On the Consistency of Twisted Gauge Theory

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Notes On Hilbert's 12th Problem

a rX iv:mat h /6511v1[mat h.NT]3M a y261NOTES ON HILBERT’S 12TH PROBLEM SIXIN ZENG Abstract.In this note we will study the Hilbert’s 12th problem for a primitive CM ﬁeld,and the corresponding Stark’s ing the idea of “Mirror Symmetry”,we will show how to generate all the class ﬁelds of a given primitive CM ﬁeld,thus complete the work of Shimura-Taniyama-Weil.Introduction 0.1.Let K be a number ﬁeld,H K be the ideal class group of K ,and let K 0be the Hilbert class ﬁeld of K .The class ﬁeld theory tells us there is a canonical isomorphism Gal (K 0/K )≃H K .In general given any integral ideal d ,let K d be the maximal abelian extension of K unramiﬁed outside d ,and let H d be the generalized ideal class group relative to d ,then a similar isomorphism holds as well:Gal (K d /K )≃H d .On the other hand,Hilbert’s 12th problem asking for an explicit generation of all the abelian extension of K ,more precisely it is asking for ﬁnding a special transcendental function,whose values at some special points would generate all the abelian extension of K .When K is the rational ﬁeld Q ,the transcendental function is the exponen-tial function and the special points are the division points on the unit circle.Indeed by the classical Kronecker-Weber theorem,all the abelian extension of Q can be obtained by adding the roots of unity to Q .When K is an imaginery quadratic ﬁeld,this problem is answered by the theory of complex multiplications.As this theory has very much inﬂuenced the later thinking about this problem,let’s recall some details.So let K be such a ﬁeld,consider the set of elliptic curves E satisfying End (E )⊗Q ≃K ,i.e.,the set of elliptic curves with complex multiplications by K .All such elliptic curves can be constructed by the following way:take the caononical embeddingι:K −→C ,let a be an integral ideal of K ,then a is a rank 2Z -module in C ,i.e.,ι(a )is a lattice in C ,so we can take the quotient C /ι(a )which is an2SIXIN ZENGelliptic curve with complex multiplication by K.From the construction it is clear that the ideal group of K operates on this set of elliptic curves,indeed for any representative b of an ideal class,we have the isogeny:C/ι(a)→C/ι(ab). On the other hand all such elliptic curves are deﬁned over some numberﬁeld, and they are represented by the moduli points on the moduli space of all elliptic curves M1=H/P SL2(Z).In particular the Galois group acts naturally on the moduli points of this set of elliptic curves.So if E=C/ι(a),let℘be a prime of K,E(℘)=C/ι(a℘),s(℘)∈H K≃Gal(K0/K)the Artin symbol,then the main result of the complex multiplication is E s(℘)≃E(℘).In more concrete terms if j is the classical modular function,and let p E be the moduli point of E on M1=H/P SL2(Z),then j(p E)is an algebraic number and generates the Hilbert classﬁeld of K.Similar statements hold for all the ray classﬁelds of K.The idea behind the theory of complex multiplication can be summerized as the following:•Given the numberﬁeld K,in order to solve the Hilbert’s12th problem,ﬁrst we need toﬁnd a suitable class of algebro-geometric objects X,say varieties;•X should be closely related to K such that the ideal classes of K cannaturally act on them;•All such X should be deﬁned over some numberﬁeld,all such X shouldbe living on some natural moduli space so theirﬁeld of moduli are givenby the coordinate function evaluated at the moduli points.The Galoisgroup can naturally acts on them;•Moreover the action of the ideal classes of K and the action of Galoisgroup on the moduli points should be related by the reciprocity law ofclassﬁeld theory and the Kronecker congruence relations;If we canﬁnd such a class of X,then theﬁeld of moduli of X give the answer to Hilbert’s12th problem.For a general numberﬁeld besides imaginery quadratic,this philosophy is diﬃcult to apply.So from now on we will concentrate on a special case.From now on let K be a primitive CMﬁeld of degree2n,n≥1.K is then an imaginery quadratic extension of a totally realﬁeld F,with[F:Q]=n. Further let K∗be the reﬂexiveﬁeld of K,F∗be the maximal totally real subﬁeld of K∗,then K∗is also a primitive CMﬁeld of degree2n,[K∗:F∗]=2. Let{σ1,σ2,···,σn}be the set of archemidean primes of F,lifted to K as the CM types,and letρbe the complex conjugate.When n>1,according to the above philosophy,we naturally consider the set of abelian varieties of dimension n with complex multiplication by K with CM type{σ1,σ2,···,σn},i.e.,those abelian varieties satisfying End(X)⊗Q≃NOTES ON HILBERT’S12TH PROBLEM3 K,and moreover for anyα∈K the action ofαon the space of holomorphic diﬀerentials of X is given as the diagonal action of diag(ασ1,···,ασn).All such X can be constructed in the following way:letι:K→C n be the embedding ι(x)=(xσ1,···,xσn),then for any integral ideal a,ι(a)⊂C n as a Z-lattice is of rank2n,hence the quotient X=C n/ι(a)is an abelian variety,one see that such X satisfying the above conditions.From the construction such set of abelian varieties are naturally associated to K,with the integral ideals of K act on them as isogenies.This is exactly the same as elliptic curves.So next we shall consider the moduli space for these X and their arithmetic properties,it is here some complication arised,let’s be careful.Let O K and O F be the rings of integers of K and F,and let a be an integral ideal of O K.Regarding a as a module of O F,it is of rank2.More precisely we have the following(see for example,Yoshita’s book[19]):Lemma0.1.For any ideal a of O K we have the isomorphism as O F-module: a≃b·ω1⊕O F·ω2,whereω1,ω2∈K,b a fractional ideal of O F.Moreover the ideal class of b is c·N K/F(a)=c·aaρ,where c is a fractional ideal of F, independent of a,and c2=D K/F.In particular O K=c·ω1⊕O F·ω2,and if a satisfying a·aρ=(µ),then a=c·ω1⊕O F·ω2.Now let X=C n/ι(a),by Shimura the polarization of X is given by the Riemann form E(x,y)which is E(x,y)=T r K/Q(ζxyρ),withζ∈K satisfying ζρ=−ζ,Im(ζσi)>0,any i.The“type”of this polarization,by deﬁnition,is the ideal class ofζd K/F aaρ,where d K/F is the relative diﬀerent of K over F. From the above lemma it is clear that b is the type of X.For any moduli problem,in order to have a good moduli space we need to ﬁx a polarization of X.For our class of X,we observe that they all have a large ample cone,in fact the dimension of the ample cone are all of n,hence it makes sense to consider the moduli problem with all the ample classesﬁxed. This is the moduli space of“type polarized abelian varieties”.Concretely for any fractional ideal b of O F,we can constructed a moduli space M n(b)which parametrizes families of abelian varieties with the form C n/v n·ι(b)⊕ι(O F),where v n is a vector in the product of upper half plane H n,and the dot product is deﬁned component-wise.It is well-known that M n(b)=H n/Γ(b)withΓ(b)={α∈SL2(O F)|α≡1mod(b)}.If X is the above abelian variety of type b,the X=C n/ι(a)with a=b·ω1⊕O F·ω2, up to isomorphism we can chooseω1,ω2∈K such thatωX=ω1/ω2satisfyingIm(ωσiX )>0for any i,i.e.(ωσ1X,···,ωσnX)is a vector in H n,hence deﬁnes amoduli point of X in M n(b).4SIXIN ZENGSo in summary given the class of CM abelian varieties with aﬁxed CM type,we can construct a natural moduli space M n(b)for aﬁxed type of X,i.e.,ifX1,X2are of the same type,they live on the same moduli space,but diﬀerenttypes can produce diﬀerent moduli spaces.So although the ideal classes of Kcan act on all of the X,the Galois group can only act on the subclass of Xwith the same type.On the other hand it is easy to show that all X are deﬁned over aﬁniteextension of the reﬂexﬁeld K∗.In fact for an ideal a∗of K∗,we deﬁnea=g(a∗)= τi a∗τi,where{τ1,···,τn}is a CM type of K∗,then g(a∗) acting on X will not change the type of X.It is from this point of view thatin1955,Shimura-Taniyama-Weil(see Shimura’s book[12])established that theﬁeld of moduli of X will generate part of the classﬁeld of K∗,precisely it isthe classﬁeld corresponding to the subgroup of the ideal class group H0K∗= {a∈H K∗|g(a)=(µ),µ∈K}.0.2.In this note we will try to extend the work of Shimura-Taniyama-Weil to cover all the classﬁelds of K.There are actually two problems here.First, the appearance of the reﬂexﬁeld K∗is quite inconvenient,since our abelian varieties X,their moduli spaces M n(a),and the CM points on the moduli are all constructed naturally from the given CMﬁeld K,it is natural for us to look for the invariants from these abelian varieties that directly generate the class ﬁelds of K,instead of the reﬂex K∗.Second and more important problem,is how can we deal with the classﬁelds that corresponding to the isogenies of abelian varieties that live on the diﬀerent type of moduli spaces.Theﬁrst problem can be solved in the following way.Since theﬁelds K and K∗are reﬂex to each other,by Shimura-Taniyama-Weil theory,the classﬁelds of K is generated by the abelian varieties associated to K∗.So the problem is toﬁnd invariants on X that somehow related to Shimura varieties associated to K∗.For this purpose Iﬁnd the following notion of“cone polarized Hodge Structure”quite useful.First we observed the for all the abelian varieties of the CM type the Kahler cone is very large.Indeed as the polarizations are determined by the Riemann form E(x,y)=T r K/Q(ζxyρ),so the polarizations are determined byζ∈K such thatζρ=−ζ,Im(ζσi)>0,any i.Suchζform a cone of dimension n, hence the Kahler cone is of n dimensional.We can also see this by the fact that since End(X)is an order in K,the automorphism group of X is then the unit group of the order,which is of the form Z n−1⊕T orsion.So the Kahler cone of X is necessarily n dimensional.Given such Kahler cone C X of X we can consider the primitive classes of X in the middle dimension relateive to this cone,i.e.,those classes of dimension n such that are annilated by any element in the Kahler cone.NOTES ON HILBERT’S12TH PROBLEM5{α∈H n(X,C) α·x=0,∀x∈C X}This is the generalization of the notion“transcendental lattice”in the theory of K3surface.The Kahler cone and these primitive classes relative to this cone should be considered as the most basic Hodge theoretical invariants of our abelian varieties.So to understand these abelian varieties,we need to construct the appropriate moduli spaces for these invariants.First let’sﬁx the Kahler cone and consider the primitive classes of the middle degree relative to this cone.Such primitive classes carries a natural Hodge structure,indeed for abelian varieties with F-multiplication the primi-tive classes can be characterized as the invariant classes of the automorphism group U F,it carries a Hodge structure of weight n,with the i-th Hodge number to be i n =n!6SIXIN ZENGTheorem0.2.(1)We have a natural isomorphism M P H≃H n/SL2(O F∗);(2)The natural morphisms M n(a)→M C→M P H are allﬁnite.By the theory of Shimura-Taniyama-Weil,the moduli points of X on this moduli space will generate the classﬁeld of K.The natural modular function on the Hilbert modular variety of K∗,when pulled back to M n(a),will become a natural modular function on M n(a).In this way,by directly considering the geometry of X,we can have the classﬁelds of K generated.This answers our ﬁrst question.Note that in our approach we do not emphasis on the use of“ﬁeld of moduli”, indeed since our moduli space of primitive Hodge structures can actually be regarded as the moduli space of abelian varieties with multiplication by F∗,the natural“ﬁeld of moduli”somehow lose its meaning on this moduli space(1). We only need the natural modular functions on the moduli spaces,which give the coordinates of the CM points.In any case our approach is more natural in view of Hodge theory,and serve the purpose of generating classﬁelds of K well.0.3.The second question is more diﬃcult.We need toﬁnd a natural way to interpolate the moduli spaces of diﬀerent types.For this purpose we will use the idea of Mirror Symmetry.Precisely if R1and R2are two ideals suchthat R1R−12is a real ideal,then although the abelian varieties X R1and X R2deﬁned by R1and R2are living on the diﬀerent moduli space,we will showtheir“Mirror partners”X′R1and X′R2are living on a single moduli,and theMirrors’ﬁeld of moduli can be used to generate the classﬁelds.To motivate our idea,let’s consider another approach to the Hilbert’s12th problem,namely the Stark’s conjectures([16]).The point of departure is to consider the Dedekind zeta function and Hecke L-functions for the numberﬁelds.Hilbert’s problem asks for a natural tran-scendental function,indeed for the abelian extension point of view,nothing can be more natural than these L-functions,as they transformed under the Galois group ually the Stark’s conjectures are formulated and studied for a totally realﬁeld,but as we shall see,it is more natural and sim-ple to study it for the CMﬁeld,because all theﬁnite extension of CMﬁelds are necessarily CM,i.e.,any extension of K has no real inﬁnity.The remarkable fact about the Stark’s conjectures is that it can be for-mulated on any classﬁelds of K uniformly,not just those classﬁelds in the Shimura-Taniyama-Weil theory,so in the explicit form it can be used as a guide for us to search for the solution of missing classﬁelds of the old theory.NOTES ON HILBERT’S12TH PROBLEM7 So let K as above,let R be an ideal class of K,recall that the Dedekind zeta function is deﬁned asζK(s)= a1s−1κK+ρK+O(s−1)whereκK=(2π)n R KN(a)s .NatuallyζK(s)= RζK(s,R),with the limitformula:ζK(s,R)=κw Ks n−1(1+δK(R)s)+O(s n+1) thenδK(R)=nγ+nlog2π−log|D K|−w K|D K|1/2ρK(R−1)w Ks n−1(1+δK s)+O(s n+1) withδK= RδK(R)•ifχ=χ0is not trivial,thenL K(s,χ)=ζK(s,R)=−R Kw K0=(−1)m(R K8SIXIN ZENGThe Stark’s conjecture predicts that if we write L K(s,χ)=R K(χ)s n+ O(s n+1),then R K(χ)also has the form of regulators,i.e.it is a determinent of a matrix whose entries are linear combination of logarithm of units of K0. Moreover we should expect R K(χ)σ=R K(χσ)for anyσ∈Aut(C).In our present case K is a primitive CMﬁeld,in this case Stark’s conjec-ture is somehow simple in the following sense:the regulator R K of K is a determinent of(n−1)×(n−1)matrix,and the regulator R Kof K0is a determinent