A note on definability and approximations

tpo61托福阅读全套解析阅读-1 (1)原文 (1)译文 (3)题目 (4)答案 (7)背景知识 (8)阅读-2 (10)原文 (10)译文 (12)题目 (13)答案 (17)背景知识 (18)阅读-3 (21)原文 (21)译文 (22)题目 (24)答案 (28)背景知识 (29)阅读-1原文Physical Properties of Minerals①A mineral is a naturally occurring solid formed by inorganic processes.Since the internal structure and chemical composition of a mineral are difficult to determine without the aid of sophisticated tests and apparatus,the more easily recognized physical properties are used in identification.②Most people think of a crystal as a rare commodity,when in fact most inorganic solid objects are composed of crystals.The reason for this misconception is that most crystals do not exhibit their crystal form:the external form of a mineral that reflects the orderly internal arrangement of its atoms.Whenever a mineral forms without space restrictions,individual crystals with well-formed crystal faces will develop.Some crystals,such as those of the mineral quartz,have a very distinctivecrystal form that can be helpful in identification.However,most of the time,crystal growth is interrupted because of competition for space,resulting in an intergrown mass of crystals,none of which exhibits crystal form.③Although color is an obvious feature of a mineral,it is often an unreliable diagnostic property.Slight impurities in the common mineral quartz,for example, give it a variety of colors,including pink,purple(amethyst),white,and even black. When a mineral,such as quartz,exhibits a variety of colors,it is said to possess exotic coloration.Exotic coloration is usually caused by the inclusion of impurities, such as foreign ions,in the crystalline structure.Other minerals—for example, sulfur,which is yellow,and malachite,which is bright green—are said to have inherent coloration because their color is a consequence of their chemical makeup and does not vary significantly.④Streak is the color of a mineral in its powdered form and is obtained by rubbinga mineral across a plate of unglazed porcelain.Whereas the color of a mineral often varies from sample to sample,the streak usually does not and is therefore the more reliable property.⑤Luster is the appearance or quality of light reflected from the surface of a mineral.Minerals that have the appearance of metals,regardless of color,are said to have a metallic luster.Minerals with a nonmetallic luster are described by various adjectives,including vitreous(glassy)pearly,silky,resinous,and earthy (dull).⑥One of the most useful diagnostic properties of a mineral is hardness,the resistance of a mineral to abrasion or scratching.This property is determined by rubbing a mineral of unknown hardness against one of known hardness,or vice versa.A numerical value can be obtained by using Mohs'scale of hardness,which consists of ten minerals arranged in order from talc,the softest,at number one,to diamond,the hardest,at number ten.Any mineral of unknown hardness can be compared with these or with other objects of known hardness.For example,a fingernail has a hardness of2.5,a copper penny5,and a piece of glass5.5.The mineral gypsum,which has a hardness of two,can be easily scratched with your fingernail.On the other hand,the mineral calcite which has a hardness of three, will scratch your fingernail but will not scratch glass.Quartz,the hardest of the common minerals,will scratch a glass plate.⑦The tendency of a mineral to break along planes of weak bonding is called cleavage.Minerals that possess cleavage are identified by the smooth,flat surfaces produced when the mineral is broken.The simplest type of cleavage is exhibited by the micas.Because the micas have excellent cleavage in one direction,they break to form thin,flat sheets.Some minerals have several cleavage planes,which produce smooth surfaces when broken,while others exhibit poor cleavage,andstill others exhibit no cleavage at all.When minerals break evenly in more than one direction,cleavage is described by the number of planes exhibited and the angles at which they meet.Cleavage should not be confused with crystal form.When a mineral exhibits cleavage,it will break into pieces that have the same configuration as the original sample does.By contrast,quartz crystals do not have cleavage,and if broken,would shatter into shapes that do not resemble each other or the original crystals.Minerals that do not exhibit cleavage are said to fracture when broken.Some break into pieces with smooth curved surfaces resembling broken glass.Others break into splinters or fibers,but most fracture irregularly.译文矿物的物理性质①矿物质是由无机过程形成的天然固体。

4月23日托福阅读答案解析词汇题：attest to=provide evidence offragments=piecespainstaking=taking great effort tosubstantial=considerableconfiguration=arrangementprecise=accuratedistinctive=recognizablein contrast to=as opposed todispersal=distributionimitator=someone who copied his workassociated with=related to第一篇：题材划分：社科类文章主要内容：制造表的发展。

先说以前一个master一年只能做十几个表，特别painstaking只有富人才能买得起。

后来有个人叫Elf，他简化了钟表制造的材料，创新了一些设备，行了一系列变革，通过专业化啊水力啊，让表产量变大，又轻，又便宜。

本来特别重，不好运输，他就把弄得更轻了，可以挂住，不用专门做cabinet了。

然后使钟表让中产阶级也买得起，从精细制造变成mass production。

后来他为了peddler就继续发明创造，然后在1816年造出了shelf clock获得专利，但是还是有很多人抄袭模仿，这些模仿也在一定程度上促进了钟表的精细化。

他有个员工叫Jerome，借鉴了上一个老板的经验，然后和Elf一起将钟表变得美观时尚又物廉价美。

解析：整体文章词汇相对较简单，没有生涩难懂的学术词汇，只是第一篇相对而言比较难进入状态，所以一定要调整好自己的心态。

相似TPO练习推荐：TPO30- The Invention of the Mechanical ClockTPO16- Development of the Periodic Table相关文章：The Invention of the Mechanical ClockIn Europe, before the introduction of the mechanical clock, people told time by sun (using, for example, shadow sticks or sun dials) and water clocks. Sun clocks worked, of course, only on clear days; water clocks misbehaved when the temperature fell toward freezing, to say nothing of long-run drift as the result of sedimentation and clogging. Both these devices worked well in sunny climates; but in northern Europethe sun may be hidden by clouds for weeks at a time, while temperatures vary not only seasonally but from day to night.Medieval Europe gave new importance to reliable time. The Catholic Church had its seven daily prayers, one of which was at night, requiring an alarm arrangement to waken monks before dawn. And then the new cities and towns, squeezed by their walls, had to know and order time in order to organize collective activity and ration space. They set a time to go to sleep. All this was compatible with older devices so long as there was only one authoritative timekeeper; but with urban growth and the multiplication of time signals, discrepancy brought discord and strife. Society needed a more dependable instrument of time measurement and found it in the mechanical clock.We do not know who invented this machine, or where. It seems to have appeared in Italy and England (perhaps simultaneous invention) between 1275 and 1300. Once known, it spread rapidly, driving out water clocks but not solar dials, which were needed to check the new machines against the timekeeper of last resort. These early versions were rudimentary, inaccurate, and prone to breakdown.Ironically, the new machine tended to undermine Catholic Church authority. Although church ritual had sustained an interest in timekeeping throughout the centuries of urban collapse that followed the fall of Rome, church time was nature’s time. Day and night were divided into the same number of parts, so that except at the equinoxes, days and night hours were unequal; and then of course the length of these hours variedwith the seasons. But the mechanical clock kept equal hours, and this implied a new time reckoning. The Catholic Church resisted, not coming over to the new hours for about a century. From the start, however, the towns and cities took equal hours as their standard, and the public clocks installed in town halls and market squares became the very symbol of a new, secular municipal authority. Every town wanted one; conquerors seized them as especially precious spoils of war; tourists came to see and hear these machines the way they made pilgrimages to sacred relics.The clock was the greatest achievement of medieval mechanical ingenuity. Its general accuracy could be checked against easily observed phenomena, like the rising and setting of the sun. The result was relentless pressure to improve technique and design. At every stage, clockmakers led the way to accuracy and precision; they became masters of miniaturization, detectors and correctors of error, searchers for new and better. They were thus the pioneers of mechanical engineering and served as examples and teachers to other branches of engineering.The clock brought order and control, both collective and personal. Its public display and private possession laid the basis for temporal autonomy: people could now coordinate comings and goings without dictation from above. The clock provided the punctuation marks for group activity, while enabling individuals to order their own work (and that of others) so as to enhance productivity. Indeed, the very notion of productivity is a by-product of the clock: once on can relate performance to uniform time units, work is never the same. One moves from the task-oriented time consciousness of the peasant (working on job after another, as time and light permit)and the time-filling busyness of the domestic servant (who always had something to do) to an effort to maximize product per unit of time.第二篇题材划分：历史类文章主要内容：在泰国附近出现的一个D文明，语言和Mon语言有联系。

