Positivity of Chern Classes for Reflexive Sheaves on P^N

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学术英语(第二版)综合教师手册unit3

Unit 3 Business EthicsI Teaching ObjectivesAfter learning Unit 3, students (Ss) are expected to develop the following academic skills and knowledge:II Teaching Activities and ResourcesReadingText ALead-inTeaching StepsAsk Ss to work in groups and complete the task in Lead-in. Then choose some groups to share their answers with the whole class.Answer Keys (Suggested Answers)1.Corporate Social Responsibility (CSR) can be defined as a self-regulatingbusiness model that helps a company be socially accountable —to itself, its stakeholders, and the public. In other words, it is the continuing commitment by business to behave ethically and contribute to economic development while improving the quality of life of the workforce and their families as well as of the local community and society at large.2.Text AnalysisTeaching Steps1.OverviewAsk Ss to preview Text A before class. Or, allocate some time for Ss to read the text quickly in class. Then invite several Ss to summarize the main idea of Text A.2.In-Depth Analysis1)Show Ss the following words and ask them to contribute to the class as muchas possible with what they know about these words. Provide additional information in Supplementary Information when necessary.•economic system•free enterprise2)Explain some important language points in Language Support to Ss.3)Discuss with Ss the features of the two versions of Adam Smith’s theory bydoing Task 1 in Critical reading and thinking.4)Organize a group discussion about the questions from Task 2 in Criticalreading and thinking. Encourage Ss to think independently, critically and creatively and share their ideas with each other.Supplementary Information1.economic systemAn economic system is a system for producing, distributing and consuming goods and services, including the combination of the various institutions, agencies, consumers, entities that comprise the economic structure of a given society or community. It also includes how these various agencies and institutions are linked to one another, how information goes between them, and the social relations within the system.Two of the basic and general economic systems are market economy and planned economy. Market economy is an economic system in which businesses and individuals decide what to produce and buy, and the market determines quantities sold and prices, whereas planned economy is an economic system in which decisions regarding production and investment are embodied in a plan formulated by a central authority, usually by a public body such as a government agency.Although a planned economy may be based on either centralized or decentralized forms of economic planning, it usually refers to a centrally planned economy.2.free enterpriseFree enterprise refers to the system of business in which individuals are free to decide what to produce, how to produce, and at what price to sell.Language Support1.Most academics today subscribe to the following modified version of AdamSmith’s theory:…(Para. 2)In the text, the phrase “subscribe to”means “agreeing with or supporting (an opinion, theory, etc.)”（同意；赞成）.e.g. I subscribe to the idea that voting is my civic duty.She subscribes to the theory that some dinosaurs were warm-blooded andothers were cold-blooded.It can also refer to “paying money to get (a publication or service) regularly”（订阅）.e.g. I subscribe to several magazines.We have subscribed to an evening newspaper.2.These constraints take a number of different forms. …Another set ofconstraints …(Para. 3)Two recent examples dramatically illustrate these points. First, …(Para. 3) Classification is employed to organize things into categories with a single organizing principle, and give examples of things that fit into each category. Here are other commonly-used words and expressions for classification:•The first (kind/type/group/class/etc.) …; the second …; the third …•sort, classify, categorize …•category, group, class, kind …3.Saving the financial system required a bailout of the banks and otherfinancial companies, and that bailout imposed huge costs on the taxpayers, and also helped push the economy into a deep recession. (Para. 5)impose sth. on sb.:i) force something on someone把......强加于e.g. He always imposes his opinion on others.ii) levy a tax or duty征税e.g. It is therefore necessary for governments to impose a higher tax on this kindof food.Here is another usage of the word “impose”:impose on sb.:i) force oneself on others强加于人e.g. Thanks for your offer to help, but I did not want to impose on you.ii) take unfair advantage of 利用e.g. Don’t you think you are imposing on your neighbor when you use histelephone for half an hour?4.be true to one’He is always true to his word and focused on the big picture.Ninety days later, true to his word, the goldsmith brought the crown.5.To date, Buffett has contributed more than $6 billion, and over time he isscheduled to contribute additional stock that is now worth in excess of $40 billion. (Para. 7)in excess of: greater than, more than 超过e.g. Luggage in excess of 100 kg will be charged extra.This plane can reach speeds in excess of 1000 kilometers an hour.Answer KeysCritical reading and thinkingTask 1 / Overview1The original version：The invisible hand; Profit maximization; Free enterprise systemThe modified version:the wealth of its stockholders; the best economic system; constraints2Argument 11) a wide range of regulations are imposed2) assessing costs on companies; BP oil spillArgument 21) behave ethically; value and reputation2) Don’t Be Evil3) creative capitalism4) contributed more than $6 billionTask 2 / Points for discussion (Suggested Answers)11) Yes, I agree. Because:• Earning profit is the main aim of every economic activity. A business is an economic activity and hence, its main aim should be to earn profit.• Profit is a measure of eff iciency and economic prosperity of the business. This justifies the concept of profit maximization.• Economic conditions do not remain the same all the time. A business can retain its profit so that it can survive the adverse situations in the future. Profit gives protection against future risks and uncertainties.• Profit is the main source of finance for growth and expansion. Profit is essential for the business in order to invest in new business propositions.• Profitability is essential for fulfilling the social goals of the business. With profit maximization a business can do socio-economic welfare and follow its policies of corporate social responsibility.2) No, I don’t agree. Because:Business should do anything they can to make a profit, but never at the cost of human welfare and natural environment. Human welfare must be considered as important as profit making. A business is successful to the extent that it provides a product that contributes to happiness in all forms. As a matter of fact, the great value of a business should be morally associated with consumer’s satisfaction and safety. On the other hand, businesses of great value should not be blind to their moral obligations of protecting the natural environment.2 Yes, it is a very effective way for society to impose such regulations to prevent companies from engaging in practices that hurt society. For most businesses their ultimate goal is to make profits. It is true that most businessmen try to abide by the laws while making profits. However we have to admit that there are some who use every means to make as much money as possible, even regardless of the interests ofemployees, communities, and environment. Therefore, the regulations such as penalties and suspension for internal rectification should be imposed to deter companies from unlawful practices.3 Yes, having a good reputation with customers, suppliers, employees and regulators is essential if value is to be maximized. Business success is associated with many entities, such as customers, suppliers, employees and regulators. If customers are satisfied with your products and service, they will be loyal to your company. If suppliers provide you with qualified products, your business will operate well. If employees are treated well, they will work very hard and are willing to be part of your company. If regulators are certain that your company acts fairly and follows rules, your company will develop sustainably. All above depends on whether the business is continually operating with society’s interests in mind and maintaining a good reputation.Language building-upAnswer keysTask 1 / Specialized vocabulary11 纳税人2 自由企业制度3 股东4 经济体制5 市场力量；市场调节作用6 金融机构7 stock price 8 mission9 corporate motto 10 assets11 profit maximization 12 financial system21 financial institutions2 free enterprise system3 assets4 Taxpayers5 stockholder6 profit maximization7 economic system 8 market forcesTask 2 / Academic vocabulary1. principal2. dramatically3. academics4. maximization5. framework6. range7. compensate 8. transfer9. inadequate 10. constraintsTask 3 / Collocations1. subscribe to2. striving to3. imposing …on4. go out of business5. as a whole6. engaged in7. go hand in hand with 8. in excess ofTask 4 / Formal English1 insights2 subscribe to3 imposes4 adverse5 mission6 philanthropic7 donated 8 famedTranslation of Text A达到适当的平衡在1776年，亚当·斯密描述了一只“看不见的手”是如何引导企业追求利润的，而这只手会引导企业做出有利于社会的决策。

