Higher loop renormalization of a supersymmetric field theory

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The Subleading Isgur-Wise Form Factor $chi_3(vcdot v')$ to Order $alpha_s$ in QCD Sum Rules

a rXiv:h ep-ph/9212266v116Dec1992SLAC–PUB–6017WIS–92/99/Dec–PH December 1992T/E The Subleading Isgur-Wise Form Factor χ3(v ·v ′)to Order αs in QCD Sum Rules Matthias Neubert Stanford Linear Accelerator Center Stanford University,Stanford,California 94309Zoltan Ligeti and Yosef Nir Weizmann Institute of Science Physics Department,Rehovot 76100,Israel We calculate the contributions arising at order αs in the QCD sum rule for the spin-symmetry violating universal function χ3(v ·v ′),which appears at order 1/m Q in the heavy quark expansion of meson form factors.In particular,we derive the two-loop perturbative contribution to the sum rule.Over the kinematic range accessible in B →D (∗)ℓνdecays,we ﬁnd that χ3(v ·v ′)does not exceed the level of ∼1%,indicating that power corrections induced by the chromo-magnetic operator in the heavy quark expansion are small.(submitted to Physical Review D)I.INTRODUCTIONIn the heavy quark eﬀective theory(HQET),the hadronic matrix elements describing the semileptonic decays M(v)→M′(v′)ℓν,where M and M′are pseudoscalar or vector mesons containing a heavy quark,can be systematically expanded in inverse powers of the heavy quark masses[1–5].The coeﬃcients in this expansion are m Q-independent,universal functions of the kinematic variable y=v·v′.These so-called Isgur-Wise form factors characterize the properties of the cloud of light quarks and gluons surrounding the heavy quarks,which act as static color sources.At leading order,a single functionξ(y)suﬃces to parameterize all matrix elements[6].This is expressed in the compact trace formula[5,7] M′(v′)|J(0)|M(v) =−ξ(y)tr{(2)m M P+ −γ5;pseudoscalar meson/ǫ;vector mesonis a spin wave function that describes correctly the transformation properties(under boosts and heavy quark spin rotations)of the meson states in the eﬀective theory.P+=1g s2m Q O mag,O mag=M′(v′)ΓP+iσαβM(v) .(4)The mass parameter¯Λsets the canonical scale for power corrections in HQET.In the m Q→∞limit,it measures theﬁnite mass diﬀerence between a heavy meson and the heavy quark that it contains[11].By factoring out this parameter,χαβ(v,v′)becomes dimensionless.The most general decomposition of this form factor involves two real,scalar functionsχ2(y)andχ3(y)deﬁned by[10]χαβ(v,v′)=(v′αγβ−v′βγα)χ2(y)−2iσαβχ3(y).(5)Irrespective of the structure of the current J ,the form factor χ3(y )appears always in the following combination with ξ(y ):ξ(y )+2Z ¯Λ d M m Q ′ χ3(y ),(6)where d P =3for a pseudoscalar and d V =−1for a vector meson.It thus eﬀectively renormalizes the leading Isgur-Wise function,preserving its normalization at y =1since χ3(1)=0according to Luke’s theorem [10].Eq.(6)shows that knowledge of χ3(y )is needed if one wants to relate processes which are connected by the spin symmetry,such as B →D ℓνand B →D ∗ℓν.Being hadronic form factors,the universal functions in HQET can only be investigated using nonperturbative methods.QCD sum rules have become very popular for this purpose.They have been reformulated in the context of the eﬀective theory and have been applied to the study of meson decay constants and the Isgur-Wise functions both in leading and next-to-leading order in the 1/m Q expansion [12–21].In particular,it has been shown that very simple predictions for the spin-symmetry violating form factors are obtained when terms of order αs are neglected,namely [17]χ2(y )=0,χ3(y )∝ ¯q g s σαβG αβq [1−ξ(y )].