a rX iv:mat h /29343v2[mat h.PR]25Apr23Conformal restriction:the chordal case Gregory Lawler ∗Oded Schramm †Wendelin Werner ‡Abstract We characterize and describe all random subsets K of a given simply connected planar domain (the upper half-plane H ,say)which satisfy the “conformal restriction”property,i.e.,K connects two fixed boundary points (0and ∞,say)and the law of K conditioned to remain in a simply connected open subset H of H is identical to that of Φ(K ),where Φis a conformal map from H onto H with Φ(0)=0and Φ(∞)=∞.The construction of this family relies on the stochastic Loewner evolution processes with parameter κ≤8/3and on their distortion under conformal maps.We show in particular that SLE 8/3is the only random simple curve satisfying conformal restriction and relate it to the outer boundaries of planar Brownian motion and SLE 6.Keywords:Conformal invariance,restriction property,random fractals,SLE.MSC Classification:60K35,82B27,60J69,30C99Contents1Introduction3 2Preliminaries7 3Two-sided restriction10 4Brownian excursions15 5Conformal image of chordal SLE19 6Restriction property for SLE8/323 7Bubbles267.1Brownian bubbles (26)7.2Adding a Poisson cloud of bubbles to SLE (29)8One-sided restriction318.1Framework (31)8.2Excursions of reflected Brownian motions (31)8.3The SLE(κ,ρ)process (34)8.4Proof of Theorem8.4 (38)8.5Formal calculations (41)9Equivalence of the frontiers of SLE6and Brownian motion449.1Full plane SLE6and planar Brownian motion (44)9.2Chordal SLE6and reflected Brownian motion (46)9.3Chordal SLE6as Brownian motion reflected on its past hull..499.4Non-equivalence of pioneer points and SLE6 (50)9.5Conditioned SLE6 (52)10Remarks5221IntroductionConformalfield theory has been extremely successful in predicting the ex-act values of critical exponents describing the behavior of two-dimensional systems from statistical physics.In particular,in the fundamental papers [5,6],which were used and extended to the case of the“surface geometry”in[9],it is argued that there is a close relationship between critical planar systems and some families of conformally invariantfields.This gave rise to intense activity both in the theoretical physics community(predictions on the exact value of various exponents or quantities)and in the mathematical community(the study of highest-weight representations of certain Lie alge-bras).However,on the mathematical level,the explicit relation between the two-dimensional systems and thesefields remained rather mysterious.More recently,a one-parameter family of random processes called stochas-tic Loewner evolution,or SLE,was introduced[44].The SLEκprocess is ob-tained by solving Loewner’s differential equation with driving term B(κt), where B is one-dimensional Brownian motion,κ>0.The SLE processes are continuous,conformally invariant scaling limits of various discrete curves arising in the context of two-dimensional systems.In particular,for the models studied by physicists for which conformalfield theory(CFT)has been applied and for which exponents have been predicted,it is believed that SLE arises in some way in the scaling limit.This has been proved for site-percolation on the triangular lattice[46],loop-erased random walks[29] and the uniform spanning tree Peano path[29](a.k.a.the Hamiltonian path on the Manhattan lattice).Other models for which this is believed include the Ising model,the random cluster(or Potts)models with q≤4,and the self-avoiding walk.In a series of papers[23,24,25,26],the authors derived various prop-erties of the stochastic Loewner evolution SLE6,and used them to compute the“intersection exponents”for planar Brownian paths.This program was based on the earlier realization[32]that any conformally invariant process satisfying a certain restriction property has crossing or intersection expo-nents that are intimately related to these Brownian intersection exponents. In particular,[32]predicted a strong relation between planar Brownian mo-tion,self-avoiding walks,and critical percolation.As the boundary of SLE6is conformally invariant,satisfies restriction,and can be well understood,com-putations of its exponents yielded the Brownian intersection exponents(in particular,exponents that had been predicted by Duplantier-Kwon[15,14],3disconnection exponents,and Mandelbrot’s conjecture[34]that the Haus-dorffdimension of the boundary of planar Brownian motion is4/3).Sim-ilarly,the determination of the critical exponents for SLE6in[23,24,25] combined with Smirnov’s[46]proof of conformal invariance for critical per-colation on the triangular lattice(along with Kesten’s hyperscaling relations) facilitated proofs of several fundamental properties of critical percolation [47,28,45],some of which had been predicted in the theoretical physics literature,e.g.,[37,35,36,38,43].The main goal of the present paper is to investigate more deeply the restriction property that was instrumental in relating SLE6to Brownian mo-tion.One of our initial motivations was also to understand the scaling limit and exponents of the two-dimensional self-avoiding walk.Another motiva-tion was to reach a clean understanding of the relation between SLE and conformalfield theory.Consequences of the present paper in this direction are the subject of[18,19].See also[2,3]for aspects of SLE from a CFT perspective.Let us now briefly describe the conformal restriction property which we study in the present paper:Consider a simply connected domain in the complex plane C,say the upper half-plane H:={x+iy:y>0}.Suppose that two boundary points are given,say0and∞.We are going to study closed random subsets K of H such that:•1.The restriction measure Pαexists if and only ifα≥5/8.2.The only measure Pαthat is supported on simple curves is P5/8.It isthe law of chordal SLE8/3.3.The measures Pαforα>5/8can be constructed by adding to thechordal SLEκcurve certain Brownian bubbles with intensityλ,where α,λandκare related byα(κ)=6−κ2κ.4.For allα≥5/8,the dimension of the boundary of K defined under Pαisalmost surely4/3and locally“looks like”an SLE8/3curve.In particular, the Brownian frontier(i.e.,the outer boundary of the Brownian path) looks like a symmetric curve.As pointed out in[30],this gives strong support to the conjecture that chordal SLE8/3is the scaling limit of the infinite self-avoiding walk in the upper half-plane and allows one to recover(modulo this conjecture)the critical exponents that had been predicted in the theoretical physics literature(e.g., [36,16]).This conjecture has recently been tested[21,22]by Monte Carlo methods.Let us also mention(but this will not be the subject of the present paper,see[18,19])that in conformalfield theory language,−λ(κ)is the central charge of the Virasoro algebra associated to the discrete models(that correspond to SLEκ)and thatαis the corresponding highest-weight(for a degenerate representation at level2).To avoid confusion,let us point out that SLE6is not a chordal restriction measure as defined above.However,it satisfies locality,which implies a different form of restriction.We give below a proof of locality for SLE6, which is significantly simpler than the original proof appearing in[23].We will also study a slightly different restriction property,which we call right-sided restriction.The measures satisfying right-sided restriction sim-ilarly form a1-parameter collection P+α,α>0.We present several con-structions of the measures P+α.First,whenα≥5/8,these can be obtained from the measures Pα(basically,by keeping only the right-side boundary). Whenα∈(0,1),the measure P+αcan also be obtained from an appropriately reflected Brownian excursion.It follows that one can reflect a Brownian ex-cursion offa ray in such a way that its boundary will have precisely the law5of chordal SLE8/3.A third construction of P+α(valid for allα>0)is given by a process we call SLE(8/3,ρ).The process SLE(κ,ρ)is a variant of SLE where a drift is added to the driving function.In fact,it is just Loewner’s evolution driven by a Bessel-type process.The word chordal refers to connected sets joining two boundary points of a domain.There is an analogous radial theory,which investigates sets joining an interior point to the boundary of the domain.This will be the subject of a forthcoming paper[31].We now briefly describe how this paper is organized.In the preliminary section,we give some definitions,notations and derive some simple facts that will be used throughout the paper.In Section3,we study the family of chordal restriction measures,and show(1.1).Section4is devoted to the Brownian excursions.We define these measures and use a result of B.Vir´a g (see[49])to show that thefilling of such a Brownian excursion has the law P1.The key to several of the results of the present paper is the study of the distortion of SLE under conformal maps,for instance,the evolution of the image of the SLE path under the mappingΦ(as long as the SLE path remains in H),which is the subject of Section5.This study can be considered as a cleaner and more advanced treatment of similar questions addressed in[23]. In particular,we obtain a new short proof of the locality property for SLE6, which was essential in the papers[23,24,25].The SLE distortion behaviour is then also used in Section6to prove that the law of chordal SLE8/3is P5/8and is also instrumental in Section7,where we show that all measures Pαforα>5/8can be constructed by adding a Poisson cloud of bubbles to SLE curves.The longer Section8is devoted to the one-sided restriction measures P+α. As described above,we exhibit various constructions of these measures and show as a by-product of this description that the two-sided measures Pαdo not exist forα<5/8.A recurring theme in the paper is the principle that the law P of a random set K can often be characterized and understood through the function A→P[K∩A=∅]on an appropriate collection of sets A.In Section9we use this to show that the outer boundary of chordal SLE6is the same as the outer boundary(frontier)of appropriately reflected Brownian motion and the outer boundary of full-plane SLE6stopped on hitting the unit circle is the same as the outer boundary of Brownian motion stopped on hitting the unit circle.6We conclude the paper with some remarks and pointers to papers in preparation.2PreliminariesIn this section some definitions and notations will be given and some basic facts will be recalled.Important domains.The upper half plane{x+iy:x∈R,y>0} is denoted by H,the complex plane by C,the extended complex plane by ˆC=C∪{∞}and the unit disk by U.Bounded hulls.Let Q be the set of all bounded A⊂A∩H and H\A is(connected and)simply connected.We call such an A a bounded hull.The normalized conformal maps g A.For each A∈Q,there is a unique conformal transformation g A:H\A→H with g A(z)−z→0as z→∞. We can then define(as in[23])z(g A(z)−z).(2.1)a(A):=limz→∞First note that a(A)is real,because g A(z)−z has a power series expansion in1/z near∞and is real on the real line in a neighborhood of∞.Also note thata(A)=limy H(i y),(2.2)y→∞where H(z)=Im z−g(z) is the bounded harmonic function on H\A with boundary values Im z.Hence,a(A)≥0,and a(A)can be thought of as a measure of the size of A as seen from infinity.We will call a(A)the half-plane capacity of A(from infinity).The useful scaling rule for a(A),a(λA)=λ2a(A)(2.3) is easily verified directly.Since Im g A(z)−Im z is harmonic,bounded,and has non-positive boundary values,Im g A(z)≤Im z.Consequently,0<g′A(x)≤1,x∈R\A.(2.4) (In fact,g′A(x)can be viewed as the probability of an event,see Proposition 4.1.)7∗-hulls.Let Q∗be the set of A∈Q with0∈A.We call such an A a∗-hull. If A∈Q∗,then H=H\A is as the H in the introduction.The normalized conformal mapsΦA.For A∈Q∗,we defineΦA(z)= g A(z)−g A(0),which is the unique conformal transformationΦof H\A onto Hfixing0and∞withΦ(z)/z→1as z→∞.Semigroups.Let A be the set of all conformal transformationsΦ:H\A→H withΦ(0)=0andΦ(∞)=∞,where A∈Q∗.That is,A={λΦA:λ> 0,A∈Q∗}.Also let A1={ΦA:A∈Q∗}.Note that A and A1are both semigroups under composition.(Of course,the domain ofΦ1◦Φ2isΦ−12(H1) if H1is the domain ofΦ1.)We can consider Q∗as a semigroup with the product·,where A·A′is defined byΦA·A′=ΦA◦ΦA′.Note thata(A·A′)=a(A)+a(A′).(2.5) As a(A)≥0,this implies that a(A)is monotone in A.