Shiing-Shen Chern

Shiing-Shen Chern (1911–2004)Shing-Tung Yau is professor of mathemat-ics at Harvard University.HIs email address is yau@.This is the speech given at the Harvard Memorial Conference for S.-S.Chern.geometric intuition will perhaps never be cleared up.…Whatever the truth of the matter,mathe-matics in our century would not have made such impressive progress without the geometric sense ofÉlie Cartan,Heinz Hopf,Chern and a very few more.It seems safe to predict that such men will always be needed if mathematics is to go on as before.”Chern:Father of Global Intrinsic Geometry Both Cartan and Chern saw the importance ofﬁber bundles to problems in diﬀerential geometry.It is certainly true that global diﬀerential geometry was studied by other great mathe-maticians:Cohn-Vossen,Minkowski,Hilbert,and Weyl,among others.However,most of their works focused on global surfaces in three-dimensional Euclidean space.Chern was theﬁrst who succeeded in building a bridge between intrinsic geometry and algebraic topology for manifolds of all dimensions,not just surface.(Cartan’s work in diﬀerential geometry was more local in nature,except his investigation of Lie groups and symmetric spaces.)The theory ofﬁber bundles was his major tool.Reﬂecting on intrinsic geometry,Chern com-mented:“Riemannian geometry and its generaliza-tion in diﬀerential geometry are local in character. It seems a mystery to me that we do need a whole1226Notices of the AMS Volume58,Number9space to piece the neighborhood together.This is achieved by topology.”Equivalence ProblemMost of the works of Chern were related to the problem of equivalence.In1869E.Christoﬀel and R.Lipschitz solved the fundamental problem in Riemannian geometry—the form problem:To determine when two ds2’s dif-fer by a change of coordinates,Christoﬀel introduced covariantdiﬀerentiation,which is now calledthe Levi-Civita connection.Cartan generalized this problem to a much more general setting;it is called the equivalence prob-lem.Given a Lie group G∈GL(n,R),given two sets of linearly indepen-dent linear diﬀerential formsθiandθ∗j in the coordinates x k andx∗l respectively,1≤i,j,k,l≤n,ﬁnd conditions under which thereare functionsx∗i=x∗i(x1,x2,...,x n)such thatθ∗j,after the substitu-tion of these functions,diﬀer fromθi by a transformation of G.This problem involves local invariants.Cartan provided a procedure to generate such invariants. Almost all of the work of Chern is related to this problem.Chern(1932–1943)During the eleven-year period from1932to1943, Chern studied web geometry,projective line geom-etry,invariants of the contact of pairs of subman-ifolds in projective space,and transformations of surfaces related to the Bäcklund transform in soli-ton theory.Chern continued this line of research in his collaborations with Griﬃths and Terng later.Between1940and1942,Chern[5]started to generalize the theory of integral geometry,an area initially developed by Crofton and Blaschke.He ob-served that this theory can best be understood in terms of two homogeneous spaces with the same Lie group G(see also Weil’s review[20]).This leads to the diagram associated to two sub-groups H and K of G:+QQQ Qs GG/H G/KTwo cosets aH and bK are incident to each other if they intersect in G.This notionﬁts nicely in mod-ern investigations of the Funk-Radon problem of determining a function on a manifold in terms of its integrals over certain submanifolds.Although the focus of this work is“classical”integral geom-etry,the doubleﬁbration diagrams depicted above preﬁgure in an uncanny way a diﬀerent,more mod-ern type of integral geometry:the theory of gener-alized Radon transforms developed by Gelfand and Graev in the lateﬁfties and early sixties.Using this approach,Chern generalized many important formulas of Crofton.In1952he[8]also generalized the kinematic formula of Poincaré, Santaló,and Blaschke.On the impact of these generalizations by Chern,Weil commented:“It lifted the whole sub-ject at one stroke to a higher plane than where Blaschke’s school had lifted it.I was impressed by the unusual talent and depth of understanding that shone through it.”Chern’s Visit to Princeton(1943–1945)In1943Chern left Kunming for Princeton.He ar-rived at the moment whenﬁber bundle theory was beginning to evolve from the works of Cartan and Whitney.When he arrived at Princeton,Weil had just pub-lished his work with Allendoerfer on the Gauss-Bonnet formula.Weil directed Chern toward the works of Todd and Eger on“canonical classes”in algebraic geometry.He pointed out to Chern that their work on characteristic classes for complex manifolds had only been completed in the spirit of Italian geometry and rested upon some unproved assumptions.Theﬁrst fundamental work Chern did on global intrinsic geometry was his intrinsic proof of the Gauss-Bonnet formula[6],re-proving the recent work of Allendoerfer and Weil[2]for general closed Riemannian manifolds.The proof of Allendoerfer-Weil rested on the use of local embeddings of the manifold in Euclidean space,isometric for an approximating real analytic metric.(The existence of local isometric embeddings for real analytic metrics had been established earlier by Burstin, Cartan,and Janet.)Weil commented on Chern’s proof of the Gauss-Bonnet formula:“Following the footsteps of H.Weyl and other writers,the latter proof, resting on the consideration of‘tubes’,did de-pend(although this was not apparent at that time) on the construction of a sphere-bundle,but of a nonintrinsic one,viz.the transversal bundle for a given immersion.…Chern’s proof operated ex-plicitly for theﬁrst time with an intrinsic bundle, the bundle of tangent vectors of length one,thus clarifying the whole subject once and for all.”A century earlier,Gauss established the concept of intrinsic geometry.Chern’s proof of Gauss-Bonnet opened up a new horizon.Global topology was now linked with intrinsic geometry through the concept ofﬁber bundle and transgression onOctober2011Notices of the AMS1227the intrinsic tangent sphere bundle.A new era of global intrinsic geometry arrived.While Hopf’s vectorﬁeld theorem had clearly in-ﬂuenced Chern’s thinking,the proof was a tour de force based on Chern’s insights and powerful al-gebraic manipulation.Hopf declared that Chern’s proof had brought diﬀerential geometry into a new era.In particular,it gave rise to the idea of trans-gression.Chern’s proof remains one of the most admired proofs in the modern history of mathe-matics.Chern ClassesReﬂecting upon his early encounter with Chern classes,Chern said:“My introduction to the char-acteristic class was through the Gauss-Bonnet formula,known to every student of surface the-ory.Long before1943,when I gave an intrinsic proof of the n-dimensional Gauss-Bonnet formula, I knew,by using orthonormal frames in surface theory,that the classical Gauss-Bonnet is but a global consequence of the Gauss formula which expresses the‘theorima egregium’.The algebraic aspect of this proof is theﬁrst instance of a con-struction later known as a transgression,which was destined to play a fundamental role in the homology theory ofﬁber bundles and in other problems.”Cartan’s work on frame bundles and de Rham’s theorem always stayed close to Chern’s thinking. The concept ofﬁber bundles stands at the very heart of modern mathematics.It’s a central uni-fying notion for many important objects in math-ematics and physics.It isﬁtting to give a brief de-scription of its history.In1937 E.Stiefel(1936)andH.Whitney(1937)introducedStiefel-Whitney classes;they wereonly deﬁned modulo integer two.From1939to1944J.Feldbau(1939),C.Ehresmann(1941,1942,1943),Chern(1944,1945)andN.Steenrod(1944)made a system-atic study of the topology ofﬁberbundles.In1942L.Pontryagin intro-duced the Pontryagin class.In1944he associated topologicalinvariants using the curvature ofRiemannian manifolds.His paperswere published in the Dokladyjournal.He was short in provingthat these curvature invariants arethe same as Pontryagin classes.Let me describe what is needed to prove the equivalence of the curvature and topological def-initions of characteristic classes.Recall that,in the proof of the Gauss-Bonnet for-mula,one uses vectorﬁelds s1,...,s k in general position.In his thesis in1936Stiefel proved that the locus at which the vectorﬁelds are linearly de-pendent forms a(k−1)-dimensional cycle whose homology class is independent of the choice of s i.In1937Whitney[21]considered sections for more general sphere bundles from the point of view of obstruction theory.Whitney noticed the importance of the universal bundle over the Grass-mannian G(q,N)of q planes in R N.He showed that any rank q bundle over the manifold is iso-morphic to the pullback of the universal bundle under a map f:M→G(q,N).Pontryagin(1942)and Steenrod[19]observed that,when N is large,the map f is unique up to homotopy.The characteristic classes of the bundle are given byf∗H∗(Gr(q,N))⊂H∗(M)In1934Ehresmann[17]studied the cohomology of H∗(Gr(q,N))and showed that it is generated by Schubert cells.Atﬁrst,Chern tried to prove the equivalence of the Pontryagin classes deﬁned using Schubert cells and classes deﬁned using the curvature form. The diﬃculty was how to integrate these diﬀeren-tial forms deﬁned by the curvature form over the Schubert cells.Chern quickly realized that it was easier to handle the case over complex numbers.Speaking of this discovery,Chern said:“It was a trivial ob-servation and a stroke of luck,when I saw in1944 that the situation for complex vector bundles is far simpler,because most of the classical complex spaces,such as the classical complex Grassmann manifolds,the complex Stiefel manifolds,etc., have no torsion.”For a complex vector bundle E,the Chern classes c i(E)belong to H2i(M,Z).By his discovery, Chern proved the equivalence of three deﬁnitions of characteristic classes:one using obstruction theory,one using Schubert cells,and the third using curvature forms of a connection on the bundle.The Fundamental Paper of Chern(1946)In the paper[7],Chern laid the foundation of Her-mitian geometry on complex manifolds.In this paper,Chern introduced the concept of Hermitian connections;using the curvature form Ωof the Hermitian connection,Chern deﬁneddet I+√2πΩ =1+c1(Ω)+···+c q(Ω).The importance of deﬁning Chern classes by dif-ferential forms cannot be overstated in mathemat-ics.It also provides fundamental tools in modern physics.An example is the concept of transgres-sion introduced by Chern.Letϕbe the connection form deﬁned on the frame bundle associated with the vector bundle.1228Notices of the AMS Volume58,Number9The curvature form isΩ=dϕ−ϕ∧ϕand c 1(Ω)=√2πTr Ω=√2πd(Tr ϕ)Tr (Ω∧Ω)=d(Tr (dϕ∧ϕ)+1−1This theorem of Chern is the only known general statement of the“Hodge conjecture”besides the case of dimension one and codimension one cycles, which is a relatively easy consequence of the Lef-schetz(1,1)theorem.Chern’s theorem also pro-vided a direct link between holomorphic K-theory and algebraic cycles.In Chicago,Chern and Lashof[12]studied the concept of tight embedding of hypersurfaces in Euclidean spaces.This work was generalized and continued by Kuiper and Banchoﬀ.Berkeley Days and Return to ChinaChern moved to Berkeley in1961.He spent all his years in Berkeley until his retirement in1979; he served at the math department for three more years after his retirement.The arrival of Chern and Smale in Berkeley coincided with the period when the mathematics department at Berkeley rose to become a major leading department in the world. Building on the strength of the existing faculties hired by Evans,Tarski,Morrey,Kelly,and others, Chern had hired many outstanding geometers and topologists who set up Berkeley to be the center in geometry and topology.Berkeley in the1960s was an extraordinarily exciting place for people interested in geometry:students,faculty,and vis-iting mathematicians alike.The graduate students felt as if they were in the center of the universe of geometry.Everyone else in the world of geometry came to visit.Chern trained many outstanding students in the period when he was in Berkeley.This group includes Garland,do Carmo,Shiﬀman,Weinstein, Banchoﬀ,Millson,S.Y.Cheng,Peter Li,Web-ster,Donnelly,and Wolfson,not counting myself. Chern organized the training of his Ph.D.students through the help of some of his older students and his friends.For example,Garland got advice from H.C.Wang,Millson from Jim Simons.The charm of Chern was essential to keeping this large group of outstanding geometers working together in Campbell Hall and in Evans Hall in Berkeley.The geometry seminar and the colloquium in Berkeley were always packed with students,faculty mem-bers,and visitors.It is well known that Chern treated every visitor with a splendid dinner in a Chinese restaurant or else an elegant party in his house.His wife was able to entertain everybody with grace and nice Chinese food.This period of Berkeley days is unforgettable to two generations of geometers.In Berkeley,Chern studied minimal surface the-ory along with Calabi and Osserman[14].He also tried to generalize Nevanlinna theory to a broader setting;his eﬀort led to the discovery of the Bott-Chern form and the Chern-Levine-Nirenberg intrinsic norms;all of these have had much impact in complex geometry beyond the original purpose. His work with Simons has had deep inﬂuence in geometry and physics,including knot theory. The work with Moser[13]on local invariants of real hypersurfaces in complex Euclidean spaces is fundamental in several complex variables.He and Griﬃths[11]generalized his old work on web geometry.In the early eighties,along with Singer and Moore,Chern founded MSRI at ter,he retired and returned to China.In China he formed a mathematics center in Nankai.That center is considered to be successful and inﬂuential. ConclusionChern’s ability to create invariants for impor-tant geometric structures was unsurpassed by any mathematician whom I have ever known.His works on the Gauss-Bonnet formula,on Chern classes,on projective diﬀerential geometry,on aﬃne geometry,and on Chern-Moser invariants for pseudo-convex domains demonstrate his strength. Before he died,he had embarked on the major un-dertaking of applying the Cartan-Kähler system to a more general geometric setting.Chern once said:“The importance of complex numbers in geometry is a mystery to me.It is well organized and complete.”Chern always regretted that ancient Chi-nese mathematicians never discovered complex numbers.Chern’s everlasting works in complex geometry made up for the earlier losses by Chinese mathematics over the last two thousand years.The Chinese astronomers named a star after Chern.May his accomplishments always shine on the future generations of mathematicians. References[1]C.B.Allendoerfer,The Euler number of aRiemann manifold,Amer.J.Math.62(1940),243–248.[2]C.B.Allendoerfer and A.Weil,The Gauss-Bonnet theorem for Riemannian polyhedra,Trans.Amer.Math.Soc.53(1943),101–129.[3]O.Bonnet,Mémoire sur la théorie généraledes surfaces,J.Ecole Polytech.19(1848),1–146.[4]R.Bott and S.-S.Chern,Hermitian vectorbundles and the equidistribution of the zeroesof their holomorphic sections,Acta Math.114(1965),71–112.[5]S.-S.Chern,On integral geometry in Kleinspaces,Ann.of Math.43(1942),178–189.[6],Characteristic classes of Hermitian manifolds,Ann.of Math.47(1946),85–121.[8],On the characteristic classes of com-plex sphere bundles and algebraic varieties,Amer.J.Math.75(1953),565–597.1230Notices of the AMS Volume58,Number9[10]F.Hirzebruch is professor emeritus at the Universität Bonn and director emeritus of the Max-Planck-Institut für Mathematik in Bonn.His email address is hirzebruch@mpim-bonn.mpg.de.c i=0for i≥n−r+1.For real diﬀerentiable man-ifolds such questions are treated in the disserta-tion of Hopf’s student Stiefel[4],later a well-known computer scientist.For a compact complex mani-fold X of dimension n,the n-dimensional products of the Chern classes of the tangent bundle(all di-mensions complex)give the Chern numbers,when integrated over X,for example c n[X]is the Euler-Poincarécharacteristic(Poincaré-Hopf theorem).From1950to1952I was scientiﬁc assistant in Erlangen and wrote the paper[6]where ideas of Hopf entered[2].Some of the results could have been generalized to higher dimensions.But the so-called“duality formula”was not yet proved. This formula says that the total Chern class1+c1+ c2+···of the direct sum of two complex vector bundles equals the product of the total Chern classes of the summands.The paper[6]has a remark written during proofreading that Chern and Kodaira told me that the“duality formula”is proved in a forthcoming paper of Chern[7].In the commentary to my paper[6]in volume1of my Collected Papers(Springer1987),I write that my knowledge about Chern classes increased with the speed of aﬂash when I came to Princeton in August1952as a member of the Institute for Advanced Study and talked with K.Kodaira,D.C. Spencer,and,a little later,with A.Borel,who told me about his thesis containing his theory about the cohomology of the classifying spaces of com-pact Lie groups.For the unitary group U(n),this implies that the Chern class c i can be considered in a natural way as the i th elementary symmetric function in certain variables x1,x2,...,x n.My two years(1952–54)at the Institute for Ad-vanced Study were formative for my mathematical career([8],[9]).I had to study and develop funda-mental properties of Chern classes,introduced the Chern character,which later(joint work with M.F. Atiyah)became a functor from K-theory to rational cohomology.I began to publish my results in1953. The main theorem is announced in[10].It concerns the Euler number of a projective algebraic variety V with coeﬃcients in the sheaf of holomorphic sec-tions of a complex analytic vector bundle W over V. Chern classes everywhere!I quote from[10]:“The main theorem expresses this Euler-Poincaréchar-acteristic as a polynomial in the Chern classes of the tangential bundle of V and in the Chern classes of the bundle W.”The Chern classes accompanied me throughout all my mathematical life;for example:In2009I gave the annual Oberwolfach lecture about Chern classes[11].Myﬁancée joined me in Princeton in November 1952.We married.A“marriage tour”was orga-nized,for which Spencer gave me some support from his Air Force project.I lectured in seven places during this trip,including Chicago,where we met the great master Shiing-Shen Chern and hisOctober2011Notices of the AMS1231charming wife.He was forty-one,I was twenty-ﬁve. For me he was a gentleman advanced in age.But all shyness disappeared.He was interested in my progress in Princeton about which I also talked in my lecture.We must have spoken about his papers[3]and[7].Chern begins in[3]with a study of the Grassmannian H(n,N)of linear subspaces of dimension n in the complex vector space of dimension n+N.He deﬁnes the Chern classes of the n-dimension tautological bundle over the Grassmannian in terms of Schubert calculus.From here Chern comes to the deﬁnition using r-tuples of sections.For N→∞,the Grassmannian be-comes the classifying space of U(n),and we are close to what I learned from Borel.For Hermit-ian manifolds Chern shows how to represent the Chern classes by diﬀerential forms.The paper[7]has the following deﬁnition of Chern classes:Let E be a complex vector bundle of dimension n over the base B.Let P be the associated projective bundle withﬁber P n−1(C). Let L be the tautological line bundle over P and g=−c1(L).Then g restricted to theﬁber of P is the positive generator of H2(P n−1(C),Z).Integra-tion of g n−1+m over theﬁber in P gives¯c m,the m th “dual”Chern class of E.The total“dual”Chern class¯c=1+¯c1+¯c2+···is deﬁned byc·¯c=1.If B=H(n,N),then¯c is the total Chern class of the complementary N-dimensional tautological bundle over B.Chern uses this to prove that the Chern classes are represented by algebraic cycles if everything happens in the projective algebraic category.The Cherns invited my wife and me for dinner in their home.For theﬁrst time we enjoyed the cook-ing of Mrs.Chern.Many meals in Berkeley would follow.The Chern family,with their two children in1950,can be seen in the photograph on page XX of his Selected Papers(Springer1978).Chern presented me a copy of this book with the dedica-tion“To Fritz.Warmest regards.June1979”.The signature is in Chinese characters.During1955–56I was an assistant professor at Princeton University.I gave a course on my book [12].Chern and Serre attended at least occasion-ally.Chern,Serre,and I wrote a paper,“On the index of aﬁbered manifold”,which was submitted in September1956[13].There the multiplicativity of the signature[=index]is proved forﬁbrations of compact connected oriented manifolds provided the fundamental group of the base acts trivially on the rational cohomology of theﬁber.In1960Chern became a professor in Berkeley.I visited him there in1962,1963,1967,1968,1973, 1974,1979,1983,1986,and1998,always with part of my family.Chern inspired an oﬃcial oﬀer to me by the University of California(November1968). He wrote to me:“We all hope that you willﬁnd Berkeley suﬃciently attractive to deserve your seri-ous consideration.Some disturbances are expected but they need not concern you.I am going to sub-mit to the NSF a new proposal for research support and will be glad to include you in the proposal.”In Bonn I was very involved in discussions with the protesting students and expected to have a qui-eter life in Berkeley as a new faculty member with more time for mathematics.Finally I decided to stay in Bonn.Chern was very disappointed.But the invitations to Berkeley continued.The Cherns were always very helpful in many practical problems: picking us up at the airport,ﬁnding a house,lend-ing us things useful for housekeeping,even lend-ing us a car,depositing items in their house we had bought to be used during the next visit….We enjoyed the Cherns’hospitality in their beautiful home in El Cerrito,overlooking the Bay with the famous Bay Bridge,or in excellent Chinese restau-rants in Berkeley and Oakland where the Cherns were highly respected guests.There were always interesting conversations with the Cherns and the other dinner guests.In1979there was a conference,“The Chern Symposium”,on the occasion of Chern’s retire-ment as a professor of the university.In the Proceedings[14]I.M.Singer writes:“The confer-ence also reﬂected Professor Chern’s personality, active yet relaxed,mixed with gentleness and good humor.We wish him good health,a long life,hap-piness,and a continuation of his extraordinary deep and original contributions to mathematics.”This came also from my heart.Chern did not really retire.In1981he became theﬁrst director of the Mathematical Sciences Re-search Institute in Berkeley.When the MSRI build-ing was ready,I sometimes used Chern’s beautiful oﬃce with a wonderful view.In1981I nominated Chern for the“Alexander von Humboldt-Preis”.He received it and spent part of the summers of1982and1984in Bonn. He talked at the Arbeitstagungen of these years on the topics“web geometry”and“some applications of the method of moving frames”.In1998I was invited to be one of theﬁrst Chern professors in Berkeley.These visiting professor-ships areﬁnanced by Robert G.Uomini,a former student of Chern,who had won an enormous sum in the lottery.In my case a one-day Chern sympo-sium was held,followed by a four-week course.The title of my Chern lecture in the symposium was “Why do I like Chern classes?”I gave four answers:(1)The Chern classes remind me of my youth.I hope this became clear in the beginningof this contribution.(2)The Chern classes have so many diﬀerentdeﬁnitions.As a joke I added:I especiallylike that all these deﬁnitions are equivalent.There are the deﬁnitions in Chern’s pa-pers[3]and[7].The statement in the joke1232Notices of the AMS Volume58,Number9needed some work,which was carriedout by Borel and me and perhaps by oth-ers,too.The diﬃculty consisted in signquestions:Are we dealing with a complexvector bundle V or its dual V∗?(3)“Chern has a beautiful character.”There was the story that during a lectureabout K-theory and its functor ch to ra-tional cohomology I cried out,“Chern hasa beautiful character!”Chern was presentand smiled.(4)Chern classes have so many applications.In1998Chern was eighty-seven years old.He did not appear so old to me.He came to my Chern lecture and also to some lectures in my four-week course.The Cherns came to an oﬃcial dinner.They invited us to a Chinese restaurant.Berkeley1998!The last time I saw Chern.The Cherns gradually moved to China.But we stayed in contact.We edited the two vol-umes on the Wolf Prize winners in mathematics (published by World Scientiﬁc in2000and2001).My retirement as director of the Max Planck In-stitute for Mathematics in Bonn in1995was cele-brated by a“party”with informal lectures,perfor-mances,music,lunches and dinners organized by Don Zagier.It lasted two or three days.Zagier had the idea to produce a book with essays or short statements by the participants and by some other people who could not attend.Chern did not come. But one page is by him(see Figure1).In2005the School of Mathematics of the In-stitute for Advanced Study in Princeton had its seventy-ﬁfth anniversary.Of the older members Chern,Bott,Hirzebruch,and Atiyah were invited to present to the inner circle how the time at the Institute was formative for their careers,Chern by television.But he died in2004.I also gave a math-ematical lecture in which Borel and Chernﬁgured prominently.Chern classes everywhere!Borel and I had shown in the1950s how to calculate the Chern classes and the Chern numbers of compact complex homogeneous spaces.An example(in a formulation by E.Calabi):Let X be the projective contravari-ant tangent bundle of P3(C)andY the projective covariant tangentbundle.Then the Chern number c51of theseﬁve-dimensional complexhomogeneous spaces X and Y,re-spectively,equals4500and4860.This is interesting because X andY are diﬀeomorphic(compare[11]and the work of D.Kotschick men-tioned there).Remark.It is unavoidable that this contribution has some overlap with[15]and with myinterviewFigure1.about Chern of December6,2010,here in Bonn [Zala Films with George Csicsery for MSRI]. References[1]F.Hirzebruch,Berichtüber meine Zeit in derSchweiz in den Jahren1948–1950,In:math.ch/100.Schweizerische Mathematische Gesellschaft1910–2010.EMS Publishing House,2010,303–315.[2]H.Hopf,Zur Topologie der komplexen Mannig-faltigkeiten,In:Studies and Essays presented to R.Courant.New York1948,167–185.[3]S.S.Chern Characteristic classes of Hermitianmanifolds,Amer.J.Math.47(1946),85–121.[4]E.Stiefel,Richtungsfelder und Fernparallelis-mus in n-dimensionalen Mannigfaltigkeiten,Comm.Math.Helvetici8(1935/36),305–353.[5]N.Steenrod,The topology ofﬁbre bundles,Princeton Math.Ser.14,Princeton Univ.Press,1951.[6]F.Hirzebruch,Übertragung einiger Sätze ausder Theorie der algebraischen Flächen auf kom-plexe Mannigfaltigkeiten von zwei komplexen Dimensionen,J.Reine Angew.Math.191(1953), 110–124.[7]S.-S.Chern,On the characteristic classes of com-plex sphere bundles and algebraic varieties,Amer.J.Math.75(1953),565–597.[8]F.Hirzebruch,The signature theorem:Reminis-cences and recreation.In:Prospects in Mathematics.Ann.Math.Stud.70(1971),3–31.[9],Arithmetic genera and the theorem of Riemann-Roch for algebraic varieties,PNAS40 (1954),110–114.October2011Notices of the AMS1233。