(7)In this approach χ3(y )is proportional to the mixed quark-gluon condensate,and it was estimated that χ3(y )∼1%for large recoil (y ∼1.5).In a recent work we have reﬁned the prediction for χ2(y )by including contributions of order αs in the sum rule analysis [20].We found that these are as important as the contribution of the mixed condensate in (7).It is,therefore,worthwhile to include such eﬀects also in the analysis of χ3(y ).This is the purpose of this article.II.DERIV ATION OF THE SUM RULEThe QCD sum rule analysis of the functions χ2(y )and χ3(y )is very similar.We shall,therefore,only brieﬂy sketch the general procedure and refer for details to Refs.[17,20].Our starting point is the correlatord x d x ′d ze i (k ′·x ′−k ·x ) 0|T[¯q ΓM ′P ′+ΓP +iσαβP +ΓM+Ξ3(ω,ω′,y )tr 2σαβ2(1+/v ′),and we omit the velocity labels in h and h ′for simplicity.The heavy-light currents interpolate pseudoscalar or vector mesons,depending on the choice ΓM =−γ5or ΓM =γµ−v µ,respectively.The external momenta k and k ′in (8)are the “residual”oﬀ-shell momenta of the heavy quarks.Due to the phase redeﬁnition of the eﬀective heavy quark ﬁelds in HQET,they are related to the total momenta P and P ′by k =P −m Q v and k ′=P ′−m Q ′v ′[3].The coeﬃcient functions Ξi are analytic in ω=2v ·k and ω′=2v ′·k ′,with discontinuities for positive values of these variables.They can be saturated by intermediate states which couple to the heavy-light currents.In particular,there is a double-pole contribution from the ground-state mesons M and M ′.To leading order in the 1/m Q expansion the pole position is at ω=ω′=2¯Λ.In the case of Ξ2,the residue of the pole is proportional to the universal function χ2(y ).For Ξ3the situation is more complicated,however,since insertions of the chromo-magnetic operator not only renormalize the leading Isgur-Wise function,but also the coupling of the heavy mesons to the interpolating heavy-light currents (i.e.,the meson decay constants)and the physical meson masses,which deﬁne the position of the pole.1The correct expression for the pole contribution to Ξ3is [17]Ξpole 3(ω,ω′,y )=F 2(ω−2¯Λ+iǫ) .(9)Here F is the analog of the meson decay constant in the eﬀective theory (F ∼f M√m QδΛ2+... , 0|j (0)|M (v ) =iF2G 2tr 2σαβΓP +σαβM (v ) ,where the ellipses represent spin-symmetry conserving or higher order power corrections,and j =¯q Γh (v ).In terms of the vector–pseudoscalar mass splitting,the parameter δΛ2isgiven by m 2V −m 2P =−8¯ΛδΛ2.For not too small,negative values of ωand ω′,the coeﬃcient function Ξ3can be approx-imated as a perturbative series in αs ,supplemented by the leading power corrections in 1/ωand 1/ω′,which are proportional to vacuum expectation values of local quark-gluon opera-tors,the so-called condensates [22].This is how nonperturbative corrections are incorporated in this approach.The idea of QCD sum rules is to match this theoretical representation of Ξ3to the phenomenological pole contribution given in (9).To this end,one ﬁrst writes the theoretical expression in terms of a double dispersion integral,Ξth 3(ω,ω′,y )= d νd ν′ρth 3(ν,ν′,y )1Thereare no such additional terms for Ξ2because of the peculiar trace structure associated with this coeﬃcient function.possible subtraction terms.Because of theﬂavor symmetry it is natural to set the Borel parameters associated withωandω′equal:τ=τ′=2T.One then introduces new variables ω±=12T ξ(y) F2e−2¯Λ/T=ω0dω+e−ω+/T ρth3(ω+,y)≡K(T,ω0,y).