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Diagonal Crossed Products by Duals of Quasi-Quantum Groups

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a rXiv:q -alg/9784v14A ug1997Diagonal Crossed Products by Duals of Quasi–Quantum Groups Frank Haußer ∗and Florian Nill †Freie Universit¨a t Berlin,Institut f¨u r theoretische Physik,Arnimallee 14,D-14195Berlin,Germany February 9,2008Abstract A two-sided coaction δ:M →G ⊗M⊗G of a Hopf algebra (G ,∆,ǫ,S )on an associative algebra M is an algebra map of the form δ=(λ⊗id M )◦ρ=(id M ⊗ρ)◦λ,where (λ,ρ)is a commuting pair of left and right G -coactions on M ,respectively.Denoting the associated commuting right and left actions of the dual Hopf algebra ˆG on M by ⊳and ⊲,respectively,we define the diagonal crossed product M ⊲⊳ˆG to be the algebra generated by M and ˆG with relations given by ϕm =(ϕ(1)⊲m ⊳ˆS −1(ϕ(3)))ϕ(2),m ∈M ,ϕ∈ˆG .We give a natural generalization of this construction to the case where G is a quasi–Hopf algebra in the sense of Drinfeld and,more generally,also in the sense of Mack and Schomerus (i.e.,where the coproduct ∆is non-unital).In these cases our diagonal crossed product will still be an associative algebra structure on M ⊗ˆG extending M ≡M ⊗ˆ1,even though the analogue of an ordinary crossed product M ⋊ˆG in general is not well defined as an associative algebra.Applications of our formalism include the field algebra constructions with quasi-quantum group symmetry given by Mack and Schomerus [MS,S]as well as the formulation of Hopf spin chains or lattice current algebras based on truncated quantum groups at roots ofunity.In the case M =G and λ=ρ=∆we obtain an explicit definition of the quantum double D (G )for quasi–Hopf algebras G ,which before had been described in the form of an implicit Tannaka-Krein reconstruction procedure by S.Majid [Ma2].We prove that D (G )is itself a (weak)quasi-bialgebra and that any diagonal crossed product M ⊲⊳ˆG naturallyadmits a two-sided D (G )-coaction.In particular,the above mentioned lattice models always admit the quantum double D (G )as a localized cosymmetry,generalizing results of Nill and Szlach´a nyi [NSz1].A complete proof that D (G )is even a (weak)quasi-triangular quasi-Hopf algebra will be given in a separate paper [HN1].Contents1Introduction and summary of results3I The Coassociative Setting7 2Coactions and crossed products8 3Two-sided coactions and diagonal crossed products12 4Examples and applications164.1Double crossed products (16)4.2Two–sided crossed products (17)4.3Hopf spin chains and lattice current algebras (19)5Generating matrices21 II The Quasi–Coassociative Setting23 6Definitions and properties of quasi-Hopf algebras25 7Coactions of quasi–Hopf algebras28 8Two–sided coactions30 9The representation theoretic interpretation33 10Diagonal crossed products3910.1The algebrasˆG⊲⊳δM and M⊲⊳δˆG (40)10.2Left and right diagonalδ–implementers (44)10.3Coherentλρ–intertwiners (49)10.4Proof of the main theorem (53)11Examples and applications5511.1The quantum double D(G) (55)11.2Two–sided crossed products (58)11.3Hopf spin chains and lattice current algebras (59)11.4Field algebra construction with quasi–Hopf symmetry (62)III Weak quasi–Hopf algebras63 12Weak quasi–bialgebras65 13Weak coactions66 14Diagonal crossed products67 15Examples and applications69 Appendix69 References741Introduction and summary of resultsDuring the last decade quantum groups have become the most fashionable candidates describing the symmetry in low dimensional quantumfield theories(QFT)1or lattice models2.Here,in an axiomatic approach by a“symmetry algebra”G one means a∗-algebra acting on the Hilbert space of physical states H,such that•observables and space-time translations commute with G,•charge creatingfields fall into multiplets transforming covariantly under the action of G,•equivalence classes of irreducible representations of G are in one-to-one correspondence with the Doplicher-Haag-Roberts(DHR)superselection sectors of the observable algebra A,such that also the fusion rules of Rep DHR A and Rep G coincide.It is well known that the results of Doplicher-Roberts[DR]characterizing G as a compact group (or the associated group algebra)break down in low dimensions due to the appearance of braid statistics.It was soon realized that at least for rational theories(i.e.with afinite number of sectors)quantum groups are also ruled out,unless all sectors have integer statistical dimensions (see e.g.[FrKe]for a review or[N2]for a specific discussion of q-dimensions infinite quantum groups).Based on the theory of quasi-Hopf algebras introduced by Drinfel’d[Dr2],G.Mack and V. Schomerus[MS]have proposed the notion of weak quasi-Hopf algebras G as appropriate symme-try candidates,where“weak”means that the tensor product of two“physical”representations of G may also contain“unphysical”subrepresentations(i.e.of q-dimension≤0),which have to be discarded.Examples are semisimple quotients of q-deformations of classical groups at q= roots of unity.In this way non-integer dimensions could successfully be incorporated.The price to pay was that now commutation relations of G-covariant chargedfields involve operator valued R-matrices and,more drastically,the operator product expansion for G-covariant multiplets of chargedfields involves non-scalar coefficients with values in G.Thus,the analogue of the “would-be”DHR-field algebra F is no longer algebraically closed.Instead,Mack and Schomerus have proposed a new“covariant product”for chargedfields,which does not lead outside of F, but which is no longer associative.In[S]Schomerus has analyzed this scenario somewhat more systematically in the framework of DHR-theory,showing that a weak quasi-Hopf algebra G and afield“algebra”F may always be constructed such that the combined algebra F∨G is associative and satisfies all desired properties,except that F⊂F∨G is only a linear subspace but not a subalgebra.Technically,the reason for this lies in the fact that the dualˆG of a quasi-Hopf algebra is not an associative algebra.One should also remark at this point that the above reconstruction of G from the category of DHR-endomorphisms is not unique.Also,in a more mathematical framework a general Tannaka-Krein like reconstruction theorem for quasi-Hopf algebras has been obtained by S. Majid[M1]and for weak quasi–Hopf algebras by[H¨a].To study quantum symmetries on the lattice in an axiomatic approach,K.Szlach´a nyi and P.Vecsernyes[SzV]have proposed an“amplified”version of the DHR-theory,which also applies to locallyfinite dimensional lattice models.This setting has been further developedby[NSz1,2],where based on the example of Hopf spin chains the authors proposed the notion of a universal localized cosymmetryρ:A→A⊗G,incorporating all sectorsρI of A via ρI=(id A⊗πI)◦ρ,πI∈Rep G.In the specific example studied by[NSz1,2]G was given by a quantum double and the cosymmetryρwas given by a coaction of G on A.Related results have later been obtained for lattice current algebras[AFFS],the later actually being a special case of the Hopf spin chains of[NSz1,2](see[N1]and Sect.11.3).The