[美]R·格伦·哈伯德《宏观经济学》R.GlennHubbard,AnthonyP

Macroeconomics R. GLENN HUBBARD COLUMBIA UNIVERSITY ANTHONY PATRICK O’BRIEN LEHIGH UNIVERSITY MATTHEW RAFFERTY QUINNIPIAC UNIVERSITY Boston Columbus Indianapolis New York San Francisco Upper Saddle RiverAmsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City So Paulo Sydney Hong Kong Seoul Singapore Taipei TokyoAbout the AuthorsGlenn Hubbard Professor Researcher and Policymaker R. Glenn Hubbard is the dean and Russell L. Carson Professor of Finance and Economics in the Graduate School of Business at Columbia University and professor of economics in Columbia’s Faculty of Arts and Sciences. He is also a research associate of the National Bureau of Economic Research and a director of Automatic Data Processing Black Rock Closed- End Funds KKR Financial Corporation and MetLife. Professor Hubbard received his Ph.D. in economics from Harvard University in 1983. From 2001 to 2003 he served as chairman of the White House Council of Economic Advisers and chairman of the OECD Economy Policy Commit- tee and from 1991 to 1993 he was deputy assistant secretary of the U.S. Treasury Department. He currently serves as co-chair of the nonpar-tisan Committee on Capital Markets Regulation and the Corporate Boards Study Group. ProfessorHubbard is the author of more than 100 articles in leading journals including American EconomicReview Brookings Papers on Economic Activity Journal of Finance Journal of Financial EconomicsJournal of Money Credit and Banking Journal of Political Economy Journal of Public EconomicsQuarterly Journal of Economics RAND Journal of Economics and Review of Economics and Statistics.Tony O’Brien Award-Winning Professor and Researcher Anthony Patrick O’Brien is a professor of economics at Lehigh University. He received a Ph.D. from the University of California Berkeley in 1987. He has taught principles of economics money and banking and interme- diate macroeconomics for more than 20 years in both large sections and small honors classes. He received the Lehigh University Award for Distin- guished Teaching. He was formerly the director of the Diamond Center for Economic Education and was named a Dana Foundation Faculty Fel- low and Lehigh Class of 1961 Professor of Economics. He has been a visit- ing professor at the University of California Santa Barbara and Carnegie Mellon University. Professor O’Brien’s research has dealt with such issues as the evolution of the U.S. automobile industry sources of U.S. economiccompetitiveness the development of U.S. trade policy the causes of the Great Depression and thecauses of black–white income differences. His research has been published in leading journals in-cluding American Economic Review Quarterly Journal of Economics Journal of Money Credit andBanking Industrial Relations Journal of Economic History Explorations in Economic History andJournal of PolicyHistory.Matthew Rafferty Professor and Researcher Matthew Christopher Rafferty is a professor of economics and department chairperson at Quinnipiac University. He has also been a visiting professor at Union College. He received a Ph.D. from the University of California Davis in 1997 and has taught intermediate macroeconomics for 15 years in both large and small sections. Professor Rafferty’s research has f ocused on university and firm-financed research and development activities. In particular he is interested in understanding how corporate governance and equity compensation influence firm research and development. His research has been published in leading journals including the Journal of Financial and Quantitative Analysis Journal of Corporate Finance Research Policy and the Southern Economic Journal. He has worked as a consultantfor theConnecticut Petroleum Council on issues before the Connecticut state legislature. He has alsowritten op-ed pieces that have appeared in several newspapers including the New York Times. iii Brief Contents Part 1: Introduction Chapter 1 The Long and Short of Macroeconomics 1 Chapter 2 Measuring the Macroeconomy 23 Chapter 3 The Financial System 59 Part 2: Macroeconomics in the Long Run: Economic Growth Chapter 4 Determining Aggregate Production 105 Chapter 5 Long-Run Economic Growth 143 Chapter 6 Money and Inflation 188 Chapter 7 The Labor Market 231 Part 3: Macroeconomics in the Short Run: Theory and Policy Chapter 8 Business Cycles 271 Chapter 9 IS–MP: A Short-Run Macroeconomic Model 302 Chapter 10 Monetary Policy in the Short Run 363 Chapter 11 Fiscal Policy in the Short Run 407 Chapter 12 Aggregate Demand Aggregate Supply and Monetary Policy 448 Part 4: Extensions Chapter 13 Fiscal Policy and the Government Budget in the Long Run 486 Chapter 14 Consumption and Investment 521 Chapter 15 The Balance of Payments Exchange Rates and Macroeconomic Policy 559 Glossary G-1 Index I-1ivContentsChapter 1 The Long and Short of Macroeconomics 1WHEN YOU ENTER THE JOB MARKET CAN MATTER A LOT ........................................................ 11.1 What Macroeconomics Is About........................................................................... 2 Macroeconomics in the Short Run and in the Long Run .................................................... 2 Long-Run Growth in the United States ............................................................................. 3 Some Countries Have Not Experienced Significant Long-Run Growth ............................... 4 Aging Populations Pose a Challenge to Governments Around the World .......................... 5 Unemployment in the United States ................................................................................. 6 How Unemployment Rates Differ Across Developed Countries ......................................... 7 Inflation Rates Fluctuate Over Time and Across Countries................................................. 7 Econo mic Policy Can Help Stabilize the Economy .. (8)International Factors Have Become Increasingly Important in Explaining Macroeconomic Events................................................................................. 91.2 How Economists Think About Macroeconomics ............................................. 11 What Is the Best Way to Analyze Macroeconomic Issues .............................................. 11 Macroeconomic Models.................................................................................................. 12Solved Problem 1.2: Do Rising Imports Lead to a Permanent Reductionin U.S. Employment. (12)Assumptions Endogenous Variables and Exogenous Variables in EconomicModels ........................................................................................................ 13 Forming and Testing Hypotheses in Economic Models .................................................... 14Making the Connection: What Do People Know About Macroeconomicsand How Do They KnowIt .............................................................................................. 151.3 Key Issues and Questions of Macroeconomics ............................................... 16An Inside Look: Will Consumer Spending Nudge Employers to Hire................................ 18Chapter Summary and Problems ............................................................................. 20 Key Terms and Concepts Review Questions Problems and Applications Data Exercise Theseend-of-chapter resource materials repeat in all chapters.Chapter 2 Measuring the Macroeconomy 23HOW DO WE KNOW WHEN WE ARE IN ARECESSION ........................................................... 23Key Issue andQuestion .................................................................................................... 232.1 GDP: Measuring Total Production and Total Income ..................................... 25 How theGovernment Calculates GDP (25)Production and Income (26)The Circular Flow of Income (27)An Example of Measuring GDP (29)National Income Identities and the Components of GDP (29)vvi CONTENTS Making the Connection: Will Public Employee Pensions Wreck State and Local Government Budgets.................................................................... 31 The Relationship Between GDP and GNP........................................................................ 33 2.2 Real GDP Nominal GDP and the GDP Deflator.............................................. 33 Solved Problem 2.2a: Calculating Real GDP . (34)Price Indexes and the GDP Deflator (35)Solved Problem 2.2b: Calculating the Inflation Rate ..........................................................36 The Chain-Weighted Measure of Real GDP ....................................................................37 Making the Connection: Trying to Hit a Moving Target: Forecasting with “Real-Time Data” .................................................................................. 37 Comparing GDP Across Countries................................................................................... 38 Making the Connection: The Incredible Shrinking Chinese Economy ................................ 39 GDP and National Income .............................................................................................. 40 2.3 Inflation Rates and Interest Rates ....................................................................... 41 The Consumer Price Index .............................................................................................. 42 Making the Connection: Does Indexing Preserve the Purchasing Power of Social Security Payments ................................................................ 43 How Accurate Is theCPI ............................................................................................... 44 The Way the Federal Reserve Measures Inflation ............................................................ 44 InterestRates .................................................................................................................. 45 2.4 Measuring Employment and Unemployment .. (47)Answering the Key Question ............................................................................................ 49 An Inside Look: Weak Construction Market Persists.......................................................... 50 Chapter 3 The Financial System 59 THE WONDERFUL WORLD OFCREDIT ................................................................................... 59 Key Issue and Question .................................................................................................... 59 3.1 Overview of the Financial System ...................................................................... 60 Financial Markets and Financial Intermediaries ................................................................ 61 Making the Connection: Is General Motors Making Cars or Making Loans .................... 62 Making the Connection: Investing in the Worldwide Stock Market . (64)Banking and Securitization (67)The Mortgage Market and the Subprime Lending Disaster (67)Asymmetric Information and Principal–Agent Problems in Financial Markets...................68 3.2 The Role of the Central Bank in the Financial System (69)Central Banks as Lenders of Last Resort ..........................................................................69 Bank Runs Contagion and Asset Deflation ....................................................................70 Making the Connection: Panics Then and Now: The Collapse of the Bank of United States in 1930 and the Collapse of Lehman Brothers in2008 (71)3.3 Determining Interest Rates: The Market for Loanable Funds and the Market forMoney .......................................................................................... 76 Saving and Supply in the Loanable Funds Market ........................................................... 76 Investment and the Demand for Loanable Funds ............................................................ 77 Explaining Movements in Saving Investment and the Real Interest Rate (78)CONTENTS .。

Asymptotic Theory for Quantum Bose Systems with Many Degrees of Freedom

s s s
=
i
ℓ,s,m,q
∂ ∂α
m
− α∗m αs ∂ ∂α |α|2
ℓ
∂ ∂α∗ α∗m αq
q
∂ ∂α |α|2
ℓ
exp
|α|2
=
i
ℓ,s,m,q
Hℓs Fmq α∗ℓ
α∗m αq − αs ∂ ∂α
ℓ
exp
=
i
ℓ,s
Hℓs
− αs
exp
α|F (t)|α .
In a slightly more general setting, let H = opWick H(z ∗ , z ) For H as in (1.1) this means H(z ∗ , z ) = Hℓs z ∗ℓ z s
+
d Φα |F Φα dt i = Φα |(HF − F H )Φα = = i
ℓ,s,m,q
(1.7)
Hℓs Fmq (t)
Φα |a†ℓ as a†m aq Φα − Φα |a†m aq a†ℓ as Φα
i
ℓ,s,m,q
Hℓs Fmq α∗ℓ αq a†s Φα |a†m Φα − α∗m αs a†q Φα |a†ℓ Φα Hℓs Fmq α∗ℓ αq α∗ℓ ∂ ∂α∗ ∂ ∂α∗ ∂ ∂α∗
∗
For the purpose of the present paper it will be suﬃcient to treat the case when H is a polynomial in z ∗ , z . We will address the mathematical problems related to a more general H in future publications. In case H(z ∗ , z ) is a polynomial, the equation (1.9) has the following explicit form: d α|F |α = dt i =

学术英语（第二版）医学教师用书Unit8

UNIT 8 Principles of Biomedical Ethics Teaching ObjectivesAfter learning Unit 8, Ss are expected to accomplish the following objectives:Professional knowledge To know the boundaries between medical research and practice To have a clear understanding of the moral principles and behavioral guidelines for the biomedical research and medical practiceReading To understand the boundaries drawn between medical research and practiceTo know three basic ethical principles of research involving human subjectsTo learn the requirements when basic principles are properly applied in researchTo be more prepared for a life-or-death decision in medical practiceTo get more insights into the ethical justification of dilemmas in medical practiceAcademic vocabulary and discourse To know some building blocks in medical terminologyTo be familiar with expressions used to define key termsTo further develop awareness of formal and informal languageViewing To get familiar with the Cornell note-taking systemTo know the two approaches to medical decisions: traditional paternalistic mode and more recent collaborative modeSpeaking To learn how to develop a strong conclusionWriting To know the format requirements of the reference listTo be able to make a reference list according to style requirementsResearching To be aware of the balance between medical authority and patients’　autonomyTeaching Activities and ResourcesPart 1 ReadingText ALead-inSuggested teaching plan1.To draw Ss’　a ttention and to raise their awareness of the importance ofbiomedical ethics, T is advised to relate the discussion of this unit to the real-world happenings. Before starting the class, search the media for the latest news reports, either at home or abroad, about controversial events in medicine community or healthcare settings.2.Start the class by doing T ask / Lead-in and relate the content of the video clip toyour findings in the pre-class searching.Key to the task2) Death4) Patient rightsScriptWell, advancements in medical science have afforded us the opportunity to live decades l onger than in previous generations. For every new possibility offered, we now face an equal number of challenges and we find ourselves confronting decisions that are unprecedented in human history. When does life begin? When should life end? How do we define death when we have the ability to keep people technically alive, or we should say, technologically alive long after their discrete.”I’m your host body parts no longer function? Welcome to “Matter and Beyondaround medical MaryLynn Schiavi. In this program we’re going to explore issuesscience that are forcing us to define life, death, quality of life, patient rights, and confront the moral and ethical questions that arise when facing critical healthcare decisions.3.Introduce the topic of Text A as a natural continuum of Lead-in.Text ComprehensionSuggested teaching plan1.Make good use of Lead-in video clip as it serves as a perfect introduction to thetopic of this unit. Elaborate on the connection of its content with the latest events in the real world. Naturally, ask Ss how medicine differs from other branches of natural science, especially when human subjects are involved in the research.Here are some hints:Medicine Other branches of science Health as the ultimate goal Knowledge and truth as the ultimate goal Morality and ethics as priority factors Honesty as a prime virtue of scientistsDoctor as a teacher, counselor, friend,advocate, protector, and healer all atthe same timeScientist as an explorerGood doctor: empathic, sympathetic, caring, patient, considerate Good scientist: inquisitive, persistent, perseverant, creative2.Analyze the text and lead Ss to discuss, integrating Task 2 / Critical reading andthinking / Text A into analysis and discussion. The presentation topics should be assigned to individual Ss for preparation at least one week in advance. Ask other Ss to preview the text with the guidance of presentation topics.3.Integrate Task 2 / Language building-up / Text A when a careful definition ofkey terms is covered.4. When analyzing the text, ask Ss to pay special attention to the sentences listed inLanguage focus below.5.If time allows, ask Ss to do Task 1 / Critical reading and thinking / Text A inabout five minutes. Check out the task by asking one or two Ss to read their answers. This is done to get an overview about the text.Language focus1.… described in a formal protocol that sets forth an objective … (P185, Para.2)set forth是动词词组，表示用清晰、具体的方式解释或描述，多用于正式的书面语中。

心理学专业外语：The behaviourist approach to psychology

The behaviourist approach to psychology心理学的行为主义研究方法J.B.Watson：‘Give me a dozen healthy infants……and my own specified world to bring them up in and I’ll guarantee to take any one at random and train him to become any type of specialist I might select-doctor, lawyer…and yes, even beggarman and thief. ’华生：“给我一打健全的婴儿和我可用以培育他们的特殊世界，我就可以保证随机选出任何一个，我都可以把他训练成为我所选定的任何类型的特殊人物如医生、律师……或甚至乞丐、小偷。

”Origins and history1.起源与历史The behaviourist approach was influenced by the philosophy of empiricism （which argues that knowledge comes from the environment via the senses,since humans are like a ‘tabula rasa’,or blank slate,at birth）and the physical sciences（which emphasise scientific and objective methods of investigation）.行为主义的研究方法受到经验主义哲学和物理科学的影响。

前者主张知识来自于感官接受的环境信息，认为人类在出生时像一块白板或空白黑板，后者强调研究方法的客观性和科学性。

Watson started the behaviourist movement in 1913 when he wrote an article entitled ‘Psychology as the behaviourist views it’,which set out its main principles and assumptions.Drawing on earlier work by Pavlov,behaviourists such as Watson,Thorndike and Skinner proceeded to develop theories of learning（such as classical and operant conditioning）that they attempted to use to explain virtually all behaviour.华生在1913年发表的论文《一个行为主义研究者眼中的心理学》标志着行为主义运动的开始，文中阐述了行为主义的主要原理和假设。

中英文论文写作(摘要)

· Write the paper before you write the abstra
1 基本特性 2 时态 3 语态 4 语法修辞 5 一个典型示例 6 化学常用句式
2 时态
以一般现在时为主, 也使用一般过去时和现在完成时从理论上讲: 说法一: 一般现在时
通过科学实验取得的研究结果、结论，揭示自然界的客观规律一般过去时
Objective 动词不定式开头 To investigate … To study … To explore … To examine … To determine … To report … To review … 使用第一人称时，用凡指的we, the author, the authors ,不用I。如: In this paper we conclude …
Result: The contents of the components of midecamyc A1 and leucomycin A6 was 30%～ 50% and 10%～20% respectively, the contents of the rest components w lower, different manufactures produces have differ components. Conclution: To revise the specificati meleumycin for quality control.
指示性文摘（indicative abstract）
This type of abstract is designed to ind the subject of a paper, making it easy fo potential readers to decide whether to r the paper.

