Distribution and Kinematics of Molecular Gas in Barred Spiral Galaxies. I. NGC 3504

GammaProbability density functionCumulative distribution functionParametersk > 0shapeθ > 0scaleα > 0shapeβ > 0 rateSupport x ∈ (0, ∞)Probabilitydensityfunction (pdf)Cumulativedistributionfunction (CDF)Mean(see digammafunction)(see digammafunction)Median No simpleclosed formNo simple closedformMode(k−1)θ for k >1Variance(see trigammafunction )(see trigammafunction )SkewnessExcessGamma distributionFrom Wikipedia, the free encyclopediaIn probability theory and statistics, the gammadistribution is a two-parameter family of continuousprobability distributions. There are three differentparameterizations in common use:1. With a shape parameter k and a scale parameter θ.2. With a shape parameter α = k and an inverse scaleparameter β = 1/θ, called a rate parameter.3. With a shape parameter k and a mean parameter μ = k/β.In each of these three forms, both parameters are positivereal numbers.The parameterization with k and θ appears to be more commonin econometrics and certain other applied fields, where e.g.the gamma distribution is frequently used to model waitingtimes. For instance, in life testing, the waiting time untildeath is a random variable that is frequently modeled with agamma distribution.[1]The parameterization with α and β is more common inBayesian statistics, where the gamma distribution is used asa conjugate prior distribution for various types of inversescale (aka rate) parameters, such as the λ of an exponentialdistribution or a Poisson distribution – or for that matter,the β of the gamma distribution itself. (The closely relatedinverse gamma distribution is used as a conjugate prior forscale parameters, such as the variance of a normaldistribution.)If k is an integer, then the distribution represents anErlang distribution; i.e., the sum of k independentexponentially distributed random variables, each of which hasa mean of θ (which is equivalent to a rate parameter of 1/θ).The gamma distribution is the maximum entropy probabilitydistribution for a random variable X for which E[X] = kθ =α/β is fixed and greater than zero, and E[ln(X)] = ψ(k) +ln(θ) = ψ(α) − ln(β) is fixed (ψ is the digammafunction).[2]Contents1 Characterization using shape k and scale θ1.1 Probability density function1.2 Cumulative distribution function2 Characterization using shape α and rate β2.1 Probability density function2.2 Cumulative distribution function3 Properties3.1 Skewness3.2 Median calculation3.3 Summation3.4 Scaling3.5 Exponential family3.6 Logarithmic expectation3.7 Information entropy3.8 Kullback–Leibler divergence3.9 Laplace transform4 Parameter estimation4.1 Maximum likelihood estimation4.2 Bayesian minimum mean-squared error5 Generating gamma-distributed random variables6 Related distributions6.1 Special caseskurtosis Entropy Moment-generating function (mgf)CharacteristicfunctionIllustration of the Gamma PDF for parameter values over k and x with θ set to1, 2, 3, 4, 5 and 6. One can see each θlayer by itself here [1](/wiki/File:Gamma -PDF-3D-by-k.png) as well as by k [2](/wiki/File:Gamma -PDF-3D-by-Theta.png) and x . [3](/wiki/File:Gamma -PDF-3D-by-x.png).6.2 Conjugate prior 6.3 Compound gamma 6.4 Others 7 Applications 8 Notes9 References10 External linksCharacterization using shape k and scale θA random variable X that is gamma-distributed with shape k and scale θ is denotedProbability density functionThe probability density function using the shape-scale parametrization isHere Γ(k ) is the gamma function evaluated at k .Cumulative distribution functionThe cumulative distribution function is the regularized gamma function:where γ(k , x /θ) is the lower incomplete gamma function.It can also be expressed as follows, if k is a positive integer (i.e., the distribution is an Erlang distribution):[3]Characterization using shape α and rate βAlternatively, the gamma distribution can be parameterized in terms of a shape parameter α = k and an inverse scale parameter β = 1/θ, called a rate parameter. A random variable X that is gamma-distributed with shape αand rate β is denotedProbability density functionThe corresponding density function in the shape-rate parametrization isBoth parametrizations are common because either can be more convenient depending on the situation.Cumulative distribution functionThe cumulative distribution function is the regularized gamma function:where γ(α, βx) is the lower incomplete gamma function.If α is a positive integer (i.e., the distribution is an Erlang distribution), the cumulative distribution function has the following series expansion:[3]PropertiesSkewnessThe skewness is equal to , it depends only on the shape parameter (k) and approaches a normal distribution when k is large (approximately when k > 10).Median calculationUnlike the mode and the mean which have readily calculable formulas based on the parameters, the median does not have an easy closed form equation. The median for this distribution is defined as the constant x0 such thatThe ease of this calculation is dependent on the k parameter. This is best achieved by a computer since the calculations can quickly grow out of control.A method of approximating the median (ν) for any Gamma distribution has been derived based on the ratio μ/(μ −ν) which to a very good approximation is a linear function of the shape parameter α when α ≥ 1.[4] This gives this approximationwhere μ is the mean.SummationIf X i has a Gamma(k i, θ) distribution for i = 1, 2, ..., N (i.e., all distributions have the same scale parameter θ), thenprovided all X i are independent.For the cases where the X i are independent but have different scale parameters see Mathai (1982) and Moschopoulos (1984).The gamma distribution exhibits infinite divisibility.ScalingIfthen for any c > 0,Hence the use of the term "scale parameter" to describe θ.Equivalently, ifIllustration of the Kullback–Leibler (KL)divergence for two Gamma PDFs. Here β = β0 + 1 which are set to1, 2, 3, 4, 5 and 6. The typical asymmetryfor the KL divergence is clearly visible.then for any c > 0,Hence the use of the term "inverse scale parameter" to describe β.Exponential familyThe Gamma distribution is a two-parameter exponential family with natural parametersk − 1 and −1/θ(equivalently, α − 1 and −β), and natural statistics X and ln(X ).If the shape parameter k is held fixed, the resulting one-parameter family of distributions is a natural exponential family.Logarithmic expectationOne can show thator equivalently,where ψ is the digamma function.This can be derived using the exponential family formula for the moment generating function of the sufficient statistic, because one of the sufficient statistics of the gamma distribution is ln(x ).Information entropyThe information entropy isIn the k , θ parameterization, the information entropy is given byKullback–Leibler divergenceThe Kullback–Leibler divergence (KL-divergence), as with the information entropy and various other theoretical properties, are more commonly seen using the α, β parameterization because of their uses in Bayesian and other theoretical statistics frameworks.The KL-divergence of Gamma(αp , βp ) ("true" distribution) from Gamma(αq , βq ) ("approximating" distribution) is given by [5]Written using the k , θ parameterization, the KL-divergence of Gamma(k p , θp ) from Gamma(k q , θq ) is given byLaplace transformThe Laplace transform of the gamma PDF isParameter estimationMaximum likelihood estimationThe likelihood function for N iid observations (x1, ..., x N) isfrom which we calculate the log-likelihood functionFinding the maximum with respect to θ by taking the derivative and setting it equal to zero yields the maximum likelihood estimator of the θ parameter:Substituting this into the log-likelihood function givesFinding the maximum with respect to k by taking the derivative and setting it equal to zero yieldsThere is no closed-form solution for k. The function is numerically very well behaved, so if a numerical solution is desired, it can be found using, for example, Newton's method. An initial value of k can be found either using the method of moments, or using the approximationIf we letthen k is approximatelywhich is within 1.5% of the correct value.[6] An explicit form for the Newton-Raphson update of this initial guess is:[7]Bayesian minimum mean-squared errorWith known k and unknown θ, the posterior density function for theta (using the standard scale-invariant prior for θ) isDenotingIntegration over θ can be carried out using a change of variables, revealing that 1/θ is gamma-distributed with parameters α = Nk, β = y.The moments can be computed by taking the ratio (m by m = 0)which shows that the mean ± standard deviation estimate of the posterior distribution for theta isGenerating gamma-distributed random variablesGiven the scaling property above, it is enough to generate gamma variables with θ = 1 as we can later convert to any value of β with simple division.Using the fact that a Gamma(1, 1) distribution is the same as an Exp(1) distribution, and noting the method of generating exponential variables, we conclude that if U is uniformly distributed on (0, 1], then −ln(U) is distributed Gamma(1, 1) Now, using the "α-addition" property of gamma distribution, we expand this result:where U k are all uniformly distributed on (0, 1] and independent. All that is left now is to generate a variable distributed as Gamma(δ, 1) for 0 < δ < 1 and apply the "α-addition" property once more. This is the most difficult part.Random generation of gamma variates is discussed in detail by Devroye,[8] noting that none are uniformly fast for all shape parameters. For small values of the shape parameter, the algorithms are often not valid.