下载文档原格式
英汉语言差异之一综合语vs 分析语Synthetic vs AnalyticWebster’s Ninth New Collegiate Dictionary定义“A synthetic language is characterized by frequent and systematic use of inflected forms to express grammatical relationships.””An analytic language is characterized by a relatively frequent use of function words, auxiliary verbs, and changes in word order to express syntactic relations, rather than of inflected forms.综合语的特征是运用形态变化来表达语法关系。
分析语的特征是不用形态变化而用词序以及虚词来表达语法关系。
现代英语是从古代英语发展出来的，仍然保留着综合语的某些特征，但是也具有分析语的特点：有形态变化，但不象典型的综合语那么复杂；词序比汉语灵活，但相对固定；虚词很多，用的也相当频繁。
现代英语运用遗留下来的形态变化形式（hereditary inflections），相对固定的词序以及丰富的虚词来表达语法关系，因此属综合－分析语（synthetic－analytic language）。
形态变化，词序和虚词是表达语法意义的三大手段。
这些语法手段在英汉语言中都具有不同的特征。
此外，英语采用拼音文字，句有语调intonation；汉字绝大多数为形声字，字有声调tone。
英汉表达方法的差异与这些因素均有密切的关系。
英语（词语）有形态变化，汉语没有严格意义上的形态变化。
英语词序比较灵活，汉语词序相对固定。
英汉都有大量虚词，但是各有特点。
英汉语言对比Synthetic vs. AnalyticⅠ. Answer QuestionsDirections: Answer the Questions in English briefly, with examples if necessary. 1.What are synthetic languages(综合语)? How are they characterized?According to Webster’s Ninth New Collegiate Dictionary, A synthetic language is “Characterized by frequent and systematic use of inflected forms to express grammatical relationships”2.What are analytical languages（分析语）? How are they characterized?According to The Random House College Dictionary, An analytic language is “Characterized by a relatively frequent use of function words, auxiliary verbs and changes in words order to express syntactic relations, rather than of inflected forms”.3.Why English language is more flexible in word order（语序）? Why is it not so inChinese?Because word order is more connected with the formal changes. If the form change is more flexible, the word order is more flexible. Chinese language is an analytic language, the word order cannot be change at random, in which the relationship between the words are closely related with word order and function words.4.What is the usual word order in English sentences? What are the nine types ofinversion in English sentences?The usual word order in English sentence is Subject-Verb-Object. The nine types of inversion in English sentences include: interrogative inversion, imperative inversion, exclamatory inversion, hypothetical inversion, balance inversion, link inversion, signpost inversion, negative inversion, metrical inversion.1. 5.What are the E—C differences in formal words（形式词）?English language is featured in its abundant function words, of which is article. Articles are frequent employed. To use an article or not, and to use a definite one or an indefinite one, makes great difference in expression of meaning. Auxiliary are more frequently used in Chinese. Chinese language contains auxiliary for tense, structural and mood. This last category is especially unique in the language for the richness for delineation of emotions, like the letters 呀、啦、哦、嘛、呢，and others.6.How many kinds of formal words （形式词）are there in English language?2.There are five types of formal words, that is:i.article, including a, an, and the;ii.preposition, like on, in, to, for, as, at, of, with, from, across, etc.;iii.auxiliary verb, like will, do, have;iv.coordinator, including and, but, or;subordinator, like unless, after, for, due to, etc.7.Why Chinese is called Tone Language（声调语言）?Chinese tone can be used for indicating the change of meaning and is not suitable for expressing the certainty, completeness, independence or finality.Ⅱ. Fill in the BlanksDirections: Fill in the blanks with the best answer you have found in the textbook.1.11.综合语的特征是经常性、系统性的运用曲折形式来表现语法关系为特征的语言，分析语的特征是分析语的特征是相对频繁地使用功能词，助词和改变词序来表达句法关系，而不用曲折形式来表达。
a rXiv:h ep-th/067243v311A pr28hep-th/0607243DISTA-UPO-06DFTT-18/2006July,2006Abstract As been recently pointed out,physically relevant models derived from string theory re-quire the presence of non-vanishing form fluxes besides the usual geometrical constraints.In the case of NS-NS fluxes,the Generalized Complex Geometry encodes these informa-tions in a beautiful geometrical structure.On the other hand,the R-R fluxes call for supergeometry as the underlying mathematical framework.In this context,we analyze the possibility of constructing interesting supermanifolds recasting the geometrical data and RR fluxes.To characterize these supermanifolds we have been guided by the fact topological strings on supermanifolds require the super-Ricci flatness of the target space.This can be achieved by adding to a given bosonic manifold enough anticommuting co-ordinates and new constraints on the bosonic sub-manifold.We study these constraints at the linear and non-linear level for a pure geometrical setting and in the presence of p-form field strengths.We find that certain spaces admit several super-extensions and we give a parameterization in a simple case of d bosonic coordinates and two fermionic coordinates.In addition,we comment on the role of the RR field in the construction of the super-metric.We give several examples based on supergroup manifolds and coset supermanifolds.1IntroductionRecently the pure spinor formulation of superstrings[1,2]and the twistor string theory [3]have promoted supermanifolds as a fundamental tool to formulate the string theory and supersymmetric models.The main point is the existence of backgroundfields of extended supergravity theory(and therefore of10dimensional superstrings)which are the p-forms of the fermionic sector of superstrings.Thosefields can be coupled to worldsheet sigma modelsfields by considering the target space as a supermanifold.Indeed,as shown in[4,5]by adding to the bosonic space some anticommuting coordinatesθ’s,one can easily encode the informations regarding the geometry and the p-formfluxes into the supermetric of a supermanifold.In the present paper,we provide a preliminary analysis of the construction of supervarieties on a given bosonic space with or without p-forms (these are usually described by a bispinor Fµνsince they couple to target space spinors). We have to mention the interesting results found in[6,7,8,9]stimulated by the work [3,10].There the case of super-CY is analyzed and it is found that by limiting the number of fermions,the constraints on the bosonic submanifold of the supermanifold become very stringent.The super-CY spaces were introduced in string theory in paper[11].There the sigma models with supertarget spaces,their conformal invariance and the analysis of some topological rings were studied.In addition,we would like also to make a bridge with the recent successes of the Generalized Complex Geometry[12,13]to construct N=1 supersymmetric vacua of type II superstrings[14].In that context,theflux of the NS-NS background contributes to the generalized geometry and space is no longer CY.In the same way for a super-CY its bosonic subspace does not need to be a CY.The differential geometry of supermanifolds is a generalization of the usual geometry bosonic manifolds extended to anticommuting coordinates.There one can define super-vectorfields,superforms and the Cartan calculus.In addition,one can extend the usual Levi-Civita calculus to the fermionic counterparts defining super-Riemann,super-Ricci and super-Weyl tensorfields.A tensor has fermionic components and each component is a superfield.Due to the anticommuting coordinates,one defines also a metric on a supermanifold which can be generically given byds2=G(mn)dx m⊗dx n+G mµdx m⊗dθµ+G[µν]dθµ⊗dθν(1.1) where G(mn)(x,θ),G mµ(x,θ),G[µν](x,θ)are superfields and the tensor product⊗respects the parity of the differentials dx m,dθµ.The superfields are polynomials ofθ’s and the coef-ficients of their expansions are ordinary bosonic and fermionicfields.For example the ex-(x) pansion of G mn(x,θ)=G(0)mn(x)+...has a direct physical interpretation:G(0)mn=g(body)mn where the latter is the metric of the bosonic submanifold and the higher components are fixed by requiring the super-Ricciflatness.The physical interpretation of Gµm and Gµνis more interesting.Indeed,as suggested by the pure spinor string theory[1,15,16]the first components of Gµνcan be identified with a combination of RRfield strengths(in the text,this point will be clarified further).Thefirst component of Gµm arefixed by consistency and,in a suitable gauge,it coincides with a Dirac matrix.This is not the only way in which the RRfields determine the geometrical structure of the supermanifold.We learnt from recent analysis[17,18,19,20]in superstrings and, consequently in supersymmetricfield theory,that the superspace can be deformed by the existence of RRfield strength Fµν(x,θ){θµ,θν}=Fµν.(1.2) This has been only verified for constant RRfield strengths.Notice that a given bispinor Fµνis decomposed into a symmetric F(µν)and antisym-metric part F[µν].Therefore,it is natural to identify the antisymmetric part with the fermion-fermion(FF)components G[µν](x)of the supermetric(1.1)and the symmetric one with the non-vanishing r.h.s.of(1.2).This is very satisfactory since it provides a complete mapping between the superstring backgroundfields and the deformations of the superspace:the non-commutativity and the non-flatness.Indeed,the presence of a superfield Gµν(x,θ)in the supermetric modifies the supercurvature of the superspace. So,finally we can summarize the situation in the following way:given the backgrounds g mn and the NSNS b mn they are responsible for the deformation of the bosonic metric and of the commutation relations between bosonic coordinates[x m,x n]=θ[mn](where θmn=(b−1)mn).On the other side,the RRfields deforms the supermetric and the anti-commutation relations.There is another important aspect to be consider.The anticommuting deformation of superspace is treatable whether thefield strength Fµνof the RRfield is constant and,in four dimensions[19],whether is self-dual.In that case,there is no back-reaction of the metric and it is a solution of the supergravity equations.In the case of antisymmetric RR fields,which deform the supermetric(1.1),we have to impose a new condition in order that the worldsheet sigma model is conformal and therefore treatable.We require that the supermanifold is super-RicciflatR MN=0.(1.3) In this way,we can still use some of the conventional technique of conformalfield theory and of topological strings to study such models.The main point is that even if there is back-reaction,this is under control since the total superspace is super-Ricciflat[4,5,21, 22,23].We would like to remind the reader that the super-Ricciflatness is the condition which guarantees the absence of anomalies in the case of B-model topological strings on supermanifolds[24].This is equivalent to the well-known condition for conventional B-model on bosonic target spaces.The latter have to be Calabi-Yau which are Ricci-flat K¨a hler spaces.A main difference is that the CY must be a3-fold in order to compensate the ghost anomaly.In the case of supermanifold this is given by a virtual dimension which is essentially the difference between the bosonic and fermionic dimensions[25].In the A-model,the CY conditions is required for open string in presence of D-branes(see[24]for a complete discussion).1We start with a metric on a given space,for example the round sphere metric for S n, or Fubini-Study metric for CP n.Then we construct the corresponding supermanifold by adding anticommuting coordinates and additional components of the metric(in some cases,the extension of the metric to a super-metric is not enough and some non-vanishing torsion components are necessary)and we require the super-Ricciflatness.As a conse-quence,we notice that thefirst coefficient of Gµνmust be different from ly,we need a non-vanishing component of the fermion-fermion part of the metric.However,in general for a given space,no invariant spinorial tensor exists to provide such component. Therefore,we argue that this should be identified with p-formfluxes needed to sustain the solution of the supergravity.As a matter of fact,super-Ricciflatness does not seems to relate the value of theflux with the geometry of the bosonic submanifold.In fact,we will see in the forthcoming sections,the value of theflux isfixed by a suitable normalization which is implemented by a gauge condition on the supermetric.So,we conclude that super Ricciflatness turns out to be a necessary ad useful condition,but it does not seem to be sufficient to characterize the vacuum of the theory.We have to divide the analysis in two parts:thefirst one is the analysis of linearized equations and the second one concerns the analysis of the non-linear theory.It turns out that for the linear equation one gets very strong constraints on the bosonic metric such as the scalar curvature must be zero(see also[6,7,9]).This is compatible with theflat or Ricciflat space,but certainly is not true for a sphere or any Einstein manifold.Therefore, it is unavoidable to tackle the non-linear analysis to see whether these constraints can be weakened.Let us explain briefly the lines of analysis.The Ricci-flatness condition(1.3) can be analyzed by expanding the super-metric in components.Since we are interested only in the vacuum solutions,we decompose the superfields of the super-metric into bosonic components by setting to zero all fermionic ones.This implies a set of equations for each single component.Among them,a subset of these equations can be easily solved; indeed,the equations for the components to the order n are solved in terms of some components at the n+1order.However,the equations for highest-components cannot be solved algebraically and in fact,by plugging the solutions of the lower orders in these equations,onefinds high-derivative equations for the lowest components.To show that our analysis is not purely academic,we give some examples of super-manifolds modeled on some bosonic submanifold.Of course,the most famous example is P SU(2,2|4)(from AdS/CFT correspondence)and SL(4|4)(appearing in twistor string theory).Moreover,we give examples based on S n,V(p,q)and CP n.As a by-product we construct a super-Hopffibration connecting the different types of supercoset manifolds. One interesting example is the construction of a supermanifold with T(1,1)as a bosonic submanifold.In addition,we propose a construction which can be applied to any Einstein spaces,and in particular to Sasaki-Einstein space and K¨a hler-Einstein.At the momentwe have not explored the role of Killing spinors,Killing vectors and the role of super-symmetry in the construction.We only argued that if the supermanifold is obtained as a single coset space and not a direct product of coset space,it has more chances to have an enhanced supersymmetry.The relation between supersymmetry and the construction of super-Ricciflat supermanifold will be explored in forthcoming papers.More important,it is not yet established the relation between the solution of supergravity and the super-Ricci flatness.The paper is organized as follows:in sec.2we recall some basic fact about super-geometry..In sec.3,we present a general strategy,we study the linearized version of the constraints and,in the case of d bosonic coordinates and2fermionic directions, we analyze completely the non-linear system.In sec.4,we study the construction of supercosets modeled on bosonic cosets.In sec.5,we add thefluxes(RRfield strengths). Appendices A and B contain some related material.2Elements of supergeometryWe adopt the definition of supermanifold given in[30]based on a superalgebra with the coarse topology.However,this is not the only way and there is an equivalent formulation based on sheaves andflag manifolds[31,32].The equivalence turns out to be useful for studying topological strings on supermanifolds[33].2.1SupermanifoldsA supermanifold M(m|n)is called Riemannian if it is endowed with a metric supertensor which is a real non-singular commuting tensorfield G MN satisfying the following graded-symmetry condition:G MN=(−1)MN G NM.(2.1) The meaning of(2.1)becomes more evident if one distinguishes between bosonic and fermionic components and rewrites the metric supertensor as a block supermatrix GG MN= g mn jµν (2.2)being g an m×m real symmetric commuting matrix,j an n×n imaginary antisymmetric commuting matrix and h an m×n imaginary anticommuting one.Obviously thefirst component of the superfield of the even-even block g is an ordinary metric for the body M(m)of the supermanifold M(m|n).Body means the bosonic submanifold.Note that the supermetric G is preserved by the orthosymplectic supergroup OSp(m|n) whose bosonic submanifold is the direct product SO(m)×Sp(n)of an orthogonal group encompassing the Lorentz transformations of the metric g with a symplectic group mixing the odd directions.Thus,we immediately see that the number n of fermionic dimensions(in the paper this is also denoted by d F)over a Riemannian supermanifold must be even, otherwise Sp(n)would not be defined.The vielbein formalism can be constructed in the same way:supervielbeins will carry a couple of superindices whose different parity combinations induce the matrix block formE A M= E a m Eαµ (2.3)with commuting diagonal blocks and anticommuting off-diagonal blocks.The correct formula to pass from supervielbeins to supermetrics isG MN=(−1)MA E A MηAB E B N(2.4)whereηdenotes theflat superspace metric diag(m1,...,1,−1,...,−1,nσ2,...,σ2).Butwhat isηµν?A question that has been raised several times in the literature(see for example [34]for a review and some comments),and it turns out that theflat super-metric in the fermionic directionsηµνcannot be always defined for any models.For example,in the case of10d supergravity IIB there is no constant tensor which can be used to raise and lower the spinorial indices and to contact to Weyl indices.However,it is also known that a typical bispinor emerges in the quantization of superstrings in the fermionic sector of the theory and these states are known as the RRfields.Indeed,in the case of constant RRfields,one can identify the fermionic components of theflat supermetric with constant RRfield strength.This will be discuss in sec.5.The inverse of a supermetric G MN is computed by inverting the supermatrix G MN. In order that the inverse exists it must be that det(G mn)and det(Gµν)do not vanish.2.2K¨a hler supermetricsA very important subclass of supermetrics consists of so-called K¨a hler supermetrics,which are a straightforward generalization of the usual K¨a hler metrics living on ordinary man-ifolds.As one can expect,the components G M¯N of such a supermetric are obtained applying superderivatives-denoted by“,”-to a superpotential K:G M¯N=K,M¯N.(2.5) As a consequence the body of a K¨a hler supermanifold with a supermetric G M¯N originated by a superpotential K is a K¨a hler manifold endowed with the metric g m¯n obtained by applying two derivatives to the bosonic part of K according to g(body)m¯n=∂m∂¯n K|θ=0. 2.3Superconnections and covariant superderivativeThe idea of connection and covariant derivative have their relative supergeometric coun-terparts.Indicating superconnections withΓ,one writes the defining rules for covariantsuperderivatives-denoted by“;”-as follows:Φ;M=Φ,M,(2.6a)X M;N=X M,N+(−1)P(M+1)X PΓM P N,(2.6b)ΦM;N=ΦM,N−ΦPΓP MN.(2.6c) A superconnection over a supermanifold M(m|n)can be chosen in many ually this freedom is restricted by demanding that the superconnection be metric-compatible, i.e.that the covariant superderivative of the supermetric vanishes,and that the coeffi-cientsΓM NP be graded-symmetric in their lower indices.These two requirements uniquely determine the superconnection to be given by the super Christoffel symbolsM N P =1andR MN=(−1)MN R NM,(2.13) while Bianchi identities readR MNP Q;R+(−1)P(Q+R)R MNQR;P+(−1)R(P+Q)R MNRP;Q=0,(2.14)1R NMN;−2 T M NP−(−1)Q(N+1)G MQ G NR T R QP−(−1)Q(P+1)+NP G MQ G P R T R QN .(2.20) The corresponding Ricci supercurvature can be obtained adding a few terms to the ex-pression valid with vanishing torsion:R MN=(2.10)+(−1)P(M+1) −K P MP;N+(−1)P(M+Q)K P QP K Q MN+(−1)NP K P MN;P−(−1)N(M+P+Q)K P QN K Q MP .(2.21) In terms of the super-vielbeins,the torsion tensor is given byT A BC E C∧E B=T A≡dE A+ΩA B∧E B.(2.22)3Supermanifolds on given bosonic manifoldsIn the present section we are interested in studying examples of supermanifolds which have a given bosonic submanifold.We construct a corresponding supermanifold by adding the anticommuting coordinates and by requiring that the supermanifold is super-Ricciflat.Before proceeding we would like to give an example of a simple model where the procedure for constructing a supermanifold is illustrated.Let us consider the superfield Φ(x,θ)and we set to zero all fermionic components.Then,Φ= nΦn(θ2)n.We can consider the naive generalization of the Klein-Gordon(KG)equation∂m∂mφ+13!Φ30=(∂m∂m+∂µ∂µ)Φ+13!Φ30+2Φ2=0,∂m∂mΦ2+13!∂2Φ30+112Φ50=0.