of(mn−1)×(mn−1)matrix.Stark’s conjecture in fact says that the quotient R K/R K is a determinent of(mn−n)×(mn−n)matrix, and this matrix should be diagonalized into m−1blocks,with each block a n×n matrix,further in this case we can use the R K matrix to simplify these blocks,so in this extension there are only m−1essential new units.In other words,U Kas a module of U K is free of rank m−1.This is very much similar to the classical case of imaginery quadraticﬁelds.By some elementry argument we can show that R K=(R K)m·vol(S), where vol(S)is a determinent of(m−1)×(m−1)matrix whose entries are linear combinations of logarithm of units in K0.These are the basis of U Kas the module of U K.On the other hand by the Frobenius determinent formula, χ=χ( Rχ(R)δK(R))=det R1,R2=1(δK(R1)−δK(R2)) Hence we should expect:•δK(R)=log|ηK(R)|;•δK(R1)−δK(R2)=log|ηK(R1)ηK(R2)is a unit in K0.More overthese units should transform under the Galois group according to thereciprocity law.0.4.To prove things like this we need to have a good expression forδK(R), this can be done by using the theory of GL(2)Eisenstein series over the totally realﬁeld F.The Eisenstein series is deﬁned asE(w,s;a)=(c,d)∈(a⊕O F)/U F,(c,d)=(0)ni=1y s i|cσi z i+dσi|−2sThe idea is a classical one,sinceζK(s,R)= a∈R1w2satisfyingIm wσi>0,∀i.Then we haveNOTES ON HILBERT’S 12TH PROBLEM 9ζK (s,R )=N (a 1)s α∈a 1/U F ,α=012n −2πn h F RF [χF (d F )L F (2,χ−1F )i Im(ωi )+πn D −3/2F 0=b ∈d −1F a σ1,χ(bda )|N (b )|−1exp (2πi (n j =1b j ℜ(w j )+i |b j Im(w j )|))]where (1)a,d ∈A ×F such that div (a −1)=a and div (d )=d F ;(2)σs,χ(x )is a function deﬁned asσs,χ(s )= v ∈(finite primes ) 1+χv (w v )q s v +···+(χv (w v )q s v )ord v (x v )if x v ∈d v ,0if x v /∈d v .Here d v denotes the ring of integers of F v ,w v is the prime elementof F v and q v =|d v /w v d v |.So we haveζK (s,R )=−R K10SIXIN ZENGδK(R)=h(ω;a)−log i Im(w i)−logN(a)We reminded that a is the type of R−1,w=(w1,···,w n)∈H n is the CM point deﬁned by R,and h(w,a)is the complicated function deﬁned above.So our basic task is to understand this function.0.5.We notice that hχFsatisfying the following modular properties([19]):for γ∈Γa we have(1)hχF (γω;a)=hχF(ω,a)ifχF is not trivial;(2)h1(γω;a)−log( i Im(γω)i)=h1(ω,a)−log( i Imωi)So in particular we haveχFχF(a)hχF(γω;a)−log( i Im(γω)i)= χFχF(a)hχF(ω,a)−log( i Imωi)which suggests that we may actually have a Hilbert modular formηK(w;a) of parallel weight such that h(w;a)=log|ηK(w;a)|.Classically in case F= Q this is indeed the case asηK is the classical Dedekind eta functionη,it is well-known thatηhas an inﬁnite product expression,which when taking the logarithm translated into a Fourier expansion,which is exactly the above Fourier series.In the higher dimensional case it is not that easy2.Besides the fact that the Fourier expansion is too complicated and diﬃcult to work with,we can not expect by directly exponenciate the above expression of h to get a meaningful function,precisely because of the inﬁnite unit group of F,as shown as the regulator term R F in the leading coeﬃcients of the Fourier expansion.The regulator R F is not a rational number,in fact we expect it to be transcendental, so even if we exponenciate h we can not get anything useful for the arithmetic purpose.In particular we can not expect to get an inﬁnite product expression as the classicalηfunction.0.6.What should I do?It turns out although we can not exponenciate theh function,can not get the explicit formula forηK(w;a),we still can say something quantitatively about it.The idea is to consider a twisted version of Eisentein series:E u,v(w,s;a)=(c,d)∈(a⊕O F)/U F,(c,d)=(0)ni=1e2πi(cσi u i+dσi v i)(Im w i)s|cσi w i+dσi|−2sNOTES ON HILBERT’S12TH PROBLEM11 where(u,v)∈R n⊕R n.This is entirely adopted from the classical Kronecker’s second limit for-mula(see[18]).To explain why we need to develop the twisted Eisenstein series,let’s recall the classical situation,i.e.,when F=Q.In this case the Eisenstein series isE(w,s)=m,n∈Z,(m,n)=0(Im(w))s2[1+(CONST+log Im(w)−4log|η(w)|)s]+O(s2)The twisted Eisenstein series is:E u,v(w,s)=m,n∈Z,(m,n)=0e2πi(mu+nv)(Im(w))s24w∞n=1(1−q n w)and g u,v is the Siegel’s function:g u,v=−q1q zφ(w,z) and we haveg u,v=q112SIXIN ZENG(3)g u,v is also closely related to Dedekindη.In fact as a function of zg u,v has a simple zero at z=0withη(w)as the coeﬃcient,i.e.,|g u,v|=|η(w)|2|q z−1|+O(z2)This shows that the absolute value|η(w)|is not a theta null,but rather a“derivative theta null”.But we note our theta functions arenormalized at z=0to be zero,φ(w,0)=0,if the theta functionnormalized in this way,their derivatives can also be used as the coor-dinates on the moduli space.By abuse of notation we still call|η(w)|a theta null,hence it gives a modular function on the moduli space.From the deﬁnition,E u+1,v=E u,v+1=E u,v,hence g u+1,v=g u,v+1= g u,v,but since|g−v,u|=|q12B2(−v)w g−v,u(w)Then from the periodic condition of g u,v we immediately see that|φ(w,z+1)=φ(w,z);|φ(w,z+w)|=|q−1z|·|φ(w,z)| That is,|φ(w,z)|satisfying the characterization of a theta function,moreover since we know it is an analytic function,it then has to be a theta function itself.This is the idea we would follow in the higher dimensional case,as we observed before,since in the higher dimension we can not expect any explicit inﬁnite product formula for the functionηK(w;a),but we still have all the periodic properties as the1-dimensional case.Now we go back to the higher dimensional case,the Eisenstein series is:E(w,s;a)=(c,d)∈(a⊕O F))/U F,(c,d)=(0)ni=1(Im(w i))s|cσi w i+dσi|−2sWe have the limit formula:E(w,s;a)=−2n−2h F R F s n−1[1+(CONST+logN(a)+log( i Im(w i))−h(w;a))s]+O(s n+1) The twisted Eisenstein series is:NOTES ON HILBERT’S12TH PROBLEM13E u,v(w,s;a)=(c,d)∈(a⊕O F)/U F,(c,d)=(0)ni=1e2πi(cσi u i+dσi v i)(Im w i)s|cσi w i+dσi|−2sand we have the limit formula:E u,v(w,s;a)=−2n−2hF R F log|g−v,u(w;a)|s n+O(s n+1)where log|g−v,u(w;a)|has an explicit Fourier expansion,just like h(w;a).Then we argue as the following:(1)Recall that u=(u1,···,u n)∈R n,v=(v1,···,v n)∈R n,and O F⊂R n as a lattice.From the deﬁnition,for anyα∈O F,we have E u+α,v=E u,v+α=E u,v,i.e.,translate invariant under O F,hence|g−v+α,u|=|g−v,u+α|=|g−v,u|.(2)Now write z=u−vw,i.e.,z=(z1,···,z n),z i=u i−v i w i,∀i.We try to write g−v,u as a function of(w,z),so we deﬁneφ(w,z)=q−12B2(−v)w= i q−112wφ(w,z)|−log(|ηK(w;a)|2 i|z i|)}=0that islim z→0|q1|ηK(w;a)|2 i|z i|=1Also we verify that our theta function is normalized at z=0to be 0.This implies thatηK(w;a)is a theta null.By the classical theory of theta function,theta null naturally gives rise to the modular forms on the moduli space.In fact this should be more or less expected.By Mumford’s theory of algebraic theta function,we may further conclude that these theta nulls in fact deﬁnes the moduli space as an integral scheme over Z,hence have all the expected integral properties.14SIXIN ZENG0.7.In summary we have found the explicit form of the functionδK(R).δK(R)=logN(a)+log i Im(w i)−h(w;a)=logN(a)+log i Im(w i)−log|ηK(w;a)|2=log[N(a) i Im(w i)|ηK(w;a)−2|]where R is an ideal class of O K,a its type,w its CM point on M n(a),and ηk(w;a)is the theta null:∂∂z nφ(w,z)|z=0=ηK(w;a)2By the Stark’s conjecture,we need to understandδK(R1)−δK(R2),i.e., we need to understand the quotientηK(w1;a1)ηK(w2;a)is meaningful,as the modular function evaluating at the CMpoints,and the natural action of Galois group on them is prescribed by the reciprocity law.But when R1and R2are of the diﬀerent type,for example, when R1R−12is a real ideal,thenηK(w;a1)andηK(w;a2)are on the diﬀerent moduli spaces,thus their quotient becomes meaningless.This is precisely the limit of Shimura-Taniyama-Weil’s theory.So what can we do?To go further we need toﬁnd a natural way to inter-polate the diﬀerent moduli spaces,and it is here the idea of Mirror symmetry comes.As we shall see,in this case this quotient will have a meaning similar to the classical one if we consider the complexiﬁed Kahler moduli of the abelian varieties.Why should we interpolate the diﬀerent moduli spaces?The functionδK(R) is deﬁned not on a single moduli space of theﬁxed type,but rather automati-cally been deﬁned on all the moduli spaces,as the type a can vary accordingly. Likewise the modular formηK is a Hilbert modular form on all the type-ﬁxed Hilbert modular varieties,and when the type vary,can be regarded as a mod-ular form on all the moduli spaces.This strongly suggests that we should have a natural way to interpolate all these moduli spaces of diﬀerent types,such that these functions can naturally deﬁned.In other words,when weﬁx the type a,we get the Hilbert modular forms,what then happens if weﬁx the CM pointsωand let the type vary?When we look the explicit form ofδK(R)and h,we note the apparent symmetric roles played by the quantities σIm(ωσi)and N(a).Indeed if we ﬁx the CM pointsωand let a vary,we should have a meaning for the quantity N(a).This can be achieved by considering the Kahler moduli of our abelian varieties.0.8.Mirror Symmetry is usually formulated for the Calabi-Yau varieties, roughly it asserts that Calabi-Yau always come in pairs,X and X′,with theNOTES ON HILBERT’S12TH PROBLEM15“complex moduli”and“Kahler moduli”exchanged.In terms of the Hodgenumber,it means the Hodge diamond of X′is a rotation of X.For abelian varieties,Mirror Symmetry is generally regarded as“trivial”,as the underlying topological type would not change.Nevertheless we canstill talk about it.There are several constructions of Mirror manifold for theabelian varieties,the simplest one I believe,is given by Manin([9]).It goes asthe following:let k be any completeﬁeld,X an abelian variety over k,T bethe algebraic torus of dimension n over k,T≃(k×)n.Then the multiplicativeuniformization is0→P X→T→X→0,where P X is a free abelian groupof rank n,P X is called the period of X.Under this uniformization the Mirrorpartner X′is then0→P X→T∨→X′→0,i.e.,we explicitly indentify theperiods in T and T∨.When k≃C one verify that the complex moduli andKahler moduli of the two are exchanged.In our situation,given the Mirror pair X and X′we will be mainly concernabout the relations of theta functions on them.Since the underlying topologicaltype would not change,we may regard the Mirror transform as a“rotation”of complex structure of X.So to compare the theta functions on X and X′we have toﬁx the underlying real structures.We begin with X=C n/(w·a⊕O F)≃R2n/Z2n,any polarization of X isgiven by an integral skew-symmetric bilinear form on R2n.Given such a formω,we canﬁnd an integral basis{λ1,···,λ2n}of the integral lattice such thatif{x1,···,x2n}is the dual basis,thenω= n i=1δi dx i∧dx n+i,withδ1|δ2|···the elementary divisors.Note in our case the biliear form is given by the trace T r K/Q(ζxyρ)withthe admissibleζ∈K such thatζρ=−ζ,Im(ζσi)>0.Thus we may regard(x1,···,x n)as an integral basis of O F,and(x n+1,···,x2n)as an integralbasis of a.In particular(x n+1,···,x2n)depends on a.In the following we willdenote it as x n+i(a)if we need to use this dependence.Next we introduce the complex structure,so X becomes a complex tori,and we can introduce the complex coordinates.To do this let e i=λi/δi,i=1,2,···,n,and let{z i}be the complex dual of{e i}.Consider the changeof coordinates transform:Ω·(x1,···,x2n)T=(z1,···,z n)TThenΩ=(∆δ,Z)with∆δ=diag(δ1,···,δn)the diagonal matrix,and Zsymmetrical,Im(Z)>0.We recogonize that∆−1δZ is the period matrix of X.Note in our case for abelian varieties with CM by K,the peiod martix Z isnecessarily diagonal∆−1δZ=diag(w1,···,w n),with w=(w1,···,w n)∈H n.In particular we have z i=δi·x i+δi·w i·x n+i(a),we may regard it as the transform from the underlying real coordinates to the complex coordinates.16SIXIN ZENGNow recall the theta function on X is characterized by the periodic condi-tion:θ(z+λi)=θ(z);θ(z+λn+i)=e−2πiz iθ(z)Taking absolute values we have:|θ(z+λi)|=|θ(z)|;|θ(z+λn+i)|=e2πIm(z i)|θ(z)|However from the above coordinates transformation,Im(z i)=δi·Im(w i)·x n+i(a)The Mirror symmetry transform says that we can exchange the complex moduli with the Kahler moduli,while the coordinates w=(w1,···,w n)∈H n can be regarded as the complex moduli of X,where is the Kahler moduli?Our Kahler moduli coordinates are actually in the variables(x n+1(a),···,x2n(a)). Since they are depend on the type a,we want to write the dependency explic-itly,in order to understand the transformation of types.For this end let’s write x n+i=x n+i(O F).The type ideal a as a Z module,is a submodule of O F of full rank,i.e.,if weﬁx an integral basis of O F,then O F/a≃⊕n i=1Z/t i Z,with x n+i(a)=t i x n+i and i t i=N(a)/D F.Thus the positive rational numbers(t1,···,t n)can be conviniently regarded as the coordinates of the ideal a,and under appropriate identiﬁcation,can be regardedas the coordinates of of the Kahler class in the the Kahler moduli.So in particular we haveIm(z i)=δi·Im(w i)·t i·x n+iBut from the above formula,when we exchange the complex moduli(w1,···,w n) and Kahler moduli(t1,···,t n),it’s not going to change the multiplier e2πIm(z i)=e2πδi·t i·Im(w i)·x n+i.Since the absolute value of theta functions can be regardedas a real analytic function on R2n,thus we conclude that for the given Mir-ror pair X and X′,their theta functions’absolute values satisfying the same periodic condition,hence must be only diﬀered by a constant!Recall our previous puzzle,when two ideal classes R1and R2of O K sat-isfying R1R−12is a real ideal,then R1and R2are of the diﬀerent type,sothe corresponding abelian varieties X1and X2living on the diﬀerent moduli spaces,soηK(w,a1)/ηK(w,a2)has no meaning.But we knowηK(w,a)is the theta null of X,thus by the above formula,ηK(w,a)is also the theta null of the Mirror X′.So although X1and X2living on the diﬀerent moduli space,if their Mirror X′1and X′2are in the same moduli space,thenηK(w,a1)/ηK(w,a2) would be meaningful!This is indeed the case,as X′1and X′2are on the sin-gle moduli space,the complexiﬁed Kahler moduli space of X.This is the underlying rationale for us to use the Mirror symmetry.Note from this relation of theta functions we also see that if X is deﬁnes over a numberﬁeld,then the Mirror X′also is deﬁned over that numberﬁeld.。