[9] Forarbitrary values of the shape parameter, one can apply the Ahrens and Dieter[10] modified acceptance-rejection method Algorithm GD (shape k ≥ 1), or transformation method[11] when 0 < k < 1. Also see Cheng and Feast Algorithm GKM 3[12] or Marsaglia's squeeze method.[13]The following is a version of the Ahrens-Dieter acceptance-rejection method:[10]1. Let m be 1.2. Generate V3m−2, V3m−1 and V3m as independent uniformly distributed on (0, 1] variables.3. If , where , then go to step 4, else go to step 5.4. Let . Go to step 6.5. Let .6. If , then increment m and go to step 2.7. Assume ξ = ξm to be the realization of Γ(δ, 1).A summary of this iswhereis the integral part of k,ξ has been generated using the algorithm above with δ = {k} (the fractional part of k),U k and V l are distributed as explained above and are all independent.While the above approach is technically correct, Devroye notes that it is linear in the value of k and in general is not a good choice. Instead he recommends using either rejection-based or table-based methods, depending on context.[14]Related distributionsSpecial casesIf X ~ Gamma(k = 1, θ = λ−1), then X has an exponential distribution with rate parameter λ.If X ~ Gamma(k = ν/2, θ = 2), then X is identical to χ2(ν), the chi-squared distribution with ν degrees of freedom. Conversely, if Q ~ χ2(ν) and c is a positive constant, then .If k is an integer, the gamma distribution is an Erlang distribution and is the probability distribution of the waiting time until the k-th "arrival" in a one-dimensional Poisson process with intensity 1/θ. Ifand , then .If X has a Maxwell-Boltzmann distribution with parameter a, then .X ~ Gamma(k, θ), then follows a generalized gamma distribution with parameters p = 2, d = 2k, and [citation needed] ., then ; i.e. an exponential distribution: see skew-logistic distribution. Conjugate priorIn Bayesian inference, the gamma distribution is the conjugate prior to many likelihood distributions: the Poisson, exponential, normal (with known mean), Pareto, gamma with known shape σ, inverse gamma with known shape parameter, and Gompertz with known scale parameter.The Gamma distribution's conjugate prior is:[15]Where Z is the normalizing constant, which has no closed form solution. The posterior distribution can be found by updating the parameters as follows.Where n is the number of observations, and x i is the observation.Compound gammaIf the shape parameter of the gamma distribution is known, but the inverse-scale parameter is unknown, then a gamma distribution for the inverse-scale forms a conjugate prior. The compound distribution, which results from integrating out the inverse-scale has a closed form solution, known as the compound gamma distribution.[16]OthersIf X ~ Gamma(k, θ) distribution, then 1/X has an inverse-gamma distribution with shape parameter k and scale parameter θ using the parameterization given by inverse-gamma distribution.If X ~ Gamma(α, θ) and Y ~ Gamma(β, θ) are independently distributed, then X/(X + Y) has a betadistribution with parameters α and β.If X i are independently distributed Gamma(αi, 1) respectively, then the vector (X1/S, ..., X n/S), where S = X1 + ... + X n, follows a Dirichlet distribution with parameters α1, …, αn.For large k the gamma distribution converges to Gaussian distribution with mean μ = kθ and variance σ2 = kθ2.The Gamma distribution is the conjugate prior for the precision of the normal distribution with known mean.The Wishart distribution is a multivariate generalization of the gamma distribution (samples are positive-definite matrices rather than positive real numbers).The Gamma distribution is a special case of the generalized gamma distribution, the generalized integer gamma distribution, and the generalized inverse Gaussian distribution.Among the discrete distributions, the negative binomial distribution is sometimes considered the discrete analogue of the Gamma distribution.Tweedie distributions – the gamma distribution is a member of the family of Tweedie exponential dispersionmodels.ApplicationsThe gamma distribution has been used to model the size of insurance claims[17] and rainfalls.[18] This means that aggregate insurance claims and the amount of rainfall accumulated in a reservoir are modelled by a gamma process. The gamma distribution is also used to model errors in multi-level Poisson regression models, because the combination of the Poisson distribution and a gamma distribution is a negative binomial distribution.In neuroscience, the gamma distribution is often used to describe the distribution of inter-spike intervals.[19] Although in practice the gamma distribution often provides a good fit, there is no underlying biophysical motivation for using it.In bacterial gene expression, the copy number of a constitutively expressed protein often follows the gamma distribution, where the scale and shape parameter are, respectively, the mean number of bursts per cell cycle and the mean number of protein molecules produced by a single mRNA during its lifetime.[20]The gamma distribution is widely used as a conjugate prior in Bayesian statistics. It is the conjugate prior for the precision (i.e. inverse of the variance) of a normal distribution. It is also the conjugate prior for the exponential distribution.Notes1. ^ See Hogg and Craig (1978, Remark 3.3.1) for an explicit motivation2. ^ Park, Sung Y.; Bera, Anil K. (2009). "Maximum entropy autoregressive conditional heteroskedasticity model"(/Master/Download/..%5C..%5CUploadFiles%5Cpaper-masterdownload%5C2009519932327055475115776.pdf).Journal of Econometrics (Elsevier): 219–230. Retrieved 2011-06-02.3. ^ a b Papoulis, Pillai, Probability, Random Variables, and Stochastic Processes, Fourth Edition4. ^ Banneheka BMSG, Ekanayake GEMUPD (2009) "A new point estimator for the median of Gamma distribution". Viyodaya J Science,14:95-1035. ^ W.D. Penny, KL-Divergences of Normal, Gamma, Dirichlet, and Wishart densities6. ^ Minka, Thomas P. (2002) "Estimating a Gamma distribution". /en-us/um/people/minka/papers/minka-gamma.pdf7. ^ Choi, S.C.; Wette, R. (1969) "Maximum Likelihood Estimation of the Parameters of the Gamma Distribution and Their Bias",Technometrics, 11(4) 683–6908. ^ Luc Devroye (1986). Non-Uniform Random Variate Generation (/rnbookindex.html). New York: Springer-Verlag. Text "." ignored (help) See Chapter 9, Section 3, pages 401–428.9. ^ Devroye (1986), p. 406.10. ^ a b Ahrens, J. H. and Dieter, U. (1982). Generating gamma variates by a modified rejection technique. Communications ofthe ACM, 25, 47–54. Algorithm GD, p. 53.11. ^ Ahrens, J. H.; Dieter, U. (1974). "Computer methods for sampling from gamma, beta, Poisson and binomial distributions".Computing12: 223–246. CiteSeerX: 10.1.1.93.3828 (/viewdoc/summary?doi=10.1.1.93.3828).12. ^ Cheng, R.C.H., and Feast, G.M. Some simple gamma variate generators. Appl. Stat. 28 (1979), 290-295.13. ^ Marsaglia, G. The squeeze method for generating gamma variates. Comput, Math. Appl. 3 (1977), 321-325.14. ^ Luc Devroye (1986). Non-Uniform Random Variate Generation (/rnbookindex.html). New York: Springer-Verlag. See Chapter 9, Section 3, pages 401–428.15. ^ Fink, D. 1995 A Compendium of Conjugate Priors (/~cook/movabletype/mlm/CONJINTRnew%2BTEX.pdf).In progress report: Extension and enhancement of methods for setting data quality objectives. (DOE contract 95‑831).16. ^ Dubey, Satya D. (December 1970). "Compound gamma, beta and F distributions"(/content/u750hg4630387205/). Metrika16: 27–31. doi:10.1007/BF02613934(/10.1007%2FBF02613934).17. ^ p. 43, Philip J. Boland, Statistical and Probabilistic Methods in Actuarial Science, Chapman & Hall CRC 200718. ^ Aksoy, H. (2000) "Use of Gamma Distribution in Hydrological Analysis"(.tr/engineering/issues/muh-00-24-6/muh-24-6-7-9909-13.pdf), Turk J. Engin Environ Sci, 24, 419– 428.19. ^ J. G. Robson and J. B. Troy, "Nature of the maintained discharge of Q, X, and Y retinal ganglion cells of the cat," J.Opt. Soc. Am. A 4, 2301-2307 (1987)20. ^ N. Friedman, L. Cai and X. S. Xie (2006) "Linking stochastic dynamics to population distribution: An analytical frameworkof gene expression," Phys. Rev. Lett. 97, 168302.ReferencesR. V. Hogg and A. T. Craig (1978) Introduction to Mathematical Statistics, 4th edition. New York: Macmillan.(See Section 3.3.)'P. G. Moschopoulos (1985) The distribution of the sum of independent gamma random variables, Annals of the Institute of Statistical Mathematics, 37, 541-544A. M. Mathai (1982) Storage capacity of a dam with gamma type inputs, Annals of the Institute ofStatistical Mathematics, 34, 591-597External linksHazewinkel, Michiel, ed. (2001), "Gamma-distribution" (/index.php?title=p/g043300), Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4Weisstein, Eric W., "Gamma distribution (/GammaDistribution.html)", MathWorld.Engineering Statistics Handbook (/div898/handbook/eda/section3/eda366b.htm) Retrieved from "/w/index.php?title=Gamma_distribution&oldid=559307728"Categories: Continuous distributions Factorial and binomial topics Conjugate prior distributionsExponential family distributions Infinitely divisible probability distributionsThis page was last modified on 1 July 2013 at 20:51.Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy.Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.。

