Generalized hypergroups and orthogonal polynomials

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Intertwining Operators of Double Affine Hecke Algebras

a rXiv:q -alg/96514v511J u l1996June (1996),1–36Dedicated to Yuri I.Manin on the occasion of his 60birthdayIntertwining operatorsof double aﬃne Hecke algebras By Ivan Cherednik*Continuing [C3,C4],we study the intertwining operators of double aﬃne Hecke algebras H .They appeared in several papers (especially in [C2,C4,C6]).However for the ﬁrst time here we apply them systematically to create the non-symmetric [M3,C4]and symmetric [M2]Macdonald polynomials for arbitrary root systems and to start the theory of induced and co-spherical H -modules.The importance of this technique was clearly demonstrated in recent pa-pers by F.Knop and S.Sahi [Kn],[KS],[S].Using the intertwiners of the double aﬃne Hecke algebras in the case of GL (dual to those considered in [C1,C2])they proved the q,t -integrality conjecture by I.Macdonald [M1]and managed to establish the positivity of the coeﬃcients of the Macdonald polynomials in the diﬀerential case.As to the integrality,we mention another approach based on the so-called Vinet operators (see [LV]and a recent work by Kirillov,Noumi),and the results by Garsia,Remmel,and Tesler.We do not try in this paper to get the best possible estimates for the denominators of the Macdonald polynomials (generally speaking,the problem looks more complicated than in the stable GL -case).However even rather straightforward analysis of the intertwiners gives a lot.For instance,it is enough to ensure the existence of the restricted Macdonald polynomials at roots of unity from [C3,C4],where we used less convenient methods based directly on the deﬁnition or on the recurrence relations.The technique of intertwiners combined with the (projective)action of GL (2,Z )from [C3]gives another proof of the norm and the evaluation formulas (see [C4]).Here the H -embedding of the space of nonsymmetricpolynomialsinto the space of functions on the aﬃne Weyl group ˜W ([C4],Proposition 5.2)plays a key role.The latter representation when restricted to the aﬃne Hecke subalgebra turns into the classical one from [IM]as t is a power of p and q →0(˜W is identiﬁed with the set of double cosets of the corresponding p -adic group with respect to the Iwahori subroup).2IV AN CHEREDNIKAnother important application is a calculation of the Fourier transforms of the Macdonald polynomials in the sense of[C3,C4].For instance,it gives a canonical identiﬁcation of the polynomial representation of the aﬃne Hecke algebra with the representation in functions on the weight lattice(which col-lapses in the p-adic limit).We introduce a proper discretization of theµ-function(the truncated theta-function making Macdonald’s polynomials pairwise orthogonal)and the corresponding discrete inner product on Funct(˜W).It readily gives the pro-portionality of the norms of the Macdonald polynomials[M2,C2,M3,C4]and those deﬁned for the Jackson integral taken instead of the constant term in the inner product.The coeﬃcient of proportionality is described by the Aomoto conjecture(see[A,Ito])recently proved by Macdonald(to calculate it one can also follow[C2],replacing the shift operators by their discretizations).We note that the Macdonald polynomials considered as functions on˜W are square integrable forﬁnitely many weights only.Here|q|=1and the real partℜ(k)for t=q k is to be negative(otherwise we have none).The program is to describe all integrable and non-integrable eigenfunctions of the discrete Dunkl operators in this representation and to study the corresponding Fourier transform.In contrast to the classical p-adic harmonic analysis(see e.g.[HO])the Plancherel measure coincides with the discretization ofµ(the Fourier transform is self-dual).More generally,we consider the action of the double aﬃne Hecke algebra in the same space Funct(˜W)depending on an arbitrary given weight.Its sub-module generated by the delta-functions is induced(from a character of the standard polynomial subalgebra)and co-spherical.Mainly following[C5],we ﬁnd out when arbitrary induced representations(in the same sense)are irre-ducible and co-spherical using the technique of intertwiners.The answer is a natural”aﬃnization”of the well-known statements in the p-adic case(see e.g.[KL],[C5]).The classiﬁcation of co-spherical representations is impor-tant for the harmonic analysis and plays the key role in the theory of aﬃne Knizhnik-Zamolodchikov equations(see[C6,C7,C8]).We also induce up irre-ducible representations of aﬃne Hecke subalgebras([C6]is devoted to appli-cations of such representations).If q is suﬃciently general the H-modules we get are irreducible,so one can use the classiﬁcation of[KL].Thus in this paper we begin a systematic study of the representations of double aﬃne Hecke algebras and related harmonic analysis.The polyno-mial representation considered in the series of papers[C2-4]devoted to the Macdonald conjectures is remarkable,but still just an example.The paper was started during my stay at RIMS(Kyoto University),con-tinued at CRM in Montreal,and completed at the University of Nijmegen.I am grateful to T.Miwa,L.Vinet,G.Heckman and my colleagues at theseINTERTWINERS OF DOUBLE HECKE ALGEBRAS3 institutes for the kind invitations and the hospitality.The author thanks E. Frenkel,G.Heckman,D.Kazhdan,I.Macdonald,and E.Opdam for useful discussions.1.Aﬃne Weyl groupsLet R={α}⊂R n be a root system of type A,B,...,F,G with respect to a euclidean form(z,z′)on R n∋z,z′,normalized by the standard condition that(α,α)=2for longα.Let usﬁx the set R+of positive roots(R−=−R+),the corresponding simple rootsα1,...,αn,and their dual counterparts a1,...,a n,a i=α∨i,whereα∨=2α/(α,α).The dual fundamental weights b1,...,b n are determined from the relations(b i,αj)=δj i for the Kronecker delta.We will also use the dual root system R∨={α∨,α∈R},R∨+,and the latticesA=⊕n i=1Z a i⊂B=⊕n i=1Z b i,A±,B±for Z±={m∈Z,±m≥0}instead of Z.(In the standard notations, A=Q∨,B=P∨-see[B].)Later on,να=να∨=(α,α),νi=ναi,νR={να,α∈R}⊂{2,1,2/3}.(1.1)ρν=(1/2) να=να=(ν/2)νi=νb i,forα∈R+.The vectors˜α=[α,k]∈R n×R⊂R n+1forα∈R,k∈Z form the aﬃne root system R a⊃R(z∈R n are identiﬁed with[z,0]).We addα0def=[−θ,1] to the simple roots for the maximal rootθ∈R.The corresponding set R a+of positive roots coincides with R+∪{[α,k],α∈R,k>0}.We denote the Dynkin diagram and its aﬃne completion with{αj,0≤j≤n}as the vertices byΓandΓa(m ij=2,3,4,6ifαi andαj are joined by0,1,2,3laces respectively).The set of the indices of the images ofα0by all the automorphisms ofΓa will be denoted by O(O={0}for E8,F4,G2). Let O∗=r∈O,r=0.The elements b r for r∈O∗are the so-called minuscule weights((b r,α)≤1forα∈R+).Given˜α=[α,k]∈R a,b∈B,lets˜α(˜z)=˜z−(z,α∨)˜α,b′(˜z)=[z,ζ−(z,b)](1.2)for˜z=[z,ζ]∈R n+1.The aﬃne Weyl group W a is generated by all s˜α(simple reﬂections s j= sαjfor0≤j≤n are enough).It is the semi-direct product W⋉A,where the non-aﬃne Weyl group W is the span of sα,α∈R+.Here and futher we identify b∈B with the corresponding translations.For instance,a=sαs[α,1]=s[−α,1]sαfor a=α∨,α∈R.(1.3)4IV AN CHEREDNIKThe extended Weyl group W b generated by W and B is isomorphic to W⋉B:(wb)([z,ζ])=[w(z),ζ−(z,b)]for w∈W,b∈B.(1.4)Given b+∈B+,letωb+=w0w+0∈W,πb+=b+(ωb+)−1∈W b,ωi=ωbi,πi=πbi,(1.5)where w0(respectively,w+0)is the longest element in W(respectively,in W b+ generated by s i preserving b+)relative to the set of generators{s i}for i>0.The elementsπr def=πbr,r∈O leaveΓa invariant and form a group denoted byΠ,which is isomorphic to B/A by the natural projection{b r→πr}.As to{ωr},they preserve the set{−θ,αi,i>0}.The relationsπr(α0)=αr= (ωr)−1(−θ)distinguish the indices r∈O∗.Moreover(see e.g.[C2]): W b=Π⋉W a,whereπr s iπ−1r=s j ifπr(αi)=αj,0≤j≤n. (1.6)Givenν∈νR,r∈O∗,˜w∈W a,and a reduced decomposition˜w=s jl ...s j2s j1with respect to{s j,0≤j≤n},we call l=l(ˆw)the length ofˆw=πr˜w∈W b.Setting(1.7)λ(ˆw)={˜α1=αj1,˜α2=s j1(αj2),˜α3=s j1s j2(αj3),......,˜αl=˜w−1s jl(αjl)},one can represent(1.8)l=|λ(ˆw)|= νlν,for lν=lν(ˆw)=|λν(ˆw)|,λν(ˆw)={˜αm,ν(˜αm)=ν(˜αjm)=ν},1≤m≤l, where||denotes the number of elements,ν([α,k])def=να.Let us introduce the following aﬃne action of W b on z∈R n:(1.9)(wb) z =w(b+z),w∈W,b∈B,s˜α z =z−((z,α)+k)α∨,˜α=[α,k]∈R a,and the pairing([z,ζ],z′+d)def=(z,z′)+ζ,where we treat d formally(see e.g. [K]).The connection with(1.2,1.3)is as follows:(1.10)(ˆw([z,ζ]),ˆw z′ +d)=([z,ζ],z′+d)forˆw∈W b.Using the aﬃne Weyl chamberC a=nj=0Lαj,L˜α={z∈R n,(z,α)+k>0},INTERTWINERS OF DOUBLE HECKE ALGEBRAS5(1.11)λν(ˆw)={˜α∈R a+, C a ⊂ˆw L˜α ,ν(˜α)=ν} ={˜α∈R a+,lν(ˆws˜α)<lν(ˆw)}.It coincides with(1.8)due to the relations(1.12)λν(ˆwˆu)=λν(ˆu)∪ˆu−1(λν(ˆw)),λν(ˆw−1)=−ˆw(λν(ˆw)) if lν(ˆwˆu)=lν(ˆw)+lν(ˆu).The following proposition is from[C4].Proposition1.1.Given b∈B,the decomposition b=πbωb,ωb∈W can be uniquely determined from the following equivalent conditionsi)l(πb)+l(ωb)=l(b)and l(ωb)is the biggest possible,ii)ωb(b)=b−∈B−and l(ωb)is the smallest possible,iii)πb 0 =b andλ(πb)∩R=∅.We will also use thatλ(b)={˜α,(b,α)>k≥0ifα∈R+,(1.13)(b,α)≥k>0ifα∈R−},λ(πb)={˜α,α∈R−,(b−,α)>k>0if(α,b)<0,(1.14)(b−,α)≥k>0if(α,b)>0},andλ(π−1b)={˜α,−(b,α)>k≥0}for˜α=[α,k]∈R a+.