reflexives提纲

Chapter 11. Purpose of the study2. Generalization3. Method of studyChapter21. Standard of identifying the reflexives1.1 Incomplete definition of reflexive不完全的反身代词定义1.2 Definitions, discrimination of reflexives in English and In ChineseChapter 3 Analyze the reflexives1)Under the constrains theory (under the jurisdiction, out of jurisdiction)( method of usage)（semantics）2）Under the recognition theory-self, intensive reflexives（logics of recognition, syntactic demonstration and semantic quality）3）Under the practical acquisition theoryExperiment procedureDiscussionSummaryChapter 4 ConclusionChapter 11. Purpose of the studyThe restriction relationship between the anaphora and antecedent has long been a touchy issue in the study of linguistics. We have known that Chomsky erected and developed his theory –constraint theory-based on the conception of governing that defines the anaphora must be constrained in the governing category. And, this theory is commonly called the first constrain theory, which arose a great repercussion in the world wide. We, naturally, did not want to fall behind of this trend of academics and have begun to study it . However, there was a misconception that the Chinese “ziji”should be identified as a reflexive after our making our first step to this area of the study, for the reason that it is constrained in its own governing category.But, after a gradual study, we have found so many exceptions to this identification that enough to overthrow the absolute ascription. Chinese, interestingly, have both similarities and differences between English and, without doubt, have its own characteristics of the reflexives and some of them can hardly been ascribe into the absolute reflexives in English context. In another word, it has some characteristic differs from normal definition of the reflexives. Give those differences; it is understandable that the practical acquisition study is being explored by academicians. We hoped that we can derive objective and accurate from this perspective.This article will aim at analyzing the reflexives in constrains theory, primarily focusing on the sentence construction, syntactic, semantic perspectives. Furthermore, it goes on to illustratesome cases of the practical acquisition to fuller the analysis of the reflexives on both side .Within this exploration, we might able to get relatively more accurate and comprehensive, objective understanding of the reflexives, which help us to further our understanding of mother tongue language and the international English.2 The generalizations on the present study of Reflexive.2.1 Present study of reflexives on sentence structure2.1 .1Present English reflexives study on sentences structureWe are primarily focusing on the Chomsky’s governing conception. He used conception of governing category to constrain the action, distribution and role of reflexives in the sentences. His idea can be briefly summarized as following points:A: Anaphora is constrained by government category.B: general pronoun is not constrained by governing category.Antecedent is the one that command the anaphora. The principle of command usually can be described as following:2) X commands Y, only when Y is ascribed and belong to the first divergent point, as well as the X and Y do not belong to each other.Figure 1 S represents Sentence.N represents a single word class, such as N, A, V, and P, and can also represent the phrase language class, such as the NP, AP, the VP, and PP. In the way to S, N1 and, N2 are nodes. Principle: each node commands the same level node; it cannot overreach their right and control their superiors or his immediate subordinates, so S cannot control NI, N2, and N3 .second. In Figure 1 the N1 is subject, commanding the entire predicate phrase.In the example of “Sara’s mother hates herself” the restriction is commanded by “Sara’s mother”, not “Sara’s”.So anaphora must be restricted in the governing category, and according to this quality, Zribi-hertz defined principle to following test of distributions (T)that can used to test the anaphora is restricted in or out of category.T1 anaphora has no ability of discriminate.Wash him （*himself）T2 Anaphora must have antecedent in the governing category.Sara has just finished, but you may catch her up tomorrow.T3 Anaphora must by command by its antecedent.Sara’s mother hates her （*himself）Sara’s mother hates herself.T4 only anaphora can be restricted in the governing category.Sara likes herself.T5 Anaphora can only be restricted in the governing category.a. Sara, insists that Judy likes her; （*herself）b. Sara insists that Judy likes herself.T6 Anaphora cannot have Split antecedents.Sara, said to Mary about them. (* themselves)According to these, an agreement has been achieved that the anaphora cannot fall into normal category, they seek and find antecedents out of governing category. This is totally different with normal understanding of English anaphora.2.1.2 Present state of the Chinese reflexives’ study on sentence structure1) Pronoun analysisWang Jia Ninng Believed that Chinese reflexives have its own character and cannot be easily ascribed to any given existent category. Linguistic follow this opinion want to s eek for another new constrain principle to define reflexives.2) Parameter analysisMazzini and Wexler and yang is the representatives of this method, who insist that governing category can be described through subset principle that has been illustrated by parameter.3) Logic shifting analysisAlthough academician haven’t reach a consensus about how shifting happened, they agree that the long distance constraint “-self” is the result of covert and cyclic shifting under the abstract and logic level. In word, it still has a local constraining relationship.4) Relative subject analysisProgovac and Frank come up with an idea that is non-shifting theory that lately (1992) be revised within the context of Chomsky principles.2.2 .Present reflexives study on semantic level2.2.1English reflexive on semantic levelAcademicians who focused on semantic level using natural language study of systemic-functional grammar ,that is the structure of the language demonstrate the objective Heraclitus combining the prediction quality of semantic, markedness of structure sign, economy in expression, redundancy of semantic and sentence structure, clarity in message transmission to illustrate the usage of English reflexive.2.2.2Chinese reflexive on semantic level(1)Theory of structuralismChen ping , A Chinese scholar believes that the base point and high subjectivity demonstration of antecedent in the sentence actually play an important role in understanding the Chinese reflexive.(2) Thematic hierarchyXu Lie Jiong thinks that the constraint theory cannot solve the “-self” pro blem. Thus, he come up with a new theory that point out that the “-self” plays a thematic roles in constrain function. (3)Pure semantic theoryThis idea, based on Huang Yan’s Neo-Gricean Theory, suggested the pure semantic level of solving the corresponding phenomenon in language. He believes that the corresponding should be explained between DRP and two usage principle of language—information and method.3.Overview of present study on contrast between English and Chinese reflexiveProfessions primarily focus on four perspectives to illustrate the difference between the English and Chinese reflexive.(1)language difference, which means the difference in entirely two languages hold theresponsibility for explaining the English and Chinese reflexive.(2)Parameter difference, which means the various parameter results the different reflexive inChinese and English. Parameterizing led the Chinese and English has various requisite, which make the “-self” have no need to be restricted in that region’s governing categ ory.(3)Shifting difference, which regards the difference as the normal syntactic principle in differentlevel that has constrained many kind of language,” the difference happened in shifting. (4)Vocabulary differences, which attribute “-self” quality is decided by vocabulary differences.“-self” demonstrate the characteristic that have been decided by its born quality that can seldom changed.4.content and analysis method1. content of the studyAccording to the present standard identification method for reflexives, the article wants to give the relatively comprehensive definition of English and Chinese reflexives definition as well as its characteristics. Within this character, we might have the ability to find their similarities and differences. This article also wants to find the origins of the differences without staying in the apparent level of finding those differences.2 analysis method研究方法This article focuses on the theory of reflexives in English and Chinese. We know that any comparison should be built on a level of relatively common level of the two parts, or the comparison will lose its significance. It also has been known that the two comparing part should be stayed in the same level, that is the reason that they can be compared. So, based on the same level of sentence structure, syntactic, semantic analysis we get great abundance of theory analysis. Within this context, the article also lends structuralism theory to analyze and define the reflexives. Moreover, based on the experiment conducted, we derived the practical acquisition theory of both English and Chinese reflexives usage.。

学术英语社科unitA翻译

1、失去一份工作可能是最痛苦的经济事件在一个人的生活。

大多数人们依靠自己的劳动收入来维持他们的生活标准,许多人会从他们的工作得到的不仅是收入，还有自己的成就感。

一个失去工作意味着现在要定一个更低的生活标准,焦虑未来,并丧失自尊心。

这并不奇怪,因此,政治家竞选办公室经常谈论他们所提出的政策将帮助创造就业机会。

2、虽然一定程度的失业是不可避免的，在一个复杂的经济与成千上万的企业和以百万计的工人，失业量的变化大致随着时间的推移和席卷整个国家。

当一国保持其尽可能充分就业的工人，它实现了更高水平的国内生产总值会比留下了不少工人闲置更好。

3、失业问题一般分为两类，长期的问题和短期的问题。

经济的自然失业率通常是指充分就业状态下的失业率。

周期性失业是指今年年失业率围绕其自然率的波动，它是密切相关的经济活动的短期起伏。

4、判断失业问题有多么严重时，其中一个问题就是要考虑是否失业通常是一个短期或长期的条件。

如果失业是短期的，人们可能会得出结论，它不是一个大问题。

工人可能需要几个星期的工作之间找到最适合他们的口味和技能的开口。

然而，如果失业是长期的，人们可能会得出结论，这是一个严重的问题。

许多个月的失业工人更容易遭受经济和心理上的困难。

5、经济引起一些失业的原因之一是寻找工作。

求职是工人与适合的职位相匹配的过程。

如果所有工人和所有工作一样，使所有工人，同样适用于所有作业，求职就不会是一个问题。

下岗职工会很快找到新的工作，非常适合他们。

但是，实际上，工人有不同的想法和技能,岗位有不同的属性，在经济生活中众多的企业和家庭关于应聘者和职位空缺的信息缓慢传播。

6、摩擦性失业往往是在不同企业之间的劳动力需求变化的结果。

当消费者决定，他们更喜欢富士通而不是宏碁，富士通增加就业岗位，宏碁就解雇工人。

前宏碁的工人必须寻找新的就业机会，而富士通必须决定雇用新工人开辟了各种作业。

这种转变的结果是一段时间的失业。

7、同样，由于不同地区的国家生产不同的商品，在一个地区就业增长，在另一个减少。

D-bar Sparks

4
A nice aspect of this theory is its natural presentation of Deligne cohomology in terms of forms and currents. In fact, we shall construct several diﬀerent spark complexes, each yielding the same ring of spark classes containing Deligne cohomology. Hence, we also obtain several other geometric constructions of Deligne cohomology. k We note that the standard short exact sequence for the Deligne group HD (X, Z(p)) sits as the left column in our 3 × 3-grid. When X is compact Kaehler and k = 2p, this is 2p (X, Z(p)) → Hdgp,p (X ) → 0 where Jp (X ) is Griﬃths’ the sequence: 0 → Jp (X ) → HD intermediate Jacobian. (See the diagrams following Proposition 14.4.) In our context it is trivial to see that every holomorphic cycle of codimension-p determines a class in 2p (X, Z(p)). Furthermore, one sees in a similar way that every maximally complex cycle HD 2p+1 (X, Z(p)), and if M bounds a M of codimension 2p + 1 determines a class [M ] ∈ HD holomorphic chain of (complex) codimension p, then [M ] = 0 (cf. Prop. 14.6). Recall that a powerful property of cohomology theory is its broad range of distinct formulations. Some presentations of the theory make it easy to compute, while others, such as de Rham theory, current theory or harmonic theory, lead to non-trivial assertions in analysis. Diﬀerential characters are similar in nature. There are many distinct formulations: some relatively simple and computable, and others rather more complicated, ˇ involving Cech-deRham complexes [19] or complexes of currents [20], [10], [14]. These latter approaches relate diﬀerential characters for example to reﬁned characteristic classes for singular connections [16], [17], [22], to Morse Theory [18] and to harmonic theory. In [19] the homological apparatus of spark complexes was introduced to establish the equivalence of the many approaches to diﬀerential characters. In §1 below, that apparatus is generalized to treat a wide range of situations. In particular, on a complex manifold one can replace the deRham component of diﬀerential character theory by the ∂ -complex of (0, q )-forms, or more generally, the deRham complex truncated at level p. The machine developed in §1 is of independent interest and applies to a broad range of interesting situations. Using this machine we show that a variety of ∂ -spark complexes are equivalent and therefore lead to isomorphic groups of spark classes. Thus we are able to relate the classes ˇ double complex, of ∂ -gerbes with connection, which are deﬁned within the Cech-Dolbeault to classes of currents satisfying a ∂ -spark equation of the form ∂a = φ − Ψ(R) where φ is a smooth ∂ -closed (0, q )-form and Ψ(R) is the (0, q )-component of a rectiﬁable cycle R of codimension q . These two are related by a larger enveloping complex which contains them both. Similar remarks apply to the case where one truncates at level p > 1. Other geometrically motivated spark complexes will be studied in forthcoming papers.

法布里珀罗基模共振英文

法布里珀罗基模共振英文The Fabryperot ResonanceOptics, the study of light and its properties, has been a subject of fascination for scientists and researchers for centuries. One of the fundamental phenomena in optics is the Fabry-Perot resonance, named after the French physicists Charles Fabry and Alfred Perot, who first described it in the late 19th century. This resonance effect has numerous applications in various fields, ranging from telecommunications to quantum physics, and its understanding is crucial in the development of advanced optical technologies.The Fabry-Perot resonance occurs when light is reflected multiple times between two parallel, partially reflective surfaces, known as mirrors. This creates a standing wave pattern within the cavity formed by the mirrors, where the light waves interfere constructively and destructively to produce a series of sharp peaks and valleys in the transmitted and reflected light intensity. The specific wavelengths at which the constructive interference occurs are known as the resonant wavelengths of the Fabry-Perot cavity.The resonant wavelengths of a Fabry-Perot cavity are determined bythe distance between the mirrors, the refractive index of the material within the cavity, and the wavelength of the incident light. When the optical path length, which is the product of the refractive index and the physical distance between the mirrors, is an integer multiple of the wavelength of the incident light, the light waves interfere constructively, resulting in a high-intensity transmission through the cavity. Conversely, when the optical path length is not an integer multiple of the wavelength, the light waves interfere destructively, leading to a low-intensity transmission.The sharpness of the resonant peaks in a Fabry-Perot cavity is determined by the reflectivity of the mirrors. Highly reflective mirrors result in a higher finesse, which is a measure of the ratio of the spacing between the resonant peaks to their width. This high finesse allows for the creation of narrow-linewidth, high-resolution optical filters and laser cavities, which are essential components in various optical systems.One of the key applications of the Fabry-Perot resonance is in the field of optical telecommunications. Fiber-optic communication systems often utilize Fabry-Perot filters to select specific wavelength channels for data transmission, enabling the efficient use of the available bandwidth in fiber-optic networks. These filters can be tuned by adjusting the mirror separation or the refractive index of the cavity, allowing for dynamic wavelength selection andreconfiguration of the communication system.Another important application of the Fabry-Perot resonance is in the field of laser technology. Fabry-Perot cavities are commonly used as the optical resonator in various types of lasers, providing the necessary feedback to sustain the lasing process. The high finesse of the Fabry-Perot cavity allows for the generation of highly monochromatic and coherent light, which is crucial for applications such as spectroscopy, interferometry, and precision metrology.In the realm of quantum physics, the Fabry-Perot resonance plays a crucial role in the study of cavity quantum electrodynamics (cQED). In cQED, atoms or other quantum systems are placed inside a Fabry-Perot cavity, where the strong interaction between the atoms and the confined electromagnetic field can lead to the observation of fascinating quantum phenomena, such as the Purcell effect, vacuum Rabi oscillations, and the generation of nonclassical states of light.Furthermore, the Fabry-Perot resonance has found applications in the field of optical sensing, where it is used to detect small changes in physical parameters, such as displacement, pressure, or temperature. The high sensitivity and stability of Fabry-Perot interferometers make them valuable tools in various sensing and measurement applications, ranging from seismic monitoring to the detection of gravitational waves.The Fabry-Perot resonance is a fundamental concept in optics that has enabled the development of numerous advanced optical technologies. Its versatility and importance in various fields of science and engineering have made it a subject of continuous research and innovation. As the field of optics continues to advance, the Fabry-Perot resonance will undoubtedly play an increasingly crucial role in shaping the future of optical systems and applications.。

湖南省长沙市雅礼中学2025届高三上学期月考(二)英语试题

C. Talk about John's progress.
5. What does the man explain about?
A. A news event.B. A class schedule.C. A holiday's meaning.
第二节（共15小题；每小题1.5分，满分22.5分）
A. By talking.B. By phone calls.C. By text messages.
7. What is the relationship between the speakers?
A. Artist and fan.
B. Teacher and student.
C. Grandfather and granddaughter.
听下面一段较长对话，回答以下小题。
8. What does the woman prefer?
A. Recipes from Europe.
B. Recipes from South Asia.
C. Recipes from North America.
9. What is the woman's job?
11. What color flowers are the speakers looking at?
A. Purple.B. White.C. Red.
12. What will the speakers do next?
A. Look at the other side of the wall.
听下面5段对话或独白。每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。每段对话或独白读两遍。