南开大学——牛津大学生命科学学术研讨吴卫辉(南开大学生命科学学院，天津300071)为推动“双一流”建设和国际化进程，南开大学 对标世界一流，精准施策发力，促进交叉融合，打造 学科高地，积极提升教学科研水平，不断拓展国际学 术交流合作。

自2018年8月以来，南开大学与英国 牛津大学达成合作意向，积极磋商探讨合作领域并 达成共识。

2019年6月1丨~13日，双方在南开大学生命科 学学院举办南开大学——牛津大学生命科学学术研 讨会。

会议开幕仪式上，南开大学校长曹雪涛与牛津 大学纳菲尔德医学院院长理查德•约翰•科纳尔共同 签署合作备忘录，双方将在学生联合培养、学术科研 交流合作、共建联合研究机构等领域，深入拓展、夯 实战略合作伙伴关系，开启国际学术交流合作的新 模式。

曹雪涛校长在开幕式致辞中指出，南开大学建 校之初心就是要面向世界，融汇中西,“知中国，服务 中国”。

张伯苓老校长曾提出“务使我南开学校，能与 英国之牛津、剑桥，美国之哈佛、耶鲁并驾齐驱，东西 称盛”的宏愿。

发展需要结伴而行，在迎接百年校庆、开启新百年征程之际，与牛津大学及其纳菲尔德医 学院这样世界级的顶尖伙伴达成合作，将加快推动 南开大学“双一流”建设和国际化进程，具有战略性 意义。

我们期待通过双方共同努力，在生命科学、医学、药学及统计与数据科学等领域进行学科交叉、创 新探索，并希望在更多学科领域开展全面深入合作，解决科研难点，培养优秀人才，产出更多成果，造福 社会。

理查德•约翰•科纳尔院长表示，牛津大学非常 重视与南开大学的合作，此次合作也是牛津大学纳 菲尔德医学院推动全球化战略的重要举措。

伙伴在于分享“难题”，我们如今生活在一个超乎传统认知的 时代，医学及生命科学面临着生存环境快速变化、生 物技术掀起变革、人口老龄化问题日益凸显等众多挑 战。

我们希望与南开大学一道，通过合作凝聚合力，共 同致力于教学科研,为师生搭建创新平台，破解人类 健康的众多奥秘和亟待解决的科学问题，对世界范 围内的医学及生命科学等领域产生深远影响。