(3.3)This is a weaker condition onΦ0than the usual KG equation and it must be solved in order that the superfieldΦ0can be thefirst component of the superfieldΦwhich solves the new KG equation.The present example has no physical relevance,but it illustrates the problem appearing in the extension of a given bosonic metric to a supermetric and the extension of the bosonic equations to super-equations.Even in this case,we assume that the background has no fermions and we add only superfields with bosonic components.We have to mention that equations similar to(3.1)where already proposed in several papers in thefirst years of supersymmetry(see for example[36,37,38]).However,this construction was abandoned since the resulting theories possess ghosts and higher-spin fields(see for example[34]and the references therein).Here,we do not pretend to interpret the super-Ricciflatness asfield equations with dynamical content,but we consider these equations a way of recasting the informations on the manifold together the RRfluxes in a single mathematical structure.This is very similar to the case of NS-NSfluxes and the generalized geometry of[12,13].3.1General FrameworkIn the present section,we give the general equations of the super-Ricci tensor R MN by expanding the supermetric in components.These are very useful in order to single outthe structure of the equations.Indeed,it can be observed that at each order there is free component of the supermetric that is used to solve the corresponding equation.First, we show that every equation at the level lower than the maximumθ-expansion can be easily algebraically solved,then we show that the remaining equations are high deriva-tives and they provide consistency conditions for the construction of the corresponding supermanifold.As in the above example,using the iterative equations,one derives the highest derivative equation.This is rather cumbersome since the iterative procedure tends to explode soon in long unmanageable expressions.Wefirst tame the linearized system and then we tackle the non-linear one.For the former we are able to provide a complete analysis;for the latter only the case(d|2)will be discussed.In order to study the structure of the equation for super Ricci-flat manifold it is convenient to consider the bosonic and fermionic components separately.For that we display the few terms coming from the superfield expansion of the supermetric:1G mn=g mn+w mνρστθτθσθρ+O(θ5),61Gµν=hµν+hρσ(hσρ;(mn)−t m[σρ];n−t n[σρ];m+f mnσρ)(3.7)2−1Rµν=−12hρσ(lµνσρ+lσρµν+lµρσν+lσνµρ)−14hρσg mn(2t m(µρ)−hµρ,m)(2t n(νσ)−hνσ,n)+O(θ2)=0.(3.8)Eq.(3.7)can be easily solved in terms of f mnρσ.In the same way,(3.8)is solved by a suitable combination of lµνρσ.At the next order,a free bosonicfield will appear from the expansion of the superfields G MN and a new equationfixes it.This iterative procedure allows us to solve the complete set of equations,starting from a given bosonic metric g mn (and with aflat supermetric in the fermionic sector g[µν]),in terms of the components of G MN.At the end of the iterative procedure,wefind the consistency conditions on the bosonic manifold.Wefirst analyze the linearized equations and we expand around the flat space and around a Ricciflat(R(body)mn)bosonic space.It turns out that variation of the bosonic Ricci tensor must satisfy a set of differential equations(with a high-derivative differential operator)and some algebraic conditions(the space must have vanishing scalar curvature).However,some of the constraints are weaker in the non-linear theory.Furthermore,one can also impose additional structure in the superspace such as a su-percomplex structure.Some simplifications are in order in the case of a K¨a hler manifolds.On a K¨a hler supermanifold the hermitian metric supertensor comes from a K¨a hler superpotential,K,by the following formula:G M¯N=K,M¯N.(3.9) As a consequence the Ricci super-tensor components in holomorphic coordinates reduce to the formR M¯N=−(−1)P+Q G¯P Q G Q¯P,M¯N+(−1)P+Q+S+M(P+R)G P¯Q G¯QR,M G R¯S G¯SP,¯N =−(ln sdet G),M¯N(3.10)We can expand again the supermetric in the odd coordinates(θµ,θ¯µ)G m¯n=g m¯n+hρ¯σ,m¯nθ¯σθρ+12f m¯n¯ρ¯σθ¯σθ¯ρ+O(θ4),G m¯ν=h¯νρ,mθρ+t m¯ν¯ρθ¯ρ+O(θ3), Gµ¯n=tµ¯nρθρ+hµ¯ρ,¯nθ¯ρ+O(θ3),Gµ¯ν=hµ¯ν+lµ¯νρ¯σθ¯σθρ+12lµ¯ν¯ρ¯σθ¯σθ¯ρ+O(θ4),f m¯n¯ρ¯σ=f∗n¯mσρ,tρ¯mσ=t∗m¯ρ¯σ,lµ¯ν¯ρ¯σ=l∗ν¯µσρ,(3.11)and obtain the equivalent of the super Ricci-flatness equation,R MN=0,for g,h,l and t.The last line expresses the constraints coming from the hermiticity of the K¨a hlerpotential.At the lowest order in the odd variables one getsR m¯n=R(body)m¯n−h¯ρσhσ¯ρ,m¯n−hµ¯νh¯νρ,m hρ¯σh¯σµ,¯n+O(θ2)==R(body)m¯n+(ln(det h)),m¯n+O(θ2)=0,Rµ¯ν=−g¯p q hµ¯ν,q¯p−h¯ρσlσ¯ρµ¯ν−hρ¯σh¯σµ,p g p¯q hρ¯ν,¯q+hρ¯σt p¯σ¯νg p¯q tρ¯qµ+O(θ2)=0,where R(body)mn is the Ricci tensor on the body of the Ricci-flat K¨a hler supermanifold(SCY)and h=(hµ¯ν),from whichR(body)2 (−1)MN H QN;MP−(−1)Q(M+N)H MN;QP+H QM;NP−(−1)P(M+N)H QP;MN ,(3.14) which,making parity of indices explicit,splits intoδR mn=12(−1)Q G P Q H Qm;µP+H Qµ;mP−(−1)Q H mµ;QP−(−1)P H QP;mµ ,(3.15b)δR µν=12g pqH qm ;np +H qn ;mp −H mn ;qp −H qp ;mn+12g pqH qm ;µp +H qµ;mp −H mµ;qp −H qp ;mµ−12g pqH qµ;νp −H qν;µp −H µν;qp −H qp ;µν+12g pqH (2k )qm [τ1...τ2k ];np +H (2k )qn [τ1...τ2k ];mp −H (2k )mn [τ1...τ2k ];qp−H (2k )qp [τ1...τ2k ];mn+12gpq(2k +2)H (2k +2)qm [µτ1...τ2k +1];p +H (2k +1)qµ[τ1...τ2k +1];mp −H (2k +1)mµ[τ1...τ2k +1];qp−(2k +2)H (2k +2)qp [µτ1...τ2k +1];m−(k +1)jρσ(2k +3)H (2k +3)σm [µρτ1...τ2k +1]+H (2k +2)σµ[ρτ1...τ2k +1];m+(2k +3)H (2k +3)mµ[σρτ1...τ2k +1]+H (2k +2)σρ[µτ1...τ2k +1];m ,(3.18b)δR (2k )µν[τ1...τ2k ]=1Analizing the recursive structure of(3.18)’s,one realizes that the only independentfields which effectively play a role in constraining g mn are obtained by contracting odd indices with j as follows:S(2k) mn =H(2k)mn[τ1...τ2k]jτ1τ2···jτ2k−1τ2k,(3.19a)T(2k+1) m =H(2k+1)mτ1[τ2...τ2k+2]jτ1τ2···jτ2k+1τ2k+2,(3.19b)U(2k)=H(2k)τ1τ2[τ3...τ2k+2]jτ1τ2jτ3τ4···jτ2k+1τ2k+2,(3.19c)V(2k)=H(2k)τ1τ2[τ3...τ2k+2]jτ1τ3jτ2τ4···jτ2k+1τ2k+2.(3.19d) From these definitions one has a few identities:V(0)=0,U(d F)=d F V(d F),S(0)mn=δg mn.(3.20) The calculation is simplified by a gauge-fixing of the supermetric(3.6):a convenient choice isG mµθµ=0,Gµνθνθµ=jµνθνθµ,(3.21) which,in terms of variations,becomesH mµθµ=0,Hµνθνθµ=0.(3.22) We notice that some of thefields defined in(3.19)are vanishing because of the gauge-fixing:T(1)m=0,U(0)=0.(3.23) Introducing S,T,U and V into(3.18)’s,one obtains in principle fourfield equations but one of them follows from the other ones when Ricci curvature of the body vanishes.The remaining threefield equations corresponding to super Ricci-flatness are(2k+2)(2k+1)S(2k+2)mn=(2k+1) T(2k+1)m;n+T(2k+1)n;m −U(2k);mn−g pq S(2k)qm;np+S(2k)qn;mp−S(2k)mn;qp−S(2k)qp;mn ,(3.24a) (2k+2)(2k+1) U(2k+2)+V(2k+2) =2 U(2k)+V(2k) ,(3.24b)2S(2k)mm−S(2k)mnmn;=2 U(2k)+V(2k) .(3.24c) Recalling the identity(3.20)and the gauge-fixing(3.23),from here wefindU(2k)+V(2k)=0,U(d F)=V(d F)=0,(3.25) so that(3.24b)is automatically solved and(3.24c)with k=0shows that,at linear order, the curvature scalar on the body has to be zero:R(body)=0.(3.26)Besides this algebraic constraint on the Ricci curvature,also some differential consis-tency condition has to be taken into account that comes from the remaining constraints. IntroducingˆS(2k+2) mn def=(2k+2)!S(2k+2)mn−(2k+1)! T(2k+1)m;n+T(2k+1)n;m +(2k)!U(2k);mn(3.27)into(3.24a)and(3.24c),one can rewrite them asˆS(2k+2) mn =2ˆS(2k)mn+2ˆS pq(2k)R(body)pmqn(k>0)(3.28)withˆS(2) mn =−2δR(body)mn,ˆS(d F+2)mn=0.(3.29)In other words,at linear order,the only condition to require in addition to(3.26)isL d F/2R R(body)mn=0(3.30) where LRis the Lichnerowicz operator defined on Ricci-flat spaces byL R X mn=2X mn+2X pq R(body)pmqn.(3.31) In conclusion,at linear order,a Ricci-flat manifold can be deformed in the body of a Ricci-flat supermanifold only if conditions(3.26)and(3.30)are satisfied,and,in that case,an overlying supergeometrical structure is constrained by(3.25),(3.28)and(3.29). As a consequence,if a consistent deformation is possible,an infinite number of Ricci-flat supermanifolds with gauge-fixed supermetric can be constructed over the same bosonic body.It would be interesting to compare the present result with the results of paper[9].We plan to explore deeply the relation between the super-Ricciflatness equations and the moduli space of the supervarieties.3.3Non-linear equationsSince a complete general analysis is rather cumbersome,we give the complete expressions only in the case of(d|2)-dimensional supermanifolds.We show that equations at the lowest order can be indeed solved by some free components of the superfields and we derive the equations for the highest components.Following the scheme given in section 3.2,by substituting the lower-order results one gets thefinal constraints on the metric of the bosonic submanifold.As in the present case there are just two fermionic directions,theθ-expansion of the supermetric with the gauge-fixing(3.21)is given byG mn=g mn+12f(2)θ2(3.32)。
解析数论是使用数学分析作为工具来解决数论问题的分支。
微积分和复变函数论发展以后，产生了解析数论。
该学科的第一个主要成就是狄利克雷用解析方法证明了Dirichlet's theorem on arithmetic progressions。
依靠黎曼zeta函数对素数定理的证明是另一个里程碑。
解析数论是解决数论中艰深问题的重要工具，数论中有些问题必须由解析方法才能提出或解决。
中国的华罗庚、王元、陈景润等人在“哥德巴赫猜想”、“华林问题”等解析数论问题上取得世界公认的成就。
黎曼ζ函数Riemann zeta functionIn mathematics, the Riemann zeta function, named after German mathematician Bernhard Riemann, is a function of great significance in number theory because of its relation to the distribution of prime numbers. It also has applications in other areas such as physics, probability theory, and applied statistics. The Riemann hypothesis, a conjecture about the distribution of the zeros of the Riemann zeta function, is considered by many mathematicians to be the most important unsolved problem in pure mathematics.[1]DefinitionThe Riemann zeta-function ζ(s) is the function of a complex variable s initially defined by the following infinite series:As a Dirichlet series with bounded coefficient sequence this series converges absolutely to an analytic function on the open half-plane of s such that Re(s) > 1 and diverges on the open half-plane of s such that Re(s) < 1. The function defined by the series on the half-plane of convergence can however be continued analytically to all complex s≠ 1. For s= 1 the series is formally identical to the harmonic series which diverges to infinity. As a result, the zeta function becomes a meromorphic function of the complex variable s, which is holomorphic in the region {s∈ C : s≠1} of the complex plane and has a simple pole at s= 1 with residue 1.Specific valuesThe values of the zeta function obtained from integral arguments are called zeta constants. The following are the most commonly used values of the Riemann zeta function.this is the harmonic series.this is employed in calculating the critical temperature for a Bose–Einstein condensate in physics, and for spin-wave physics in magnetic systems.the demonstration of this equality is known as the Basel problem. The reciprocal of this sum answers the question: What is the probability that two numbers selected at random are relatively prime? [2]this is called Apéry's constant.Stefan–Boltzmann law and Wien approximation in physics.Euler product formulaThe connection between the zeta function and prime numbers was discovered by Leonhard Euler, who proved the identitywhere, by definition, the left hand side is ζ(s) and the infinite product on the right hand side extends over all prime numbers p (such expressions are called Euler products):Both sides of the Euler product formula converge for Re(s) > 1. The proof of Euler's identity uses only the formula for the geometric series and the fundamental theorem of arithmetic. Since the harmonic series, obtained when s= 1, diverges, Euler's formula implies that there are infinitely many primes. For s an integer number, the Euler product formula can be used to calculate the probability that s randomly selected integers are relatively prime. It turns out that this probability is indeed 1/ζ(s). The functional equationThe Riemann zeta function satisfies the functional equationvalid for all complex numbers s, which relates its values at points s and 1 −s. Here, Γ denotes the gamma function. This functional equation was established by Riemann in his 1859 paper On the Number of Primes Less Than a Given Magnitude and used to construct the analytic continuation in the first place. An equivalent relationship was conjectured by Euler in 1749 for the functionAccording to André Weil, Riemann seems to have been very familiar with Euler's work on the subject.[3]The functional equation given by Riemann has to be interpreted analytically if any factors in the equation have a zero or pole. For instance, when s is 2, the right side has a simple zero in the sine factor and a simple pole in the Gamma factor, which cancel out and leave a nonzero finite value. Similarly, when s is 0, the right side has a simple zero in the sine factor and a simple pole in the zeta factor, which cancel out and leave a finite nonzero value. When s is 1, the right side has a simple pole in the Gamma factor that is not cancelled out by a zero in any other factor, which is consistent with the zeta-function on the left having a simple pole at 1.There is also a symmetric version of the functional equation, given by first definingThe functional equation is then given by(Riemann defined a similar but different function which he called ξ(t).)The functional equation also gives the asymptotic limit(GergőNemes, 2007)Zeros, the critical line, and the Riemann hypothesisThe functional equation shows that the Riemann zeta function has zeros at −2, −4, ... . These are called the trivial zeros. They are trivial in the sense that their existence is relatively easy to prove, for example, from sin(πs/2) being 0 in the functional equation. The non-trivial zeros have captured far more attention because their distribution not only is far less understood but, more importantly, their study yields impressive results concerning prime numbers and related objects in number theory. It is known that any non-trivial zero lies in the open strip {s∈ C: 0 < Re(s) < 1}, which is called the critical strip. The Riemann hypothesis, considered to be one of the greatest unsolved problems in mathematics, asserts that any non-trivial zero s has Re(s) = 1/2. In the theory of the Riemann zeta function, the set{s∈ C: Re(s) = 1/2} is called the critical line. For the Riemann zeta function on the critical line, see Z-function.The location of the Riemann zeta function's zeros is of great importance in the theory of numbers. From the fact that allnon-trivial zeros lie in the critical strip one can deduce the prime number theorem. A better result[4]is that ζ(σ+ i t) ≠ 0 whenever |t| ≥ 3 andThe strongest result of this kind one can hope for is the truth of the Riemann hypothesis, which would have many profound consequences in the theory of numbers.It is known that there are infinitely many zeros on the critical line. Littlewood showed that if the sequence (γn) contains the imaginary parts of all zeros in the upper half-plane in ascending order, thenThe critical line theorem asserts that a positive percentage of the nontrivial zeros lies on the critical line.In the critical strip, the zero with smallest non-negative imaginary part is 1/2 + i14.13472514... Directly from the functional equation one sees that the non-trivial zeros are symmetric about the axis Re(s) = 1/2. Furthermore, the fact that ζ(s) = ζ(s*)* for all complex s≠1 (* indicating complex conjugation) implies that the zeros of the Riemann zeta function are symmetric about the real axis.The statistics of the Riemann zeta zeros are a topic of interest to mathematicians because of their connection to big problems like the Riemann hypothesis, distribution of prime numbers, etc. Through connections with random matrix theory and quantum chaos, the appeal is even broader. The fractal structure of the Riemann zeta zero distribution has been studied using rescaled range analysis.[5] The self-similarity of the zero distribution is quite remarkable, and is characterized by a large fractal dimension of 1.9. This rather large fractal dimension is found over zeros covering at least fifteen orders of magnitude, and also for the zeros of other L-functions.The properties of the Riemann zeta function in the complex plane, specifically along parallels to the imaginary axis, has also been studied, by the relation to prime numbers, in recentphysical interference experiments, by decomposing the sum into two parts with opposite phases, ψ and ψ*, which then are brought to interference. [6]For sums involving the zeta-function at integer and half-integer values, see rational zeta series.[O] ReciprocalThe reciprocal of the zeta function may be expressed as a Dirichlet series over the Möbius functionμ(n):for every complex number s with real part > 1. There are a number of similar relations involving various well-known multiplicative functions; these are given in the article on the Dirichlet series.The Riemann hypothesis is equivalent to the claim that this expression is valid when the real part of s is greater than 1/2. [O] UniversalityThe critical strip of the Riemann zeta function has the remarkable property of universality. This zeta-function universality states that there exists some location on the critical strip that approximates any holomorphic function arbitrarily well. Since holomorphic functions are very general, this property is quite remarkable.[O] Representations[O] Mellin transformThe Mellin transform of a function f(x) is defined asin the region where the integral is defined. There are various expressions for the zeta-function as a Mellin transform. If the real part of s is greater than one, we havewhere Γ denotes the Gamma function. By subtracting off the first terms of the power series expansion of 1/(exp(x) −1) around zero, we can get the zeta-function in other regions. In particular, in the critical strip we haveand when the real part of s is between −1 and 0,We can also find expressions which relate to prime numbers and the prime number theorem. If π(x) is the prime-counting function, thenfor values with We can relate this to the Mellin transform of π(x) bywhereconverges forA similar Mellin transform involves the Riemann prime-counting function J(x), which counts prime powers p n with a weight of 1/n,so that Now we haveThese expressions can be used to prove the prime number theorem by means of the inverse Mellin transform. Riemann's prime-counting function is easier to work with, and π(x) can be recovered from it by Möbius inversion.Also, from the above (specifically, the second equation in this section), we can write the zeta function in the commonly seen form:[O] Laurent seriesThe Riemann zeta function is meromorphic with a single pole of order one at s= 1. It can therefore be expanded as a Laurent series about s= 1; the series development then isThe constants γn here are called the Stieltjes constants and can be defined by the limitThe constant term γ0 is the Euler-Mascheroni constant.[O] Rising factorialAnother series development valid for the entire complex plane iswhere is the rising factorial This can be used recursively to extend the Dirichlet series definition to all complex numbers.The Riemann zeta function also appears in a form similar to the Mellin transform in an integral over the Gauss-Kuzmin-Wirsing operator acting on x s−1; that context gives rise to a series expansion in terms of the falling factorial.[O] Hadamard productOn the basis of Weierstrass's factorization theorem, Hadamard gave the infinite product expansionwhere the product is over the non-trivial zeros ρ of ζ and the letter γ again denotes the Euler-Mascheroni constant. A simpler infinite product expansion isThis form clearly displays the simple pole at s = 1, the trivial zeros at −2, −4, ... due to the gamma function term in the denominator, and the non-trivial zeros at s = ρ.[O] Globally convergent seriesA globally convergent series for the zeta function, valid for all complex numbers s except s = 1, was conjectured by Konrad Knopp and proved by Helmut Hasse in 1930:The series only appeared in an Appendix to Hasse's paper, and did not become generally known until it was rediscovered more than 60 years later (see Sondow, 1994).Peter Borwein has shown a very rapidly convergent series suitable for high precision numerical calculations. The algorithm, making use of Chebyshev polynomials, is described in the article on the Dirichlet eta function.[O] ApplicationsAlthough mathematicians regard the Riemann zeta function as being primarily relevant to the "purest" of mathematical disciplines, number theory, it also occurs in applied statistics (see Zipf's law and Zipf-Mandelbrot law), physics, and the mathematical theory of musical tuning.During several physics-related calculations, one must evaluate the sum of the positive integers; paradoxically, on physical grounds one expects a finite answer. When this situation arises, there is typically a rigorous approach involving much in-depth analysis, as well as a "short-cut" solution relying on the Riemann zeta-function. The argument goes as follows: we wish to evaluate the sum 1 + 2 + 3 + 4 + · · ·, but we can rewrite it as a sum of reciprocals:The sum S appears to take the form of However, −1 lies outside of the domain for which the Dirichlet series for thezeta-function converges. However, a divergent series of positive terms such as this one can sometimes be represented in a reasonable way by the method of Ramanujan summation (see Hardy, Divergent Series.) Ramanujan summation involves an application of the Euler–Maclaurin summation formula, and when applied to the zeta-function, it extends its definition to the whole complex plane. In particularwhere the notation indicates Ramanujan summation.[7]For even powers we have:and for odd powers we have a relation with the Bernoulli numbers:Zeta function regularization is used as one possible means of regularization of divergent series in quantum field theory. In one notable example, the Riemann zeta-function shows up explicitly in the calculation of the Casimir effect.[O] GeneralizationsThere are a number of related zeta functions that can be considered to be generalizations of Riemann's zeta-function. These include the Hurwitz zeta functionwhich coincides with Riemann's zeta-function when q = 1 (note that the lower limit of summation in the Hurwitz zeta function is 0, not 1), the Dirichlet L-functions and the Dedekind zeta-function. For other related functions see the articles Zeta function andL-function.The polylogarithm is given bywhich coincides with Riemann's zeta-function when z = 1.The Lerch transcendent is given bywhich coincides with Riemann's zeta-function when z = 1 and q = 1 (note that the lower limit of summation in the Lerch transcendent is 0, not 1).The Clausen function that can be chosen as the real orimaginary part ofThe multiple zeta functions are defined byOne can analytically continue these functions to then-dimensional complex space. The special values of these functions are called multiple zeta values by number theorists and have been connected to many different branches in mathematics and physics.[O] Zeta-functions in fiction。