analogue of a DHR–field algebra for these models is now given by the standard crossed product F≡A⋊ˆG[NSz2], whereˆG is the Hopf algebra dual to G.Now the methods and results of these works were still restricted to ordinary Hopf algebras and therefore to integer dimensions.To formulate lattice current algebras at roots of unity one may of course identify them with the boundary part of lattice Chern-Simons algebras[AGS,AS] defined on a disk.Nevertheless,it remains unclear whether and how for q=root of unity the structural results of[AFFS]survive the truncation to the semi-simple(“physical”)quotients. Similarly,the generalizations of the model,the methods and the results of[NSz]to weak quasi quantum groups are by no means obvious.In particular one would like to know whether and in what sense in such models universal localized cosymmetriesρ:A→A⊗G still provide coactions and whether G would still be(an analogue of)a quantum double of a quasi-Hopf algebra,possibly in the sense recently described by Majid[M2].In this work we present a theory of left,right and two-sided coactions of a(weak)quasi-Hopf algebra G on an associative algebra M.Based on these structures we then provide a new construction of what we call the diagonal crossed product M⊲⊳ˆG,which we will show to be the appropriate mathematical structure underlying all constructions discussed above.In particular,M⊲⊳ˆG will always be an associative algebra extending M≡M⊲⊳ˆ1.On the other hand,the linear subspace1M⊲⊳ˆG will in general not be a subalgebra of M⊲⊳ˆG,unless G is an ordinary(i.e.coassociative)Hopf algebra.The basic idea for this construction comes from generalizing the relations defining the quantum double.To this end we start from an algebra M equipped with a(quasi-)commuting pair of right and left G-coactions,ρ:M→M⊗G andλ:M→G⊗M and denote δℓ:=(λ⊗id)◦ρandδr:=(id⊗ρ)◦λas the associated equivalent two-sided coactions.In the simplest case of G being an ordinary Hopf algebra and(λ,ρ)being strictly commuting(i.e.δℓ=δr)this amounts to providing a commuting pair of left and right Hopf module actions ⊲:ˆG⊗M→M(dual toρ)and⊳:M⊗ˆG→M(dual toλ)of the dual Hopf algebraˆG on M.In this case our diagonal crossed product M⊲⊳ˆG is defined to be generated by M andˆG as unital subalgebras with commutation relations given by(ˆS:ˆG→ˆG being the antipode)ϕm=(ϕ(1)⊲m⊳ˆS−1(ϕ(3)))ϕ(2),m∈M,ϕ∈ˆG.(1.1) Note that for M=G andρ=λ=∆the coproduct on G,these are the defining relations of the quantum double D(G)[Dr1],and therefore G⊲⊳ˆG=D(G).Introducing the“generating matrix”Γ:= µeµ⊗eµ∈G⊗ˆG⊂G⊗(M⊲⊳ˆG),where eµ∈G is a basis with dual basis eµ∈ˆG,Eq.(1.1)is equivalent toΓλ(m)=ρop(m)Γ,∀m∈M.(1.2) Moreover,in this caseˆG⊂M⊲⊳ˆG being a unital subalgebra is equivalent to(ǫ⊗id)(Γ)=1(1.3)Γ13Γ23=(∆⊗id)(Γ)(1.4)where (1.4)is an identity in G ⊗G ⊗(M ⊲⊳ˆG ),the indices denoting the embeddings of tensor factors.We call Γthe universal normal and coherent λρ-intertwiner in G ⊗(M ⊲⊳ˆG),where normality is the property (1.3)and coherence is the property (1.4).Again,for M =G and M ⊲⊳G =D (G )Eqs.(1.2)-(1.4)are precisely the defining relations for the generating matrix D ≡ΓD (G )of the quantum double (see e.g.[N1,Lem.5.2]).Inspired by the techniques of [AGS,AS]we show in the main body of this work how to generalize the notion of coherent λρ-intertwiners to the case of (weak)quasi-Hopf algebras G ,such that analogues of the Eqs.(1.2)-(1.4)still serve as the defining relations of an associative algebra extending M ≡M ⊲⊳ˆ1.We also show that diagonal crossed products may equivalently be modeled on the linear spaces M ⊗ˆGor ˆG ⊗M (or –in the weak case –certain subspaces thereof).The basic model for this generalization is again given by M =G with its natural two-sided G -coactions δℓ:=(∆⊗id)◦∆and δr :=(id ⊗∆)◦∆.In this case our construction provides a definition of the quantum double D (G )for (weak)quasi-Hopf algebras G .In fact,we show that Rep D (G )coincides with what has been called the “double of the category”Rep G in [M2].Hence our definition provides a concrete realization of the abstract Tannaka-Krein like reconstruction of the quantum double given by [M2].We also give a proof that D (G )is a (weak)quasi-bialgebra.In [HN1]we will show,that D (G )is in fact a (weak)quasi-triangular quasi-Hopf algebra,and there we will also visualize many of our (otherwise almost untraceable)algebraic identities in terms of graphical proofs.The field algebra construction of [MS,S]may also be described as a diagonal crossed product M ⊲⊳ˆGwithin our formalism by putting M =A ⊗G ,where A is the observable algebra.In this case the right G -coaction ρ:M →M ⊗G is a localized cosymmetry acting only on A ,whereas the left G -coaction λ:M →G ⊗M only acts on G ,where it is given by the coproduct ∆,see Sect.11.4for a rough sketch.A more detailed account of this within an appropriate von-Neumann algebraic framework will be given elsewhere.The application of our formalism to G -spin quantum chains is given by putting in the previous example also A =G and ρ=∆,in which case M ⊲⊳ˆG ∼=G ⋊ˆG⋉G becomes a two–sided crossed product .We take this construction as building block of a quantum chain living on two neighboring sites (carrying the copies of G )joined by a link (carrying the copy of ˆG).We show how this construction iterates to provide a local net of associative algebras A (I )for any lattice interval I bounded by sites.Generalizing the methods of [NSz]we also construct localized coactions of the quantum double D (G )on such (weak)quasi-Hopf spin chains.Periodic boundary conditions for these models are again described as a diagonal crossed product of the open chain by a copy of ˆGsitting on the link joining the end points.In this way we arrive at a formulation of lattice current algebras at roots of unity by adjusting the transformation rules of [N1]to the quasi-coassociative setting.We expect to have more detailed results also on these models in the near future.We now describe the plan of this paper.In Part I we prepare our language and develop our basic ideas within a strictly coassociative setting,putting emphasis on a pedagogical pre-sentation of the “read thread”.In Sect.2we start with reviewing the notions of left and right coactions and crossed products.In Sect.3we introduce two-sided coactions δ:M →G⊗M⊗G and identify them with pairs (λ,ρ)of commuting left and right coactions.We then define the diagonal crossed product M λ⊲⊳ρˆG and show that it may be identified with the subalgebra of ˆG λ⋉M ⋊ρˆG generated by M and the “diagonal”ˆ∆op (ˆG )⊂ˆG ⊗ˆG .For M =G this gives the quantum double D (G ).Moreover any diagonal crossed product M ⊲⊳ˆGcanonically admits a two-sided D (G )-coaction.In Sect.4we give examples and applications of our formalism.Section4.1discusses the relation of our diagonal crossed products with Majid’s notion of double crossed products[M3,4]. In Section4.2we introduce two-sided crossed products A⋊ˆG⋉B as special examples obtained for the case M=A⊗B,whereρacts trivially on B andλacts trivially on A.By putting A=B=G and iterating,these become the building structures of Hopf spin chains described in Section4.3.In