THE RISE OF GRAPHENEA.K. Geim and K.S. NovoselovManchester Centre for Mesoscience and Nanotechnology,University of Manchester, Oxford Road M13 9PL, United KingdomGraphene is a rapidly rising star on the horizon of materials science and condensed matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of “relativistic” condensed matter physics, where quantum relativistic phenomena, some of which are unobservable in high energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.Graphene is the name given to a flat monolayer of carbon atoms tightly packed into a two-dimensional (2D) honeycomb lattice, and is a basic building block for graphitic materials of all other dimensionalities (Figure 1). It can be wrapped up into 0D fullerenes, rolled into 1D nanotubes or stacked into 3D graphite. Theoretically, graphene (or “2D graphite”) has been studied for sixty years1-3 and widely used for describing properties of various carbon-based materials. Forty years later, it was realized that graphene also provides an excellent condensed-matter analogue of (2+1)-dimensional quantum electrodynamics4-6, which propelled graphene into a thriving theoretical toy model. On the other hand, although known as integral part of 3D materials, graphene was presumed not to exist in the free state, being described as an “academic” material5 and believed to be unstable with respect to the formation of curved structures such as soot, fullerenes and nanotubes. All of a sudden, the vintage model turned into reality, when free-standing graphene was unexpectedly found three years ago7,8 and, especially, when the follow-up experiments9,10 confirmed that its charge carriers were indeed massless Dirac fermions. So, the graphene “gold rush” has begun.MATERIALS THAT SHOULD NOT EXISTMore than 70 years ago, Landau and Peierls argued that strictly two-dimensional (2D) crystals were thermodynamically unstable and could not exist11,12. Their theory pointed out that a divergent contribution of thermal fluctuations in low-dimensional crystal lattices should lead to such displacements of atoms that they become comparable to interatomic distances at any finite temperature13. The argument was later extended by Mermin14 and is strongly supported by a whole omnibus of experimental observations. Indeed, the melting temperature of thin films rapidly decreases with decreasing thickness, and they become unstable (segregate into islands or decompose) at a thickness of, typically, dozens of atomic layers15,16. For this reason, atomic monolayers have so far been known only as an integral part of larger 3D structures, usually grown epitaxially on top of monocrystals with matching crystal lattices15,16. Without such a 3D base, 2D materials were presumed not to exist until 2004, when the common wisdom was flaunted by the experimental discovery of graphene7 and other free-standing 2D atomic crystals (for example, single-layer boron nitride and half-layer BSCCO)8. These crystals could be obtained on top of non-crystalline substrates8-10, in liquid suspension7,17 and as suspended membranes18.Importantly, the 2D crystals were found not only to be continuous but to exhibit high crystal quality7-10,17,18. The latter is most obvious for the case of graphene, in which charge carriers can travel thousands interatomic distances without scattering7-10. With the benefit of hindsight, the existence of such one-atom-thick crystals can be reconciled with theory. Indeed, it can be argued that the obtained 2D crystallites are quenched in a metastable state because they are extracted from 3D materials, whereas their small size (<<1mm) and strong interatomic bonds assure that thermal fluctuations cannot lead to the generation of dislocations or other crystal defects even at elevated temperature13,14.Figure 1. Mother of all graphitic forms. Graphene is a 2D building material for carbon materials of all other dimensionalities. It can be wrapped up into 0D buckyballs, rolled into 1D nanotubes or stacked into 3D graphite.A complementary viewpoint is that the extracted 2D crystals become intrinsically stable by gentle crumpling in the third dimension on a lateral scale of ≈10nm 18,19. Such 3D warping observed experimentally 18 leads to a gain in elastic energy but suppresses thermal vibrations (anomalously large in 2D), which above a certain temperature can minimize the total free energy 19.BRIEF HISTORY OF GRAPHENEBefore reviewing the earlier work on graphene, it is useful to define what 2D crystals are. Obviously, a single atomic plane is a 2D crystal, whereas 100 layers should be considered as a thin film of a 3D material. But how many layers are needed to make a 3D structure? For the case of graphene, the situation has recently become reasonably clear. It was shown that the electronic structure rapidly evolves with the number of layers, approaching the 3D limit of graphite already at 10 layers 20. Moreover, only graphene and, to a good approximation, its bilayer have simple electronic spectra: they are both zero-gap semiconductors (can also be referred to as zero-overlap semimetals) with one type of electrons and one type of holes. For 3 and more layers, the spectra become increasingly complicated: Several charge carriers appear 7,21, and the conduction and valence bands start notably overlapping 7,20. This allows one to distinguish between single-, double- and few- (3 to <10) layer graphene as three different types of 2D crystals (“graphenes”). Thicker structures should be considered, to all intents and purposes, as thin films of graphite. From the experimental point of view, such a definition is also sensible. The screening length in graphite is only ≈5Å (that is, less than 2 layers in thickness)21 and, hence, one must differentiate between the surface and the bulk even for films as thin as 5 layers.21,22Earlier attempts to isolate graphene concentrated on chemical exfoliation. To this end, bulk graphite was first intercalated (to stage I)23so that graphene planes became separated by layers of intervening atoms or molecules.This usually resulted in new 3D materials23. However, in certain cases, large molecules could be inserted between atomic planes, providing greater separation such that the resulting compounds could be considered as isolated graphene layers embedded in a 3D matrix. Furthermore, one can often get rid of intercalating molecules in a chemical reaction to obtain a sludge consisting of restacked and scrolled graphene sheets24-26. Because of its uncontrollable character, graphitic sludge has so far attracted only limited interest.There have also been a small number of attempts to grow graphene. The same approach as generally used for growth of carbon nanotubes so far allowed graphite films only thicker than ≈100 layers27. On the other hand, single- and few-layer graphene have been grown epitaxially by chemical vapour deposition of hydrocarbons on metal substrates28,29 and by thermal decomposition of SiC30-34. Such films were studied by surface science techniques, and their quality and continuity remained unknown. Only lately, few-layer graphene obtained on SiC was characterized with respect to its electronic properties, revealing high-mobility charge carriers32,33. Epitaxial growth of graphene offers probably the only viable route towards electronic applications and, with so much at stake, a rapid progress in this direction is expected. The approach that seems promising but has not been attempted yet is the use of the previously demonstrated epitaxy on catalytic surfaces28,29 (such as Ni or Pt) followed by the deposition of an insulating support on top of graphene and chemical removal of the primary metallic substrate.THE ART OF GRAPHITE DRAWINGIn the absence of quality graphene wafers, most experimental groups are currently using samples obtained by micromechanical cleavage of bulk graphite, the same technique that allowed the isolation of graphene for the first time7,8. After fine-tuning, the technique8 now provides high-quality graphene crystallites up to 100 µm in size, which is sufficient for most research purposes (see Figure 2). Superficially, the technique looks as nothing more sophisticated than drawing by a piece of graphite8 or its repeated peeling with adhesive tape7 until the thinnest flakes are found. A similar approach was tried by other groups (earlier35 and independently22,36) but only graphite flakes 20 to 100 layers thick were found. The problem is that graphene crystallites left on a substrate are extremely rare and hidden in a “haystack” of thousands thick (graphite) flakes. So, even if one were deliberately searching for graphene by using modern techniques for studying atomically thin materials, it would be impossible to find those several micron-size crystallites dispersed over, typically, a 1-cm2 area. For example, scanning-probe microscopy has too low throughput to search for graphene, whereas scanning electron microscopy is unsuitable because of the absence of clear signatures for the number of atomic layers.The critical ingredient for success was the observation7,8 that graphene becomes visible in an optical microscope if placed on top of a Si wafer with a carefully chosen thickness of SiO2, owing to a feeble interference-like contrast with respect to an empty wafer. If not for this simple yet effective way to scan substrates in search of graphene crystallites, they would probably remain undiscovered today. Indeed, even knowing the exact recipe7,8, it requires special care and perseverance to find graphene. For example, only a 5% difference in SiO2 thickness (315 nm instead of the current standard of 300 nm) can make single-layer graphene completely invisible. Careful selection of the initial graphite material (so that it has largest possible grains) and the use of freshly -cleaved and -cleaned surfaces of graphite and SiO2 can also make all the difference. Note that graphene was recently37,38 found to have a clear signature in Raman microscopy, which makes this technique useful for quick thickness inspection, even though potential crystallites still have to be first hunted for in an optical microscope.Similar stories could be told about other 2D crystals (particularly, dichalcogenides monolayers) where many attempts were made to split these strongly layered materials into individual planes39,40. However, the crucial step of isolating monolayers to assess their properties individually was never achieved. Now, by using the same approach as demonstrated for graphene, it is possible to investigate potentially hundreds of different 2D crystals8 in search of new phenomena and applications.FERMIONS GO BALLISTICAlthough there is a whole class of new 2D materials, all experimental and theoretical efforts have so far focused on graphene, somehow ignoring the existence of other 2D crystals. It remains to be seen whether this bias is justified but the primary reason for it is clear: It is the exceptional electronic quality exhibited by the isolated graphene crystallites7-10. From experience, people know that high-quality samples always yield new physics, and this understanding has played a major role in focusing attention on graphene.Figure 2. One-atom-thick single crystals: the thinnest material you will ever see. a, Graphene visualized by atomic-force microscopy (adapted from ref. 8). The folded region exhibiting a relative height of ≈4Å clearly indicates that it is a single layer. b, A graphene sheet freely suspended on a micron-size metallic scaffold. The transmission-electron-microscopy image is adapted from ref. 18. c, scanning-electron micrograph of a relatively large graphene crystal, which shows that most of the crystal’s faces are zigzag and armchair edges as indicated by blue and red lines and illustrated in the inset (T.J. Booth, K.S.N, P. Blake & A.K.G. unpublished). 1D transport along zigzag edges and edge-related magnetism are expected to attract significant attention.Graphene’s quality clearly reveals itself in a pronounced ambipolar electric field effect (Fig. 3a) such that charge carriers can be tuned continuously between electrons and holes in concentrations n as high as 1013cm-2 and their mobilities µ can exceed 15,000 cm2/Vs even under ambient conditions7-10. Moreover, the observed mobilities weakly depend on temperature T, which means that µ at 300K is still limited by impurity scattering and, therefore, can be improved significantly, perhaps, even up to ≈100,000 cm2/Vs. Although some semiconductors exhibit room-temperature µ as high as ≈77,000 cm2/Vs (namely, InSb), those values are quoted for undoped bulk semiconductors. In graphene, µ remains high even at high n (>1012cm-2) in both electrically- and chemically- doped devices41, which translates into ballistic transport on submicron scale (up to ≈0.3 µm at 300K). A further indication of the system’s extreme electronic quality is the quantum Hall effect (QHE) that can be observed in graphene even at room temperature (Fig. 3b), extending the previous temperature range for the QHE by a factor of 10.An equally important reason for the interest in graphene is a unique nature of its charge carriers. In condensed matter physics, the Schrödinger equation rules the world, usually being quite sufficient to describe electronic properties of materials. Graphene is an exception: Its charge carriers mimic relativistic particles and are easier and more natural to describe starting with the Dirac equation rather than the Schrödinger equation4-6,42-47. Although there is nothing particularly relativistic about electrons moving around carbon atoms, their interaction with a periodic potential of graphene’s honeycomb lattice gives rise to new quasiparticles that at low energies EFigure 3. Ballistic electron transport in graphene. a , Ambipolar electric field effect in single-layer graphene. The insets show its conical low-energy spectrum E (k ), indicating changes in the position of the Fermi energy E F with changing gate voltage V g . Positive (negative) V g induce electrons (holes) in concentrations n =αV g where the coefficient α ≈7.2⋅1010cm -2/V for field-effect devices with a 300 nm SiO 2 layer used as a dielectric 7-9. The rapid decrease in resistivity ρwith adding charge carriers indicates their high mobility (in this case, µ ≈5,000cm 2/Vs and does not noticeably change with temperature up to 300K). b , Room-temperature quantum Hall effect (K.S.N., Z. Jiang, Y. Zhang, S.V. Morozov, H.L. Stormer, U. Zeitler,J.C. Maan, G.S. Boebinger, P. Kim & A.K.G. Science 2007, in the press). Because quasiparticles in graphene are massless and also exhibit little scattering even under ambient conditions, the QHE survives up to room T . Shown in red is the Hall conductivity σxy that exhibits clear plateaux at 2e 2/h for both electrons and holes. The longitudinal conductivity ρxx (blue) reaches zero at the same gate voltages. The inset illustrates the quantized spectrum of graphene where the largest cyclotron gap is described by δE (K)≈420⋅B (T). are accurately described by the (2+1)-dimensionalDirac equation with an effective speed of lightv F ≈106m/s. These quasiparticles, called masslessDirac fermions, can be seen as electrons that losttheir rest mass m 0 or as neutrinos that acquired theelectron charge e . The relativistic-like descriptionof electron waves on honeycomb lattices has beenknown theoretically for many years, never failingto attract attention, and the experimental discoveryof graphene now provides a way to probe quantumelectrodynamics (QED) phenomena by measuringgraphene’s electronic properties.QED IN A PENCIL TRACEFrom the point of view of its electronic properties,graphene is a zero-gap semiconductor, in whichlow-E quasiparticles within each valley canformally be described by the Dirac-likeHamiltoniank v ik k ik k v H F y x y x F r r h h ⋅=⎟⎟⎠⎞⎜⎜⎝⎛+−=σ00ˆwhere k r is the quasiparticle momentum, σr the2D Pauli matrix and the k -independent Fermivelocity v F plays the role of the speed of light. TheDirac equation is a direct consequence ofgraphene’s crystal symmetry. Its honeycomblattice is made up of two equivalent carbonsublattices A and B , and cosine-like energy bandsassociated with the sublattices intersect at zero Enear the edges of the Brillouin zone, giving rise toconical sections of the energy spectrum for |E | <1eV (Fig. 3).We emphasize that the linear spectrumk v E F h = is not the only essential feature of the band structure. Indeed, electronic states near zeroE (where the bands intersect) are composed ofstates belonging to the different sublattices, andtheir relative contributions in quasiparticles’make-up have to be taken into account by, forexample, using two-component wavefunctions(spinors). This requires an index to indicatesublattices A and B , which is similar to the spinindex (up and down) in QED and, therefore, isreferred to as pseudospin. Accordingly, in theformal description of graphene’s quasiparticles bythe Dirac-like Hamiltonian above, σr refers topseudospin rather than the real spin of electrons(the latter must be described by additional terms inthe Hamiltonian). Importantly, QED-specificphenomena are often inversely proportional to thespeed of light c and, therefore, enhanced ingraphene by a factor c /v F ≈300. In particular, thisρ(kΩ)n(1012 cm-2)σ(4e2/h)277321−21+23255-82-2-4-664Vg(V)σ2EDEdecEFigure 4. Chiral quantum Hall effects.a, The hallmark of massless Dirac fermions is QHE plateaux in σxy at half integers of 4e2/h (adapted from ref. 9). b, Anomalous QHE for massive Dirac fermions in bilayer graphene is more subtle (red curve55): σxy exhibits the standard QHE sequence with plateaux at all integer N of 4e2/h except for N=0. The missing plateau is indicated by the red arrow. The zero-N plateau can be recovered after chemical doping, which shifts the neutrality point to high V g so that an asymmetry gap (≈0.1eV in this case) is opened by the electric field effect (green curve; adapted from ref.59). c-e, Different types of Landau quantization in graphene. The sequence of Landau levels in the density of states D isdescribed by NEN∝ for massless Dirac fermions in single-layer graphene (c) and by )1(−∝NNENfor massive Dirac fermions in bilayer graphene (d). The standard LL sequence )(21+∝NENis expected to recover if an electronic gap is opened in the bilayer (e).means that pseudospin-related effects should generally dominate those due to the real spin.By analogy with QED, one can also introduce a quantity called chirality6 that is formally a projection of σr on the direction of motion kr and is positive (negative) for electrons (holes). In essence, chirality in graphene signifies the fact that k electron and -k hole states are intricately connected by originating from the same carbon sublattices. The concepts of chirality and pseudospin are important because many electronic processes in graphene can be understood as due to conservation of these quantities.6,42-47It is interesting to note that in some narrow-gap 3D semiconductors, the gap can be closed by compositional changes or by applying high pressure. Generally, zero gap does not necessitate Dirac fermions (that imply conjugated electron and hole states) but, in some cases, they may appear5. The difficulties of tuning the gap to zero, while keeping carrier mobilities high, the lack of possibility to control electronic properties of 3D materials by the electric field effect and, generally, less pronounced quantum effects in 3D limited studies of such semiconductors mostly to measuring the concentration dependence of their effective masses m (for a review, see ref. 48). It is tempting to have a fresh look at zero-gap bulk semiconductors, especially because Dirac fermions were recently reported even in such a well-studied (small-overlap) 3D material as graphite.49,50CHIRAL QUANTUM HALL EFFECTSAt this early stage, the main experimental efforts have been focused on electronic properties of graphene, trying to understand the consequences of its QED-like spectrum. Among the most spectacular phenomena reported so far, there are two new (“chiral”) quantum Hall effects, minimum quantum conductivity in the limit of vanishing concentrations of charge carriers and strong suppression of quantum interference effects.Figure 4 shows three types of the QHE behaviour observed in graphene. The first one is a relativistic analogue of the integer QHE and characteristic to