±-hulls.Let Q+be the set of A∈Q∗with A∩R⊂(0,∞).Letσdenote the orthogonal reflection about the imaginary axis,and let Q−={σ(A):A∈Q+}be the set of A∈Q∗with A∩R⊂(−∞,0).If A∈Q∗,then we can find unique A1,A3∈Q+and A2,A4∈Q−such that A=A1·A2=A4·A3. Note that Q+,Q−are semigroups.Smooth hulls.We will call A∈Q a smooth hull if there is a smooth curveγ:[0,1]→C withγ(0),γ(1)∈R,γ(0,1)⊂H,γ(0,1)has no self-intersections,and H∩∂A=γ(0,1).Any smooth hull in Q∗is in Q+∪Q−. Fillings.If A⊂H such that any path from z to∞inH\A.Similarly, F R H(A)denotes the union of A with the connected components ofH\A which do not intersect[0,∞).Also,for closed A⊂C, F C(A)denotes the union of A with the bounded connected components of C\A.Approximation.We will sometimes want to approximate A∈Q by smooth hulls.The idea of approximating general domains by smooth hulls is standard (see,e.g.,[17,Theorem3.2]).8Lemma2.1.Suppose A∈Q+.Then there exists a decreasing sequence of smooth hulls(A n)n≥1such that A= ∞n=1A n and the increasing sequence Φ′An(0)converges toΦ′A(0).Proof.The existence of the sequence A n can be obtained by various means,for example,by considering the image underΦ−1A of appropriately chosenpaths.The monotonicity ofΦ′An (0)follows immediately from the monotonic-ity of A n and(2.4).The convergence is immediate by elementary properties of conformal maps,sinceΦAnconverges locally uniformly toΦA on H\A. Covariant measures.Our aim in the present paper is to study measures on subsets of H.In order to simplify further definitions,we give a general definition that can be applied in various settings.Suppose thatµis a measure on a measurable spaceΩwhose elements are subsets of a domain D.Suppose thatΓis a set of conformal transformations from subdomains D′⊂D onto D that is closed under composition.We say thatµis covariant underΓ(orΓ-covariant)if for allϕ∈Γ,the measureµrestricted to the setϕ−1(Ω):={ϕ−1(K):K⊂D}is equal to a constant Fϕtimes the image measureµ◦ϕ−1.Ifµis afiniteΓ-covariant measure,then Fϕ=µ[ϕ−1(Ω)]/µ[Ω].Note that a probability measure P onΩisΓ-covariant if and only if for allϕ∈Γwith Fϕ=P[ϕ−1(Ω)]>0,the conditional law of P onϕ−1(Ω)is equal to P◦ϕ−1.Also note that ifµis covariant underΓ,then Fϕ◦ψ=FϕFψfor allϕ,ψ∈Γ, because the image measure ofµunderϕ−1is F−1ϕµrestricted toϕ−1(Ω),sothat the image underψ−1of this measure is F−1ϕF−1ψµrestricted toψ−1◦ϕ−1(Ω).Hence,the mapping F:ϕ→Fϕis a semigroup homomorphism fromΓinto the commutative multiplicative semigroup[0,∞).Whenµis a probability measure,this mapping is into[0,1].We say that a measureµisΓ-invariant if it isΓ-covariant with Fϕ≡1. Chordal Loewner chains.Throughout this paper,we will make use of chordal Loewner chains.Let us very briefly recall their definition(see[23]for details).Suppose that W=(W t,t≥0)is a real-valued continuous function. Define for each z∈g t(z)−W t,g0(z)=z.(2.6) For each z∈Loewner evolution is defined as K t:={z∈κB t,where B is a standard one-dimensional Brownian motion,then the corresponding random Loewner chain is chordal SLEκ(SLE stands for stochastic Loewner evolution).3Two-sided restrictionIn this section we will be studying certain probability measures on a collection Ωof subsets of H.We start by definingΩ.Definition3.1.LetΩbe the collection of relatively closed subsets K of H such that1.K is connected,K is connected.A simple example of a set K∈Ωis a simple curveγfrom0to infinity in the upper half-plane.Ifγis just a curve from zero to infinity in the upper half-plane with double-points,then one can take K=F R H(γ)∈Ω,which is the set obtained byfilling in the loops created byγ.We endowΩwith theσ-field generated by the events{K∈Ω:K∩A=∅},where A∈Q∗.It is easy to check that this family of events is closed underfinite intersection,so that a probability measure onΩis characterized by the values of P[K∩A=∅]for A∈Q∗.Thus:Lemma3.2.Let P and P′be two probability measures onΩ.If P[K∩A=∅]=P′[K∩A=∅]holds for every A∈Q∗,then P=P′.It is worthwhile to note that theσ-field onΩis the same as the Borel σ-field induced by the Hausdorffmetric on closed subsets of2.P is A-covariant.3.There exists anα>0such that for all A∈Q∗,P[K∩A=∅]=Φ′A(0)α.4.There exists anα>0such that for all smooth hulls A∈Q∗,P[K∩A=∅]=Φ′A(0)α.Moreover,for eachfixedα>0,there exists at most one probability measure Pαsatisfying these conditions.Definition3.4.If the measure Pαexists,we call it the two-sided restriction measure with exponentα.Proof.Lemma3.2shows that a measure satisfying3is unique.A probability measure isΓ-covariant if and only if it isΓ-invariant.Therefore,1and2are equivalent.As noted above,any A∈Q∗can be written as A+·A−with A±∈Q±.Using this and Lemma2.1,we may deduce that conditions3and4are also equivalent.SinceΦ′λA(0)=Φ′A(0)for A∈Q∗,λ>0,3together withLemma3.2imply that P isΓ-invariant.BecauseΦ′A1·A2(0)=Φ′A1(0)Φ′A2(0),3also implies that for all A1,A2∈Q∗,P[K∩(A1·A2)=∅]=P[K∩A1=∅]P[K∩A2=∅],which implies1.Hence,it suffices to show that1implies4.Suppose1holds.Define the homomorphism F of Q∗onto the multiplica-tive semigroup(0,1]by F(A)=P[K∩A=∅].We also write F(ΦA)for F(A).Let G t(z)be the solution of the initial value problem∂t G t(z)=2G t(z)H.Note that this function can equivalently be defined as G t(z)= g t(z)−g t(0)=g t(z)+2t,where(g t)is the chordal Loewner chain driven by the function W t=1−2t.Hence,G t is the unique conformal map from H\K t onto H such that G t(0)=0and G t(z)/z→1when z→∞.(Here,K t is the evolving hull of g t.)Also,and this is why we focus on these functions G t,one has G t◦G s=G t+s in H\K t+s,for all s,t≥0.Since F is a homomorphism,11this implies that F (G t )=exp(−2αt )for some constant α≥0and all t ≥0,or that F (G t )=0for all t >0.However,the latter possibility would imply that K ∩K t =∅a.s.,for all t >0.Since t>0K t ={1}and 1/∈H \A and n A n is bounded away from 0and ∞.(Thisis very closely related to what is known as the Carath´e odory topology.)Now assume that A n →A ,where A n ,A ∈Q +.It is immediate that Φ′A n (0)→Φ′A (0),by Cauchy’s derivative formula (the maps may be extended to a neighborhood of 0by Schwarz reflection in the real line).Set A +n =ΦA n (A \A n )and A −n =ΦA (A n \A ).We claim that there is a constant δ>0and a sequence δn →0such thatA +n ∪A −n ⊂{x +iy :x ∈[δ,1/δ],y ≤δn }.(3.3)Indeed,since the map ΦA n ◦Φ−1A converges to the identity,locally uniformlyin H ,it follows (e.g.,from the argument principle)that for every compact set S ⊂H for all sufficiently large n ,S is contained in the image of ΦA n ◦Φ−1A ,which means that A +n ∩S =∅.Similarly,Φ−1A ◦ΦA n converges locally uniformly inthere is someǫ>0such that for infinitely many n P[K∩A−n]>ǫ.There-fore,with positive probability,K intersects infinitely many A−n.Since K is closed and(3.3)holds,this would then imply that P K∩[δ,1/δ] >0,a contradiction.Thus lim sup n→∞F(A n)≤F(A).A similar argument alsoshows that lim inf n→∞F(A n)≥F(A),and so lim n→∞F(A n)=F(A),and the continuity of F is verified.To complete the proof of the Lemma,we now show that A0is dense in Q+.Let A∈Q+.Set A′:=A∪[x0,x1],where x0:=inf(A∩R)and x1:=sup(A∩R).Forδ>0,δ<ΦA(x0)/2,let Dδbe the set of points in H with distance at mostδfrom[ΦA(x0),ΦA(x1)].Let Eδdenote theclosure of A∪Φ−1A (Dδ).It is clear that Eδ→A asδ→0+in the topologyconsidered above.It thus suffices to approximate Eδ.Note thatH withβ(0),β(s)∈R.We may assume thatβis parametrized by half-plane capacity from∞,so that a β[0,t] = 2t,t∈[0,s].Set g t:=gβ[0,t],Φt:=Φβ[0,t]=g t−g t(0),U t:=g t β(t) ,˜Ut:=U t−g t(0)=Φt β(t) ,t∈[0,s].By the chordal version of Loewner’s theorem,we have∂t g t(z)=2Φt(z)−˜U t +2(Φt(z)−˜U t)˜U t,Φ0(z)=z.(3.4)Since˜U t is continuous and positive,there is a sequence of piecewise constant functions˜U(n):[0,s]→(0,∞)such that sup{|˜U(n)t−˜U t|:t∈[0,s]}→0 as n→∞.LetΦ(n)t be the solution of(3.4)with˜U(n)t replacing˜U t.Then, clearly,Φ(n)s(z)→Φs(z)=ΦEδlocally uniformly inΦ′A+(0)are bounded away from zero,but limǫց0Φ′A(0)=0.AsΦA∗−◦ΦA+=ΦA=ΦA∗+◦ΦA−,(3.5) we haveΦ′A∗−(0)→0whenǫ→0.By applying F to(3.5)we getΦ′A∗−(0)α−Φ′A+(0)α=Φ′A∗+(0)αΦ′A−(0)α−.AsΦ′A∗−(0)=Φ′A∗+(0)(by symmetry),this means thatΦ′A∗−(0)α−α−staysbounded and bounded away from zero asǫց0,which givesα−=α.Since every A∈Q∗can be written as A+·A−this establishes4withα≥0.The caseα=0clearly implies K=∅a.s.,which is not permitted.This completes the proof.Let us now conclude this section with some simple remarks:Remark3.6.If K1,...,K n are independent sets with respective laws Pα1,...,Pαn,then the law of thefilling K:=F R H(K1∪...∪K n)of the union of the K j’s is Pαwithα=α1+···+αn becauseP[K⊂Φ−1(H)]=nj=1P[K j⊂Φ−1(H)]=Φ′(0)α1+···+αn.Remark3.7.Whenα<1/2,the measure Pαdoes not exist.To see this, suppose it did.Since it is unique,it is invariant under the symmetryσ: x+iy→−x+iy.Let A={e iθ:θ∈[0,π/2]}.Since K is almost surely connected and joins0to infinity,it meets either A orσ(A).Hence,symmetry implies thatΦ′A(0)α=P[K∩A=∅]≤1/2.On the other hand,one can calculate directlyΦ′A(0)=1/4,and henceα≥1/2.We will show later in the paper(Corollary8.6)that Pαonly exists for α≥5/8.Remark3.8.We have chosen to study subsets of the upper half-plane with the two special boundary points0and∞,but our analysis clearly applies to any simply connected domain O=C with two distinguished boundary points a and b,a=b.(We need to assume that the boundary of O is sufficiently nice near a and b.Otherwise,one needs to discuss prime ends in place of the distinguished points.)For instance,if∂O is smooth in the neighborhood of a and b,then for a conformal mapΦfrom a subset O′of O onto O,we getP[K∩(O\O′)=∅]=(Φ′(a)Φ′(b))α,14where P denotes the image of Pαunder a conformal map from H to O that takes a to0and b to∞.Remark3.9.The proof actually shows that weaker assumptions onΩare sufficient for the proposition.DefineΩb just asΩwas defined,except that Condition1is replaced by the requirements that K=∅andH\{0} such thatγ[0,1]∩R={γ(0),γ(1)}and and with positive P-probability K∩γ[0,1]=∅andγ[0,1]separates K inK and K is unbounded.Thus,P[Ω]=1. Using this fact,Lemma3.2may be applied,giving the remaining implication 3⇒2.4Brownian excursionsAn important example of a restriction measure is given by the law of the Brownian excursion from0to infinity in H.Loosely speaking,this is simply planar Brownian motion started from the origin and conditioned to stay in H at all positive times.It is closely related to the“complete conformal invariance”of(slightly different)measures on Brownian excursions in[32,27].Let X be a standard one-dimensional Brownian motion and Y an inde-pendent three-dimensional Bessel process(see e.g.,[41]for background on three-dimensional Bessel processes,its relation to Brownian motion condi-tioned to stay positive and stochastic differential equations).Let us briefly re-call that a three-dimensional Bessel process is the modulus(Euclidean norm) of a three-dimensional Brownian motion,and that it can be defined as the solution to the stochastic differential equation dY t=dw t+dt/Y t,where w is standard Brownian motion in R.It is very easy to see that(1/Y t,t≥t0)is15a local martingale for all t0>0,and that if T r denotes the hitting time of rby Y,then the law of(Y Tr+t ,t<T R−T r)is identical to that of a Brownianmotion started from r and conditioned to hit R before0(if0<r<R).Note that almost surely lim t→∞Y t=∞.The Brownian excursion can be defined as B t=X t+iY t.In other words, B has the same law as the solution to the following stochastic differential equation:dB t=dW t+i1Proof.LetΦ=ΦA.Suppose that W is a planar Brownian motion and Z is a Brownian excursion in H,both starting at z∈H\A.When Im(z)→∞, Im(Φ−1(z))=Im(z)+o(1).Hence,with a large probability(when R is large),a Brownian motion started from z∈I R(respectively,z∈Φ−1(I R)) will hitΦ−1(I R)(resp.,I R)before R.The strong Markov property of planar Brownian motion therefore shows that when R→∞,P[W hits I R before A∪R]∼P[W hitsΦ−1(I R)before A∪R].But sinceΦ◦W is a time-changed Brownian motion,andΦ:H\A→H,the right-hand is equal to the probability that a Brownian motion started from Φ(z)hits I R before R,namely,Im(Φ(z))/R.Hence,P[Z hits I R before A]=P[W hits I R before A∪R]Im(z)+o(1)when R→∞.In the limit R→∞,we getP[Z⊂H\A]=Im[Φ(z)]Im(z).(4.2)When z→0,Φ(z)=zΦ′(0)+O(|z|2)so thatP[B[0,∞)∩A=∅]=lims→0P[B[s,∞)⊂H\A]=lims→0E Im(Φ(B s))Figure R×[0,1].Using almost the same proof as in Proposition4.1(but keeping track ofthe law of the path),one can prove the following:Lemma4.2.Suppose A∈Q∗and B is a Brownian excursion in H starting at0.Then the conditional law of(ΦA(B(t)),t≥0)given B∩A=∅is the same as a time change of B.Finally,let us mention the following result that will be useful later on. Lemma4.3.Let P x+iy denote the law of a Brownian excursion B starting at x+iy∈y=a(A)yx2+y2 ,and the lemma readily follows.18Figure5.1:The various maps.Using Cauchy’s Theorem,for example,it is easy to see that the second statement of the lemma may be strengthened toy ∞−∞P x+iy B[0,∞)∩A=∅ dx=πa(A),y>sup{Im z:z∈A}.(4.3) 5Conformal image of chordal SLELet W:[0,∞)→R be continuous with W0=0,and let(g t)be the(chordal) Loewner chain driven by W satisfying(2.6).It is easy to verify by differen-tiation and(2.6)that the inverse map f t(z)=g−1t(z)satisfies2f′t(z)∂t f t(z)=−+o(z−1),z→∞,zwhere the coefficient a(t)depends on G and W t.Note that˜g t satisfies the Loewner equation∂t a(t)∂t˜g t(z)=where ˜Wt :=h t (W t ),h t :=˜g t ◦G ◦g −1t =g A t .(This follows from the proof of Loewner’s theorem,because ˜g t (˜K t +δ\˜K t )lies in a small neighborhood of ˜W t when δ>0is small.Also see [23,(2.6)].)The identity (2.5)gives a (g t (K t +∆t \K t ))=2∆t .The image of ˜K t +∆t \˜K t under˜g t is h t g t (K t +∆t \K t ) .The scaling rule (2.3)of a tells us that as ∆t →0+,the half-plane capacity of h t g t (K t +∆t \K t ) is asymptotic to h ′t (W t )2·2∆t .(The higher order derivatives of h t can be ignored,as follows from (2.2).Also see [23,(2.7)].)Hence,∂t a (t )=2h ′t (W t )2.(5.1)Using the chain rule we get[∂t h t ](z )=2h ′t (W t )2z −W t .(5.2)This formula is valid for z ∈H \g t (A )as well as for z in a punctured neighborhood of W t in R .In fact,it is also valid at W t with[∂t h t ](W t )=lim z →W t 2h ′t (W t )2z −W t =−3h ′′t (W t ).Computations of a similar nature appear (in a deterministic setting)in [11].Differentiating (5.2)with respect to z gives the equation[∂t h ′t ](z )=−2h ′t (W t )2h ′t (z )(z −W t )2−2h ′′t (z )2h ′t (W t )−4h ′′′t (W t )κdB tfor some measurable process b t adapted to the filtration of B t which satisfies t 0|b s|ds <∞a.s.for every t >0.20。