Sect.5we reformulate our constructions using the generating matrix formalism.This leads to the description of diagonal crossed products as being generated by M and the“matrix entries”of a normal coherentλρ-intertwinerΓ∈G⊗(M⊲⊳ˆG)subjected to the relations (1.2)-(1.4).This is the appropriate language to be generalized to the quasi-coassociative setting in Part II.Sect.6starts with a short review of Drinfeld’s axioms for quasi-Hopf algebras G and some of their properties.In Sects.7and8we provide a generalization of the notions of left, right and two-sided G-coactions on an associative algebra M.We also show that up to twist equivalence two-sided G-coactions are in one-to-one correspondence with quasi-commuting pairs of(left and right)G-coactions(λ,ρ).In Sect.9we give a representation theoretic interpretation of these concepts by showing that they give rise to left,right and two-sided“actions”of Rep G on Rep M,respectively.By this we mean that representationsγof M may be“tensored”with representationsπof G to yield again representations of M,such that an analogue of McLane’s natural associativity constraints for monoidal categories is satisfied.This formalism allows to motivate and explain many otherwise almost untraceable algebraic identities in terms of commuting diagrams.Yet, the most technical parts of these proofs are deferred to an Appendix.In Sect.10we proceed to the generalized construction of diagonal crossed products asso-ciated with any two-sided G-coactionδ:M→G⊗M⊗G.Sect.10.1gives the associativity proof and states the equivalence of a“left”and a“right”convention for this construction.In Sect.10.2we describe these two conventions by the associated generating matrices L and R, called left(right)diagonalδ-implementers.In Sect10.3we generalize the notion of coherent λρ-intertwinersΓto the quasi-coassociative setting and show that they are always in one-to-one correspondence with the above coherent left(or right)diagonalδ-implementers.This provides a proof of our main result in Sect.10.4,showing that diagonal crossed products are uniquely(up to equivalence)described by a quasi-coassociative version of the relations(1.2)-(1.4),see Theo-rem II on page24.In Sect.11we provide examples and applications by discussing the quantum double D(G),the two-sided crossed products A⋊ˆG⋉B and their appearance in quasi-Hopf spin chains and lattice current algebras,andfinally a reformulation of the Mack-Schomerus scenario within our formalism.Finally,in Part III we generalize all results to weak quasi-Hopf algebras G.In conclusion we point out that most of our algebraic constructions are based on represen-tation categorical concepts and may therefore also be visualized by graphical proofs.We will put more emphasis on this technique in[HN1]when providing further results on the quantum double D(G).We also remark that without mentioning explicitly at every instance the(weak,quasi)Hopf algebras G are always supposed to befinite dimensional.Although we believe that many aspects of our formalism would also carry over to an infinite dimensional setting,we don’t consider it worthwhile to discuss this complication at present.More importantly,in applications to quantum physics one should extend our formalism to incorporate C∗-or von-Neumann algebraic structures,which we will come back to in the near future when discussing our examples in more detail.Part IThe Coassociative SettingTo strip offall technicalities from the main ideas,in thisfirst part we restrict ourselves to strictly coassociative Hopf algebras G.Throughout by an algebra we will mean an associative unital algebra over C and unless stated differently all algebra morphisms are supposed to be unit preserving.Given an algebra M,two algebra extensions M1⊃M and M2⊃M are called equivalent,if there exists an isomorphism M1∼=M2restricting to the identity on M. The main result we are going for is given byTheorem I Let(G,∆,ǫ,S)be afinite dimensional Hopf algebra and let(λ,ρ)be a commuting pair of(left and right)G–coactions on an associative algebra M.1.Then there exists a unital associative algebra extension M1⊃M together with a linearmapΓ:ˆG−→M1satisfying the following universal property:M1is algebraically generated by M andΓ(ˆG)and for any algebra mapγ:M−→A into some target algebra A the relationγT(Γ(ϕ))=(ϕ⊗id)(T),ϕ∈ˆG(1.5) provides a one–to–one correspondence between algebra mapsγT:M1−→A extendingγand elements T∈G⊗A satisfying(ǫ⊗id A)(T)=1A andTλA(m)=ρop A(m)T,∀m∈M(1.6)T13T23=(∆⊗id A)(T),(1.7) whereλA(m):=(id G⊗γ)(λ(m))andρA(m):=(γ⊗id G)(ρ(m)).2.If M⊂˜M1and˜Γ:ˆG−→˜M1satisfy the same universality property as in part1.),thenthere exists a unique algebra isomorphism f:M1−→˜M1restricting to the identity on M,such that˜Γ=f◦Γ3.The linear mapsµL:ˆG⊗M∋(ϕ⊗m)→Γ(ϕ)m∈M1(1.8)µR:M⊗ˆG∋(m⊗ϕ)→mΓ(ϕ)∈M1(1.9) provide isomorphisms of vector spaces.PuttingΓ:=eµ⊗Γ(eµ)∈G⊗M1Theorem II implies thatΓitself satisfies the defining relations(1.6)and(1.7),see also(1.2)and(1.4).We callΓthe universalλρ–intertwiner in M1.We emphasize that once being stated Theorem I almost appears trivial.Its true power only arises when generalized to the quasi-coassociative setting in Part II.Note that part2.ofTheorem I implies that the algebraic structures induced onˆG⊗M and M⊗ˆG viaµ−1L/R fromM1are uniquelyfixed.We denote them asˆGλ⊲⊳ρM≡µ−1L(M1)(1.10)Mλ⊲⊳ρˆG≡µ−1R(M1).(1.11) and call them left(right)diagonal crossed products,respectively.(The right diagonal version (1.11)will be shown to be the one described by Eq.(1.1)).To actually prove Theorem I we willfirst construct the algebras Mλ⊲⊳ρˆG andˆGλ⊲⊳ρM explicitly as equivalent extensions of M in Proposition3.3and Corollary3.7,respectively.The description in terms of(λ,ρ)-intertwiners will then be given in Sect.5.In order to carefully prepare the much more complicated quasi-coassociative scenario we deliberately present these arguments in rather elementary steps.2Coactions and crossed productsTofix our conventions and notations we start with shortly reviewing some basic notions on Hopf module actions,coactions and crossed products.For full textbook treatments see e.g. [A,M3,Sw].Let G andˆG be a dual pair offinite dimensional Hopf algebras.We denote elements of G by Roman letters a,b,c,...and elements ofˆG by Greek lettersϕ,ψ,ξ,....The units are denoted by1∈G andˆ1∈ˆG.IdentifyingˆˆG=G,the dual pairing G⊗ˆG→C is written asa|ψ ≡ ψ|a ∈C,a∈G,ψ∈ˆG.We denote∆:G→G⊗G the coproduct,ǫ:G→C the counit and S:G→G the antipode. Similarly,ˆ∆,ˆǫandˆS are the structural maps onˆG.We will use the Sweedler notation∆(a)= a(1)⊗a(2),(∆⊗id)(∆(a))≡(id⊗∆)(∆(a))=a(1)⊗a(2)⊗a(3),etc.where the summation symbol and the summation indices are suppressed.Together with G we have the Hopf algebras G op,G cop and G copop,where“op”refers to opposite multiplication and“cop”to opposite comultiplication.Note that the antipode of G op and G cop is given by S−1and the antipode of G copop by S.Also, G op=(ˆG)cop, G cop=(ˆG)op and G cop op=(ˆG)cop op.A right coaction of G on an algebra M is an algebra mapρ:M→M⊗G satisfying(ρ⊗id)◦ρ=(id⊗∆)◦ρ(2.1)(id⊗ǫ)◦ρ=id(2.2) Similarly,a left coactionλis an algebra mapλ:M→G⊗M satisfying(id⊗λ)◦λ=(∆⊗id)◦λ(2.3)(ǫ⊗id)◦λ=id(2.4) Obviously,after a permutation of tensor factors M⊗G↔G⊗M a left coaction of G may always be viewed as a right coaction by G cop and vice versa.Similarly as for coproducts we will also use the suggestive notationsρ(m)=m(0)⊗m(1)(2.5) (ρ⊗id)(ρ(m))≡(id⊗∆)(ρ(m))=m(0)⊗m(1)⊗m(2)(2.6)λ(m)=m(−1)⊗m(0)(2.7) (∆⊗id)◦λ≡(id⊗λ)(λ(m))=m(−2)⊗m(1)⊗m(0)(2.8)etc.,where again summation indices and a summation symbol are suppressed.In this way we will always have m(i)∈G for i=0and m(0)∈M.Next,we recall that there is a one-to-one correspondence between right(left)coactions of G on M and left(right)Hopf module actions, respectively,ofˆG on M given forψ∈ˆG and m∈M byψ⊲m:=(id⊗ψ)(ρ(m))(2.9)m⊳ψ:=(ψ⊗id)(λ(m))(2.10) One easily verifies the defining properties of Hopf module actions,i.e.