工程常用专业英语

平整度
flatness
同心度
concentricity
同轴度
axiality
平行度
parallelism
圆度
roundness
平面度
planeness
随机的
random
不平
uneven
空心
hollow
同心
concentricity
偏心
eccentric
表面粗糙度
surface roughness
尺寸公差
基准
datum
水平基准线
horizontal reference line
精度
accuracy
余量
allowance
组件
assemble
分装件
subassemble
包装
package
外协件
cooperation
外购件
purchase part
备件
spare part
裸装件
nudes
散装件
odd lot, odds & ends
清除
decontaminate
失败，故障
failure
断裂
fracture
塌陷，凹陷
collapse
中断
discontinuity
裂缝
crack
发裂
flaw
龟裂
fissure
毛细裂纹
capillary crack
起始裂纹
incipient crack
断层裂纹
fault fissure
积水
stagnant water
保证
assure

两根电线对接的方法

两根电线对接的方法英文回答：Splicing Electrical Wires.Splicing electrical wires is a common task for electricians and DIY enthusiasts. It involves joining two or more wires together to create a continuous electrical circuit. There are two main types of splices:1. Western Union Splice: Also known as a lineman's splice, this is the most common type of splice and is used to connect two wires of the same gauge.2. Tap Splice: This type of splice is used to connect a smaller wire to a larger wire.To splice electrical wires, you will need the following tools and materials:Wire strippers.Electrical tape.Wire nuts (for Western Union splices)。

Crimp connectors (for tap splices)。

Crimping tool.Steps for Western Union Splice:1. Strip about 1 inch of insulation from the ends of both wires.2. Twist the bare wires together clockwise.3. Wrap electrical tape around the twisted wires, starting at the center and working your way outward.4. Make sure the electrical tape extends at least 1 inch beyond the exposed wires on both sides.Steps for Tap Splice:1. Strip about 1/2 inch of insulation from the end of the smaller wire.2. Insert the bare wire into the hole in the crimp connector.3. Crimp the connector using the crimping tool.4. Strip about 3/4 inch of insulation from the end of the larger wire.5. Wrap the stripped wire around the crimp connector and secure it with electrical tape.Tips for Splicing Electrical Wires:Use the correct size wire nuts or crimp connectors for the gauge of wires you are splicing.Make sure the wires are twisted together securely before applying electrical tape.Wrap the electrical tape tightly around the splice, overlapping each layer by at least half.Inspect the splice carefully for any loose connections or exposed wires before energizing the circuit.中文回答：电线对接方法。

英语800句

奢侈的野蛮人制定了腐败的内外标准。
55. No, nobody's body is noble, nor is his.
围绕着圆形场地的边界将我们同四周隔开。
19. The blunder made the underground instrument undergo an undermining of the thunderbolt.
这个失策让地下仪器经受了一次雷电的破坏。
20. The tilted salt filters halt alternately for altering.
拼写气味（一词）！很好，人类的福利将会膨胀。
45. Once none of you is here, the man in throne will live alone in the lonely zone.
一旦你们没有人在此,王位上的人就要孤独地生活在这个孤寂的地带。
46. Nowadays the once unknown snowy hill is well-known for snowstorm.
军旗旁那位有男子气概的古罗马女经理具有男子风度。 23. In the lane the planer saw a planet airplane under the crane.
在巷道里，刨工看见了起重机下的行星飞机。
24. The wet pet in the net hasn't got on the jet plane yet.
我暗示说虚弱的圣徒用了一品脱油漆涂印刷机。
17. At any rate, the separation ratio is accurate.
无论如何,这个分离比是精确的。