托福阅读真题第177篇ConstraintsonNaturalSelectionParagraph 1：Natural selection is the process in which organisms with certain traits survive and reproduce while organisms that are less able to adapt to their environment die off. As Darwin pointed out, natural selection does not necessarily produce evolutionary progress, much less perfection. The limits to the effectiveness of natural selection are most clearly revealed by the universality of extinction. More than 99.9 percent of all evolutionary lines that once existed on Earth have become extinct. Mass extinctions remind us forcefully that evolution is not a steady approach to an ever-higher perfection but an unpredictable process in which the best-adapted organisms may be suddenly exterminated by a catastrophe and their place taken by lineages that prior to the catastrophe seemed to be without distinction or prospects.1. Which of the sentences below best expresses the essential information in the highlighted sentence in the passage? Incorrect choices change the meaning in important ways or leave out essential information.O Evolution is an unpredictable process because in mass extinctions highly-evolved organisms are exterminated.O Evolution does not progress steadily to ever-higher levels of perfection because, as shown by mass extinctions, lineages favored by evolution can be suddenly replaced by those not favored previously when circumstances change.O Catastrophes remind us that evolution is a process in which the best-adapted organisms are exterminated and their place taken by lineages shown to be poorly adapted.O When mass extinctions exterminate the best-adaptedorganisms, less important lineages suddenly become better adapted and take their place.2. According to paragraph 1, which of the following provides evidence that natural selection does not always lead to evolutionary progress?O Most evolutionary lines that once existed on Earth have become extinct.O Evolutionary lines usually weaken as they increase in age.O The history of evolution shows that many evolutionary lines can become extinct at the same time.O So far, less than one percent of evolutionary lines have achieved such perfect adaptation to their environment that they will never become extinct.Paragraph 2：There are numerous constraints, or limits, on the power of natural selection to bring about change. First, the genetic variation needed to perfect a characteristic may not be forthcoming. Second, during evolution, the adoption of one among several possible solutions to a new environmental opportunity may greatly restrict the possibilities for subsequent evolution. For instance, when a selective advantage for a skeleton developed among the ancestors of the vertebrates and the arthropods, the ancestors of the arthropods had the prerequisites for developing an external skeleton, and those of the vertebrates had the prerequisites for acquiring an internal skeleton. The entire subsequent history of these two large groups of organisms was affected by the two different paths taken by their remote ancestors. The vertebrates were able to develop such huge creatures as dinosaurs, elephants, and whales. A large crab is the largest type that the arthropods were able to achieve.3. In paragraph 2, why does the author discuss the ancestorsof vertebrates and arthropods?O To explain how a single feature can cause the extinction of entire groups of organismsO To identify some factors that determine how large an organism can becomeO To illustrate the point that earlier developments influence the possibilities for future developmentO To emphasize the role of the environment in the development of organisms4. Which of the following can be inferred from paragraph 2 about arthropods?O There are fewer of them than there are of vertebrates.O Their ancestors had a selective advantage over the ancestors of vertebrates.O Their ancestors once possessed internal skeletons.O Their body features prevent them from becoming large organisms.Paragraph 3：Another constraint on natural selection is developmental interaction. The different components of an individual organism—its structures and organs—are not independent of one another, and none of them responds to selection without interacting with the others. The whole developmental machinery is a single interacting system. Organisms are compromises among competing demands. How far a particular structure or organ can respond to the forces of selection depends, to a considerable extent, on the resistance offered by other structures and organs, as well as components of the genotype (the totality of an individual’s genes).5. According to paragraph 3, why must organisms compromise between competing demands?O A particular organ or structure may be unable to respond to selection pressures due to the needs of other parts of the organism.O An organism’s ability to respond to the forces of selection depends on the demands of other organisms within its environment.O An organism’s environment and its genotype try at the same time to influence its ability to respond to natural selection.O Different elements of the environment call for adaptations that are often incompatible with one another.Paragraph 4：The structure of the genotype itself imposes limits on the power of natural selection. The classical metaphor of the genotype was that of a beaded string on which the genes were lined up like pearls in a necklace. According to this view, each gene was more or less independent of the others. Not much is left of this previously accepted image. It is now known that there are different functional classes of genes, some charged to produce material, others to regulate it, and still others that are apparently not functioning at all. There are single coding genes, moderately repetitive DNA, highly repetitive DNA, and many other kinds of DNA. Discovering exactly how they all interact with one another is still a rather poorly understood area of genetics.6. Paragraph 4 supports all of the statements about genes EXCEPT:O Our understanding of the extent to which genes act independently has changed over time.O Genes are classified into groups on the basis of their function.O Some genes seem to have no function.O Studies to identify ways that genes interact have beenlargely successful.Paragraph 5：A further constraint on natural selection is the capacity for nongenetic modification. The more plastic the organism’s body characteristics are (owing to developmental flexibility), the more this reduces the force of adverse selection pressures. Plants, and particularly microorganisms, have a far greater capacity for individual modification than do animals. Natural selection is involved even in this phenomenon, since the capacity for nongenetic adaptation is under strict genetic control. When a population shifts to a new specialized environment, genes will be selected during the following generations that reinforce and may eventually largely replace the capacity for nongenetic adaptation.Paragraph 6：Finally, which organisms survive and reproduce in a population is partly the result of chance, and this also limits the power of natural selection. Chance operates at every level of the process of reproduction, from the transmission of parental chromosomes to the survival of the newly formed individual. Furthermore, potentially favorable gene combinations are often destroyed by indiscriminate environmental forces such as storms, floods, earthquakes, or volcanic eruptions, without natural selection being given the opportunity to favor these genotypes. Yet over time, in the survival of those few individuals that become the ancestors of subsequent generations, relative fitness always plays a major role.7. What point does paragraph 6 make about the individuals that survive a particular natural disaster?O They were the small number of organisms that happened to be well-adapted to survive that kind of natural disaster.O Their descendants will likely be shaped by natural selectionto evolve genes that will make them fit to survive the next natural disaster.O Their survival may have been due to chance, but fitness also contributes to their survival over time.O They will probably have comparatively weak offspring because the natural disaster eliminated the individuals that had more favorable gene combinations.8. According to paragraph 6, environmental forces limit the power of natural selection in which of the following ways?O They change the reproductive process in significant ways.O They destroy potentially favorable gene combinations before they can be selected.O They interfere with the transmission of chromosomes from parent to offspring.O They weaken the ability of individuals to maintain high fitness levels.Paragraph 4：The structure of the genotype itself imposes limits on the power of natural selection. The classical metaphor of the genotype was that of a beaded string on which the genes were lined up like pearls in a necklace. ■According to this view, each gene was more or less independent of the others. ■Not much is left of this previ ously accepted image. ■It is now known that there are different functional classes of genes, some charged to produce material, others to regulate it, and still others that are apparently not functioning at all. ■There are single coding genes, moderately repetitive DNA, highly repetitive DNA, and many other kinds of DNA. Discovering exactly how they all interact with one another is still a rather poorly understood area of genetics.9. Look at the four squares [■] that indicate where the following sentence could be added to the passage.New models of the genotype depict a much more complicated relationship among genes.Where would the sentence best fit? Click on a square [■] to add the sentence to the passage.10. Directions: An introductory sentence for a brief summary of the passage is provided below. Complete the summary by selecting the THREE answer choices that express the most important ideas in the passage. Some answer choices do not belong in the summary because they express ideas that are not presented in the passage or are minor ideas in the passage. This question is worth 2 points. Drag your choices to the spaces where they belong. To review the passage, click on View Text.Genetics and environmental factors often prevent organisms from achieving evolutionary perfection.O Darwin first challenged the idea of evolutionary progress by observing that more than 99.9 percent of all evolutionary lines that once existed on Earth have become extinct.O A single adaptation to an organism’s environment may dete rmine the way in which the organism’s subsequent ancestors are able to evolve.O The structure of the genotype itself restricts natural selection, since genes must line up like pearls on a necklace and cannot be moved out of their proper order.O The development of vertebrates and arthropods from a single ancestor demonstrates the power of the environment to limit natural selection.O A single structure or gene in an organism cannot respond to the forces of natural selection without affecting the functioning of other structures or genes.O Both environmental and genetic chance may prevent eventhe fittest organisms from surviving and reproducing.。