ϕ⊲(ψ⊲m)=(ϕψ)⊲m,(m⊳ϕ)⊳ψ=m⊳(ϕψ)ˆ1⊲m=m,m⊳ˆ1=m(2.11)ϕ⊲(mn)=(ϕ(1)⊲m)(ϕ(2)⊲n),(mn)⊳ϕ=(m⊳ϕ(1))(n⊳ϕ(2))ϕ⊲1M=ˆǫ(ϕ)1M,1M⊳ϕ=1Mˆǫ(ϕ)whereϕ,ψ∈ˆG and m,n∈M.As a particular example we recall the case M=G with ρ=λ=∆.In this case we denote the associated left and right actions ofψ∈ˆG on a∈G by ψ⇀a and a↼ψ,respectively.Given a right coactionρ:M→M⊗G with dual leftˆG-action⊲one defines the(untwisted) crossed product(also called smash product)M⋊ˆG to be the vector space M⊗ˆG with associative algebra structure given for m,n∈M andϕ,ψ∈ˆG by(m⋊ϕ)(n⋊ψ)=(m(ϕ(1)⊲n)⋊ϕ(2)ψ)(2.12) where we use the notation m⋊ψin place of m⊗ψto emphasize the new algebraic structure. Then1M⋊ˆ1is the unit in M⋊ˆG and m→(m⋊ˆ1),ϕ→(1M⋊ϕ)provide unital inclusions M→M⋊ˆG andˆG→M⋊ˆG,respectively.Similarly ifλ:M→G⊗M is a left coaction with dual right action⊳thenˆG⋉M denotes the associative algebra structure onˆG⊗M given by(ϕ⋉m)(ψ⋉n)=(ϕψ(1)⋉(m⊳ψ(2))n)(2.13) containing again M andˆG as unital subalgebras.If there are several coactions under consid-eration we will also write M⋊ρˆG andˆG⋉λM,respectively.We note that Eq.(2.12)implies that as an algebraM⋊ˆG=MˆG=ˆGM(2.14) where we have identified M≡M⋊ˆ1andˆG≡1M⋊ˆG.In fact using the antipode axioms one easily verifies from(2.12)m⋊ϕ=(m⋊ˆ1)(1M⋊ϕ)=(1M⋊ϕ(2))((ˆS−1(ϕ(1))⊲m)⋊ˆ1)(2.15) Similar statements hold inˆG⋉M.More generally we haveLemma 2.1.Let⊲:ˆG⊗M→M be a left Hopf module action and let A be an algebra containing M andˆG as unital subalgebras.Then in A the relationϕm=(ϕ(1)⊲m)ϕ(2),∀ϕ∈ˆG,∀m∈M(2.16) is equivalent tomϕ=ϕ(2)(ˆS−1(ϕ(1))⊲m),∀ϕ∈ˆG,∀m∈M(2.17)and if these hold then MˆG=ˆGM⊂A is a subalgebra andM⋊ˆG∋(m⋊ϕ)→mϕ∈MˆG,(2.18) is an algebra epimorphism.The proof of Lemma2.1is obvious from the antipode axioms and therefore omitted.A similar statement of course holds for the crossed productˆG⋉M.As an application we remark that any left crossed productˆG⋉λM can be identified with an associated right crossed product(G op)and whereρ:M→M⊗G op is the right coaction given byM⋊ρˆG cop,whereˆG cop≡ρ=(id⊗S−1)◦τG,M◦λ(2.19)τG,M:G⊗M→M⊗G being the permutation of tensor factors.In fact we haveLemma 2.2.Letλ:M→G⊗M andρ:M→M⊗G op be a pair of left and right coactions, respectively,related by(2.19).Thenf(m⋊ϕ):=(ˆ1⋉m)(ϕ⋉1M)(2.20) defines an algebra isomorphism f:M⋊ρˆG cop→ˆG⋉λM with inverse given byf−1(ϕ⋉m)=(1M⋊ϕ)(m⋊ˆ1)(2.21) Proof.Let⊲:ˆG cop⊗M→M and⊳:M⊗ˆG→M be the left and right actions dual toρandλ,respectively.Then(2.19)is equivalent toϕ⊲m=m⊳ˆS−1(ϕ)for allϕ∈ˆG and m∈M. Putting A=ˆG⋉λM in Lemma2.1we have from(2.13)mϕ=ϕ(1)(ˆS(ϕ(2))⊲m)which is the relation(2.17)withˆG replaced byˆG cop.Hence,by Lemma2.1f is an algebra map whose inverse is easily verified to coincide with(2.21).We conclude this introductory part by describing crossed products in terms of the“generating matrix”formalism as advocated by the St.Petersburg school.Our presentation will closely follow the review of[N1].First we note that since G isfinite dimensional we may identify Hom C(ˆG,V)∼=G⊗V for any C-vector space V.In particular,the relationT(ϕ)=(ϕ⊗id)(T),∀ϕ∈ˆG,(2.22) provides a one-to-one correspondence between algebra maps T:ˆG→A into some target algebra A and elements T∈G⊗A satisfyingT13T23=(∆⊗id)(T)(2.23) where Eq.(2.23)is to be understood as an identity in G⊗G⊗A,the upper indices indicating the canonical embedding of tensor factors(e.g.T23=1G⊗T,etc.).Throughout,we will call elements T∈G⊗A normal,if(ǫ⊗id)(T)=1Awhich in Eq.(2.22)is equivalent to T:ˆG→A being unit preserving.In what follows,the target algebra A may always be arbitrary.In the particular case A=End V we would be talking of representations ofˆG on V,or more generally,as discussed in Lemma2.4below,of representations of M⋊ˆG orˆG⋉M,respectively,on V.Definition 2.3.Letλ:M→G⊗M be a left coaction and letγ:M→A be an algebra map.An implementer ofλin A(with respect toγ)is an element L∈G⊗A satisfying[1G⊗γ(m)]L=L[(id G⊗γ)(λ(m))](2.24) for all m∈M.Similarly,an implementer in A of a right coactionρ:M→M⊗G is an element R∈G⊗A satisfyingR[1G⊗γ(m)]=[(id⊗γ)(ρop(m))]R(2.25) whereρop=τM⊗G◦ρ.We remark that Eq.(2.25)suggests that for right coactions one should rather use the convention R∈A⊗G in place of introducingρop as a left coaction of G cop.However,for later purposes it will be more convenient to place the“auxiliary copy”of G in the definition of implementers always to the left of M.We now haveLemma 2.4.Letλ:M→G⊗M be a left coaction and letγ:M→A be an algebra map. Then the relationγL(ϕ⋉m):=(ϕ⊗id)(L)γ(m)(2.26)provides a one-to-one correspondence between algebra mapsγL:ˆG⋉λM→A extendingγand normal implementers L∈G⊗A ofλsatisfyingL13L23=(∆⊗id)(L)(2.27) Similarly,ifρ:M→M⊗G is a right coaction,then the relationγR(m⋊ϕ)=γ(m)(ϕ⊗id)(R)(2.28)provides a one-to-one correspondence between algebra mapsγR:M⋊ˆG→A extendingγand normal implementers R∈G⊗A ofρsatisfyingR13R23=(∆⊗id)(R)(2.29)Proof.Writing R(ϕ):=(ϕ⊗id)(R)≡γR(1M⋊ϕ)∈A and using Hom C(ˆG,A)∼=G⊗A the relation R↔γR is one-to-one.The implementer property(2.25)is then equivalent to R(ϕ)γ(m)=γ(ϕ(1)⊲m)R(ϕ(2))and R is normal iffγR is unit preserving.Together with the remarks(2.22)-(2.23)this is further equivalent toγR defining an algebra map,similarly as in Lemma2.1.The argument forγL is analogous.Next,we note that the equivalence(2.16)⇔(2.17)can be reformulated for implementers as followsLemma 2.5.Under the conditions of Lemma1.4denoteλ(m)=m(−1)⊗m(0)andρ(m)= m(0)⊗m(1)and let T∈G⊗A be normal.Dropping the symbolγwe then havei)T is an implementer ofρif and only if[1G⊗m]T=[S−1(m(1))⊗1A]T[1G⊗m(0)],∀m∈M(2.30) ii)T is an implementer ofλif and only ifT[1G⊗m]=[1G⊗m(0)]T[S−1(m(−1))⊗1A],∀m∈M(2.31)。

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小学下册第七次英语第四单元综合卷[有答案]

小学下册第七次英语第四单元综合卷[有答案]