(12)The eﬀective spectral density ρth3arises after integration of the double spectral density over ω−.Note that for each contribution to it the dependence onω+is known on dimensionalgrounds.It thus suﬃces to calculate directly the Borel transform of the individual con-tributions toΞth3,corresponding to the limitω0→∞in(12).Theω0-dependence can be recovered at the end of the calculation.When terms of orderαs are neglected,contributions to the sum rule forΞ3can only be proportional to condensates involving the gluonﬁeld,since there is no way to contract the gluon contained in O mag.The leading power correction of this type is represented by the diagram shown in Fig.1(d).It is proportional to the mixed quark-gluon condensate and,as shown in Ref.[17],leads to(7).Here we are interested in the additional contributions arising at orderαs.They are shown in Fig.1(a)-(c).Besides a two-loop perturbative contribution, one encounters further nonperturbative corrections proportional to the quark and the gluon condensate.Let usﬁrst present the result for the nonperturbative power corrections.WeﬁndK cond(T,ω0,y)=αs ¯q q TT + αs GG y+1− ¯q g sσαβGαβq√y2−1),δn(x)=1(4π)D×1dλλ1−D∞λd u1∞1/λd u2(u1u2−1)D/2−2where C F=(N2c−1)/2N c,and D is the dimension of space-time.For D=4,the integrand diverges asλ→0.To regulate the integral,we assume D<2and use a triple integration by parts inλto obtain an expression which can be analytically continued to the vicinity of D=4.Next we set D=4+2ǫ,expand inǫ,write the result as an integral overω+,and introduce back the continuum threshold.This givesK pert(T,ω0,y)=−αsy+1 2ω0dω+ω3+e−ω+/T(16)× 12−23∂µ+3αs9π¯Λ,(17)which shows that divergences arise at orderαs.At this order,the renormalization of the sum rule is thus accomplished by a renormalization of the“bare”parameter G2in(12).In the9π¯Λ 1µ2 +O(g3s).(18)Hence a counterterm proportional to¯Λξ(y)has to be added to the bracket on the left-hand side of the sum rule(12).To evaluate its eﬀect on the right-hand side,we note that in D dimensions[17]¯Λξ(y)F2e−2¯Λ/T=3y+1 2ω0dω+ω3+e−ω+/T(19)× 1+ǫ γE−ln4π+2lnω+−ln y+12T ξ(y) F2e−2¯Λ/T=αsy+1 2ω0dω+ω3+e−ω+/T 2lnµ6+ y r(y)−1+ln y+1According to Luke’stheorem,theuniversalfunction χ3(y )vanishes at zero recoil [10].Evaluating (20)for y =1,we thus obtain a sum rule for G 2(µ)and δΛ2.It reads G 2(µ)−¯ΛδΛ224π3ω00d ω+ω3+e −ω+/T ln µ12 +K cond (T,ω0,1),(21)where we have used that r (1)=1.Precisely this sum rule has been derived previously,starting from a two-current correlator,in Ref.[16].This provides a nontrivial check of our ing the fact that ξ(y )=[2/(y +1)]2+O (g s )according to (19),we ﬁnd that the µ-dependent terms cancel out when we eliminate G 2(µ)and δΛ2from the sum rule for χ3(y ).Before we present our ﬁnal result,there is one more eﬀect which has to be taken into account,namely a spin-symmetry violating correction to the continuum threshold ω0.Since the chromo-magnetic interaction changes the masses of the ground-state mesons [cf.