(1.15)Convexity.Let us introduce two orderings on B.Here and further b±are the unique elements from B±which belong to the orbit W(b).Namely, b−=ωbπb=ωb(b),b+=w0(b−)=ω−b(b).So the equality c−=b−(or c+=b+)means that b,c belong to the same orbit.Setb≤c,c≥b for b,c∈B if c−b∈A+,(1.16)b c,c b if b−<c−or b−=c−and b≤c.(1.17)We use<,>,≺,≻respectively if b=c.For instance,c≻b+⇔b+>W(c)>b−,c b−⇔c∈W(b−)or c≻b+.The following sets(1.18)σ(b)def={c∈B,c b},σ∗(b)def={c∈B,c≻b},σ+(b)def={c∈B,c−>b−}=σ∗(b+).are convex.Moreoverσ+is W-invariant.By convex,we mean that if c,d= c+rα∨∈σforα∈R+,r∈Z+,then{c,c+α∨,...,c+(r−1)α∨,d}⊂σ.(1.19)6IV AN CHEREDNIKThe elements fromσ(b)strictly between c and d(i.e.c+qα,0<q<r) belong toσ+(b).πb,where i p are from any se-Proposition 1.2.a)Letˆu=s˜αi m...s˜αi1quence1≤i1<i2<...<i m≤l=l(b)in a reduced decomposition of ˆw=π−1b(see(1.7)).In other words,ˆu is obtained by crossing out any number of{s j}from a reduced decomposition ofπb.Then c def=ˆu 0 ∈σ∗(b).More-over,c∈σ+(b)if and only if at least one of˜αi p=[α,k]for1≤p≤m has k>0.b)If c,b belong to the same W-orbit then the converse is ly, settingωbc def=πbπ−1c,the following relations are equivalent:(i)c≻b(which means that c>b),(ii)(α,c)>0for allα∈λ(ωbc),(iii)l(πb)=l(ωbc)+l(πc),It also results from(i)thatωbc is the smallest possible element w∈W such that b=w(c).Proof.Assertion a)is a variant of Proposition1.2from[C4].For the sake of completeness we will outline the proof of b).Taking u(c)≤b<c,we will check(ii),(iii)by induction supposing that{u′(c)≤b′<c}⇒{(ii),(iii)}for all b′,u′such that l(u′)<l(u),which is obvious when l(u′)=0.Settingβ=u(α)forα∈λ(u),u(sα(c))=u(c)−(α,c)β∨andβ∈R−(see the deﬁnition ofλ(α)).One can assume that(α,c)>0for all suchα. Otherwise usα(c)≤u(c)≤c and we can argue by induction.Applying(1.12) and(1.13),we see that l(uc)=l(u)+l(c).Indeed,the intersection ofλ(c)andc−1(λ(u))={[α,(c,α)],α∈λ(u)}is empty.Hence the product uπc is reduced(i.e.l(uπc)=l(u)+l(πc))and λ(uπc)=ωc c−1(λ(u))∪λ(πc)contains no roots from R+.Finally,Proposition 1.1leads to(iii)(and the uniqueness of u of the minimal possible length).This reasoning gives the equivalence of(ii)and(iii)as well.Assertion(i)readily results from(ii).We will also use(cf.Proposition5.2,[C4])the relationsπb=πrπc for b=πr c and any c∈B,r∈O and the equivalence of the following three conditions:(1.20)(αj,c+d)>0⇔αj∈λ(π−1c)⇔{s jπc=πb,c≻b}for0≤j≤n.When j>0it is a particular case of Proposition1.2b). Assuming that(α0,c+d)=1−(θ,c)>0,b=s0 c =c+(α0,c+d)θ>c>c−θ=sθ(b).INTERTWINERS OF DOUBLE HECKE ALGEBRAS7 Hence c∈σ+(b).If the product s0πc is reducible then we can apply statement a)to come to a contradiction.Therefore s0πc=πb,since s0is simple.The remaining implications are obvious.2.Intertwining operatorsWe put m=2for D2k and C2k+1,m=1for C2k,B k,otherwise m=|Π|.Let us sett˜α=tν(˜α),t j=tαj,where˜α∈R a,0≤j≤n,X˜b =ni=1X k i i q k if˜b=[b,k],(2.1)for b=ni=1k i b i∈B,k∈18IV AN CHEREDNIKdoes not depend on the choice of the reduced decomposition(because{T} satisfy the same“braid”relations as{s}do).Moreover,Tˆv Tˆw=Tˆvˆw whenever l(ˆvˆw)=l(ˆv)+l(ˆw)forˆv,ˆw∈W b.(2.3)In particular,we arrive at the pairwise commutative elementsY b=ni=1Y k i i if b=ni=1k i b i∈B,where Y i def=T bi,(2.4)satisfying the relations(2.5)T−1iY b T−1i=Y b Y−1a iif(b,αi)=1,T i Y b=Y b T i if(b,αi)=0,1≤i≤n.The following maps can be extended to involutions of H(see[C1,C3]):ε:X i→Y i,Y i→X i,T i→T−1i ,(2.6)tν→t−1ν,q→q−1,τ:X b→X b,Y r→X r Y r q−(b r,b r)/2,Yθ→X−10T−20Yθ,(2.7)T i→T i,tν→tν,q→q,1≤i≤n,r∈O∗,X0=qX−1θ.Let us give some explicit formulas:(2.8)ε(T0)=XθT−1Yθ=XθT sθ,ε(πr)=X r Tω−1r,τ(T0)=X−10T−1,τ(πr)=q−(b r,b r)/2X rπr=q(b r,b r)/2πr X−1r∗,πr X r∗π−1r=q(b r,b r)X−1r,X r∗TωrX r=T−1ωr∗.Theorem2.3from[C3]says that the map(2.9) 0−1−10 →ε, 1101→τcan be extended to a homomorphism of GL2(Z)up to conjugations by the central elements from the group generated by T1,...,T n.The involutionη=τ−1ετcorresponding to the matrix −1011 will play an important role in the paper:η:X r→q(b r,b r)/2X−1r Y r=πr X r∗Tωr ,(2.10)Y r→q(b r,b r)/2X−1r Y r X r=πr T−1ωr∗,Yθ→T−10T−1sθ,T j→T−1j(0≤j≤n),πr→πr(r∈O∗),tν→t−1ν,q→q−1.INTERTWINERS OF DOUBLE HECKE ALGEBRAS9 We note thatεandηcommute with the main anti-involution∗from[C2]:(2.11)X∗i=X−1i,Y∗i=Y−1i,T∗i=T−1i,tν→t−1ν,q→q−1,0≤i≤n,(AB)∗=B∗A∗.The X-intertwiners(see e.g.[C2,C5,C6])are introduced as follows:Φj=T j+(t1/2j −t−1/2j)(X aj−1)−1,G j=Φj(φj)−1,˜G j=(φj)−1Φj,(2.12)φj=t1/2j +(t1/2j−t−1/2j)(X aj−1)−1,for0≤j≤n.They belong to the extension of H by theﬁeld C q,t(X)of rational functions in{X}.The elements G j and G′j satisfy the same relations as{s j,πr}do,{Φj}satisfy the relations for{T j}(i.e.the homogeneous Coxeter relations and those withπr).Hence the elements(2.13)Gˆw=πr G jl ···G j1,whereˆw=πr s jl···s j1∈W b,are well-deﬁned and G is a homomorphism of W b.The same holds for˜G.AstoΦ,the decomposition ofˆw should be reduced.The simplest way to see this is to use the following property of{Φ}which ﬁxes them uniquely up to left or right multiplications by functions of X:Φˆw X b=Xˆw(b)Φˆw,ˆw∈W b.(2.14)Oneﬁrst checks(2.14)for s j andπr,then observes thatΦfrom(2.13)satisfy (2.14)for any choice of the reduced decomposition,and uses the normalizing conditions to see that they are uniquely determined from the intertwining relations(2.14).We note thatΦj,φj are self-adjoint with respect to the anti-involution (2.11).HenceΦ∗ˆw=Φˆw−1,G∗ˆw=˜Gˆw−1,ˆw∈W b.(2.15)It follows from the quadratic relations for T.To deﬁne the Y-intertwiners we apply the involutionεtoΦˆw and to G,˜G. The formulas can be easily calculated using(2.8).In the case of GL n one getsthe intertwiners from[Kn].For w∈W,we just need to replace X b by Y−1b and conjugate q,t(cf.[C4]).However it will be more convenient to consider η(Φ)instead ofε(Φ)to create the Macdonald polynomials.Both constructions gives the intertwiners satisfying the∗-relations from(2.15).3.Standard representationsIt was observed in[C4],Section5that there is a natural passage from the representation of H in polynomials to a representation in functions on10IV AN CHEREDNIKW b.We will continue this line,beginning with the construction of the basic representaions of level0,1.Settingx˜b =ni=1x k i i q k if˜b=[b,k],b=ni=1k i b i∈B,k∈1representation V0is induced from the character{T j→t j,πr→1}.Namely, the imageˆH is uniquely determined from the following condition:(3.7)ˆH(f(x))=g(x)for H∈H if Hf(X)−g(X)∈ni=0H(T i−t i)+ r∈O∗H(πr−1).To make the statement about V1quite obvious let us introduce the Gauss-ianγ=Const qΣn i=1z i zαi/2,where formallyx b=q z b,z a+b=z a+z b,z i=z bi,(wa)(z b)=z w(b)−(a,b),a,b∈R n. More exactly,it is a W-invariant solution of the following diﬀerence equations:(3.8)b j(γ)=Const q(1/2)Σn i=1(z i−(b j,b i))(zαi−δj i)=q−z j+(b j,b j)/2γ=q(b j,b j)/2x−1jγfor1≤j≤n.The Gaussian commutes with T j for1≤j≤n because it is W-invariant.A straightforward calculation gives that(3.9)γ(X)T0γ(X)−1=X−10T−1=τ(T0),γ(X)Y rγ(X)−1=q−(b r,b r)/2X r Y r=τ(Y r),r∈O.Hence the conjugation byγinducesτ.We can put in the following way.There is a formal H-homomorphism:(3.10)V0∋v→ˆv def=vγ−1∈V1.One has to complete V0,1to make this map well-deﬁned(see the discrete rep-resentations below).We will later need an extended version of Proposition3.6from[C2].Proposition3.2.a)The operators{Y i,1≤i≤n}acting in V0preserve Σ(b)def=⊕c∈σ(b)C q,t x c andΣ∗(b)(deﬁned forσ∗(b))for arbitrary b∈B.b)The operators{T j,0≤j≤n}acting in V0preserveΣ+(b)=Σ∗(b+):(3.11)ˆTj(x b)modΣ+(b)=t1/2jx b if(b,αj)=0,=t1/2js j(x b)+(t1/2j−t−1/2j)x b if(b,αj)<0,=t−1/2js j(x b)if(b,αj)>0.c)Coming to V1,if(αj,b+d)>0(0≤j≤n)then(3.12)ˆT j x b modΣ+(s j b )=t−1/2js j x b .Otherwise,(αj ,b +d )≤0and(3.13)ˆTj x b ∈Σ(b )for (αj ,b +d )≤0,ˆT j x b =t 1/2jx b if (αj ,b +d )=0.Proof.Due to Proposition 3.3from [C4]it suﬃces to check c)for j =0.The ﬁrst inequality,the deﬁnition of ˆT 0 x b = c ∈B u bc x c ,and (1.20)readily give that (for nonzero u )c =b +rθ(r ∈Z )and(3.14)s θ(b ′)=b −θ<b <c ≤b +(α0,b +d )θ=s 0 b def =b ′.Hence c ∈σ+(b ′)if c =b ′.The coeﬃcient u bb ′equals t −1/20.Let (α0,b +d )≤0.Then(3.15)s θ(b )=b −(b,θ)θ<c ≤b and c ∈{Σ+(b )∪b }∈Σ(b )(cf.Proposition 1.2,a)).Discretization.We go to the lattice version of the functions and opera-tors.Let ξbe a ”generic”character of C [x ]:x a (ξ)def =n i =1ξk i i ,a =n i =1k i b i ∈B,for independent parameters ξi .The discretizations of functions g (x )in x ∈C n and the operators from the algebra A def =⊕ˆu ∈W b C q,t (X )ˆu ,are described by the formulas:δx a (bw )=x a (q b w (ξ))=q (a,b )x w −1(a )(ξ),(δˆu (δg ))(bw )=δg (ˆu −1bw ).