小学下册英语第四单元综合卷[有答案]英语试题一、综合题(本题有50小题，每小题1分，共100分.每小题不选、错误，均不给分)1 What do we call a person who plays the guitar?A. PianistB. GuitaristC. DrummerD. Violinist2 The country known for its maple syrup is ________ (以枫糖浆闻名的国家是________).3 How many legs does a spider have?A. 6B. 8C. 10D. 12答案:B4 A substance that can donate protons in a reaction is called a _______.5 The bat flies at _____.6 The __________ (历史的回顾性) fosters reflection.7 I like to watch ______ (体育) events on TV.8 I love to ______ (与朋友一起) enjoy new experiences.9 The first modern Olympic Games were held in ________ (1896).10 A solution that contains a high concentration of ions is called a ______ solution.11 Carta was signed in _______. (1215年) The Magn12 We built a castle with our ____. (玩具名称)13 The boiling point of water is __________ (100度) Celsius at sea level.14 The chemical formula for glucose is ______.15 They are wearing _____ (sunglasses/hats) at the beach.16 The chemical formula for ammonia is __________.17 The _____ (小猫) loves to play with balls of yarn.18 A _______ is a special type of mixture with tiny particles that never settle.19 What is the name of the activity where you throw a ball into a hoop?A. BasketballB. FootballC. SoccerD. Baseball答案: A20 __________ are used in electrical circuits to control current flow.21 What is the largest mammal in the ocean?A. SharkB. DolphinC. WhaleD. Seal答案: C22 I like to go ______ (滑雪) during winter vacations.23 Which of these is a type of tree?A. RoseC. DaisyD. Tulip24 The first man to dive into the Mariana Trench was _______. (维尔德)25 She loves to _______ (sing) in the shower.26 What is the opposite of 'new'?A. UsedB. OldC. FreshD. Recent答案:B27 I can _____ my bed every morning. (make)28 The ______ is a talented actress.29 What is the capital city of Brazil?A. São PauloB. Rio de JaneiroC. BrasíliaD. Salvador答案:C30 A _______ can change colors throughout the seasons.31 The area where an oceanic plate meets a continental plate is called a ______.32 The classroom is ________ and clean.33 What instrument has keys and is played by pressing?A. GuitarB. ViolinD. Flute答案:C34 What is the largest continent?A. AfricaB. AsiaC. EuropeD. North America答案:B35 The ________ (藤) climbs up the wall.36 The boat is ___ (sailing) on the water.37 I can ________ (ride) a skateboard.38 The _______ in the garden are blooming beautifully.39 My favorite toy is a stuffed ______.40 My favorite toy is a ______ (机器人). It can talk and ______ (跳舞).41 We have a ______ (特别的) event this weekend.42 __________ are known to migrate long distances during winter.43 The boy is watching a ________.44 What is the name of the famous American holiday celebrated in December?A. ThanksgivingB. ChristmasC. New Year's DayD. Halloween答案:B45 The __________ is known for its diverse wildlife. (大堡礁)46 What is the name of the famous American actress known for "Gravity"?A. Sandra BullockB. Cate BlanchettC. Jennifer LawrenceD. Emma Stone答案：A47 His favorite game is ________.48 The __________ was a period of exploration and colonization. (大航海时代)49 The fish are ______ (swimming) in the pond.50 What is the capital of China?A. BeijingB. ShanghaiC. GuangzhouD. Shenzhen51 The __________ can provide critical insights into the impacts of climate change.52 What is the name of the famous American national park located in California?A. YellowstoneB. YosemiteC. Grand CanyonD. Zion答案：B53 What is the name of the process by which seeds grow into plants?A. GerminationB. PollinationC. FertilizationD. Propagation答案:A54 What is 15 divided by 3?A. 3B. 4C. 5D. 6答案:C55 A ______ is a substance that can exist in multiple states.56 The chemical formula for -ethoxybutanoic acid is ______.57 How many continents are there?A. 5B. 6C. 7D. 858 What do we call the process of liquid turning into vapor?A. CondensationB. FreezingC. EvaporationD. Sublimation答案:C59 A __________ (科学探索) expands our understanding of the natural world.60 Chemical reactions involve the breaking and forming of ________.61 Comets are often described as "dirty snowballs" made of ice and ______.62 A homogeneous mixture is uniform in _____.63 What do we call the first woman to fly solo across the Atlantic Ocean?A. Amelia EarhartB. Bessie ColemanC. Harriet QuimbyD. Jacqueline Cochran答案:A64 In a chemical equation, reactants are found on the ______.65 What do we call the primary source of energy for living organisms?A. WaterB. SunlightC. AirD. Food答案:B66 What is the main ingredient in mayonnaise?A. OilB. VinegarC. MustardD. Sugar67 He is _____ (playing/doing) video games.68 ts can be grown ______ (室内). Some pla69 My mom enjoys gardening and growing __________ (植物).70 Tokyo is the capital of __________.71 She is a friendly ________.72 What do you call the study of living things?A. BiologyB. ChemistryC. PhysicsD. Geography答案: A73 He is my _____ (好友) from childhood.74 Planting flowers can attract ______ (蜜蜂) to your garden.75 A __________ is a substance made up of only one type of atom.76 The ancient Romans celebrated festivals to honor their _____.77 What is the name of the famous detective created by Arthur Conan Doyle?A. Hercule PoirotB. Sam SpadeC. Sherlock HolmesD. Philip Marlowe答案: C78 What do we call a scientist who studies chemistry?A. ChemistB. BiochemistC. PhysicistD. Pharmacologist79 The _______ (The American Revolution) established the US as an independent nation.80 The flowers are ________ (多彩).81 The singer has a ______ (beautiful) voice.82 The ______ teaches us about different countries.83 What is the opposite of up?A. DownB. LeftC. RightD. Forward84 The study of matter and its changes is called _______. (化学)85 She is a _____ (护士) who helps deliver babies.86 Chemical reactions can be influenced by temperature and _____.87 __________ are found in many types of detergents.88 What do we call the part of the brain that controls balance?A. CerebrumB. CerebellumC. BrainstemD. Hypothalamus答案:B89 What is the main ingredient in bread?A. FlourB. SugarC. RiceD. Salt90 What do we call the process of water turning into vapor?A. CondensationB. EvaporationC. PrecipitationD. Sublimation答案:B91 The _______ of an atom is determined by the number of protons.92 I like to ______ (参与) in student council meetings.93 I saw a ________ hopping along the path.94 Which planet is known for its rings?A. MarsB. VenusC. SaturnD. Jupiter答案: C. Saturn95 Planting bulbs can lead to beautiful ______ (花朵) in spring.96 A hamster is a small ______.97 The __________ is a region known for its social movements.98 A crab can pinch with its ________________ (钳子).99 A _____ (植物分类) can help identify different species. 100 The kitten is ___ (pouncing) on a toy.。

药物分析英语词汇

药物分析英语词汇

药物分析英语词汇Abbe refractometer 阿贝折射仪absorbance 吸收度absorbance ratio 吸收度比值absorption 吸收absorption curve 吸收曲线absorption spectrum 吸收光谱absorptivity 吸收系数accuracy 准确度acid-dye colorimetry 酸性染料比色法acidimetry 酸量法acid-insoluble ash 酸不溶性灰分acidity 酸度activity 活度additive 添加剂additivity 加和性adjusted retention time 调整保留时间adsorbent 吸附剂adsorption 吸附affinity chromatography 亲和色谱法aliquot （一）份alkalinity 碱度alumina 氧化铝ambient temperature 室温ammonium thiocyanate 硫氰酸铵analytical quality control（AQC）分析质量控制anhydrous substance 干燥品anionic surfactant titration 阴离子表面活性剂滴定法antibiotics-microbial test 抗生素微生物检定法antioxidant 抗氧剂appendix 附录application of sample 点样area normalization method 面积归一化法argentimetry 银量法arsenic 砷arsenic stain 砷斑ascending development 上行展开ash-free filter paper 无灰滤纸（定量滤纸）assay 含量测定assay tolerance 含量限度atmospheric pressure ionization(API) 大气压离子化attenuation 衰减back extraction 反萃取back titration 回滴法bacterial endotoxins test 细菌内毒素检查法band absorption 谱带吸收baseline correction 基线校正baseline drift 基线漂移batch, lot 批batch(lot) number 批号Benttendorff method 白田道夫（检砷）法between day (day to day, inter-day) precision 