(10)],it also changes the masses of higher resonance states.Expanding the physical threshold asωphys =ω0 1+d M8π3 22 δ3 ω032π2ω30e −ω0/T 26π2−r (y )−ξ(y ) δ0 ω096π 248T 1−ξ(y ).It explicitly exhibits the fact that χ3(1)=0.III.NUMERICAL ANALYSISLet us now turn to the evaluation of the sum rule (23).For the QCD parameters we take the standard values¯q q =−(0.23GeV)3,αs GG =0.04GeV4,¯q g sσαβGαβq =m20 ¯q q ,m20=0.8GeV2.(24) Furthermore,we useδω2=−0.1GeV from above,andαs/π=0.1corresponding to the scale µ=2¯Λ≃1GeV,which is appropriate for evaluating radiative corrections in the eﬀective theory[15].The sensitivity of our results to changes in these parameters will be discussed below.The dependence of the left-hand side of(23)on¯Λand F can be eliminated by using a QCD sum rule for these parameters,too.It reads[16]¯ΛF2e−2¯Λ/T=9T4T − ¯q g sσαβGαβq4π2 2T − ¯q q +(2y+1)4T2.(26) Combining(23),(25)and(26),we obtainχ3(y)as a function ofω0and T.These parameters can be determined from the analysis of a QCD sum rule for the correlator of two heavy-light currents in the eﬀective theory[16,18].Oneﬁnds good stability forω0=2.0±0.3GeV,and the consistency of the theoretical calculation requires that the Borel parameter be in the range0.6<T<1.0GeV.It supports the self-consistency of the approach that,as shown in Fig.2,weﬁnd stability of the sum rule(23)in the same region of parameter space.Note that it is in fact theδω2-term that stabilizes the sum rule.Without it there were no plateau.Over the kinematic range accessible in semileptonic B→D(∗)ℓνdecays,we show in Fig.3(a)the range of predictions forχ3(y)obtained for1.7<ω0<2.3GeV and0.7<T< 1.2GeV.From this we estimate a relative uncertainty of∼±25%,which is mainly due to the uncertainty in the continuum threshold.It is apparent that the form factor is small,not exceeding the level of1%.2Finally,we show in Fig.3(b)the contributions of the individual terms in the sum rule (23).Due to the large negative contribution proportional to the quark condensate,the terms of orderαs,which we have calculated in this paper,cancel each other to a large extent.As a consequence,ourﬁnal result forχ3(y)is not very diﬀerent from that obtained neglecting these terms[17].This is,however,an accident.For instance,the order-αs corrections would enhance the sum rule prediction by a factor of two if the ¯q q -term had the opposite sign. From thisﬁgure one can also deduce how changes in the values of the vacuum condensates would aﬀect the numerical results.As long as one stays within the standard limits,the sensitivity to such changes is in fact rather small.For instance,working with the larger value ¯q q =−(0.26GeV)3,or varying m20between0.6and1.0GeV2,changesχ3(y)by no more than±0.15%.In conclusion,we have presented the complete order-αs QCD sum rule analysis of the subleading Isgur-Wise functionχ3(y),including in particular the two-loop perturbative con-tribution.Weﬁnd that over the kinematic region accessible in semileptonic B decays this form factor is small,typically of the order of1%.When combined with our previous analysis [20],which predicted similarly small values for the universal