电线电缆专业英语

电线电缆专业英语电线电缆专业英语电线电缆常用英文单词! 一、 COLOR TYPE<颜色类> Black<黑色> Brown<棕色> Yellow<黄色> Green<绿色> White<白色> Gray/Grey<灰色> Red<红色> Orange<橙色> Blue<蓝色> Pink<粉红色> Purple/Violet<紫色>Beige<贝吉色> Ivory<象牙色> Frost White<霜白> Light Green<浅绿色> 二、Month Type<月份类> January<Jan.> 一月 February<Feb.> 二月 March<Mar.> 三月April<Apr.> 四月 May<May> 五月 June<Jun.> 六月July<Jul.> 七月 August<Aug.> 八月 September<Sep.> 九月 October<Oct.> 十月 November<Nov.> 十一月 December<Dec.>十二月三、Week Type<星期类>Monday<Mon.>星期一 Tuesday<Tue.>星期二 Wednesday<Wed. >星期三 Thursday<Thu.>星期四 Friday<Fri.>星期五 Saturday<Sat.>星期六 Sunday<Sun.>星期日铜包铝镁英文全称：Copper clad aluminum magnesium wire四、Length Type<长度类> 1foot<英尺>=12inches<英寸>=0.3048meter<米>1yard<码>=3feet<英尺>=0.9144meter<米> 1mile<英里>=1760yards<码>=1.609kilometers<千米>1meter<米>=10dm<分米>=1.0936yards<码>=3.2808<英尺> 1centimeter<厘米>=10mm<亳米>=0.3937inch<英寸> 五、Cable Type<电线类>Cable<电缆线> Jacket<外被> Conductor<导体/芯线> Braid<编织> Spiral<缠绕>Drain Wire<地线> Al-Foil/Mylar<铝箔/麦拉> Paper<包纸> P-P-Foamed<发泡P.P>Paper + Braid<包纸+编织> Paper +Spiral<包纸+缠绕> Matted<雾面> Slot<直条文>Smooth<光滑面> Tape<包带> Al-Mylar + Braid<铝箔麦拉+编织> Coaxial<同轴线>Aluminum Foil<铝箔> Foamed PP + AL-Mylar +Braid<发泡pp+铝箔/唛拉+编织>Jump Wire<跳线> Insulator<绝缘> Tissue Paper<棉纸> Impedance<特性阻抗>Overall<总隔离> Contact Resistance<导通阻抗> Insulance<绝缘阻抗> Dupont<小杜邦>Non migration<非移性> Flexible<柔软> Filler<填充物> Color Chip<色板>Dentation<齿状> Insulator Color<胶芯颜色> Shield<隔离> Spiral Shield<缠绕隔离>Twisted<对绞> ABS Non-Migration<ABS 非移行性> Twisted Pairs<对绞线>Round Cable<圆线> A.W.G<AmericanWire Gauge>美国线规 S.W.G<英国线规> U.L<美国认证> C.S.A<加拿大认证> J.I.S<日本工业规格> T.U.V<欧共体认证>Hook Up Wire<电子线> Flat Cable<排线> Coaxial Cable<同轴线> ShieldCable<隔离线>Telephone Cable<电话线> Power Supply Cable<电源线> Mouse Cable<鼠标线>Multiconductor Cable<多芯线/多芯电缆> Signal Cable<信号线> Process Wire<半成品线>Multiconductor Plug<多线插头> Multipaired Cable<多对线> Computer Cable<计算机线> RetractileCable<掷线> Communication Cable<通讯线> With Adhesive<含热溶胶>Teflon Hook-Up Wire<铁弗龙线> Without Adhesive<不含热溶胶> Construction<构成>Flammability<耐燃性> VW-1<美国直燃烧试验> Monitor Tube<头像管> Configuration<结构> Used to Printer<用于打印机> Insulation Color Code<芯线色码>Stranded Conductors<铜绞线> Application Wiring Material<电线用料>Wire Harnesses Low Voltage Control Cable<低压控制电缆> ComputerInterconnectionCableAssembly<计算机周边连接线>Electrical Characteristics<电气特性> 六、Connector Type<插头类>Connector<插头/连接器> Male<公> Female<母> Plug/Jack/Socket<插头> Terminal<端子> Housing<P 架> Tube<套管> Core<铁粉芯> Screw<螺丝> Shell<铁壳> Clamp<线夹> Series<系列> Loose Terminal<单粒端子> Molding Tooling<模具编号>Serial Terminal<连续端子> Contact<接触> PBT Insulator<PBT 材质> Front Shell<前铁壳>Back Shell<后铁壳> Assembly<组合件/组装/装配> Solder Type<焊线式>Recognize<标志>Crimp Type<铆合式/打端子式> IDC Type<装配式> Flash<闪光/飘金> Gold Flash<飘金>Gold Flash Contacts<飘薄金> Gold Flash Pin<pin 针飘金> Brass<黄铜>Copper<红铜>Tin Plated<镀锡> Phosphor Bronze<磷青铜> Nickel Plated<镀镍> Copper Alloys<铜合金>Adapter<转接头/连接器> Stainless/Steel<不锈钢/钢料>Chemical Grinding<化学研磨>Silver Plating<镀银> Zinc Plating<镀锌> Pre-Tin<预镀锡> Pre-Nickel<预镀镍>Pre-Gold<预镀金> Tin-Dip<沾锡性>Surface Treatment<表面处理> Material<材料/材质>Specification/Spec.<规格书> Metal Clamp<地线夹> Density<密度>Supplier/Supply<供货商>None<素材> Nickel Plated Front Shell, Tin Plated Back Shell<前镍后锡> Accept<承认/接受>Dimension<呎寸> Condition<条件> High-Density<高密度> Thumbscrew<螺丝,指可旋转式>Label<贴纸/标签> Scanner Plug<单声插头> Stereo Plug<立体插头> DC Plug<DC 头> BNC Net-Work<BNC 网络头> Scanner Plug<扫把头> Diode<二极体> Sheet<页次>Scale<比例> Unit<单位> Date<日期>Hood<头部> Molded<成型> Customer<客户>Strain Relief Molded<SR成型>Customer Consign<客户提供> Molded Hood<成型头部>Removable<可移动的/可转动的>Hex-nut<六角螺丝> Heat Shrink Tube<热缩套管>Meta Can<马口铁> Washer<垫圈/垫片>Wafer<薄片/芯片> Sample<样品>Talc<云母/滑石粉> Socket<插座> Direct Current<DC 直流电> Alternation Current<交流电>Half Pitch<半间距> Pitch<间距>Ground<地线> Plug Adapter<插头> Paper Wrap<包纸>Outer Molding<外模> Inner Molding<内模> Molded Color<外模色泽>Finished Molding<成型完毕> Bump<点>Result<结果> Accepted<承认/出货/接受> Inspector<品管>Confirmation<确认> Rejected<不可出货/拒收> Equivalent<替代品> Position<位置>Section<方向> IEEE<电子电气工程师协会> Material Desciption<材料规格/说明>Wire Connection/Pin Out/Wiring Diagram/Assignment<接点>Part List/Item List/Bom<材料表> Sample Inspection Record<样品检验报告/样品检验记录>七、Packing Type<包装类>Round<绕线> Circle Form<圆形> Print<印刷> Mark<标示/标记> Packing<包装>Mini Tie<迷你带> Cable Tie/Nylon<束带> Polybag PE<PE袋> Zip-Lock Bag<由任>Bubble Pacl<真空罩> Polylon<保丽龙> Sponge/Bubble Swab<舒服多> Elastic<橡皮筋>Back Card<背卡> Staple<订书订> Guide<说明书> PE Film<PE膜> ClearTape<透明带>Air Bubble Polybag<汽泡袋> Boarding Cap<防尘盖> Big Polybag<大防水袋> Inner White Box<小白盒> Inner Carton<内箱> Heat Seal<热封> OuterCarton<外箱>Fold<反折> Floor Paper<隔板> Black Words With Silver Label<银底黑字>Be Careful The Label Direction<注意贴纸方向> Single<单一> GroundIndent<打点>#4-40UNC+Washer<半螺丝+梯形垫片> Gold Plated Contacts 30U’’<镀金30u’’插头>Ribbon IDC Type<带状刺破式> Final Drawing<总图> Blue PBT Insulator<蓝胶芯>Label+ Clear Heat Shrink Tube<贴纸/标签+透明热缩管> Pre-Mold<内模>With Mini Tie Fasten<用迷你带固定> Female Screw Lock<六角螺丝>Black PBT Insulator<黑胶芯> Locking Posts<锁螺栓> Color Code<色码> Major<主要>Minor<次要的> ID<内径> OD<外径> REV.<版次> REF.<大约> Size<呎寸>Stripe<色条> Bump<凸点> Cut<剪/切> Power<电源> Empty<空的> List<清单>Front View<前视图> Back View<后视图> Should<应该> With Bump<有凸点>Min<最小> Max<最大> Logo<符号/记号> Test<测试> Pull<推/拉>Shell<铁壳>Bottom<底部> Die-Cast<压模>Wrapped<包裹> Sub’ Pack’ Age<分装>Protect<保护>Prompt<提示> Supply<产地/供货商>IS<绝缘> Short<短路> Open<开路>Checked<审核>Draw By<制表> Approved<核准>Erected<超过> Insertion<插入>Withdraw<取出>OHM<欧姆> Tolerance<公差> Double<双数> Serial<连续> Loose<单粒>Packing Classification<包装分类>Materials Classification<材质分类>八、包装外表标志Bottom<底部/下端> Top<顶端/上部>Care<小心> Fragile<易碎> Don’tCast<勿掷>Inflammable<易燃物/怕火> Keep Dry<保持干凈> Hamdle With Care<小心卸装/小心搬运>Heave Here<从此处提起> Keep Upright<勿倒置> Not Be Protected From Heat<怕热>Not To Be Tipped<勿倾倒> Keep In ACool Place<在冷处保管> Use Rollers<在子上移动>Keep In A Dry Place<在干处保管> No BeProtected From Cold<怕冷>九、其它SR-PVC<半硬质PVC> PVC<聚已烯树脂>PP<聚丙烯> FPE<发泡PE>PU<一般用于发泡线外被> Carton<纸箱>Rated Voltage<额定电压> PE<聚已烯>Rated Temperature<额定温度> OrderNo.<工令单号> Title<品名/题目>Quantity<数量>Intermittent<接触不良> Wrong Wiring<接反线> Pull Force<拉拔力>Twist-Force<扭力>Flex-ups<摇摆力> Terminal-Strength<端子强度> Anti-Pressure<耐压强度>Appearance<外箱>Following Letters Are Printed On TheTubing<套管表面印有下列字样>Anti-Temperature<耐温度>keyboard 键盘computer 计算机mouse 鼠标 under plate 底尘电镀disk 磁盘connector 连接器terminal 终端 male 公shell 外壳pitch 间距single row单排 double row双排rivet 铆钉 combination组合线round row圆排 hook-up wire电子线filler 填充物 rubber band 橡皮筋shield 隔离,遮蔽 roll 打卷bracket 支架nickel 镍hexagonal standoff六角 right angle 90度pillar 圆柱plug 插头saddle washer 鞍状垫片 wire 芯线electrical test 电测 UL recognized UL认证insulation/conductorresistance绝缘/导通阻抗screw 螺丝钉 printing text high6mm 印字高6mmcontact material 接点材质engagement 插力 separtion force拔力pe bag pe袋 conductor size芯线规格 slits 裂缝,切开voids 空的,无用 pe board pe板envelope信卦,卦套 hood 装配盒plating 电镀flat cable 排线crimp 压着 phone cable 电话线jacket 外被separator 隔离线length 长度 separator 隔离纸tin 锡 mater cover/can 马口铁clinch 螺母 spring washer 弹簧垫片whit 配合processing 程序socket connectors of 40f 40P pin插座式接头fill up the 3th hole 塞第3PINphosphor bronze 磷铜monitor 显示器 all coverage 铝装保护(铝箔) heat shrinkable tube 热缩管gnd(GND) 接地 outer 外部的(外壳)insert mark插入标记 nickes缺口delay time 延迟时间 copper foil 铜管长度 double shield双隔离 singleshield 单隔离resistor 电阻器 aluminum mylar foil铝箔麦拉connector 连接器transistor 晶体管net income 纯收入 settle an account清帐 interest 利息 rate ofinterest利率discount 打折 creditor 债权人debtor 债务人standardcosts 标准成本commerce 商业 sea freight 海运air freight 空运 standard hours标准工时commercial商业的,贸易的 import,importation 进口export,exportation 出口commercial channels 商业渠道importer 进口商 exporter出品商international trade 国际贸易 stereoplug 立体插头stripping 剥线band 摇摆,弯折terms of trade 贸易条件 mono plug单音插头 damage 损伤 inquiry质询free-trade area 自由贸易区 develop 开发 quotation 报价单 earphone 耳机vendor 供应量note 注释order 订单 revision修订shipping 出货 jump wire 跳线twisted pair 双绞线 edition 版别tinned copper 镀锡铜 sales 业务usage 用量全导体 perfect conductor全铝导体 all aluminium conductor全套挤塑-成缆生产线complete extrusion-cabling line全自动圈线包装机full automatic coil packaging plant全自动双头编织机full automatic dual-head braider缺陷数、(漆包线)、针孔数 number of faults 燃气或电热式漆包装置gas-fired or electrically heated wire enamelling plant 绕包 lapp.(lapping)绕包、缠绕、电缆填充物 wormings绕包、带绕包、包带 lapping绕包层 lapped covering绕包层 taped covering绕包车间 wrapping workshop绕包带 taping绕包方向 lapping direction绕包方向 wrapping direction绕包机 wrapper绕包机 wrapping machine绕包机、包带机 lapping machine绕包机、包带机 lapping-machine绕包间隙 butt gap绕包间隙 butt space绕包角 angle of wrap绕包角 lapping angle绕包节距 lay of lapping绕包浸渍绝缘lapped impregnated dielectric绕包绝缘、带(状)绝缘 lapped insulation绕包屏蔽 assembing screen绕包屏蔽 lapped screen绕包屏蔽 wrapped screen绕包屏蔽(层) assembly screen绕包式电缆终端头hand-wrapped termination绕包式电缆终端头 lapped termination绕包式电缆终端头、绕包终端taped termination绕包头 flier绕包头、带包头、包带头 lapping head绕包头、绕包装置 lapper绕包头、旋转式浮拉器 rotating flier 绕包线 lapped wire绕包型接头 hand-wrapped splice绕包型接头 lapped joint绕包型接头 taped joint绕包张力 lapping tension绕包转速、纸包头转速 lapping head speed绕接、缠绕接线法、导体的扭绞连接wire-wrap connection绕线、收线 spool绕线、收线 take up绕线、收线 wind up绕线、收线、绕包 wind绕线、收线、收线(装置) take-up绕线机、收线机 wire winding machine绕线轴架、多轴放线架 creel热导体 thermal conductor热电偶补偿线thermocouple extensioncable热电偶补偿线 thermocouple extension wire热挤出 hot extrusion热挤出用润滑剂 hot extrusion lubricant热塑流试验、软化击穿试验 thermoplasticflow test热塑性氯化聚乙烯护套thermoplasticchlorinated polyethylene jacket热塑性塑料绝缘及护套电缆 thermoplasticinsulated and jacketed cable热缩护套 the heath shrinkable sleeves热液控制、液体控温(法) thermal liquidcontrol热轧铜杆 hot-rolled copper rod热粘合或溶剂自焊性漆包铜圆线heat orsolvent bonding self-gluxing enamelledround copper wire热震试验(对钢化玻璃绝缘子) thermal shocktest(for toughened glass insulator)人造丝包铜线rayon-covered copperconductor溶剂粘接直焊性漆包线solvent bondingself-fluxing enamelled wire柔软)复合材料；复合箔combined(flexible)material柔软的 flexible柔软度试验 flexibility test柔软控制电缆 FCC(flexible control cable)柔软性 flexibility柔软云母材料 flexible mica material软[花、皮]线 flexible wire软导体 flexible conductor软导体、柔软导体、软线 flexible conductor软电缆 BX cable软电缆 flexible cable软电缆 soft cable软管、橡皮管 hose软管；套管 sleeving(软管电缆 cab-tire cable软焊料钎焊、锡焊 soft soldering软焊料钎焊、锡焊 soft-solder软化 softening软化[退火]装置 softening plant软化点 softening point软化击穿 cut-through软化剂 softener软化剂 softening agent软化区、增塑区 softening region软化温度；软化点softeningtemperature;softening point软或退火铜线、软铜线 soft or annealedcopper wire软绞线 flexible stranded conductor软绞线 flexible stranded wire软接线 flexible circuit conductor软拉 s.d.