体裁议论文主题气候变化与因纽特人构造A 段：概述北极罕见事件敲响警钟 B 段：因纽特人对于环境变化做出的反响 C 段：艰辛恶劣的自然条件 D 段：生活必需品来源的替代品 E 段：安逸生活的负面影响 F 段：因纽特人对于环境的建议逐渐被考虑和重视G 段：人们对于环境的认识非常有限A 段incident n. 事件abstract adj. 抽象的snowmobile n. 雪地汽车shrink v. 收缩thaw n. 融雪ice-free adj. 不冻的igloo n. 圆顶建筑knock-on adj. 连锁的insulating adj. 绝缘的precipitation n. 降水permafrost n. 永久冰冻( 永久冻土，永久冻地) canary n. 金丝雀B 段urgent adj. 急迫的，紧要的，紧急的hard-won adj. 难得的，来之不易的precarious a. 不确定的；危险的autonomy n. 自治. 自治权threat n. 威胁lie in 在于content adj. 满足的combine v. 结合stand back 退后( 靠后站，不介入) ancestral a. 祖先的，祖传的C 段vast adj. 广阔的vanish v. 消失polar adj. 两极的，极地的adapt to 适应venture v. 冒险cope with 对付( 应付，抑制) terrain n. 地带Thule n. 古人相信存在于世界北端的国家，极北之地meagre adj. 瘦的，缺乏的exploit v. 开发，开拓kayak n.( 爱斯基摩人用的) 皮船mammal n. 哺乳动物sled n. 雪撬D 段descendant n.子孙，后代rely on 依赖，依靠harsh adj. 艰辛的；苛刻的provision n. 供应品，必需品indigenous adj. 外乡的replace with 取代，以……代替abandon v. 放弃scarce adj. 缺乏的，缺乏的nomadic adj. 游牧的 E 段curtail v. 缩减，减少identity n. 身份；特性obesity n. 肥胖，肥大depression n. 沮丧，情绪低落；忧郁症diabetes n. 糖尿病F 段at stake 在危险中( 处于成败关头) credibility n. 可信性tease out 梳理，挑出consult v.商议；请教vital adj. 至关重要的；所必需的agenda n. 议程wisdom n. 明智的行为：智慧impinge v. 进犯G 段occupation n. 占有tremendous adj. 宏大的，惊人的onslaught n.冲击capriciousness n. 任性；善变F prediction n. 预言，预报难句解析 1. While the Inuit may not actually starve if hunting and trapping are curtailed by climate change, there has certainly been an impact on people‟s health. 参考译文：即使气候变化阻碍了狩猎和诱捕，因纽特人或许也不会真的挨饿受冻，但气候变化确实影响了人们的安康。

1、目标和结果不清晰。

It is noted that your manuscript needs careful editing by someone with expertise in technical English editing paying particular attention to English grammar, spelling, and sentence structure so that the goals and results of the study are clear to the reader.2、未解释研究方法或解释不充分。

◆In general, there is a lack of explanation of replicates and statistical methods used in the study.◆Furthermore, an explanation of why the authors did these various experiments should be provided.3、对于研究设计的rationale:Also, there are few explanations of the rationale for the study design.4、夸张地陈述结论/夸大成果/不严谨：The conclusions are overstated. For example, the study did not showif the side effects from initial copper burst can be avoid with the polymer formulation.5、对hypothesis的清晰界定：A hypothesis needs to be presented。