自动化英语专业英语词汇表文章摘要：本文介绍了自动化英语专业的一些常用的英语词汇，包括自动化技术、控制理论、系统工程、人工智能、模糊逻辑等方面的专业术语。
本文按照字母顺序，将这些词汇分为26个表格，每个表格包含了以相应字母开头的词汇及其中文释义。
本文旨在帮助自动化专业的学习者和从业者掌握和使用这些专业英语词汇，提高他们的英语水平和专业素养。
A英文中文acceleration transducer加速度传感器acceptance testing验收测试accessibility可及性accumulated error累积误差AC-DC-AC frequency converter交-直-交变频器AC (alternating current) electric drive交流电子传动active attitude stabilization主动姿态稳定actuator驱动器，执行机构adaline线性适应元adaptation layer适应层adaptive telemeter system适应遥测系统adjoint operator伴随算子admissible error容许误差aggregation matrix集结矩阵AHP (analytic hierarchy process)层次分析法amplifying element放大环节analog-digital conversion模数转换annunciator信号器antenna pointing control天线指向控制anti-integral windup抗积分饱卷aperiodic decomposition非周期分解a posteriori estimate后验估计approximate reasoning近似推理a priori estimate先验估计articulated robot关节型机器人assignment problem配置问题，分配问题associative memory model联想记忆模型associatron联想机asymptotic stability渐进稳定性attained pose drift实际位姿漂移B英文中文attitude acquisition姿态捕获AOCS (attritude and orbit control system)姿态轨道控制系统attitude angular velocity姿态角速度attitude disturbance姿态扰动attitude maneuver姿态机动attractor吸引子augment ability可扩充性augmented system增广系统automatic manual station自动-手动操作器automaton自动机autonomous system自治系统backlash characteristics间隙特性base coordinate system基座坐标系Bayes classifier贝叶斯分类器bearing alignment方位对准bellows pressure gauge波纹管压力表benefit-cost analysis收益成本分析bilinear system双线性系统biocybernetics生物控制论biological feedback system生物反馈系统C英文中文calibration校准，定标canonical form标准形式canonical realization标准实现capacity coefficient容量系数cascade control级联控制causal system因果系统cell单元，元胞cellular automaton元胞自动机central processing unit (CPU)中央处理器certainty factor确信因子characteristic equation特征方程characteristic function特征函数characteristic polynomial特征多项式characteristic root特征根英文中文charge-coupled device (CCD)电荷耦合器件chaotic system混沌系统check valve单向阀，止回阀chattering phenomenon颤振现象closed-loop control system闭环控制系统closed-loop gain闭环增益cluster analysis聚类分析coefficient of variation变异系数cogging torque齿槽转矩，卡齿转矩cognitive map认知图，认知地图coherency matrix相干矩阵collocation method配点法，配置法combinatorial optimization problem组合优化问题common mode rejection ratio (CMRR)共模抑制比，共模抑制率commutation circuit换相电路，换向电路commutator motor换向电动机D英文中文damping coefficient阻尼系数damping ratio阻尼比data acquisition system (DAS)数据采集系统data fusion数据融合dead zone死区decision analysis决策分析decision feedback equalizer (DFE)决策反馈均衡器decision making决策，决策制定decision support system (DSS)决策支持系统decision table决策表decision tree决策树decentralized control system分散控制系统decoupling control解耦控制defuzzification去模糊化，反模糊化delay element延时环节，滞后环节delta robot德尔塔机器人demodulation解调，检波density function密度函数，概率密度函数derivative action微分作用，微分动作design matrix设计矩阵E英文中文eigenvalue特征值，本征值eigenvector特征向量，本征向量elastic element弹性环节electric drive电子传动electric potential电势electro-hydraulic servo system电液伺服系统electro-mechanical coupling system电机耦合系统electro-pneumatic servo system电气伺服系统electronic governor电子调速器encoder编码器，编码装置end effector末端执行器，末端效应器entropy熵equivalent circuit等效电路error analysis误差分析error bound误差界，误差限error signal误差信号estimation theory估计理论Euclidean distance欧几里得距离，欧氏距离Euler angle欧拉角Euler equation欧拉方程F英文中文factor analysis因子分析factorization method因子法，因式分解法feedback反馈，反馈作用feedback control反馈控制feedback linearization反馈线性化feedforward前馈，前馈作用feedforward control前馈控制field effect transistor (FET)场效应晶体管filter滤波器，滤波环节finite automaton有限自动机finite difference method有限差分法finite element method (FEM)有限元法finite impulse response (FIR) filter有限冲激响应滤波器first-order system一阶系统fixed-point iteration method不动点迭代法flag register标志寄存器flip-flop circuit触发器电路floating-point number浮点数flow chart流程图，流程表fluid power system流体动力系统G英文中文gain增益gain margin增益裕度Galerkin method伽辽金法game theory博弈论Gauss elimination method高斯消元法Gauss-Jordan method高斯-约当法Gauss-Markov process高斯-马尔可夫过程Gauss-Seidel iteration method高斯-赛德尔迭代法genetic algorithm (GA)遗传算法gradient method梯度法，梯度下降法graph theory图论gravity gradient stabilization重力梯度稳定gray code格雷码，反向码gray level灰度，灰阶grid search method网格搜索法ground station地面站，地面控制站guidance system制导系统，导航系统gyroscope陀螺仪，陀螺仪器H英文中文H∞ control H无穷控制Hamiltonian function哈密顿函数harmonic analysis谐波分析harmonic oscillator谐振子，谐振环节Hartley transform哈特利变换Hebb learning rule赫布学习规则Heisenberg uncertainty principle海森堡不确定性原理hidden layer隐层，隐含层hidden Markov model (HMM)隐马尔可夫模型hierarchical control system分层控制系统high-pass filter高通滤波器Hilbert transform希尔伯特变换Hopfield network霍普菲尔德网络hysteresis滞后，迟滞，磁滞I英文中文identification识别，辨识identity matrix单位矩阵，恒等矩阵image processing图像处理impulse response冲激响应impulse response function冲激响应函数inadmissible control不可接受控制incremental encoder增量式编码器indefinite integral不定积分index of controllability可控性指标index of observability可观测性指标induction motor感应电动机inertial navigation system (INS)惯性导航系统inference engine推理引擎，推理机inference rule推理规则infinite impulse response (IIR) filter无限冲激响应滤波器information entropy信息熵information theory信息论input-output linearization输入输出线性化input-output model输入输出模型input-output stability输入输出稳定性J英文中文Jacobian matrix雅可比矩阵jerk加加速度，冲击joint coordinate system关节坐标系joint space关节空间Joule's law焦耳定律jump resonance跳跃共振K英文中文Kalman filter卡尔曼滤波器Karhunen-Loeve transform卡尔胡南-洛维变换kernel function核函数，核心函数kinematic chain运动链，运动链条kinematic equation运动方程，运动学方程kinematic pair运动副，运动对kinematics运动学kinetic energy动能L英文中文Lagrange equation拉格朗日方程Lagrange multiplier拉格朗日乘子Laplace transform拉普拉斯变换Laplacian operator拉普拉斯算子laser激光，激光器latent root潜根，隐根latent vector潜向量，隐向量learning rate学习率，学习速度least squares method最小二乘法Lebesgue integral勒贝格积分Legendre polynomial勒让德多项式Lennard-Jones potential莱纳德-琼斯势level set method水平集方法Liapunov equation李雅普诺夫方程Liapunov function李雅普诺夫函数Liapunov stability李雅普诺夫稳定性limit cycle极限环，极限圈linear programming线性规划linear quadratic regulator (LQR)线性二次型调节器linear system线性系统M英文中文machine learning机器学习machine vision机器视觉magnetic circuit磁路，磁电路英文中文magnetic flux磁通量magnetic levitation磁悬浮magnetization curve磁化曲线magnetoresistance磁阻，磁阻效应manipulability可操作性，可操纵性manipulator操纵器，机械手Markov chain马尔可夫链Markov decision process (MDP)马尔可夫决策过程Markov property马尔可夫性质mass matrix质量矩阵master-slave control system主从控制系统matrix inversion lemma矩阵求逆引理maximum likelihood estimation (MLE)最大似然估计mean square error (MSE)均方误差measurement noise测量噪声，观测噪声mechanical impedance机械阻抗membership function隶属函数N英文中文natural frequency固有频率，自然频率natural language processing (NLP)自然语言处理navigation导航，航行negative feedback负反馈，负反馈作用neural network神经网络neuron神经元，神经细胞Newton method牛顿法，牛顿迭代法Newton-Raphson method牛顿-拉夫逊法noise噪声，噪音nonlinear programming非线性规划nonlinear system非线性系统norm范数，模，标准normal distribution正态分布，高斯分布notch filter凹槽滤波器，陷波滤波器null space零空间，核空间O英文中文observability可观测性英文中文observer观测器，观察器optimal control最优控制optimal estimation最优估计optimal filter最优滤波器optimization优化，最优化orthogonal matrix正交矩阵oscillation振荡，振动output feedback输出反馈output regulation输出调节P英文中文parallel connection并联，并联连接parameter estimation参数估计parity bit奇偶校验位partial differential equation (PDE)偏微分方程passive attitude stabilization被动姿态稳定pattern recognition模式识别PD (proportional-derivative) control比例-微分控制peak value峰值，峰值幅度perceptron感知器，感知机performance index性能指标，性能函数period周期，周期时间periodic signal周期信号phase angle相角，相位角phase margin相位裕度phase plane analysis相平面分析phase portrait相轨迹，相图像PID (proportional-integral-derivative) control比例-积分-微分控制piezoelectric effect压电效应pitch angle俯仰角pixel像素，像元Q英文中文quadratic programming二次规划quantization量化，量子化quantum computer量子计算机quantum control量子控制英文中文queueing theory排队论quiescent point静态工作点，静止点R英文中文radial basis function (RBF) network径向基函数网络radiation pressure辐射压random variable随机变量random walk随机游走range范围，区间，距离rank秩，等级rate of change变化率，变化速率rational function有理函数Rayleigh quotient瑞利商real-time control system实时控制系统recursive algorithm递归算法recursive estimation递归估计reference input参考输入，期望输入reference model参考模型，期望模型reinforcement learning强化学习relay control system继电器控制系统reliability可靠性，可信度remote control system遥控系统，远程控制系统residual error残差误差，残余误差resonance frequency共振频率S英文中文sampling采样，取样sampling frequency采样频率sampling theorem采样定理saturation饱和，饱和度scalar product标量积，点积scaling factor缩放因子，比例系数Schmitt trigger施密特触发器Schur complement舒尔补second-order system二阶系统self-learning自学习，自我学习self-organizing map (SOM)自组织映射sensitivity灵敏度，敏感性sensitivity analysis灵敏度分析，敏感性分析sensor传感器，感应器sensor fusion传感器融合servo amplifier伺服放大器servo motor伺服电机，伺服马达servo valve伺服阀，伺服阀门set point设定值，给定值settling time定常时间，稳定时间T英文中文tabu search禁忌搜索，禁忌表搜索Taylor series泰勒级数，泰勒展开式teleoperation遥操作，远程操作temperature sensor温度传感器terminal终端，端子testability可测试性，可检测性thermal noise热噪声，热噪音thermocouple热电偶，热偶threshold阈值，门槛time constant时间常数time delay时延，延时time domain时域time-invariant system时不变系统time-optimal control时间最优控制time series analysis时间序列分析toggle switch拨动开关，切换开关tolerance analysis公差分析torque sensor扭矩传感器transfer function传递函数，迁移函数transient response瞬态响应U英文中文uncertainty不确定性，不确定度underdamped system欠阻尼系统undershoot低于量，低于值unit impulse function单位冲激函数unit step function单位阶跃函数unstable equilibrium point不稳定平衡点unsupervised learning无监督学习upper bound上界，上限utility function效用函数，效益函数V英文中文variable structure control变结构控制variance方差，变异vector product向量积，叉积velocity sensor速度传感器verification验证，校验virtual reality虚拟现实viscosity粘度，黏度vision sensor视觉传感器voltage电压，电位差voltage-controlled oscillator (VCO)电压控制振荡器W英文中文wavelet transform小波变换weighting function加权函数Wiener filter维纳滤波器Wiener process维纳过程work envelope工作空间，工作范围worst-case analysis最坏情况分析X英文中文XOR (exclusive OR) gate异或门，异或逻辑门Y英文中文yaw angle偏航角Z英文中文Z transform Z变换zero-order hold (ZOH)零阶保持器zero-order system零阶系统zero-pole cancellation零极点抵消。
Chapter 15Audit Sampling for Tests of Controls andSubstantive Tests of TransactionsReview Questions15-1 A representative sample is one in which the characteristics of interest for the sample are approximately the same as for the population (that is, the sample accurately represents the total population). If the population contains significant misstatements, but the sample is practically free of misstatements, the sample is nonrepresentative, which is likely to result in an improper audit decision. The auditor can never know for sure whether he or she has a representative sample because the entire population is ordinarily not tested, but certain things, such as the use of random selection, can increase the likelihood of a representative sample.15-2Statistical sampling is the use of mathematical measurement techniques to calculate formal statistical results. The auditor therefore quantifies sampling risk when statistical sampling is used. In nonstatistical sampling, the auditor does not quantify sampling risk. Instead, conclusions are reached about populations on a more judgmental basis.For both statistical and nonstatistical methods, the three main parts are:1. Plan the sample2. Select the sample and perform the tests3. Evaluate the results15-3In replacement sampling, an element in the population can be included in the sample more than once if the random number corresponding to that element is selected more than once. In nonreplacement sampling, an element can be included only once. If the random number corresponding to an element is selected more than once, it is simply treated as a discard the second time. Although both selection approaches are consistent with sound statistical theory, auditors rarely use replacement sampling; it seems more intuitively satisfying to auditors to include an item only once.15-4 A simple random sample is one in which every possible combination of elements in the population has an equal chance of selection. Two methods of simple random selection are use of a random number table, and use of the computer to generate random numbers. Auditors most often use the computer to generate random numbers because it saves time, reduces the likelihood of error, and provides automatic documentation of the sample selected.15-5In systematic sampling, the auditor calculates an interval and then methodically selects the items for the sample based on the size of the interval. The interval is set by dividing the population size by the number of sample items desired.To select 35 numbers from a population of 1,750, the auditor divides 35 into 1,750 and gets an interval of 50. He or she then selects a random number between 0 and 49. Assume the auditor chooses 17. The first item is the number 17. The next is 67, then 117, 167, and so on.The advantage of systematic sampling is its ease of use. In most populations a systematic sample can be drawn quickly, the approach automatically puts the numbers in sequential order and documentation is easy.A major problem with the use of systematic sampling is the possibility of bias. Because of the way systematic samples are selected, once the first item in the sample is selected, other items are chosen automatically. This causes no problems if the characteristics of interest, such as control deviations, are distributed randomly throughout the population; however, in many cases they are not. If all items of a certain type are processed at certain times of the month or with the use of certain document numbers, a systematically drawn sample has a higher likelihood of failing to obtain a representative sample. This shortcoming is sufficiently serious that some CPA firms prohibit the use of systematic sampling. 15-6The purpose of using nonstatistical sampling for tests of controls and substantive tests of transactions is to estimate the proportion of items in a population containing a characteristic or attribute of interest. The auditor is ordinarily interested in determining internal control deviations or monetary misstatements for tests of controls and substantive tests of transactions.15-7 A block sample is the selection of several items in sequence. Once the first item in the block is selected, the remainder of the block is chosen automatically. Thus, to select 5 blocks of 20 sales invoices, one would select one invoice and the block would be that invoice plus the next 19 entries. This procedure would be repeated 4 other times.15-8 The terms below are defined as follows:15-8 (continued)15-9The sampling unit is the population item from which the auditor selects sample items. The major consideration in defining the sampling unit is making it consistent with the objectives of the audit tests. Thus, the definition of the population and the planned audit procedures usually dictate the appropriate sampling unit.The sampling unit for verifying the occurrence of recorded sales would be the entries in the sales journal since this is the document the auditor wishes to validate. The sampling unit for testing the possibility of omitted sales is the shipping document from which sales are recorded because the failure to bill a shipment is the exception condition of interest to the auditor.15-10 The tolerable exception rate (TER) represents the exception rate that the auditor will permit in the population and still be willing to use the assessed control risk and/or the amount of monetary misstatements in the transactions established during planning. TER is determined by choice of the auditor on the basis of his or her professional judgment.The computed upper exception rate (CUER) is the highest estimated exception rate in the population, at a given ARACR. For nonstatistical sampling, CUER is determined by adding an estimate of sampling error to the SER (sample exception rate). For statistical sampling, CUER is determined by using a statistical sampling table after the auditor has completed the audit testing and therefore knows the number of exceptions in the sample.15-11 Sampling error is an inherent part of sampling that results from testing less than the entire population. Sampling error simply means that the sample is not perfectly representative of the entire population.Nonsampling error occurs when audit tests do not uncover errors that exist in the sample. Nonsampling error can result from:1. The auditor's failure to recognize exceptions, or2. Inappropriate or ineffective audit procedures.There are two ways to reduce sampling risk:1. Increase sample size.2. Use an appropriate method of selecting sample items from thepopulation.Careful design of audit procedures and proper supervision and review are ways to reduce nonsampling risk.15-12 An attribute is the definition of the characteristic being tested and the exception conditions whenever audit sampling is used. The attributes of interest are determined directly from the audit program.15-13 An attribute is the characteristic being tested for in a population. An exception occurs when the attribute being tested for is absent. The exception for the audit procedure, the duplicate sales invoice has been initialed indicating the performance of internal verification, is the lack of initials on duplicate sales invoices.15-14 Tolerable exception rate is the result of an auditor's judgment. The suitable TER is a question of materiality and is therefore affected by both the definition and the importance of the attribute in the audit plan.The sample size for a TER of 6% would be smaller than that for a TER of 3%, all other factors being equal.15-15 The appropriate ARACR is a decision the auditor must make using professional judgment. The degree to which the auditor wishes to reduce assessed control risk below the maximum is the major factor determining the auditor's ARACR.The auditor will choose a smaller sample size for an ARACR of 10% than would be used if the risk were 5%, all other factors being equal.15-16 The relationship between sample size and the four factors determining sample size are as follows:a. As the ARACR increases, the required sample size decreases.b. As the population size increases, the required sample size isnormally unchanged, or may increase slightly.c. As the TER increases, the sample size decreases.d. As the EPER increases, the required sample size increases.15-17 In this situation, the SER is 3%, the sample size is 100 and the ARACR is 5%. From the 5% ARACR table (Table 15-9) then, the CUER is 7.6%. This means that the auditor can state with a 5% risk of being wrong that the true population exception rate does not exceed 7.6%.15-18 Analysis of exceptions is the investigation of individual exceptions to determine the cause of the breakdown in internal control. Such analysis is important because by discovering the nature and causes of individual exceptions, the auditor can more effectively evaluate the effectiveness of internal control. The analysis attempts to tell the "why" and "how" of the exceptions after the auditor already knows how many and what types of exceptions have occurred.15-19 When the CUER exceeds the TER, the auditor may do one or more of the following:1. Revise the TER or the ARACR. This alternative should be followed onlywhen the auditor has concluded that the original specifications weretoo conservative, and when he or she is willing to accept the riskassociated with the higher specifications.2. Expand the sample size. This alternative should be followed whenthe auditor expects the additional benefits to exceed the additionalcosts, that is, the auditor believes that the sample tested was notrepresentative of the population.3. Revise assessed control risk upward. This is likely to increasesubstantive procedures. Revising assessed control risk may bedone if 1 or 2 is not practical and additional substantive proceduresare possible.4. Write a letter to management. This action should be done inconjunction with each of the three alternatives above. Managementshould always be informed when its internal controls are notoperating effectively. If a deficiency in internal control is consideredto be a significant deficiency in the design or operation of internalcontrol, professional