single-layer graphene9,10. It shows up as an uninterrupted ladder of equidistant steps in Hall conductivity σxy which persists through the neutrality (Dirac) point, where charge carriers change from electrons to holes (Fig. 4a). The sequence is shifted with respect to the standard QHE sequence by ½, so that σxy= ±4e2/h(N + ½) where N is the Landau level (LL) index and factor 4 appears due to double valley and double spin degeneracy. This QHE has been dubbed “half-integer” to reflect both the shift and the fact that, although it is not a new fractional QHE, it is not the standard integer QHE either. The unusual sequence is now well understood as arising due to the QED-like quantization of graphene’s electronic spectrumin magnetic field B , which is described 44,51-53 by BN e v E F N h 2±= where sign ± refers to electrons and holes. The existence of a quantized level at zero E , which is shared by electrons and holes (Fig. 4c), is essentially everything one needs to know to explain the anomalous QHE sequence.51-55 An alternative explanation for the half-integer QHE is to invoke the coupling between pseudospin and orbital motion, which gives rise to a geometrical phase of π accumulated along cyclotron trajectories and often referred to as Berry’s phase.9,10,56 The additional phase leads to a π-shift in the phase of quantum oscillations and, in the QHE limit, to a half-step shift. Bilayer graphene exhibits an equally anomalous QHE (Fig 4b)55. Experimentally, it shows up less spectacular: One measures the standard sequence of Hall plateaux σxy = ±N 4e 2/h but the very first plateau at N =0 is missing, which also implies that bilayer graphene remains metallic at the neutrality point.55 The origin of this anomaly lies in a rather bizarre nature of quasiparticles in bilayer graphene, which are described 57 by⎟⎟⎠⎞⎜⎜⎝⎛+−−=0)()(02ˆ222y x y x ik k ik k m H h This Hamiltonian combines the off-diagonal structure, similar to the Dirac equation, with Schrödinger-like terms m p2ˆ2. The resulting quasiparticles are chiral, similar to massless Dirac fermions, but have a finite mass m ≈0.05m 0. Such massive chiral particles would be an oxymoron in relativistic quantum theory. The Landau quantization of “massive Dirac fermions” is given 57 by )1(−±=N N E c N ωh with two degenerate levels N =0 and 1 at zero E (c ω is the cyclotron frequency). This additional degeneracy leads to the missing zero-E plateau and the double-height step in Fig. 4b. There is also a pseudospin associated with massive Dirac fermions, and its orbital rotation leads to a geometrical phase of 2π. This phase is indistinguishable from zero in the quasiclassical limit (N >>1) but reveals itself in the double degeneracy of the zero-E LL (Fig. 4d).55It is interesting that the “standard” QHE with all the plateaux present can be recovered in bilayer graphene by the electric field effect (Fig. 4b). Indeed, gate voltage not only changes n but simultaneously induces an asymmetry between the two graphene layers, which results in a semiconducting gap 58,59. The electric-field-induced gap eliminates the additional degeneracy of the zero-E LL and leads to the uninterrupted QHE sequence by splitting the double step into two (Fig. 4e)58,59. However, to observe this splitting in the QHE measurements, one needs to probe the region near the neutrality point at finite V g , which can be achieved by additional chemical doping 59. Note that bilayer graphene is the only known material in which the electronic band structure changes significantly by the electric field effect and the semiconducting gap ∆E can be tuned continuously from zero to ≈0.3eV if SiO 2 is used as a dielectric.CONDUCTIVITY “WITHOUT” CHARGE CARRIERSAnother important observation is that graphene’s zero-field conductivity σ does not disappear in the limit of vanishing n but instead exhibits values close to the conductivity quantum e 2/h per carrier type 9. Figure 5 shows the lowest conductivity σmin measured near the neutrality point for nearly 50 single-layer devices. For all other known materials, such a low conductivity unavoidably leads to a metal-insulator transition at low T but no sign of the transition has been observed in graphene down to liquid-helium T . Moreover, although it is the persistence of the metallic state with σ of the order of e 2/h that is most exceptional and counterintuitive, a relatively small spread of the observed conductivity values (see Fig. 5) also allows one to speculate about the quantization of σmin . We emphasize that it is the resistivity (conductivity) that is quantized in graphene, in contrast to the resistance (conductance) quantization known in many other transport phenomena.Minimum quantum conductivity has been predicted for Dirac fermions by a number of theories 5,44,45,47,60-64. Some of them rely on a vanishing density of states at zero E for the linear 2D spectrum. However, comparison between the experimental behaviour of massless and massive Dirac fermions in graphene and its bilayer allows one to distinguish between chirality- and masslessness- related effects. To this end, bilayer graphene also exhibits a minimum conductivity of the order of e 2/h per carrier type,55,65 which indicates that it is chirality, rather than the linear spectrum, that is more important. Most theories suggest σmin =4e 2/h π, which is of about π times smaller than the typical values observed experimentally. One can see in Fig. 5 that the experimental data do not approach this theoretical value and mostly cluster around σmin =4e 2/h (except for one low-µ sample that is rather unusual by also exhibiting 100%-normal weak localization behaviour at high n ; see below). This disagreement has become known as “the mystery of a missing pie”, and it remains unclear whether it is due toσm i n (4e 2/h )11/µ(cm 2/Vs)012,0004,0008,0000Figure 5. Minimum conductivity of graphene.Independent of their carrier mobility µ, different graphene devices exhibited approximately the same conductivity at the neutrality point (open circles) with most data clusteringaround ≈4e 2/h indicated for clarity by the dashed line (A.K.G. & K.S.N. unpublished; includes the published datapoints from ref. 9). The high-conductivity tail is attributed to macroscopic inhomogeneity: by improving samples’ homogeneity, σmin generally decreases, moving closer to ≈4e 2/h . The green arrow and symbols show one of the devices that initially exhibited an anomalously large value of σmin but after thermal annealing at 400K its σmin moved closer to the rest of the statistical ensemble. Most of thedata are taken in the bend resistance geometry where themacroscopic inhomogeneity plays the least role.theoretical approximations about electron scatteringin graphene or because the experiments probed onlya limited range of possible sample parameters (e.g., length-to-width ratios 47). To this end, note that close to the neutrality point (n ≤1011cm -2) graphene islikely to conduct as a random network of electronand hole puddles (A.K.G. & K.S.N . unpublished).Such microscopic inhomogeneity is probablyinherent to graphene (because of graphene sheet’swarping/rippling)18,66 but so far has not been taken into account by theory. Furthermore, macroscopicinhomogeneity (on the scale larger than the meanfree path l ) also plays an important role in measurements of σmin . The latter inhomogeneity canexplain a high-σ tail in the data scatter in Fig. 5 by the fact that σ reached its lowest values at slightly different V g in different parts of a sample, whichyields effectively higher values of experimentally measured σmin .WEAK LOCALIZATION IN SHORT SUPPLYAt low temperatures, all metallic systems with high resistivity should inevitably exhibit large quantum-interference (localization) magnetoresistance,eventually leading to the metal-insulator transition at σ ≈e 2/h . Until now, such behaviour has been absolutely universal but it was found missing in graphene. Even near the neutrality point, no significant low-field (B <1T) magnetoresistance has been observed down to liquid-helium temperatures 66 and, although sub-100 nm Hall crosses did exhibit giant resistance fluctuations (S.V. Morozov, K.S.N., A.K.G. et al , unpublished), those could be attributed to changes in the distribution of electron and holepuddles and size quantization. It remains to be seen whether localization effects at the Dirac point recover at lower T , as the phase-breaking length becomes increasingly longer,67 or the observed behaviour indicates a “marginal Fermi liquid”68,43, in which the phase-breaking length goes to zero with decreasing E . Further experimental studies are much needed in this regime but it is difficult to probe because of microscopic inhomogeneity.Away from the Dirac point (where graphene becomes a good metal), the situation has recently become reasonably clear. Universal conductance fluctuations (UCF) were reported to be qualitatively normal in this regime, whereas weak localization (WL) magnetoresistance was found to be somewhat random, varying for different samples from being virtually absent to showing the standard behaviour 66. On the other hand, early theories had also predicted every possible type of WL magnetoresistance in graphene, from positive to negative to zero. Now it is understood that, for large n and in the absence of inter-valley scattering, there should be no magnetoresistance, because the triangular warping of graphene’s Fermi surface destroys time-reversal symmetry within each valley.69 With increasing inter-valley scattering, the normal (negative) WL should recover. Changes in inter-valley scattering rates by, for example, varying microfabrication procedures can explain the observed sample-dependent behaviour. A complementary explanation is that a sufficient inter-valley scattering is already present in the studied samples but the time-reversal symmetry is destroyed by elastic strain due to microscopic warping 66,70. The strain in graphene has turned out to be equivalent to a random magnetic field, which also destroys time-reversal symmetry and suppresses WL. Whatever the mechanism, theory expects (approximately 71) normal UCF at high n , in agreement with the experiment 66.。