(soft drawn)软拉 soft drawn软连接用电缆cable for flexibleconnections软链段 soft segment软钎焊(缝、点、头) soldered joint软钎焊(缝、点、头) soldering joint软陶瓷绝缘电磁线 soft ceramic insulatedmagnet wire软涂层 soft coating软线 flex conductor软线、连接塞绳 flexible cord软线、连接塞绳、软电缆确良 adj软线、软绳 flexibles软线[绳]、电线电缆、塞绳 cord软线布线 flexible wiring软橡胶 soft rubber润滑脂填充线芯 grease-filled core弱导光波导weakly guiding opticalwaveguide三包层光纤 triple clad fiber三层共挤 boned triple extrusion三层共挤 triple extrusion三层环氧漆包圆铜电磁线tripleepoxy-coated round copper magnet wire三层挤出(机)头 triple extruder head三层挤出(机)头 triple extrusion head三层挤出机 triple extruder三层挤出绝缘电缆three-layer extrudedcable(三层绕包线 triply covered wire三层纱包的 triple cotton-covered三层丝包线 triplex silk covered wire三层同心绞合电缆、三相同轴电缆 tripleconcentric cable三层纸包的 TPC (triple-paper covered)三层纸包的 TPC(triper-paper covered)三股编包线 triple-braided三辊式机架 three-high stand三聚氰胺石棉塑料asbestos filledmelamine plastics三明治(夹心面包片) sandwich三涂层[三包层]光纤 triply-coated fiber三芯电缆 three-conductor cable三芯电力软线 three conductor power cord 三芯软线 three-core cord三芯软线 three-way cord色标聚乙烯石油膏填充 CCP-JF(color code polyethylene-jelly filled)色标聚乙烯石油膏填充电话电缆 color coded polyethylene jelly filled cable色调控制孔径 toll-control aperture色散波长 dispersion wavelength色散补偿光纤dispersion compensated fiber纱(编)丝包线 silk and cotton covered wire 纱包 cotton wrapping纱包 cotton-covering纱包层 cotton sleeving纱包电缆 cotton-covered cable纱包电缆 cotton-insulation cable纱包机 yarn wrapping machine纱包机)的纱碗 cup纱包漆包线 cotton-covered enamelled wire 纱包漆包线 cotton-enamel covered wire纱包漆包线 enamelled and cotton-covered wire纱包铜线 cotton-covered copper conductor 纱包头 cotton covering machine纱包头 cotton lapping head纱包头 cotton yarn wire纱包头 yarn covering head纱包头 yarn-spinning head纱包头、扎纱头 cotton wrapping head纱包头[装置] cotton covering unit纱包线 cotton-covered wire纱包线 cotton-insulated wire纱包圆铜电磁线cotton-covered round copper magnet wire扇形(软线)接头 spade terminal扇形导体 sector shaped conductor扇形导体 sector-shaped conductor扇形实心铝导体sector-shaped solid aluminium conductor扇形铜导体 segment copper conductor扇形线芯的)棱角半径、弯边半径 corner radius扇形线芯的)弯曲半径、棱角半径 edge radius 扇形线芯电缆 segment conductor cable上引法连续铸杆机组upward continuous casting system设备安装线 equipment hook-up wire设定值、控制点 setpoint伸缩补偿电缆 offset cable深凹陷内包层光纤depressed cladding fiber深漆玻璃丝包铜线varnish-bonded glass-lapped copper conductor深漆玻璃丝包铜线varnish-bonded glass-lapped copper conductor生产过程控制 manufacturing control生产过程控制 production control 生产过程控制、程序控制 process control绳、纱、丝、麻)绕包头 spining head绳绕包 string spinning绳绕包机、绕绳机 string spinning machine湿式中拉机 medium wet drawing machine十八盘绞笼 18- bobbin bay十八盘绞笼18- bobbin bay十八盘两段卧式绞线成缆机18-bobbin2-cage horizontal wire stranding andlaying-up machine十八盘两段卧式绞线成缆机18- bobbin2-cage horizontal wire stranding andlaying-up machine十八盘两段卧式绞线成缆机18- bobbin2-cage horizontal wire stranding andlaying-up machine2/2十二头三层绕包机 triple covering machinewith 12 individual heads十六锭高速编织机 16-carrier high-speedbraiding machine十六锭高速编织机16- carrier high-speedbraiding machine24十六锭台式编织机16- carrier benchbraiding machine16十三头绞线机13- fold twisting machine十字并纱机 cross-slubbing machine十字机头、直角机头 cross head十字机头、直角机头 cross-head十字头、直角机头 crosshead石蜡油填充聚乙烯绝缘电缆petrolatum-filled polyethylene-insulatedcable石英包层光纤 silica cladded fiber石英玻璃 silex石英玻璃、熔凝硅石 fused silica石油膏填充 petrojelly filling石油膏填充 petroleum jelly filling石油膏填充设备 jelly-filling equipment石油膏填充塑料电缆 jelly filled plasticcable石油膏填充物、石油膏填充器petroleumjelly cable filler石油膏填充粘结护套联合设备combinedpetro-jelly filling and bonded sheathequipment实路对幻路的串音side-to-phantomcrosstalk实路对幻路的远端串音side-to-phantomfar-end crosstalk实路对实路的串音、实线间串音side-to-side crosstalk实路对实路的串音耦合、实线间串音耦合side-to-side crosstalk coupling实线间的远端串音side-to-side far-endcrosstalk实心导体 solid conductor实心铝导体 solid aluminium conductor实心铝导体 solid aluminum conductor实心铝导体电缆 solid aluminum conductorcable使安全、偿付 indemnify室内导线 interak conductor室温固化 cold curing cold setting适合 fit收、放线设备 pay-off and take-up equipment收、放线装置 pay-off and take-up收放线(装置) take-up and pay-off收放线装置 spooler-unspooler收线成圈机 take-up coiler收线储存器、收线储线器take-upaccumulator收线电机 take-up motor收线架 spooling stand收线架 take-off rack收线架 take-up frame收线架、收线框 take-up drum frame收线架[装置] take-up stand收线架[装置]、收线装置 take-up unit收线绞线机 take-up strander收线篮架 take-up drum carrier收线盘 take-up drum收线盘 take-up reel收线盘 take-up spool收线盘撑架 take-up drum cantilever收线器[机]绕线机 wire spooler收线牵引轮 take-up capstan收线绕线装置 take-up and winding unit收线设备、收线、绕线 spooling equipment收线速度 take-up speed收线张力 take-up tension收线装置 spooling machine收线装置 take-up block收线装置 wire take-up device手动螺杆升降式放线装置 manual screw liftpay-off书包 schoolbag疏绕、间隙绕包 open lapping束(绞)线、编织线 litz wire束(绞)线、编织线 litzen wire束(绞)线、编织线 litzenwire束(绞)线、编织线 litzwire束合导体 bunched conductor束绞导线 bunch-stranded conductor束绞铜束线bunch-stranded copperconductor束绞铜束线bunch-stranded copperconductor束线 bunch v束线、绞合线 bunched wire束线、束绞 bunch-strand束线、束绞 n束线机 buncher束线机 bunching machine数据包 data packing双包层光纤 double-coated optical fiber双包层光纤、双涂层光纤double-coatedfiber双包层条形介质波导 doubly-cladded slab dielectric waveguide双包层条形介质波导 doubly-cladded slab dielectric waveguide双玻璃包扁线 double glass-fiber covered rectangular wire双玻璃包扁线 double glass-fiber covered rectangular wire双玻璃丝包圆线double glass-fiber covered roundr wire双玻璃丝包圆线double glass-fiber covered roundr wire双层编包风雨线 weatherproof double braid 双层编包风雨线 weatherproof double braid 双层编织的 double-braid双层编织的 double-braid双层编织机double tier type braiding machine双层编织机double tier type braiding machine双层编织式外导体同轴电缆 double-braid type coaxial cable双层编织式外导体同轴电缆 double-braid type coaxial cable双层的 double-layer双层的 duplex双层的 twin-layer双层钢带铠装 d.s.t.a.(double layer of steel-tape armour)双层钢带铠装 double layer of steel-tape armour双层钢带铠装 d.s.t.a.(double layer of steel-tape armour)双层钢带铠装 double layer of steel-tape armour(d.s.t.a.)双层钢丝铠装 double wire armour双层钢丝铠装电缆double wire-armoured cable双层鼓轮 double block双层鼓轮 double-deck bull block双层鼓轮拉线机double block drawing machine双层鼓轮拉线机double-capstan wire drawing machine双层鼓轮拉线机twin capstan drawing machine双层滚筒六头拉线机double-deck 6 head type machine双层护套、焊接的皱纹金属管护套 duplex sheath双层护套、焊接的皱纹金属管护套 duplex sheath双层护套电缆的内护套直径 DOIJ双层护套电缆的内护套直径 DOIJ双层环氧漆包圆铜电磁线double epoxy-coated round copper magnet wire双层环氧漆包圆铜电磁线heavy epoxy-coated round copper magnet wire双层环氧漆包圆铜电磁线doubleepoxy-coated round copper magnet wire双层环氧漆包圆铜电磁线heavyepoxy-coated round copper magnet wire双层挤出(机)头 double(extruder)head双层挤出(机)头double-layer extrusionhead双层挤出(机)头 dual (extruder) head双层挤出(机)头 twin (extruder) head双层挤出(机)头 double(extruder)head双层挤出(机)头double-layer extrusionhead双层挤出(机)头 dual (extruder) head双层挤出(机)头 twin (extruder) head双层挤出机 dual extruder双层挤出机 dual extruder双层绝缘导线 double insulated condutor双层绝缘的 double-insulated双层铠装 double armo(u)ring双层拉线鼓轮 double deck drawing capstan双层拉线鼓轮 double-deck drawing block双层绕包头 dual lapping head双层绕包头 duplicate lapping head双层绕包头 dual lapping head双层绕包头 duplicate lapping head双层一次挤出(法) double-layer coatingco-extrusion双层一次挤出(法) double-layer coatingco-extrusion双层直角挤出机头 double layer crosshead双层直角挤出机头 double layer crosshead双层纸 double-ply paper双层纸 duplex paper双窗口光纤(波长为850和1300 nm) doublewindow fiber双分裂导线 double bundle conductor双钢带铠装 double tape armour双钢带绕包头 dual steel taping head双股导线 twin conductor双辊机架 duo rolling stand双辊机架 two-high rolling stand双辊式机架 double-high stand双护套 double sheath双护套电缆 double-sheathed cable双护套电缆 dual jacketed cable双护套光纤 double-jacketed optical fiber双活塞电缆护套挤压机 double-acting cablesheathing press双活塞电缆护套挤压机double-ram cablesheathing press双活塞电缆护套挤压机twin-ram cablesheathing press双机架线材压扁机two-stand wireflattening mill双绞和四线组对绞电缆twin and quadpairing cable双绞式[双节距]成缆机double-twistflyer-type high-speed stranding machine双绞式[双节距]成缆机double-twiststrander/laying-up machine双节距[双倍]束线机 double-twist bunchingmachine双节距成缆机double-twist cablingmachine双节距高速束线机 double-twist laying-upmachine双节距束线机 double twist buncher双节距束线机 double-twist bunch strander双金属挤压、多层一次挤出、共挤出(法)co-extrusion双列[双重]拉丝机 double row wire drawingmachine双螺杆挤出机 double screw extruder双螺杆挤出机 twin-screw extruder双面漆包机double-side enamellibgmachine双面双层十六头纱包机16- headdouble-side douoble-rosette cottoncovering machine)双面双层十六头纱包机 16-head double-sidedouoble-rosette cotton covering machine)双盘放线装置 dual pay-off双盘放线装置 dual pay-off unit双盘收线架 twin drum take-up stand双盘收线装置 twin spooler双盘越端放线(装置) dual flyer pay-off双盘越端放线(装置) dual flyer typepay-off双漆包纸绝缘电线 Tietgen conductor双纱包的 double-cotton covered双纱包机 double-cotton covering machine双纱包线 double cotton-covered wire双丝包的、双层丝绝缘 double-silk covered双丝包的、双层丝绝缘 double-silk covered双丝包机 double-silk covering machine双丝包漆包线eds(enameldouble-silk-covered wire)双丝包漆包线 enamel double-silk-coveredwire双丝包线 double silk-covered wire双头编织机 dual-head braider(双头挤出、双层挤出 twin-head extrusion双头挤出、双层挤出 twin-head extrusion双头立式放线架 twin headed swift双芯电缆 two-conductor cable双芯电缆、对绞电缆 twin cable双芯软线 double conductor cord双纸包头 double-paper head双重纵包 double longitudinal application水线电码直接打印机cable code directprinter瞬变[断]直流电压 chopped d.c. voltage丝包机 silk covering machine丝包机 silk wrapping machine丝包机 silk yarn covered wire丝包漆包线 enamel silk-covered wire丝包软线 silk-covered cord丝包束合漆包铜线textile -covered bunched enamelled copper wire丝包铜线 silk-covered copper conductor 丝包线 silk-covered wire丝包圆铜电磁线 silk-covered round copper magnet wire丝编织线 silk braided wire四(线组)串四(线组) crosstalk between star quad四(线组)串同(轴对) crosstalk between star quad and coaxial pair四层聚酯漆包扁铜电磁线quadruple polyester-coated rectangular copper magnet wire四带绕包头 four-tape lapping head四辊机架 quarto stand四辊式机架 four-roller stand四辊式轧机机架 four-high mill stand四机架线材压偏生产线four stand wire flattening line四节距束线机 four twist bunching machine 四路导线 quadruple conductor四盘偏心式包带机 four pad eccentric tape head松包 loose covering松包的 loosely wrapped松包光缆 loose tube fiber cable松包光纤 loose tube optical fiber松包光纤 loosely packaged fiber松包光纤光缆optical fiber cable with fibers loosely packaged松包缓冲套[层]<光纤的> loose buffer jacket松包结构 loose structure松套管-紧包缓冲层光纤生产线loose tube.tight buffer fiberoptic production line松套聚合物包层石英光纤loose polymer-clad silica fiber送料螺杆 stockscrew苏维埃苏维埃的 Soviet素炼机、软胶机 homogenizing roller塑料[非金属]护套电缆 plastic-sheathed cable塑料包层石英(光纤) PCS(plastic-clad silica)塑料包层石英光纤 PCS(plastic-clad silica fiber)塑料包覆光纤、塑料包层光纤 plastic-clad fiber塑料薄膜 plastic film塑料薄膜包线 plastic film covered wire 塑料薄膜带 plastic film tape塑料护套 plastic sheath塑料护套厚度检测装置 plastic thickness test unit 塑料护套软线 plastic-sheathed flexiblecord塑料挤出机 plastic extruder塑料绝缘导体 plastic insulated conductor塑料绝缘线芯 plastic insulated conductor塑料绝缘线芯电缆plastic-insulatedconductor cable塑料绕包绝缘 lapped plastic insulation缩)到岸价 CIF缩醛漆包铝圆线polyvinyl acetalenamelled round aluminium wire缩醛漆包铜扁线polyvinyl acetalenamelled rectangular copper wire缩醛漆包铜圆线polyvinyl acetalenamelled round copper wire缩醛漆包线polyvinyl formal enamelledwire缩醛漆包线polyvinylacetal enamelledwire塔轮式拉丝[线]机cone-type drawingmachine碳化钨(拉丝)模、硬质合金(拉线)模tungsten-carbide(drawing) die特软绞线extra-flexible strandedconductor特细丝导线 extra-fine wire conductor体现、包括(含) embody天安门广场 Tian An Men Square天然橡胶护套 natural rubber jacket填充、充填、填料 filling填充、填料、锁紧装置 blocking填充[封]物、填料、填芯 filler填充包套联合生产线integrated fillingand sheathing line填充材料 filling material填充电缆 filled cable填充复合物、填料、填充剂、填充混合物、浇注料、浇注剂 filling compound填充机 filling machine填充剂 filler compound填充率 compaction ratev填充四线组、间充四线组 interstitial quad填充温度、浇注温度 filling temperature填充物、填料 loading material填充系数 fill factor填充系数、占体率 fill in ratio填充系数、占体率 fill-in ratio填充线芯导线 fill-core conductor填充用户电缆 filled service cable填料、填充、塞入 stuffing填料[填充]法 stuffing process条形介质光波导 slab dielectric opticalwaveguide条形介质光波导 slab dielectric waveguide通信软件 communication software通用单芯无护套电缆general purposesingle-core nonsheathed cable通用丁腈/聚氯乙烯护套general-purposeacrylonitrile-butadiene/polyvinylchloride(NBR/PVC) jacket通用回转式挤出机versatile turretextruder通用氯化聚乙烯护套general-purposechlorinated polyethylene(CPE) jacket通用绕包机 universal wrapping machine通用乙丙烯橡皮护套general-purposeethylene-propylene rubber jacket通用乙丙烯橡皮护套general-purposeethylene-propylene rubber jacket同(轴对)串四(线组) crosstalk betweencoaxial pair and quad同(轴对)串同(轴对) crosstalk between twocoaxial pairs同节距绞合 unilay stranding同向绞合 unidirectional lay同心层绞导线 concentric lay conductor同心导体 concentric conductor同心绞合线芯concentric strandedconductor同心螺绞导线 rope-lay stranded conductor同心式包带机、同心式绕包机 concentrictype taping machine同心式包带头 concentric taping head同心式绞合1350铝导线concentric-lay-stranded aluminium 1350conductor同心式绞合5005- H19同心式绞合6201- T81同心式绞合钢芯铝绞线concentric-lay-stranded aluminiumconductor,coated steel-reinforced同心式绞合铝包钢导线concentric-lay-stranded aluminium-cladsteel conductor同心式绞合铝导体concentric-lay-stranded aluminiumconductor同心式绞合铜包钢导线concentric-lay-stranded copper and cladsteel conductor同心式绞合铜导线concentric-lay-stranded copper conductor同心式绞合铜和铜包钢复合导线concentric-lay-stranded copper andcopper-clad steel composite conductor同心式绕包机 concentric lapping machine同心式绕包机 concentric taper同心式绕包头 concentric lapping head同心式绕包头、同心式绕包机centralspinner同心式绕包头、同心式绕包机 concentriclapper同心中性导体concentric neuttralconductor同心中性线 concentric neutral conductor同轴内导体 coaxial inner conductor。