异构催化剂生产生物柴油1111

Heterogeneous Catalysts for Biodiesel ProductionMartino Di Serio,†Riccardo Tesser,†Lu Pengmei,‡and Elio Santacesaria*,†Dipartimento di Chimica,Uni V ersitàdi Napoli “Federico II”,V ia Cintia 80126Napoli,Italy,andGuangzhou Institute of Energy Con V ersion,Academy of Science,ChinaRecei V ed May 17,2007.Re V ised Manuscript Recei V ed September 7,2007The production of biodiesel is greatly increasing due to its enviromental beneﬁts.However,production costs are still rather high,compared to petroleum-based diesel fuel.The introduction of a solid heterogeneous catalyst in biodiesel production could reduce its price,becoming competitive with diesel also from a ﬁnancial point of view.Therefore,great research efforts have been underway recently to ﬁnd the right catalysts.This paper will be concerned with reviewing acid and basic heterogeneous catalyst performances for biodiesel production,examining both scientiﬁc and patent literature.IntroductionNowadays,biodiesel (a mixture of fatty acid methyl esthers,FAMEs)has become very attractive as a biofuel because of its environmental beneﬁts s it has less air pollutants per net energy than diesel and is nontoxic and biodegradable s and because it is produced from renewable sources with high energetic efﬁciency:biodiesel yields from an estimated 90%1to 40%2more energy than the energy invested in producing it.Most biodiesel is produced today by the transesteriﬁcation of triglycerides of reﬁned/edible type oils using methanol and an alkaline catalyst (NaOH,NaOMe):3–5The reaction isnormally performed at 60–80°C.The glycerol and FAME are separated by settling after catalyst neutralization.The crude glycerol and biodiesel obtained are then puriﬁed.However,production costs are still rather high,compared to petroleum-based diesel fuel.3There are two main factors that affect the cost of biodiesel:the cost of raw materials and the cost of processing.3Processing costs could be reduced through simpliﬁed opera-tions and eliminating waste streams.6–9A solution to thisproblem could be transesteriﬁcation in supercritical methanol without using any catalyst.6,7As a matter of fact,in this case,the reaction is very fast (less than 5min)and the absence of catalyst decreases downstream puriﬁcation costs.6,7Even if some production plants use this technology in Europe,6the reaction requires very high temperatures (350–400°C)and pressures (100–250bar)and thus high capital costs.6,7The use of heterogeneous catalysts could be an attractive solution.8,9As a matter of fact,heterogeneous catalysts can be separated more easily from reaction products and the reaction conditions could be less drastic than the methanol supercritical process.In 2006a 160000t/y commercial plant started up using a heterogeneous catalyst.8The plant is based on the Hesterﬁp-H technology developed by the Institute Français du Petrole (IFP).8,9The catalyst employed in the Hesterﬁp-H technology is a mixed oxide of zinc and aluminum.9The Hesterﬁp-H technology operates at 200–250°C but does not require catalyst recovery and aqueous biodiesel treatment steps:the puriﬁcation steps of products are therefore much more simpliﬁed and very high yields of methyl esters s close to theoretical values s are obtained.6,9Glycerol is directly produced with high purity levels (at least 98%)and is free from any salt contaminants.9This aspect is very important from the economical point of view because it reduces the cost of obtaining high-grade glycerol,thus increasing the proﬁtability of the process.Moreover,in order to lower the costs and make biodiesel competitive with petroleum-based diesel,less-expensive feed-stocks such as waste fats or nonedible type oils,could be used.3–7,10However homogeneous alkaline catalysts in the transesteriﬁcation of such fats and oils cannot directly be used due to the presence of large amounts of free fatty acids (FFAs);3–5for the use of these catalysts,the FFA concentration should be less than 0.5%(w/w)to avoid the formation of high*Corresponding author.Fax:0039081674026.E-mail:elio.santacesaria@unina.it.†Universitàdi Napoli “Federico II”.‡Academy of Science.(1)Hill,J.;Nelson,E.;Tilman,D.;Polasky,S.;Tiffany,D.Proc.Natl.Acad.Sci.2006,103,11206–11210.(2)Wesseler,J.Energy Policy 2007,35,1414–1416.(3)Ma,F.;Hanna,M.A.Bioresour.Technol.1999,70,1–15.(4)Pinto,A.C.;Guarieiro,L.L.N.;Rezende,M.J.C.;Ribeiro,N.M.;Torres,E.A.;Lopes,W.A.;de P.Pereira,P.A.;de Andrade,J.B.J.Braz.Chem.Soc.2005,16,1313–1330.(5)Lotero,E.;Liu,Y.;Lopez,D.E.;Suwannakaran,K.;Bruce,D.A.;Goodwin,J.G.,Jr.Ind.Eng.Chem.Res.2005,44,5353–5363.(6)Huber,G.W.;Iborra,S.;Corma,A.Chem.Re V .2006,106,4044–4098.(7)Demirbas,A.Prog.Energy Combust.Sci.2007,33,1–18.(8)Dupraz,C.BIO-Energy -Prospect for India-France Partnership -18th April 2007-New Delhi,/events/4001/Mr_Dupraz.pdf (accessed Aug 2007).(9)Bournay,L.;Casanave,D.;Delfort,B.;Hillion,G.;Chodorge,J.A.Catal.Today 2005,106,190–192.(10)Kulkarni,M.G.;Dalai,A.K.Ind.Eng.Chem.Res.2006,45,2901–2913.Energy &Fuels 2008,22,207–21720710.1021/ef700250g CCC:$40.75 2008American Chemical SocietyPublished on Web 12/04/2007soap concentrations as a consequence of the reaction of FFAs with the basic catalyst:R-COOH +NaOH f R-COOHNa +H 2OThe soap causes downstream processing problems in product separation because of emulsion formation.3,6Several methods have been proposed to solve these prob-lems,11but the most useful seem to be the following:5,10,12–15(a)use of enzymes.A Lypase enzyme catalyzes both transesteriﬁcation of triglycerides and esteriﬁcation of FFAR-COOH +MeOH a R-COOMe +H 2Oin one step.9,11–13(b)use of acid catalysts.Acid catalyst can also promote esteriﬁcation and transesteriﬁcation.5,10,15(c)pre-esteriﬁcation method.FFAs are ﬁrst esteriﬁed to FAMEs using an acid catalyst,and then,transesteriﬁcation is performed,as usual,by using an alkaline catalyst.5,10Enzyme-based transesteriﬁcation is carried out at moderate temperatures with high yields,but this method cannot be used in industry today due to high enzyme costs,and the problems related to its deactivation caused by feed impurities.10,12–14The enzyme can be immobilized on a support to obtain a heterogeous catalyst,but again,the use will only be possible if the enzyme costs are reduced s as in the case of enzyme use in detergents,dairy products,textile,and leather processing.12However,the use of enzymes is not explored in this review which will be devoted to the use of heterogeneous acid and basic catalysts.More information on the use of enzymes in biodiesel production can be found in recent papers.10,12–14Methods b and c seem to be more attractive.Concerning method b s use of an acid catalyst for both esteriﬁcation and transesteriﬁcation reactions s Zhang et al.16,17recently showed,by a technological assessment of different continuous processes,that the homogeneous H 2SO 4-catalyzed process using waste oil is technically feasible and less complex than a two-step process (pre-esteriﬁcation with homogeneous acid catalyst and alkali-catalyzed steps).However,this process gives rise to problems linked with the corrosive action of the liquid acid catalyst and to the high quantity of byproduct obtained.5,15Basu and Norris 18and more recently Di Serio et al.15and Siano et al.19showed the possibility to perform triglyceride (TG)transesteriﬁcation and FFA esteriﬁcation in a single step,using low concentrations of Lewis acid homoge-neous catalysts (carboxylic acid of particular metals).However,this process also gives rise to problems linked with the need to remove catalysts from products by downstream puriﬁcation.15A solid acid catalyst could eliminate these problems.5,8The homogeneous acid-catalyzed pre-esteriﬁcation of FFA s method c s is a common practice in reducing FFA levels in high FFA feedstock,before performing the base-catalyzed transesteri-ﬁcation.4,5,10The main drawback of the pre-esteriﬁcation method c consists again in the necessity to remove the homogeneous acid catalyst from the oil after pre-esteriﬁcation.So for improving the process,the solution is again the use of a heterogeneous esteriﬁcation catalyst.5From the above discussion,it is clear that the introduction of a solid catalyst in biodiesel production could reduce its price,so biodiesel could become competitive with diesel also from an economic point of view.Therefore,great research efforts have been underway recently to ﬁnd the right catalysts.Several general reviews on biofuels and biodiesel production have been published:3–7,10one concerns both homogeneous and heterogeneous acid catalysts.5In the second part of a general review on biodiesel production,Lotero et al.20also included an in-depth review on heterogeneous catalysts used in transesteri-ﬁcation reactions.Together with the scientiﬁc and patent literature concerning biodiesel production,in some cases,we have also considered results reported on the transesteriﬁcation or esteriﬁcation of model molecules like triacetin or acetic acid to explain the reaction mechanisms and catalytic behavior of heterogeneous catalysts.However,it must be pointed out that in some cases the data obtained with model molecules cannot be used to predict the behavior of oils/fats and fatty acids because the polar and steric effects of the alpha-substituent group can greatly inﬂuence the reactivity.21Heterogenous CatalystsReaction Mechanisms:A General Overview.Heteroge-neous acid and basic catalysts could be classiﬁed as Brönsted or Lewis catalysts,though in many cases both types of sites could be present and it is not easy to evaluate the relative importance of the two types of sites in the reaction.A detailed description of some reaction mechanisms can be found in the paper of Lotero et al.20Here for brevity’s sake,we will report only a general overview on reaction mechanisms of the different catalyst types.When homogeneous Brönsted basic catalysts,i.e.,NaOH,KOH,Na 2CO 3,were mixed with alcohol,the actual catalyst is formed.This is the alkoxide group:Na +OH -+CH 3OH f H 2O +CH 3O -Na +which attacks the carbonyl carbon atom of the triglyceride molecule.3,20Often an alkoxide (NaOCH 3,KOCH 3)is directly used as catalyst.A similar mechanism is operative in the case of a heteroge-neous basic Bronsted catalyst such as basic zeolite:20Also inthis case,the formed catalytic specie is a homogeneous alkoxide.In the case of heterogeneous basic Bronsted catalyst such as resin with quaternary ammonium functionality (QN +OH -),the positive counterions (organic ammonium groups),being bonded(11)Ono,T.,Yoshiharu,K.Process for producing lower alcohol esters or fatty acids.U.S.Patent 4,164,506,Aug 14,1979.(12)Fukuda,H.;Kondo,A.;Noda,H.J.Biosci.Bioeng.2001,92,405–416.(13)Haas,M.J.;Piazza,G.J.;Foglia,T.A.Lipid Biotechol.2002,587–598.(14)Kumari,V.;Shah,S.;Gupta,M.N.Energy Fuels 2007,21,368–372.(15)Di Serio,M.;Tesser,R.;Dimiccoli,M.;Cammarota,F.;Nastasi,M.;Santacesaria,E.J.Mol.Catal.A:Chem.2005,239,111–115.(16)Zhang,Y.;Dubè,M.A.;McLean,D.D.;Kates,M.Bioresour.Technol.2003,89,1–16.(17)Zhang,Y.;Dubè,M.A.;McLean,D.D.;Kates,M.Bioresour.Technol.2003,90,229–240.(18)Basu,H.N.;Norris,M.E.U.S.Patent 5,525,126,June 11,1996.(19)Siano,D.;Di Serio,M.;Tesser,R.;Dimmicoli,M.;Cammarota,F.;Santacesaria,E.;Siano,L.;Nastasi,M.Process for the production of esters from V egetables oils or animal fats.PCT No.WO2006/006033,Jan 19,2006.(20)Lotero,E.;Goodwin,J.G.,Jr.;Bruce,D.A.;Suwannakarn,K.;Liu,Y.;Lopez,D.E.Catalysis 2006,19,41–84.(21)Liu,Y.;Lotero,E.;Goodwin,J.G.,Jr.J.Catal.2006,243,221–228.208Energy &Fuels,Vol.22,No.1,2008Di Serio et al.directly to the support surface,electronically retain the catalytic anions on the solid surface:The reaction occurs betweenmethanol adsorbed on the cation and ester from the liquid (Eley–Rideal mechanism).The formation of alkoxide groups is also a fundamental step for heterogeneous basic Lewis catalyst.For example,in the case of ethylacetate transesteriﬁcation,catalyzed by MgO,the reaction occurs between the methanol molecules adsorbed on a magnesium oxide free basic sites and the ethyl acetate moleculesfrom the liquid phase (Eley–Rideal mechanism).22,23Both homogeneous Brönsted (H 2SO 4,p -toluensolfonic acid 5,20)and Lewis (metal acetate,10,15,18–20metal complexes 24)acid catalysts have been used in biodiesel synthesis,and both catalyze either transesteriﬁcation and esteriﬁcation reactions.25Brönsted acid catalysts are active mainly in esteriﬁcation reactions while Lewis acid catalysts are more active in transesteriﬁcation reactions (see,for example,Table 126).Table 1reports data of runs performed by using a series of small stainless steel vial reactors.Both the reagents (oil (FFA )0.2%w/w))2.0g,methanol )0.88g)and a speciﬁed amount of the catalyst were introduced into each reactor.All the reactors were then heated in a ventilated oven.The temperature of the oven was initially ﬁxed at 50°C for 14min and then increased at a rate of 20°C/min until the reaction temperature was reached,where the samples were kept for the ﬁxed reaction time.At the end of the reaction,the temperature was quenched by putting the vials in a cold bath.Experimental runs were also performed by adding oleic acid to the reaction mixture.Oleic acid has been chosen as a test molecule for simulating the behavior of FFA.The lead acetate (Lewis acid)has greater transesteriﬁcation activity than p -toluenesulfonic (Brønsted acid)acid,while on the contrary p -toluenesulfonic acid is more active than lead acetate in esteriﬁcation reactions.The lower yield obtained with lead acetate using an acid oil is justiﬁed by the strong deactivation of the Lewis catalyst due to the water formed in the esteriﬁcation reaction.15In both homogeneous and heterogeneous Brønsted acid catalysis,the mechanism pathways proceed through the protonation of the carbonyl group:increasing its electrophi-licity and rendering it more susceptible to alcohol nucleo-philic attack.21In the case of Naﬁon supported on silica (Naﬁon SAC-13),Lopez et al.27proposed a mechanistic pathway for triacetin transesteriﬁcation s a mechanism similar to that accepted for a homogeneous Brønsted acid catalyst.They found activation energy and reaction orders similar to the ones showed by sulfuric acid.27The reaction mechanism in esteriﬁcation reactions promoted by solid acid Brønsted catalysts is also similar to the homoge-neous one.28Liu et al.,28found that Naﬁon supported on silica has comparable turnover frequencies (TOF)to H 2SO 4and a similar reaction mechanism in esteriﬁcation of the liquid acetic acid with methanol.The reaction occurs via a single-site Eley–Rideal mechanism involving a nucleophilic attack between adsorbed carboxylic acid and unadsorbed alchohol as the rate-determining step.28The formation of a more electrophilic species also occurs with homogeneous and heterogeneous Lewis acid catalysts as the ﬁrst step in the reaction mechanism:15,29–31In this case,therate-determining step depends on the Lewis catalyst’s acid strength.After the Lewis complex formation (stage 1),the alcohol nucleophilic bonding (stage 2),and the new ester formation (stage 3),the new ester desorbs from the Lewis site (stage 4)and the cycle is repeated.If the strength of acidic sites is too high,the desorption of the product is not favored,(22)Dossin,T.F.;Reyniers,M.F.;Marin,G.B.Appl.Cat.B.2006,61,35–45.