standards require the auditor to communicatethe significant deficiency to the audit committee or its equivalent inwriting. If the client is a publicly traded company, the auditor mustevaluate the deficiency to determine the impact on the auditor’sreport on internal control over financial reporting. If the deficiency isdeemed to be a material weakness, the auditor’s report on internalcontrol would contain an adverse opinion.15-20 Random (probabilistic) selection is a part of statistical sampling, but it is not, by itself, statistical measurement. To have statistical measurement, it is necessary to mathematically generalize from the sample to the population.Probabilistic selection must be used if the sample is to be evaluated statistically, although it is also acceptable to use probabilistic selection with a nonstatistical evaluation. If nonprobabilistic selection is used, nonstatistical evaluation must be used.15-21 The decisions the auditor must make in using attributes sampling are: What are the objectives of the audit test?Does audit sampling apply?What attributes are to be tested and what exception conditions are identified?What is the population?What is the sampling unit?What should the TER be?What should the ARACR be?What is the EPER?What generalizations can be made from the sample to thepopulation?What are the causes of the individual exceptions?Is the population acceptable?15-21 (continued)In making the above decisions, the following should be considered: The individual situation.Time and budget constraints.The availability of additional substantive procedures.The professional judgment of the auditor.Multiple Choice Questions From CPA Examinations15-22 a. (1) b. (3) c. (2) d. (4)15-23 a. (1) b. (3) c. (4) d. (4)15-24 a. (4) b. (3) c. (1) d. (2)Discussion Questions and Problems15-25a.An example random sampling plan prepared in Excel (P1525.xls) is available on the Companion Website and on the Instructor’s Resource CD-ROM, which is available upon request. The command for selecting the random number can be entered directly onto the spreadsheet, or can be selected from the function menu (math & trig) functions. It may be necessary to add the analysis tool pack to access the RANDBETWEEN function. Once the formula is entered, it can be copied down to select additional random numbers. When a pair of random numbers is required, the formula for the first random number can be entered in the first column, and the formula for the second random number can be entered in the second column.a. First five numbers using systematic selection:Using systematic selection, the definition of the sampling unit for determining the selection interval for population 3 is the total number of lines in the population. The length of the interval is rounded down to ensure that all line numbers selected are within the defined population.15-26a. To test whether shipments have been billed, a sample of warehouse removal slips should be selected and examined to see ifthey have the proper sales invoice attached. The sampling unit willtherefore be the warehouse removal slip.b. Attributes sampling method: Assuming the auditor is willing toaccept a TER of 3% at a 10% ARACR, expecting no exceptions inthe sample, the appropriate sample size would be 76, determinedfrom Table 15-8.Nonstatistical sampling method: There is no one right answer tothis question because the sample size is determined usingprofessional judgment. Due to the relatively small TER (3%), thesample size should not be small. It will most likely be similar in sizeto the sample chosen by the statistical method.c. Systematic sample selection:22839 = Population size of warehouse removal slips(37521-14682).76 = Sample size using statistical sampling (students’answers will vary if nonstatistical sampling wasused in part b.300 = Interval (22839/76) if statistical sampling is used(students’ answers will vary if nonstatisticalsampling was used in part b).14825 = Random starting point.Select warehouse removal slip 14825 and every 300th warehouseremoval slip after (15125, 15425, etc.)Computer generation of random numbers using Excel (P1526.xls):=RANDBETWEEN(14682,37521)The command for selecting the random number can be entereddirectly onto the spreadsheet, or can be selected from the functionmenu (math & trig) functions. It may be necessary to add theanalysis tool pack to access the RANDBETWEEN function. Oncethe formula is entered, it can be copied down to select additionalrandom numbers.d. Other audit procedures that could be performed are:1. Test extensions on attached sales invoices for clericalaccuracy. (Accuracy)2. Test time delay between warehouse removal slip date andbilling date for timeliness of billing. (Timing)3. Trace entries into perpetual inventory records to determinethat inventory is properly relieved for shipments. (Postingand summarization)15-26 (continued)e. The test performed in part c cannot be used to test for occurrenceof sales because the auditor already knows that inventory wasshipped for these sales. To test for occurrence of sales, the salesinvoice entry in the sales journal is the sampling unit. Since thesales invoice numbers are not identical to the warehouse removalslips it would be improper to use the same sample.15-27a. It would be appropriate to use attributes sampling for all audit procedures except audit procedure 1. Procedure 1 is an analyticalprocedure for which the auditor is doing a 100% review of the entirecash receipts journal.b. The appropriate sampling unit for audit procedures 2-5 is a line item,or the date the prelisting of cash receipts is prepared. The primaryemphasis in the test is the completeness objective and auditprocedure 2 indicates there is a prelisting of cash receipts. All otherprocedures can be performed efficiently and effectively by using theprelisting.c. The attributes for testing are as follows:d. The sample sizes for each attribute are as follows:15-28a. Because the sample sizes under nonstatistical sampling are determined using auditor judgment, students’ answers to thisquestion will vary. They will most likely be similar to the samplesizes chosen using attributes sampling in part b. The importantpoint to remember is that the sample sizes chosen should reflectthe changes in the four factors (ARACR, TER, EPER, andpopulation size). The sample sizes should have fairly predictablerelationships, given the changes in the four factors. The followingreflects some of the relationships that should exist in student’ssample size decisions:SAMPLE SIZE EXPLANATION1. 90 Given2. > Column 1 Decrease in ARACR3. > Column 2 Decrease in TER4. > Column 1 Decrease in ARACR (column 4 is thesame as column 2, with a smallerpopulation size)5. < Column 1 Increase in TER-EPER6. < Column 5 Decrease in EPER7. > Columns 3 & 4 Decrease in TER-EPERb. Using the attributes sampling table in Table 15-8, the sample sizesfor columns 1-7 are:1. 882. 1273. 1814. 1275. 256. 187. 149c.d. The difference in the sample size for columns 3 and 6 result fromthe larger ARACR and larger TER in column 6. The extremely largeTER is the major factor causing the difference.e. The greatest effect on the sample size is the difference betweenTER and EPER. For columns 3 and 7, the differences between theTER and EPER were 3% and 2% respectively. Those two also hadthe highest sample size. Where the difference between TER andEPER was great, such as columns 5 and 6, the required samplesize was extremely small.Population size had a relatively small effect on sample size.The difference in population size in columns 2 and 4 was 99,000items, but the increase in sample size for the larger population wasmarginal (actually the sample sizes were the same using theattributes sampling table).f. The sample size is referred to as the initial sample size because itis based on an estimate of the SER. The actual sample must beevaluated before it is possible to know whether the sample issufficiently large to achieve the objectives of the test.15-29 a.* Students’ answers as to whether the allowance for sampling error risk is sufficient will vary, depending on their judgment. However, they should recognize the effect that lower sample sizes have on the allowance for sampling risk in situations 3, 5 and 8.b. Using the attributes sampling table in Table 15-9, the CUERs forcolumns 1-8 are:1. 4.0%2. 4.6%3. 9.2%4. 4.6%5. 6.2%6. 16.4%7. 3.0%8. 11.3%c.d. The factor that appears to have the greatest effect is the number ofexceptions found in the sample compared to sample size. For example, in columns 5 and 6, the increase from 2% to 10% SER dramatically increased the CUER. Population size appears to have the least effect. For example, in columns 2 and 4, the CUER was the same using the attributes sampling table even though the population in column 4 was 10 times larger.e. The CUER represents the results of the actual sample whereas theTER represents what the auditor will allow. They must be compared to determine whether or not the population is acceptable.15-30a. and b. The sample sizes and CUERs are shown in the following table:a. The auditor selected a sample size smaller than that determinedfrom the tables in populations 1 and 3. The effect of selecting asmaller sample size than the initial sample size required from thetable is the increased likelihood of having the CUER exceed theTER. If a larger sample size is selected, the result may be a samplesize larger than needed to satisfy TER. That results in excess auditcost. Ultimately, however, the comparison of CUER to TERdetermines whether the sample size was too large or too small.b. The SER and CUER are shown in columns 4 and 5 in thepreceding table.c. The population results are unacceptable for populations 1, 4, and 6.In each of those cases, the CUER exceeds TER.The auditor's options are to change TER or ARACR, increase the sample size, or perform other substantive tests todetermine whether there are actually material misstatements in thepopulation. An increase in sample size may be worthwhile inpopulation 1 because the CUER exceeds TER by only a smallamount. Increasing sample size would not likely result in improvedresults for either population 4 or 6 because the CUER exceedsTER by a large amount.d. Analysis of exceptions is necessary even when the population isacceptable because the auditor wants to determine the nature andcause of all exceptions. If, for example, the auditor determines thata misstatement was intentional, additional action would be requiredeven if the CUER were less than TER.15-30 (Continued)e.15-31 a. The actual allowance for sampling risk is shown in the following table:b. The CUER is higher for attribute 1 than attribute 2 because the sample sizeis smaller for attribute 1, resulting in a larger allowance for sampling risk.c. The CUER is higher for attribute 3 than attribute 1 because the auditorselected a lower ARACR. This resulted in a larger allowance for sampling risk to achieve the lower ARACR.d. If the auditor increases the sample size for attribute 4 by 50 items and findsno additional exceptions, the CUER is 5.1% (sample size of 150 and three exceptions). If the auditor finds one exception in the additional items, the CUER is 6.0% (sample size of 150, four exceptions). With a TER of 6%, the sample results will be acceptable if one or no exceptions are found in the additional 50 items. This would require a lower SER in the additional sample than the SER in the original sample of 3.0 percent. Whether a lower rate of exception is likely in the additional sample depends on the rate of exception the auditor expected in designing the sample, and whether the auditor believe the original sample to be representative.15-32a. The following shows which are exceptions and why:b. It is inappropriate to set a single acceptable tolerable exception rateand estimated population exception rate for the combinedexceptions because each attribute has a different significance tothe auditor and should be considered separately in analyzing theresults of the test.c. The CUER assuming a 5% ARACR for each attribute and a samplesize of 150 is as follows:15-32 (continued)d.*Students’ answers will most likely vary for this attribute.e. For each exception, the auditor should check with the controller todetermine an explanation for the cause. In addition, the appropriateanalysis for each type of exception is as follows:15-33a. Attributes sampling approach: The test of control attribute had a 6% SER and a CUER of 12.9%. The substantive test of transactionsattribute has SER of 0% and a CUER of 4.6%.Nonstatistical sampling approach: As in the attributes samplingapproach, the SERs for the test of control and the substantive testof transactions are 6% and 0%, respectively. Students’ estimates ofthe CUERs for the two tests will vary, but will probably be similar tothe CUERs calculated under the attributes sampling approach.b. Attributes sampling approach: TER is 5%. CUERs are 12.9% and4.6%. Therefore, only the substantive test of transactions resultsare satisfactory.Nonstatistical sampling approach: Because the SER for the test ofcontrol is greater than the TER of 5%, the results are clearly notacceptable. Students’ estimates for CUER for the test of controlshould be greater than the SER of 6%. For the substantive test oftransactions, the SER is 0%. It is unlikely that students will estimateCUER for this test greater than 5%, so the results are acceptablefor the substantive test of transactions.c. If the CUER exceeds the TER, the auditor may:1. Revise the TER if he or she thinks the original specificationswere too conservative.2. Expand the sample size if cost permits.3. Alter the substantive procedures if possible.4. Write a letter to management in conjunction with each of theabove to inform management of a deficiency in their internalcontrols. If the client is a publicly traded company, theauditor must evaluate the deficiency to determine the impacton the auditor’s report on internal control over financialreporting. If the deficiency is deemed to be a materialweakness, the auditor’s report on internal control wouldcontain an adverse opinion.In this case, the auditor has evidence that the test of control procedures are not effective, but no exceptions in the sampleresulted because of the breakdown. An expansion of the attributestest does not seem advisable and therefore, the auditor shouldprobably expand confirmation of accounts receivable tests. Inaddition, he or she should write a letter to management to informthem of the control breakdown.d. Although misstatements are more likely when controls are noteffective, control deviations do not necessarily result in actualmisstatements. These control deviations involved a lack ofindication of internal verification of pricing, extensions and footingsof invoices. The deviations will not result in actual errors if pricing,extensions and footings were initially correctly calculated, or if theindividual responsible for internal verification performed theprocedure but did not document that it was performed.e. In this case, we want to find out why some invoices are notinternally verified. Possible reasons are incompetence,carelessness, regular clerk on vacation, etc. It is desirable to isolatethe exceptions to certain clerks, time periods or types of invoices.Case15-34a. Audit sampling could be conveniently used for procedures 3 and 4 since each is to be performed on a sample of the population.b. The most appropriate sampling unit for conducting most of the auditsampling tests is the shipping document because most of the testsare related to procedure 4. Following the instructions of the auditprogram, however, the auditor would use sales journal entries asthe sampling unit for step 3 and shipping document numbers forstep 4. Using shipping document numbers, rather than thedocuments themselves, allows the auditor to test the numericalcontrol over shipping documents, as well as to test for unrecordedsales. The selection of numbers will lead to a sample of actualshipping documents upon which tests will be performed.c. Note: The sampling data sheet that follows assumes an attributessampling approach. The only difference between the sampling datasheet for attributes sampling and for nonstatistical sampling is theactual determination of sample size. For nonstatistical sampling,students’ answers will vary, but will most likely be comparable tothe sample sizes determined under attributes sampling.。
美国大学生数学建模MCM 数学专用名词augmented matrix增广矩阵asymptotic渐进的asymptote渐进线asymmetrical非对称的associative law结合律ascending上升的arrangement排列arithmetic算术argument幅角，幅度，自变量，论证area面积arc length弧长apothem边心距apex顶点aperiodic非周期的antisymmetric反对称的antiderivative原函数anticlockwise逆时针的annihilator零化子angular velocity角速度angle of rotation旋转角angle of incidence入射角angle of elevation仰角angle of depression俯角angle of circumference圆周角analytic space复空间analytic geometry解析几何analytic function解析函数analytic extension解析开拓amplitude幅角，振幅alternative互斥的alternate series交错级数almost everywhere几乎处处algebraic topology代数拓扑algebraic expression代数式algebraic代数的affine仿射(几何学)的admissible error容许误差admissible容许的adjugate伴随转置的adjoint operator伴随算子adjoint伴随的adjacency邻接additive加法，加性acute angle锐角accumulation point聚点accidential error偶然误差accessible point可达点abstract space抽象空间abstract algebra抽象代数absolute value绝对值absolute integrable绝对可积absolute convergent绝对收敛Abelian阿贝尔的，交换的balance equation平衡方程bandwidth带宽barycenter重心base基base vectors基向量biased error有偏误差biased statistic有偏统计量bilinear双线性的bijective双射的bilateral shift双侧位移的binomial二项式bisector二等分线，平分线boundary边界的，边界bounded有界的broken line折线bundle丛，把，卷calculus微积分calculus of variations变分法cancellation消去canonical典型的，标准的canonical form标准型cap交，求交运算capacity容量cardinal number基数Cartesian coordinates笛卡尔坐标category范畴，类型cell单元，方格，胞腔cell complex胞腔复形character特征标characterization特征circuit环路，线路，回路circular ring圆环circulating decimal循环小数clockwise顺时针方向的closed ball闭球closure闭包cluster point聚点coefficient系数cofinal共尾的cohomology上同调coincidence重合，叠和collinear共线的collective集体的columnar rank列秩combinatorial theory组合理论common tangent公切线commutative交换的compact紧的compact operator紧算子compatibility相容性compatible events相容事件complementary余的，补的complete完全的，完备的complex analysis复变函数论complex potential复位势composite复合的concave function凹函数concentric circles同心圆concurrent共点conditional number条件数confidence interval置信区间conformal共形的conic圆锥的conjugate共轭的connected连通的connected domain连通域consistence相容，一致constrained约束的continuable可延拓的continuity连续性contour周线，回路，轮廓线convergence收敛性convexity凸形convolution对和，卷积coordinate坐标coprime互质的，互素的correspondence对应coset陪集countable可数的counterexample反例covariance协方差covariant共变的covering覆盖critical临界的cubic root立方根cup并，求并运算curl旋度curvature曲率curve曲线cyclic循环的decade十进制的decagon十边形decimal小数的，十进制的decision theory决策论decomposable可分解的decreasing递减的decrement减量deduction推论，归纳法defect亏量，缺陷deficiency亏格definition定义definite integral定积分deflation压缩deflection挠度，挠率，变位degenerate退化的deleted neighborhood去心邻域denominator分母density稠密性，密度density function密度函数denumerable可数的departure偏差，偏离dependent相关的dependent variable因变量derangement重排derivation求导derivative导数descent下降determinant行列式diagram图，图表diameter直径diamond菱形dichotomy二分法diffeomorphism微分同胚differentiable可微的differential微分differential geometry微分几何difference差，差分digit数字dimension维数directed graph有向图directed set有向集direct prodect直积direct sum直和direction angle方向角directional derivative方向导数disc圆盘disconnected不连通的discontinuous不连续的discrete离散的discriminant判别式disjoint不相交的disorder混乱，无序dissection剖分dissipation损耗distribution分布，广义函数divergent发散的divisor因子，除数division除法domain区域，定义域dot product点积double integral二重积分dual对偶dynamic model动态模型dynamic programming动态规划dynamic system动力系统eccentricity离心率econometrics计量经济学edge棱，边eigenvalue特征值eigenvector特征向量eigenspace特征空间element元素ellipse椭圆embed嵌入empirical equation经验公式empirical assumption经验假设endomorphism自同态end point端点entropy熵entire function整函数envelope包络epimorphism满同态equiangular等角equilateral等边的equicontinuous等度连续的equilibrium平衡equivalence等价error estimate误差估计estimator估计量evaluation赋值，值的计算even number偶数exact sequence正合序列exact solution精确解excenter外心excision切割，分割exclusive events互斥事件exhaustive穷举的expansion展开，展开式expectation期望experimental error实验误差explicit function显函数exponent指数extension扩张，外延face面factor因子factorial阶乘fallacy谬误fiducial置信field域，场field theory域论figure图形，数字finite有限的finite group有限群finite iteration有限迭代finite rank有限秩finitely covered有限覆盖fitting拟合fixed point不动点flag标志flat space平旦空间formula公式fraction分数，分式frame架，标架free boundary自由边界frequency频数，频率front side正面function函数functional泛函functor函子，算符fundamental group基本群fuzzy模糊的gain增益，放大率game对策gap间断，间隙general topology一般拓扑学general term通项generalized普遍的，推广的generalized inverse广义逆generalization归纳，普遍化generating line母线genus亏格geodesic测地线geometrical几何的geometric series几何级数golden section黄金分割graph图形，网格half plane半平面harmonic调和的hexagon六边形hereditary可传的holomorphic全纯的homeomorphism同胚homogeneous齐次的homology同调homotopy同伦hyperbola双曲线hyperplane超平面hypothesis假设ideal理想idempotent幂等的identical恒等，恒同identity恒等式，单位元ill-condition病态image像点，像imaginary axis虚轴imbedding嵌入imitation模仿，模拟immersion浸入impulse function脉冲函数inclination斜角，倾角inclined plane斜面inclusion包含incomparable不可比的incompatible不相容的，互斥的inconsistent不成立的indefinite integral不定积分independence无关（性），独立（性）index指数，指标indivisible除不尽的inductive归纳的inductive