6、对某个概念或工具使用的rationale/定义概念：What was the rationale for the film/SBF volume ratio?7、对研究问题的定义：Try to set the problem discussed in this paper in more clear,write one section to define the problem8、如何凸现原创性以及如何充分地写literature review:The topic is novel but the application proposed is not so novel.9、对claim,如A＞B的证明，verification:There is no experimental comparison of the algorithm with previously known work, so it is impossible to judge whether the algorithm is an improvement on previous work.10、严谨度问题：MNQ is easier than the primitive PNQS, how to prove that.11、格式（重视程度）：◆In addition, the list of references is not in our style. It is close but not completely correct. I have attached a pdf file with "Instructions for Authors" which shows examples.◆Before submitting a revision be sure that your material is properly prepared and formatted. If you are unsure, please consult the formatting nstructions to authors that are given under the "Instructions and Forms" button in he upper right-hand corner of the screen.12、语言问题（出现最多的问题）：有关语言的审稿人意见：◆It is noted that your manuscript needs careful editing by someone with expertise in technical English editing paying particular attention to English grammar, spelling, and sentence structure so that the goals and results of the study are clear to the reader.◆The authors must have their work reviewed by a proper translation/reviewing service before submission; only then can a proper review be performed. Mostsentences contain grammatical and/or spelling mistakes or are not complete sentences.◆As presented, the writing is not acceptable for the journal. There are problems with sentence structure, verb tense, and clause construction.◆The English of your manuscript must be improved before resubmission. We str ongly suggest that you obtain assistance from a colleague who is well-versed in English or whose native language is English.◆Please have someone competent in the English language and the subject matter of your paper go over the paper and correct it. ?◆the quality of English needs improving.来自编辑的鼓励：Encouragement from reviewers:◆I would be very glad to re-review the paper in greater depth once it has been edited because the subject is interesting.◆There is continued interest in your manuscript titled "……" which you submitted to the Journal of Biomedical Materials Research: Part B - Applied Biomat erials.◆The Submission has been greatly improved and is worthy of publication.•The paper is very annoying to read as it is riddled with grammatical errors and poorly constructed sentences. Furthermore, the novelty and motivation of the work is not well justified. Also, the experimental study is shallow. In fact, I cant figure out the legends as it is too small! How does your effort compares with state-of-the-art??•The experiment is the major problem in the paper. Not only the dataset is notpublished, but also the description is very rough. It is impossible to replicate the experiment and verify the claim of the author. Furthermore, almost no discussion for the experimental result is given. E.g. why the author would obtain this result? Which component is the most important? Any further improvement?•the author should concentrated on the new algorithm with your idea and explained its advantages clearly with a most simple words.•it is good concept, but need to polish layout, language.•The authors did a good job in motivating the problem studied in the introduction.The mathematic explanation of the proposed solutions is also nice. Furthermore, the paper is accompanied by an adequate set of experiments for evaluating the effectiveness of the solutions the authors propose.•Apparently，Obviously ,Innovation ,refine ,In my humble opinion如果仍然有需要修改的小毛病，一般你可以用you paper has been conditionally accepted. Please revise .....according to review comments.如果是接受，你可以用We are very pleased to inform you that your paper "xxxxx" has been accepted by [journal name]. Please prepare your paper by journal template...............At a first glance, this short manuscript seems an interesting piece ofwork, reporting on ×××. Fine, good quality, but all this has been done and published, and nearly become a well-known phenomenon. Therefore, there is insufficient novelty or significance to meet publication criteria. Also, I did not see any expermental evidence how the ** is related with **, except for the hand-waving qualitativediscussion. Therefore, I cannot support its publication in JPD in its present form. It should be rejected.建议去小木虫问问，那里有一些资源。

On Definability in Dependence LogicJuha Kontinen Department of Mathematicsand StatisticsUniversity of HelsinkiFinlandJouko V¨a¨a n¨a nenILLC University of Amsterdam The Netherlands23rd April2007AbstractWe study the expressive power of open formulas of Dependence Logic introduced in[9].In particular,we answer a question raised byWilfrid Hodges:how to characterize the sets of teams definable bymeans of identity only in dependence logic,or equivalently in inde-pendence friendly logic.1IntroductionThe Independence Friendly(IF)Logic,incorporating explicit dependence of quantifiers from each other,was introduced in[4,3].By the method of[2]and[10]it can be seen that every sentence of IF logic has a definition inΣ11,and vice versa.Hodges gave in[5]a compositional semantics for IF logic in terms of,what he calls trumps.He showed in[6]that every formula of IFlogic can be represented in an equivalent form inΣ11with an extra predicateinterpreting the trump.Hodges went on to ask about the converse:what sets of subsets of an infinite domain M are expressible as the set of trumps of a formula of the logic IF by means of identity only.We show in this paperthat the answer is:exactly those that can be defined inΣ11with an extrapredicate,occurring only negatively,for the trump.We use the framework of[9]and accordingly talk about dependence logic rather than IF logic.At the end of the paper we state our results also for IF logic.12PreliminariesIn this section we define Dependence Logic(D)and recall some of its prop-erties.Definition2.1([9]).The syntax of D extends the syntax of FO,defined in terms of∨,∧,¬,∃and∀,by new atomic(dependence)formulas of the form=(t1,...,t n),(1) where t1,...,t n are terms.If L is a vocabulary,we use D[L]to denote the set of formulas of D based on L.The intuitive meaning of the dependence formula(1)is that the value of the term t n is determined by the values of the terms t1,...,t n−1.As singular cases we have=(),which we take to be universally true,and=(t),which declares that the value of the term t depends on nothing,i.e.,is con-stant.In order to define the semantics of D,wefirst need to define the concept of a team.Let A be a model with domain A.Assignments of A arefinite mappings from variables to A.The value of term t in the assignment s is denoted byt A 1 s .If s is an assignment,x a variable in the domain of s and a∈A,thens(a/x)denotes the assignment obtained from s by changing the value of s at x to a.Let A be a set and{x1,...,x k}afinite set of variables.A team X of A with domain{x1,...,x k}is any set of assignments from the variables {x1,...,x k}into the set A.We denote by rel(X)the k-ary relation of A corresponding to X rel(X)={(s(x1),...,s(x k))|s∈X}.If X is a team of A, and F:X→A,we use X(F/x n)to denote the team{s(F(s)/x n):s∈X} and X(A/x n)the team{s(a/x n):s∈X and a∈A}.We are now ready to define the semantics of D.We restrict attention to formulas in negation normal form,i.e.,negation is assumed to appear only in front of atomic formulas.Definition2.2([9]).Let A be a model and X a team of A.The satisfaction relation A|=Xϕis defined as follows:1.A|=X t1=t2ifffor all s∈X we have t A1 s =t A2s .22.A|=X¬t1=t2ifffor all s∈X we have t A1 s =t A2s .3.A|=X=(t1,...,t n)ifffor all s,s ∈X such that t A1 s =t A1s ,...,t An−1s =t A n−1 s ,we have t Ans =t Ans .4.A|=X¬=(t1,...,t n)iffX=∅.5.A|=X R(t1,...,t n)ifffor all s∈X we have(t A1 s ,...,t Ans )∈R A.6.A|=X¬R(t1,...,t n)ifffor all s∈X we have(t A1 s ,...,t Ans )∈R A.7.A|=Xψ∧φiffA|=Xψand A|=Xφ.8.A|=Xψ∨φiffX=Y∪Z such that A|=Yψand A|=Zφ.9.A|=X∃x nψiffA|=X(F/xn)|=ψfor some F:X→A.10.A|=X∀x nψiffA|=X(A/xn)ψ.Finally,a sentenceϕis true in a model A if A|={∅}ϕ.Our goal in this paper is to characterize definable sets of teams,i.e.sets of the form{X:A|=Xφ},(2) where A is afixed model andφ∈D.For reasons that we discuss in the next section we attempt to characterize the set(2)in the special case that the vocabulary of A is empty.Note that this case is still non-trivial.For example,if the domain of A is infinite,the set ofφsuch that{∅}is in theset(2),is non-recursive(in factΠ01-complete,by Theorem2.4)even if thevocabulary of A is empty.The following fact[5]is very basic:Proposition2.3(Downward closure).Suppose Y⊆X.Then A|=Xϕimplies A|=Yϕ.Another basic fact is the result that the expressive power of sentences of D coincides with that of existential second-order sentences(Σ11):Theorem2.4([10,2]).For every sentenceφof D there is a sentenceΦofΣ11such thatFor all models A:A|={∅}φ⇐⇒A|=Φ.(3)Conversely,for every sentenceΦofΣ11there is a sentenceφof D such that(3)holds.3However,Theorem2.4does not–a priori–tell us anything about de-finable sets of teams.In our main result below(Theorem4.9)we generalize Theorem2.4from sentences to formulas.Since formulas of D define sets ofteams and formulas ofΣ11define sets of assignments,the two concepts cannotbe directly compared.To remedy this we compare definability by a formula of D to definability by a sentence ofΣ11with an extra predicate.3Two examplesThe two examples of this section demonstrate the difficulties in characterizing all definable properties of teams.Thefirst example is from[5].It shows that, over afixed model,the family of teams satisfying a formula can be extremely complex.Example3.1.Let A be a set,n a positive integer,and F a family of sets of n-tuples of A which is closed under taking subsets.Suppose that there happens to be an n+1-ary relation R on A such that for every set T⊆A n, T∈F⇔there is b∈A such that R(ab)for all a∈T.Letϕ(x)be the formula∃y(=(y)∧R(x,y)),then(A,R)|=Xϕ(x)⇔rel(X)∈F.As emphasized in[5],this shows that it is very difficult to say anything more about definable properties of teams on arbitrary structures except that they are closed downwards.This example is elaborated in[1].The previous example used in an essential way the predicate R.In the next example,we construct formulas defining certain downward closed prop-erties of teams over the empty vocabulary.Proposition 3.2.Let k∈N and let P(x)be a polynomial with positive integer coefficients.Then there is a formulaϕ(x)∈D such that for allfinite sets A and teams X over{x1,...,x k}A|=Xϕ⇔|X|≤P(|A|).Proof.Supposefirst that P(x)=c∈N.Note that|X|≤1can be defined by the formulaψ:=(x1)∧···∧=(x k).Therefore,|X|≤c can be expressed asψ∨ψ···∨ψ,4where the disjunction is taken c times.Suppose then that P(x)=x c.Now the following formula can be used∃y1...∃y c(1≤i≤k=(y1,...,y c,x i)).This formula declares that there is a function from the set X to the set A c which is one-to-one.Finally,note that|X|≤(P1+P2)(|A|)can be expressed asψ1∨ψ2assuming thatψi defines the property|X|≤P i(|A|).4Characterizing definable properties of teamsIn this section we restrict attention to properties of teams definable over the empty vocabulary.We show that,over the empty vocabulary,definable teamproperties correspond exactly to the downwards closed quantifiers ofΣ11.Definition4.1.Letϕ(y1,...,y k)∈D[∅]and R a k-ary predicate.We denote by Qϕthe following class of{R}-structuresQϕ={(A,rel(X))|A|=Xϕ}.Lemma4.2.For every formulaϕ(y1,...,y k)∈D[∅],the class Qϕis closed under isomorphisms.Since satisfiability is preserved in subteams,the quantifier Qϕis always monotone downwards.The question we are studying can be formulated as follows.Question1.For which downwards monotone quantifiers Q we canfind a formulaϕ∈D[∅]such that Q=Qϕ.Denote byΣ11[{R}]existential second-order sentences of vocabulary{R}.It is easy to see thatΣ11-definability is an upper bound for the solution. Proposition4.3.For everyϕ(y1,...,y k)∈D[∅]the quantifier Qϕis defin-able inΣ11[{R}].Proof.By[6],for everyϕ(y1,...,y k)∈D[∅],there is a sentenceψ∈Σ11[{R}]such that for all sets A and teams X over{y1,...,y k}it holds thatA|=Xϕ⇔(A,rel(X))|=ψ.5Corollary4.4.Let k∈N.There is no formulaϕ(x1,...,x k)∈D[∅]such that for all A and teams XA|=Xϕ⇔|X|isfinite.Proof.This follows by Proposition4.3and the Compactness Theorem of Σ11.Since,e.g.,transitivity is not a downward monotone property,the familyof quantifiers we are looking for will be a proper subclass ofΣ11[{R}].Weshall next show that there is a syntactic criterion for aΣ11[{R}]sentence tobe monotone downwards.Definition4.5.Let R be a k-ary relation symbol andϕ∈Σ11[{R}]a sen-tence.We say thatϕis downwards monotone with respect to R if for all A and B ⊆B⊆A n(A,B)|=ϕ⇒(A,B )|=ϕ.Definition4.6.An occurence of a relation symbol R in a formulaϕis called positive(negative)if it is in the scope of an even(odd)number of nested negation symbols.Proposition4.7.A sentenceϕ∈Σ11[{R}]is downwards monotone withrespect to R iffthere isψ∈Σ11[{R}]such that|=ϕ↔ψ, and R appears only negatively inψ.Proof.Assume thatϕ∈Σ11[{R}]is monotone downwards.Letϕ∗be aformula acquired by replacing all the occurences of R inϕby a new predicate variable R .Using the downwards monotonicity ofϕ,it is straightforward to verify that|=ϕ↔∃R (ϕ∗∧∀x(R(x)→R (x))).Note that,on the right hand side,the predicate R appears only negatively.For the other direction,we may assume that negation appears inϕonly in front of atomic formulas.Now the claim follows by induction on the construction ofϕ(caseϕ=¬R(t)being the only non-trivial one).In the following,we shall be using the fact thatΣ11formulas can betransformed to the so-called Skolem Normal Form[7](see[8]).6Theorem4.8(Skolem Normal Form Theorem).EveryΣ11formula is equiv-alent to a formula of the form∃f1...∃f n∀x1...∀x mψ,whereψis a quantifier-free formula.We are now ready to prove the main result of this paper.Theorem4.9.Let Q be a downwards monotone quantifier.Then there is a formulaϕ∈D[∅]such that Q=Qϕif and only if Q isΣ11[{R}]-definable. Proof.Note that Proposition4.3already gives the other half of the claim.Assume that Q is a downwards monotoneΣ11-quantifier.We need tofind aformulaϕ∈D[∅]such that Q=Qϕ.By Theorem4.8,there is a sentenceλof the form∃f1...∃f n∀x1...∀x mψ(4) defining Q.We may assume thatψis in conjunctive normal form and that for all the function symbols appearing inψthere are unique pairwise distinct variables z1,...,z s((z1,...,z s)a subsequence of(x1,...,x m))such that all occurences of f are of the form f(z1,...,z s)(see[9]for details).As in the proof of Proposition4.7,we then pass on to the equivalent formula∃R (λ∗∧∀x(R(x)→R (x)))and translate it again to Skolem normal form∃f1...∃f n∃f n+1∃f n+2∀x1...∀x m (ψ ∧(¬R(x)∨f n+1(x)=f n+2(x))),i.e.,we replace all subformulas of the form R (t1,...,t k)by the formula f n+1(t1,...,t k)=f n+2(t1,...,t k)and place the universal quantifiers in front by changing bound variables if necessary.We still need to make sure that all the occurences of the new function symbols f n+1and f n+2are of the form f(z1,...,z s)for some pairwise distinct variables z1,...,z s((z1,...,z s) a subsequence of(x1,...,x m)).This requires some transformations on the quantifier-free part since we want it to maintain conjunctive normal form. These transformations might add a new conjunct(a disjunction of identities) to(ψ ∧(¬R(x)∨f n+1(x)=f n+2(x))or add new disjuncts(identity atoms)to all the conjucts via the equivalence p∨(q∧r)≡(p∨q)∧(p∨r).However,after these trasformations,only one of the conjuncts has a literal of the form¬R(x).In other words,the predicate R has in total only one occurence in the formula and it is negative.7Let us now assume that the formula in(4)defines Q and satisfies all the conditions required above.The formulaχ(y1,...,y k)∈D[∅]defining Q is now defined as∀x1...∀x m∃x m+1...∃x m+n(θ1∧θ2),whereθ1is the formula1≤i≤n =(z i1,...,z is i,x m+i),and(z i1,...,z is i)is the unique tuple of variables to which f i is applied inψ.The formulaθ2is acquired fromψbyfirst replacing the terms f i(z i1,...,z is i)by the corresponding variables x m+i inψ.Note that the assumptions on the way function terms can occur guarantee that the variable x m+i always denotesthe same element as the term f i(z i1,...,z is i)in the translation.Finally,wereplace the subformula¬R(x1,...,x k)inψby the formula1≤i≤ky i=x i.We shall next show that the translation works as intended,i.e.,that for all A and teams X over{y1,...,y k}A|=Xχ(y1,...,y k)⇔(A,rel(X))|=ϕ.Clearly,it suffices to show that for all functions f of the appropriate arity A|=X∗θ2⇔(A,rel(X),f)|=∀x1...∀x mψ,whereX∗={saf1(a)···f n(a)|s∈X and a∈A k}and f i(a)denotes the result of applying function f i to the appropriate sub-sequence of a determined by the way z i1,...,z is ireside in x1,...,x m.Recallthatψis assumed to be in conjunctive normal formψ=1≤j≤e1≤i≤r jαji.Hence,the formulaθ2can be written asψ=1≤j≤e1≤i≤r jα∗j i,whereα∗j i arises fromαjiby replacing the terms f i(z i1,...,z is i)by the variablesx m+i and¬R(x1,...,x k)by1≤i≤ky i=x i.8Let us assumefirst that the claim holds for all the conjuncts ofψ.Supposethat(A,rel(X),f)|=∀x1...∀x m1≤j≤e1≤i≤r jαji.Then,for all j we have that(A,rel(X),f)|=∀x1...∀x m1≤i≤r j αji.By the assumption,it holds thatA|=X∗1≤i≤r j α∗j ifor all j,and thusA|=X∗1≤j≤e1≤i≤r jα∗j i.The other direction is analogous.Therefore,it suffices to show the claim for disjunctions of atomic formulas.Suppose that∨1≤i≤rαi is a disjunction of atomic formulas in which R appears only negatively.Assume that(A,rel(X),f)|=∀x1...∀x m1≤i≤rαi.Then,for each a∈A k,someαi is satisfied.Define a partition Y1,...Y r of X∗as follows:saf1(a)···f n(a)is put to Y v iffv is the least index j for which(A,rel(X),f)|=αj(a).It is easy to verify that X∗=∪1≤i≤r Y i and thatA|=Yi α∗i .For the other direction,(here we need the assumption that at most one αj is of the form¬R(t1,...,t k)),suppose thatA|=X∗1≤i≤r α∗i.(5)By definition,there is a partition of X∗to sets Y1,...,Y r such thatA|=Yi α∗i .9We may assume thatα1is the formula¬R(x1,...,x k).We next define a new partition of X∗in the following way.In the natural order,starting with Y2, we inflate Y2to the maximal W2⊆X∗satisfyingA|=W2α∗2 .Then,we keep W2fixed and replace Y3with the maximal subset of X∗\W2satisfyingα∗3.Finally,we define W1=Y1\(W2∪···∪W r).Since W1⊆Y1,this new partition also witnesses(5)by the downward closure.If,in the new partition,some tuple saf1(a)···f n(a)∈W1,then we must haves af1(a)···f n(a)∈W1for all s ∈X.This follows from the maximality of the sets W2,...,W r and the fact that the variables y1,...,y k do not appear in any of the formulasα∗i for i>1.Therefore,A|=W11≤i≤ky i=x iimplies that(A,rel(X),f)|=¬R(t)(a)for all a∈A k such that,for some s,we have saf1(a)···f n(a)∈W1.We may conclude that(A,rel(X),f)|=∀x1...∀x m1≤i≤rαi.Note that the defining formulaχ(y1,...,y k)in Theorem4.9can be trans-lated to a formula of Independence Friendly Logic as∀x1...∀x m(∃x m+1/W1)...(∃x m+n/W n)θ2,where W i=({x1,...,x m}∪{y1,...,y k})\{z i1,...,z is}.Therefore,the ana-logue of Theorem4.9also holds for Independence Friendly Logic. Corollary4.10.The properties of trumps over variables{y1,...,y k}defin-able in Independence Friendly Logic over the empty vocabulary are exactly the downwards monotoneΣ11[{R}]quantifiers.Recall that the existential quantifier of D is defined byA|=X∃x nψiffA|=X(F/xn)|=ψfor some F:X→A.10Denote by∃1the following variant of the existential quantifier|=ψ.A|=X∃1x nψiffthere is a∈A such that A|=X(a/xn)It is easy to see that∃1xψcan be expressed in a“uniform”way as∃x(=(x)∧ψ).The analogue of∃1for the universal quantifier is|=ψ.A|=X∀1x nψifffor all a∈A it holds that A|=X(a/xn)It is an open question whether the quantifier∀1can be given a uniform definition in the logic D.It is easy to verify that extending the syntax of D by∀1does not increase the expressive power of D.This follows from the fact that Theorem68in[9]generalizes to cover also the case of∀1.More interestingly,Theorem4.9,and the fact that∀1is downwards monotone, shows that the quantifier∀1does not increase the expressive power of D with respect to open formulas either.It remains open whether the quantifier ∀1is“uniformly”definable in the logic D.References[1]P.Cameron and W.Hodges.Some combinatorics of imperfect informa-tion.J.Symbolic Logic,66(2):673–684,2001.[2]H.B.Enderton.Finite partially-ordered quantifiers.Z.Math.LogikGrundlagen Math.,16:393–397,1970.[3]J.Hintikka.The principles of mathematics revisited.Cambridge Uni-versity Press,Cambridge,1996.[4]J.Hintikka and rmational independence as a semanticalphenomenon.In Logic,methodology and philosophy of science,VIII (Moscow,1987),volume126of Stud.Logic Found.Math.,pages571–589.North-Holland,Amsterdam,1989.[5]positional semantics for a language of imperfect infor-mation.Log.J.IGPL,5(4):539–563(electronic),1997.[6]W.Hodges.Some strange quantifiers.In Structures in logic and com-puter science,volume1261of Lecture Notes in Comput.Sci.,pages 51–65.Springer,Berlin,1997.11[7]T.Skolem.Logisch-kombinatorische Untersuchungen¨u ber die Erf¨u ll-barkeit oder Beweisbarkeit mathematischer S¨a tze nebst einem Theoreme ¨u ber dichte Mengen.Skrifter utgit av Videnskappsselskapet i Kristiania, 1920.[8]T.Skolem.Selected works in logic.Edited by Jens Erik Fenstad.Uni-versitetsforlaget,Oslo,1970.[9]J.V¨a¨a n¨a nen.Dependence Logic,volume70of London MathematicalSociety Student Texts.Cambridge University Press,Cambridge,2007.[10]W.J.Walkoe,Jr.Finite partially-ordered quantification.J.SymbolicLogic,35:535–555,1970.12。