(23)Dossin,T.F.;Reyniers,M.F.;Berger,R.J.;Marin,G.B.Appl.Cat.B.En V iron.2006,67,136–148.(24)Abreu,F.R.;Lima,D.G.;Hamù,D.G.;Einloft,S.;Rubim,J.C.;Suarez,P.A.Z.J.Am.Oil Chem.Soc.2003,80,601–604.(25)López,D.E.;Suwannakarn,K.;Bruce,D.A.;Goodwin,J.G.,Jr.J.Cat.2007,247,43–50.(26)DiSerio,M.;Tesser,R.;Mandato,N.;Santacesaria,E.Unpublished data.(27)López,D.E.;Goodwin,J.G.,Jr.;Bruce,D.A.J.Cat.2007,245,381–391.(28)Liu,Y.;Lotero,E.;Goodwin,J.G.,Jr.J.Cat.2006,242,278–286.(29)Parshall,G.W.Ittel SI Homogeneous Catalysis:The Applications and Chemistry of Catalysis by Soluble Transition Metal ,2nd ed.;Wiley-Interscience:New York,2005.(30)Di Serio,M.;Apicella,B.;Grieco,G.;Iengo,P.;Fiocca,L.;Po,R.;Santacesaria,E.J.Mol.Cat.A.Chem.1998,130,233–240.(31)Bonelli,B.;Cozzolino,M.;Tesser,R.;Di Serio,M.;Piumetti,M.;Garrone,E.;Santacesaria,E.J.Cat.2007,246,293–300.Table 1.Oil )Soybean,8g;Methanol/Oil Molar Ratio )12:126catalyst initial FFA conc (%wt)reaction temp (°C)reaction time (min)cat (mol)FAME yield (%)ﬁnal FFA conc (%wt)uncatalyzed 180402uncatalyzed 20.5180602210.7Pb(Ac)218040 5.4710-592p -toluenesulfonic acid 18040 5.3510-529Pb(Ac)220.518060 5.3810-557 6.8p -toluenesulfonic acid20.5180606.4010-5481.1Catalysts for Biodiesel Production Energy &Fuels,Vol.22,No.1,2008209determining a slow reaction rate.15,29–31This mechanism was conﬁrmed for both homogeneous15,29,30and heterogeneous catalysts31by the observation that an optimal range of strength for Lewis acidic sites exists and that very strong Lewis acidic catalysts are less active in transesteriﬁcation reactions.15,29–31 Basic Catalysts.Gryglewicz32investigated the possibility of using alkaline-earth metal hydroxides,oxides,and alkoxides to catalyze the transesteriﬁction of rapeseed oil at methanol reﬂux temperature.He found that sodium hydroxide was the most active,barium hydroxide was slightly less active,and that calcium methoxide showed medium activity.The reaction rate was lowest when CaO powder was used as catalyst while magnesium oxide and calcium hydroxide showed no catalytic activity.32The high activity of barium hydroxide is due to its higher solubility in methanol with respect to other compounds. The order of reactivity Ca(OH)2<CaO<Ca(CH3O)2agrees with the Lewis basic theory:the methoxides of alkaline-earth metals are more basic than their oxides which are more basic than their hydroxides.32Table2reports some data about CaO catalytic performance.32,33The yield of biodiesel using CaO as a catalyst increases with increase in the temperature and methanol/oil molar ratio,especially in the case of the methanol supercritical state33,34s see Table3entries1–3.In the methanol supercritical state,good performances were obtained also with Ca(OH)2and CaCO334s see Table3entries4–6.Increases in CaO performances can be obtained using nanocrystalline calcium oxides.35The nanocrystalline calcium oxides(crystal size)20nm;speciﬁc surface area)90m2/g) give100%conversion of soybean oil at room temperature after 12h while the conversion obtained with commercial CaO (crystal size)43nm;speciﬁc surface area)1m2/g)is only 2%.35López Granados et al.36studied the activity of activated CaO as a catalyst in the production of biodiesel by the transesteri-ﬁcation of triglycerides with methanol.The active surface sites of CaO are poisoned by the atmospheric H2O and CO2.The catalytic activity of CaO can be improved if CaO is subjected to an activation treatment at high temperature(g700°C)before the reaction s to remove the main poisoning species(the carbonate groups)from the surface s and if the contact with atmospheric air is prevented after this treatment.36Even if the catalyst can be reused for several runs without signiﬁcant deactivation,dissolution of CaO does occur.The catalytic reaction is the result of the contribution of both heterogeneous and homogeneous catalysis for the formation of leached active species and further investigation is necessary to quantify this aspect.36The transesteriﬁcation rate can be increased using microwave energy,37,38because the microwave energy selectively energizes the catalyst’s interaction with the reactants.38Table4(entries1and2)reports results obtained with Ca(OH)238and Ba(OH)2.37The data of Mazzochia et al.37 conﬁrm that Ba(OH)2is not a completely heterogeneous catalyst. As a matter of fact,when the product obtained after reaction is not washed several times with distilled water,the resulting FAME and glycerine contain ca.0.06%and0.25%of barium, respectively.Good results in transesteriﬁcation of soybean oil were obtained using ZnO loaded Sr(NO3)2followed by calcination at873K for5h.39When the transesteriﬁcation reaction was carried out at reﬂux of methanol(65°C),with a12:1molar ratio of methanol to soybean oil and a catalyst amount of5wt %,the conversion of soybean oil was94.7%.39The SrO derived from thermal decomposition of Sr(NO3)2at high calcination temperatures is probably the main catalytically active specie.39 However,the used catalyst was signiﬁcantly deactivated and could not be directly reused for transesteriﬁcation.39Yang and Xie39explained the deactivation by the deposition of reactants and products on the active sites and/or by a transformation of the active sites and their interactions during the reaction. However,the leaching of SrO was not examined;notwithstand-ing,its high solubility in the reaction environment36is known. Sodium silicate catalyzes the transesteriﬁcation of oils with high rates at moderate temperatures(60–120°C)s even if no data on catalyst reusability was reported.38Also in this case, the use of microwave energy and high methanol/oil ratio greatly increases the performances s see Table4entries3and4. Corma et al.,40in a patent mainly devoted to the transesteri-ﬁcation of triglycerides with glycerol to prepare monoglycerides, claimed the possibility to use calcined hydrotalcites and magnesium oxides in promoting the transesteriﬁcation of triglycerides with monoalcohols,even if no examples or experimental data for this reaction are reported in the mentioned patent.Leclercq et al.41tested the use of commercial MgO/Al2O3 hydrotalcites and MgO(300m2/g)in the transesteriﬁcation of rapeseed oil.They found that MgO was more active than hydrotalcite s see Tables5and6entry1.On the other hand, Cantrell et al.,42successfully used calcined hydrotalcites in promoting the transesteriﬁcation of glycerol tributyrate with methanol at60°C.The rate increases steadily with Mg content, and the most active catalyst Al/(Mg+Al))0.25was10times more active than MgO.42Xie et al.,43for soybean oil transes-teriﬁcation at methanol reﬂux,found that the most active calcined hydrotalcite has again an atomic ratio Al/(Mg+Al) )0.25s see Table6entries2–4s and that a higher active solid is obtained by calcining it at500°C;see Table6entries3,5, and6.Di Serio et al.44and Siano et al.45showed the possibility(32)Gryglewicz,S.Bioresour.Technol.1999,70,249–253.(33)Demirbas,A.Energy Con V ers.Manage.2007,48,937–941.(34)Tateno T.,Sasaki T.Process for producing fatty acid fuels comprising fatty acids esters.U.S.Patent6,818,026,Nov16,2004.(35)Reddy,C.;Reddy,V.;Oshel,R.;Verkade,J.G.Energy Fuels2006, 20,1310–1314.(36)Lopez Granados,M.;Zafra Poves,M.D.;Martin Alonso,D.; Mariscal,R.;Cabello Galisteo,F.;Moreno Tost,R.;Santamaria,J.;Fierro, J.L.G.App.Cat.B.2007,73,317–326.(37)Mazzocchia,C.;Modica,G.;Nannicini,R.;Kaddouri,A.C.R. Chim.2004,7,601–605.(38)Portnoff,M.A.;Purta,D.A.;Nasta,M.A.;Zhang,J.Pourarian,F.Methods for producing biodiesel.PCT No.WO2006/002087,Jan5,2006.(39)Yang,Z.Q.;Xie,W.L.Fuel Process.Technol.2007,88,631–638.(40)Corma,A.,Iborra,S.,Miquel,S.,Primo Millo,J.Process and Catalysts for the Selective production of Esters of fatty Acids.PCT No WO98/56747,Dec17,1998.(41)Leclercq,E.;Finiels,A.;Moreau,C.J.Amer.Oil Chem.Soc.2006, 78,1161–1165.(42)Cantrell,D.G.;Gillie,L.J.;Lee,A.F.;Wilson,K.Appl.Catal., A2005,287,183–1990.(43)Xie,W.;Peng,H.;Chen,L.J.Mol.Cat.A.2006,246,24–32.(44)Di Serio,M.;Ledda,M.;Cozzolino,M.;Minutillo,G.;Tesser,R.; Santacesaria,E.Ind.Eng.Chem.Res.2006,45,3009–3014.Table2.FAME Yield Using CaO as Catalyst at15min ofReaction Timeref oilreactiontemp(°C)methanol/oilmolar ratiocat conc(%w/w)FAMEyield(%)32rapeseed methanol reﬂux 4.5:10.81033sunﬂower19241.1:1 3.050210Energy&Fuels,Vol.22,No.1,2008Di Serio et al.to use calcined hydrotalcites and MgO for industrial biodiesel production at moderately high temperature.High yields of methyl esters were obtained in1h of reaction time at180–200°C s see Tables5(entries2–3)and6(entry7).At least four different types of basic sites have been indentiﬁed on the surface of MgO and calcined hydrotalcite catalysts.44The strongest basic sites(superbasic)promote the transesteriﬁcation reaction also at very low temperatures(100°C),while the basic sites of medium strength require higher temperatures to promote the same reaction.44The experimental data reported show a correlation not only with the catalyst basicity but also with its structural texture.44However,the structural texture of the catalysts examined is dependent on both the precursor and the preparation method.44,46MgO catalyst used to promote transesteriﬁcation strongly increases the reaction rate in supercritical conditions,34as can be seen in Table3entry7.As vegetable oils,animal fats,and alcohols usually contain water,44the inﬂuence of the presence of water on MgO and calcined hydrotacite performances have also been investigated.44,45 Some runs have been performed at180°C in the presence of high water concentration(10000ppm).44The results show that the activity of both magnesium oxide and calcined hydrotalcite is not affected by the presence of an excess of water.44This lastﬁnding is relevant for industrial purposes,because the possibility to operate in the presence moisture reduces the raw material pretreatment costs and opens the possibility to use unreﬁned bioethanol.However,Oku et al.47showed that in a run performed at150°C with60g of triolein,20g of methanol,and2.5g of Mg/Al hydrotalcite after24h of reaction,a FAME yield of77was produced,but a very high concentration of Mg and Al ions were detected in the products(Mg17800ppm;Al6900ppm).So, the problems of catalyst leaching need more in-depth study to conﬁrm the possibility of using MgO and related hydrotalcites as industrial catalysts.Corma et al.48have reported that calcined Li/Al hydrotalcites are more active in glycerolysis of fatty acid methyl esters than the Mg/Al material(or MgO)due to their higher Lewis basicity. Starting from this observation,Shumaker et al.49studied the transesteriﬁcation of soybean oil to fatty acid methyl esters using a calcined Li/Al layered double hydroxide catalyst.It was found that,at the reﬂux temperature of methanol,near-quantitative conversion of the soybean oil was achieved at low catalyst loadings(2–3wt%)and short reaction times(∼2h).49Catalyst recycling runs showed that the catalyst maintained a high level(45)Siano,D.;Nastasi,M.;Santacesaria,E.;Di Serio,M.;Tesser,R.; Minutillo,G.;Ledda,M.;Tenore,T.Process for Producing esters from vegetable oils or animal fats using heterogeneous catalysts.PCT Application No WO2006/050925,May18,2006.(46)Choudhary,V.R.;Pandit,M.Y.Appl.Catal.1991,71,265–274.(47)Oku,T.;Nonoguchi,M.;Moriguchi,T.Method of producing of fatty alkyl esters and/or glycerine and fatty acid alkyl ester-containing composition.PCT Application No WO2005/021697,Mar10,2005.(48)Corma,A.;Hamid,S.B.A.;Iborra,S.;Velty,A.J.Catal.2005, 234,340–347.(49)Shumaker,J.L.;Crofcheck,C.;Tackett,S.A.;Santillan-Jimenez,E.;Crocker,M.Cat.Lett.2007,115,56–61.Table3.FAME Yield Using Basic Catalysts in Methanol Supercritical Conditionsentry ref oil catalystreactiontemp(°C)methanol/oilmolar ratioreacttime(min)cat conc(%w/w)FAMEyield(%)133sunﬂower CaO252 6.0:115 3.065 233sunﬂower CaO25241.1:115 3.099 334soybean CaO30039.3:1100.5897 434soybean CaCO325039.3:110 1.1487 534soybean CaCO330039.3:1100.6799 634soybean Ca(OH)230039.4:1100.6898 734soybean MgO30039.6:110 1.2991 parison of the Transesteriﬁcation Tests of Oil with Methyl Alcohol Carried out under Microwave Irradiationentry ref oil catalystreactiontemp(°C)methanol/oilmolar ratioreactiontime(min)cat conc(%w/w)FAMEyield(%)137rapeseed Ba(OH)2methanol reﬂux9:1150.597–98 238soybean Ca(OH)21006:120 2.081 338castor oil sodium silicate1206:110 1.570 438castor oil sodium silicate12019:110 1.5100Table5.FAME Yield Using MgO as Catalystentry ref oil surfaceareareactiontemp(°C)methanol/triglyceridesmolar ratioreactiontime(h)cat conc(%w/w)FAMEyield(%)141rapeseed300methanol reﬂux75:1221064 244soybean3618012:11 5.072 344soybean22918012:11 5.090Table6.FAME Yield Using Calcined MgO/Al2O3as Catalystentry ref oil Al/(Mg+Al)surfaceareacalcinationtemp(°C)reactiontemp(°C)methanol/oilmolarratioreactiontime(h)cat conc(%w/w)FAMEyield(%)141rapeseed0.30160450methanol reﬂux275:1221034 243soybean0.28500methanol reﬂux15:197.528 343soybean0.25500methanol reﬂux15:197.566 443soybean0.22500methanol reﬂux15:197.550 543soybean0.25450methanol reﬂux15:197.545 643soybean0.25600methanol reﬂux15:197.557 744soybean0.2514450018012:11 5.092 Catalysts for Biodiesel Production Energy&Fuels,Vol.22,No.1,2008211。

