smaller: 1.20 guilders, or less thanhalf the effect estimated by simple regression. (v After controlling for the average of past gifts – which we can view as measuring the “typical” generosity of the person and is positively related to the current gift level – we find that the current gift amount is negatively related to the most recent gift. A negative relationship makes some sense, as people might follow a large donation with a smaller one. 27 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher. 课 n = 4,268, R 2 = .2005 后 (iii Because propresp is a proportion, it makes little sense to increase it by one. Such an increase can happen only if propresp goes from zero to one. Instead, consider a .10 increase in propresp, which means a 10 percentage point increase. Then, gift i s estimated to be 15.36(.1 ≈ 1.54 guilders higher. 答案 (ii Holding giftlast and propresp fixed, one more mailing per year is estimated to increase gifts by 2.17 guilders. The simple regression estimate is 2.65, so the multiple regression estimate is somewhat smaller. Remember, the simple regression estimate holds no other factors fixed. 网 ww The R-squared is now about .083, compared with about .014 for the simple regression case. Therefore, the variables giftlast and propresp help to explain significantly more variation in gifts in the sample (although still just over eight percent. w. n = 4,268, R 2= .0834 kh gift = −4.55 + 2.17 mailsyear + .0059 giftlast + 15.36 propresp da w. co m。
相对论效应英文
相对论效应英文The Theory of Relativity。
The theory of relativity, proposed by Albert Einstein in the early 20th century, revolutionized our understanding of space, time, and gravity. It has since become one of the cornerstones of modern physics and has had a profound impact on various scientific disciplines. In this article, we will explore the key concepts and implications of the theory of relativity.The theory of relativity consists of two major parts: the special theory of relativity and the general theory of relativity. The special theory of relativity, published by Einstein in 1905, deals with the behavior of objects moving at constant speeds in the absence of gravitational forces. It introduced the concept of spacetime, which combines the three dimensions of space with the dimension of time into a four-dimensional continuum. According to the special theory of relativity, the laws of physics are the same for all observers in uniform motion relative to each other, regardless of their speed. This means that the perception of time and space can vary depending on the relative motion of observers.One of the most well-known consequences of the special theory of relativity is the time dilation effect. Time dilation refers to the fact that time appears to pass more slowly for objects in motion relative to an observer at rest. This effect becomes significant as the speed of the object approaches the speed of light. For example, if a spaceship travels near the speed of light for a certain period, when it returns to Earth, more time would have passed for the people on Earth compared to the astronauts on the spaceship. This phenomenon has been experimentally verified and has important implications for space travel and our understanding of the universe.The general theory of relativity, published by Einstein in 1915, extends the special theory of relativity to include the effects of gravity. It describes gravity as the curvature of spacetime caused by the presence of mass and energy. According to the general theory of relativity, massive objects, such as planets and stars, deform the fabric of spacetime,causing nearby objects to move along curved paths. This explains why objects fall towards the Earth and why planets orbit around the Sun.Another key prediction of the general theory of relativity is the gravitational time dilation effect. In regions of strong gravitational fields, such as near black holes, time appears to pass more slowly compared to regions with weaker gravitational fields. This has been confirmed through precise measurements of time on Earth and in space. The gravitational time dilation effect has practical applications in the field of global positioning systems (GPS), where accurate timekeeping is essential for determining positions on Earth.In addition to these effects, the theory of relativity has also led to the discovery of new phenomena, such as gravitational waves. Gravitational waves are ripples in spacetime caused by the acceleration of massive objects. They were first detected in 2015, confirming a major prediction of the general theory of relativity. This discovery opened up a new window for observing the universe and has opened up new avenues for research in astrophysics and cosmology.In conclusion, the theory of relativity has revolutionized our understanding of the fundamental concepts of space, time, and gravity. It has provided a framework for explaining a wide range of phenomena and has been confirmed through numerous experiments and observations. The theory of relativity continues to be a vibrant field of research, with ongoing efforts to further refine our understanding and explore its implications for the nature of the universe.。
Globally networked risks and how to respond
BOX 1
Risk, systemic risk and hyper-risk
According to the standard ISO 31000 (2009; /iso/ catalogue_detail?csnumber543170), risk is defined as ‘‘effect of uncertainty on objectives’’. It is often quantified as the probability of occurrence of an (adverse) event, times its (negative) impact (damage), but it should be kept in mind that risks might also create positive impacts, such as opportunities for some stakeholders.