制作德式香肠英语作文

制作德式香肠英语作文German Sausage MakingTraditional German sausages are not only a culinary delight but also a cultural symbol that dates back centuries. The meticulous art of creating these savory delights involves a blend of precise techniques, quality ingredients, and a true passion for preserving heritage. Let's delve into thefascinating world of German sausage making.The key to crafting authentic German sausages lies in the selection of meat. Typically, a mix of pork and beef is used, with specific cuts like shoulder, belly, and back fat to achieve the perfect balance of flavor and texture. The meat is then meticulously ground to a fine consistency, ensuring that each bite is a harmonious blend of juicy meat and subtle fat.Seasoning is another crucial aspect of the process. A blend of spices such as salt, pepper, marjoram, and caraway seeds is added to the meat mixture, infusing it with the distinctive flavors that characterize German sausages. Some variations may include garlic, nutmeg, or coriander for added complexity.Once the meat is seasoned, it is time to encase it in natural casings. Traditionally, intestines are used to hold the meat mixture, giving the sausages their signature shape and snap. The filled casings are then twisted or linked into individualsausages, each one a testament to the artisanal skill of the sausage maker.Cooking methods vary depending on the type of sausage being prepared. While some sausages are smoked to perfection over beechwood chips, others are simmered in broth or grilled to achieve a crispy exterior. Regardless of the cooking technique, the goal remains the same – to lock in the flavors and create a delectable sausage that is rich in taste and history.German sausages come in a myriad of varieties, each with its own unique recipe and regional influence. From the hearty Bratwurst of Bavaria to the spicy Currywurst of Berlin, these sausages reflect the diverse culinary landscape of Germany. Whether enjoyed at a bustling beer hall or sizzling on a backyard grill, German sausages are a beloved staple that brings people together in celebration of good food and good company.In conclusion, the art of making German sausages is a timehonored tradition that continues to thrive in kitchens and butcher shops across Germany and beyond. With a blend of topquality ingredients, timetested techniques, and a dash of creativity, anyone can embark on a culinary journey to create these flavorful sausages at home. So, gather your ingredients, roll up your sleeves, and savor the satisfaction of crafting your very own batch of authentic German sausages. Guten Appetit!。

电线电缆专业术语翻译[整理版]

电线电缆常用英语Color 颜色Red 红色Black 黑色Blue 蓝色White 白色Brown 棕色Green 绿色Y ellow 黄色Orange 橙色Pink 粉红色Purple 紫色Tan茶色Gray 灰色Cool gray 冷灰Ivory 象牙色Golden 金黄色Aqua 浅绿色Light Green 浅绿色Lavender 淡紫色Light blue 浅蓝色Dark blue 深蓝色Beige 贝吉色Silvery gray 银灰色Misty-white 雾白色Natural自然色Milk-white/Milky 乳白色Green/Y ellow绿黄色Test 测试Electrical test 电气测试Open 开路Short 短路Miss wire 错线Resistance 电阻Bend test 弯折测试Hi-pot高压/耐压V oltage电压/伏特数Ampere=A 安培Capacitance=C 电容Measure 测量Insulation resistance 绝缘电阻Conductor resistance 导通电阻Alternate Current=AC 交流电Direct Current=DC 直流电Pull force test 拉力测试Tester 测试机Meter 仪表Leakage current 漏电流Less than 小于Impedance阻抗Frequency频率Attenuation衰减Standing wave/Stationary wave 驻波Cable 线材Conductor 导体Material 材质Diameter 直径Solid copper 硬铜(线) Unshielded 无屏蔽Annealed copper 软铜(线) Tinned copper 镀锡铜Aluminum 铝Al/foil 铝箔Al/mylar 铝箔麦拉Braid 编织Drain 地线Clear mylar 透明麦拉Spiral 缠绕Shield 遮蔽Separator 隔离层Cover 覆盖Filler 填充物Insulation 绝缘Jacket 外被Twisted pair 双绞线Lead导线/铅Coaxial=Coax(同轴线) Solid 实心的Strand wire多股线American Wire Gauge=AWG 美国线规Crimping 铆压Crescent 月牙型Oval 椭圆形Shape 形状Rectangular 矩形Tetra- 四方Front cut off tab 前切料带Rear cut off tab 后切料带Front bell-mouth 前喇叭口Rear bell-mouth 后喇叭口Wire barrel 导体包铜Insulation barrel 绝缘包铜Wire barrel seam 导体包铜接合处Mating area 适配区Bell-mouth 喇叭口Conductor extension导体突出Wire end protrusion length 铜丝伸出长度Insulation protrusion length 绝缘伸出长度Wire barrel flash 导体包铜披锋Crimping height 铆高Crimping depth 铆压深度Crimping width 铆宽Material 物料Terminal 端子Housing 胶芯Tin plated 浸锡/镀锡Gold Flash 镀金Nickel Plated 镀镍Screw 螺丝Tissue Tape 棉带Mini Tie 小扎带Diode 二极管PVC 聚氯乙烯PE聚乙烯Label 标签Label Text 标签印字Marking 印字Text height 印字高度Box 盒子Carton 纸箱Jumper wire 跳线PE film PE膜Bubble pad 气泡片Foamed paper 珍珠棉Red strip 红边Dust cover/cap 防尘罩Hood-plastic塑胶壳Metal hood 金属壳Connector 插头Cable tie 扎带Ferrite core 铁粉芯Short bar 短路片Heat Shrink Tubing=HST 热缩套管Adhesive 带粘性的light-emitting diode=LED发光二极管-free无---的,免除---的Tape带子Row排/行Coil 卷/盘绕Copper foil 铜箔Nylon尼龙Location位置Double 双的Individual单独的Width宽度Height高度Switch开关Antistatic抗静电的Socket插座Plug插头Fuse保险丝Clamp夹子Ring环/环状物Bundle捆/束Brass黄铜Bar code条形码ESD:electrostatics discharge 静电放电Vice versa:反之亦然RoHS:Restrictions on the use of Certain Hazardous Substances限制物质使用Unit/Equipment 单位/仪器pound磅inch英寸Feet英尺Newton=N 牛顿Hour 小时Minute分钟Second秒Decimeter 分米kilometer=KM千米meter=M 米centimeter=CM 厘米millimeter=mm毫米kilogram=KG 千克gram=G克megohm 兆欧姆ohm欧姆milliohm 毫欧lb./lbs.磅Square 平方Cubic 立方cubic foot 立方英尺cubic meter立方米square inch 平方英寸square meter 平方米tapeline卷尺Steel rule 钢尺micrometer千分尺vernier caliper游标卡尺Magnifier放大镜Microscope显微镜profile projector 投影仪Defect 不良断裂Broken 水纹Water Mark 裂纹/裂缝Crack脏污Dirty 起泡Bubbling 冲胶Expose凹痕Dent 水口Gate 缺口/缝隙Gap变形Deformation 金属批锋Burr 杂色Coloration露铜丝Exposed wire 弯曲Bending 缺料Lack Material生锈Rusty 缩水Shrinkage 杂质Impurity刮花Scratch 灰尘Dust 氧化Oxidized错位Miss Wire 开/短路Open/Short circuitOthers 其他semi- 半,不完全地semi-strip半剥Removed 除去Pitch 间距Single 单的Pair 双的Double两倍的Triple 三倍的Male 公Female 母Minor 次要的Main主要的Minimum=Min 最小值Maximum=Max 最大值Anode 正极Cathode 负极Molding 成型Inner molding 内模成型Outer molding 外模成型Solder 焊接Crimping 铆压Revision修订版本SR:strain relief 应力消除Length长度Stripping 开剥Dimension尺寸Tolerance 公差Reference=REF参考UL:Underwriters`laboratories (美国)保险商实验所PRC:People’s Republic of China 中华人民共和国Made 制造Country国家Origin起源Cover覆盖Bulk散装Lubricate 润滑Position位置Tinned浸锡Customer客户Detail 细节Per 由/每Center中心Degree度数/度Dot圆点/点Pre- ---之前Scan扫描Expose暴露Cross section横截面Retain/Remain保留Ink墨水Key关键/键,栓Content内容Twist绞/扭Top顶部Bottom底部Middle中间Dimension尺寸Tolerance公差Empty空的Stamp印记/标记Ratio比率Pull 拉/拉力Force力量Overlap与---交迭Flag旗形Around周围/环绕Angle角/角度Quality term 品质术语IQC:incoming quality control 进料检验IPQC:in process quality control 制程品质控制OQC:outgoing quality control 出货品质控制FQC:final quality control 最终品质控制DCC:document control center 文控中心QCC:quality control circle 品管圈QA:quality assurance or quality audit 品质保证/品质稽核QC:quality control品质控制QE:quality engineering品质工程Training 培训ZD:zero defect 零缺陷。