(3.16)For instance,(δX a (δg ))(bw )=x a (bw )g (bw )(we will sometimes omitδand put g (ˆw )instead of δg (ˆw )).The image of g ∈C q,t (x )belongs to the space F ξdef=Funct(W b ,C ξ)of C ξ-valued functions on W b ,where C ξdef =C q,t (ξ1,...,ξn ).Considering the discretizations of operators ˆHfor H ∈H we come to the functional representation of H in F ξ.Similarly,introducing the group algebra C ξ[W b ]=⊕ˆw ∈W b C ξδˆwfor (for-mal)delta-functions ,we can consider the dual anti-action on the indices:(3.17)δ(g (x )ˆu )( ˆw ∈W b c ˆw δˆw )= ˆw ∈W bc ˆw g (ˆw )δˆu −1ˆw ,c ˆw ∈C ξ.Composing it with the anti-involution of H(3.18)T ⋄j =T j (0≤j ≤n ),π⋄r =π−1r (r ∈O ),X ⋄i =X i (0≤i ≤n ),sending q,t to q,t(and AB to B⋄A⋄),we get the delta-representation∆ξof H in Cξ[W b]:(3.19)H→δ(ˆH⋄)def=δ(H)for H∈H.Explicitly,δπr=πr=δ(πr),r∈O,and forˆw=bwδ(Ti(g))(ˆw))=t1/2ix ai(w(ξ))q(a i,b)−t−1/2ix ai(w(ξ))q(a i,b)−1g(ˆw)for0≤i≤n,(3.20)δ(T i)(δˆw)=t1/2ix ai(w(ξ))q(a i,b)−t−1/2x ai(w(ξ))q(a i,b)−1δˆw for0≤i≤n.(3.21)There is a natural Cξ-linear pairing between Fξand∆ξ.Given g∈Funct(W b,Cξ),ˆw∈W b,{g,δˆw}def=g(ˆw),{H(g),δˆw}={g,H⋄(δˆw)},H∈H.(3.22)It also gives a nondegenerate pairing between V0and∆ξ.For arbitrary ope-rators A∈A,the relation is as follows:{δA(g),δˆw}={g,δA(δˆw)}.Let us extend the discretization map and the pairing with∆ξto V1.We use the map from(3.10)for theδ-Gaussian:(3.23)δγ(bw)def=q(b,b)/2xb(w(ξ)),which satisﬁes(3.8)and is a discretization ofγfor a proper constant(cf.[C4], (6.20)).The representations Fξand∆ξcan be introduced when q,t,{ξi}are con-sidered as complex numbers ensuring that x˜a(ξ)=1for all˜a∈(R a)∨.Follow-ing Proposition5.2from[C4],let us specialize the deﬁnition of∆forξ=t−ρ. In this casex a(bw)=x a(q b t−w(ρ))=q(a,b) νt−(w(ρν),a)ν.(3.24)Proposition3.3.The H-module∆(−ρ)def=∆t−ρcontains the H-sub-module∆#def=⊕b∈B Cδπb.This also holds for any q∈C∗and generic t. Moreover,∆#is irreducible if and only if q is not a root of unity.When q→0and t is a power of prime p the action of the algebra H a generated by{T j,0≤j≤n}in∆(−ρ)coincides with the standard action ofthe p-adic Hecke algebra H(G//I)∼=H a on the(linear span of)delta-functions on I\G/I∼=W a.Here I is the Iwahori subgroup of the split semisimple p-adic group G(see[IM]).However∆#does not remain a submodule in this limit.Multiplying the delta-functions on the right by the operator of t-symmet-rization we can get an H a-submodule isomorphic to∆#(upon the restriction to H a).Its limit readily exists and coincides with the space of delta-functions on I\G/K for the maximal parahoric subgroup K.However the latter space can be identiﬁed with neither spaces of delta-functions for smaller subsets of W a(as in Proposition3.3).It is possible only for the q-deformation under consideration.Practically,when calculating with right K-invariant functions in the p-adic case one needs to consider their values on the whole W a(that is an obviousﬂaw since much fewer number of points is enough to reconstruct them uniquely).4.OrthogonalityThe coeﬃcient of x0=1(the constant term)of a polynomilal f∈C q,t[x] will be denoted by f 0.Let(4.1)µ= a∈R∨+∞ i=0(1−x a q i a)(1−x−1a q i+1a).(1−x a(tρ)t a q i a)(1−x a(tρ)t−1a q i a)Here x b(t±ρq c)=q(b,c) νt±(b,ρν)ν.We note thatµ∗0=µ0with respect to the involutionx∗b=x−b,t∗=t−1,q∗=q−1.Setting(4.3)f,g 0= µ0f g∗ 0= g,f ∗0for f,g∈C(q,t)[x],we introduce the non-symmetric Macdonald polynomials e b(x),b∈B−,by means of the conditions(4.4)e b−x b∈Σ∗(b), e b,x c =0for c∈σ∗={c∈B,c≻b}in the setup of Section1.They can be determined by the Gram-Schmidt process because the pairing is non-degenerate and form a basis in C(q,t)[x].This deﬁnition is due to Macdonald[M3](for tν=q k,k∈Z+)who extended Opdam’s nonsymmetric polynomials introduced in the degenerate (diﬀerential)case in[O2].He also established the connection with the Y-operators.The general case was considered in[C4].The notations are from Proposition1.1and(1.1).We use the involution ¯x a=x−1a,¯q=q,¯t=t,a∈B.Proposition4.1.a)For any H∈H and the anti-involution∗from (2.11), ˆH(f),g 0= f,ˆH∗(g) 0.Here f,g are either from V0or from V1.All products of{X b,Y b,T j,πr,q,tν}are unitary operators.b)The polynomials{e b,b∈B}are eigenvectors of the operators{L f def= f(Y1,···,Y n),f∈C[x]}:L¯f(e b)=f(#b)e b,where#b def=πb=bω−1b ,(4.5)x a(#b)def=x a(q b t−ω−1b(ρ))=q(a,b) νt−(ω−1b(ρν),a)ν,w∈W.(4.6)Proof.Assertion a)for V0is from[C2].Using(3.10)we come to V1(a formal proof is equally simple).Since operators{Y b}are unitary relative to , 0and leave allΣ(a),Σ∗(a)invariant(Proposition3.2),their eigenvectors in C q,t[x]are exactly{e}.See[M3,C4].The theorem results immediately in the orthogonality of{e b}for pairwise distinct b.Macdonald also gives the formula for the squares of e b(for tν= q k,k∈Z+)and writes that he deduced it from the corresponding formula in the W-symmetric case(proved in[C2]).The general case was considered in [C4]where we used the recurrence relations.A direct simple proof(based on the intertwiners)will be given below.The symmetric Macdonald polynomials form a basis in the space C q,t[x]W of all W-invariant polynomials and can be expressed as follows:(4.7)p b=P t b e b=P1b e b,b=b+∈B+,P t def= c∈W(b) νt lν(w c)/2νˆTw c,w cdef=ω−1c w0,P1b=P t=1b.This presentation is from[M3,C4](from[O2]in the diﬀerential case). Here one can take the complete symmetrizations(with proper coeﬃcients) since e b is W b-invariant for the stabilizer W b of b.Macdonald introduced these polynomials in[M1,M2]by the conditionsp b−m b∈Σ+(b), p b,m c 0=0,b∈B+,c≻b,(4.8)for the monomial symmetric functions m b= c∈W(b)x c.One can also deﬁne {p}as eigenvectors for the(W-invariant)operators L f,f∈C q,t[x]W:L f(p b)=f(q b o tρ)p b,b∈B+,b o=−w0(b),(4.9)normalized as above.Applying any elements from H Y=<T j,Y b>to e c(c∈W(b+))we get solutions of(4.9),because symmetric Y-polynomials are central in H Y(due to I.Bernstein).It readily gives the coincidence of(4.7)and(4.9).Functional representations.The representations Fξ,∆ξalso have in-variant skew-symmetric forms.Letµ1(bw)=µ(bw)/µ(1)def=(4.10)a∈R∨+∞i=0(1−x a(bw)q i a)(1−x−1a(bw)q i+1a)(1−x a(1)t a q i a)(1−x−1a(1)t a q i+1a)t1/2α−qjαt−1/2αx a(ξ),(4.11)where a=α∨,and we extend the conjugation∗from C q,t to Cξsettingξ∗i=ξ−1i.b)The following Cξ-valued scalar product is well-deﬁned for f,g from the H-submodule ofﬁnitely supported functions Fξ⊂Fξ=Funct(W b,Cξ):f,g 1= ˆw∈W bµ1(ˆw)f(ˆw)g(ˆw)∗= g,f ∗1.(4.12)c)Assertion a)from Proposition4.1holds for Fξand∆ξ,where the latter module is endowed with the scalar productf,g −1= ˆw∈W b(µ1(ˆw))−1uˆw v∗ˆw,f= uˆwδˆw,g= vˆwδˆw.(4.13)Namely, H(f),g ±1= f,H∗(g) ±1.Proof.Since x˜a(ˆw)=x˜a′(1)for˜a=˜α∨∈(R a+)∨,where˜a′def=ˆw−1(˜a), one has forˆw=bw:(4.14)µ1(ˆw)= ˜α∈R a+(1−x˜a(ˆw))(1−t a x˜a(1))(1−x˜a(1))(1−t a x˜a′(1)) = ˜α∈λ(ˆw)(1−x−1˜a(1))(1−t a x˜a(1))Here we use thatˆw−1(R a+)={−λ(ˆw)}∪{R a+\λ(ˆw)}.The invariance of µ1(ˆw)∈Cξwith respect to the conjugation∗is obvious.Other statements are completely analogous to those forµ0(and follow from them).The key relation(4.15)ˆHµ(X)=µ(X)(ˆH∗)+,H∈H,readily holds after the discretization.Here by+we mean the anti-involutionˆw+=ˆw−1∈W b,x+b=x−1b,b∈B,q,t→q−1,t−1.Its discretization conjugates the values of functions from Fξand the coeﬃcients ofδˆw in∆ξ(ﬁxingδˆw).The characteristic functions fˆw∈Fξ(ˆw∈W b)are deﬁned from the rela-tions fˆw(ˆu)=δˆw,ˆu for the Kronecker delta.The action of the operators X b on them is the same as for{δˆw}:X b(fˆw)=x b(ˆw)fˆw,X b(δˆw)=x b(ˆw)δˆw,b∈B,ˆw∈W b.Moreover the mapfˆw→µ1(ˆw)δˆw,ˆw∈W b,(4.16)establishes an H-isomorphism between Fξand∆ξ,taking , 1to , −1.It readily results from the formulas:δTi(fˆw)=t1/2ix−1ai(w(ξ))q−(a i,b)−t−1/2x ai(w(ξ))q(a i,b)−1fˆw for0≤i≤n,(4.17)and the formulas for the action of{πr}.Let us consider the special caseξ=t−ρ(see(3.24)).Using the pairing(3.22),we see that the subspace(4.18)F#=⊕ˆw∈#B C q,t fˆw⊂F(−ρ)=F t−ρ,where#B={#b=πb∈W b,b∈B},is an H-submodule.It is exactly the radical of the form , 1,which is well-deﬁned for suchξ.Indeed,anyˆw can be uniquely represented in the form(see[C2])ˆw=πb w,where b=ˆw b ,w∈W,l(ˆw)=l(πb)+l(w). Hence,{ˆw∈#B}⇒{αi∈λ(ˆw)for some i>0}⇒{µ1(ˆw)=0}.On the other hand,µ1(#b)= a∈R∨+ t−1/2α−q jαt1/2αx a(tρ)。