The theory of Ostwald ripening
Journal of Statistical Physics, Vol. 38, Nos. 1/2, 1985
The Theory of Ostwald Ripening
P. W. Voorhees 1
Received August 7, 1984
Developments in the theory of Ostwald ripening since the classic work of I. M. Lifshitz and V. V. Slyozov (LS) are reviewed and directions for future work are suggested. Recent theoretical work on the role of a finite volume fraction of coarsening phase on the ripening behavior of two-phase systems is reformulated in terms of a consistent set of notation through which each of the theories can be compared and contrasted. Although more theoretical work is necessary, these theories are in general agreement on the effects of a finite volume fraction of coarsening phase on the coarsening behavior of two-phase systems. New work on transient Ostwald ripening is presented which illustrates the broad range of behavior which is possible in this regime. The conditions responsible for the presence of the asymptotic state first discovered by LS, as well as the manner in which this state is approached, are also discussed. The role of elastic fields during Ostwald ripening in solid-solid mixtures is reviewed, and it is shown that these fields can play a dominant role in determining the coarsening behavior of a solid-solid system.
the_most_well-known_being_the_general_theory_概述说明
the most well-known being the general theory 概述说明1. 引言1.1 概述在这篇长文中, 我们将详细探讨“the most well-known being the general theory”。
这个引人瞩目的理论是指泛化理论，是一个被广泛接受和使用的理论框架。
通过本文，我们将深入剖析该理论的实质并探讨其影响力。
1.2 文章结构本文分为五个主要部分：引言、正文一、正文二、正文三以及结论。
引言部分将提供对文章整体内容的概述，并简要介绍各个部分的目标与内容。
随后的三个正文部分将详细探讨该理论的不同层面和观点。
最后，结论部分将总结讨论结果，并提出关于该研究课题可进一步研究方向的建议。
1.3 目的本文旨在介绍和分析“the most well-known being the general theory”这一著名理论的核心思想以及它对相关领域产生的影响。
我们将重点关注该理论在实践中所起到的作用，并提取其中主要观点进行详细解析。
通过深入研究该理论，我们期望读者能够更好地了解其重要性，并认识到它对学术和实践的贡献。
此外，本文还将指出该理论可能存在的局限性，并探讨未来研究可能的拓展方向。
以上就是文章“1. 引言”部分的详细内容。
希望对您的长文撰写有所帮助！2. 正文一:2.1 主要观点一:One of the main points regarding the general theory is its application in the field of physics. The general theory, proposed by Albert Einstein, revolutionized our understanding of gravity and the structure of the universe. It introduced the concept of spacetime curvature caused by massive objects, explaining the force of gravity as a geometric effect rather than a conventional force.Additionally, the general theory also predicted the existence of black holes, which are incredibly dense objects with gravitational fields so strong that nothing can escape them, not even light. This prediction was later confirmed through various astronomical observations and experiments.2.2 主要观点二:Another important aspect to highlight is the impact of the general theory on cosmology - the study of the origin and evolution of the universe. According to this theory, the universe is not static but expanding. This insight led to groundbreaking discoveries such as the Big Bang theory, which suggests that our universe originated from an extremely hot and dense state billions of years ago.The general theory also provided a framework for understanding the distribution of matter in space and how it shapes cosmic structures like galaxies and galaxy clusters. Through its mathematical equations, scientists have been able to model and simulate these large-scale structures, further advancing our knowledge about the universe's composition and evolution.2.3 主要观点三:A third significant point pertains to technological applications stemming from the general theory. One notable example is GPS (Global Positioning System) technology. The accuracy of GPS