机械专业英语词汇

General 通用法规，规范, code标准, standard暂行标准, tentative standard达到标准, come up to the standard 定标准, fix (set up) a standard 标书，技术规格, specification 要求, requirement满足要求, fulfill requirement 细则, regulation规则, rule法律, law条款, provision总则, general provision附带条件，限制性条款, proviso 判椐, criterion (pl. criteria) 约定条件, stipulation合同规定, on the stipulation that合同, contract签订合同, sign a contract拟订合同, draw up a contract 违约, breach of contract代理人, mandatory强制性的, mandatory,restrictive非强制性的, optional条件, condition符合, conform to (with)遵守, comply with确认, confirm证书, certificate认可, approve (v), approval (n.) 接收, accept (v.), acceptance (n.), acceptable (a.)评定, qualify (v.) qualification (n.)满足, meet许可, permit拒收, reject废品, rejection鉴别, identify提交, submit to论证, demonstrate公约, convention仲裁, arbitration公证, notarization公证人, public notary商检, commodity inspection & testing独立检验员, independent inspector业主代表, representative of S / V业主, owner委托人, client签署, sign要求, request监理员, supervisor, surveyor检查鉴定, survey检查, inspect, check,验证, verify目击，见证, witness禁止, prohibit建议, recommend满意的, satisfactory 授权, authorize文件, document审查, review监控, monitor测定, detect逐个检验, individual inspection 抽样检验, sampling inspection, cross check巡检, touring inspection, patrol inspection评价, evaluate试验, test实验, experiment试样, specimen可跟踪性, traceability预先具有资格, prequalify判定，评价, judge责任, responsibility, obligation, duty折衷，兼顾, compromise官方，管理局, authority样本, sample保证, assure通知单, notification通知, notify (v.) notice (n.) 会议纪要, minutes数量, quantity质量, quality质量控制, quality control(Q.C) 质量保证, qualityassurance(Q.A)缺陷, defect损坏, damage临界的, critical受控文件, valid document停止点, hold point(H)交货, delivery竣工图, as-built drawing原始记录, original record传阅, recycle批注, comment答复, reply紧急, urgent宣读, read out 直线度, straightness垂直度, perpendicular平整度, flatness同心度, concentricity同轴度, axiality平行度, parallelism圆度, roundness平面度, planeness随机的, random不平, uneven空心, hollow同心, concentricity偏心, eccentric表面粗糙度, surface roughness 尺寸公差, dimension tolerance 允许误差, admissible error上偏差, upper deviation下偏差, lower deviation尺寸, dimension长度, length宽度, width高度, height厚度, thickness深度, depth跨度, span直径, diameter半径, radius外径, outer diameter内径, inner diameter口径, caliber拱度, camber挠度, deflection旁弯, lateral flexure径向跳动, runout端面跳动, endface runout中心线偏斜, lack of alignment 弯曲, flexure, bending斜度, slope角度, angle对角线, diagonal平行线, parallel中心线, center line斜线, oblique line切线, tangential line 轮廓线, contour line原点，起点, original指标, index转速, rotary speed方向, direction指南, guide选定, choose选择, select挑选, pick炉批号, heat / plate number, heat batch炉、批, lot or heat编制, drafting签发, sign & issue执行, performance报标, invitation for tender投标, tender, bid开标, bid opening中标, success of bid询价, inquiry标价, quotation of prices, offer 不相符, non-conformance遗漏, omission去掉, remove更换, renew修补, repair几何形状, geometry型号, model暂时, temporarily测量, measure附件, annex, attachment 修正, amend型材, bar stock湿气, moisture发出, issue填写, fill in开工会, kick-off meeting 间距, interval承包商, contractor分保商, subcontractor供货商, supplier操作错误, operate missing 签证, visa敲打检查, hammering test 拉伸试验, tensile test冲击韧性, impact toughness冲击功, impact work抗拉强度, tensile strength屈服强度, yield strength弯曲角, angle of bending冲击韧性试验, impact cupping test压扁试验, squeezing test侧弯试验, side bend test背弯试验, root bend test面弯试验, face bend test纵弯试验, axial bend test硬度试验, hardness test破断延伸率, percentage of elongation of break断面收缩率, percentage seduction of area无损检测, nondestructive test (NDT)破坏试验, destructive test外观检查, visual examination超声波探伤, ultrasonic test (UT) 射线探伤, radiographic test(RT) 磁粉探伤, magnetic particle test (MT)渗透探伤, penetrant test (PT) 密封性试验, leak test气密试验, air tight test压力试验, pressure test水压试验, hydraulic test气压试验, pneumatic test冲水试验, fill water test宏观组织检查, macroscopic examination微观组织检查, microcosmic examination侵蚀, erosion底片, radiographic test film变形, distortion试运行, trial operation永久变形, permanent deformation 凸起, camber凸出, protrusion 凹进, concave超出, protrude beyond清除, decontaminate失败，故障, failure断裂, fracture塌陷，凹陷, collapse中断, discontinuity裂缝, crack发裂, flaw龟裂, fissure毛细裂纹, capillary crack 起始裂纹, incipient crack 断层裂纹, fault fissure积水, stagnant water船舱, cabinProcessing 工艺加工, processing, working 工艺学, technology工艺技术, technique工艺的, technologic工位, station, position工序, procedure, operation工步, step车间, shop, workshop工厂, mill, factory, manufacturer工地、现场, site外场, yard, field侧面, side断面, section结构, structure, construction 构件,部件, member, component 零件, part, element机构, mechanism装置, device机件, machinery机械零件, mechanical element 基准, datum水平基准线, horizontal reference line精度, accuracy余量, allowance组件, assemble分装件, subassemble 包装, package外协件, cooperation外购件, purchase part备件, spare part裸装件, nudes散装件, odd lot, odds & ends拆包, unpackaging工件, workpiece装箱单, packing list焊接, Welding对接焊, butt welding角焊, fillet welding搭接焊, lap welding船形焊, fillet welding in down hand塞焊, plug welding平焊, down hand welding横焊, horizontal position welding立焊, vertical position welding 仰焊, overhead position welding 全位置焊, all position welding平角焊, horizontal fillet welding仰角焊, fillet welding in the overhead衬垫焊, welding with backing 单面焊双面成形, one-side welding with back formation定位焊, tack welding堆焊, surfacing返修焊, rewelding补焊, repair welding隔离层堆焊, buttering手工焊, manual welding自动焊, automatic welding焊条电弧焊, shielded metal arc welding(SMAW)埋弧焊, submerged arcwelding(SAW)气保焊, gas shielded arc welding 氩弧焊, argon arc welding钨极氩弧焊, argon tungsten arc welding 熔化极惰性气体保护焊, MIG钨极惰性气体保护焊, TIG活性气体保护电弧焊, metal active-gas arc welding (MAG) CO2气保焊, carbon-dioxide arc welding药芯焊丝CO2气保焊, arcos arc process, dual shielded arc welding单面焊, welding by one side 双面焊, welding by both sides 单道焊, single pass welding 多道焊, multi-pass welding单层焊, single layer welding 多层焊 , multi-layer welding 连续焊, continuous welding断续焊, intermittent welding 打底焊, backing welding盖面焊, cosmetic welding分段退焊, backstep welding纵缝, longitudinal seam横缝, transverse seam环缝, circumferential seam螺旋缝, spiral seam坡口, groove坡口面, groove face坡口面角度, level angle坡口角度, groove angle坡口高度, groove depth钝边, root face钝边高度, thickness of root face 根部间隙, root gap根部半径, root radius根部锐边, root edgeI型坡口, square groove坡形板边（削薄）, tapered edge 焊缝表面, weld face焊缝背面, back of weld焊缝尺寸, size of weld焊缝厚度, throat thickness熔深, penetration焊缝成形, appearance of weld余高, reinforcement背面余高, root reinforcement 焊脚, leg焊缝腰高, theoretical throat焊根, weld root焊趾, weld toe凸形角焊缝, convex fillet weld 凹形角焊缝, concave fillet weld 交错断续角焊缝, staggered intermittent fillet weld并列断续角焊缝, chain intermittent fillet weld密封焊缝, seal weld熔透焊缝, penetration bead保留垫板, permanent临时垫板, temporary backing垫板, backing铜垫板, copper backing焊剂垫, flux backing引弧板, run-on tab end tab引出板, run-off tab end tab 引弧, arc start, arc burning熄弧, arc outage, arc blowout 焊接工艺评定, welding procedurequalification(WPQ)焊接工艺规程, welding procedure specification(WPS)焊接工艺参数, welding parameter 焊接电流, welding current电弧电压, arc voltage焊接速度, weld travel speed预热, preheat后热, postheat层间温度, interpass temperature 焊后热处理, post weld heat treatment焊接环境, welding surroundings 焊工考试, welder qualification test清根, root back gouged, back chipping清渣, slag removal定位板（马〕, strong-back电弧偏吹, arc flow熔滴, droplet拼接, splice 焊缝清理, weld cleaning气刨, gouge批凿, chip锤击, peening捻缝, caulking中间焊层, intermediate weld layer划线, mark off熔渣, slag焊缝穿越孔, weld access hole 焊态, as-weld过热组织, overheated structure 魏氏组织, Widmannst?tten structure层状偏析, lamellar segregation 熔合线, bound line热影响区, heat-affected zone (HAZ)碳当量, carbon equivalent晶间腐蚀, intercryctalline corrosion敏化区腐蚀, weld decay焊接残余应力, welding residual stress消除应力, stress relieving退火消除应力, stress relieving by annealing焊接残余变形, welding residual deformation角变形, angular distortion波浪变形, wave-like deformation 扭曲, twisted收缩, shrinkage反变形, backward deformation刚性固定, rigid fixing校正, straighten火焰校正, flame straightening 焊接缺陷, weld defect裂纹, crack层状撕裂, lamellar tearing气孔, blowhole密集气孔, porosity虫形气孔, worm hole咬边, undercut 焊瘤, overlap凹坑, pit烧穿, burn through塌陷, excessive penetration未焊透, incomplete penetration 未熔合, incomplete fusion未焊满, Incompletely filled weld 根部缺陷, root concaving电弧擦伤, arc scratch, arc strike夹渣, slag inclusion白点, fish eye错边, dislocation, mismatching, misalignment分层, stratification嵌条, insert飞溅, spatter机械擦伤, mechanical damage焊缝成形差, rough weld锤痕, hammering pit麻点, pock边缘不平整, rough edge剥落, peel弧坑, crater焊道曲折, zigzag weld外形规整, smooth contour歪斜, crooked翘曲, warping焊接材料, welding consumables 焊条, electrode酸性焊条, acid electrode碱性焊条, basic electrode低氢焊条, low hydrogen type electrode焊剂, welding flux焊丝, welding wire镀铜焊丝, copper -plating welding wire药心焊丝, flux-cored wire电弧焊机, arc welding machine 弧焊电源, arc welding power source焊条保温筒, thermostat for electrode 干燥箱, dryer地线, earth lead地线夹头, earth clamp平台, platen滚轮架, turning roll胎架, placentas压缩空气, compressed air焊接量规, weld gauge测温笔, tempil stick打磨, grind (ground)焊钳, electrode holder砂轮机, grinder钢丝刷, wire brush砂纸, sand-paper砂布, emery cloth气焊, gas welding氧-乙炔焊, oxy-acetylene welding热喷涂, thermal spraying气割, gas cutting电弧切割, arc cutting等离子弧切割, plasma arc cutting(PAC)空气等离子弧切割, air plasma arc cutting仿形切割, shape cutting数控切割, NC cutting碳弧气刨, carbon arc air gouging 坡口切割, bevel cutting切割面质量, quality of cut face 缺口, notch挂渣, adhering slag结瘤, dross周边焊, around welding电弧偏吹, arc blow焊态, as-welded铜垫板, copper chill plate焊接熔池, weld pool焊接区, weld region送丝速度, wire feed speed反变形, backward deformation收缩变形, contraction deformation翘曲变形, deflection deformation油漆, Painting底漆, primer painting, under coating中层漆, intermediary painting 面漆, finishing painting, top coating锌粉底漆硬化剂, curing agent, hardener溶剂, solvent溶剂气化, solvent boiling稀释剂, thinner环氧富锌漆, epoxy zinc rich primer磷化漆, Phosphorized painting 沥青, asphalt表面预处理, surface pretreatment喷砂, sand blasting喷丸, shot blasting除锈, rust removal, derusting 除漆, depainting脱脂, degreasing除氧化皮, scaling喷涂, spray painting刷涂, brushing防锈, antirust辊涂, roller-painting电镀, electroplating镀锌, galvanized腻子, putty刮腻子, puttying擦净, scouring晾干, airing嵌填, implant防滑面漆, finishing non-slip paint清漆, varnish防锈漆, rust preventive oil 脱脂漆, antirust grease防锈纸, rust preventive paper 搅拌, stirring条纹状涂层, stripe coating色素, pigment 沉淀, sediment无空气喷漆, airless spray相对湿度, relative air humidity 湿度计, moisture gauge, psychomotor粗躁度, profile roughness干膜厚度,湿膜厚度,膜厚仪, film thickness gauge粘度计, viscosity meter露天, open含水量, moisture content混合比例, mixing ratio风向, fan angle清洁度 , cleanliness覆盖度, coverage露点测量器, dew point calculation汽化, flash off再喷涂最小间隔, minimum recoating interval附着力试验, paint adherence test,cross-hatch test附着力 , adhesion密度, density起泡, blistering气泡, bubble气孔, blowhole针孔, pin