荷兰医学文摘

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【精品】翻译综合

一个抑制肿瘤的连续模型-------艾丽斯H伯杰，阿尔弗雷德G. Knudson 与皮埃尔保罗潘多尔菲今年，也就是2011 年，标志着视网膜母细胞瘤的统计分析的第四十周年，首次提供了证据表明，肿瘤的发生，可以由两个突变发起。

这项工作提供了“二次打击”的假说，为解释隐性抑癌基因（TSGs）在显性遗传的癌症易感性综合征中的作用奠定了基础。

然而，四十年后，我们已经知道，即使是部分失活的肿瘤抑制基因也可以致使肿瘤的发生。

在这里，我们分析这方面的证据，并提出了一个关于肿瘤抑制基因功能的连续模型来全方位的解释肿瘤抑制基因在癌症过程中的突变。

虽然在1900 年之前癌症的遗传倾向已经被人认知，但是，是在19 世纪曾一度被忽视的孟德尔的遗传规律被重新发现之后，癌症的遗传倾向才更趋于合理化。

到那时，人们也知道，肿瘤细胞中的染色体模式是不正常的。

接下来对癌症遗传学的理解做出贡献的人是波威利，他提出，一些染色体可能刺激细胞分裂，其他的一些染色体 a 可能会抑制细胞分裂，但他的想法长期被忽视。

现在我们知道，这两种类型的基因，都是存在的。

在这次研究中，我们总结了后一种类型基因的研究历史，抑癌基因（TSGs），以及能够支持完全和部分失活的肿瘤抑制基因在癌症的发病中的作用的证据。

我们将抑制肿瘤的连续模型与经典的“二次打击”假说相结合，用来说明肿瘤抑制基因微妙的剂量效应，同时我们也讨论的“二次打击”假说的例外，如“专性的单倍剂量不足”，指出部分损失的抑癌基因比完全损失的更具致癌性。

这个连续模型突出了微妙的调控肿瘤抑制基因表达或活动的重要性，如微RNA（miRNA）的监管和调控。

最后，我们讨论了这种模式在┲⒌恼锒虾椭瘟乒讨械挠跋臁！岸未蚧鳌奔偎?第一个能够表明基因的异常可以导致癌症的发生的证据源自1960 年费城慢性粒细胞白血病细胞的染色体的发现。

后来，在1973 年，人们发现这个染色体是是第9 号和第22 号染色体异位的结果，并在1977 年，在急性早幼粒细胞白血病患者中第15 号和第17 号染色体易位被识别出来。

宫腹腔镜联合手术治疗剖宫产术后子宫瘢痕憩室相关异常子宫出血患者的可行性分析

宫腹腔镜联合手术治疗剖宫产术后子宫瘢痕憩室相关异常子宫出血患者的可行性分析周君①　杨美娟①　彭如情① 【摘要】　目的：分析剖宫产术后子宫瘢痕憩室（CSD）相关异常子宫出血患者应用宫腹腔镜联合手术治疗的可行性。

方法：回顾性分析2018年1月—2023年5月于贵溪市人民医院就诊的80例CSD相关异常子宫出血患者的临床资料，按照治疗方式的不同将其分为联合组（n=38）和基础组（n=42），其中基础组采用宫腔镜手术进行治疗，联合组采用宫腹腔镜联合手术治疗。

比较两组患者的围手术期相关指标，观察两组术后月经改善率，对比两组子宫憩室深度，比较两组手术并发症（伤口感染、膀胱损伤、大出血）发生率。

结果：联合组患者的手术用时显著长于基础组，差异有统计学意义（P<0.05）；联合组患者的手术出血量少于基础组，排净恶露时间及住院时长均显著短于基础组，差异均有统计学意义（P<0.05）。

联合组痊愈率高于基础组，好转率低于基础组，差异均有统计学意义（P<0.05）；两组无效率及改善率比较，差异均无统计学意义（P>0.05）。

术后，两组宫憩室深度情况均较术前显著改善（P<0.05）；术后，两组子宫憩室深度情况比较，差异均无统计学意义（P>0.05）。

两组伤口感染、膀胱损伤、大出血发生率比较，差异均无统计学意义（P>0.05），但联合组并发症总发生率显著低于基础组，差异有统计学意义（P<0.05）。

结论：CSD相关异常子宫出血患者应用宫腹腔联合手术用时较长，但可加快术后康复及月经恢复正常，疗效与安全性较好。

【关键词】剖宫产术后瘢痕憩室　异常子宫出血　宫腔镜　宫腹腔镜联合手术 Feasibility Analysis of Hysteroscope Combined Laparoscope Surgery in the Treatment of Patientswith Cesarean Scar Diverticulum Related Abnormal Uterine Bleeding/ZHOU Jun, YANG Meijuan, PENGRuqing. //Medical Innovation of China, 2024, 21(13): 113-117 [Abstract]　Objective: To analyze the feasibility of hysteroscope combined laparoscope surgery in thetreatment of patients with cesarean scar diverticulum (CSD) related abnormal uterine bleeding. Method: The clinicaldata of 80 patients with CSD related abnormal uterine bleeding in Guixi People's Hospital from January 2018 toMay 2023 were retrospectively analyzed. According to different treatment methods, they were divided into combinedgroup (n=38) and basic group (n=42), in which the basic group was treated with hysteroscopy and the combinedgroup was treated with hysteroscope combined laparoscope surgery. The perioperative related indexes of the twogroups were compared. The improvement rate of menstruation after surgery of the two groups were observed. Thedepth of uterine diverticulum was compared between the two groups. The incidence of surgical complications (woundinfection, bladder injury and massive bleeding) were compared between the two groups. Result: The operation timeof patients in the combined group was significantly longer than that in the basic group, the difference was statisticallysignificant (P<0.05). The surgical bleeding volume in the combined group was less than that in the basic group,and the time to clear lochia and the length of hospital stay were significantly shorter than those in the basic group,the differences were statistically significant (P<0.05). The recovery rate of the combined group was higher than thatof the basic group, and the effective rate was lower than that of the basic group, the differences were statisticallysignificant (P<0.05). There were no significant differences in the inefficiency and improvement rate between thetwo groups (P>0.05). After surgery, the depth of uterine diverticulum in both groups were significantly improvedcompared with that before operation (P<0.05). After surgery, there was no significant difference in the depth ofuterine diverticulum between the two groups (P>0.05). There were no significant differences in the incidence ofwound infection, bladder injury and massive bleeding between the two groups (P>0.05), but the total incidenceof complications in the combined group was significantly lower than that in the basic group, the difference was①贵溪市人民医院妇产科　江西　贵溪　335400通信作者：周君- 113 - 剖宫产术后子宫瘢痕憩室（CSD）是剖宫产术后切口愈合不良导致的，由于我国的剖宫产率较高，作为剖宫产的远期并发症之一，其主要临床症状表现为子宫异常出血、痛经甚至不孕，对有生育需求的患者来说，其影响是十分不利的[1]。

Submanifolds of generalized complex manifolds

SUBMANIFOLDS OF GENERALIZED (ALMOST) COMPLEX MANIFOLDS
arXiv:math/0309013v1 [math.DG] 1 Sep 2003
OREN BEN-BASSAT AND MITYA BOYARCHENKO Abstract. The main goal of our paper is the study of several classes of submanifolds of generalized complex manifolds. Along with the generalized complex submanifolds deﬁned by Gualtieri and Hitchin in [4], [8] (we call these “generalized Lagrangian submanifolds” in our paper), we introduce and study three other classes of submanifolds. For generalized complex manifolds that arise from complex (resp., symplectic) manifolds, all three classes specialize to complex (resp., symplectic) submanifolds. In general, however, all three classes are distinct. We discuss some interesting features of our theory of submanifolds, and illustrate them with a few nontrivial examples. We then support our “symplectic/Lagrangian viewpoint” on the submanifolds introduced in [4], [8] by deﬁning the “generalized complex category”, modelled on the constructions of Guillemin-Sternberg [5] and Weinstein [14]. We argue that our approach may be useful for the quantization of generalized complex manifolds.

探讨两种不同方式修补有生育要求的子宫瘢痕憩室患者的临床疗效

临床医学China &Foreign Medical Treatment 中外医疗探讨两种不同方式修补有生育要求的子宫瘢痕憩室患者的临床疗效张国辉，施飞凤，方炜烨福建医科大学附属漳州市医院妇科，福建漳州 363000［摘要］目的探讨不同手术方法治疗有生育需求的剖宫产瘢痕憩室的临床效果。

方法回顾性选取2016年1月—2021年1月福建医科大学附属漳州市医院手术修补的剖宫产术后有生育要求的子宫瘢痕憩室患者41例的临床资料。

宫腹腔镜子宫瘢痕憩室切除修补23例为研究组，阴式子宫瘢痕憩室切除修补18例为对照组，术后均口服避孕药3个周期。

对比两组患者的有效率，术后活产率及手术并发症。

结果研究组有效率为91.30%，对照组有效率为88.89%，差异无统计学意义（χ2=0.074，P >0.05）；研究组无并发症，对照组并发症发生率为5.56%，差异无统计学意义（χ2=0.015，P >0.05）；研究组术后活产率为91.30%，对照组术后活产率为83.33%，差异无统计学意义（χ2=0.086，P >0.05）。

结论两种术式效果相当，手术并发症无差别，术后活产率相当。

［关键词］子宫瘢痕憩室；宫腔镜手术；腹腔镜手术；阴式子宫瘢痕修补术［中图分类号］ R713 ［文献标识码］ A ［文章编号］ 1674-0742（2023）12(b)-0033-04Clinical Efficacy of Two Different Approaches to Repairing Cesarean Scar Diverticulum in Patients with Fertility RequirementsZHANG Guohui, SHI Feifeng, FANG WeiyeDepartment of Gynecology, Zhangzhou Hospital Affiliated to Fujian Medical University, Zhangzhou, Fujian Province, 363000 China[Abstract] Objective To explore the clinical efficacy of different surgical methods for the treatment of cesarean sec⁃tion scar diverticulum with fertility requirements. Methods The clinical data of 41 patients with cesarean scar diver⁃ticulum with fertility requirements after cesarean section who were surgically repaired in Zhangzhou Hospital from January 2016 to January 2021 were retrospectively selected. 23 cases of uterine laparoscopic cesarean scar diverticu⁃lum resection and repair were in the study group, and 18 cases of vaginal cesarean scar diverticulum resection and re⁃pair were in the control group, and all of them took oral contraceptive pills for 3 cycles after surgery. The effective rate, postoperative live birth rate and surgical complications of the two groups were compared. Results The effective rate was 91.30% in the study group and 88.89% in the control group, and the difference was not statistically signifi⁃cant (χ2=0.074, P >0.05). There were no complications in the study group and 5.56% in the control group, the differ⁃ence was not statistically significant (χ2=0.015, P >0.05). The postoperative live birth rate was 91.30% in the studygroup and 83.33% in the control group, the difference was not statistically significant (χ2=0.086, P >0.05). Conclusion The results of the two surgical procedures were comparable, there was no difference in surgical complications, and the postoperative live birth rate was comparable.[Key words] Cesarean scar diverticulum; Hysteroscopic surgery; Laparoscopic surgery; Vaginal uterine scar repair子宫瘢痕憩室（cesarean scar diverticulum, CSD ），指剖宫产术后子宫瘢痕处较正常子宫肌层薄，构成一个与宫腔相通并突向子宫膀胱浆膜层的凹陷或者腔隙，并导致一部分患者出现相关的临床DOI ：10.16662/ki.1674-0742.2023.35.033[作者简介] 张国辉（1978-），男，本科，副主任医师，研究方向为妇科微创治疗。

医药卫生霍奇金淋巴瘤诊治进展

R-S cells CD30+
二、临床分期与危险因子
• 早期:I-ⅡA不伴RF （低危组） • 中期:I-IIA伴RF无X （高危组)
• 进展期(晚期):Ⅰ-ⅡB-X；III-Ⅳ
Risk factors （RF） • 大病灶X (>7.5-10cm；≧1/3最大胸腔截面) • ≥ 50岁 • 结外病变（脾累及，IV期） • B症状 • ESR ＞ 50mm/h或＞ 30mm/h伴B症状 • ≥3病变部位
第20页/共55页
（四）进展期霍奇金淋巴瘤的治疗
• MOPP（1960’s）
5年 OS 66%
• ABVD（1970’s）
5年 OS 73%
• 是目前进展期HL的标准治疗方案
• MOPP/ABVD杂交方案疗效与ABVD方案相同
• BEACOPP（1990’s），3年 OS 91%，强化组 92%
• Stanford V（1990’s）6年 EFS 89%，OS 96%
• 260例Ⅱa期伴危险因素和Ⅱb~Ⅳ期无年龄限制的（IV 期仅占17％）HL 患者入组
• PET-2阳性 50例 19％
• IPS 0－2 分组
13%
• IPS 3-7 分组
38％
• 预期2年FFS PET-2阴性组95%；阳性组28％ P
＜0.01
• 多因素分析显示PET-2、IV期、>45岁具有预测作用
• 证实了霍奇金氏病RS细胞来源于生发中心阶段的克隆性B淋巴细胞。
第4页/共55页
霍奇金淋巴瘤：WHO 2000年分类
•结节性淋巴细胞为主型 5%
（lymphocyte predominance, nodular ）