relies on precise timing measurements using satellite signals traveling at high speeds relative to Earth's surface. However, without accounting for relativisticeffects predicted by Einstein's general theory, GPS calculations would yield errors exceeding several kilometers within just a day.By incorporating corrections based on relativistic principles into GPS algorithms, accurate positioning can be achieved. Therefore, it is evident that the general theory has real-world applications beyond scientific research, impacting everyday life and facilitating modern technologies.Overall, the general theory, with its profound implications in physics, cosmology, and technology, stands as one of the most well-known and influential concepts in scientific history. Its impact continues to shape our understanding of the universe and has broad applications that extend far beyond theoretical realms.3. 正文二3.1 主要观点一：在本部分中，我们将讨论关于"the most well-known being the general theory（最著名的是广义相对论）"的一些主要观点。
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a r X i v :c o n d -m a t /0606231v 7 [c o n d -m a t .s u p r -c o n ] 31 D e c 2006Theory of the proximity effect in junctions with unconventional superconductorsY .Tanaka 1,2and A.A.Golubov 31Department of Applied Physics,Nagoya University,Nagoya,464-8603,Japan2CREST Japan Science and Technology Cooperation (JST)464-8603Japan3Faculty of Science and Technology,University of Twente,The Netherlands(Dated:February 6,2008)We present a general theory of the proximity effect in junctions between diffusive normal metals (DN)and superconductors.Various possible symmetry classes in a superconductor are considered:even-frequency spin-singlet even-parity (ESE)state,even-frequency spin-triplet odd-parity (ETO)state,odd-frequency spin-triplet even-parity (OTE)state and odd-frequency spin-singlet odd-parity (OSO)state.It is shown that the pair ampli-tude in a DN belongs respectively to an ESE,OTE,OTE and ESE pairing state since only the even-parity s-wave pairing is possible due to the impurity scattering.PACS numbers:74.45.+c,74.50.+r,74.20.RpIt is well established that superconductivity is realized due to the formation of Cooper pairs consisting of two electrons.In accordance with the Pauli principle,it is customary to dis-tinguish spin-singlet even-parity and spin-triplet odd-parity pairing states in superconductors,where odd (even)refer to the orbital part of the pair wave function.For example,s -wave and d -wave pairing states belong to the former case while p -wave state belongs to the latter one [1].In both cases,the pair amplitude is an even function of energy.However,the so-called odd-frequency pairing states when the pair am-plitude is an odd function of energy can also exist.Then,the spin-singlet odd-parity and the spin-triplet even-parity pairing states are possible.The possibility of realizing the odd-frequency pairing state was first proposed by Berezinskii in the context of 3He,where the odd-frequency spin-triplet hypothetical pairing was discussed [2].The possibility of the odd-frequency super-conductivity was then discussed in the context of various mechanisms of superconductivity involving strong correla-tions [3,4].There are several experimental evidences [5]which are consistent with the realization of the odd-frequency bulk superconducting state in Ce compounds [4,5].In more accessible systems (ferromagnet/superconductor heterostruc-tures with inhomogeneous magnetization)the odd-frequency pairing state was first proposed in Ref.6and then various as-pects of this