Lesson 1World English: A Blessing or a Curse (p7)1. There has been much opposition from social groups, B from the farmingcommunity.A. straightforwardly(直接地)B. notably（显著地，尤其）C. virtually（事实上）D. exceptionally（例外地）译文：社会团体，尤其是农业团体，对此有许多反对意见。

2. The A view in Britain and other Western countries associates aging with decline, dependency, isolation, and often poverty.A. predominant（占支配地位的）B. credulous（轻信的）C. inclusive（包含的）D. sustainable（可持续的）译文：英国和其他西方国家的主流观点认为，老龄化意味着衰落、依赖、孤立，而且往往是贫穷。

3. But gifts such as these cannot be awarded to everybody, either by judges or by the most D of governments.A. tough（困难的）B. demanding（苛求的）C. diverse（不同的）D. benign（有利的；善良的）译文：但是，这样的礼物不可能由法官或最仁慈的政府颁发给所有人。

4. The foreman read the C of guilty fourteen times, one for each defendant.A. prejudice（偏见）B. verification（政审）C. verdict（判断；裁决）D. punishment（惩罚）译文：陪审团念了十四遍有罪判决，为每位被告都念了一遍。

In academic work students are often expected to give definitions of key words and phrases in order to demonstrate to their tutors that they understand these terms clearly. More generally, however, academic writers define terms so that their readers understand exactly what is meant when certain key terms are used. When important words are not clearly understood misinterpretation may result. In fact, many disagreements (academic, legal, diplomatic, personal) arise as a result of different interpretations of the same term. In academic writing, teachers and their students often have to explore these differing interpretationsbefore moving on to study a topic.Introductory phrasesIt is necessary here to clarify exactly what is meant by …There is a degree of uncertainty around the terminology in …This shows a need to be explicit about exactly what is meant by the word X.X is a term frequently used in the literature, but to date there is no consensus about …The term X is generally understood to mean …The term X has been applied to situations where students …In the literature, the term tends to be used to refer to …The broad use of the term X is sometimes equatedwith …Whereas X refers to the operatio ns of …, Y refers to the …The term disease refers to a biological event characterised by …The term X is a relatively new name for a Y, commonly referred to…In broad biological terms, X can be defined as any stimulus that is …Defined as XYZ, obesity is now considered a worldwide epidemic and is associated with …Indicating difficulties in defining a termA generally accepted definition of X is lacking. Unfortunately, X remains a poorly defined term.The term X embodies a multitude of concepts which …A further definition is given by Smith (1982) who describes …In the field of language teaching, various definitions of X are found.Smith (2001) identified four abilities that might be subsumed under the term X: a) …Although differences of opinion still exist, there appears to be some agreement that X refers to …X is a commonly-used notion in language learning and yet it is a concept difficult to define precisely. Specifying terms that are used in an essay or thesis The term X will be used solely when refer ring to …In the present report, X was therefore defined in termsof …In this essay, the term X will be used in its broadest sense to refer to all …In this paper, the term that will be used to describe this phenomenon is X.In this dissertation, the terms X and Y are used interchangeably to mean …Throughout this thesis, the term education is used to refer to informal systems as well as …While a variety of definitions of the term X have beensuggested, this paper will use the definition first suggested b y Smith (1968) who saw it as …Referring to people’s definitions: author prominent For Smith (2001), fluency means/refers to …Smith (2001) uses the term ‘fluency’ to refer to …Smith (1954) was apparently the first to use the term …The term ‘fluency’ is used by Smith (2001) to refer to …Macro-stabilisation policy is defined by Smith (2003: 119) as ‘… …’This definition is close to those of Smith (2012) and Jones (2013) who define X as …In 1987, sports psychologist John Smith popularized the term ‘X’ to describe …According to a definition provided by Smith (2001:23), fluency is ‘the maximally …Aristotle defines the imagination as ‘the movement which results upon an actual sensation.’One of the first people to define nursing was Florence Nightingale (1860), who wrote: ‘… …’Chomsky writes that a grammar is a ‘device of some sort for producing the ….’ (1957, p.11).Smith, has shown that, as late as 1920, Jones was using。