definition归纳定义induced诱导的inequality不等式inertia law惯性律inference推理，推论infimum下确界infinite无穷大的infinite decimal无穷小数infinite series无穷级数infinitesimal无穷小的inflection point拐点information theory信息论inhomogeneous非齐次的injection内射inner point内点instability不稳定integer整数integrable可积的integrand被积函数integral积分intermediate value介值intersection交，相交interval区间intrinsic内在的，内蕴的invariant不变的inverse circular funct反三角函数inverse image逆像，原像inversion反演invertible可逆的involution对合irrational无理的，无理数irreducible不可约的isolated point孤立点isometric等距的isomorphic同构的iteration迭代joint distribution联合分布kernel核keyword关键词knot纽结known已知的large sample大样本last term末项lateral area侧面积lattice格子lattice point格点law of identity同一律leading coefficient首项系数leaf蔓叶线least squares solution最小二乘解lemma引理Lie algebra李代数lifting提升likelihood似然的limit极限linear combination线性组合linear filter线性滤波linear fraction transf线性分linear filter线性滤波式变换式变换linear functional线性泛函linear operator线性算子linearly dependent线性相关linearly independent线性无关local coordinates局部坐标locus(pl.loci)轨迹logarithm对数lower bound下界logic逻辑lozenge菱形lunar新月型main diagonal主对角线manifold流形mantissa尾数many-valued function多值函数map into映入map onto映到mapping映射marginal边缘master equation主方程mathermatical analysis数学分析mathematical expectati数学期望matrix(pl. matrices)矩阵maximal极大的，最大的maximum norm最大模mean平均，中数measurable可测的measure测度mesh网络metric space距离空间midpoint中点minus减minimal极小的，最小的model模型modulus模，模数moment矩monomorphism单一同态multi-analysis多元分析multiplication乘法multipole多极mutual相互的mutually disjoint互不相交natural boundary自然边界natural equivalence自然等价natural number自然数natural period固有周期negative负的，否定的neighborhood邻域nil-factor零因子nilpotent幂零的nodal节点的noncommutative非交换的nondense疏的，无处稠密的nonempty非空的noncountable不可数的nonlinear非线性的nonsingular非奇异的norm范数normal正规的，法线normal derivative法向导数normal direction法方向normal distribution正态分布normal family正规族normal operator正规算子normal set良序集normed赋范的n-tuple integral重积分number theory数论numerical analysis数值分析null空，零obtuse angle钝角octagon八边形octant卦限odd number奇数odevity奇偶性off-centre偏心的one-side单侧的open ball开球operations reserach运筹学optimality最优性optimization最优化optimum最佳条件orbit轨道order阶，级，次序order-preserving保序的order-type序型ordinal次序的ordinary寻常的，正常的ordinate纵坐标orient定方向orientable可定向的origin原点original state初始状态orthogonal正交的orthonormal规范化正交的outer product外积oval卵形线overdetermined超定的overlaping重叠，交迭pairity奇偶性pairwise两两的parabola抛物线parallel平行parallel lines平行线parallelogram平行四边形parameter参数parent population母体partial偏的，部分的partial ordering偏序partial sum部分和particle质点partition划分，分类path space道路空间perfect differential全微分period周期periodic decimal循环小数peripheral周界的，外表的periphery边界permissible容许的permutable可交换的perpendicular垂直perturbation扰动，摄动phase相，位相piecewise分段的planar平面的plane curve平面曲线plane domain平面区域plane pencil平面束plus加point of intersection交点pointwise逐点的polar coordinates极坐标pole极，极点polygon多边形polygonal line折线polynomial多项式positive正的，肯定的potency势，基数potential位势prime素的primitive本原的principal minor主子式prism棱柱proof theory证明论probability概率projective射影的，投影proportion比例pure纯的pyramid棱锥，棱锥体quadrant像限quadratic二次的quadric surface二次曲面quantity量，数量quasi-group拟群quasi-norm拟范数quasi-normal拟正规queuing theory排队论quotient商radial径向radical sign根号radication开方radian弧度radius半径ramified分歧的random随机randomize随机化range值域，区域，范围rank秩rational有理的raw data原始数据real function实函数reciprocal倒数的，互反的reciprocal basis对偶基reciprocity互反性rectangle长方形，矩形rectifiable可求长的recurring decimal循环小数reduce简化，化简reflection反射reflexive自反的region区域regular正则regular ring正则环related function相关函数remanent剩余的repeated root重根residue留数，残数resolution分解resolvent预解式right angle直角rotation旋转roundoff舍入row rank行秩ruled surface直纹曲面runs游程，取遍saddle point鞍点sample样本sampling取样scalar field标量场scalar product数量积，内积scale标尺，尺度scattering散射，扩散sectorial扇形self-adjoint自伴的semicircle半圆semi-definite半定的semigroup半群semisimple半单纯的separable可分的sequence序列sequential相继的，序列的serial序列的sheaf层side face侧面similar相似的simple curve简单曲线simplex单纯形singular values奇异值skeleton骨架skewness偏斜度slackness松弛性slant斜的slope斜率small sample小样本smooth manifold光滑流形solid figure立体形solid geometry立体几何solid of rotation旋转体solution解solvable可解的sparse稀疏的spectral theory谱论spectrum谱sphere球面，球形spiral螺线spline function样条函数splitting分裂的statistics统计，统计学statistic统计量stochastic随机的straight angle平角straight line直线stream-line流线subadditive次可加的subinterval子区间submanifold子流形subset子集subtraction减法sum和summable可加的summand被加数supremum上确界surjective满射的symmetric对称的tabular表格式的tabulation列表，造表tangent正切，切线tangent space切空间tangent vector切向量tensor张量term项terminal row末行termwise逐项的tetrahedroid四面体topological拓扑的torsion挠率totally ordered set全序集trace迹trajectory轨道transcendental超越的transfer改变，传transfinite超限的transformation变换式transitive可传递的translation平移transpose转置transverse横截、trapezoid梯形treble三倍，三重trend趋势triad三元组triaxial三轴的，三维的trigon三角形trigonometric三角学的tripod三面角tubular管状的twist挠曲，扭转type类型，型，序型unbiased无偏的unbiased estimate无偏估计unbounded无界的uncertainty不定性unconditional无条件的unequal不等的uniform一致的uniform boundness一致有界uniformly bounded一致有界的uniformly continuous一致连续uniformly convergent一致收敛unilateral单侧的union并，并集unit单位unit circle单位圆unitary matrix酉矩阵universal泛的，通用的upper bound上界unrounded不舍入的unstable不稳定的valuation赋值value值variation变分，变差variety簇vector向量vector bundle向量丛vertex顶点vertical angle对顶角volume体积，容积wave波wave form波形wave function波函数wave equation波动方程weak convergence弱收敛weak derivatives弱导数weight权重，重量well-ordered良序的well-posed适定的zero零zero divisor零因子zeros零点zone域，带</Words>。
amorphous state 非晶态amorphous substance 无定形物质amount 数量amount of evaporation 蒸发量amount of information 信息量amount of precipitation 降水量amount of substance 物质量ampere 安ampere hour 安时ampere meter 安培计ampere second 安秒ampere turn 安匝ampere turn per meter 每米安匝数ampere turns 安匝数amphoteric 两性的amphoteric ion 两性离子amplidyne 放大发电机amplification 放大amplification constant 放大系数amplification factor 放大系数amplified spontaneous emission 放大自发射amplifier 放大器amplifying tube 放大管amplitude 振幅amplitude characteristic 振幅特性amplitude discriminator 脉冲高度鉴别器amplitude distortion 振幅失真amplitude function 振幅函数amplitude mode 振幅模amplitude modulated oscillations 爹振荡amplitude modulation 爹amplitude reflectance 振幅反射度amplitude selector 振幅选择器amplitude transmittance振幅透过率anabatic wind 谷风anaclastics 屈光学anafront 上滑锋anallobar 正变压中心analog 数学模型analog circuit 模拟电路analog computer 模拟计算机analog method 相似法analog signal 模拟信号analog switch 模拟开关analog to digitalconversion 模拟数字转换analog to digitalconverter a d 变换器模数变换器analogous 类似的analogue 数学模型analogue computer 模拟计算机analogue display 相似表示analogue method 相似法analogy 模拟analyser 分析器analysis 分析analysis centre 分析中心analysis of covariance协方差解析analysis of variance 方差分析analysis of weather map天气图分析analysis situs 拓扑学analytic 分析的analytic continuation 解析开拓analytic curve 分析曲线analytic dynamics 解析动力学analytic expression 分析式analytic form 分析形式analytic function 解析函数analytic geometry 分析几何学analytic line 分析线analytic manifold 分析簇analytic method 分析法analytic perturbationtheory 解析微扰论analytic set 分析集analytic signal 分析信号analytic transformation分析变换analytic vector 解析向量analytical balance 分析天平analytical dynamics 分析力学analytical mechanics 分析力学analyzer 分析器analyzing magnet 磁分析器anamorphotic lens 象歪曲透镜anastigmat 消象散透镜anastigmatic 去象散的anastigmatic lens 消象散透镜anastigmatism 消象散性anchor ring 锚环and circuit 与电路and or circuit 与或电路anderson localization 安德森定域anderson model 安德森模型anderson orthogonalitytheorem 安德森正交定理anderson's delocalization theory 安德森非定域理论andreev reflection 安德列耶夫反射andromeda 仙女座andromeda galaxy 仙女座星云andromeda nebula 仙女座星云anechoic 无回声的anechoic chamber 无回声室anechoic room 静室anelasticity 滞弹性anemogram 风力自记曲线anemograph 风速计anemometer 风速表anemoscope 测风器风速仪anergy 无力aneroid barograph 膜盒气压表aneroid barometer 空盒气压表angle 角angle at centre 中心角angle correlation 角关联angle of advance 超前角angle of attack 迎角angle of contact 接触角angle of contingence 切线角angle of declination 偏角angle of deflection 偏转角angle of deviation 偏向角angle of diffraction 衍射角angle of friction 摩擦角angle of incidence 入射角angle of intersection 交叉角angle of lag 滞后角angle of lead 超前角angle of minimumdeviation 最小偏角angle of polarization 偏振角angle of reflection 反射角angle of refraction 折射角angle of rotation 旋转角angle of scattering 散射角angle of slide 滑动角angle of view 视角angle preserving 保角的angle preserving map 保角映象angstrom 埃angstrom unit 埃单位angular 角的angular acceleration 角加速度angular coefficient 角系数angular coordinates 角座标angular correlation 角关联angular derivative 角微离angular dispersion 角色散angular displacement 角位移angular distance 角距angular distribution 角分布angular frequency 角频angular magnification 角放大率angular measure 角度angular momentum 角动量angular momentumconservation law 角动量守恒定律angular motion 角动angular quantum number角量子数angular resolution 角分辨率angular separation 角距angular unit 角的单位angular velocity 角速度angular vibrations 角振动anharmonic 非低的anharmonic oscillation非谐振动anharmonic oscillator 非谐振子anharmonic ratio 非低比anharmonic term 非谐项anharmonicity 非谐振性anhysteric magnetizationcurve 无磁滞曲线animal electricity 动物电anion 阴离子anisometric crystal 非等轴晶体anisotropic 蛤异性的anisotropic body 蛤异性体anisotropic exchangeinteraction 蛤异性交换相互酌anisotropic fluid 蛤异性铃anisotropic hamiltonian蛤异性哈密顿函数anisotropic medium 蛤异性介质anisotropic superfluid蛤异性超铃anisotropic turbulence蛤异性湍流anisotropic universe 蛤异性宇宙anisotropy 蛤异性anisotropy constant 蛤异性常数anisotropy energy 蛤异性能anisotropy magnetic field 蛤异性磁场anisotropy ratio 蛤异性比annealing 退火annihilation 湮没annihilation operator 湮没算符annihilation radiation 湮没辐射annual 年刊annual aberration 周年光行差annual amount of precipitation 年降水量annual equation 周年差annual mean 年平均annual parallax 周年视差annual precession 年岁差annual range 年较差annual variation 年变化annular 环annular eclipse 环食annular focus 环形焦点annulation 取消anode 阳极anode battery 阳极电池组anode compartment 阳极空间anode current 板极电流anode dark space 阳极暗区anode detection 板极检波anode fall 阳极势降anode glow 阳极辉光anode rays 极隧射线anode resistance 板极电阻anode voltage 板极电压anomalistic 近点的anomalistic month 近点月anomalistic year 近点年anomalon 反常子anomaloscope 色盲检查镜anomalous 反常的anomalous absorption 反常吸收anomalous diffusion 反常扩散anomalous dimension 反常量纲anomalous dispersion 反常色散anomalous electricresistivity 反常电阻率anomalous hall effect 反常霍耳效应anomalous magneticmoment 反常磁矩anomalous propagation 反常传播anomalous propagation ofsound 声的反常传播anomalous scattering 反常散射anomalous skin effect 反常囚效应anomalous transmission反常透射anomalous zeeman effect反常塞曼效应anomaly 反常antagonism of ions 离子的对抗酌antapex 背点antarctic circle 南极圈antarctic circle ozonhole 南极圈臭氧孔antecedent 前项antenna 天线antenna aperture 天线孔径antenna array 天线阵antenna circuit 天线电路antenna current 天线电流antenna efficiency 天线效率antenna element 天线元件antenna gain 天线增益antenna impedance 天线阻抗antenna resistance 天线电阻antenna tuning 天线党anthracene 蒽anti clockwise 反时针的anti corrosive 防锈剂;防锈的anti hyperon 反超子anti isomorphism 反同构性anti trade winds 反信风anti trades 反信风antibaryon 反重子antibonding electron 反键电子antibonding orbital 反键轨函数anticathode 对阴极anticoincidence 反符合anticoincidence analyzer舛符合分析器anticoincidence circuit反符合线路anticoincidence method反符合法anticommutation relation反对易关系anticommutative 反对易的anticyclogenesis 反气旋发生anticyclolysis 反气旋消散anticyclone 反气旋区域anticyclonic 反气旋的anticyclonic inversion 反气旋逆温antiderivative 不定积分antideuterium 反氘antideuteron 反氘核antiepicentre 震中对点antiferroelectrics 反铁电体antiferromagnet 反铁磁体antiferromagnetic domain 反铁磁畴antiferromagnetic resonance 反铁磁性共振antiferromagnetism 反铁磁性antiferromagnon 反铁磁振子antihadron 反强子antihydrogen 反氢antila 唧筒座antilepton 反轻子antilogarthm 反对数antimatter 反物质antimeson 反介子antimetrical circuit 相反电路antimonsoon 反季风antimony 锑antineutrino 反中微子antineutron 反中子antinomy 谬论antinucleon 反核子antiparallel 逆平行的antiparallelogram 等边梯形antiparticle 反粒子antiphase boundary 反相边界antipod 对映体antiproton 反质子antiproton atom 反质子原子antiproton beam 反质子束antiquark 反夸克antireflection coating透光镀膜;增透膜antiresonance *振antistokes line 反斯托克斯线antistokes raman laser反斯托克斯喇曼激光器antisymmetric 斜对称的antisymmetric tensor 斜对称张量;反对称张量antisymmetrical state 反对称态antisymmetry 反对称antithesis 反题antitrigonometricfunction 反三角函数antitriptic wind 减速风antitwilight 反曙暮光antiunitary operator 反幺正算符antlia 唧筒座antonoff rule 安托诺夫定则anvil 铁砧anvil cloud 砧状云anyon 任意子apastron 远星点aperiodic 非周期的aperiodic damping 非周期衰减aperiodic motion 非周期运动aperiodicity 非周期性aperture 口径aperture diaphragm 孔径光栏aperture ratio 口径比aperture stop 孔径光栏aperture synthesis 孔径综合法apex 顶apex angle 顶角apex of the sun 太阳向点aphakic eye 欠晶眼aphelion 远日点apical angle 顶角aplanat 消球差镜aplanatic 等光程的aplanatic lens 消球差镜aplanatic point 等光程点aplanatism 消球差性apochromat 复消色差镜apochromatic 复消色差的apochromatic lens 复消色差镜apodization 切趾法apogee 远地点apolar 非极性的apollo 阿波罗飞船apollo type asteroid 阿波罗型小行星apostilb 亚熙提apothem 垂幅apparatus 仪器装置apparent absorptioncoefficient 表观吸收系数apparent density 视在密度apparent diameter 视直径apparent force 表观力apparent horizon 可见地平apparent lifetime 表观寿命apparent magnitude 视星等apparent motion 视运动apparent noon 视午apparent orbit 视轨道apparent palce 视位apparent position 视位apparent solar day 真太阳日apparent solar time 真太阳时apparent structure 表观结构apparent sun 真太阳apparition 出现appearance potential 表观势appendix 附录application 应用applied 应用的applied acoustics 应用声学applied climatology 应用气候学applied elasticity 应用弹性理论applied mathematics 应用数学applied mechanics 应用力学applied meteorology 应用气象学applied optics 应用光学applied physics 应用物理学approach 接近approximability 可逼近性approximable 可逼近的approximate 近似的;使近似approximate caculation 近似计算approximate formula 近似公式approximate method 近似法approximate number 近似数approximate solution 近似解approximate value 近似值approximatintegration近似积分approximation 近似approximation calculus近似计算apsidal motion 拱线运动apus 天燕座apw method 增广平面波法aquarius 宝瓶座aqueous solution 水溶液aquila 天鹰座ara 天坛座arc 电弧arc discharge 电弧放电arc lamp 弧光灯arc line 弧光谱线arc spectrum 电弧光谱arc trigonometricfunction 反三角函数archimedes' principle 阿基米德原理architectural acoustics建筑声学arctic circle 北极圈ardometer 光学高温计areal velocity 面积速度areography 火星表面学areometer 比重计areometry 液体比重测定法areophysics 火星物理学argon 氩argon instability 氩不稳定性argon laser 氩激光器aries 白羊座arithmetic circuit 运算电路arm 边armature 电枢armature reaction 电枢反应array processor 排列信息处理装置arrester 避雷器arsenic 砷articulation 清晰度artificial daylight 人工昼光artificial ear 仿真耳artificial gravity 人造重力artificial hologram 人工全息图artificial illumination人造煦明artificial intelligence人工智能artificial isotope 人造同位素artificial light 人造光artificial lighting 人造煦明artificial lightning 人造电闪artificial line 仿真线路artificial magnet 人造磁铁artificial metal 人造金属artificial minisun 人造小太阳artificial nuclearreaction 人工核反应artificial nucleartransformation 人工核转化artificial radioactivity人工放射性artificial radionuclide人造放射性核素artificial rainfall 人造雨artificial satellite 人造卫星aser 量子放大器aspect ratio 展弦比aspheric lens 非球面透镜aspherics 非球面镜光学assembler 汇编程序assembler language 汇编程序语言associated quantum number 轨道量子数associated wave 缔合波association 结合associative detachment 结合性分离associative ionization 结合性电离assumption about the number of collisions 碰撞数的假定astatic 无定向的astatic galvanometer 无定向电疗astatine 砹asterism 星座asteroid 小行星asteroid belt 小行星带asthenosphere 岩力astigmatic difference 象散差astigmatic pencil 象散光束astigmatism 象散astigmatism correction 象散校正astigmometry 散光测定法aston's dark space 阿斯顿暗区astrionics 天文电子学astrobiology 天体生物学astroclimatology 天体气候学astrodynamic 天体动力学的astrodynamics 天体动力学astrogation 宇宙航行学astrogeodynamics 天文地球动力学astrogeophysics 天文地球物理学astrognosy 恒星学astrographic camera 天体照相机astrology 星占术astromagnetics 天体磁学astrometeorology 天体气象学astrometer 天体测量仪astrometric 天体测量的astrometry 天体测量学astron 阿斯特隆astronomical constant 天文常数astronomical maser 天文脉泽astronomical observatory天文台astronomical photography天体照相学astronomical photometry天体光度学astronomicalspectroscopy 天体光谱学astronomical telescope天文望远镜astronomical unit 天文单位astronomy 天文学astrophotography 天体照相学astrophysical 天体物理的astrophysical maser 天文脉泽astrophysical plasma 天体等离子体astrophysics 天体物理学astrorelativity 天体相对论astrospectroscope 天体分光镜astrospectroscopy 天体光谱学asymmetric 非对称的asymmetric top 非对称陀螺asymmetrical 非对称的asymmetry 非对称asymptotic expansion 渐近展开asymptotic field 渐近场asymptotic formula 渐近公式asymptotic freedom 渐近自由性asymptotic solution 渐近解asymptotic stability 渐近稳定性asymptotic theorem 渐近定理asynchronous 异步的asynchronous motor 感应电动机atiyah singer indextheorem 阿奇娅辛谔指数定理atmosphere 大气atmosphere absorption 大气吸收atmospheric acoustics 大气声学atmospheric attenuation大气衰减atmospheric circulation大气环流大气循环atmospheric discharge 大气放电atmospheric dispersion大气色散atmospheric disturbances大气扰动atmospheric electricity大气电atmospheric extinction大气消光atmospheric humidity 大气湿度atmospheric ion 大气离子atmospheric ozone 大气臭氧atmospheric ozone content 大气臭氧含量atmospheric phenomena 大气现象atmospheric pressure 气压atmospheric radiation 大气辐射atmospheric refraction 大气折射atmospheric science 大气科学atmospheric turbulence 大气湍流atmospheric waves 大气波atmospherics 天电atom 原子atom probe 原子探测器atomic absorption 原子吸收atomic absorption coefficient 原子吸收系数atomic battery 原子电池atomic beam 原子束atomic beam laser 原子束激光器atomic beam magnetic resonance 原子束磁共振atomic beam resonating method 原子束共振法atomic bomb 原子弹atomic bond 原子键atomic chart 原子量表atomic clock 原子钟atomic collision 原子碰撞atomic configuration 原子组态atomic constant 原子常数atomic core 原子芯atomic core polarization原子芯极化atomic disintegration 原子衰变atomic dispersion 原子弥散atomic electron shell 原子的电子壳层atomic energy 原子能atomic energy level 原子能级atomic fluorescenceanalysis 原子荧光分析atomic form factor 原子结构因数atomic frequencystandard 原子标准频率atomic fuel 核燃料atomic heat capacity 原子热容量atomic interspace 原子间空间atomic laser 原子激光器atomic lattice 原子点阵atomic layer epitaxy 原子层外延atomic magnetic moment原子磁矩atomic mass unit 原子质量单位atomic model 原子模型atomic nucleus 原子核atomic number 原子序数atomic orbital 原子轨函数atomic permeability 原子磁导率atomic physics 原子物理学atomic polarization 原子极化atomic power 原子能atomic power plant 核电站atomic reaction 原子反应atomic refraction 原子折射atomic scattering factor原子散射因子atomic shell 原子的电子壳层atomic spectroscopy 原子光谱学atomic spectrum 原子光谱atomic stopping power 原子阻止本领atomic structure 原子结构atomic structure factor原子结构因数atomic susceptibility 原子磁化率atomic symbol 原子符号atomic theory 原子论atomic time 原子时atomic unit 原子单位atomic volume 原子体积atomic weight 原子量atomic weight unit 原子量单位atomichran 原子钟atomicity 原子价atomistic 原子论的atomistics 原子论atomization 喷雾atomizing 喷雾attenuated totalinternal reflection 衰减全内反射attenuation 衰减attenuation constant 衰减常数attenuation distortion衰减畸变attenuation factor 衰减因数attenuation length 衰减长度attenuator 衰减器atto 渺attraction 引力attractive 有吸引力的attractive force 引力attribute 属性audibility 可闻性audibility factor 可闻度系数audibility threshold 听阈audible 可闻的audible signal 可闻信号audible sound 可闻音audio amplifier 音频放大器audio frequency 声频audio frequency amplifier 音频放大器audio frequency generator 声频发生器audiogram 声波图audiometer 听力计audiometry 测听术audioreproduction 声的再生audition 听觉auditory nerve 听觉神经auger effect 俄歇效应auger electron 俄歇电子auger electron emission 俄歇电子发射auger electron spectroscopy 俄歇电子能谱学auger recombination 俄歇复合auger shower 广延空气簇射auger spectrum 俄歇光谱augmented plane wave method 增广平面波法aural 听觉的aural masking 听觉掩蔽aural range 可闻带aureole 日晕auriga 御夫座aurora 极光aurora australis 南极光aurora borealis 北极光aurora polaris 极光auroral line 极光线auroral zone 极光带austausch coefficient 交换系数austenite 奥氏体auto photoelectriceffect 自生光电效应autocatalytic reaction自催化反应autochrome plate 彩色摄影胶片autocollimation 自准直autocollimation camera自准直摄影机autocorrelation 自相关autocorrelation function自相关函数autocorrelator 自动相关器autodyne 自拍autoelectronic 自动电子的autoelectronic emission场致发射autogyro 旋翼飞机autoionization 自电离automat 自动机automatic control 自动控制automatic control system自动控制系统automatic control theory自动控制理论automatic diffractometer自动衍射仪automatic focusing 自动聚焦automatic frequencycontrol 自动频率控制automatic powderdiffractometer 自动粉末衍射仪automatic regulator 自动第器automatic tuning 自动党automation 自动化automaton 自动机autopilot 自动驾驶仪autoradiography 放射自显影法autotransformer 自耦变压器autumnal equinox 秋分auxiliary equipment ofnuclear power plant 原子能发电站辅助设备auxiliary quantum number辅量子数available energy 有效能available head 有效落差available heat 有效热avalanche 雪崩avalanche diode 雪崩二极管avalanche laser 雪崩式激光器avalanche ofdislocations 位错崩avalanche photodiode 雪崩光二极管avalanche transistor 雪崩三极管average 平均;平均的average error 平均误差average speed 平场速度average time 平均时间average value 平均值avf cyclotron avf 回旋加速器avogadro's number 阿伏加德罗数avrami's equation 阿夫拉米公式axial angle 轴角axial current 轴向流axial flow 轴向流axial flow pump 轴撩axial force 轴向力axial magnification 轴向放大率axial mode 轴向波型axial pressure 轴向压力axial ratio 轴率axial rays 近轴光线axial stress 轴向应力axial symmetry 轴对称axial vector 轴矢量axial vector current 轴矢流axial vector interaction 轴矢量相互酌axially symmetric flow 轴对称怜axino 轴微子axiom 公理axiomatic field theory 公理化场论axiomatic method 公理法axion 轴子axis 轴axis of collimation 视准轴axis of lens 透镜轴axis of projection 射影轴axis of revolution 回转轴axis of rotation 旋转轴axis of rotatory inversion 旋转反演轴axis of rotatory reflection 旋转反射轴axis of symmetry 对称轴axoid 轴面azbel kaner effect 阿兹贝尔卡纳效应azbel kaner resonance 阿兹贝尔卡纳效应azimuth 方位角azimuth polarimeter 偏振计azimuth rotator 方位旋转子azimuthal mounting 地平经装置azimuthal quantum number角量子数azure 绀青物理专业英语词汇(A)1/8 fluctuation 1/8 起伏1/f noise 1/f 噪声1/n expansion 1/n 展开3k cosmic blackbodyradiation 3k 宇宙黑体辐射4 counter 4 计数器a battery a电池组a posteriori probability后验概率a priori probability 先验概率a15 structure a15 结构abbe coefficient 阿贝数abbe invariant 阿贝不变量abbe number 阿贝数abbe prism 阿贝棱镜abbe refractometer 阿贝折射计abbe sine condition 阿贝正弦条件abel theorem 阿贝尔定理abelian group 可换群abelian integral 阿贝尔积分aberage life 平均寿命aberration 象差aberration constant 光行差常数aberration of light 光行差aberrational ellipse 光行差椭圆ablation 烧蚀abm state abm 态abnormal 反常的abnormal cathode fall 反常阴极势降abnormal crystallization异常晶化abnormal dispersion 异常色散abnormal glow 反常辉光放电abnormal grain growth 反常晶粒生长abnormal liquid 反常液体abnormal reflection 异常反射abnormal series 反常系abrasion 磨损abrasion test 磨损试验abrasives 研磨材料abrikosov's structure offlux lines 阿布里科蓑磁通线结构absence of gravity 失重absolute 绝对的absolute acceleration 绝对加速度absolute angularmomentum 