Non-Equilibrium in Adsorbed Polymer Layers

a r X i v :c o n d -m a t /0407246v 2 [c o n d -m a t .s o f t ] 1 N o v 2004TOPICAL REVIEWNon-Equilibrium in Adsorbed Polymer LayersBen O’Shaughnessy and Dimitrios Vavylonis Department of Chemical Engineering,Columbia University,New York,NY 10027,USA E-mail:bo8@,dv35@ Abstract.High molecular weight polymer solutions have a powerful tendency to deposit adsorbed layers when exposed to even mildly attractive surfaces.The equilibrium properties of these dense interfacial layers have been extensively studied theoretically.A large body of experimental evidence,however,indicates that non-equilibrium eﬀects are dominant whenever monomer-surface sticking energies are somewhat larger than kT ,a common case.Polymer relaxation kinetics within the layer are then severely retarded,leading to non-equilibrium layers whose structure and dynamics depend on adsorption kinetics and layer ageing.Here we review experimental and theoretical work exploring these non-equilibrium eﬀects,with emphasis on recent developments.The discussion addresses the structure and dynamics in non-equilibrium polymer layers adsorbed from dilute polymer solutions and from polymer melts and more concentrated solutions.Two distinct classes of behaviour arise,depending on whether physisorption or chemisorption is involved.A given adsorbed chain belonging to the layer has a certain fraction of its monomers bound to the surface,f ,and the remainder belonging to loops making bulk excursions.A natural classiﬁcation scheme for layers adsorbed from solution is the distribution of single chain f values,P (f ),which may hold the key to quantifying the degree of irreversibility in adsorbed polymer layers.Here we calculate P (f )for equilibrium layers;we ﬁnd its form is very diﬀerent to the theoretical P (f )for non-equilibrium layers which are predicted to have inﬁnitely many statistical classes of chain.Experimental measurements of P (f )are compared to these theoretical predictions.PACS numbers:82.35.-x,68.08.-p,05.40.-a Submitted to:J.Phys.:Condens.Matter1.IntroductionHigh molecular weight polymers are extremely surface-active molecules.Even a weak interaction between a single monomer and a surface tends to be magniﬁed into a powerful attraction or repulsion when many of these monomers are linked together to form a polymeric chain.It is a remarkable fact that surfaces contacting even extremely dilute polymer solutions can readily develop very dense polymer layers.Technologies revolving around the properties of either synthetic or biological polymer layers are many and varied,including adhesion [1,2],coating[3],colloid stabilization[4],ﬁber reinforced thermoplastics[5,6],ﬂocculation processes[7],DNA microaarrays[8]and biocompatibilization[9].Motivated both by fundamental questions and by technology, understanding and predicting the structure and formation kinetics of these soft layers is a major concern of polymer science[10].A crucial aspect of experimental studies is that adsorbed polymer dynamics are typically extremely slow for long chains:an individual chain has many surface stickers and interacts with numerous other chains impeding its motion.Irreversibility and non-equilibrium eﬀects are therefore very common.The subject of this review is experimental and theoretical work on these non-equilibrium eﬀects, and though we consider adsorption from dilute solutions,semi-dilute solutions and melts our main emphasis is neutral homopolymer adsorption from dilute solutions.This is the simplest and most widely studied class.Polymer-surface adsorption systems are naturally classiﬁed according to the mode of adsorption. Roughly,there are two classes:chemisorption and physisorption(seeﬁgure1).The clearest example of irreversibility arises in chemisorption(ﬁgure1(b))where the covalent polymer-surface bonds which develop are often essentially irreversible on experimental timescales.Monomer sticking free energies,ǫ,have values typical of covalent bonds which are one to two orders of magnitude greater than kT.Chemical adsorption is employed in various technologies where polymers are attached by chemical reactions to solid surfaces either from a polymer melt as in the reinforcement of polymer-polymer or polymer-solid interfaces[2,6,11,12],or from solution as in colloid stabilization by chemically grafting polymers onto particle surfaces[13–15].What is less obvious is why non-equilibrium eﬀects are so widely observed in physisorbing systems, even for rather weak sticking energies.Available experimental evidence suggests that irreversibility eﬀects become important as soon asǫbecomes somewhat larger than kT.For example the experiments by Schneider et al.[16,17]for polymethylmethacrylate(PMMA)adsorption onto oxidized silica via hydrogen bonding in dilute CCl4solutions(ǫ≈4kT)show essentially frozen-in adsorbed chain conﬁrge physisorption sticking energies(ǫ>kT)originate in hydrogen bonding or other dipolar forces,dispersion forces or attractions between charged groups.Metal and silicon-based surfaces are usually oxidized and many polymer species form strong hydrogen bonds with the surface oxygen or silanol groups[18,19].Biopolymers such as proteins and DNA attach tenaciously to many surfaces due to their many charged,polar and hydrophobic groups[8,9,20].Since hydrogen bonds,for instance,typically have energies of several kT[21,22]it is apparent that strong physical bonds are very common.This suggests that whether physical or chemical bonding is involved,for long chains irreversible eﬀects may in practice be the rule rather than the exception.Figure 1.(a)Schematic of physisorption from aﬂuid polymer phase onto a surface.Adsorbed chainsconsist of loops,tails and sequences of bound monomers(“trains”).When non-equilibrium eﬀects becomeimportant,layer structure depends on kinetics of adsorption.This review addresses phyisorption from dilutesolutions in sections2,3and4and physisorption from melts in section6.(b)As in(a)but for chemisorption.In this case chains carry reactive groups which can form covalent bonds(shown black)with a functionalizedsurface.Chemisorption from dilute solutions is reviewed in section5and from concentrated solutions insection6.To understand non-equilibrium layers,one must identify how they diﬀer from equilibrium layers.The theory of fully equilibrated layers is far more advanced,at both the mean-ﬁeld[23]and scaling[24–31]level of description.A main result of these theories is expressions for the decay of the monomer density proﬁle asFigure2.The two broad classes of polymer adsorption,physisorption and chemisorption,have very diﬀerentvalues of the parameter Q,the local monomer-surface association rate.Q can be thought of as the conditionalmonomer-surface sticking probablity per unit time,given the unattached monomer contacts the surface.Though many systems are in practice mixtures of chemisorption and physisorption,a simpliﬁed view ofmonomer free energy as a function of distance between monomer and surface is shown.(a)For physisorbingpolymers,the activation barrier is very small and and monomer-surface association is very likely upon contact,i.e.Qt a is of order unity,where t a the monomer relaxation time.When the sticking energyǫexceeds a fewkT,experiment indicates that chains need large amounts of time to escape the surface,presumably due tocomplex many-chain eﬀects.(b)Chemisorption typically involves a large activation barrier,u≫kT.Manymonomer-surface collisions are needed to traverse this barrier,Qt a≪1.The adsorbed state is also usuallystrongly favored,ǫ≫kT.a function of the distance z from the surface.For adsorption from dilute solutions for example,in the scaling picture originally developed by de Gennes[24,25],Eisenriegler et al.[26,27],and de Gennes and Pincus[28], each adsorbed chain has sequences of surface-bound monomers(trains)interspersed with portions extending away from the surface(tails and loops of size s)with distributionΩ(s)∼s−11/5[29–31]leading to a self-similar density proﬁle c(z)∼z−4/3.Experimentally,the existence of an extended diﬀuse layer is well established by a large number of neutron scattering[32–37]and neutron reﬂectivity[38–40]studies.However a universally accepted quantitative test of the predicted density proﬁles has been diﬃcult to achieve,both due to intrinsic limitations of the experimental techniques[41]and to the asymptotic nature of many of the theoretical results which are valid in the limit of very long chains.Furthermore,for experiments speciﬁcally directed at equilibrium,ensuring that equilibrium conditions are realised is diﬃcult when the very non-equilibrium eﬀects one wishes to avoid are poorly identiﬁed.Understanding the origin of the observed deviations from equilibrium for weakly adsorbing systems in dilute solutions is a major unresolved puzzle in polymer science.At present it is unclear how universal these non-equilibrium eﬀects may be.Various eﬀects have been speculated to play important roles.Kremer[42] and de Gennes[43]have suggested that if the solution temperature is below the polymer melt glass transition temperature,glassy eﬀects may onset at the interface where polymer densities are similar to those of melts. Interactions with the surface might further enhance glassiness.Chakraborty and coworkers[44–47]suggested ﬂattened-down chains experience strong kinetic barriers due to local steric constraints which drastically slow down dynamics.Ideas related to slow cooperative motions,mutual pinning,development of entanglements at the interface and crystalization have been proposed by Johner and Semenov[48],Sommer[49],Granick[50] and Raviv et el.[51]in a series of comments following a recent theoretical work by Raviv et al.[52]which interpreted past experiments[53,54]exhibiting non-equilibrium eﬀects.In this review we do not attempt an exhaustive review of the vast body of past research work involving strongly physisorbing or chemisorbing polymers at interfaces.Instead,with fundamental issues in mind,our aim is to(i)assemble and classify a number of theoretical ideas and numerical simulations which articulate the community’s current level of understanding of equilibrium and non-equilibrium polymer adsorption,and (ii)summarize a number of experimental results which we believe are particularly pertinent and which still demand a theoretical explanation.The emphasis is on the simplest case:adsorption of neutralﬂexible polymers from dilute bulk solutions.We also review work on irreversible adsorption from semi-dilute bulk solutions and melts,motivated by ideas initiated by Guiselin[55].Polyelectrolyte solutions,polymers with complex architectures and non-ﬂat surfaces are beyond the scope of the present review.Physisorption and chemisorption will be carefully distinguished.These are characterized by very diﬀerent values of the local monomer-surface association rate,Q(seeﬁgure2).In physisorption,monomer attachment is usually essentially diﬀusion-limited,Q=C/t a,where t a is monomer relaxation time and C is a system-dependent constant of order unity[56].Chemisorption is normally much slower[56–58]with Q values typically 8or more orders of magnitude smaller than those of physisorption.The origin of this diﬀerence is that chemical bond formation usually involves a large activation barrier(seeﬁgure2).Similarly,desorption ratesafter chemisorption are usually very small and can be ignored.The eﬀect of desorption on physisorbing systems is more subtle and is discussed in section4.The above two classes naturally lead to very diﬀerent adsorption kinetics.This is analogous to bulk polymer-polymer reaction kinetics where depending on Q, polymer length N,and solvent conditions,the kinetics are described by one of a range of“diﬀusion-controlled”and“mean-ﬁeld”kinetic regimes[58–61].Such regimes also arise for end-adsorbing polymers[56,57,62–67].In section2we brieﬂy review the equilibrium picture for dilute solutions and in section3we discuss experimental evidence for non-equilibrium departures from this picture.Theoretical work related to physisorbing non-equilibrium layers from dilute solution is reviewed in section4.We move to chemisorption, again from dilute solution,in section5.Section6addresses irreversibility eﬀects involving melts and semi-dilute solutions.We conclude with a brief discussion of the experimental and theoretical outlook.2.Adsorption from Dilute Solutions:The Equilibrium Picture2.1.Structure of Equilibrium LayersThis section brieﬂy outlines some central results of equilibrium theories of adsorbed polymer layers.Much more extensive reviews can be found in refs.[41,68–71].In the scaling picture developed mainly in the 1980’s[24–28],each adsorbed chain consists of surface-bound monomers and large loops and tails generating a monomer density proﬁle c(z)as a function of distance from the surface,z.Eisenriegler et al.[26–28]showed that very close to the surface,in the“proximal”region,the density decays as a power law,c(z)∼z−m,where the critical exponent m≈1/3represents competion between surface-sticking energy gain,chain entropy,and excluded volume interactions.The proximal region decay law crosses over to de Gennes’“self-similar grid”regime[24,25,28],c(z)∼z−4/3,beyond a certain distance h prox.For z>h prox the polymer layer can be thought of as a semi-dilute solution with continously varying local concentration c(z).In this region the correlation length measuring the range of excluded-volume interactions,ξ=a−5/4c−3/4,is proportional to the distance from the surface,z,since this is the only relevant length scale:ξ≈z.Here a is deﬁned to be the monomer size.Expressingξin terms of c leads to†a3c(z)≈ (a/h prox)(a/z)1/3,a<z<h proxh prox=a kT/ǫ,R F=aN3/5(1)(a/z)4/3,h prox<z<R FUnless the bulk polymer concentration,c,is extremely small[72],then the equilibrium layer height is of order the Flory bulk coil radius R F as indicated in equation(1).In this same range of c the adsorption isotherm exhibits a large plateau,i.e.surface coverageΓis weakly dependent on c.Even in weakly adsorbing polymer systems,e.g.adosrption through weak van der Waals interactions,the value ofǫis usually of order kT.By studying the adsorption/desorption transition in binary solvent mictures, van der Beek et al.[18]estimated the sticking energies per monomer of many typicalﬂexible polymers onto silica and alumina surfaces from organic solvents to lie in the range0.5to6kT.Hence the width of the proximal region is typically of order the monomer size,h prox≈a,and a clear signature of the proximal region is hard to probe experimentally.In the following we considerǫof order kT or larger.We remark that the net monomer free energy of adsorptionǫincludes both the“stickiness”a monomer feels for the surface, but also the entropic disadvantage due to constraining local orientational degrees of freedom upon contact with the surface.Thus,crudely speaking one can say the stickiness contribution must exceed a crtical value ǫc representing the entropic disadvantage before a monomer can puter simulations showǫc is of order kT and is lattice-dependent[27].The real situation is more complex,with various contributions from electronic and structural factors such as solvent molecule entropy eﬀects,etc[21].The density decay law of equation(1)reﬂects a power law distribution of loop and tail sizes.Neglecting diﬀerences between loops and tails and the details associated with the proximal region,then the loop size distribution per surface site is[29–31]Ω(s)≈a−2s−11/5.(2) Beyond this,Semenov and Joanny[31]showed that the inner region of the layer,z<z∗≡aN1/2,is dominated by loops while the outer region,z>z∗,is dominated by tails;the resulting density proﬁle obeys a z−4/3law above and below z∗,respectively,but with diﬀerent numerical prefactors.Support for the scaling conclusions of equations(1)and(2)is provided by Monte-Carlo simulations of Zajac and Chakrabarti[73], de Joannis et al.[74,75],and Cifra[76].These produce a density decay consistent with the z−4/3law for long chains.Zajac and Chakrabarti[73]additionally report agreement with equation(2).†The cross-over distance h prox and the prefactor in the proximal region density law can be determined by demanding(i)a smooth cross-over at h prox and(ii)the osmotic free energy per unit area, R F a dzkT/ξ3,balances the sticking free energy per unit area,ǫa c(a).Complementary to the scaling approach outlined above has been the numerical lattice model of Scheutjens and Fleer(SF)[77,78].This is a self-consistent meanﬁeld theory which averages excluded volume interactions and thus treats self-avoidance in an approximate manner.This approximation however allows numerical solutions for the density proﬁle and for the loop and tail distributions and can additionally describe chains of ﬁnite length.The meanﬁeld description becomes more accurate for solvents near the theta temperature(a common case)where self-avoidance is a weak perturbation except for the longest loops and tails.The existence of the loop-and tail-dominated regions of the layer was in factﬁrst established by the SF model[78,79].The layer height in the SF theory scales as h∼N1/2[77,78]while the density proﬁle decays as c(z)∼z−2(for suﬃciently long chains),diﬀerent to the z−4/3decay predicted by the scaling approach,as shown by van der Linden and Leermakers[80].Analytical meanﬁeld solutions for the density proﬁle in the limit of very long chains were derived within the ground-state dominance approximation[81] by Jones and Richmond[82].Going beyond the ground state dominance approximation,Semenov et al.[23] subsequently generalized this approach to account forﬁnite length eﬀects to leading order and analytically describe the diﬀerent contributions of loops and tails to the density proﬁle.They found that loops dominate for z<z∗MF≡aN1/3while tails dominate for z>z∗MF,similarly to the scaling approach of Semenov and Joanny[31].These new methods have revived interest in analytical and numerical meanﬁeld approaches to polymer adsorption[83–89].Turning now to experiment,the fundamentals of polymer adsorption at the solid/liquid and air/liquid interface have been studied in a vast number of experiments.Research prior to1993is reviewed in the book by Fleer et al.[41].Given the strong evidence for nonequilibrium eﬀects(see below),in general one should be very cautious when comparing experimentalﬁndings to equilibrium expectations.Overall,experiment is consistent with the general trend predicted by equilibrium theories regarding structure of the polymer layers which were studied,although theﬁne diﬀerences between the meanﬁeld and scaling pictures are hard to distinguish.Very brieﬂy,measurements of the layer’s surface bound monomer fraction as a function of total adsorbed amount and molecular weight(MW)by techniques such as NMR[90,91],ESR[92,93],or infrared spectroscopy[94]give results fairly consistent with the predictions of the SF theory[41].The thickness, h exp,of polymer layers has been probed as a function of chain length by hydrodynamic methods[41,95–97], ellipsometry[98],and the surface force apparatus[99].Depending on the method,h exp is proportional to a certain moment of the density proﬁle and many existent measurements are compatible with a power law,h exp∼Nα.Certain studies have favored the SF theory predictions[41,96]while others support the scaling predictions[97,99].Forﬂexible polymer species the total surface coverageΓas a function of bulk concentration is found to be very weakly dependent on the polymer concentration in the bulk except for very dilute solutions,in qualitative agreement with both the scaling and the SF theories[41].For a given bulk concentration,meaurements ofΓas a function of N in good solvents typically show a weak dependence on chain length for large N[41].This is consistent with the SF and scaling theories which predictΓ∼ h a dz c(z) is dominated by the lower,N-independent limit.Small angle neutron scattering(SANS)and neutron reﬂectivity have been used to probe the density proﬁle.These experiments established the existence of a diﬀuse extended layer but at present there is no general agreement as to the exact form of the density decay.A techical diﬃculty intrinsic to SANS,as dicussed in ref.[41],is its limited sensitivity to the more dilute regions of the layer.Neutron reﬂectivity experiments are also often ambiguous,since multiple density proﬁles can beﬁtted to the same data.The SANS experiments of Auvray and Cotton[35]and Hone et al.[37]are consistent with the z−4/3scaling law.However the results of Hone et al.could also be described by an exponential proﬁle(see also[32]). SANS experiments by Cosgrove et al.[33,34]do not support the scaling predictions,but are more consistent with the SF theory.Other SANS studies by Rennie et al.[36]are inconsistent with both scaling and SF predictions,while neutron reﬂectivity experiments of Lee et al.[38,39]and Sun et al.[40]have generated data consistent with the scaling predictions.2.2.Single Chain Statistics and the Equilibrium Distribution of Bound FractionsSo far this section has discussed many-chain layer properties.Equally important,and characteristic of the layer-forming processes,are properties of individual surface-adsorbed chains in the layer.What is the spectrum of conﬁgurations of individual chains?According to the scaling picture,a typical chain has ND(s) loops of length s or greater,where D(s)≡ ∞s ds′Ω(s′)∼s−6/5after using equation(2).Semenov and Joanny[100]argue that because of screening eﬀects these are essentially independent blobs and their2D spatial extent parallel to the surface is[ND(s)]1/2as3/5=aN1/2.This occurs for all scales s;in particular, a given chain has of order one loop of length N5/6,also of size aN1/2.Hence a typical chain has a lateral size of order aN1/2,the ideal result(to within logarithmic corrections[100]).Figure3.Equilibrium probabilty distribution P eq of chain bound fraction,f,in good solvents.For verylong chains the distribution is sharply peaked at a value¯f of order unity.For realistic values of N thedistribution is rather broad.A special role is played by another single chain property,directly reﬂecting the degree to which individual chains are bound to the surface.This is the probability distribution P eq(f)that a chain has a fraction f of its monomers touching the surface.This property plays a central role in this review,since its features closely reﬂect whether irreversible eﬀects matter or not.In two independent Monte Carlo studies by Wang and Rajagopalan[101]and Zajac and Chakrabarti[73]an equilibrium distribution was found with a single peak at a value of f of order unity.To our knowledge,P eq(f)has not been calculated analytically,at least at the scaling level.In order to compare equilibrium predictions with experimental measurements of bound fractions in non-equilibrium layers in later sections,we have calculated P eq(f)by relating an adsorbed chain to a1D unidirectional walk combining an initial tail,a sequence of intermediate steps,and aﬁnal tail.The result,which is derived in the appendix and is shown inﬁgure3,reads:N−1/5P eq(f)≈Figure4.Schematic of new chain adsorption in an equilibrium polymer layer(shown as a self-similar grid)as described in ref.[102].(a)Entry:a bulk chain reptates into the layer and makes aﬁrst attachment to thesurface.(b)Spreading:the incoming chain establishes an increasing number of contacts with the surface.(c)A typical adsorbed chain conﬁguration is adopted,consisting of trains,loops and tails.A similar picturewas used in ref.[100].Chain desorption follows the same path in the reverse order.3.1.Theories of Dynamics in Equilibrium LayersCompared to static properties,much less is established theoretically about equilibrium dynamics.These have been studied for good solvents by de Gennes[43,102–105],Semenov and Joanny[100],and Baschnagel et al.[106]for bidisperse solutions.The picture emerging from these works is that the layer of bound chains has a certain characteristic equilibration timeτeq.This can be thought of as the time after which the chains following the distribution P eq(f)ofﬁgure3are completely reshuﬄed among themselves.The exchange of chains between the bulk and the layer was predicted to be a slower process due to the fact that incoming and outgoing chains have to pass through unfavored conﬁgurations having a small fraction of bound monomers (seeﬁgure4).de Gennes assumed reptation dynamics(i.e.entangled layers)and found the longest relaxation time of the layer to scale as[102,104,105]τeq≈t s N3(entangled layers).(4) Here t s is the relaxation time of an adsorbed monomer which,due to wall-polymer interactions,may be much larger than the corresponding time in the bulk,t a[107].Semenov and Joanny[100]assumed unentangled layers and Rouse-Zimm dynamics and obtainedτeq≈t a N2(in their work t s≈t a was assumed).In equilibrium,layer and bulk chains desorb and adsorb at the same average rate,respectively.In de Gennes’picture bulk chains adsorb in two stages(seeﬁgure4).During theﬁrst“entry”stage,the bulk chain overcomes the exclude-volume barrier presented by the layer’s loops and tails and makes itsﬁrst contact with the surface,i.e.f=1/N.During a second“spreading”stage the chain continues to make an increasing number of surface-contacts,f increases up to f min,and the chain becomes part of the bound layer. When entry is rate-limiting he found that the mean lifetime of an adsorbed chain before its desorption is τex≈t a N3.7/φ,whereφis the volume fraction of polymer in the bulk.Semenov and Joanny[100]described the dynamics using a similar picture,but assuming unentangled layers and Rouse-Zimm dynamics.They obtained a slighlty diﬀerent chain lifetime,τex≈t a N2.42/φ(to within logarithmic corrections).Note that the exchange timescale,τex,has a weak power law dependence on N rather than exponential because the incoming/outgoing barrier is small.The scalingτex∼1/φreﬂects the linear dependence on concentration of the rate of chain arrival at the surface.Note also that even for the highest dilute solution concentrations,φ=φ∗,whereφ∗≡N−4/5is the chain overlap threshold concentration[81],one still has τeq≪τex.A prediction of the above works is that chain desorption into pure solvent,φ→0,is extremely slow,which is well-established experimentally[108].Now suppose one starts with a layer of labeled chains in equilibrium and replaces the bulk solution with identical but unlabeled chains of the same concentration at t=0.An important prediction of the above theories is that the decay of the surface coverage of labeled chains,Γ,is a simple exponential for all times[43,100]:Γ(t)=Γ(0)e−t/τex(5) An implicit feature of equation(5)is that there is a single observed desorption rate sinceτex≫τeq,i.e.the desporption process is slow enough to sample an average over all equilibrium chain states in the layer.Note this result in fact assumes a given desorbed labeled chain does not readsorb,i.e.memory is lost instantly. Experimentally,this necessitates a mixing process in the bulk to dilute the desorbed chains.In the absence of such mixing diﬀusion returns a desorbed chain to the surface repeatedly,an eﬀect which can lead to non-exponential decay[60,109,110].The kinetics of polymer layer build up starting from empty or“starved”surfaces is more complex and has been considered in refs.[43,100,102,111].3.2.Dynamics of Adsorbed Polymer Layers:Monte Carlo SimulationsThis sub-section provides a brief review of numerical Monte Carlo simulations of dynamics in many-chain polymer layers in contact with dilute solutions(for dynamics of single chains see refs.[112–116]).The simulations reported here did not include hydrodynamic interactions.The main results of the simulations by Wang et al.[101,117]are qualitatively in agreement with the theoretical picture of the previous subsection. They found that the lateral dynamics of adsorbed chains up to N=100are consistent with Rouse dynamics. For suﬃciently sticky surfaces(0<ǫ≤1.5kT withǫc=0.5kT)the value ofτex was found to be much larger than the lateral relaxation time,even though the scaling dependence on N was the same.This should be contrasted with the Semenov and Joanny prediction that the two exponents diﬀer by a small value,0.42. Wang et al.observed non-exponential exchange kinetics arising from readsorption of desorbed chains.Lai[113,118]studied the layer dynamics as a function ofǫfor N≤80and interestingly found that for ǫ>∼1kT(withǫc≈0.9kT)the lateral chain dynamics started to slow down and to approach apparently glassy dynamics atǫ≈4kT.This result was claimed to be valid despite an omission in the implemented algorithm[113,119].This report is important since it indicates that the value ofǫis crucial in polymer adsorption.Zajac and Chakrabarti[120]studied the dynamics for N=100and N=200andǫ+ǫc=1.8kT near and aboveφ=φ∗.Their algorithm involved unphysical reptation moves in order to speed up the dynamics. In equilibrium they found a distribution of bound fractions similar to the one ofﬁgure3and observed that the internal dynamics of reshuﬄing of chains between diﬀerent f values is complex.The timescale for the exchange of adsorbed chains by bulk chains was found to be slower than internal equilibration processes. Simple exponential exchange kinetics were observed as in equation(5).Takeuchi[121]also used the Monte Carlo method with extra reptation moves.For surfaces withǫ≈1.6kT he observed exponential exchange kinetics while forǫ≈0.9kT readsorption eﬀects were important leading to non-exponential exchange kinetics.3.3.Experiment:Departure from Equilibrium PictureTheﬁrst experimental studies of exchange kinetics onﬂexible polymers were performed by Peﬀerkon et al.[122–125]using radioactive labeling techniques.One study[122,124,125]involved labeled polyacrylamide (PAM)in water adsorbed through hydrogen bonding onto aluminol-grafted glass beads.The beads were exposed to a dilute solution of labeled PAM for approximately30min until time-independent coverage was achieved.The labeled solution was then replaced by a dilute unlabeled PAM solution of varying concentration c and the amount of labeled PAM which remained adsorbed,Γ,was monitored as a function of time as shown inﬁgure5(i).An interesting result of this experiment was that the exchange rate per labeled chain,shown inﬁgure5(ii),was time-dependent and reached a constant value after a cross-over period of≈300min which was approximately the same for every c.This asymptotic rate was found to increase linearly with c,as shown inﬁgure5(iii).The observed spectrum of exchange times disagrees with equation(5)and this can be interpreted in many ways as follows:(i)The observed non-exponential exchange kinetics is a signature of non-equilibrium.Peﬀerkorn et al.[122,124]argued that the interface is populated with a spectrum of diﬀerent frozen or slowly changing conﬁgurations and,consequently,diﬀerent kinetic properties.(They proposed that the layer consists of aﬂat sublayer of tightly bound chains which exchange slowly,plus a less tightly bound population which exchange more rapidly).(ii)The layer is not in equilibrium when the exchange experiment starts but it equilibrates afterτeq≈300min which is larger than the layer’s preparationg time.The asymptotic exchange rate then becomes constant and equal to1/τex.The fact that asymptoticallyτex∼1/c as seen inﬁgure5(iii)and the fact that τex>300min as can be seen inﬁgure5(ii),are consistent with this interpretation and the theories reviewed in subsection3.1.Assuming reptation dynamics,equation(4),and given N≈1400,this implies a relaxation time of adsorbed monomers of order t s≈10−5s.This is much larger than monomer relaxation times in the bulk,t a≈10−10s.(iii)The layer is in fact in equilibrium but its exchange kinetics and internal equilibration processes are much more complex than assumed by existent theories,at least for this system.For example,if the equilibrium P eq(f)is very broad and chains with diﬀerent f values have very diﬀerent exchange times,then the intial drop inΓwill be due mainly to the most rapidly desorbing chains if their desorption times are less than τeq.Issues related to surface density of aluminol groups,polydispersity,and eﬀect of pH(this experiment was performed at pH=4where PAM is neutral while many of the surface aluminol groups were positively。