《2023年美国肝病学会实践指南：+肝硬化门静脉高压和静脉曲张的风险分层及管理》摘译

《2023年美国肝病学会实践指南：肝硬化门静脉高压和静脉曲张的风险分层及管理》摘译雒博晗，韩国宏西安国际医学中心医院消化内科，西安 710100通信作者：韩国宏，139****************（ORCID： 0000-0003-4568-3776）摘要：本实践指南旨在整合最佳实践建议，用于在慢性肝病患者中识别门静脉高压、预防首次肝功能失代偿、管理急性静脉曲张出血以及降低静脉曲张再出血的风险。

该指南中最重要的变化涉及承认代偿期进展性慢性肝病的概念，使用无创评估识别临床有意义的门静脉高压，在发现门静脉高压时建议尽早使用非选择性β-受体阻滞剂，进一步探讨门静脉高压的潜在未来药物治疗选择，阐明优先经颈静脉肝内门体静脉分流术在急性静脉曲张出血中的作用，以及讨论胃底静脉曲张治疗相关的最新数据，并提出了新的主题，如门静脉高压性胃病、经食管超声心动图和抗肿瘤治疗前的内窥镜检查。

关键词：肝硬化；门静脉高压；食管和胃静脉曲张；美国An excerpt of AASLD practice guidance on risk stratification and management of portal hypertension and varices in cirrhosis （2023）LUO Bohan， HAN Guohong.（Department of Gastroenterology， Xi’an International Medical Center Hospital， Xi’an 710100， China）Corresponding author： HAN Guohong，139****************（ORCID： 0000-0003-4568-3776）Abstract：This Practice Guidance intends to coalesce best practice recommendations for the identification of portal hypertension （PH），for prevention of initial hepatic decompensation，for the management of acute variceal hemorrhage （AVH），and for reduction of the risk of recurrent variceal hemorrhage in chronic liver disease. The most significant changes in the current Guidance relate to recognition of the concept of compensated advanced chronic liver disease， codification of methodology to use noninvasiveassessments to identify clinically significant PH （CSPH）， and endorsement of a change in paradigm with the recommendation of early utilization of nonselective beta-blocker therapy when CSPH is identified. The updated guidance further explores potential future pharmacotherapy options for PH，clarifies the role of preemptive transjugular intrahepatic portosystemic shunt in AVH，discusses more recent data related to the management of cardiofundal varices， and addresses new topics such as portal hypertensive gastropathy and endoscopy prior to transesophageal echocardiography and antineoplastic therapy.Key words：Liver Cirrhosis； Portal Hypertension； Esophageal and Gastric Vorrices； United States本实践指南［1］更新并扩展了美国肝病学会（AASLD）于2017年发布的门静脉高压（portal hypertension，PH）和胃食管静脉曲张管理的实践指南，为预防和管理PH提供了数据支持。

非等位基因

非等位基因概述非等位基因是指同一基因座上的不同等位基因。

等位基因是指在某个给定的基因座上，可以存在多种不同的变体。

每个个体继承了一对等位基因，一对等位基因可能会导致不同的表型表达。

非等位基因的存在使得遗传学研究更加复杂，因为不同的等位基因会对个体的表型产生不同的影响。

背景在生物学中，基因座是指染色体上一个特定的位置，该位置上的基因决定了某个特征的表达方式。

每个基因座上可以有多种不同的等位基因。

等位基因是指在某个特定基因座上的不同基因变体。

每个个体都会继承一对等位基因，通过这对等位基因的不同组合，决定了个体的表型。

然而，并非所有基因座上的等位基因都具有相同的表现型。

非等位基因的影响非等位基因的存在导致不同等位基因会对个体表型产生不同的影响。

有些非等位基因会表现出显性效应，也就是说，当个体继承了一个突变的等位基因时，即使同时继承了一个正常的等位基因，但显性效应会使得突变的等位基因的表型表达得到体现。

相反，有些非等位基因会表现出隐性效应，当个体继承了两个突变的等位基因时，才会表现出突变的表型。

除了显性和隐性效应之外，非等位基因还可能发生两种其他类型的表型效应。

一种是共显效应，当个体继承了两个不同的突变等位基因时，在表型表达上会表现出一种新的特征，这个特征并不是单个突变等位基因所能导致的。

另一种是部分显性效应，当个体继承了两个不同的突变等位基因时，表型表达将介于两个单独突变等位基因的表型之间。

重组和非等位基因重组是指两个不同的染色体交换部分基因序列的过程。

在重组的过程中，非等位基因可能会发生改变，导致新的等位基因组合形成。

这一过程使得非等位基因的表型效应更加复杂，因为新的等位基因可能将不同基因座的效应组合起来。

非等位基因的重要性非等位基因对生物的适应性和多样性起着重要作用。

通过对等位基因的各种组合的研究，人们可以更好地理解基因与表型之间的关系，并揭示遗传变异对物种适应环境的重要性。

总结非等位基因是指同一基因座上的不同等位基因。

神经内镜微创和传统开颅血肿清除术治疗高血压脑出血的疗效及安全性比较

论著·临床论坛CHINESE COMMUNITY DOCTORS 中国社区医师2020年第36卷第29期高血压脑出血是严重的高血压并发症，与过度脑力、体力劳动或情绪激动等因素造成的血管破裂出血有关。

发病时，患者多出现恶心呕吐、躁动、头痛等临床症状，若未及时治疗将造成血压升高、脉搏减慢、呼吸障碍等，严重者将导致中枢性衰竭，威胁患者生命安全和生活质量[1]。

目前，临床上多采用传统开颅血肿清除术、神经内镜微创等手术治疗高血压脑出血，均能有效清除患者脑部血肿，效果良好。

基于此，本文将比较神经内镜微创和传统开颅血肿清除术治疗高血压脑出血的疗效及安全性，现报告如下。

资料与方法2018年6月-2019年7月收治高血压脑出血患者64例，随机分为两组，各32例。

观察组男23例，女10例；年龄38～79岁，平均(58.53±1.20)岁；平均血肿量(67.45±32.54)mL；脑出血部位：基底节区26例、小脑3例、颞叶2例、额叶1例。

对照组男22例，女11例；年龄39～80岁，平均(58.48±1.24)岁；平均血肿量(67.56±32.45)mL；脑出血部位：基底节区25例、小脑4例、颞叶2例、额叶1例。

两组一般资料比较，差异无统计学意义(P ＞0.05)，具有可比性。

诊断标准：经CT 检查确诊，伴有失语、偏瘫、呕吐和意识障碍等症状。

纳入标准：①符合《高血压合并脑出血的临床诊治分析》中有关高血压脑出血诊断标准[2]；②术前格拉斯哥昏迷评分(GCS)＞3分；③发病至手术的时间＜6h；④患者及家属均签署知情同意书。

排除标准：①凝血功能障碍、语言听力障碍或精神疾病；②心、肝、肾等重要脏器病变；③治疗依从性较差；④中途退出。

方法：①对照组采用传统开颅血肿清除术治疗：给予患者全身麻醉后，在其血肿部位头皮作一切口，将骨窗钻孔扩大、将硬脑膜剪开，经穿刺确认血肿后，再将患者脑皮层切开，清除血肿并止血，将引流管放置在术腔，并缝合头皮各层和肌肉层。