state were intensively studied [7].At the same time,the very important issue of the manifestation of the odd-frequency pairing in proximity systems without magnetic or-dering received no attention yet.This question is addressed in the present Letter.Coherent charge transport in structures involving diffusive normal metals (DN)and superconductors (S)was extensively studied during the past decade both experimentally and the-oretically.However,almost all previous work was restricted to junctions based on conventional s -wave superconductors [8].Recently,new theoretical approach to study charge trans-port in junctions based on p -wave and d -wave superconduc-tors was developed and applied to the even-frequency pairing state [9,10].It is known that in the anisotropic paring state,due to the sign change of the pair potential on the Fermi sur-face,a so-called midgap Andreev resonant state (MARS)is formed at the interface [11,12].As was found in [9,10],MARS competes with the proximity effect in contacts with spin-singlet superconductors,while it coexists with the prox-imity effect in junctions with spin-triplet superconductors.In the latter case,it was predicted that the induced pair amplitude in the DN has a peculiar energy dependence and the resulting local density of states (LDOS)has a zero energy peak (ZEP)[10].However,the relation of this unusual proximity effect to the formation of the odd-frequency pairing state was not yet clarified.Furthermore,there was no study of the proximity effect in junctions with odd-frequency superconductors.The aim of the present paper is to formulate a general theory of the proximity effect in the DN/S junctions applicable to any type of symmetry state in a superconductor forming the junc-tion in the absence of spin-dependent electronic scattering at the DN/S interface.It will be shown that for spin-triplet [spin-singlet]superconductor junctions,odd-frequency spin-triplet even-parity (OTE)pairing state [even-frequency spin-singlet even-parity (ESE)pairing state]is generated in DN indepen-dent of the parity of the superconductor.Before proceeding with formal discussion,let us present qualitative arguments illustrating the main conclusions of the paper.Two constrains should be satisfied in the considered system:(1)only the s -wave even-parity state is possible in the DN due to isotropization by impurity scattering [1],(2)the spin structure of induced Cooper pairs in the DN is the same as in an attached superconductor.Then the Pauli prin-ciple provides the unique relations between the pairing sym-metry in a superconductor and the resulting symmetry of the induced pairing state in the ly,for even-parity su-perconductors,ESE and OTE states,the pairing symmetry in the DN should remain ESE and OTE.On the other hand,for odd-parity superconductors,even-frequency spin-triplet2 odd-parity(ETO)and odd-frequency spin-singlet odd-parity(OSO)states,the pairing symmetry in the DN should be OTEand ESE,respectively.The above results are based on generalproperties and independent of the details of the geometry andthe spin structure of the spin-triplet superconductors.The generation of the OTE state in the DN attached to theETO p-wave superconductor is of particular interest.Simi-lar OTE state can be generated in superconducting junctionswith diffusive ferromagnets[6,7]but due to different physicalmechanism.Although the symmetry properties can be derivedfrom the basic arguments given above,the quantitative modelhas to be considered to prove the existence of nontrivial so-lutions for the