绝对角动量absolute atomic weight原子的绝对重量absolute black body 绝对黑体absolute configuration绝对组态absolute counting 绝对计数absolute electrometer 绝对静电计absolute electrostatic system 绝对静电制absolute error 绝对误差absolute geopotential 绝对位势absolute humidity 绝对湿度absolute index of refraction 绝对折射率absolute instability 绝对不稳定性absolute magnitude 绝对星等absolute measurement 绝对测量absolute motion 绝对运动absolute ohm 绝对欧姆absolute orbit 绝对轨道absolute permeability 绝对磁导率absolute permittivity 绝对电容率absolute pressure 绝对压力absolute rest 绝对静止absolute rest frame 绝对静止系absolute rotation 绝对转动absolute scale 绝对度标absolute space 绝对空间absolute stability 绝对稳定absolute system of units 绝对单位制absolute temperature 绝对温度absolute temperature scale 绝对温标absolute thermometer 绝对温度表absolute time 绝对时空间absolute topography 绝对形势absolute unit 绝对单位absolute vacuum gage 绝对真空计absolute velocity 绝对速度absolute viscosity 绝对粘度absolute vorticity 绝对涡度absolute weight 绝对重量absolute zero 绝对零度absolute zero point 绝对零度absorb 吸收absorbed dose 吸收剂量absorbent 吸收剂absorber 吸收体absorbing medium 吸收媒质absorptiometer 吸收计absorption 吸收absorption band 吸收带absorption coefficient吸收系数absorption cross section吸收截面absorption curve 吸收曲线absorption edge 吸收端absorption equilibrium吸收平衡absorption factor 吸收因子absorption filter 吸收滤光器absorption hygrometer 吸收湿度表absorption index 吸收指数absorption jump 吸收跃迁absorption limit 吸收端absorption line 吸收线absorption method 吸收法absorption model 吸收模型absorption of sound 声的吸收absorption spectrometer吸收光谱仪absorption spectroscopy吸收光谱学absorption spectrum 吸收光谱absorption test 吸收试验absorptive 吸收的absorptive power 吸收本领absorptivity 吸收本领abstract algebra 抽象代数abstract group 抽象群abstract space 抽象空间abstraction 抽象abundance of elements 元素的丰度ac bias 交莲压ac circuit 交羚路ac galvanometer 交羚疗ac voltage 交羚压accelerated motion 加速运动accelerating chamber 加速室accelerating electrode加速电极accelerating field 加速场accelerating gap 加速隙缝accelerating period 加速周期accelerating slit 加速隙缝accelerating tube 加速管accelerating voltage 加速电压acceleration 加速度acceleration cavity 加速共振腔acceleration gap 加速隙acceleration of gravity 重力加速度accelerator 加速器accelerometer 加速计acceptance 肯定acceptor 受主acceptor center 受中心acceptor impurity 受钟质acceptor level 受周级access 选取access speed 选取速度access time 选取时间accessibility 可达性accessible point 可达点accessories 附件accidental coincidence 偶然符合accidental degeneracy 偶然退化accidental error 偶然误差accidental reflection 偶然反射acclimation 气候驯化acclimatization 气候驯化acclimazation 气候驯化accommodation 第accommodationcoefficient 适应系数accommodation of the eye 眼的第accord 和音accreting black hole model 吸积黑洞模型accretion 吸积accretion disk 吸积盘accumulated dose 累积剂量accumulated error 累积误差accumulated temperature 积温accumulation 蓄集accumulation layer 累积层accumulation point 聚点accumulation ring 累积环accumulator 二次电池accuracy 准确度accuracy grade 准确度accuracy of measurement测量精确度accuracy of readings 读数准确度accuracy rating 准确度acetone 丙酮achondrite 无球粒陨石achromat 消色差透镜achromatic 消色的achromatic color 无彩色achromatic condition 消色差achromatic lens 消色差透镜achromatic prism 消色差棱镜achromatic quarter waveprism 四分之一波长消色棱镜achromatic sensation 无色感觉achromatic stimulus 无色剌激achromatism 消色差acid 酸acnod 孤点acoumeter 测听计acount 计算acoustic 声的acoustic absorptioncoefficient 吸声系数acoustic absorptivity 吸声系数acoustic admittance 声导纳acoustic analysis 声分析acoustic conductivity 声导率acoustic diffraction 声衍射acoustic dispersion 声弥散acoustic disturbance 声扰动acoustic electron spinresonance 声电子自旋共振acoustic emission 声发射acoustic far field 远程声场acoustic field 声场acoustic filter 滤声器acoustic fraunhoferfield 夫琅和费声场acoustic frequency 音频acoustic fresnel field非涅耳声场acoustic gravity wave 声力波acoustic image 声象acoustic impedance 声阻抗acoustic instrument 声学仪器acoustic interferometer声波干涉计acoustic lens 声透镜acoustic line 声传输线acoustic load 声负载acoustic material 吸音材料acoustic measurement 声学量度acoustic microscope 超声显微镜acoustic mode 声学模acoustic near field 近程声场acoustic nuclearmagnetic resonance 声核磁共振acoustic ohm 声欧姆acoustic paramagnetic resonance 声顺磁共振acoustic power 声功率acoustic pressure 声压acoustic radiator 声辐射体acoustic reactance 声抗acoustic resistance 声阻acoustic resonance 声共振acoustic resonator 声共振器acoustic shadow 声影acoustic signal 声信号acoustic sounding 声学探测acoustic streaming 声风acoustic transducer 声能转换器acoustic transformer 声变换器acoustic velocity 声速acoustic wave 声波acoustic wind 声风acoustical 声的acoustical holography 声全息学acoustical spectroscopy 声谱学acoustically induced birefringence 声诱发双折射acoustics 声学acoustimeter 声强计acoustodynamic 声动力学的acoustoelectric amplification 声电放大acoustoelectric effect 声电效应acoustoelectron interaction 声电子相互酌acoustoelectronics 声电子学acoustomagnetoelectriceffect 声磁电效应acoustooptic effect 光声效应acoustooptical 声光的acoustooptical modulator声光灯器acoustooptical q switch声光 q 开关acoustoopticalradiospectrometer 声光射电光谱仪acoustooptics 声光学acre 英亩acrobatic metal 特技的金属acryl resin 丙烯酸尸actinic 有光化性的actinic photometer 光化光度计actinic rays 光化射线actinic value of light 光化度actinides 锕系actinism 光化酌actinium 锕actinium emanation 锕射气actinium series 锕系actinograph 日射仪actinoid nuclei 锕系元素核actinometer 日射表actinometry 辐射测量;光能强度测定actinomorphy 辐射对称性actinon 锕射气action 酌action at a distance 超距酌action centre of theatmosphere 大气活动中心action integral 酌积分action principle 酌原理action spectrum 酌谱action through medium 媒递酌action variable 酌变量activated 激化了的activated adsorption 活性吸附activated atom 激活原子activated molecule 激活分子activating agent 活化剂activation 活化activation analysis 放射化分析activation cross section放射化截面activation energy 激活能activation method 激活法activator 活化剂active 活性的active carbon 活性炭active current 有效电流active front 活跃锋active galactic nucleus活动星系核active galaxy 活动星系active hydrogen 活性氢active laser element 激活激光元件active laserspectroscopy 活性激光光谱学active laser substance激活物质active lattice 放射性栅格active locking 受迫模同步active material 放射材料active network 有源网络active oxygen 活性氧active power 有效功率active product 放射性产物active prominence 活动日珥active q switching 激活q 开关active sun 活动太阳active volcano 活火山activity 放射性activity coefficient 活度系数activity unit 放射性单位actual 真实的actual load 有效的acumulative temperature 积温acute 尖锐acute angle 锐角acute angled 锐角的acute angled triangle 锐角三角形acute triangle 锐角三角形acuteness 锐度acyclic 非循环的ada ada 语言adamantine luster 金刚光泽adaptability 适应性adaptation 适应adaptive antenna 自适应天线adaptive optics 自适应光学adaptometer 适应测量计adatom 吸附原子add 加add circuit 加法电路addend 加数adder 加法器adding element 求和器addition 加法additional 加法的additional code 补码additional heating 附加加热additional mass 附加质量additive 加法的additive group 加法群additive method 加色法additive property 加和性additive theory ofnumbers 加性数论additivity 加和性address 地址address part 地址部分address register 地址寄存器adenosine triphosphate三磷酸腺苷adequate 适合的adhere 粘着adherence 附着adhesion 附着adhesive force 附着力adhesives 粘接剂adiabat 绝热线adiabatic 绝热的adiabatic approximation绝热近似adiabatic atmosphere 绝热大气adiabatic calorimeter 绝热式量热器adiabatic change 绝热变化adiabatic compression 绝热压缩adiabatic cooling 绝热冷却adiabatic curve 绝热线adiabaticdemagnetization 绝热退磁adiabatic equilibrium 绝热平衡adiabatic expansion 绝热膨胀adiabatic exponent 绝热指数adiabatic free expansion绝热自由膨胀adiabatic heating 绝热增温adiabatic hypothesis 绝热假说adiabatic index 绝热指数adiabatic invariant 绝热不变量adiabatic lapse rate 绝热温度梯度adiabatic magneticsusceptibility 绝热磁化率adiabatic nucleardemagnetization 绝热核去磁adiabatic potentialcurve 绝热势能曲线adiabatic potentialsurface 绝热位势面adiabatic principle 浸渐原理adiabatic process 绝热过程adiabatic pulsations 绝热脉动adiabatic temperaturegradient 绝热温度梯度adiabatic theorem 绝热定理adiabaticity 绝热性adiabatics 绝热线adjacent angles 邻角adjacent side 邻边adjoint differentialequation 伴随微分方程adjoint operator 伴随算符adjoint system 伴随系。
英语语法术语语法grammar句法syntax词法morphology结构structure层次rank句子sentence从句clause词组phrase词类part of speech单词word实词notional word虚词structural word单纯词simple word派生词derivative复合词compound词性part of speech名词noun专有名词proper noun普通名词common noun可数名词countable noun不可数名词uncountable noun 抽象名词abstract noun具体名词concret noun物质名词material noun集体名词collective noun个体名词individual noun介词preposition连词conjunction动词verb主动词main verb及物动词transitive verb不及物动词intransitive verb 系动词link verb助动词auxiliary verb情态动词modal verb规则动词regular verb不规则动词irregular verb 短语动词phrasal verb限定动词finite verb非限定动词infinite verb使役动词causative verb感官动词verb of senses动态动词event verb静态动词state verb感叹词exclamation形容词adjective副词adverb方式副词adverb of manner程度副词adverb of degree时间副词adverb of time地点副词adverb of place修饰性副词adjunct连接性副词conjunct疑问副词interrogative adverb关系副词relative adverb代词pronoun人称代词personal pronoun物主代词possessive pronoun反身代词reflexive pronoun相互代词reciprocal pronoun指示代词demonstrative pronoun 疑问代词interrogative pronoun 关系代词relative pronoun不定代词indefinite pronoun物主代词possessive pronoun名词性物主代词nominal possessive pronoun形容词性物主代词adjectival possessive pronoun冠词article定冠词definite article不定冠词indefinite article数词numeral基数词cardinal numeral序数词ordinal numeral分数词fractional numeral形式form单数形式singular form复数形式plural form限定动词finite verb form非限定动词non-finite verb form 原形base form从句clause从属句subordinate clause并列句coordinate clause名词从句nominal clause定语从句attributive clause状语从句adverbial clause宾语从句object clause主语从句subject clause同位语从句appositive clause时间状语从句adverbial clause of time地点状语从句adverbial clause of place方式状语从句adverbial clause of manner让步状语从句adverbial clause of concession原因状语从句adverbial clause of cause结果状语从句adverbial clause of result目的状语从句adverbial clause of purpose条件状语从句adverbial clause of condition真实条件状语从句adverbial clause of real condition 非真实条件状语从句adverbial clause of unreal condition含蓄条件句adverbial clause of implied condition错综条件句adverbial clause of mixed condition句子sentence简单句simple sentence并列句compound sentence复合句complex sentence并列复合句compound complex sentence陈述句declarative sentence疑问句interrogative sentence一般疑问句general question特殊疑问句special question选择疑问句alternative question 附加疑问句tag question反义疑问句disjunctive question 修辞疑问句rhetorical question感叹疑问句exclamatory question存在句existential sentence肯定句positive sentence基本句型basic sentence pattern 否定句negative sentence祈使句imperative sentence省略句elliptical sentence感叹句exclamatory sentence句子成分members of sentences 主语subject谓语predicate宾语object双宾语dual object直接宾语direct object间接宾语indirect object复合宾语complex object同源宾语cognate object补语complement主补subject complement宾补object complement 表语predicative定语attribute同位语appositive状语adverbial句法关系syntactic relationship 并列coordinate从属subordination修饰modification前置修饰pre-modification后置修饰post-modification限制restriction双重限制double-restriction非限制non-restriction数number单数形式singular form复数形式plural form规则形式regular form不规则形式irregular form格case普通格common case所有格possessive case主格nominative case宾格objective case性gender阳性masculine阴性feminine通性common中性neuter人称person第一人称first person第二人称second person第三人称third person时态tense过去将来时past future tense过去将来进行时past future continuous tense过去将来完成时past future perfect tense一般现在时present simple tense 一般过去时past simple tense一般将来时future simple tense 现在完成时past perfect tense 过去完成时present perfect tense 将来完成时future perfect tense 现在进行时present continuous tense过去进行时past continuous tense将来进行时future continuous tense过去将来进行时past future continuous tense现在完成进行时present perfect continuous tense过去完成进行时past perfect continuous tense语态voice主动语态active voice被动语态passive voice语气mood陈述语气indicative mood祈使语气imperative mood虚拟语气subjunctive mood否定negation否定范围scope of negation全部否定full negation局部否定partial negation转移否定shift of negation语序order自然语序natural order倒装语序inversion全部倒装full inversion部分倒装partial inversion直接引语direct speech间接引语indirect speech自由直接引语free direct speech 自由间接引语free indirect speech一致agreement主谓一致subject-predicate agreement语法一致grammatical agreement 概念一致notional agreement就近原则principle of proximity 强调emphasis重复repetition语音pronunciation语调tone升调rising tone降调falling tone降升调falling-rising tone文体style正式文体formal非正式文体informal口语spoken/oral English套语formulistic expression英国英语British English美国英语American English用法usageTerms of English Language Teaching Methodology感情色彩emotional coloring褒义commendatory贬义derogatory幽默humorous讽刺sarcastic挖苦ironic英语教学法术语Aachievement test 成绩测试acquisition 习得，语言习得acquisition 语言习得顺序active mastery 积极掌握active vocabulary 积极词汇，主动词汇affective filtering 情感筛选aim,objective 目的，目标analysis of errors 错误分析analytic approach 分析教学法，分析法analytical reading 分析性阅读application to practice 运用于实践applied linguistics 应用语言学approach 教学路子aptitude test 能力倾向测验Army method 陆军法associative learning 联想性学习auditory discrimination 辨音能力auditory feedback 听觉反馈auditory memory 听觉记忆auditory perception 听觉audio-lingual method 听说法audio-visual method 视听法aural-oral approach 听说教学法，听说法aural-oral method 听说法Bbasic knowledge 基本知识basic principle 基本原则basic theory 基本理论basic training 基本训练basic vocabulary 基本词汇behaviourism 行为主义bilingual 双语的bilingual education 双语教育blank filling 填空Cchain drill 链式操练，连锁操练choral repetition 齐声照读，齐声仿读class management 课常管理classroom interaction 课常应对cloze 完形填空coach 辅导cognitive approach 认知法common core 语言的共同核心，语言共核communicative drill 交际性操练communicative exercise 交际练习communicative langunge teaching 交际派语言教学法，交际教学法community language learning 集体语言学习法comparative method 比较法communicative approach 交际法comprehensible input 不难理解的输入comprehensive method 综合法computer-managed instruction 计算机管理教学concord and coordination 默契与配合console 控制台consonant cluster 辅音连缀context 上下文controlled composition 控制性作文course density 课堂密度course design 课程设计cramming method 灌输式cue word 提示词curriculum 课程，教学大纲curriculum development 课程编制，课程设计cultrual objective,aim 教养目的cclical approach 循环教学法，循环法Ddeductive learning 演绎性学习deductive method 演绎法delayed auditory feedback 延缓听觉反馈demonstration 演示demonstration lesson 示范教学describe a picture in writing 看图说话describe a picture orally 描写语言学diagram 图解diagnostic test 诊断性测验dicto-comp 听写作文direct application 直接应用direct comprehension 直接理解direct learning 直接学习direct method 直接教学法Eeducational objective, aim 教育目的EFL 英语作为外语EGP 通用英语ELT 英语教学English as a Foreign Language 英语作为外语English as an International Language 英语作为国际语言English environment 英语环境English for Academic Purposes 学术英语English for general prupose 普通英语English for General Purposes 通用英语English for specific purposes 专用英语ESOL English for Speakers of Other Languages 供非英语民族使用的英语English medium school 英语授课学校English teaching;teaching English 英语教学WSD（English as a Second Dialect）英语作为第二方言WSL（English as a Second Language）英语作为第二语言ESL Programme（English as a Second Language Programme）英语（第二语言）教程ESP（English for Special Purposes）专用英语EST（English for Science and Technology）科技英语evaluation 评语，评价examination 考试examination question 考题experimental method 实验法extensive reading 泛读external speech 外语言语extra-curiculum activity 课外活动extra-curriculum club,group 课外小组Ffacial expression 面部表情feedbace 反馈film projector 电影放映机filmstrip 电影胶片final stage 高级阶段first language 第一语言，母语formative evaluation 自由作文free practice 自由练习frequency of word 词的频率al approach 功能法al syllabus 功能派教学大纲word 功能词Ggeneral linguistics 普通语言学gestalt style 格式塔式（学习），整体式（学习）gesture 手势getting students ready for class 组织教学global learning 整体式学习，囫囵吞枣式学习global question 综合性问题gradation 级进法，分级递升法graded direct method 循序直接法grading 级进法，分级递升法；评分grammar lesson 语法课grammar method 语法法grammar translation method 语法翻译法grammatical analysis 语法分析group reading 集体朗读group training 集体练习guided composition 引导性作文Hheuristic method of teaching 启发式教学法heurstics 启发法；探索法humanistic approach 人本主义教学法Iidealism 唯心主义imitatiom 模仿immersion programme 沉浸式教学imparting knowledge 传授知识incomplete plosive 不完全爆破independent composition 独立作文individualized instruction 个别教学individual training 个别练习inductive learning 归纳性学习inductive method 归纳法inflection,inflexion 词形变化information,processing 信息处理initial beginning stage 初级阶段inner speech 内语言语in-service training 在职培训instructional objective 语言教学目标integrative teaching 综合教学integrated approach 综合教学法，综合法intelligent memory 理解性记忆language training 强化教学intensive training 精读intermediate stage 中级阶段interpretation 头口翻译International Phonetic Alphabet 国际音标Jjuncture 连读，音渡junior high school 初级中学junior school 初级学校junior sceondary school 初级中等学校junior-senior high school 初高中junior technical college(or school) 初级职业学院（或学校）junior year 大学三年级Kkey words 基本词，关键字kinesics 身势语，身势学kinesthetic memory 动觉记忆knowledge 知识knowledge structure 知识结构Llanguage acquisition 语言习得language acquisition device 语言习得机制language arts 语言技能language competence,or knowledge 语言知识language learning capability 语言学习能力language laboratory;lab 语言实验室language leaning capacity 语言学习能力language pedagogy 语言教育language performance 语言行为language program design 语言课程设计language test 语言测试learning by deduction 演绎性学习learning by induction 归纳性学习learning process 学习过程learning style 学习方式lesson conducting 教课lesson plan 课时计划，教案lesson preparation 备课lesson type 课型linguistics 语言学linguistic competence 语言能力linguistic method 口语领先教学法living language 活的语言long-term memory 长期记忆look-and-say method 看图说话法Mmeaningful drill 有意义的操练neabubgful exercise 有意义的练习meaningful learning 理解性学习means of teaching 教学手段mechanical drill 机械操练mechanical exercise 机械练习mechanical memory 机械记忆mechanical translation 机器翻译medium of instruction 教学媒介语，教学语言memory 记忆，记忆力memory span 记忆幅度memorizing 用记记住method 方法methodology of teaching 教学法methodology of teaching English 英语教学法microteaching 微型教学mim-mem method 模仿—记忆法minimal pair 最小对立体（一种辨音练习）model 模型modeling 示范教学modern equipment 现代化设备modern language 现代语言monitor hypothesis 语言监控说mother tongue 母语motivation 引起动机Nnative language 本族语natural appoach 自然教学法，自然法natural method 自然法needs analysis 需要分析new lesson 新课nine-pile grading 九堆法notional approach 意念法notional-al syllabus 意念-功能派教学大纲notional syllabus 意念大纲、意念派教学大纲Oobservation lesson 观摩教学objective 教学目标optimum age hypothesis 学习最佳年龄说operating principle 操作原则oral approach 口语教学法，口语法oral exercise 口语练习oral method 口授法oral reading 朗读order of acquisition 语言习得顺序organization of teaching materials 教材组织organs of speech 发音器官outside reading 课外阅读overlearing 过量学习Ppaired-associate learning 配对联想学习法pair work 双人作业，双人练习passive vocabulary 消极词汇pattern drill 句型操练pattern practice 句型练习pdeagogical grammar 教学语法pedagogy 教育法peer teaching 同学互教penmanship handwriting 书法perception 知觉performance objective 语言实践目标personality 个性philosophy 哲学phoneme 音素phonetics 语音法phonetic method 按字母音值拼读法phonology 音位学picture 图画phasement test 分班测验plateau of learning 学习高原practical objective 实用目的practice effect 练习效应practice of teaching 教学实践presentation of new materials 提出新材料pre-teaching 预教primary of speech 口语领先principle of communication 交际性原则principle of teaching 教学原则problem solving 习题解答production stage 活用阶段，产出阶段productive exercise 活用练习productive mastery 活用掌握productive vocabulary 活用词汇proficiency 熟练program desing 课程设计psycho-linguistics 心理语言学psychological method 心理法Qqualified teacher 合格教师question band 试题库questionnaire 调查问卷questions 提问Rrapid reading 快速阅读，快读rate of reading 阅读速度readability 易读性read by turns 轮读reading 阅读reading lesson 阅读课reading method 阅读法reading speed 阅读速度reading vocabulary 阅读词汇，阅读词汇量receptive language knowledge 接受性语言知识receptive vocabulary 领会词汇reformed method 改良法regression 回看，重读reinforcement 巩固reinforcement lesson 巩固课repetition drill 复述操练repetition-stage 仿照阶段response 反应retelling 复述retention 记忆teview;tevision 复习review（revise）and check up 复习检查review（revision）lesson 复习课rewriting 改写rhythm 节奏role-play 扮演角色rote learning 强记学习法，死记硬背Sscanning 查阅，扫瞄school practice 教学实习scientific way of thinking 科学的思想方法second language 第二语言segment 音段，切分成分semantics 语义学seminar 课堂讨论sentence completion 完成句子short-term memory 短期记忆sight vocabulary 一见即懂的词汇silent reading 默读silent way 沉默法，静授法simplification 简写simplified reader 简写读本simulation 模拟，模拟性课堂活动simultaneous interpretation 同声翻译situational method 情景法situational language teaching 情景派语言教学法，情景教学法situational method 情景教学法situational syllabus 情景派教学大纲situation reinforcement 情景强化法skimming 略读，济览slide 幻灯片slide projector 幻灯片socialized speech 社会化言语socio-linguistics 社会语言学soft ware 软件speech disorder 言语缺陷speech pathology 言语病理学speech perception 言语知觉speech reading 唇读法speed reading 快速阅读，快读speelling 正字法spiral approach 螺旋式教学法，螺旋法spoken lauguang 口语stage of teaching 教学阶段stick drawing;mathch drawing 简笔画stimulus and response 刺激与反应stress accent 重音，重读structuralism 结构主义（语言学）structural method 结构法student-centered 学生中心student-centered learning 学生为主学习法student teacher 实习教师student teaching 教育实习submersion programme 沉浸式教程substitution 替换substitution table 替换表subvocal reading 默读suggestopaedia 暗示教学法syllabus 教学大纲syllabus design 教学大纲设计syllabus for middle school English 中学英语教学大纲synthetic approach 综合性教学法，综合法synthetical reading 综合性阅读Ttarget language 目的语，译文语言teacher’s book 教师用书teacher’s manual 教师手册teaching experience 教学经验teaching objective,aim 教学目的teaching procedure 教学过程teaching tools;property 教具teaching words in isolation 孤立教单词theory of teaching 教学理论TEFL 英语（外语）教学TESL 英语（第二语言）教学TESOL 对非英语民族教英语time allotment 时间分配total physical response method 整体动作反应法transformation drill 转换操练translation method 翻译法transformational generative grammar 转化生成语法Uunconscious 潜意识underclassman 低年级学生undergraduate 大学本科生undergraduate course 大学本科课程undergraduate school 大学本科学院undergraduate special 大学特殊课程unified studied 统一课程university high school 大学附属中学university of the air 广播电视大学updating courses/training 现代化课程/训练upgrading courses/training 进修课程/训练upperclassman 高年级学生use and usage 使用和用法utterance 语段Vverbal association 词语联想verbal learning 语言学习，单词学习video 电视，影象videotape 录象磁带visual perception 视觉visual aid 直观手段visit a class 听课visual memory 视觉记忆vocabulary control 词汇控制Wword association 词际联想word list 词表word study 词的研究word frequency 词汇重复率written language 书面语感情色彩emotional coloring褒义commendatory贬义derogatory幽默humorous讽刺sarcastic挖苦ironic英语教学术语Approach教学路子Communicative approach交际法Communicative language teaching 交际语言教学Method教学方法Syllabus design教学大纲设计Frist language母语Second language第二语言Foreign language外语Target language目的语言Techniques技巧Brainstorm指就某一问题随便发表观点或建议的过程Group-work小组活动Pair-work两人一组的活动View of work语言理论或对语言的认识Structural view结构主义语言理论Functional view功能主义语言理论Interactional view交互语言理论Behaviourist theory行为主义学习理论Cognitive theory认知学习理论Process-oriented theory强调过程的语言学习理论Condition-oriented theory强调条件的语言学习理论Audiolingual theory外语教学听说法TPR:total physical respone 全身反应法Silent way沉默法Natural approach自然法Reflective teaching反思教学Communicative approach交际法或交际路子Communicative competence交际能力Linguistic competence语言能力Teaching procedures教学步骤Teaching aids教学辅助材料和设备Variety多样性Flexibility灵活性Learnability可学性Linkage连接Micro planning微观备课Macro planning宏观备课RP:received pronunciation英国伦敦附近的一种方言。