日间精密度between run (inter-run) precision 批间精密度biotransformation 生物转化bioavailability test 生物利用度试验bioequivalence test 生物等效试验biopharmaceutical analysis 体内药物分析，生物药物分析blank test 空白试验boiling range 沸程British Pharmacopeia (BP) 英国药典bromate titration 溴酸盐滴定法bromimetry 溴量法bromocresol green 溴甲酚绿bromocresol purple 溴甲酚紫bromophenol blue 溴酚蓝bromothymol blue 溴麝香草酚蓝bulk drug, pharmaceutical product 原料药buret 滴定管by-product 副产物calibration curve 校正曲线calomel electrode 甘汞电极calorimetry 量热分析capacity factor 容量因子capillary zone electrophoresis (CZE) 毛细管区带电泳capillary gas chromatography 毛细管气相色谱法carrier gas 载气cation-exchange resin 阳离子交换树脂ceri(o)metry 铈量法characteristics, description 性状check valve 单向阀chemical shift 化学位移chelate compound 鳌合物chemically bonded phase 化学键合相chemical equivalent 化学当量Chinese Pharmacopeia (ChP) 中国药典Chinese material medicine 中成药Chinese materia medica 中药学Chinese materia medica preparation 中药制剂Chinese Pharmaceutical Association (CPA) 中国药学会chiral 手性的chiral stationary phase (CSP) 手性固定相chiral separation 手性分离chirality 手性chiral carbon atom 手性碳原子chromatogram 色谱图chromatography 色谱法chromatographic column 色谱柱chromatographic condition 色谱条件chromatographic data processor 色谱数据处理机chromatographic work station 色谱工作站clarity 澄清度clathrate, inclusion compound 包合物clearance 清除率clinical pharmacy 临床药学coefficient of distribution 分配系数coefficient of variation 变异系数color change interval （指示剂）变色范围color reaction 显色反应colorimetric analysis 比色分析colorimetry 比色法column capacity 柱容量column dead volume 柱死体积column efficiency 柱效column interstitial volume 柱隙体积column outlet pressure 柱出口压column temperature 柱温column pressure 柱压column volume 柱体积column overload 柱超载column switching 柱切换committee of drug evaluation 药品审评委员会comparative test 比较试验completeness of solution 溶液的澄清度compound medicines 复方药computer-aided pharmaceutical analysis 计算机辅助药物分析concentration-time curve 浓度－时间曲线confidence interval 置信区间confidence level 置信水平confidence limit 置信限congealing point 凝点congo red 刚果红（指示剂）content uniformity 装量差异controlled trial 对照试验correlation coefficient 相关系数contrast test 对照试验counter ion 反离子（平衡离子）cresol red 甲酚红（指示剂）crucible 坩埚crude drug 生药crystal violet 结晶紫（指示剂）cuvette, cell 比色池cyanide 氰化物cyclodextrin 环糊精cylinder, graduate cylinder, measuring cylinder 量筒cylinder-plate assay 管碟测定法daughter ion （质谱）子离子dead space 死体积dead-stop titration 永停滴定法dead time 死时间decolorization 脱色decomposition point 分解点deflection 偏差deflection point 拐点degassing 脱气deionized water 去离子水deliquescence 潮解depressor substances test 降压物质检查法derivative spectrophotometry 导数分光光度法derivatization 衍生化descending development 下行展开desiccant 干燥剂detection 检查detector 检测器developer, developing reagent 展开剂developing chamber 展开室deviation 偏差dextrose 右旋糖，葡萄糖diastereoisomer 非对映异构体diazotization 重氮化2,6-dichlorindophenol titration 2,6-二氯靛酚滴定法differential scanning calorimetry (DSC) 差示扫描热量法differential spectrophotometry 差示分光光度法differential thermal analysis (DTA) 差示热分析differentiating solvent 区分性溶剂diffusion 扩散digestion 消化diphastic titration 双相滴定disintegration test 崩解试验dispersion 分散度dissolubility 溶解度dissolution test 溶出度检查distilling range 馏程distribution chromatography 分配色谱distribution coefficient 分配系数dose 剂量drug control institutions 药检机构drug quality control 药品质量控制drug release 药物释放度drug standard 药品标准drying to constant weight 干燥至恒重dual wavelength spectrophotometry 双波长分光光度法duplicate test 重复试验effective constituent 有效成分effective plate number 有效板数efficiency of column 柱效electron capture detector 电子捕获检测器electron impact ionization 电子轰击离子化electrophoresis 电泳electrospray interface 电喷雾接口electromigration injection 电迁移进样elimination 消除eluate 洗脱液elution 洗脱emission spectrochemical analysis 发射光谱分析enantiomer 对映体end absorption 末端吸收end point correction 终点校正endogenous substances 内源性物质enzyme immunoassay(EIA) 酶免疫分析enzyme drug 酶类药物enzyme induction 酶诱导enzyme inhibition 酶抑制eosin sodium 曙红钠（指示剂）epimer 差向异构体equilibrium constant 平衡常数equivalence point 等当点error in volumetric analysis 容量分析误差excitation spectrum 激发光谱exclusion chromatography 排阻色谱法expiration date 失效期external standard method 外标法extract 提取物extraction gravimetry 提取重量法extraction titration 提取容量法extrapolated method 外插法，外推法factor 系数，因数，因子feature 特征Fehling’s reaction 费林反应field disorption ionization 场解吸离子化field ionization 场致离子化filter 过滤，滤光片filtration 过滤fineness of the particles 颗粒细度flame ionization detector(FID) 火焰离子化检测器flame emission spectrum 火焰发射光谱flask 烧瓶flow cell 流通池flow injection analysis 流动注射分析flow rate 流速fluorescamine 荧胺fluorescence immunoassay(FIA) 荧光免疫分析fluorescence polarization immunoassay(FPIA) 荧光偏振免疫分析fluorescent agent 荧光剂fluorescence spectrophotometry 荧光分光光度法fluorescence detection 荧光检测器fluorimetyr 荧光分析法foreign odor 异臭foreign pigment 有色杂质formulary 处方集fraction 馏分freezing test 结冻试验funnel 漏斗fused peaks, overlapped peaks 重叠峰fused silica 熔融石英gas chromatography(GC) 气相色谱法gas-liquid chromatography(GLC) 气液色谱法gas purifier 气体净化器gel filtration chromatography 凝胶过滤色谱法gel permeation chromatography 凝胶渗透色谱法general identification test 一般鉴别试验general notices （药典）凡例general requirements （药典）通则good clinical practices(GCP) 药品临床管理规范good laboratory practices(GLP) 药品实验室管理规范good manufacturing practices(GMP) 药品生产质量管理规范good supply practices(GSP) 药品供应管理规范gradient elution 梯度洗脱grating 光栅gravimetric method 重量法Gutzeit test 古蔡（检砷）法half peak width 半峰宽[halide] disk method, wafer method, pellet method 压片法head-space concentrating injector 顶空浓缩进样器heavy metal 重金属heat conductivity 热导率height equivalent to a theoretical plate 理论塔板高度height of an effective plate 有效塔板高度high-performance liquid chromatography (HPLC) 高效液相色谱法high-performance thin-layer chromatography (HPTLC) 高效薄层色谱法hydrate 水合物hydrolysis 水解hydrophilicity 亲水性hydrophobicity 疏水性hydroscopic 吸湿的hydroxyl value 羟值hyperchromic effect 浓色效应hypochromic effect 淡色效应identification 鉴别ignition to constant weight 灼烧至恒重immobile phase 固定相immunoassay 免疫测定impurity 杂质inactivation 失活index 索引indicator 指示剂indicator electrode 指示电极inhibitor 抑制剂injecting septum 进样隔膜胶垫injection valve 进样阀instrumental analysis 仪器分析insulin assay 胰岛素生物检定法integrator 积分仪intercept 截距interface 接口interference filter 干涉滤光片intermediate 中间体internal standard substance 内标物质international unit(IU) 国际单位in vitro 体外in vivo 体内iodide 碘化物iodoform reaction 碘仿反应iodometry 碘量法ion-exchange cellulose 离子交换纤维素ion pair chromatography 离子对色谱ion suppression 离子抑制ionic strength 离子强度ion-pairing agent 离子对试剂ionization 电离，离子化ionization region 离子化区irreversible indicator 不可逆指示剂irreversible potential 不可逆电位isoabsorptive point 等吸收点isocratic elution 等溶剂组成洗脱isoelectric point 等电点isoosmotic solution 等渗溶液isotherm 等温线Karl Fischer titration 卡尔·费歇尔滴定kinematic viscosity 运动黏度Kjeldahl method for nitrogen 凯氏定氮法Kober reagent 科伯试剂Kovats retention index 科瓦茨保留指数labelled amount 标示量leading peak 前延峰least square method 最小二乘法leveling effect 均化效应licensed pharmacist 执业药师limit control 限量控制limit of detection(LOD) 检测限limit of quantitation(LOQ) 定量限limit test （杂质）限度（或限量）试验limutus amebocyte lysate(LAL) 鲎试验linearity and range 线性及范围linearity scanning 线性扫描liquid chromatograph/mass spectrometer (LC/MS) 液质联用仪litmus paper 石蕊试纸loss on drying 干燥失重low pressure gradient pump 低压梯度泵luminescence 发光lyophilization 冷冻干燥main constituent 主成分make-up gas 尾吹气maltol reaction 麦牙酚试验Marquis test 马奎斯试验mass analyzer detector 质量分析检测器mass spectrometric