pair amplitude in the DN in each of the abovecases.Let us start with the general symmetry properties of thequasiclassical Green’s functions in the considered system.The elements of retarded and advanced Nambu matrices g R,Ag R,A= g R,A f R,A g R,A (1)are composed of the normal g Rα,β(r,ε,p)and anomalousf Rα,β(r,ε,p)components with spin indicesαandβ.Herep=p F/|p F|,p F is the Fermi momentum,r andεdenotecoordinate and energy of a quasiparticle measured from theFermi level.The function f R and the conjugated function¯f R satisfy thefollowing relation[13,14]¯f Rα,β(r,ε,p)=−[f Rα,β(r,−ε,−p)]∗.(2)The Pauli principle is formulated in terms of the retardedand the advanced Green’s functions in the following way[13]f Aα,β(r,ε,p)=−f Rβ,α(r,−ε,−p).(3)By combining the two above equations,we obtain¯f R β,α(r,ε,p)=[f Aα,β(r,ε,p)]∗.Further,the defini-tions of the even-frequency and the odd-frequency pairing are f Aα,β(r,ε,p)=f Rα,β(r,−ε,p)and f Aα,β(r,ε,p)=−f Rα,β(r,−ε,p),respectively.Finally we get¯f Rβ,α(r,ε,p)=[f Rα,β(r,−ε,p)]∗(4) for the even-frequency pairing and¯f Rβ,α(r,ε,p)=−[f Rα,β(r,−ε,p)]∗(5) for the odd-frequency pairing.In the following,we will focus on Cooper pairs with S z=0for the simplicity,remove the external phase of the pair potential in the superconductor and concentrate on the retarded part of the Green’s function.In the case of pairing with S z=1ourfinal results will not be changed.We consider a junction consisting of a normal(N) and a superconducting reservoirs connected by a quasi-one-dimensional diffusive conductor(DN)with a length L much larger than the mean free path.The interface between the DN and the superconductor(S)at x=L has a resistance R b and the N/DN interface at x=0has a resistance R b′.For R b′=∞,the present model is reduced to the DN/S bilayer with vac-uum at the DN free surface.The Green’s function in the super-conductor can be parameterized as g±(ε)ˆτ3+f±(ε)ˆτ2using Pauli matrices,where the suffix+(−)denotes the right(left) going quasiparticles.g±(ε)and f±(ε)are given by g+(ε)= g Rα,β(r,ε,p)g−(ε)=g Rα,β(r,ε,¯p)f+(ε)=f Rα,β(r,ε,p), and f−(ε)=f Rα,β(r,ε,¯p),respectively,with¯p=¯p F/|p F| and¯p F=(−p F x,p F y).Using the relations(4),(5),we ob-tain that f±(ε)=[f±(−ε)]∗for the even-frequency pairing and f±(ε)=−[f±(−ε)]∗for the odd-frequency pairing,re-spectively,while g±(ε)=[g±(−ε)]∗in both cases.In the DN region only the s-wave even-parity pairing state is allowed due to isotropization by impurity scattering[1]. The resulting Green’s function in the DN can be parameter-ized by cosθˆτ3+sinθˆτ2in a junction with an even-parity superconductor and by cosθˆτ3+sinθˆτ1in a junction with an odd-parity superconductor.The functionθsatisfies the Usadel equation[15]D∂2θR d(∂θR b,(7) F1=2T1(f S cosθL−g S sinθL)R d(∂θR b′,F2=2T2sinθ0Z2+4cos2φ,T2=4cos2φε2−∆2±and f±=∆±/3Ψ(φ±)is the form factor withφ+=φandφ−=π−φ.∆is the maximum value of the pair potential for even-frequencypairing.In the following,we will consider four possible symmetryclasses of superconductor forming the junction and consistentwith the Pauli principle:ESE,ETO,OTE and OSO pairingstates.We will use the fact that only the even-parity s-wavepairing is possible in the DN due to the impurity scatteringand that the spin structure of pair amplitude in the DN is thesame as in an attached superconductor.