hole起皱, wrinkling, crumple凹坑, pitting流淌, running流挂, sagging起皮, peeling桔皮状, orange peeling发黑, blackening泛黄, yellowing开裂, cracking颜色和光泽不均匀, uneven colour & gloss涂层中夹灰和砂, retention of dust &sand厚度不均匀, uneven thickness of film 露底, holiday剥落, peel off脱皮, spalling刷痕, brush mark渗色, bleeding自然老化, weathering飞漆, overspray漆渣, paint dregs油漆烧焦, burnt &charred paint 褪色, discolour; fading粉状表面, powdery surface污染, contamination鳞片, lamination刮痕, scratch堆积, accumulation混浊膜, blushing烤焦, boiling粘附, sticks浪费油漆, over consumption of paint隐蔽部位, hidden past散布, scattered残余物, residues光泽, gloss均匀地, evenly尾状漆, tailing灰尘, dust锈, rust干燥, drying油漆附着力强度值, painting adherence strength value 氧化皮, oxide scale冷作, cold work配作, matching making对称制作, symmetrical排料, blank layout放样, lofting, layout展开, development号料, layout off胀形, bulging扩口, flaring ,expanding 缩口, necking拱曲, arching放边, release side 卷边, curling, crimping折边, hemming, folding翻边, flanging刨边, edge planning修边, trimming拔缘, side bending矫正、校形, correction, rectification矫直, straightening, leveling 校平, flattening划线, laying out切断, cutting打样冲眼, center-punching锯切, sawing錾削, chipping铲去, chips off压皱, corrugate锉削, filing堵孔, hole plugging出白, baring工件, work piece嵌补, inserting贴补, patching榫接, rabbet抛光, polishing机械加工, Machining, Mechanical working钳工加工, bench working砂纸打磨, sanding找正, centering配键, key fitting刮研, spotting-in, rescraping 配研, running-in, facing-up 毛刺, burr去毛刺, deburring无毛刺, out buss打磨修正, dress修磨光滑, dressed smooth滚花, knurling倒角, chamfering倒圆角, sounding, filleting 倒钝锐边, breaking sharp corners，rounding sharp edges 车削, turning rolls 铣削, milling刨削, planning, shaping钻孔, drilling铰孔, reaming锪削, spotting镗削, boring插削, slotting拉削, (pull) broaching推削, push broaching铲削, relieving, backing-off 刮削, scraping磨削, grinding滚削, hobbing扩孔, counterboring, core drilling冲孔, punching, piercing, perforation钻中心孔, centering模具, die, mould力矩扳手, torque wrench铆接, riveting剪断, shearing锯断, sawing粘接, glued joint, adhesive-bonding热处理, Heat treatment 表面热处理, surface heat treatment固溶处理, solution heat treatment稳定化处理, stabilizing treatment水韧处理, water toughening 渗碳, carburization, carburizing渗氮, nitriding磷化, phosphating硬化,强化, hardening时效, ageing退火, annealing正火, normalizing淬火, quenching回火, tempering调质, quenching& tempering 脱碳, decarbonization过烧, burning过热, overheating冷脆, cold brittleness热(红)脆, hot(red) shortness 氢脆, hydrogen embrittlement 蓝脆, blue brittleness回火脆性, temper brittleness 偏析, segregation白点, flake, white spot软点, soft spot晶粒, grain晶界, grain boundary断口, fracture总装, general assembly零件装配, component assembly 部件装配, subassembly配合, fit安装, erection, installation 拆卸, disassembly, dismantle 磨擦, friction磨损, abrasion, wear润滑, Lubrication集中润滑, central lubrication 分散润滑, separate lubrication 泄漏, leakage密封, seal填料函(箱), stuffing box填料, packing铸造, Casting冒口, riser, feeder浇口, gate, sprue粘砂, burning-on砂眼, sand hole气眼, air pocket结瘤, heel多肉, metallic projections残缺, incompleteness冷隔, cold shut缩孔, shrinkage清砂, cleaning铸型, mold型芯, core铸件, casting 锻造, Forging锻件, forge piece成形, forming辊形, roll forming冲压, stamping, pressing, punching冲裁,落料, blanking旋压, spinning滚压, rolling拉延, drawing拉拔, drawing, draft轧制, rolling弯形, bending弯管, pipe bending卷园, edge coiling切口, lancing翻孔, hole flanging滚园, rolling circle下料, cropping冲压件, stamping回弹, spring-back展宽, spreading角裂, chink飞边, flash off连皮, wad, slug凸耳, earing隆起、堆积, piling, build-up烧损, scale (heating)loss缩孔, shrinkage cavity缺肉, underfill非金属夹杂, non-metallic inclusions折（重）叠, lap, overlap错差, mismatch粉末冶金, Powder metallurgy 粉末冶金制品, powder product烧结结构零件, sintered structural part手提电脑, notepad, laptop程序, program软盘, floppy disk软件, software光盘, CD-ROM病毒, virus 杀毒, kill virus数码像机, digital camera容量, capacityCrane起重机桥吊, quayside crane轮胎吊, rubber tyred gantry crane(RTG)装船机, ship loader卸船机, ship unloader堆取料机, stacker-reclaimer 前大梁, boom后大梁, girder立柱，支腿, leg海侧, seaside陆侧, landside上横梁, upper beam下横梁, sill beam连接横梁, horizontal beam 梯形架, A-frame, pylon大平衡梁, upper equalizer 中平衡梁, intermediate equalizer小平衡梁, lower equalizer主动车架, driving bogie从动车架, driven bogie前拉杆, forestay后拉杆, backstay斜撑杆, diagonal bar机器房, machinery house司机室, operator's cab电器房, electrical room理货室, check's cab俯仰操纵室, boom hoist cab小车, trolley大车, gantry托缆小车, catenary trolley吊具, spreader上架, headblock电梯, elevator吊钩横梁, hook beam辅助结构, auxiliary structure 后置平台, rear platform倾转平台, trim / list / skew (T / L / S) platform 上铰座, upper bracket下铰座, lower bracket防挂仓装置, snag load device锚定装置, anchor device顶轨装置 , rail brake device防风系缆, tie down防碰撞装置, bumper轨道夹钳, rail clamp吊具调整装置, trim, list & skew device安全钩, boom latch, safe hook 电缆卷筒, cable drum, cable winder电缆拖令, festoon cable车挡, stopper避雷针, lightning rod灭火器, fire extinguisher防摇装置, anti-sway device防跳装置, anti-bouncer防松装置, slack-preventing device起升滑轮, main hoist reel牵引滑轮, trolley travel reel 俯仰滑轮, boom hoist reel出绳罩, ropes outlet hood吊耳, lifting lug铰点, hinge隔板, diaphragm腹板, web盖板, flange纵向加筋, longitudinal fillet 承轨梁, track girder, rail beam 横梁, transverse beam, cross beam伸缩梁, telescopic beam吊具导板, flipper吊具转销, spreader twistlock梯子, ladder阶梯, stop, stair平台, platform走台, footwalk, walkway扶手, hand rail栏杆, railing护栏, protection cage 直梯, vertical stair斜梯, inclined stairs(ladder) 踢脚板, skirting boards, foot panel波纹板, corrugated plate花纹板, chequered plate网板, wire-mesh plate格栅板, grating plate, grid plate折边板, edgefold plate支承板, bracket支架, support拉板, tie plate档板, baffle钩销, hook pin联接板, link plate泄水孔, drainage hole排水孔, outlet entrance排水管, draw-off tube铭牌, name plate钢丝绳, steel wire, rope卷扬筒, drum马达, motor减速器, reducer滑轮, reel, sheave, pulley制动器, brake制动盘, brake disc制动瓦块, brake shoe制动鼓, brake drum制动带, brake belt制动杠杆, 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† Jan
Abstract It is argued that the twisted gauge theory is consistent provided it exhibits also the standard noncommutative gauge symmetry.
1
Supported by the grant no 1P03B02128 of the Polish Ministry of Science
On the Consistency of Twisted Gauge Theory
Stefan Giller† Cezary Gonera‡ Piotr Kosi´ nski‡ Pawel Ma´ slanka‡
பைடு நூலகம்
1
arXiv:hep-th/0701014v2 4 Jan 2007
Dlugosz Academy in Czestochowa Institute of Physics ul. Armii Krajowej 13/15, 42-200 Czestochowa, Poland e-mail: sgiller@uni.lodz.pl ‡Theoretical Physics Department II, University of L´ od´ z, Pomorska 149/153, 90-236 L´ od´ z, Poland e-mail: cgonera@uni.lodz.pl pkosinsk@uni.lodz.pl pmaslan@uni.lodz.pl
In the recent years the noncommutative ﬁeld theories [1, 2, 3] have gained much attention. This is in part due to the fact that they emerge as a speciﬁc limit of string theory and, being much simpler than the original string theory, yet keep some of its properties [4, 5]. Moreover, they can be viewed as an attempt to describe the space-time at very short distances where the very idea of space-time as a smooth manifold may lack any meaning. Due to the crucial role played by gauge theories it is natural to ask whether the idea of gauge symmetry can be generalized to the case of the ﬁeld theory on noncommutative space-time. When trying to extend in this direction the notion of gauge transformations one is faced with some serious problems because for many classical groups the modiﬁcation consisting in replacing the product with star product leads to the transformations which do not close to form a group. These problems lead to some no-go theorems restricting the group and representing content of noncommutative gauge theories [6]. A number of more or less sophisticated proposals has been made to avoid the troubles with the idea of the localization of symmetry on noncommutative space-time [7, 8, 9]. The most ﬂexible one seems to be the approach based on the idea of twisted gauge symmetry [10, 11, 12, 13]. Putting aside all formal details one can summarize the notion of twisted gauge transformations as follows: in order to compute the gauge variation of starproduct monomial in ﬁelds and their derivatives one applies the Leibnitz rule but always keeping the gauge parameter function leftmost. It is easily seen that in this case any gauge group can be closed and the twisted gauge invariance imposes rather mild restrictions on the form of the action. The idea of twisted gauge transformations seems to provide a general method of introducing the gauge symmetry for ﬁeld theories on noncommutative space-time. However, according to Milton Friedman, there are no lunches for free. This observation applies here as well. First it has been argued the the approach based on twisted gauge transformations is in contradiction with the very concept of gauge ﬁelds [14]. Another serious arguments are given in the paper of Alvarez-Gaume et al. [15]. They noticed that the modiﬁed Leibnitz rule (due to the fact that the gauge parameter function is kept leftmost) means that the twisted symmetry is not a physical symmetry in the usual sense and it is not clear whether the Noether theorem can be derived. For the case of twisted U (N ) gauge theory the action is also invariant under the standard noncommutative U (N ) symmetry and this could be the reason for the existence of conserved current. This observation may be linked with the one made in Refs. [11, 12]. It has been observed [11, 12] that, in spite of the fact that one can gauge any group, when writting the invariant action one must admit that the gauge potential takes values in larger algebra than the Lie algebra of the gauge group. This is not only because the ﬁeld strength takes necessarily values in enveloping algebra but is also somehow necessary for the consistency of ﬁeld equations [12]. In fact, it appears that in all examples considered so far the range of values of the gauge potential is such that the action invariant under twisted gauge transformations is also invariant under standard noncommutative gauge symmetry; the latter enforces the consistency of current conservation and ﬁeld equations. In the present note we argue that this is generally the case. Namely, if one considers the theory invariant under twisted gauge symmetry then, in general, the current conservation implies some constraints which are not automatically fulﬁled by virtue of ﬁeld equations; more speciﬁcally, these constraints follow by taking the divergence of ﬁeld equtaions. If one demands no such constraints exist, the range of gauge potentials must be enlarged so that the action exhibits also standard noncommutative gauge symmetry. Therefore, the twisted gauge theory, if consistent, posses a custodial standard symmetry enforcing current conservation. 1