Aa horizon 腐殖堆积层aa lava 块熔岩abandoned field 撩荒地abandoned lands 撩荒地abandoned mine 废弃矿山abandoned shoreline 旧岸线aberration 像差abiogenesis 自然发生abiotic factor 非生物因素ablation 水蚀ablation moraine 消融冰碛abnormality 反常aboriginal 土着的abrasion 海蚀abrasion platform 浪蚀台地abrasion shore 浪蚀海岸abrasion surface 浪蚀面abrasion terrace 海蚀阶地abrasive 研磨剂abrupt slope 陡坡abrupt textural change 质地突变abscissa 横坐标absolute age 绝对年龄absolute age determination 绝对年代测定absolute age of groundwater 地下水绝对年龄absolute altitude 绝对高度absolute amplitude 绝对振幅absolute chronology 绝对年代absolute convergence 绝对收敛absolute dating 绝对年代测定absolute error 绝对误差absolute extremes 绝对极值absolute geochronology 绝对地质年代学absolute geopotential 绝对重力势absolute gravity 绝对重力absolute humidity 绝对湿度absolute instability 绝对不稳定性absolute maximum 绝对极大absolute measure 绝对尺度absolute minimum 绝对极小absolute orientation 绝对定向absolute parallax 绝对视差absolute precision 绝对精度absolute representation 绝对值表示法absolute temperature 绝对温度absolute value 绝对值absolute zero 绝对零度absorbed radiant flux 吸收辐射absorbed radiation 吸收辐射absorbent 吸收剂absorbing capacity 吸收能力absorbing complex 吸收性复合体absorptance 吸收系数absorption 吸收absorption band 吸收带absorption coefficient 吸收系数absorption curve 吸收曲线absorption factor 吸收因素absorption filter 吸收滤光片absorption of energy 能量吸收absorption of light 光吸收absorption spectrum 吸收光谱absorption surface 吸收面absorptive capacity 吸收本领absorptivity 吸收能力absorptivity emissivity ratio 吸收发射比abstract symbol 抽象符号abundance of isotopes 同位素的丰度abundance of the elements 元素丰度abundance ratio of isotopes 同位素的相对丰度abundant rainfall 过量降雨abyss 深渊abyssal 深海的abyssal basins 深海盆地abyssal benthos 深海底栖生物abyssal deposits 深海沉积物abyssal facies 深海相abyssal hill 深海丘陵abyssal plain 深海平原abyssal region 深海区abyssal sediment 深海沉积物abyssal zone 深海带acariasis 螨病acarinosis 螨病acaustobiolite 非可燃性生物岩accelerated erosion 加速侵蚀accelerated weathering 加速风化acceleration 加速度acceptance 接收acceptor 收体acceptor atom 受体原子acceptor bond 接体合accessory element 伴随元素accessory mineral 副次要accessory species 次要种accidental ejecta 外源喷出物accidental error 偶然误差accidental species 偶见种acclimatization 气候驯化acclivity 上行坡accompaniment element 伴生元素accordance of summit levels 峰顶面等高性accordant junction 协和汇流平齐汇流交合汇流accordant junction of streams 协合流accretion gley 淤积潜育层accumulated temperature 积温accumulation 堆积accumulation curve 累积曲线accumulation horizon 聚积层accumulation mountains 堆积山地accumulation of assimilation products 同化物累积accumulation of humus 腐殖质蓄积accumulation of organic matter 有机质堆积accumulative coast 堆积海岸accumulative relief 堆积地形accuracy 准确度accuracy of measurement 测定准确度acetic acid 醋酸acetic acid bacteria 醋酸菌acetic fermentation 醋酸发酵achromatic objective 消色差物镜achromatopsia 色盲acid alkaline barriers 酸碱障acid base balance 酸碱平衡acid base equilibrium 酸碱平衡acid brown forest soils 酸性棕色森林土acid earth 酸性白土acid fast bacteria 抗酸菌acid fastness 抗酸性acid fermentation 酸性发酵acid geochemical barrier 酸性地球化学障acid group 酸根acid humus 酸性腐殖质acid igneous rock 酸性火成岩acid medium 酸性介质acid peat soil 酸性泥炭土acid rain 酸雨acid residue 酸性残余物acid rock 酸性岩acid rocks 酸性岩acid soil 酸性土acid solution 酸性溶液acid spring 酸性泉acid tolerant species 耐酸品种acid value 酸值acidic lava 酸性熔岩acidification 酸化acidite 酸性岩acidity 酸度acidity of soil 土壤酸度acidoid 酸性胶体acidophile organisms 嗜酸有机体acidophilous plant 喜酸植物acidophyte 喜酸植物acidosis 酸中毒acidotrophic lake 酸性营养湖acidulation 酸化acotyledon 无子叶植物acquired character 获得特性acric ferralsols 强淋溶铁铝土acrisols 强淋溶土acrorthox 强酸性正常氧化土acrospore 顶生孢子acrox 高风化氧化土acstivation 夏眠actinium 锕actinolite schist 阳起片岩actinometer 日光辐射计actinometry 日射测定法actinomorphic 辐射对称的actinomycetes 放线菌actinomycosis 放线菌病analog information 模拟信息analogue 类似analogy 相似analysis 分析analysis by sedimentation 沉降分析analysis by titration 滴定分析analysis model 分析模型analysis of covariance 协方差分析analysis of variance 方差分析analysis of weather map 天气图分析analytic character 分析特性analytic map 解析地图analytic photogrammetry 解析摄影测量analytical aerial triangulation 解析空中三角测量analytical balance 分析天平analytical geochemistry 分析地球化学analytical method 分析方法analytical model 分析模型analytical plotter 解析测图仪analytical thematic map 解析肘地图anamesite 中粒玄武岩anatexis 深溶酌anchor ice 底冰ancient glaciation 古代冰川酌ancient lake mire 湖泊排水的沼泽ancient platform 古地台ancient sediments 古代沉积物andept 火山灰始成土andesine 中长石andesite 安山岩andesite line 安山岩线andic cambisols 暗色始成土andosols 暗色土anemia 贫血anemochores 风播植物anemochorous plants 风播植物anemochory 风播anemogram 风力自记曲线anemograph 风速计anemology 测风学anemometer 风速表anemometry 风速测定法anemophilous flower 风媒花anemophilous plant 风媒植物anemophily 风媒anemorumbograph 风向风速计anemorumbometer 凤向风速计anemothermometer 风速风温计aneroid barograph 空盒气压计aneroid barometer 空盒气压表aneroidograph 无液气压记录器angiosperms 被子植物angle equation 角方程angle of attachment 闭合角angle of bank 曲折角angle of direction 方位角angle of divergence 发散角angle of emergence 出射角angle of field 视场角angle of incidence 入射角angle of inclination 倾斜角angle of obliquity 倾斜角angle of pitch 府仰角angle of reflection 反射角angle of refraction 折射角angle of rotation 旋转角angle resolution 角分辨率anglesite 硫酸铅矿angular blocky structure 角块状结构angular deviation 角度偏差angular difference 角度不符值angular distance 角距angular distortion 角度畸变angular error 角度误差angular fold 尖褶皱angular measurement 角度观测angular unconformity 斜交不整合angular variation 角变化angulate drainage pattern 角状水系anhydrite 硬石膏anhydrous ammonia 无水氨animal debris 动物残屑animal husbandry 畜牧业animal remains 动物残屑animal resting place vegetation 牲畜休息地植被animal sociology 动物社会学animated mapping 动画地图制作animation 动画anion exchange 阴离子交换anionogenic element 阴离子基因元素anisotropism 蛤异性anisotropy 蛤异性ankaramite 富辉橄玄岩ankaratrite 黄橄霞玄岩ankerite 铁白云石annual 一年生植物annual aberration 周年光行差annual amount of precipitation 年雨量annual change 年变化annual flow 年径流annual march 年变程annual mean 年平均annual parallax 周年视差annual plant 一年生植物annual range 年较差annual ring 年轮annual runoff 年径流annual storage 年蓄水量annual variation 年变化annual zone 生长轮annular pattern 环状水系anomalous field 异常场anomalous geochemical gradient 异常地球化学梯度anomaly 异常anomaly in alluvium 冲积物异常anomaly in colluvium 塌积物异常anomaly in residual 残积异常anomaly ratio 异常比anorthite 钙长石anorthitite 钙长岩anorthoclase 歪长石anorthosite 斜长岩anosmia 嗅觉缺失antagonism 拮抗antagonist 对抗剂antarctic 南极antarctic air 南极气团antarctic anticyclone 南极反气旋antarctic belt 南极带antarctic circle 南极圈antarctic climate 南极气候antarctic continent 南极大陆antarctic faunistic region 南极动物区antarctic front 南极锋antarctic high 南极反气旋antarctic regions 南极区antarctic zone 南极带antarctica 南极大陆antecedent drainage 先成水系antecedent precipitation index 前期降水量指数antecedent river 先成河antecedent river network 先成水系antecedent stream 早期河流antecedent valley 先成谷anteklise 台背斜anthophyte 有花植物anthracite 无烟煤anthraconite 沥青灰岩anthrax bacillus 炭疽杆菌anthraxolite 碳沥青anthraxylon 纯木煤anthropic epipedon 耕醉层anthropic soil 人为土壤anthropochores 人播草anthropochorous plants 人播草anthropochory 人为传播anthropoclimatology 人类气候学anthropogene 人类纪anthropogenesis 人类发生anthropogenic factor 人为因素anthropogenic influence 人类影响anthropogenic landscape 人为景观anthropogenic load 人为负载anthropogenic pollution 人为污染anthropogenic soil 人为土壤anthropogenic succession 人为演替anthropogeography 人类地理学anthropological remote sensing 人类学遥感anthropology 人类学anthropophyte 人为植物anthroposphere 人类圈antiaircraft weapon position 防空兵企地antibacterial spectrum 抗细菌性光谱antiballistic missile system 反弹道导弹系统antibiosis 抗生antibodies 抗体anticlinal axis 背斜轴anticlinal fault 背斜断层anticlinal fold 背斜褶皱anticlinal limb 背斜翼anticlinal mountain 背斜脊anticlinal ridge 背斜脊anticlinal trap 背斜圈闭anticlinal valley 背斜谷anticlinorium 复背斜anticoagulant 抗凝剂anticyclogenesis 反气旋发生anticyclolysis 反气旋消散anticyclone 反气旋anticyclonic eddy 反气旋涡旋anticyclonic inversion 反气旋逆温anticylonic vortex 反气旋涡旋antierosion measures 防侵蚀措施antiform 背斜形态antimeridian 反面子午线antimonite 辉锑矿antimonsoon 反季风antimony deposit 锑矿床antinodes 波腹antiseptic 防腐剂antithyroid substance 抗甲状腺物质antitoxin 抗毒素antitrade wind 反信风antitrades 反信风antitriptic current 减速流antitriptic wind 摩擦风antitwilight 反曙暮光anvil cloud 砧状云apatite 磷灰石apex of anticline 背斜顶aphanitic texture 隐晶结构aphelion 远日点aphotic zone 无光带aphylactic projection 任意投影aphylly 无叶性apiculture 养蜂aplite 细晶岩aplogranite 淡云花岗岩apochromatic lens 复消色差镜头apogamy 无配生殖apogee 远地点apogee altitude 远地点高度apolar adsorption 非极性吸附apophyte 固有栽培植物apophytic plants 固有栽培植物apparatus 仪器频apparent density 表观密度apparent dip 视倾斜apparent heave 视平错apparent horizon 视地平apparent resistivity 视在电阻率apparent wind 视风appearance of maps 地图整饰apple coal 软煤applied climatology 应用气候学applied geochemistry 应用地球化学applied geomorphology 应用地形学applied hydrology 应用水文学applied meteorology 应用气象学appreciation 评价approximate analysis 近似分析approximate calculation 概算approximate coordinate 近似坐标approximate value 近似值aqualf 潮淋溶土aquatic animals 水栖动物aquatic life 水生生物aquatic organism 水生生物aquatic plants 水生植物aquatic products industry 水产业aquatic vegetation 水生植被aquent 潮新成土aqueoglacial deposits 冰水沉积物aqueous deposit 水成沉积aqueous rock 水成岩aqueous soil 水成土aqueous solution 水溶液aquept 潮始成土aquiclude 弱透水层aquifer 蓄水层aquiferous 含水的aquifuge 不透水层aquitard 半透水层aquod 潮灰土aquoll 潮软土aquox 潮氧化土aquult 潮老成土arable 可耕的arable land 耕地arable layer 耕层arable soil 可耕土壤arachnida 蛛形纲aragonite 霰石arber 乔木arbitrary projection 任意投影arbovirus 虫媒病毒arc of compression 压缩弧arc of folding 压缩弧arch dam 拱坝arch gravity dam 重力拱坝archaeocyte 原始细胞archaeohydrology 考古水文学archaeological culture 考古学文化archaeological remote sensing 考古遥感archaeological remote sensor 考古遥感器archaeological site 考古遗址archaeopteryx 始祖鸟archean 太古代的arched mountains 穹形山archeozoic 太古代的archeozoic era 太古代archipelago 群岛arctic 北极地区arctic air 北极气团arctic air mass 北极气团arctic circle 北极圈arctic climate 北极气候arctic desert 北极荒漠arctic desert zone 北极荒漠带arctic front 北极锋arctic high 北极高压arctic mire 极地沼泽arctic plants 极地植物arctic polygon desert 北极多边形荒漠arctic soil 极地土壤arctic subregion 北极亚区arctic tundra 北极冻原arctic zone 北极带arctoalpine 北极高山的arcuate delta 弧形三角洲arcuate structure 弧形构造arcuate tectonic belt 弧形构造带area 地区area aerial photography 区域航空摄影area color 背景色area computation 面积计算area distortion 面积变形area eruption 区城喷溢area measuring equipment 面积测量设备area method 区域法area of artesian flow 自霖区area of influence 影响面积area pattern 面状要素area survey 面积测量area target 地区目标area under crops 播种面积area weighted average resolution 面积加权平均分辨率areal rainfall depth 地域平均雨量areal survey 分段测量arenaceous quartz 石英砂arenaceous shale 砂质页岩arenopelitic 砂泥质的arenosols 红砂土arent 耕种混合新成土argialboll 粘化漂白软土argiaquoll 粘化潮软土argiboroll 粘化极地软土argil 白土argillaceous rock 泥质岩argillic horizon 粘化层argillite 泥板岩argillization 泥化argit 粘化旱成土argiudoll 粘化湿软土argiustoll 粘化干软土argon 氩arid climate 干燥气候arid cycle 干燥周期arid cycle of erosion 干燥侵蚀循环arid geomorphic cycle 干燥地貌旋回arid landforms 干燥地形arid region 干燥区arid soil 旱境土壤aridisol 旱成土aridity 干燥度aridity index 干燥指数arithmetic mean 算术平均arithmetical unit 运算器运算部件arkose 长石砂岩aromatic base crude oil 芳香基原油aromatic plant 芳香植物arrangement 配置array processor 阵列处理机arrow 箭头arsenic 砷arsenic pollution 砷污染arsenopyrite 毒砂arterial drainage 排水干渠系统artesian aquifer 自连水层artesian basin 自联盆地artesian ground water 自霖下水artesian head 承压水头artesian pressure 自凉力artesian water 自廉水artesian well 自廉arthritis 关节炎arthropoda 节肢动物artiad 偶价元素articular rheumatism 关节风湿病artificial climate 人工气候artificial culture media 人工培养基artificial drainage system 人工排水系统artificial earth satellite 人造卫星artificial earthquake 人为地震artificial forest regeneration 森林人工更新artificial ground target 航测地面标志artificial ground water 人工地下水artificial intelligence 人工智能artificial manure 堆肥artificial mineral 人造矿物artificial pollination 人工授粉artificial precipitation 人工降水量artificial radioactive element 人工放射元素artificial radioactive nuclide 人工放射性核素artificial radioactivity 人工放射性artificial rain 人造降雨artificial recharge 人工补给artificial satellite 人造卫星artificial sea water 人造海水artificial selection 人工选择artificial soil 人工土壤artificial sub irrigation 人工地下灌溉artificial water application 人工供水asbestos 石棉asbestos deposit 石棉矿床asbolane 钴土矿asbolite 钴土矿ascend curve 上升曲线ascending air current 上升气流ascending development 上升发展ascending node 升交点ascending water 上升水ascharite 硼镁石asexual generation 无性世代asexual reproduction 无性生殖ash cloud 尘云ash cone 凝灰火山锥ash content 灰分含量ash fall 火山灰下降ash forest 秦手ash shower 火山灰下降ashless filter 无灰滤纸asiatic schistosomiasis 日本血吸虫病aspect 季相aspect ratio 纵横比aspen 白杨aspen forest 白杨林asphalt 地沥青asphaltic pyrobitumen 焦性沥青asphaltite 沥青岩aspiration psychrometer 吸气式湿度计assemblage 集合assemble 集合assembly area 集结地域assessment of yield capacity of soil 土地评价assimilability 可同化性assimilate 同化物assimilation 同化酌assistentrenched meander 嵌入曲流深切曲流assisttrade wind desert 信风沙漠associated species 伴生种association 群丛association complex 群丛复合体association table 群丛表astatic magnetometer 无定向磁力计astatine 砹astenosphere 软力astro geodetic net adjustment 天文大地网平差astro geodetic network 天文大地网astrograph 天体摄影仪astrolabe 等高仪astrometry 天体测量学astronautics 宇宙航行学astronomic point 天文点astronomic theodolite 天文经纬仪astronomical azimuth 天文方位角astronomical coordinate system 天文坐标系astronomical coordinates 天文坐标astronomical geodesy 天文大地测量学astronomical levelling 天文水准测量astronomical longitude 天文经度astronomical meridian 天文子午线astronomical objective 天文对物镜astronomical unit 天文单位astronomy 天文学astrophotography 天体摄影学asymmetric carbon atom 不对称碳原子asymmetric fold 不对称褶皱asymmetrical anticline 不对称背斜asymmetrical ridge 不对称山脊asymmetrical valley 不对称谷asymmetry of relief 地形的不对称性asymptote 渐近线asynapsis 不联会asyndesis 不联会atavism 返祖atlantic time 大误期atlas 地图集atlas cartography 地图集制图学atlas dummy 图集装帧样本atlas grid 图集位置指示格网atlas leaf 地图集图页atlas of morbidity 发病率地图册atlas type 地图集类型atmometer 蒸发表atmophile elements 亲气元素atmosphere 大气圈atmospheric absorption 大气吸收atmospheric air 大气atmospheric attenuation 大气衰减atmospheric attenuation correction 大气衰减订正atmospheric circulation 大气循环atmospheric condensation 大气凝结atmospheric disturbance 大气扰动atmospheric dust 大气尘埃atmospheric electricity 大气电atmospheric factor 大气因素atmospheric front 大气锋atmospheric humidity 大气湿度atmospheric ion 大气离子atmospheric perturbations 大气扰动atmospheric phenomenon 大气现象atmospheric pollution 大气污染atmospheric pressure 气压atmospheric radiation 大气辐射atmospheric refraction 大气折射atmospheric remote sensing 大气遥感atmospheric rock 气成岩atmospheric sounding 大气探测atmospheric stability 大气稳定性atmospheric swamp 天然沼泽atmospheric transmittance 大气透过率atmospheric turbulence 湍馏气atmospheric wave 大气波atoll 环礁atoll lake 环礁湖atomic adsorption spectrometry 原子吸收分光光度法atomic arrangement 原子排列atomic bond 原子键atomic disintegration 原子蜕变atomic energy level 原子能级atomic group 原子团atomic mass unit 原子质量单位atomic number 原子序数atomic orbital function 原子轨函数atomic radius 原子半径atomic ratio 原子比atomic size 原子大小atomic spectrum 原子光谱atomic structure 原子结构atomic unit 原子单位atomic volume 原子体积atomic weight 原子量atomism 原子论atomistics 原子论atomizer 喷雾器atrio 火口原atrio lake 火口原湖attached ground water 附着地下水attached island 陆系岛attenuation coefficient 衰减系数attenuator 衰减器attraction 引力attractive wave 引力波attribute 属性attrition 磨损aubrite 顽火无球粒陨石aufeis 积冰augen gneiss 眼状片麻岩augen structure 眼状构造auger 土钻augite 辉石augitite 辉石岩augmented matrix 增广矩阵aureole 接触变质带auripigment 雌黄aurora 极光auroral zone 极光带autecology 个体生态学authigenesis 自生酌authigenic element 自生元素authigenic mineral 自生矿物authigenous mineral 自生矿物autocartograph 自动测图仪autochorous 自布的autochthonous deposit 原地沉积autochthonous stream 原地河autoclastic rock 自碎岩autocorrelation coefficient 自相关系数autocovariance 自协方差autogenic succession 自发演替autograph 立体测图仪autographometer 自动地形仪automated cartographic generalization 自动制图综合automated cartographic system 自动制图系统automated draughting 自动绘图automated plotting of points 自动展点automatic air camera 自动航摄仪automatic control 自动控制automatic data processing system 自动数据处理系绕automatic focussing 自动倒automatic lettering on map 地图自动注记automatic level 补偿飘准仪automatic meteorological station 自动气象站automatic microdensitometer 自动测微密度计automatic monitoring 自动监测automatic programming 自动程序编制automatic tracking 自动跟踪autometamorphism 自变质酌automorphous process 自型过程autonomous guidance 自制导autoparasitism 自寄生autopneumatolysis 自气化酌autoreduction alidade 曲线归算望远镜照准仪autoreduction tacheometer 自动归算视距仪autotrophic lake 自养型湖autotrophic organisms 自养生物autotrophism 自养autotrophs 自养生物autumn equinoctial point 秋分点autumnal equinox 秋分autunite 钙铀云母auxiliary contour 辅助等高线auxiliary data 辅助数据auxiliary fault 副断层auxiliary point 辅助点availability 有效度available accuracy 可达精度available fertilizer 有效肥料available field capacity 有效田间持水量available ground water 有效地下水available relief 有效地势available storage of water 有效容量available water 有效水分available water capacity 有效水容量available water holding capacity 有效水保持能力avalanche 雪崩avalanche lake 堰塞湖aventurine 砂金石average 平均average amount of effective information 平均有效信息量average background 背景平均值average deviation 平均偏差average error 平均误差average life 平均寿命average sample 平均样品average slope 平均坡度average temperature 平均温度average year 平均年averaging of multiple image 多图像平均法aviation weather service 航空气象服务avitaminosis 维生素缺乏症axial surface of fold 褶皱轴面axillary bud 腋芽axis of abscissas 横坐标轴axis of coordinates 坐标轴axis of level 水准漆axis of ordinates 纵坐标轴axis of rotation 旋转轴axis of symmetry 对称轴azilian age 阿齐尔时代azimuth 方位角azimuth circle 方位圈azimuth direction 方位方向azimuth measurement 方位角测定azimuth observation 水平角观测azimuth resolution 方位分辨率azimuthal autogonal projection 方位等角投影azimuthal equal area projection 等积方位投影azimuthal equidistant projection 等距方位投影azimuthal error 方位误差azimuthal movement 方位移动azimuthal orthomorphic projection 方位正形投影azimuthal projection 方位投影azimuthal quantum number 方位角量子数azimuthal unconformity 向位不整合azonal soil 泛域土azonality 非地带性azure stone 蓝铜矿azurite 蓝铜矿Bb horizon 淀积层back action 反酌back azimuth 反方位角back flow 逆流back marsh 漫滩沼泽back radiation 反向辐射back sight 后视back slope 反向斜面back swamp 漫滩沼泽back titration 回滴定back traverse 逆行back up 背面印刷back up water level 回升水位backed blade 刀形石器backflow 逆流回流background noise 背景噪声background pollution 背景污染background value 背景值backing of the wind 风向反转backscattering spectrometry 后散射能谱测定法backshore 滨后backstromite 氢氧锰矿backwash 洄流backwater 壅水backwater curve 回水曲线bacterial equilibrium 细菌平衡bacterial fertilizer 细菌肥料bacterial manure 细菌肥料bacterial prospecting 细菌勘探bacteriolysis 溶菌bacteriophage 噬菌体bacteriostatic agent 抑菌剂bad land 崎岖地baddeleyite 斜锆石baectuite 白头岩baer's law 贝尔定律bajirs 沙丘长湖baking coal 粘结煤balance 平衡balanced solution 平衡溶液balka 平谷balka relief 平谷地貌ball lightning 球状闪电ball structure 球状结构balloon 气球balloon remote sensing 气球遥感balloon satellite 气球卫星balneology 浴疗学band 夹层band model method 带模式法band pass filter 带通滤光器band reject filter 带阻滤波器band spectrum 带谱banded cloud 带状云系banded gneiss 带状片麻岩banded structure 带状结构banding 条状bandspread 频带扩展bandy clay 带状粘土bank 砂洲bank erosion 堤岸侵蚀bankful stage 漫滩水位banking angle 倾斜角banner cloud 旗状云bar 沙洲barchan chains 新月形沙丘链barchane 新月形砂丘bare karst 裸喀斯特baric low 低气压baric topography 气压形势barite 重晶石barium 钡bark beetles 小蠹虫barkhan 新月形砂丘barkhan ridges 新月形沙丘链barkhan sand 新月形砂丘砂barocline 斜压baroclinic atmosphere 斜压大气barogradient current 气压梯度流barogram 气压自记曲线barograph 气压记录仪;气压仪;气压计barogyroscope 气压陀螺仪barometer 气压表barometer correction 气压计改正barometric altimeter 气压测高计barometric depression 低气压barometric distribution 气压分布barometric gradient 气压梯度barometric height 气压计高程barometric tendency 气压倾向barometric tube 气压计管barometrical levelling 气压计高程测量barophilic bacterium 适压细菌barothermograph 气压温度计barotropic atmosphere 正压大气barotropic fluid 正压铃barrage 拦河坝barranco 峡谷barren 无矿的barren lands 瘠地barren limestone plateau 不毛石灰岩高原barren sand 不毛沙地barrens 瘠地barrier 障碍barrier lake 堰塞湖barrier reef 堤礁barrow 矸石埸barthite 砷锌铜矿barysphere 重圈baryta paper 钡白纸baryte 重晶石basal area 底面积basal conglomerate 底砾岩basal dressing 施基肥basal granule 基粒basal metabolism 基础代谢basal sandstone 基底砂岩basal zone of mountains 山基面带basalt 玄武岩basaltic augite 玄武辉石basaltic layer of the earth's crust 地壳玄武岩层basaltic wacke 玄土basanite 碧玄岩base 基线base apparatus 基线测量器base carriage 基线架base desaturation 盐基脱饱和base direction 基线方向base exchange 盐基交换base exchange capacity 盐基交换量base exchange complex 盐基交换复合体base height ratio 基线航高比base level of corrosion 溶蚀基准面base level of denudation 剥蚀基准面base level of erosion 侵蚀基面base line 基线base line equation 基线方程base map 基本地图base measurement 基线测量base network 基线网base of bed 层底base saturation 盐基饱和baseband signal 基带信号baselevel of erosion 侵蚀基面basement 基底basement fold 基底褶皱basement of platform 地台基底basement rock 基岩basic geochemical law 地球化学基本定律basic geochemical maps 基本地球化学图basic igneous rock 基性火成岩basic lava 基性熔岩basic map 基本地图basic rock 基性岩basicity 碱度basin 盆地basin irrigation 漫灌basin karst 盆地喀斯特basin landscape 盆地景观basin mire 盆地沼泽basin of volcanic origin 火山盆地basin perimeter 硫周长basin shape 盆地形状basin soil 盆地土壤basin without outflow 无排水盆地basiphile plants 好碱土植物basiphilous plants 好碱土植物basis 基线basite 基性岩basoid 碱性胶体basophilia 嗜碱性basophilic plant 喜碱植物basophilous vegetation 喜碱植被bastard measles 风疹batholite 岩基batholith 岩基bathyal deposits 半深海沉积物bathygraph 海水探测仪bathylith 岩基bathymetric chart 水深图bathymetric curve 等深线bathymetry 测深法bathymetry using remote sensing 遥感海洋测深bathythermograph 深水温度表batukite 暗色白玄岩bauxite 铝土矿bay 湾bayleyite 菱镁铀矿bayou lake 旧河道湖beach 海岸beach cusps 海滩嘴beach drifting 沿滩漂移beach erosion 海岸侵蚀beach gravel 海滨砾石beach material 海滩泥沙beach placer 海滨砂矿beach plain 海滩平原beach ridge 滩脊beach slope 海滨坡度beach terrace 滨岸阶地beacon 航标beaded valley 串珠状谷beam compasses 杠规beam spliter 