医学英语词根词缀记忆

neonate: n, 新生儿, neonatal: adj，新生期的neo: 新neomycin, 新霉素，neoplasm, 新生物，natus: 出生, prenatal: 产前的，出生前的Gastrointestinal: 胃肠道的gastro : 胃，intesto : 肠，Gastrointestinal system:胃肠系统，或消化系统Antibody: 抗体anti-: 对抗，antigen: 抗原antibiotics: 抗生素Psychosexual: 性心理Psycho: 心理，精神，psychology: 心理学Carbohydrate: 碳水化合物Carbo: 碳carbonate: 碳酸盐hydrate: 水化物，含水物hydratase: 水和酶ase 酶，lipase：脂肪酶Auditory: adj. 听觉的audi-: 听如：audiometer: 听力计meter: 测量kinetic: 运动的kine-: 运动kinesimeter: 运动测量计akinesia：运动不能Congenital: 先天性的con- 和genitor-: 生殖，生殖器genitourinary：泌尿生殖的Defect：缺点，瑕疵de：否定，脱离，缺乏，不足degeneration：恶化fect：做infect：感染，影响Oxygenated: 含氧的，氧合的oxygen：氧气-ate：词尾，表示某种行为，状态Deoxygenate：去氧，脱氧de- 前缀，去离脱Unoxygenated：不含氧的，含氧低un-前缀，用于形容词之前，不Pulmonary：肺的pulmo-：肺pulmometer：肺量计Tachycardia: 心动过速tachy：快，迅速tachypnea：呼吸过快cardio-心脏Cardiovascular：心血管的Stenosis：狭窄steno-：狭窄stenocephaly：头狭窄，小头Hypertrophy：肥大，增生hyper：高于，超越，多于hypercardia：心肥大trophy：战利品，促，增加gonadotrophin：促性腺激素Hypotrophy：不足生长，萎hypo-：低于，少于，不足Cyanosis：发绀Acyanotic：不发绀的a-：不，没有anemia：贫血（-emia是血症）cyanotic：发绀的Hypoxia：低氧血症hypo（少）+ox（ygen）（氧气）+ia（血症）Dyspnea：呼吸困难dys-：前缀，困难dyskinesia：运动障碍pnea：气体，呼吸apnea：呼吸停止Leukemia: 白血病leuk- 同leuc-，白leucocyte：白细胞-emia-：同-hemia，血，血液Leukopenia：白细胞减少症-penia：血细胞减少thrombocytopenia：血小板减少症neutropenia：中性粒细胞减少症-neutro-：中，中间，中性neutrocyte：中性粒细胞Thrombocytopenia：血小板减少症-thrombo-：血小板，血栓thrombosis：血栓症thrombocyte：血小板-cyte：细胞erythrocyte：红细胞Infiltration: 渗透-in：向里filtrate：过滤，滤出Reticuloendothelia: 网状内皮reticulo-：网状的reticular：网状组织-endo-：内，内部endotrachea：气管内-theli-：乳头，皮瓣Chemotherapy：化疗chemo-: 化学的chemoanalysis：化学分析therapy：治疗Anesthetics：麻醉剂an-：前缀，否定的，相反的（同a-）-esthe-：感觉esthesia：感觉，感知Cystitis：膀胱炎cyst-囊，胞，膀胱cystalgia：膀胱痛-itis：炎gastritis：胃炎hemophilia 血友病hemo- 血，血液hemoglobin: 血红蛋白-phil: 亲，嗜neutrophil: 嗜中性白细胞neutron-: 中-ia: 词尾，表示—血症，petechia：淤血，淤点hemolyze: 溶血hemo-血-ly-：溶解fibrolysin: 纤维溶解素hemorrhage: 出血hemo- 血，血液-rrha-: 大量的流出diarrhea: 腹泻umbilical cord: 脐带umbil- 脐umbilectomy: 脐切除术cord 绳索，带子circumcision: 包皮环切术circum- 周围，环circumcorneal: 角膜周围（corneal 是角膜的意思）-cision 切开，切口incision：切割, 切开, 切口intracranial: adj 颅内的intra-: 内，内部intracellular: 细胞内的-cranio-: 颅的，颅骨的craniofacial: 颅面的laceration: 伤口，裂口lacer-: 撕裂lacerant：折磨人的，令人痛苦的hemarthrosis: 关节积血arthro-: 关节arthritis: 关节炎（-it is: 是炎症）-osis：词尾，疾病的状态petechia 瘀点，瘀斑peti：皮肤上的斑点impetigo：（皮肤）脓疱病-ia：词尾，血症anemia: 贫血an- 无，不，缺乏-emia：血症leukemia：白血病follow-up: 随诊，复诊immobilize: v 制动，不活动im-是前缀，同in，不，相反，没有mobile: 移动比如大家都熟悉的mobile phone: 移动电话antihemophili：抗血友病的anti- 对抗antiembolic：抗栓hemophilia 血友病degeneration 退化，变性de- 去，离，脱，除degrowth: 降低生长gene：基因，generation: 产生，发生, 生殖disability: 无能力，残疾dis-:分开，分离，否定，不disadjust：失调的able: 能，可以，ability: 能力，才干disable: 不能，disability: 残疾genetic: 遗传的gene: 基因hemolytic: 溶血性的hemo- 血，血液hemoglobin：血红蛋白-lyse-：溶解cytolysis: 细胞溶解precipitate：促成，使…陷入pre-：先于，…之前preplan：预先计划cipit：头dehydration：脱水de- 去，离，脱hydro-：水，含氢的hydrogen：氢Hematocrit：红细胞压积，红细胞比容hemato-：血液，血crit：同krites，判断Lethargy：无精打采，嗜睡les-：健忘的-argos-：懒散的Malaise：身体不适，不舒服，疲倦mal- 坏的，错误的malformation：畸形，难看-aise：同ease，悠闲，轻松，安逸Vaso-occlusion 血管堵塞vaso-：血管，输精管vasodilation：血管扩张occlusion：闭塞，阻塞Perfusion：灌注per-：通，穿透，支持，携带，向前fuse：熔化，合并，注入 infusion：灌输，输液Overheating：过热的over- 超过，高过，过分Pneumococcus：肺炎球菌pneumo-: 肺，气pneumonia：肺炎-coccus：球菌diplococcus：双球菌transfusion：输血trans-：转移transfer：转移，转让，传递fuse：合并，注入infusion：灌输，输液electrolyte：电解质electro-：电，电子的electroconvulsion：电击lyte：溶解Apnea: 无呼吸的，呼吸停止的a-：否定，相反的, 不，没有absent：缺席，不在-pnea-: 呼吸dyspnea：呼吸困难Bradycardia：心动过缓brady-：缓慢的bradypnea：呼吸过慢-cardio-：心脏cardigram：心电图Hypotonic：张力下降hypo-：少于，低于hypotension：低血压tonic：紧张的，张力的Autopsy：尸检auto-自己，自体autograft：自体移植物-opsis-：检查，看Bronchiolitis: 细支气管炎bronchio- 细支气管bronchiole: 细支气管-itis: 炎症meningitis: 脑膜炎Laryngitis: 喉炎laryngo- 喉laryngoscopy: 喉镜检查Laryngotracheobronchitis: 喉气管支气管炎-tracheo-: 气管tracheotomy: 气管切开术-broncho-: 支气管bronchitis: 气管炎Epiglottitis: 会厌炎epiglott-：会厌Syncytial: 合胞病毒的syn-: 共同，联合，相似synkinesia: 协同性运动, 辅助运动-cyto-: 细胞Hyperinflation: 过度膨胀hyper：高，过多hypertension：高血压-in-：相反的，否定的flat: 平坦的，扁的，漏气的Inspiratory: 吸气的in: 向内，进入insight：内在，见识-spirate-: 通气respiration: 呼吸Dysphagia: 吞咽困难dys- : 困难的-phago-: 吞咽，吞噬Phagocyte: 吞噬细胞Trecheostomy: 气管切开术-ostomy-: 切开术，造瘘术colostomy: 结肠造瘘术Epinephrine: 肾上腺素-epi-: 在…之上，在…之外epigastric：上腹部-nephro-: 肾脏的nephrosis: 肾病-ine: 素Corticosteroid: 皮质激素cortico-：皮，皮质corticose: 外皮的，皮层的steroid: 激素Endotracheal: 气管内的-endo-: 内，内部endocrine：内分泌Cystic 囊性的cyst-: 前缀表示“囊, 胞”之义cystectomy: 胆囊切除术Fibrosis: 纤维化，纤维变性fibr(o)- 纤维fibrocyte: 纤维细胞-cyte: 细胞-sis: --词尾，…化, …状态Dysfunction: 功能紊乱，机能不良dys: 困难dysphagia：吞咽困难Function: 功能Autosome: 常染色体，正染色体auto-自体，身体，自动-soma-: 体s omatic：肉体的Exocrine: 外分泌exo- 外部的exotoxin: 外毒素crinein: 分离Endocrine: 内分泌endo-: 内，内部endotoxin: 内毒素malabsorption: (营养）吸收不良mal-: 坏，错误，疾病malignant: 恶性的absorb: 吸收steatorrhea: 脂肪泻steato- 脂肪steatoma: 脂肪瘤-rrhea：大量流出diarrhea：腹泻expectorant：adj 化痰的，n 化痰剂ex-: 自…出来, 排出excrete: 排泄pector: 胸，胸腔mucolytics: 粘液溶解剂muco- 粘液mucoid: 粘液样的-lyte-: 溶解hemolysis: 溶血bronchodilator: 气管扩张剂broncho- 气管bronchitis: 气管炎dilate: 扩张dehydration: 脱水de- 前缀，去、脱hydro- 水，氢Prodromal ：前驱的,有前驱症状的pro：居前，领先proenzyme：酶原dromos：跑，进行maculopapular：斑丘疹macule：斑疹papule：丘疹Centripetal: 向心的centro-：中心Antihistamine: 抗组胺药anti-：对抗antibody：抗体-histo-：组织histocyte：组织细胞-amine：胺Globulin：球蛋白globule：球，-in：素，酶，蛋白encephalitis：脑炎-encepho-：脑encephalopathy：脑病-itis：炎Paramyxovirus：副粘病毒para-: 副，旁，侧面parablast：副胚层-myxo-：粘，粘液myxocyte：粘液细胞virus：病毒Parotitis：腮腺炎，腮腺肿大Paroti-：腮腺，耳旁的parotin：腮腺激素Submaxillary：下颌的sub：下，亚，次subcutenous：皮下-maxill-: 颌Orchitis：睾丸炎-orcho-：睾丸orchotomy：睾丸切开术Epididymo-orchitis：附睾炎epididymo-：附睾teratogenic：产生畸形的-terato-：畸形teratosis：畸胎，怪胎Hydrogen peroxiede：过氧化氢，双氧水hydrogen：氢per-：携带，支持-oxide：氧化物dioxide：二氧化物Desquamation：脱皮，脱屑de-：去，脱，离squama：鳞片Arthralgia：关节痛-arthro-：关节arthritis：关节炎-gia：疼痛neuralgia：神经痛vasculitis：脉管炎，血管炎-vascul-：血管Hyperthermia：高热-thermo-：体温，热度thermometer：体温计Unremitting：不间断的un-：前缀，没有，不remit：宽恕，赦免Lymphadenopathy：淋巴腺疾病-lymph-：淋巴-adeno-：腺体adenoma：腺瘤Erythematous：红斑的-erythro-：红，红色Erythromycin：红霉素-ma：斑，瘤myoma：肌瘤Febrile：热性的febri-：发烧febricide：退热剂Conjunctivitis：结膜炎conjunctiva：结膜Oropharyngeal：口咽的-oro-：口Oral：口头的-pharyngo-：咽 Pharyngitis：咽炎Mucocutaneous：粘膜皮肤的-muco-：粘膜mucosa：黏膜-cutaneo-：皮肤subcutaneous：皮下的医学英语词根词缀记忆10Rheumatic: 风湿性的rheumato-:风湿rheumatoid: 类风湿的rheumatic fever: 风湿热Autoimmune: 自身免疫的auto-: 自身，自体autoantibody：自身抗体immune：免疫immune globulin：免疫球蛋白Streptococcus: 链球菌strepto-：链状的streptolysin: 链球菌溶血素streptomycin：链霉素-coccus: 球菌diplococcus:双球菌Peumococcus：肺炎双球菌Carditis: 心脏炎，心肌炎cardio-:心脏cardiovascular：心血管的myocardial：心肌的-itis：炎myocarditis：心肌炎Polyarthritis:多发性关节炎poly-: 多，多个，多种polycyte: 多型核细胞polyphagia：多食-arthro-: 关节arthrology: 关节学Erythema:红斑erythe: 红，红色erythromycin: 红霉素-ma: 肿物，斑myoma：肌瘤Subcutaneous: 皮下的Sub-: 在下；低于，次于，副，次Subadult:接近成年的人-cutan-: 皮肤percutaneous：经皮的ROM: Range Of Motion 环绕关节地运动，全关节运动Prophylactic:预防疾病的；预防性的pro-：在…之前-phylax-: 保卫phylaxin：抵抗素Glomerulonephritis:肾小球肾炎glomerulus ：肾小球glomerulitis：肾小球炎glomerulopathy：肾小球病-nephro-：肾nephrocyte：肾原细胞nephrotoxicity: 肾毒性Bilateral：双侧的，有两面的bi-：两，双bipolar：双极的，两极的lateral：侧边unilateral：单侧的Noninfectious：非传染的non-：非，不，无nonabsorbable：不能被吸收的infectious：传染性的Streptococcus：链球菌strepto-：链状streptomycin：链霉素-coccus: 球菌diplococcus：双球菌Hypertension：高血压hyper：高于，多于h yperthermia：高温，发热tension：压力，张力Antihypertensive：抗高血压药anti：抗，对抗antibiotics：抗生素Retention：保留，储留Hematuria: 血尿Hemato-：血hematogenous：血源性的-uria：尿oliguria：少尿Integrity：完整，完全Specific gravity：比重Recurrence：复发，重现re-：再次retake：重摄reread：再读rewrite：再写-cur-：发生occur：发生，出现 concur:同时发生（con：共同）Otitis media: 中耳炎Otitis: 耳炎-oto-: 耳otophone: 助听器otolith：耳石-itis：炎Meningitis: 脑膜炎-meningo-: 脑膜meningocele: 脑膜膨出meningioma：脑（脊）膜瘤Eradicate: 根治，根除e-: 免，除去erase：抹去，擦掉-radic-: 根polyradiculitis：多神经根炎Decongestant:解充血药de-：去除，剥夺，脱离dehydration：脱水congest: 充血，充塞congestive heart failure：充血性心力衰竭-ant：药，剂absorbant：吸收剂Analgesic: 止痛的；镇痛剂an- : 无，没有，缺乏anacid：酸缺乏，无酸的anemia：贫血-algea-: 同algia，痛苦，感到痛苦neuralgia：神经痛Antipyretic:退热药anti-：抗antacid：抗酸剂antibacterial：抗菌的-pyreto-: 热pyretology: 热病学Myringotomy:鼓膜切开术-myringo-: 鼓膜myringitis: 鼓膜炎-otomy：切开术atriotomy：心房切开术Photophobia: 畏光-photo-: 光，相片phobia: 恐惧症acrophobia：恐高症basophobia：步行恐惧症Opisthotonos：角弓反张opistho-：后，体后 opisthion：颅后点，枕骨tonic：紧张，强直Multisystem：多系统的multi-：多，多种，多个 multiple：多样的，多重的Encephalopathy：脑病encephal-：脑encephalitis：脑炎-pathy：疾病neuropathy：神经病nephropathy：肾病持续更新，所需资料请私信，必尽最大努力尽快提供。

个性化护理联合降压药物对老年高血压患者血压控制效果的影响观察

中国实用医药2019年7月第14卷第19期China Prac Med,Jul2019,Vol.14,No.19・147・个性化护理联合降压药物对老年高血压患者血压控制效果的影响观察郑秀云【摘要】目的观察老年高血压患者采用个性化护理联合降压药物对血压控制效果的影响。