高分子物理常见名词Θ溶剂(Θ solvent)：链段-溶剂相互吸引刚好抵消链段间空间排斥的溶剂，形成高分子溶液时观察不到远程作用，该溶剂中的高分子链的行为同无扰链Θ温度(Θ temperature)：溶剂表现出Θ溶剂性质的温度Argon理论(Argon theory)：一种银纹扩展过程的模型，描述了分子链被伸展将聚合物材料空化的过程Avrami方程(Avrami equation)：描述物质结晶转化率与时间关系的方程：Kt-α，α为转化率，K与n称Avrami常数(Avrami constants) =-1n)exp(Bingham流体(Bingham liquid)：此类流体具有一个屈服应力σy，应力低于σy时不产生形变，当应力大于σy时才发生流动，应力高于σy的部分与应变速率呈线性关系Boltzmann叠加原理(Blotzmann superposition principle)：Boltzmann提出的粘弹性原理：认为样品在不同时刻对应力或应变的响应各自独立并可线性叠加Bravais晶格(Bravais lattice)：结构单元在空间的排列方式Burger's模型(Burger's model)：由一个Maxwell模型和一个Kelvin模型串联构成的粘弹性模型Cauchy应变(Cauchy strain)：拉伸引起的相对于样品初始长度的形变分数，又称工程应变Charpy冲击测试(Charpy impact test)：样品以简支梁形式放置的冲击强度测试，测量样品单位截面积的冲击能Considère构图(Considère construction)：以真应力对工程应作图以判定细颈稳定性的方法Eyring模型(Eyring model)：一种描述材料形变过程的分子模型，认为形变是结构单元越过能垒的跳跃式运动Flory-Huggins参数(Flory-Huggins interaction parameter)：描述聚合物链段与溶剂分子间相互作用的参数，常用χ表示，物理意义为一个溶质分子被放入溶剂中作用能变化与动能之比2.11.2Flory构图(Flory construction)：保持固定拉伸比所需的力f对实验温度作图得到，由截距确定内能对拉伸力的贡献，由斜率确定熵对拉伸力的贡献Flory特征比(characteristic ratio)：无扰链均方末端距与自由连接链均方末端距的比值Griffith理论(Griffith theory)：一种描述材料断裂机理的理论，认为断裂是吸收外界能量产生新表面的过程Hencky应变(Hencky strain)：拉伸引起的相对于样品形变分数积分，又称真应变Hermans取向因子(Hermans orientation factor)：描述结构单元取向程度的参数，是结构单元与参考方向夹角余弦均方值的函数Hoffman-Weeks作图法(Hoffman-Weeks plot)：一种确定平衡熔点的方法。