analysis 质谱分析mass spectrum 质谱图mean deviation 平均偏差measuring flask, volumetric flask 量瓶measuring pipet(te) 刻度吸量管medicinal herb 草药melting point 熔点melting range 熔距metabolite 代谢物metastable ion 亚稳离子methyl orange 甲基橙methyl red 甲基红micellar chromatography 胶束色谱法micellar electrokinetic capillary chromatography(MECC, MEKC) 胶束电动毛细管色谱法micelle 胶束microanalysis 微量分析microcrystal 微晶microdialysis 微透析micropacked column 微型填充柱microsome 微粒体microsyringe 微量注射器migration time 迁移时间millipore filtration 微孔过滤minimum fill 最低装量mobile phase 流动相modifier 改性剂，调节剂molecular formula 分子式monitor 检测，监测monochromator 单色器monographs 正文mortar 研钵moving belt interface 传送带接口multidimensional detection 多维检测multiple linear regression 多元线性回归multivariate calibration 多元校正natural product 天然产物Nessler glasses(tube) 奈斯勒比色管Nessler’s reagent 碱性碘化汞钾试液neutralization 中和nitrogen content 总氮量nonaqueous acid-base titration 非水酸碱滴定nonprescription drug, over the counter drugs (OTC drugs) 非处方药nonproprietary name, generic name 非专有名nonspecific impurity 一般杂质non-volatile matter 不挥发物normal phase 正相normalization 归一化法notice 凡例nujol mull method 石蜡糊法octadecylsilane chemically bonded silica 十八烷基硅烷键合硅胶octylsilane 辛（烷）基硅烷odorless 无臭official name 法定名official specifications 法定标准official test 法定试验on-column detector 柱上检测器on-column injection 柱头进样on-line degasser 在线脱气设备on the dried basis 按干燥品计opalescence 乳浊open tubular column 开管色谱柱optical activity 光学活性optical isomerism 旋光异构optical purity 光学纯度optimization function 优化函数organic volatile impurities 有机挥发性杂质orthogonal function spectrophotometry 正交函数分光光度法orthogonal test 正交试验orthophenanthroline 邻二氮菲outlier 可疑数据，逸出值overtones 倍频峰，泛频峰oxidation-reduction titration 氧化还原滴定oxygen flask combustion 氧瓶燃烧packed column 填充柱packing material 色谱柱填料palladium ion colorimetry 钯离子比色法parallel analysis 平行分析parent ion 母离子particulate matter 不溶性微粒partition coefficient 分配系数parts per million (ppm) 百万分之几pattern recognition 模式识别peak symmetry 峰不对称性peak valley 峰谷peak width at half height 半峰宽percent transmittance 透光百分率pH indicator absorbance ratio method pH指示剂吸光度比值法pharmaceutical analysis 药物分析pharmacopeia 药典pharmacy 药学phenolphthalein 酚酞photodiode array detector(DAD) 光电二极管阵列检测器photometer 光度计pipeclay triangle 泥三角pipet(te) 吸移管，精密量取planar chromatography 平板色谱法plate storage rack 薄层板贮箱polarimeter 旋光计polarimetry 旋光测定法polarity 极性polyacrylamide gel 聚丙酰胺凝胶polydextran gel 葡聚糖凝胶polystyrene gel 聚苯乙烯凝胶polystyrene film 聚苯乙烯薄膜porous polymer beads 高分子多孔小球post-column derivatization 柱后衍生化potentiometer 电位计potentiometric titration 电位滴定法precipitation form 沉淀形式precision 精密度pre-column derivatization 柱前衍生化preparation 制剂prescription drug 处方药pretreatment 预处理primary standard 基准物质principal component analysis 主成分分析programmed temperature gas chromatography 程序升温气相色谱法prototype drug 原型药物provisions for new drug approval 新药审批办法purification 纯化purity 纯度pyrogen 热原pycnometric method 比重瓶法quality control(QC) 质量控制quality evaluation 质量评价quality standard 质量标准quantitative determination 定量测定quantitative analysis 定量分析quasi-molecular ion 准分子离子racemization 消旋化radioimmunoassay 放射免疫分析法random sampling 随机抽样rational use of drug 合理用药readily carbonizable substance 易炭化物reagent sprayer 试剂喷雾器recovery 回收率reference electrode 参比电极refractive index 折光指数related substance 有关物质relative density 相对密度relative intensity 相对强度repeatability 重复性replicate determination 平行测定reproducibility 重现性residual basic hydrolysis method 剩余碱水解法residual liquid junction potential 残余液接电位residual titration 剩余滴定residue on ignition 炽灼残渣resolution 分辨率，分离度response time 响应时间retention 保留reversed phase chromatography 反相色谱法reverse osmosis 反渗透rider peak 驼峰rinse 清洗，淋洗robustness 可靠性，稳定性routine analysis 常规分析round 修约（数字）ruggedness 耐用性safety 安全性Sakaguchi test 坂口试验salt bridge 盐桥salting out 盐析sample applicator 点样器sample application 点样sample on-line pretreatment 试样在线预处理sampling 取样saponification value 皂化值saturated calomel electrode(SCE) 饱和甘汞电极selectivity 选择性separatory funnel 分液漏斗shoulder peak 肩峰signal to noise ratio 信噪比significant difference 显著性差异significant figure 有效数字significant level 显著性水平significant testing 显著性检验silanophilic interaction 亲硅羟基作用silica gel 硅胶silver chloride electrode 氯化银电极similarity 相似性simultaneous equations method 解线性方程组法size exclusion chromatography(SEC) 空间排阻色谱法sodium dodecylsulfate, SDS 十二烷基硫酸钠sodium hexanesulfonate 己烷磺酸钠sodium taurocholate 牛璜胆酸钠sodium tetraphenylborate 四苯硼钠sodium thiosulphate 硫代硫酸钠solid-phase extraction 固相萃取solubility 溶解度solvent front 溶剂前沿solvophobic interaction 疏溶剂作用specific absorbance 吸收系数specification 规格specificity 专属性specific rotation 比旋度specific weight 比重spiked 加入标准的split injection 分流进样splitless injection 无分流进样spray reagent （平板色谱中的）显色剂spreader 铺板机stability 稳定性standard color solution 标准比色液standard deviation 标准差standardization 标定standard operating procedure(SOP) 标准操作规程standard substance 标准品stationary phase coating 固定相涂布starch indicator 淀粉指示剂statistical error 统计误差sterility test 无菌试验stirring bar 搅拌棒stock solution 储备液stoichiometric point 化学计量点storage 贮藏stray light 杂散光substituent 取代基substrate 底物sulfate 硫酸盐sulphated ash 硫酸盐灰分supercritical fluid chromatography(SFC) 超临界流体色谱法support 载体（担体）suspension 悬浊液swelling degree 膨胀度symmetry factor 对称因子syringe pump 注射泵systematic error 系统误差system model 系统模型system suitability 系统适用性tablet 片剂tailing factor 拖尾因子tailing peak 拖尾峰tailing-suppressing reagent 扫尾剂test of hypothesis 假设检验test solution(TS) 试液tetrazolium colorimetry 四氮唑比色法therapeutic drug monitoring(TDM) 治疗药物监测thermal analysis 热分析法thermal conductivity detector 热导检测器thermocouple detector 热电偶检测器thermogravimetric analysis(TGA) 热重分析法thermospray interface 热喷雾接口The United States Pharmacopoeia(USP) 美国药典The Pharmacopoeia of Japan(JP) 日本药局方thin layer chromatography(TLC) 薄层色谱法thiochrome reaction 硫色素反应three-dimensional chromatogram 三维色谱图thymol 百里酚（麝香草酚）（指示剂）thymolphthalein 百里酚酞（麝香草酚酞）（指示剂）thymolsulfonphthalein ( thymol blue) 百里酚蓝（麝香草酚蓝）（指示剂）titer, titre 滴定度time-resolved fluoroimmunoassay 时间分辨荧光免疫法titrant 滴定剂titration error 滴定误差titrimetric analysis 滴定分析法tolerance 容许限toluene distillation method 甲苯蒸馏法toluidine blue 甲苯胺蓝（指示剂）total ash 总灰分total quality control(TQC) 全面质量控制traditional drugs 传统药traditional Chinese medicine 中药transfer pipet 移液管turbidance 混浊turbidimetric assay 浊度测定法turbidimetry 比浊法turbidity 浊度ultracentrifugation 超速离心ultrasonic mixer 超生混合器ultraviolet irradiation 紫外线照射undue toxicity 异常毒性uniform design 均匀设计uniformity of dosage units 含量均匀度uniformity of volume 装量均匀性（装量差异）uniformity of weight 重量均匀性（片重差异）validity 可靠性variance 方差versus …对…，…与…的关系曲线viscosity 粘度volatile oil determination apparatus 挥发油测定器volatilization 挥发法volumetric analysis 容量分析volumetric solution(VS) 滴定液vortex mixer 涡旋混合器watch glass 表面皿wave length 波长wave number 波数weighing bottle 称量瓶weighing form 称量形式weights 砝码well-closed container 密闭容器xylene cyanol blue FF 二甲苯蓝FF（指示剂）xylenol orange 二甲酚橙（指示剂）zigzag scanning 锯齿扫描zone electrophoresis 区带电泳zwitterions 两性离子zymolysis 酶解作用。

小学上册第15次英语第一单元真题试卷(含答案)

小学上册第15次英语第一单元真题试卷(含答案)