方法98例老年高血压患者，采用随机数字表法分为观察组和参照组，各49例。

参照组接受降压药物治疗，观察组在参照组基础上联合个性化护理干预。

比较两组患者的并发症发生情况、临床疗效及焦虑抑郁评分。

结果观察组患者并发症发生率为2.04%,低于参照组的18.37%,差异具有统计学意义(“2=7.1273,P<0.05)o观察组患者总有效率为93.88%,高于参照组的71.43%,差异具有统计学意义(^=8.6115,P<0.05)。

观察组患者焦虑自评量表(SAS)和抑郁自评量表(SDS)评分分别为(32.1±1.1)、(33.1±2.2)分,均低于参照组的(42.6±2.8)、(43.1士1.4)分,差异均具有统计学意义(=24.4322、26.8438,P<0.05)。

结论老年高血压患者采用个性化护理联合降压药物，可以控制患者血压，提高治疗效果,改善负性情绪，促进患者康复。

［关键词】个性化护理；降压药物；高血压；老年D0I:10.14163/ki.ll-5547/r.2019.19.080Observation on effect of personalized nursing combined with antihypertensive drugs on blood pressurein elderly patients with hypertension ZHENG Xiu-yun.Department of Nursing,Shandong Junan CountyPeople*s Hospital,Linyi276600,China[Abstract]Objective To observe the effect of personalized nursing combined with antihypertensivedrugs on blood pressure in elderly patients with hypertension.Methods A total of98elderly patients withhypertension were divided into observation group and control group according to random number table method,with49cases in each group.The control group was treated with antihypertensive drugs,and the observation groupwas treated with personalized nursing on the basis of the control parison were made on occurrenceof complications,clinical efficacy and anxiety and depression score in two groups.Results The observationgroup and lower incidence of complications as2.04%than18.37%in the control group,and the difference wasstatistically significant(^2=7.1273,P<0.05).The observation group had higher total effective rate as93.88%than71.43%in the control group,and the difference was statistically significant(比'8.6115,P<0.05).The observationgroup had self-rating anxiety scale(SAS)score and self-rating depression scale(SDS)score respectively as(32.1±1.1)and(33.1±2.2)points,which were all lower than(42.6±2.8)and(43.1±1.4)points in the controlgroup.Their difference was statistically significant¢=24.4322,26.843&Pv0.05).Conclusion Combination ofindividualized nursing and antihypertensive drugs can control blood pressure,improve treatment effect,improvenegative emotions and promote rehabilitation of elderly patients with hypertension.[Key words]Personalized nursing;Antihypertensive drugs;Hypertension;Elderly高血压为临床多发的慢性疾病之一，且该疾病多发于老年群体中，病情长期发展会诱发患者出现肾、脑、心等脏器的病变及损害,严重影响患者身体健康及生命安全⑴。

基因组学英语

基因组学英语Genomics is the study of an organism's complete set of DNA, including all of its genes. It is a rapidly evolving field that has had a significant impact on many areas of scientific research and human health. Genomic research has led to breakthroughs in our understanding of the genetic basis of disease, as well as new approaches to diagnosing and treating genetic disorders.One of the key goals of genomics is to sequence and analyze the entire genome of an organism. This involves determining the order of all the DNA base pairs that make up an organism's genetic code. The first complete human genome sequence was published in 2003 as part of the Human Genome Project, a massive international effort to map and sequence the entire human genome. Since then, the cost of sequencingDNA has dropped dramatically, making it possible to sequence entire genomes much more quickly and affordably.Genomics has numerous practical applications in fields such as medicine, agriculture, and evolutionary biology. In medicine, genomic research has led to the development of personalized medicine, which aims to tailor medical treatment to an individual's genetic makeup. This has the potential to revolutionize the way we diagnose and treat many diseases, including cancer, diabetes, and heart disease. Genomic data can also be used to identify individuals who are at risk of developing certain diseases, allowing for earlierintervention and prevention.In agriculture, genomics has led to the development of genetically engineered crops that have improved resistance to pests and environmental stress. By understanding the genetic makeup of plants and animals, scientists can develop new breeding strategies to improve crop yields and livestockproductivity. This has the potential to improve food security and reduce the environmental impact of agriculture.Genomic research also has important implications for evolutionary biology. By comparing the genomes of different species, scientists can study the genetic basis of speciation and evolutionary change. This has led to new insights into the evolutionary history of life on Earth, as well as the genetic mechanisms that drive evolution.The field of genomics is also generating vast amounts of data, which presents new challenges and opportunities for scientific research. Advances in computational biology and bioinformatics are making it possible to analyze andinterpret this data, leading to new insights into the complexity of the genome and its role in health and disease.In conclusion, genomics is a rapidly advancing field with profound implications for human health, agriculture, and our understanding of the natural world. The ability to sequenceand analyze entire genomes has opened up new possibilitiesfor personalized medicine, improved crop and livestock production, and the study of evolution. As genomic research continues to advance, it holds the promise of revolutionizing many aspects of our lives.。

Topology Lecture Notes - Ward, Thomas

3
1. TOPOLOGICAL SPACES
4
Lemma 1.3. Let X and Y be metric spaces, and f : X → Y a function. The following are equivalent: 1. f is continuous; 2. for every open set U in Y , f −1 (U ) is open in X ; 3. for every closed set C in Y , f −1 (C ) is closed in X . Try to understand what this lemma is telling you about functions mapping from a discrete space as in Example 1.1(6) above. Also as an exercise, prove the following. Lemma 1.4. Let X be a metric space. Then 1. The empty set ∅ and the whole space X are open sets. 2. If U and V are open sets, then U ∩ V is an open set. 3. If {Uα }α∈A is any collection of open sets, then α∈A Uα is an open set. Notice that the index set A in Lemma 1.4 does not need to be countable. Lemma 1.4 suggests the following generalization of a metric space: think of Lemma 1.4 as deﬁning certain properties of open sets. By Lemma 1.3 we know that the open sets tell us all about continuity of functions, so this will give us a language for talking about continuity and so on without involving metrics. This turns out to be convenient and more general – by simply dealing with open sets, we are able to deﬁne topological spaces, which turns out to be a strictly bigger collection of spaces than the collection of all metric spaces. Definition 1.5. If X is a set, a topology on X is a collection T of subsets of X satisfying: 1. ∅, X ∈ T , 2. U, V ∈ T =⇒ U ∩ V ∈ T , 3. if Uα ∈ T for all α ∈ A, then α∈A Uα ∈ T . The pair (X, T ) is called a topological space, and the members of T are called the open sets. If the space is also a metric space, then the open sets will be called metric open sets if the distinction matters. We now have a new deﬁnition of continuity – make sure you understand why this is now a deﬁnition and not a theorem. Definition 1.6. A function f : X → Y between topological spaces (X, TX ) and (Y, TY ) is continuous if and only if U ∈ TY =⇒ f −1 (U ) ∈ TX . Lemma 1.7. Let (X, TX ), (Y, TY ) and (Z, TZ ) be topological spaces. If functions f : X → Y and g : Y → Z are continuous, so is the composition gf : X → Z . Proof. If U ∈ TZ , then g −1 (U ) ∈ TY since g is continuous. It follows that f −1 (g −1 (U )) ∈ TX since f is continuous. Therefore (gf )−1 (U ) = f −1 (g −1 (U )) ∈ TX for all open sets U in Z .

医学免疫学名词解释含英文

《医学免疫学》名词解释1.免疫immunity：机体识别和排除抗原性异物的生理反应。

2.抗原Ag：能刺激机体的免疫系统发生免疫应答，并能与免疫应答产物发生特异性结合的物质。

3.表位（抗原决定簇）epitope：抗原分子中决定抗原特异性的特殊化学基团。

4.半抗原hapten：某些小分子物质只可与应答产物特异性结合，而不能刺激机体产生免疫应答。

即只具备免疫反应性，不具备免疫原性的物质。

5.异嗜性抗原heterophilic antigen：存在于人、动物、微生物等不同种属之间的共同抗原。

6.佐剂adjuvant：预先或与抗原同时注入体内，可增强机体对抗原的免疫应答或改变免疫应答类型的非特异性免疫增强物质。

7.抗体Ab：免疫系统在抗原刺激下，由B淋巴细胞或记忆B细胞增殖分化成的浆细胞所产生的、可与相应抗原发生特异性结合的免疫球蛋白。

8.免疫球蛋白Ig：血清中一类主要的蛋白，由α1、α2、β和γ球蛋白组成。

9.超抗原Superantigen SAg：仅需极低浓度即可非特异性激活高达2%～20%的T细胞克隆，产生极强免疫应答的抗原。

10.单克隆抗体：由单一杂交瘤细胞产生，针对单一抗原表位的特异性抗原。

11.抗体依赖的细胞介导的细胞毒作用（ADCC）：抗体Fab段结合病毒感染的细胞或肿瘤细胞表面的抗原表位，其Fc段与NK细胞表面的FcR结合，介导NK细胞直接杀伤靶细胞。