(1)Junction with ESE superconductorIn this case,f±(ε)=f∗±(−ε)and g±(ε)=g∗±(−ε)are sat-isfied.Then,f S(−ε)=f∗S(ε)=f∗S and g S(−ε)=g∗S(ε)=g∗S and we obtain for F∗1(−ε)F∗1(−ε)=2T1[f S cosθ∗L(−ε)−g S sinθ∗L(−ε)]2−T1+T1[cosθ∗L (−ε)g S−sinθ∗L(−ε)f S].It follows from Eqs.6-9that sinθ∗(−ε)=−sinθ(ε)andcosθ∗(−ε)=cosθ(ε).Thus the OTE state is formed in the DN.Remarkably,the appearance of the OTE state is the only possibility to satisfy the Pauli principle,as we argued above. Interestingly,the OTE pairing state can be also realized in superconductor/ferromagnet junctions[6,7],but the physical mechanism differs from the one considered here.(3)Junction with OTE superconductorIn this case f±(ε)=−f∗±(−ε)and g±(ε)=g∗±(−ε). Then f S(−ε)=−f∗S(ε)and g S(−ε)=g∗S(ε)and one can show that F∗1(−ε)has the same form as in the case of ETO superconductor junctions.Then,we obtain sinθ∗(−ε)=−sinθ(ε)and cosθ∗(−ε)=cosθ(ε).These relations mean that the OTE pairing state is induced in the DN.(4)Junction with OSO superconductorWe have f±(ε)=−f∗±(−ε),g±(ε)=g∗±(−ε)and f S(−ε)=f∗S(ε),g S(−ε)=g∗S(ε).One can show that F∗1(−ε)takes the same form as in the case of ESE supercon-ductor junctions.Then,we obtain that sinθ∗(−ε)=sinθ(ε) and cosθ∗(−ε)=cosθ(ε).Following the same lines as in case(1),we conclude that the ESE pairing state is induced in the DN.We can now summarize the central conclusions in the table below.Symmetry of thepairing in the DNEven-frequencyspin-singlet even-parity(ESE)(2)OTEOdd-frequency spin-triplet even-parity(OTE)(4)ESENote that for even-parity superconductors the resulting symmetry of the induced pairing state in the DN is the same as that of a superconductor(the cases(1),(3)).On the other hand,for odd-parity superconductors,the induced pairing state in the DN has symmetry different from that of a super-conductor(the cases(2),(4)).In order to illustrate the main features of the proximity ef-fect in all the above cases,we calculate the LDOSρ(ε)= Real[cosθ(ε)]and the pair amplitude f(ε)=sinθ(ε)in the middle of the DN layer at x=L/2.Wefix Z=1,Z′=1, R d/R b=1,R d/R b′=0.01and E T h=0.25∆.We start from junctions with ESE superconductors and choose the s-wave pair potential withΨ±=1.The LDOS has a gap and the Real(Imaginary)part of f(ε)is an even(odd) function ofεconsistent with the formation of the even-frequency pairing.In junctions with ETO superconductors, we choose p x-wave pair potential withΨ+=−Ψ−=cosφas a typical example.In this case,an unusual proximity ef-fect is induced where the resulting LDOS has a zero energy peak(ZEP)[10].The resulting LDOS has a ZEP[10]since g2(ε)+f2(ε)=1and f(ε=0)becomes a purely imag-inary number.This is consistent with f(ε)=−f∗(−ε) and the formation of the OTE pairing in the DN.To discuss junctions with an odd-frequency superconductor we choose ∆odd(ε)=¯Cε/[1+(ε/∆)2]as the simplest example of the εdependence of an odd-frequency superconductor pair poten-tial.Atε=∆,the magnitude of∆odd(ε)becomes maximum. Here we choose¯C<1when LDOS of bulk superconductor does not have a gap aroundε=0.Let usfirst consider junc-tions with OTE superconductors and choose an s-wave pair potential as an example.The resulting LDOS has a ZEP,in contrast to junctions with ESE superconductors where the re-sulting LDOS has no ZEP.The formation of the ZEP is due to the similar reason in the ETO superconductor junctions, where f(ε=0)is a pure imaginary number.Finally,let us discuss junctions with OSO superconductors and choose p x-wave pair as an example.In this case,the ESE pairing is induced in the DN and f(ε)=f∗(−ε)is satisfied.The result-ing LDOS has a gap since f(ε=0)becomes a real number, in contrast to junctions with OTE superconductors.4−0.300.301ESE (s −wave) superconductorε/∆ρ(ε)(a)−0.300.3−11f (ε)−0.300.301ETO (px−wave) superconductor(b)−0.100.1−105−0.300.301OTE (s−wave) superconductorρ(ε)(c)−0.300.3−202−0.300.301OSO(px−wave) superconductorρ(ε)(d)−0.300.3−11ρ(ε)f (ε)f (ε)ε/∆ε/∆ε/∆ε/∆ε/∆ε/∆ε/∆f (ε)Ref Ref Ref Ref Imf Imf ImfImfFIG.1:Local density of states ρ(ε)and pair amplitude f (ε)at the center of the DN,x =L/2is plotted.Re f and Im f denote the real and imaginary part of f (ε).The pairing symmetry of the supercon-ductor is (a)ESE,(b)ETO (c)OTE and (d)OSO,respectively.For(c)and (d),we choose ¯C=0.8.The resulting symmetry of f (ε)is (a)ESE,(b)OTE (c)OTE and (d)ESE,respectively.In summary,we have formulated a general theory of the proximity effect in superconductor /diffusive normal metal junctions.Four symmetry classes in a superconductor allowed by Pauli principle are considered:1)even-frequency spin-singlet even-parity (ESE),2)even-frequency spin-triplet odd-parity (ETO),3)odd-frequency spin-triplet even-parity (OTE)and 4)odd-frequency spin-singlet odd-parity (OSO).We have found that the resulting symmetry of the induced pairing state in the DN is 1)ESE 2)OTE 3)OTE and 4)ESE,respectively.The symmetry in DN is established due to the isotropization of the pair wave function by the impurity scattering and spin conservation across the interface.This universal feature is very important to classify unconventional superconductors byusing proximity effect junctions.One of the authors Y .T.expresses his sincerest gratitude to clarifying discussions with M.Eschrig and Ya.V .Fominov.Discussions with Y .Fuseya,K.Miyake,Yu.V .Nazarov,A.D.Zaikin,A.F.V olkov and K.Efetov are gratefully acknowl-edged.This work is supported by Grant-in-Aid for Scien-tific Research (Grant Nos.17071007and 17340106)from the Ministry of Education,Culture,Sports,Science and Technol-ogy of Japan.[1]M.Sigrist and K.Ueda,Rev.Mod.Phys.63239(1991).[2]V .L.Berezinskii,JETP Lett.20,287(1974).[3]A.Balatsky and E.Abrahams,Phys.Rev.B 4513125(1992);M.V ojta and E.Dagotto,Phys.Rev.B 59R713(1999),P.Cole-man,E.Miranda and A.Tsvelik,Phys.Rev.B 49,8955,(1994).[4]Y .Fuseya,H.Kohno and K.Miyake,J.Phys.Soc.Jpn.72,2914(2003).[5]G.Q.Zheng,et al .,Phys.Rev.B,70,014511(2004);S.Kawasaki et al .,Phys.Rev.Lett.91,137001(2003).[6]F.S.Bergeret,A.F.V olkov,and K.B.Efetov,Phys.Rev.Lett.864096(2001).[7]F.S.Bergeret,A.F.V olkov,and K.B.Efetov,Rev.Mod.Phys.771321(2005);I.Sosnin,et al.,Phys.Rev.Lett.96,157002(2006);A.Kadigrobov,R.I.Shekhter,and M.Jonson,Euro-phys.Lett.90,394(2001);M.Eschrig,et al.,Phys.Rev.Lett.90137003(2003);R.S.Keizer,et al .Nature 439,825(2006);Y .V .Fominov,A.A.Golubov,and M.Y .Kupriyanov,JETP Leet.77,510(2003).[8]W.Belzig,et al.,Superlattices and Microstructures,25,1251(1999);A.A.Golubov,M.Yu.Kupriyanov,and E.Il’ichev,Rev.Mod.Phys.76,411(2004).[9]Y .Tanaka,Y .V .Nazarov and S.Kashiwaya,Phys.Rev.Lett.90,167003(2003);Y .Tanaka,et al.,Phys.Rev.B 69,144519(2004).[10]Y .Tanaka and S.Kashiwaya,Phys.Rev.B 70,012507(2004);Y .Tanaka,S.Kashiwaya and T.Yokoyama,Phys.Rev.B 71,094513(2005),Y .Tanaka,et al.,Phys.Rev.B 72,140503(R)(2005),Y .Asano,Y .Tanaka and S.Kashiwaya,Phys.Rev.Lett.96,097007(2006).[11]Y .Tanaka and S.Kashiwaya,Phys.Rev.Lett.74,3451(1995);S.Kashiwaya and Y .Tanaka,Rep.Prog.Phys.63,1641(2000),T.L¨o fwander,V .S.Shumeiko and G.Wendin,Supercond.Sci.Technol.14,R53(2001).[12]L.J.Buchholtz and G.Zwicknagl,Phys.Rev.B 23,5788(1981);J.Hara and K.Nagai,Prog.Theor.Phys.74,1237(1986);C.Bruder,Phys.Rev.B 41,4017(1990);C.R.Hu,Phys.Rev.Lett.72,1526(1994).[13]J.W.Serene and D.Rainer,Phys.Rep.101221(1983).[14]M.Eschrig,Phys.Rev.B 619061(2000).[15]adel,Phys.Rev.Lett.25,507(1970).。