Chapter 1 Structure of the legal system1. ESSENTIAL ELEMENTS OF THE LEGAL SYSTEMLaw•Law is a formal control mechanism.•It provides a structure for dealing with and resolving disputes.•It also provides some deterrent to those wishing to disrupt social order.Common law•Common law developed in England during the period following the Norman Conquest.•It was made by judges who travelled around the country to keep the King’s peace and made law by merging local customary laws into one ‘law of the land’.•Today, the concept of PRECEDENT continues to be the key feature of commom law, and distinguishes it from other legal systems.•Remedies under common law are monetary, and are known as damages.Equity•Common law does not provide justice to the wronged person if monetary compensation is not suitable.•Equity developed two or three hundred years after common law as a system to resolve disputes where damages are not a suitable remedy and therefore introduced fairnessinto the legal system.•For example, where a person needs to stop another person’s behaviour or to force them to act as they agreed to, equity provides remedies to achieve this.Civil law•Civil law exists to resolve disputes over the rights and obligations of persons dealing with each other and seeks to compensate wronged parties.•It is a form of private law (between individuals) and covers areas such as tort, contract and employment law.•In civil proceedings, the case must be proved on the balance of probability, the object is to convince the court that it is probable that a person’s assertions are ture.•There is no concept of punishment in the civil law and compensation is paid to the wronged person.•If they wish, both parties may choose to settle the dispute out of court.Criminal law• A crime is conduct that is prohibited by the law.•Criminal law is a form of public law (betweent the State and individuals).•In criminal proceedings, the State is the procecutor because it is the community as a whole which suffers as a result of the law being broken.•The burden of proof to convict the accused(认定被告有罪) rests with the procecution, which must prove its case beyond reasonble doubt.•In the UK, the police take the initial decision to prosecute, this is then reviewed by the Crown Prosecution Service. However, some prosecutions are started by the Director of Public Prosecutions, who is the head of the Crown Prosecution Service.•Persons guilty of crime may be punished by fines payable to the State, imprisonment, ora community-based punishment.The distinction between civil law and criminal lawThis is not an act or event which creates the distinction between civil and criminal law, but the legal consequences. A single event might give rise to both civil and criminal proceedings.2. JURISDICTION OF CIVIL COURTS•The nature of the case and the size of the claim will determine which court hears a civil case.•The County courts hear small cases ( claims under £5,000) or those which are deemed to be ‘FAST TRACK’ cases. The case is heard by a Circuit Judg e assisted by DistrictJudges.•Complicated cases or those which are deemed to be ‘MULTI TRACK’ cases are heard at the High Court.•The Queen’s Bench Division hears cases concerning contract and tort issues.•The Family Division hears cases concerning children and matrimonial issues.•The Chancery Division hears cases concerning trusts, bankruptcy and corporate issures.•Appeals are to the Civil Division of the Court of Appeal and are heard by three judges who will decide the outcome by a majority.• A further appeal to the Supreme Court for the United Kingdom may be permitted if it involves an issue of public interests.3. JURISDICTION OF CRIMINAL COURTS•All criminal cases begin in magistrates’ courts where the case is introduced into the system.•Certain types of offences are known as indictable offences, these are serious offences and can only be heard in Crown Court. Other less serious summary offences are heard summarily in the magistrates’court.•Where an offence falls in between the two, it can be ‘triable either way’, the defendant will have the choice to be tried at the magistrates’ court or at the Crown Court.•Where the decision in a criminal case is appealled against, a court further up the hierarchy will hear it.•Appeals from magistrates’ courts are either to the Crown Court or the Queen’s Bench Division of the High Court.•Case stated appeals from the Crown Court are made to QBD. ‘Case stated’ is a legal function to review a magistrates’ court decision on a point of law , it means the law w as misinterpreted by the magistrate.•Appeals from the Crown Court are made to the Court of Appeal and this may be appealled to the Supreme Court for the United Kingdom if it involves an issue of publicinterests.4. THE MAIN CIVIL COURTS IN THE ENGLISH LEGAL SYSTEMMagistrates’ court•The magistrates’ court is mainly a criminal court, but it also has original jurisdiction in many civil cases, such as liscensing and family issues.•It will also hear claims for recovery of unpaid local authority charges and council tax(英国家庭税).County CourtCounty courts have civil jurisdiction only, it deal with almost every kind of civil case within its serve areas. The main limits to its jurisdiction are financial. It is involved in the following matters: •Contact and tort•Equity matters•Probate matters•Disputes concerning land•Undefended matrimonial cases•Some bankruptcy, company winding-up and admiralty cases（海事裁判）.High CourtThe High Court are divided into three divisions.•The Queen’s Bench Divison hears cases concerning contract and tort issues. It also hasa Commercial Court and an Admiralty Court. A divisionl court of the QBD has anappellate jurisdiction on appeals from magistrates’ court and tribunals.•The Family Division hears cases concerning children and matrimonial issues. The Family Division also has a limited appellate jurisdiction on some appeals from theMagistrates’ Court.•The Chancery Division hears cases concerning trusts, mortgage, bankruptcy, taxation, probate and corporate issures. It also has a Patents Court and a Company Court, which deals with liquidations and other company proceedings.Appeal courtsThe civil court which have an exclusively appellate jurisdiction are the Civil Division of the Court of Appeal and the Supreme Court for the United Kingdom.Court of Appeal•The Court of Appeal hears appeals from the County Court, High Court and several sepcial tribunals.•It reviews the evidence and the legal opinions and makes its decisions based on them.•Cases are heard by three judges ( known as Lord Justices of Appeal) who will decide the outcome by a majority..Supreme Court for the United Kingdom•The Supreme Court for the United Kingdom is the highest appeal court in the English legal system. Cases are heard by Justices of the Supreme Court.•The court hears appeals from the Court of Appeal and also appeals from the High Court, under the ‘leapfrog procedure’ .5. THREE TRACK SYSTEM FOR THE ALLOCATION OF CIVIL CASESThe Civil Procedure Rules (CPR 民事程序规定) introduced a three track system for the allocation of civil cases. Generally speaking, county courts hear small track cases and fast track cases and the High Court hears multi-track cases.•In the small claims track, claims of no more than £5,000 will be heard. These are cases to be dealt with quickly and informallly, often without the need for legal represetation or a full hearing. Parties can consent to use the small claims track if the value of the claimexceeds the limits, but this has to be subject to the court's approval.•In the fast claims track, claims under £25,000 may be heard. There is a strictly limited procedure designed to enable cases to be heard within a short but reasonable timescale.Costs are fixed and hearings are no longer than one day.•The multi-track is intended to provide a new and more flexible regime for the more complex claims, which has a value of more than £15,000. An initial ‘case managementconference’ will be held to encourage the parties to resolve the dispute or to consider the alternative dispute resolution. The trial judge sets a budget and a final timetable for thetrial.•Claimants of cases between £15,000 and £25,000 have the choice of using the fast or multi track, although judges may insist complex cases are heard under the multi track.Chapter 2 Sources of English lawSOURCESCase law Statute CustomCommon Equity Primary SecondarylawSources of English law•There are three main sources of English law, namely case law, legislation (statute) and custom.•Broadly speaking, case law is made and developed in the courts and legislation is made by the legislature（立法机关，立法团体） in Parliament.•Since both of these sources create law today, they can be considered as contemporary.•However, local customs, which developed historically and have existed for a very long time, are not considered as contemporary.1. CASE LAW AS A SOURCE OF LAW•Case law is is made in the courts according to the common law and equity.•Both common law and equity are the product of decisions in the courts made by judges who interpret and apply previous cases based on the doctrine of binding precedent.•This doctrine provides that once a principle of law has been decided, it becomes a precedent which binds the lower courts in cases with materially the same facts.•If the facts of the case are not materially the same as those of the relevant precedent, the precedent may be ‘distinguished’ and not be followed.•Only statements of law made by judges can form precedent.•These statements can be divided into ratio decidendi and obiter dicta.•Only the ratio decidendi forms the basis of precedent as it is this reasoning which is vital to his decision.•Obiter dicta are statements of general law (or hypothetical situations) which are not necessary for the decision and hence are not binding.•Whether the doctrine applies will depend on the status of the court dealing with the case.There is a hierarchy of courts with the lower courts being bound to follow thedecisions of the higher courts.•For example, magistrates’ courts and county courts are bound by the decision of the High Court, the Court of Appeal and the Supreme Court for the United Kingdom.2. DOCTRINE OF PRECEDENTThe doctrine of binding precedent•The doctrine of binding precedent, or stare decisis, is essential to the English legal system.•This doctrine provides that once a principle of law has been decided in court, it becomes a precedent which binds the lower courts in cases with materially the samefacts.•The purpose of the doctrine is to provide consistency, coherency and therefore predictablity and fairness in the development of the case law.Judgements• A judgement in a case will start with a description of the facts and probably a review of earlier precedents.•Then the judge will make statements of law applicable to the legal problems raised by the material facts.•These statements can be divided into ratio decidendi and obiter dicta.Ratio dicidendi•Only a proposition(论点，主张) of law, rather than a statement of fact, will be binding.•Ratio dicidendi can be difined as ‘any rule of law, express or implied, treated by a judge as a necessary step in reaching his conclusion, having regard to the line of reasoning adopted by him, or a necessary part of his direction to the jury. ‘ (Cross)Obiter dicta•Obiter dicta are statements of general law (or hypothetical situations) which are not necessary for the decision in the case.•The obiter dicta are of persusive authority only and do not bind lower court. They may be taken into account but need not be followed.Difference between them•The ratio decidendi forms the basis of precedent as it is this reasoning which is vital to judge’s decision.•It is not always easy to distinguish between the ratio decidendi and the obiter dicta.Judges do not always make clear in their comments whether a particular statement orconclusion is ratio or obiter. Indeed, in a case heard by more than one judge, each judge may provide a different ratio decidendi in support of a common decision.The hierarchy of the courts in relation to the operation of precedent(a) the Supreme Court for the United Kindom – binds all lower courts but itself(exceptional cases)(b) Court of Appeal–binds all lower courts and itself(c) High CourtJudge sitting alone – binds all lower courts not divisional courtsJudges sitting together – binds all lower courts and divisional courts(d) CrownMagistrates–bind no-one at allCountyMagistrates’, County and Crown Courts•Decisions of the Magistrates’ Courts and County Courts do not consititute precedent and thereofore not bind on any court, but each of them is bound by decisions of the High Court, Court of Appeal and the Supreme Court for the United Kingdom.•The Crown Court is also bound by the superior courts and its decisions are of persuasive authority only.High court• A decision of the High Court made by an individual judge binds all lower courts, but not another High Court judge. However, it is of persuasive authority and tends to befollowed in practice.• A decison of Divisional Court usually binds another divisional court.Court of Appeal•Decisions of the Court of Appeal binds all English courts except the Supreme Court for the United Kingdom.•The court is normally bound by its own previous majority and unanimous (意见一致的) decisions, and by those of the Supreme Court for the United Kingdom.The Supreme Court for the United Kingdom•The Supreme Court for the United Kingdom stands at the apex of the English judicial system. Its decisions binds all other English courts.•Itself is bound by its own previous decisions, but it reserves the rights to depart from its own precedents in exceptional cases, although this is rarely exercised.Reversing, overruling and distinguishingPrecedent• A precedent is a previous court decision which another court is bound to follow by deciding a subsequent case in the same way.•In certain circumstances, a judge may not wish to follow an previous decision and it may be open to them to reverse, overrule or distinguish the precedent.Reverse•When the decision of a lower court is appealled to a higher one, the higher court may reverse the decision if they feel the lower court has wrongly interpreted the law. Theoriginal decision cannot form a precedent.•For example, if the Court of Appeal reverse the decision of the High Court, the first decision cannot be a precedent but the reversed decision can.•When a decision is reversed, the higher court is usually also overruling the lower court’s statement of the law.Overrule•Higher courts may overrule the decisions of lower courts, depriving (剥夺) their precedent status, if they di sagree with the lower court’s statement of law.•Overruling involves an earlier case, rather than a case which is the subject of an appeal.•When a decision is overruled, the law is changed with retrospective effect. Judges are usually cautious before overruling a long-standing precedent, but this is sometimesnecessary, for example where what is acceptable within a particular society changes. Distinguishing•For a precedent to be followed, the facts of the previous case and the case under consideration must be materially the same.•If not, the precedent may be ‘distinguished’ and not followed.3. THE ADVANTAGES AND DISADVANTAGES OF THE DOCTRINEAdvantagesCertainty•Law is decided fairly and predictably.•The need for costly and time-consuming litigation can be avoided.•The doctrine also gives guidance to the judges and leads to consistency in decisions from different judges in different courts and in different parts of the country.Clarity•The doctrine gives rise to a healthy source of statements of legal principle that can helpfully and clearly be applied to new cases generally.•This leads to a saving of time for all concerned, it don’t need to be put before the courts and argued again.Flexibility•The doctrine allows the law to grow and be developed in accordance with changing needs and circumstances of society.•It also allows a much more flexible judge-made law than Parliament-enacted legislation. PracticalityFaineasDisvantages•Bulk.•Restricts judicial discretion.•reactive system.•Lack of democratic accountability.4. LEGISLATION AS A SOURCE OF LAW AND ITS ADVANTAGES•Statute law is made by Parliament.•Parliament may make law as it sees fit – it may repeal(撤销) earlier statutes, overrule case law or make law in new areas previously unregulated.•The validity of an Act of Parliament cannot be questioned. ( Cheney v Conn 1968).•However, this principle of Parliamentary sovereignty[ˈsɔvərɪnti:](最高统治权、君权) has been reduced somewhat by the UK’s membership of the European Union which requires its law to be brought into line with the EU’s treaties and directives.•Additionally, the Human Rights Act 1998 requires new laws to be compatible with the European Convention on Human Right.•Statute law may be fresh legislation or may be a consolidation of existing statutes and their amendment, for example the Company Act 2006.•It may also be a codification (法律汇编) of existing statute and case law, for example the Sale of Goods Act 1979.•The courts are bound to apply relevant statute law and cannot disregard or rewrite it.•Whatever the nature of the legislation, the role of judges to interpret and apply it is the same.•Judicial interpretation (司法解释) might be needed because of ambiguity in drafting or uncertainty as to whether a particular set of facts are within the scope of a statute, orwhere unforeseeable developments have occurred since the statute was passed.•The complexity of modern legislation makes a great deal of details which cannot be easily included in an Act.•Therefore, powers may be given to a minister or a public body to make laws for specified purpose in the form of statutory instruments, bye-law and Rules of Court.•Such delegated legislation has the same effect as the empowering act itself. Advantages•They can in theory deal with any problem•They are carefully constructed codes of law•New problems in society or unwelcome development can be dealt with quickly•Reponsive to public opinion as parliament is elected at least every five years5. DELEGATED LEGISLATION•The complexity of modern legislation makes a great deal of details which cannot be easily included in an Act.•Therefore, powers may be given to a minister or public body to make laws for specified purpose in the form of statutory instruments, bye-law and Rules of Court.•The legislation sets out the broad objective and purpose of the Act, leaving the detail to be delegated to individuals or bodies outside Parliament.•Such delegated legislation has the same effect as the empowering act itself.There are various forms of delegated legislation•Statutory instruments: these are made by government minister who has delegated the relevant powers.•Bye-laws: these are made by local authorities and apply within a specific locality•Rules of court: these may be made by the judiciary (法官) to control court procedure.•Orders in council: these are often made by the Privy Council (枢密院).•Professional rules: Parliament also gives powers to various professional bodies to regulate the conduct of its members.The control over the delegated legislationAs delegated legislation is often created by unelected individuals and bodies, there are controls over it.•It may have to be approved by an affirmative resolution of Parliament and/or be laid before Parliament for 40 days before it takes effect.•It may be challeged in the courts. Firstly, on the ground that Parliament exceeded its authority to delegate and has acted ultra vires, or secondly, the lagislation has beenmade without the correct procedure.•There are standing (永久的，常设的) Scrutiny Committees (检查委员会) of both Houses whose duty is to examine delegated legislation from a technical point of view and theymay raise objections if necessary. However, they have no authority to its nature orcontent.•The Human Rights Act 1998 gives courts power to strike out any delegated lagislation that runs contrary to the HRA.Advantages•Volume of work. Delegated lagislation enables Parliament to concentrate on the broader principles of the legislative framework, rather than getting bogged down indetails.•Speed. Delegated legislation enables new laws to be passed much more quickly, especially advantageous in times of emergency.•Flexibility. Delegated legislation enables great flexibility, because regulations can be altered later without the need to revert to (回到) Parliament.•Expertise. The subject of new legislation is often highly detailed, technical and complex. It therefore makes sense for the exact content, and the wording（措辞） isarrived at by consultation with professional, commercial or industrial groups outsideParliament who have the relevant expertise.•Tider primary legislation. The primary legislation is more concise (精炼) because the details are left to other delegated legislation documentation(程序说明书). Disadvantages:•Volume. The volume of delegated legislation means that it can become difficult for Parliment ( and others) to keep track of the effect of the legislation.•Unconstitutional.（违反宪法的) Although Parliament is ultimately responsible for the legislation, it is likely that much of the detail has actually been drafted and finalised by individual ministers or by civil servants. Since civil servants are unelected, the degree to which law-making powers should be delegated to them is a matter for some debate. 6. STATUTORY INTERPRETATIONLegislation must be interpreted correctly before judges can apply it fairly. In order to determine the meaning of such legislation, the court will apply a number of well-established rules and principles to interpret the statute.•Literal rule: The literal rule requires the words to be given their literal and grammatical meaning rather than what the judges think they mean.•Golden rule: The golden rule expands the literal rule. It requires the words to be given their plain, ordinary and literal meaning unless this would give rise to manifest (明显的) absurdity(谬论) or inconsistency with the rest of the statute.•Mischief rule: Under the mischief rule, a judges considers what mischief (损害) the Act .Where a statute is designed to remedy a weakness in the law, the correct interpretation is the one that achieves it.•Purposive approach : It requires the words to be given not only their ordinary, literal and grammatical meaning, but also with reference to the context and purpose of thelegislation.•Ejusdem generis (同类) : Where general words follow specific words, the general words must be interpreted by reference to(参考) the specific words used.7. HUMAN RIGHTS ACT 1998The Articles of the European Convention on Human Rights have now been enshrined(铭记) into English law as the Human Right Act 1998, enacted in 2000. The main provisions are: •The right to life•The right to property•The right to education•The right to marry•The right to a fair trial•The right to liberty and security•The right to free elections.•The right to respect for privacy, family life•Freedom of thought, conscience and religion•Freedom of expression, assembly and association•No punishment without law•No discrimination in rightsThe Act binds the pubilc authorities•The Act binds the pubilc authorities, which can be defined as bodies undertaking functions of a public nature, including government departments, local authorities, courts and schools.Non-government individuals or bodies can rely on the actImpact on UK law•The main impact of the HRA1998 on UK law is that UK courts are now required to interpret UK law in a way that is compatible with the Convention. It means that a courtmust take into account the previous decisions of the European Court of Human Rights.•If a court feels that a provision of primary legislation ( ie an Act of Parliament) is incompatible with the Convention, it can make a declaration of incompatibility. It is thenup to the Government to take action to remedy the incompatibility.Chapter 3 Offer and AcceptanceNature of a contractFORMATION & NATURE OF A CONTRACTAgreement Intention ConsiderationThe first essential element in the formation of a binding contract is agreement. This is ususlly evidenced by offer and acceptance.1. OFFER•In the law of contract , an offer is a definite promise to another to be bound on specific terms. It is capable of (能够) acceptance so as to form a binding contract.•An offer cannot be in vague terms, for example a promise to buy a horse if it is ‘lucky’ (Gunthing v Lynn 1831).•An offer can be made to an induvidual, a class of persons or to the world at large and it can be accepted by the conduct of the offeree ( Carlill v Carbolic Smoke Ball Co 1893).•Once an offer has been accepted, a binding contract is created. Either party may legally enforce the promise of the other.•Ture offers must be distinguished from a mere supply of information and statement of intention.Supply of information• A mere supply of information is not an offer, because there is no intention to be bound.•For example, stating the minimum price that one would consider if a sale were to be agreed does not make an offer ( Harvey v Facey 1893).Statement of intention•Similarly, a mere statement of intention is not an offer neither.•For example, advertising that an event such as an auction will take place does not make an offer. (Harris v Nickerson 1873).•Only the offer made with the intention that it shall become binding when accepted may form a binding contract.2. INVITATION TO TREAT•An invitation to treat is an indication that someone is prepared to receive offers with the intention to form a binding contract.•There is no binding contract until this offer is made and, in turn , accepted.Case law has established a number of accepted principles to determine whether a statement is an offer or merely an invitation to treat.Advertisements•An advertisement of goods for sale is usually an attempt to induce offers (Partridge v Crittenden 1968)•However, in limited circumstances, words of an advertisement can be an offer made to the whole world (Carlill v Carbolic Smoke Ball Co. 1893)Display of goods in a shop window•In Fisher v Bell 1961, a shopkeeper was prosecuted for offering for sale an offensive weapon by exhibiting a flick knife in the shop window.•It was held that this was not an offer for sale, but an invitation to treatExhibitions of goods in a self –service shop•In Pharmaceutical Society of G.B. v Boots Cash Chemists 1952, the chemists exhibited various goods on self-service shelves.•It was held that this was not an offer for sale, but an invitation to treat. Customers took up the invitation by taking the goods to the cash point, thereby making an offer to buy which was accepted by the shopkeeper.Auction sales（拍卖）•An auctioneer’s request for bid is not an offer to sell to the highest bidder, but an invitation to treat.•The bid itself is an offer, which the auctioneer is then free to accept or reject ( Payne v Cave 1789).Invitations for tenders (竞标)•An invitation to tender is not an offer to contract with the party offering the lowest price, but an invitation to treat.•The tender itself is an offer, which the person who issued the invitation is then free to accept or reject.3. ACCEPTANCE OF AN OFFERACCEPTANCE•Valid acceptance of a valid offer is one of the essencials of a contract•An acceptance must be an unqualified (无条件的) agreement to the terms of the offer.•Acceptance is generally not effective until communicated to the offeror, except where the ‘postal rule’ applies.• A purported acceptance which introduces any new terms is a counter-offer, which has the effect of terminating the original offer ( Hyde v Wrench 1840).Request for information• A response to an offer which is actually a request for further information will not form an acceptance.Acceptance ‘ subject to contract’•Acceptance ‘ subject to contract’ means tha t the offeree is agreeable to the terms of the offer but proposes that the parties should negotiate a formal contract.•Neither party is bound until the formal contract is signed.Letters of intent (LOI 合作意向书)• A letter of intent is a strong indication given by one party to another to say that he is likely to place a contract with him.Method of acceptance•The acceptance of an offer is made by a person authorised to do so, usually the offeree or his authorised agent.•The acceptance may be by express words or be inferred from conduct (Brogden v Metropolitan Rly Co 1877).•In some circumstance (Carlill v Carbolic Smoke Ball Co 1893), performance of the act required by the offer or advertisement consititutes an acceptacne.•There must be some act on the part of the offeree since passive inaction or silence is not capable of acceptance ( Felthose v Bindley 1862).The communication of acceptance•Acceptance is generally not effective until communicated to the offeror, except where the ‘postal rule’ applies, or t he offeror waives the need for communication.•The offeror may specify the sole means of communication, in which case only compliance with their terms will suffice （满足……的需要）.•If the offeror specifies a means of communication but does not make it absolutely compulsory, then acceptance by another means which is equally expeditious and does。