12.互补性决定区（CDR）：VH和VL中的3个可形成与抗原表位互补的空间构象的区域。

13.补体Complement：正常人或动物体液中存在的一组与免疫有关，并具有免疫活性的免疫球蛋白。

14.膜攻击复合物（MAC）：由补体系统的C5b～C9组成的复合物，可牢固附着于靶细胞表面，最终造成靶细胞死亡溶解。

15.细胞因子CK：由免疫细胞及组织细胞分泌的具有生物学活性的小分子蛋白。

16.CSF（集落刺激因子）：能刺激多能造血干细胞和不同发育分化阶段的造血祖细胞分化、增殖的细胞因子。

矩阵满秩分解的一些应用

矩阵满秩分解的一些应用第35卷第5期2005年9月中国海洋大学PERIoDICALoFoCEANUNIVERSITY oFCHINA35(5):761～762Sept.,2005矩阵满秩分解的一些应用姚增善,刘新国(中国海洋大学数学系,山东青岛266071)摘要:把矩阵的满秩分解用于分析广义投影矩阵及双曲广义投影矩阵,得到了新的特征刻画.关键词:广义投影矩阵;Moore-Penrose广义逆;Hermite矩阵中图法分类号:O172.1文献标识码:A文章编号:1672—5174(2005)05—761—020引言首先给出有关的定义.定义1设K为7/阶复方阵,记K为矩阵K的共轭转置.(1)如果K2=K=K,则称K为正交投影矩阵;(2)如果存在/./阶方阵K,使KK及KK都是Hermite矩阵,且满足KKK=K及KKK=K,则称K为矩阵K的Moore—Penrose广义逆.Moore-Penrose广义逆和正交投影矩阵都是代数学中的基本概念.前者在最zb--乘法等问题中有许多应用;而后者用来刻画子空间与投影矩阵的一一对应性,从而把有关子空间的定量研究转化为矩阵分析.1997年,Grofl和Trenkler[推广正交投影矩阵而引入了下面的广义投影矩阵及双曲广义投影矩阵.定义2设K为n阶复方阵,K和K分别为矩阵K的共轭转置及Moore—Penrose广义逆.(1)如果K2=K,则称K为广义投影矩阵;(2)如果K2=K,则称K为双曲广义投影矩阵.最近,Baksalary和Xiao—jiLiu等详细地讨论了定义2给出的这两类矩阵[2-3J.本文继续他们的讨论.但使用的方法不同,本文的基本工具是矩阵的满秩分解_4J:任何秩为r的m×7/矩阵A都可分解为A=BC其中,B和c分别为m×r和7/×r的列满秩矩阵.为了叙述方便,文中使用了下述记号:c表示7/阶复方阵所成的线性空间,矩阵A的列向量张成的线性空间记为R(A).上标及+分别表示共轭转置及Moore—Penrose广义逆,I表示适当阶数的单位阵.1主要结果及其证明设K是秩为r的n阶复方阵,本节考虑下述集合:收稿日期:2005.06.01;修订日期:2005.07.07作者简介:姚增善(1963.),男,硕士,副教授.Tel:(0532)85901953 c={KIK∈C,K:K);cP』={KiK∈c,K=K};c={KIK∈C,K:K);c={KIK∈C,KK=KK);c={KIK∈C,K=K);c={KIK∈c,KKKK=KKKK).显见,cGP为广义投影矩阵构成的集合,c为双曲广义投影矩阵构成的集合.易知cGPc,而且c口P还有下述重要的子集c={KIK∈C,K=K).同时,K为正交投影矩阵当且仅当K:K,K=K,还易知,K为正交投影矩阵的充要条件为K=K= K.因此,广义投影矩阵及双曲广义投影矩阵确实是正交投影矩阵的推广.首先给出c的特征.考虑K的满秩分解K=BC,那么K=K甘B(CB)0C=BC错(CB)0=I.命题1K∈c当且仅当K的满秩分解K=BC满足(CB).=I.接下来考虑cP』.记K=BC,则K=C(CC)I1(BB)I1B.从而K=K错CB=C(CC)(BB)B甘(BB)(CC)=I.再作B和C的极分解B=QlHl,C=Q2H2,这里Hl 和H2为Hermite正定矩阵,且QQl=QQ2=I.则BB=H},CC=H;.总结上述,有命题2cP』={QlQIQl,Q2为竹×r阵,QQl=QQ2=I}.再考虑cGP.考虑K的特殊满秩分解K=BC,cC=I,,那么中国海洋大学K2=K甘BCBC=CB,这说明R(B)=R(C).从而存在r阶可逆方阵G,使B=CG.且K2=K甘(CGC)(CGC)=CGC甘G=G.又由Schur分解,G可分解为G=Q0R0Q,Q0为酉阵,R.为上三角阵,而G=G甘R8=R甘R0=diag(dl,dE,…,d).其中,dj(j=1,2,…,r)为三次单位根,即d;=1,d=d.综上所述,有命题3c?e={QDQIQ为×r阵,QQ=J,D=diag(dI'2,…,d),d=1}.注:三次单位根集合为{?,一号一,/5吉+譬}o再讨论c.令K=BC为满秩分解,那么KK=KK甘BB=CC甘C=BG.这里G=BC为r×r可逆方阵.因此有命题4={QGQIQ为×r阵,QQ=I,G为r×r可逆阵}.再分析cW.考虑K的满秩分解变形K=QlGQ,其中,G为r×r可逆方阵,Ql,Q2为×r矩阵,QQl=QQ2=J.那么K=K甘QlGQQlGQ=Q2G-1Q,从而R(Q1)=R(Q2).因此,不妨取Ql=Q2,此时K=QlGQ.又K=K甘QlGQ=QlG一Q甘G=G一甘G.=J,而G.=J甘G=Q0diag(dl,2,…,d)Q,QQ0=J,d;=1.命题5cW={QDQIQ为×r阵,QQ=I,,D=diag(dI'2,…,d),d=1}.最后考虑cUe.令K=BC,记PK=KK,PK=KK,贝0有PK=BB,PK=CC.可见K∈cUe甘BBCC=CCBB.注意到,PK和PK?为正交投影矩阵且为Hermite阵,上式表明PK和PK.可交换,因而存在酉阵Q,使BB=Qdiag(aI'a2,…,a)Q,CC=Qdiag(卢l,卢2,…,卢)Q,这里ai和取0或1.取R(B)nR(C)的标准正交基(为列)构成矩阵Q,Q适当排列后可用分块阵表示为Q=[QI'Q')],这样BB=[QI'QB],CC=[Ql,Qc],而[Ql,QB,Qc]是列规范正交阵.这表明B=[Ql,QBJGB,C=【QI'QcJGc,其中GB,Gc为r阶可逆阵.从而K=[QI'QB]?G[Ql,Qc],G为可逆阵.易知K∈cW,故有下述结论:命题6cUe=I[QI'Q2]G[QI'Q3]_[QI'Q2,Q3]列规范正交,G为可逆阵}.本文得到的结果大部分是新的,使用的基本工具是矩阵的满秩分解.Baksalary等人使用Jordan分解或Schur分解以及奇异值分解,分析了G及G中矩阵的谱特征,得到的结果很有趣.不难看出,本文的结论可以很容易地导出他们得到的大部分结果.而且,作者认为,从应用的角度看这里得到的结论更便于应用.参考文献:Gro口J,TrenklerG.Generalizedandhypergeneralizedproiectors [J].LinAlgAppl,1997,264:463—474.BaksalaryJK.Baksalary0M.LIUXiao—ji.Furtherpropertiesof generalizedandhypergeneralizedprojectors[J].LinAlgAppl, 2004,389:295—303.BaksalaryJK,LIUXiao-Ji.Analternativecharacterizationofgener—alizedprojectors[J].LinAlgAppl.2004,388:61—65.北京大学数学系编.高等代数第二版[M].北京:高等教育出版社.1988.SomeApplicationsoftheFull-RankDecompositionofMatricesY AOZeng—Shan,LIUXin—Guo(DepartmentofMathematics,OceanUniversityofChina,Qingdao266071,China) Abstract:Inthispaper,thefull—rankdecompositionofmatricesisusedtoanalysegeneralizedprojectionma—tricesandhypergeneralizedprojectionmatrices,andsomenewcharacteristicdescriptionsar eobtained.Keywords:Orthogonalprojectionmatrix;Moore—Penrosegeneralizedinverse;HermitematrixAMSSubjectClassifications:15A23。

分子生物学名词解释最全（2）

分子生物学名词解释最全（2）分子生物学名词解释最全abundantmrna(高丰度mrna)：由少量不同种类mrna组成，每一种在细胞中出现大量拷贝。

acceptor splicing site(受体剪切位点)：内含子右末端和相邻外显子左末端的边界。

acentricfragment(无着丝粒片段)：(由打断产生的)染色体无着丝粒片段缺少中心粒，从而在细胞分化中被丢失。

active site(活性位点)：蛋白质上一个底物结合的有限区域。

allele(等位基因)：在染色体上占据给定位点基因的不同形式。

allelicexclusion(等位基因排斥)：形容在特殊淋巴细胞中只有一个等位基因来表达编码的免疫球蛋白质。

allostericcontrol(别构调控)：指蛋白质一个位点上的反应能够影响另一个位点活性的能力。

alu-equivalent family(alu 相当序列基因)：哺乳动物基因组上一组序列，它们与人类alu家族相关。

alu family (alu家族)：人类基因组中一系列分散的相关序列，每个约300bp长。

每个成员其两端有alu切割位点(名字的由来)。

α-amanitin(鹅膏覃碱)：是来自毒蘑菇amanita phalloides 二环八肽，能抑制真核rna聚合酶，特别是聚合酶ii转录。

amber codon(琥珀密码子)：核苷酸三联体uag，引起蛋白质合成终止的三个密码子之一。

amber mutation (琥珀突变)：指代表蛋白质中氨基酸密码子占据的位点上突变成琥珀密码子的任何dna改变。

amber suppressors (琥珀抑制子)：编码trna的基因突变使其反密码子被改变，从而能识别uag密码子和之前的密码子。

aminoacyl-trna (氨酰-trna)：是携带氨基酸的转运rna，共价连接位在氨基酸的nh2基团和trna终止碱基的3￠或者2￠－oh 基团上。

aminoacyl-trna synthetases (氨酰-trna 合成酶)：催化氨基酸与trna3￠或者2￠－oh基团共价连接的酶。

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Lnf (m)g(m)h(m) = f (m)Lm˜ g˜(n)h(m) = f (m)(Ln˜g)(m)h(m). (7)
m
m
m
Proof: We use (5) and (4) to obtain
(Lnf )(m)g(m)h(m) =
g(k˜, n, m˜ )h(k)f (k)g(m) = f (k)Lk˜g˜(n)h(k)
A bijection˜on K is deﬁned by
cn˜ = c∗n.
(1)
Further, let
h(n) = g(n˜, n, 0)−1.
(2)
Due to (A3) we have h(n) > 0 for all n and h(0) = 1. If K is hermitian or commutative then h(n) = h(n˜). In the following lemma some useful properties of the structure constants are summarized.
2 Semi-bounded generalized hypergroups
The discrete structure of a generalized hypergroup was introduced by Obata and Wildberger in [13]. Let us recall the basic deﬁnition.
1 Introduction
Locally compact hypergroups were independently introduced around the 1970’s by Dunkl [4], Jewett [7] and Spector [18]. They generalize the concepts of locally compact groups with the purpose of doing standard harmonic analysis. Similar structures had been studied earlier in the 1950’s by Berezansky and colleagues, and even earlier in works of Delsarte and Levitan.
(5)
g(n, m, k)g(k, l, j) = g(n, k, j)g(m, l, k) for all n, m, l, j.
(6)
k
k
Generalized hypergroups
3
Proof: For (3)–(5) see [13, Lemma 1.1]. Now, on the one hand we have (cncm)cl = k,j g(n, m, k)g(k, l, j)cj and on the other hand cn(cmcl) = k,j g(m, l, k)g(n, k, j)cj. From
Holger Rauhut University of Vienna, Faculty of Mathematics, NuHAG
Nordbergstr. 15, A-1090 Vienna, Austria rauhut@ma.tum.de
Abstract The concept of semi-bounded generalized hypergroups (SBG hypergroups) is developed which are more special then generalized hypergroups introduced by Obata and Wildberger and which are more general then discrete hypergroups or even discrete signed hypergroups. The convolution of measures and functions is studied. In case of commutativity we deﬁne the dual objects and prove some basic theorems of Fourier analysis. Furthermore, we investigate the relationship between orthogonal polynomials and generalized hypergroups. We discuss the Jacobi polynomials as an example. Mathematics subject classiﬁcation: 43A62, 43A99, 46J10, 05E35, 33C80 Keywords: generalized hypergroup, semi-bounded generalized hypergroup, bounded generalized hypergroups, signed hypergroup, discrete hypergroup, convolution, dual object, Fourier transform, orthogonal polynomials, Jacobi polynomials
Deﬁnition 2.4 A positive discrete measure ω = 0 on K is called (left) Haar measure if for all f with ﬁnite support and all n ∈ K it holds
Institute of Biomathematics and Biometry Ingolst¨adter Landstrasse 1, D–85764 Neuherberg, Germany
lasser@gsf.de, josef.obermaier@gsf.de fax: +49 (0)89 3187 3029
(A3) The structure constants or linearization coeﬃcients g(n, m, k) ∈ C which are deﬁned by
satisfy the condition
cncm =
g(n, m, k)ck

g(n, m, 0)
> 0 if c∗n = cm, = 0 if c∗n = cm.
the associativity of A0 and from the linear independence of the set K follows (6).
We deﬁne translation operators Ln, Ln for complex valued functions f on K by
Later on results of harmonic analysis on hypergroups were transferred to diﬀerent applications. For example a Bochner theorem is used essentially in the context of weakly stationary processes indexed by hypergroups, see [10] and [12]. Hypergroup structure is also heavily used in probability theory, see the monograph [2], and in approximation with respect to orthogonal polynomial sequences, see [5] and [11]. However, not the whole set of axioms (see [2]) is used in these application areas. So concentrating on orthogonal polynomials, Obata and Wildberger
1
2
Lasser, Obermaier and Rauhut
studied in [13] a very general concept and called it “generalized hypergroups”. The purpose of the present paper is to derive results of harmonic analysis for generalized hypergroups in more detail than in [13]. Our main interest is to include all orthogonal polynomial systems with respect to a compactly supported orthogonalization measure in our investigations.
A generalized hypergroup is called hermitian if c∗n = cn, commutative if cncm = cmcn, real if g(n, m, k) ∈ R, positive if g(n, m, k) ≥ 0 and normalized if j g(n, m, j) = 1 for all n, m, k.
m
m,k
k
= f (k)g(n˜, k, m)g(m)h(k) = f (k)(Ln˜g)(k)h(k).
k,m
k
We write ν(k) = ν({k}) for a discrete measure ν on K. Let n denote the Dirac-measure at n ∈ K, i.e., n(k) = 1 if k = n and n(k) = 0 else.