calculus

( 9)
5
Properties of Exponents
1.
2.
xa ⋅ xb = xa+b Examples: x3 ⋅ x2 = x5, x1/2 ⋅ x1/3 = x5/6, x3 ⋅ x−1/2 = x5/2 xa a −b xb = x (xa)b = xab x5 x3 x3 Examples: x3 = x2, x5 = x−2, x1/2 = x5/2 Examples: (x3)2 = x6, (x−1/2)7 = x−7/2, (x2/3)5/7 = x10/21
for any two points (x1, y1) and (x2, y2) that lie on the line. For example, for the two points (0, 3) and 0−3 ∆y = = 2, which confirms our observation. (−1.5, 0) on our line, the slope is m = ∆x −1.5 − 0 • y = f (x) = x2: This is not the equation of a straight line (because of the “squaring” operation). The set of all points that satisfies this quadratic equation – e.g., (–3, 9), (–2, 4), (–1, 1), (0, 0), (1, 1), (2, 4), (3, 9), etc. – forms a curved parabola in the XY-plane. (In this case, the curve is said to be concave up, i.e., it “holds water.” Similarly, the graph of –x2 is concave down; it “spills water.”) Exercise: How does this graph differ from y = f(x) = x3 ? x4 ? Formulate a rule for xn, for n = 1, 2, 3, 4, 5,…

帕尔曼英语阅读理解

帕尔曼英语阅读理解When a new movement in art attains a certain f ashion, it is advisable to find out what its advoc ates are aiming at, for, however farfetched and unr easonable their principles may seem today, it is po ssible that in years to come they may be regarded as normal. With regard to Futurist poetry, however , the case is rather difficult, for whatever Futuri st poetry may be―even admitting that the theory on which it is based may be right―it can hardly be classed as Literature。

This, in brief, is what the Futurist says: for a century, past conditions of life have been cond itionally speeding up, till now we live in a world of noise and violence and speed. Consequently, our feelings, thoughts and emotions have undergone a c orresponding change. This speeding up of life, says the Futurist, requires a new form of expression. We must speed up our literature too, if we want t o interpret modern stress. We must pour out a larg e stream of essential words, unhampered by stops, o r qualifying adjectives, or finite verbs. Instead ofdescribing sounds we must make up words that imit ate them; we must use many sizes of type and diff erent colored inks on the same page, and shorten lengthen words at will。

FRA-OISExplodes：HereIsTheOnlyChartPowellIsClo。。。

FRA-OISExplodes ：HereIsTheOnlyChartPowellIsClo 。

FRA-OIS Explodes: Here Is The Only Chart Powell Is Closely Watching, And Why It Is Soaring 17 hours agoFRA-OIS Explodes: Here Is The Only Chart Powell Is Closely Watching, And Why It Is Soaring Some were quick to mock repo guru and former NY Fed staffer that the unexpected western blockade of Russia had the feel of a Lehman weekend,because virtually nobody had any idea what the forced exclusion of a G-20 economy from the global financial system would lead to. In fact, just yesterday Jerome Powell admitted that he had not been consulted, suggesting that arguably the most momentous financial decision in modern history has made without consulting the single most important financial person in the world.However, it appears that while Pozsar may have been ahead of the curve, as usual, he was not wrong, and today the all important FRA-OIS indicator of interbank funding stress (and money-market risk) is surging, and at last check was above 37bps, up a whopping 12 pts...... amid relentless selling in March 2022 eurodollar futures with the contract off session lows but remains cheaper by around 10bp on the day, with some speculating that at least some funding markets are starting to grind to a halt.One can argue that while Powell and the Fed may be oblivious to the ongoing collapse in stocks, which they view as overvalued and as having enough buffer to drop especiallyhe is closely watching every uptick in this most critical stress indicator.A very quick primer on this all important spread:What is FRA? A forward rate agreement is a deal to swap future fixed interest payments for variable ones, or vice versa. The key rate for U.S. markets is the three-month London interbank offered rate, or Libor, in U.S. dollars. The benchmark is derived by major banks submitting rates based on transactions that are compiled to establish benchmark for five different currencies across seven different loan periods. Those benchmarks underpin interest rates on trillions of dollars of financial instruments and products from student and car loans to mortgages and credit cards.What is OIS? The Overnight Index Swap rate is calculated from contracts in which investors swap fixed- and floating-rate cash flows. Some of the most commonly used swap rates relate to the Federal Reserve’s main interest-rate target, and those are regarded as proxies for where markets see U.S. central bank policy headed at various points in the future.Oh, that's the theory. But why does the FRA-OIS spread matter in practice?Well, it’s regarded as the markets’ measure of how expensive or cheap it will be for banks to borrow in the future, as shown by Libor, relative to a risk-free rate, the kind that’s paid by highly rated sovereign borrowers such as the U.S. government. The FRA-OIS spread provides another snapshot of how the market is viewing credit conditions because of the fact that traders are betting on where Libor-OIS -- its underlying spread -- will be.As a further reminder, there are typically 3 reasons why it would blow out:1. the risk premium for uncertainty of US monetary policy,2. recently elevated credit spreads (CDS) of banks, and3. demand for funds in preparation for market stress.While FRA-OIS exploded to 80bps in March 2020, at the peak of the covid crash, and is currently at just half that level, never before has funding stress been so high with a Fed balance sheet near $9 trillion and with some $1.6 trillion in the Fed's overnight reverse repo facility.In other words, when adjusted for the statutory level of liquidity in the market, which we don't need to tell readers is at an all time high, the FRA-OIS would almost certainly be at all time Zoltan Pozsar when he warnedhighs.Whatever the reasons, a blow out in FRA/OIS means that dollar funding is becomingincreasingly problematic, and absent a sharp tightening in the Libor-OIS and FRA-OIS spread,while bank credit concerns may not have been the catalyst for the sharp spike, it will be banks that are eventually impacted by what is increasingly emerging as an acute tightening in short-term funding markets and/or a global dollar shortage. And in another indication that the FRA-OIS is indeed spiking in response to an ominous global dollar shortage - just the outcome Pozsar warned about and one which shouldn't be happening when factoring in the record endogenous market liquidity - we find that the average cross-currency basis swap is tumbling.This global liquidity proxy tends to shrink any time there is prevailing dollar tightness in the market.While this is a topic we covered extensively back in March 2020 (see "), especially right before the Fed unleashed itsmonetary bazooka with trillions in QE and opening up repos to virtually unlimited amount, as well as announcing it would buy corporate bonds and ETFs, expect to hear much more about this in the days and weeks ago come.Meanwhile, if the FRA-OIS spikes another 10-15 points, the Fed will have no choice but to emerge from its paralysis and reassure markets that the financial system isn't about toexperience another paralysis (oh, and unless the Ukraine war magically ends in the next few weeks, say goodbye to "six or seven" rate hikes this year).Fri, 03/04/2022 - 11:06There Is No Liquidity" -Market Paralyzed As FRA/OIS Explodes Tyler Durden。