functionχ2(y),these results strongly indicate that power corrections in the heavy quark expansion which are induced by the chromo-magnetic interaction between the gluonﬁeld and the heavy quark spin are small.ACKNOWLEDGMENTSIt is a pleasure to thank Michael Peskin for helpful discussions.M.N.gratefully acknowl-edgesﬁnancial support from the BASF Aktiengesellschaft and from the German National Scholarship Foundation.Y.N.is an incumbent of the Ruth E.Recu Career Development chair,and is supported in part by the Israel Commission for Basic Research and by the Minerva Foundation.This work was also supported by the Department of Energy,contract DE-AC03-76SF00515.REFERENCES[1]E.Eichten and B.Hill,Phys.Lett.B234,511(1990);243,427(1990).[2]B.Grinstein,Nucl.Phys.B339,253(1990).[3]H.Georgi,Phys.Lett.B240,447(1990).[4]T.Mannel,W.Roberts and Z.Ryzak,Nucl.Phys.B368,204(1992).[5]A.F.Falk,H.Georgi,B.Grinstein,and M.B.Wise,Nucl.Phys.B343,1(1990).[6]N.Isgur and M.B.Wise,Phys.Lett.B232,113(1989);237,527(1990).[7]J.D.Bjorken,Proceedings of the18th SLAC Summer Institute on Particle Physics,pp.167,Stanford,California,July1990,edited by J.F.Hawthorne(SLAC,Stanford,1991).[8]M.B.Voloshin and M.A.Shifman,Yad.Fiz.45,463(1987)[Sov.J.Nucl.Phys.45,292(1987)];47,801(1988)[47,511(1988)].[9]A.F.Falk,B.Grinstein,and M.E.Luke,Nucl.Phys.B357,185(1991).[10]M.E.Luke,Phys.Lett.B252,447(1990).[11]A.F.Falk,M.Neubert,and M.E.Luke,SLAC preprint SLAC–PUB–5771(1992),toappear in Nucl.Phys.B.[12]M.Neubert,V.Rieckert,B.Stech,and Q.P.Xu,in Heavy Flavours,edited by A.J.Buras and M.Lindner,Advanced Series on Directions in High Energy Physics(World Scientiﬁc,Singapore,1992).[13]A.V.Radyushkin,Phys.Lett.B271,218(1991).[14]D.J.Broadhurst and A.G.Grozin,Phys.Lett.B274,421(1992).[15]M.Neubert,Phys.Rev.D45,2451(1992).[16]M.Neubert,Phys.Rev.D46,1076(1992).[17]M.Neubert,Phys.Rev.D46,3914(1992).[18]E.Bagan,P.Ball,V.M.Braun,and H.G.Dosch,Phys.Lett.B278,457(1992);E.Bagan,P.Ball,and P.Gosdzinsky,Heidelberg preprint HD–THEP–92–40(1992).[19]B.Blok and M.Shifman,Santa Barbara preprint NSF–ITP–92–100(1992).[20]M.Neubert,Z.Ligeti,and Y.Nir,SLAC preprint SLAC–PUB–5915(1992).[21]M.Neubert,SLAC preprint SLAC–PUB–5992(1992).[22]M.A.Shifman,A.I.Vainshtein,and V.I.Zakharov,Nucl.Phys.B147,385(1979);B147,448(1979).FIGURESFIG.1.Diagrams contributing to the sum rule for the universal form factorχ3(v·v′):two-loop perturbative contribution(a),and nonperturbative contributions proportional to the quark con-densate(b),the gluon condensate(c),and the mixed condensate(d).Heavy quark propagators are drawn as double lines.The square represents the chromo-magnetic operator.FIG.2.Analysis of the stability region for the sum rule(23):The form factorχ3(y)is shown for y=1.5as a function of the Borel parameter.From top to bottom,the solid curves refer toω0=1.7,2.0,and2.3GeV.The dashes lines are obtained by neglecting the contribution proportional toδω2.FIG.3.(a)Prediction for the form factorχ3(v·v′)in the stability region1.7<ω0<2.3 GeV and0.7<T<1.2GeV.(b)Individual contributions toχ3(v·v′)for T=0.8GeV and ω0=2.0GeV:total(solid),mixed condensate(dashed-dotted),gluon condensate(wide dots), quark condensate(dashes).The perturbative contribution and theδω2-term are indistinguishable in thisﬁgure and are both represented by the narrow dots.11。