分光镜bean shaped structure 豆形结构bearing 方位bearing point 方位点beat 露头bed 层bed development 河床演变bed load 推移质bed pattern 河床型式bed succession 层序bed toxin 蜂毒bed vein 层状脉bedded alluvium 层状冲积层bedded clay 层状粘土bedded deposit 层状矿床bedded rock 层状岩bedded structure 层状结构bedding 层理bedding fault 层面断层bedding joint 层面节理bedding plane 层理面bedrock 基岩behavior 行为behavior of elements 元素的行为beheaded river 夺劣beheaded valley 断头谷beidellite 贝得石belt area 带状分布区belt of equatorial calm 赤道无风带belt of soil water 土壤水分带belt of transition 过渡带belt of weathering 风化带belt transect 样带belt transect method 样带法belted coastal plain 带状沿岸平原bench 阶地bench border irrigation method 条田灌溉法bench gravel 阶地砾石bench mark 水准点bench terraces 一阶式梯bending 弯曲bending test 弯曲试验benioff zone 贝尼奥夫带bent test 弯曲试验bentgrass meadow 翦股颖草甸benthos 底栖生物bentonite 膨润土beringite 棕闪粗面岩berkelium 锫berm 后滨阶地bernoulli's polynomial 伯努利多项式beryl 绿柱石beryllium 铍beryllium pollution 铍污染beta ray detector 计数器计数管betterment of land 土地改良between class distance 类间距离bicarbonate 重碳酸盐bidentate ligand 二合配位体bidirectional reflectance distribution function 双向反射比分布函数biennial fruit 隔年果biennial plant 二年生植物bifurcation 分枝bight 大湾bilateral geochemical barrier 两侧地球化学障碍bilateral symmetry 左右对称bilberry heath 越桔灌木丛bilberry pine forest 越桔松林bilberry spruce forest 越桔云杉林bilinear interpolation method 双线性内插法billow cloud 浪云bimetal plate 双层金属版bimetallic thermometer 双金属温度表binary search 折半查找法binding 装订binding coal 粘结煤binding force 结合力binocular 双筒望远镜binocular telescope 双筒望远镜binocular vision 双目观察binomial nomenclature 二名法bioaccumulation of elements 元素的生物累积biocatalyst 生物催化剂biochemical evolution 生化进化biochemical oxygen demand 生化需氧量biochemistry 生物化学biochore 生物区域界线bioclast 生物碎屑岩bioclastic rock 生物碎屑岩bioclimate 生物气候bioclimatics 生物气候学bioclimatogram 气物气候图bioclimatological 生物气候学的bioclimatology 生物气候学biocoenology 生物群落学biocoenose 生物群落biocoenosis 生物群落biocolliod 生物胶体bioelectric potential 生物电位biofacies 生物相biogenesis 生源说biogenetic law 生物发生律biogenic anomaly 生物成因异常biogenic deposits 生物沉积物biogenic element 生物起源元素biogenic landforms 生物成地形biogenic rock 生物岩biogeochemical anomaly 生物地球化学异常biogeochemical barrier 生物地球化学障biogeochemical cycle of pollutants 污染物生物地球化学循环biogeochemical disease 生物地球化学性疾病biogeochemical prospecting 生物地球化学勘探biogeochemistry 生物地球化学biogeocoenology 生物地理群落学biogeocoenosis 生物地理群落biogeography 生物地理学biohydrological 生物水文的biohydrology 生物水文学biolith 生物岩biological activity of soil 土壤生物活性biological cycle 生物循环biological decomposition 生物分解biological mineralization 生物矿化biological monitoring 生物监测biological pest control 生物虫防治bioluminescence 生物荧光biomass 生物量biomass pyramid 生物量金字塔biome 生物群落biometrics 生物统计学biometry 生物统计学biomineralogy 生矿物学bionidicator 生物指示物bionomics 生态学biophile elements 亲生元素biophysicgraphy 生物自然地理学biospeleology 洞穴生物学biosphere 生物圈biostatistics 生物统计字biostratigraphy 生物地层学biota 生物相biotic environment 生物环境biotic succession 生物性演替biotite 黑云母biotope 生活小区biotype 生物型biozone 生物带bipolar distribution 两极分布birch 桦木birch forest 桦手bird foot delta 鸟足状三角洲birds of passage 候鸟bireflection 反射多色性birefringence 双折射birth rate 出生率bischofite 水氯镁石bisectrix 二等分线bismalith 岩柱bismuth 铋bismuth glance 辉铋矿bismuthinite 辉铋矿bit error rate 比特误码率bitumen 沥青bituminization 沥青化bituminous coal 烟煤black acid prairie soils 黑色酸性湿草原土black alkali soil 黑碱土black and white aerial photograph 黑白航摄照片black and white film 黑白胶片black and white infrared image 黑白红外影像black and white map 单色图black and white picture 黑白图像black box 黑盒black calcareous soil 黑色石灰土black cobalt 钴土矿black manganese 黑锰矿black meadow soils 暗色草甸土。
英汉语言对比-3-Synthetic-vs-Analytic1. inflectional vs. non-inflectionalInflection: a change in the form of a word to indicate a change in its grammatical function.（只改变语法形态，不改变词义的变化）1）构词形态，即起构词作用的词缀变化（affixation），包括大量的前缀（prefix）和后缀（suffix）。
E.g. read; serious; consider;The publishing house has to take into serious consideration whether the readers will like to read / reading the books or not.The publishing house has to take into serious consideration whether the books will be readable or not.The publishing house has to take the readability of the books into serious consideration.The publishing house has to consider seriously whether the readers will like to read / reading the books or not.The publishing house has to consider seriously whether the books will be readable or not.The publishing house has to consider seriously the readability of the books.2）构形形态，即表达语法意义的词形变化。
a rXiv:as tr o-ph/1843v124Aug21A Complete Analytic Inversion of Supernova Lines in the Sobolev Approximation Daniel Kasen 1,2dnkasen@ David Branch 2,1branch@ E.Baron 2,1baron@ and David Jeffery 3jeffery@ ABSTRACT We show that the shape of P-Cygni line profiles of photospheric phase supernova can be analytically inverted to extract both the optical depth and source function of the line –i.e.all the physical content of the model for the case when the Sobolev approximation is valid.Under various simplifying assumptions,we derive formulae that give S (r )and τ(r )in terms of derivatives of the line flux with respect to wavelength.The transition region between the minimum and maximum of the line profile turns out to give especially interesting information on the optical depth near the photosphere.The formulae give insights into the relationship between line shape and physical quantities that may be useful in interpreting observed spectra and detailed numerical calculations.Subject headings:line:formation —line:profiles —line:identification —radiative transfer —supernovae1.IntroductionThe Sobolev approximation (Sobolev 1960;Castor 1970;Rybicki &Hummer 1978)allows for a simplified solution to the radiative transfer equation in media with high velocity gradients,such assupernovae.The Sobolev approximation has been used to calculate synthetic spectra in stars with strong winds(Castor&Nussbaumer1972;Pauldrach et al.1986)and tofit observed supernova spectra and place constraints on explosion models(Branch et al.1983;Jeffery&Branch1990; Mazzali et al.1992;Deng et al.2000).Typically these models assume spherical symmetry and ignore continuous opacity.Despite the simplifying assumptions,the synthetic spectrafit the data quite well.To calculate line profiles in the Sobolev case two physical quantities must be specified:(1)τ(r): the optical depth of a line as a function of radius(often assumed to be a power law),and(2)S(r): the source function of the line as a function of radius(often assumed to be a resonant scattering source function).The Sobolev approximation has most often been used,like more sophisticated radiative transfer techniques,in a direct analysis of data,where the physical quantities are specified or calculated and the resulting spectrum is compared to observed data.On the other hand,there has been some interest in taking the inverse approach,ing the line shape of observed data to infer the physical conditions in the atmosphere.Fransson&Chevalier(1989)showed that the emissivity could be calculated for forbidden lines by differentiating the observed line profile with respect to wavelength and estimated the effects of electron scattering.Ignace&Hendry(2000), using the Sobolev approximation,derived an analytic formula that gave a combination of S(r)and τ(r)as a function of the derivative of the red side of an emission feature of arbitrary optical depth. The run of the optical depth of a line is then given if one specifies a form for the source function. For instance S(r)in the case of pure resonance scattering is given by:S(r)=I ph W(r),(1) whereW(r)=11− r phthe formulae should still give considerable insight into the physical conditions in the atmosphere. On the other hand,the limitations of the formulae provide an interesting result in their own right –they clearly show what type of features are impossible under the above assumptions,making it is obvious where more complicated scenarios must be invoked to explain a spectrum.2.The Sobolev ApproximationIn the most often used Sobolev model,one begins with a perfectly sharp,spherical photosphere that emits radiation as a blackbody,and which is surrounded by a moving atmosphere with large velocity gradient.The basic idea behind the Sobolev approximation is that a photon emitted from the photosphere only interacts with a line in the small region of the atmosphere where the photon is Doppler shifted into resonance with the line.Since the source function can be assumed to be constant over this small resonance region,the solution of the radiative transfer equation is greatly simplified.It also becomes simpler to visualize line formation,as the lineflux at a given wavelength comes from a2-dimensional resonance surface in the atmosphere.The criterion for the validity of the Sobolev approximation is that the resonance regions be sufficiently small,and this is characterized by the ratio of the atmosphere’s thermal velocity(or mean microturbulent velocity, if significant)to the velocity scale height(i.e the velocity range over which temperature,density, and occupation numbers change by a factor of order2(Jeffery1993)).Quantitative accuracy is found for velocity ratios 0.1(Olson1982).For photospheric phase supernovae thermal velocities are of order10km s−1and velocity scale heights are∼103km s−1,giving a ratio of∼10−2.For supernova atmospheres,homology is established shortly after the explosion,so that v=r/t, where t is the time since explosion.In this case the resonance surface for a wavelength is a plane perpendicular to the line of sight.We label the line of sight with a coordinate z,with origin at the center of expansion and with z increasing away from the observer(see Figure1).A plane at coordinate z has a z-component velocity of v z=z/t=z v ph/r ph where v ph is the velocity of the photosphere.This plane is then responsible for the lineflux at a wavelengthλ=λ0[1+(z/r ph)(v ph/c)],i.e the rest wavelength,λ0,Doppler shifted by the z-component velocity.Theflux at a given wavelength is calculated by integrating over all the characteristic rays of the corresponding plane.Figure1shows that the formation of the line profile breaks up schematically into three regions.For z≥0,theflux is redshifted with respect to the line center so we call this the red side.This leads to an expression for theflux as an integral over impact parameter p(the coordinate perpendicular to the line of sight):F(z)r2ph I ph+ ∞r ph S(r)(1−ζ(r))p dp2whereζ(r)=e−τ(r)and F(z)is the observedflux(apart from a factor of1/D2,where D is thedistance to the supernova)at wavelength∆λ=λ−λ0=λ0zv ph/cr ph=λ0z/ct.Thefirst term in Eqn.(3)accounts for theflux coming directly from the photosphere,and the second term for photons scattered or created to emerge along the line of site.We have assumed for convenience an infinite atmosphere although none of our results is altered in the case that the atmosphere terminates at some radius r max.For z<0,the integral has three terms in general,with the third term in Eqn.(4)now representing the region where material intervening between the photosphere and the observer leads to absorption of the continuum radiation:F(z)p20I ph+ ∞p0S(r)(1−ζ(r))p dp+ r ph p0I phζ(r)p dp.2The limit p0is given by the p location of the spherical photosphere for a given z,namelyp0=2r phWe consider the inversion of each region of the line in turn,beginning with the mid region. The mid region of the line profile turns out to be only sensitive to the optical depth of the line near the ing Eqn.(4),we change the integration variable from p to r=f(z)= r ph|z|r dr+ ∞r ph s(r)(1−ζ(r))r dr+2obscured by the optical depth of the line.One then expects the derivative d fdz η(z)ξ(z)g(t)dt=g(η)dηdz(6) Applying Eqn.(6)to Eqn.(5)allows us to solve forζ(r):ζ(r= 2|z|d f2|∆λ|d f c 2(7)which is valid for−r ph<z<0.In using Eqn.(7)to calculateζ(r)from a spectrum,one can choose either∆λ,z,or r as the independent parameter.For instance,from∆λ(which is always less than zero for Eqn.[7])the other two parameters are determined by z=r ph(∆λ/λ0)(c/v ph) and r==0and hencedzζ=1(i.eτ=0).Thus the absence of a feature implies either negligible line optical depth or the breakdown of our assumptions–in this formalism there is no choice for the source function that allows a line to“erase”itself.A stair-step mid region could be a signal that the optical depth near the photosphere is oscillating between small and large values(i.e.the medium is clumpy).Note that sinceζ≤1,Eqn.(7)implies that the derivative d fdz≥0also implies that an emission feature cannot peak blueward of its rest wavelength(at the most it can remainflat into the mid region as one would have for a detached atmosphere).However,the peaks of emission features are indeed found to be blue-shifted,both in real data and in spherically symmetric NLTE models.Jeffery&Branch(1990)and Duschinger et al. (1995)attribute the blueshift to an NLTE effect where a large source function near the photosphere enhances theflux in the mid region.Under our assumptions this cannot be correct,since Eqn.(5) shows that the shape of the mid region is independent of the source function.Various second order physical effects,not included in the inversion formulae,could possibly explain the blueshifts,for example:continuous opacity added to the model could preferentially extinguish photons from the red side of the envelope;an absorption from another line to the red could cut into the emission peak;a large slope in the continuum could shift the peak;clumpiness of the photosphere(Wang &Hu1994)could break the spherical symmetry of the problem;relativistic effects can cause asignificant blueshift for high photospheric velocities(≥approximately15,000km/s(Jeffery1993)); or line-scattered light could be diffusely reflected offand blueshifted by the photosphere,causing a blueshift of the emission peak(Chugai1988).A few points must be made concerning the applicability of Eqn.(7):(1)near the rest wavelength the equation may not yield reliable results,since the∆λin the denominator goes to zero and must be delicately canceled by theflux derivative also going to zero.Thus any noise in theflux derivative (which must be evaluated numerically from the data)will be inflated at small∆λ.(2)one can not extract realistic values forτ≫1sinceζdepends exponentially onτ.One will knowτis large but not its exact value;(3)at late times(the nebular phase)the photosphere may become negligibly small and so there is no mid region–in this case,as we will see,our analysis reduces to that of Ignace&Hendry(2000);(4)Eqn.(7)only gives the value ofζfor the radial region r ph<r<√2r ph the optical depth has already fallen to1/16of its photospheric value.Nevertheless,in the following we show how it is possible to extend the solution forζ(r)to arbitrary r by using information from the blue and red sides of the line profile.3.2.Inversion for S(r)We next consider the inversion of the red side of the line,which will allow us to solve for the source function.Changing variables in Eqn.(3),we see that theflux is now given by a source term plus an unobstructed photosphere term:r2ph2r2ph+ ∞r2ph+z2)=−r2ph2zd f1−ζ(r)λ20d∆λ v phFor large optical depth,ζ=0,and the shape of the red side depends on the source function only.Since s ≥0and ζ≤1we must have d f2r phFinally the flux from the blue side of the profile will allow us to extend the solution of ζto large r .The flux is given by a source term plus a fully obstructed photosphere:r 2phr 2ph +z 2|z |ζ(r )r dr.(10)The same differentiation technique yields:ζ(r = 2|z |d f2z +d f (z +)z 2−r 2ph.Combining Eqns.(11)and (12)we obtain:ζ(r =2 v ph∆λd f ct |∆λ|d f ct .where |z |>r ph is the independent parameter for evaluating ζ(r = dz .Given ζ(r )for r ∈[nr ph ,√n +1r ph ,√2r ph ],givenby Eqn.(7),we can in fact use Eqn.(13)to find ζ(r )for all r .4.DiscussionFor late times when the photosphere becomes negligibly small (r ph −→0),the mid region disappears and Eqn.(7)becomes meaningless.We cannot use the reduced quantities f (z )and s (r )in this case.Instead the counterpart to Eqns.(8)and(10)is:F(z)2π1dz=−1ct 21d∆λ(15)where r=|z|=ct|∆λ|.Since the profile is symmetric one obtains the same information using either z≤0or z≥0.Thus without a photosphere it is not possible to separate S andζ,however the product S{1−ζ}can be determined for all radii.To demonstrate that the above equations really do allow for a clean inversion,we have generated line profiles under the given assumptions and using S(r)andτ(r)given by power laws of various exponents.Figure2shows that the power law behavior can be recovered by applying the inversion formulae to the line shape.Although here we have assumed that the functions are monotonically decreasing with r,this is not a necessary condition for our derivations and the formulae apply also for non-monotonic distributions.Because the inversions in Figure2were applied to pristine model lines,the results show very little noise(the small amount is due to numerical error),however in application to real data,the quality of the inversion will of course depend upon the signal to noise and spectral resolution of the data.Because derivatives are especially sensitive to a high frequency noise component,smoothing of the spectrum or some other stabilization technique may need to be applied,which typically amounts to assuming a priori some level of smoothness of the functionsτ(r)and S(r)(c.f.Craig &Brown1986).5.ConclusionEqns.(7),(9),and(13),taken together constitute a complete analytic inversion of supernova lines in the Sobolev approximation.Given the present assumptions,some of the more interesting facts are:(1)the steepness of the mid region reflects the size of the optical depth;(2)the absence of a line implies negligible optical depth;(3)a jagged mid region signals a clumpy absorbing region near the photosphere;(4)the emission feature may have no rising humps;(5)emission features cannot be blueshifted or redshifted simply by varying the line source function or optical depth. When applied under the right circumstances,the formulae may provide useful information on the physical conditions in the atmosphere as well as constraints on supernova explosion models.It is also interesting that this inversion problem possesses a unique solution for both S(r)and τ(r).A persistent worry in supernova modeling is that very different physical parameters may leadto identical looking synthetic spectra.The analytic solutions above demonstrate that,at least in principle,each different choice of S(r)andτ(r)produces a distinct line profile(although in practice it may be impossible to discern the differences from noisy data).Although for more general models the inversion will not be unique,the success in the present case does give some support that a good fit to a line does indeed imply realistic physical parameters.We would like to thank Peter Nugent and R.Ignace for helpful comments and suggestions. This work was supported in part by NSF grants AST-9731450,AST-9986965and NASA grant NAG5-3505.REFERENCESBranch,D.et al.1983,ApJ,270,123Castor,J.I.1970,MNRAS,149,111Castor,J.I.&Nussbaumer,H.1972,MNRAS,155,293Chugai,N.N.1988,Soviet Astronomy Letters,14,334Craig,I.&Brown,J.1986,Inverse Problems in Astronomy(Bristol:Adam Hilger Ltd)Deng,J.S.,Qiu,Y.L.,Hu,J.Y.,Hatano,K.,&Branch,D.2000,ApJ,540,452 Duschinger,M.,Puls,J.,Branch,D.,H¨oflich,P.,&Gabler,A.1995,A&A,297,802 Fransson,C.&Chevalier,R.1989,ApJ,343,323Hamann,W.-R.1981,A&A,93,353Ignace,R.&Hendry,M.A.2000,ApJ,537,L131Jeffery,D.&Branch,D.1990,in Supernovae,ed.J.C.Wheeler&T.Piran(Singapore:World Scientific),149Jeffery,D.J.1993,ApJ,415,734Mazzali,P.A.,Lucy,L.,&Butler,K.1992,A&A,258,399Mihalas,D.1978,Stellar Atmospheres(New York:W.H.Freeman)Millard,J.,Branch,D.,Baron,E.,Hatano,K.,Fisher,A.,Filippenko,A.V.,et al.1999,ApJ,527, 746Olson,G.1982,ApJ,255,267Pauldrach,A.,Puls,J.,&Kudritzki,R.P.1986,A&A,164,86Rybicki,G.B.&Hummer,D.G.1978,ApJ,219,654Sobolev,V.V.1960,Moving Envelopes of Stars(Cambridge,MA:Harvard Univ.Press) Wang,L.&Hu,J.1994,Nature,369,380Fig. 1.—Schematic diagram of how line profiles are calculated in the Sobolev approximation. Thefigure is a cross-sectional view of the supernova with the sphere in the center representing the photosphere.The dotted/dashed lines show the region of integration for three points on the line profile,one each on the red side,the mid region,and the blue side.In each case the integration over that region of the atmosphere produces theflux at the wavelength where the dotted line intersects the line profile.On the mid and red side,the dashed lines represent the region of the atmospherewhere light comes directly from the photosphere.Fig.2.—Examples of the application of the inversion formulae.Panels(a)and(b)show the source function and optical depth obtained from the inversion of line profiles generated with the same source function S=W(r),but different power indices(n=2,4,8,12)for the optical depth.Panels (c)and(d)show the the source function and optical depth obtained from the inversion of line profiles generated with the same optical depth power law(n=8),but different source functions (S(r)∝r−n,n=0,1,2,4).The solid lines are the exact input functions and the diamonds are the functions extracted using the inversion formulae.The small amount of noise in the plots is due to numerical error.。