生物英语测试题及答案一、选择题（每题2分，共20分）1. Which of the following is not a characteristic of living organisms?A. Cellular structureB. Metabolic processesC. Response to stimuliD. Inability to grow答案：D2. What is the basic unit of all living organisms?A. MoleculesB. AtomsC. CellsD. Organs答案：C3. Which of the following is not a process involved in cellular respiration?A. GlycolysisB. Krebs cycleC. PhotosynthesisD. Electron transport chain答案：C4. What is the term for the flow of genetic information from DNA to RNA to protein?A. Central dogmaB. Genetic codeC. TranscriptionD. Translation答案：A5. Which of the following is not a type of biomolecule?A. CarbohydratesB. LipidsC. ProteinsD. Plastics答案：D6. What is the primary function of chlorophyll in plants?A. To provide structural supportB. To store energyC. To absorb light for photosynthesisD. To transport water答案：C7. What is the term for the process by which an organism develops from a fertilized egg?A. ReproductionB. GrowthC. DevelopmentD. Metamorphosis答案：C8. Which of the following is not a type of symbiotic relationship?A. MutualismB. CommensalismC. ParasitismD. Competition答案：D9. What is the term for a group of similar cells that work together to perform a specific function?A. TissueB. OrganC. OrganelleD. System答案：A10. Which of the following is not a characteristic of eukaryotic cells?A. Presence of a nucleusB. Presence of membrane-bound organellesC. Lack of a cell wallD. Prokaryotic DNA答案：D二、填空题（每题2分，共20分）11. The process by which organisms inherit traits from their parents is called _______.答案：Inheritance12. The study of the relationships between organisms and their environment is known as _______.答案：Ecology13. In genetics, the term _______ refers to the complete set of genetic information in an organism.答案：Genome14. The process of an organism becoming less active or entering a state of rest during periods of unfavorable conditions is called _______.答案：Dormancy15. The term _______ is used to describe the variation in traits among individuals of a species.16. The scientific method involves making observations, forming hypotheses, and then _______.答案：Experimentation17. The process by which an organism's cells divide to produce two identical cells is called _______.答案：Cell division18. The study of the structure and function of living organisms at the molecular and cellular level is known as _______.答案：Molecular biology19. The term _______ is used to describe the process by which new species evolve from existing ones.答案：Speciation20. The process by which organisms obtain energy by breaking down organic molecules is called _______.三、简答题（每题10分，共30分）21. Explain the difference between mitosis and meiosis.答案：Mitosis is a type of cell division that results in two daughter cells that are genetically identical to the parent cell, and it is the process by which the body grows and replaces old cells. Meiosis, on the other hand, is a type of cell division that results in four daughter cells that are genetically unique from the parent cell and each other, and it is the process by which gametes (sperm and egg cells) are produced for sexual reproduction.22. Describe the role of DNA in the cell.答案：DNA (deoxyribonucleic acid) is the molecule that carries the genetic instructions used in the growth, development, functioning, and reproduction of all known living organisms and many viruses. It is the primary genetic material of cells and is organized into structures called chromosomes. DNA contains the instructions needed for an organism to develop, survive, and reproduce. It is also the means by which genetic information is passed from one generation to the next.23. What are the main differences between prokaryotic and eukaryotic cells?答案：Prokaryotic cells are simpler and lack a nucleus and membrane-bound organelles. They are generally smaller than eukaryotic cells and include bacteria and archaea. Eukaryotic cells, which include plants, animals, fungi, and protists, have a nucleus and other membrane-bound organelles such as mitochondria and chloroplasts. Eukaryotic cells are generally larger and more complex than prokaryotic cells.四、论述题（每题15分，共30分）24. Discuss the importance of biodiversity and the threats it faces.答案：Biodiversity is crucial for the health of ecosystems as it allows for a variety of species to interact and support each other, which can lead to a more stable and productive environment. It also provides a wide range of resources and services for human use, such as food, medicine, and materials. Biodiversity faces threats from habitat destruction, climate change, pollution, overexploitation, and the introduction of invasive species. These threats can lead to the loss of species and a reduction in ecosystem services, which can have significant impacts on human well-being and the planet's health.25. Explain the concept of natural selection and how it contributes to evolution.答案：Natural selection is the process by which organisms with traits that are better suited to their environment are more likely to survive and reproduce. Over time, this leads to an increase in the frequency of these advantageous traits in the population, which can result in the evolution of new species. Charles Darwin's theory of natural selection is a fundamental concept in evolutionary biology and explains how species change over time in response to environmental pressures. It is a key mechanism by which evolution occurs, leading to the diversity of life we see today.。