小学上册英语第一单元真题试卷(含答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1. A __________ is a large forest area.2.The atomic number tells you the number of ______ in an atom.3.Hydrogen bonds are weak attractions between _____ (polar molecules).4.The teacher, ______ (老师), encourages creativity in class.5.The parakeet sings sweet _________. (歌曲)6.My brother is very ___. (tall)7.The _____ (常春藤) climbs the wall.8.The _______ (Ancient Egyptians) built many temples and monuments along the Nile.9.I see a deer in the ___. (forest)10.My mom _____ breakfast every morning. (prepares)11. A snail carries its _______ on its back.12.My grandma enjoys sewing ____ (quilts).13.The cat is _____ on the couch. (sleeping)14.Many plants have _____ (叶子) that change color in fall.15. A ______ (蜗牛) carries its home on its back.16.The movie starts at _______ (七点).17.What is the shape of a basketball?A. SquareB. RectangleC. TriangleD. Circle答案:D18.The ______ (水文条件) affect plant distribution.19.What is the capital of Costa Rica?A. San JoseB. San SalvadorC. ManaguaD. Panama City答案: A. San Jose20.在历史上，________ (battles) 常常改变了国家的命运。

小学上册第7次英语第五单元期末试卷

小学上册第7次英语第五单元期末试卷

小学上册英语第五单元期末试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.What do we call a person who studies marine life?A. Marine BiologistB. EcologistC. ZoologistD. BiologistA2.The ancient Chinese invented _____ for long-distance communication.3.Which animal is known for its striped fur?A. LionB. TigerC. BearD. LeopardB Tiger4.The ________ loves to play tag with its friends.5.The ________ was a famous document that promoted equality.6.The sun is ______ in the sky. (bright)7.I think exercising is important for staying __________.8.I enjoy _____ (吃) ice cream.9.The moon reflects light from the _______.10.What is the capital of New Zealand?A. WellingtonB. AucklandC. ChristchurchD. DunedinA11.My grandparents are very ____.12.Which shape has three sides?A. SquareB. TriangleC. CircleD. RectangleB13. A lion is a majestic _______ that roams its territory with pride.14.The butterfly lands softly on a _______ (花).15.I have a red ______ (气球) for my birthday party. It floats high in the ______ (天空).16.Learning about _____ (传统) plants is interesting.17.What is the capital of the Democratic Republic of the Congo?A. KinshasaB. LubumbashiC. KisanganiD. Mbuji-MayiA18.__________ are used in the production of explosives.19.What is the name of the red fruit that keeps the doctor away?A. BananaB. PearC. AppleD. OrangeC20.The __________ can provide critical insights into the Earth's natural systems.21.What do we call a piece of fruit that is often orange?A. AppleB. BananaC. OrangeD. Grape22.The chemical formula for silver chloride is _____.23.What is the capital of Solomon Islands?A. HoniaraB. GizoC. AukiD. TulagiA24.The chemical formula for sodium hydroxide is ______.25.Which animal can live both in water and on land?A. FishB. FrogC. BirdD. Cat26.What is the chemical symbol for silver?A. AuB. AgC. PbD. FeB27.What do you call the force that pulls objects toward the Earth?A. MagnetismB. GravityC. FrictionD. Pressure28.We had a _____ (party/picnic) last weekend.29.What is the opposite of strong?A. WeakB. FeebleC. FragileD. All of the aboveD30. A __________ is a small creature that often hides under rocks.31.The ________ (生态伦理) guides conservation efforts.32.The snowman is ______ (big) and tall.33. A whale is a ______ that lives in the ocean.34.What is the shape of a basketball?A. SquareB. RectangleC. OvalD. CircleD35. A __________ (化学安全) is crucial in laboratory settings to prevent accidents.36.What do we call the process of water falling from the sky?A. EvaporationB. PrecipitationC. CondensationD. Sublimation37.The _____ (pen/pencil) is on the desk.38. A _______ is a substance that can increase the concentration of hydroxide ions in a solution.39.The process of turning liquid into vapor is called ______.40. A ______ (刺猬) can curl up into a ball for protection.41.The __________ (历史的叙述模式) shape our perceptions.42.What do you call the study of the earth and its features?A. BiologyB. GeographyC. ChemistryD. PhysicsB43.I enjoy playing ________ (卡牌游戏) with my family.44.The country known for its coffee is ________ (巴西).45.My pet rabbit is very __________ (可爱的) and fluffy.46.The chemical symbol for carbon is _____.47.We are going to ___ a trip. (take)48.My pet _____ loves to play fetch.49.What do you call a young vulture?A. ChickB. EagletC. CubD. Hatchling50.What is the name of the famous American holiday celebrated on the fourth Thursday in November?A. ChristmasB. HalloweenC. ThanksgivingD. New YearC51.What do you call a person who studies plants?A. BotanistB. BiologistC. EcologistD. Horticulturist52.environmental awareness) promotes stewardship. The ____53.The baby is _____ (crying/sleeping) in the crib.54. A ______ is often used to represent the composition of a compound.55.ssance artist Michelangelo painted the ceiling of the ______ (西斯廷教堂). The Rena56.My brother is good at ____ (drawing) cartoons.57.My sister is a great __________ (歌手).58.What do we call a group of lions?A. PackB. PrideC. SchoolD. FlockB Pride59.The ________ can climb trees very well.60.How many letters are in the word "elephant"?A. 6B. 7C. 8D. 9B61.My ________ (玩具) is easy to carry around.62.My grandpa tells stories that make me ____.63.My brother is a ________.64.I have a special ______ (笔) that changes color when I write.65.The _______ (The Enlightenment) emphasized reason and scientific inquiry.66.What is the main ingredient in sushi?A. NoodlesB. RiceC. BreadD. Potatoes67. A _______ is a mixture where one substance is dissolved in another. (溶液)68.What is 10 ÷ 2?A. 3B. 4C. 5D. 6C69.My cousin has a pet ____ (fish) in a tank.70. A ______ is a natural phenomenon that can cause destruction.71. A __________ is known for its ability to spin webs.72.The chemical formula for magnesium oxide is _______.73.The sandwich is very ___ (tasty/bland).74.What do we call a person who plays music?A. ArtistB. MusicianC. PainterD. Writer75.What is the opposite of 'in'?A. OutB. InsideC. WithinD. IntoA76.The flowers in my garden are _______ (我花园里的花是_______).77.My cat loves to play with _______ (毛线).78.I like to ________ (explore) caves.79.My brother is always full of __________ (活力).80.The chemical formula for sodium bicarbonate is ______.81._____ (阳光) helps plants make food through photosynthesis.82.The ______ helps people find jobs.83.The bat can fly _______ at night.84.What is the name of the animal that builds dams?A. BeaverB. OtterC. FoxD. WolfA85.What is the main source of light during the day?A. MoonB. StarsC. SunD. FireC86.The boy likes to play ________.87.How do you say "happy" in Spanish?A. FelizB. TristeC. EnojadoD. Contento88.My mom loves __________ (参与公益活动).89.I can see a ___ in the garden. (flower)90.The __________ (历史的叙述风格) influence interpretation.91.The ________ was a famous ancient empire that ruled over Persia.92.The ______ (果实) can be red or green.93.What is the main ingredient in cereal?A. FlourB. OatsC. SugarD. RiceB94. A _______ is the smallest unit of matter.95.How many teeth does an adult human typically have?A. 20B. 24C. 28D. 32D96.The Renaissance was a time of great ________ in art and science.97. A __________ is a natural resource-rich area.98. a ________ (信) to her friend. Small pl99.I have a collection of __________ (玩具名) from __________ (地方). 100.My favorite author is _______ (名字). 她写的书很 _______ (形容词).。