二叠纪-三叠纪灭绝事件

二叠纪-三叠纪灭绝事件二叠纪-三叠纪灭绝事件（Permian–Triassic extinction event）是一个大规模物种灭绝事件，发生于古生代二叠纪与中生代三叠纪之间，距今大约2亿5140万年[1][2]。

若以消失的物种来计算，当时地球上70%的陆生脊椎动物，以及高达96%的海中生物消失[3]；这次灭绝事件也造成昆虫的唯一一次大量灭绝。

计有57%的科与83%的属消失[4][5]。

在灭绝事件之后，陆地与海洋的生态圈花了数百万年才完全恢复，比其他大型灭绝事件的恢复时间更长久[3]。

此次灭绝事件是地质年代的五次大型灭绝事件中，规模最庞大的一次，因此又非正式称为大灭绝（Great Dying）[6]，或是大规模灭绝之母（Mother of all mass extinctions）[7]。

二叠纪-三叠纪灭绝事件的过程与成因仍在争议中[8]。

根据不同的研究，这次灭绝事件可分为一[1]到三[9]个阶段。

第一个小型高峰可能因为环境的逐渐改变，原因可能是海平面改变、海洋缺氧、盘古大陆形成引起的干旱气候；而后来的高峰则是迅速、剧烈的，原因可能是撞击事件、火山爆发[10]、或是海平面骤变，引起甲烷水合物的大量释放[11]。

目录? 1 年代测定? 2 灭绝模式o 2.1 海中生物o 2.2 陆地无脊椎动物o 2.3 陆地植物? 2.3.1 植物生态系统? 2.3.2 煤层缺口o 2.4 陆地脊椎动物o 2.5 灭绝模式的可能解释? 3 生态系统的复原o 3.1 海洋生态系统的改变o 3.2 陆地脊椎动物? 4 灭绝原因o 4.1 撞击事件o 4.2 火山爆发o 4.3 甲烷水合物的气化o 4.4 海平面改变o 4.5 海洋缺氧o 4.6 硫化氢o 4.7 盘古大陆的形成o 4.8 多重原因? 5 注释? 6 延伸阅读? 7 外部链接年代测定在西元二十世纪之前，二叠纪与三叠纪交界的地层很少被发现，因此科学家们很难准确地估算灭绝事件的年代与经历时间，以及影响的地理范围[12]。

应用地球化学元素丰度数据手册-原版

应用地球化学元素丰度数据手册迟清华鄢明才编著地质出版社·北京·1内容提要本书汇编了国内外不同研究者提出的火成岩、沉积岩、变质岩、土壤、水系沉积物、泛滥平原沉积物、浅海沉积物和大陆地壳的化学组成与元素丰度，同时列出了勘查地球化学和环境地球化学研究中常用的中国主要地球化学标准物质的标准值，所提供内容均为地球化学工作者所必须了解的各种重要地质介质的地球化学基础数据。

本书供从事地球化学、岩石学、勘查地球化学、生态环境与农业地球化学、地质样品分析测试、矿产勘查、基础地质等领域的研究者阅读，也可供地球科学其它领域的研究者使用。

图书在版编目（CIP）数据应用地球化学元素丰度数据手册/迟清华，鄢明才编著. －北京：地质出版社，2007.12ISBN 978－7－116－05536－0Ⅰ. 应… Ⅱ. ①迟…②鄢…Ⅲ. 地球化学丰度－化学元素－数据－手册Ⅳ. P595－62中国版本图书馆CIP数据核字（2007）第185917号责任编辑：王永奉陈军中责任校对：李玫出版发行：地质出版社社址邮编：北京市海淀区学院路31号，100083电话：（010）82324508（邮购部）网址：电子邮箱：zbs@传真：（010）82310759印刷：北京地大彩印厂开本：889mm×1194mm 1/16印张：10.25字数：260千字印数：1－3000册版次：2007年12月北京第1版•第1次印刷定价：28.00元书号：ISBN 978－7－116－05536－0（如对本书有建议或意见，敬请致电本社；如本社有印装问题，本社负责调换）2关于应用地球化学元素丰度数据手册（代序）地球化学元素丰度数据，即地壳五个圈内多种元素在各种介质、各种尺度内含量的统计数据。

它是应用地球化学研究解决资源与环境问题上重要的资料。

将这些数据资料汇编在一起将使研究人员节省不少查找文献的劳动与时间。

这本小册子就是按照这样的想法编汇的。

sigmaaldrich引用英文全名

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It's like a magical laboratory where you can find all sorts of chemicals, reagents, and tools to help you do your science projects.Sigma-Aldrich is super popular because it has tons ofhigh-quality products that scientists all around the world trust and use. From fancy chemicals to fancy equipment,Sigma-Aldrich has everything a scientist could ever need. And not just that, they also have all these super helpful resources liketechnical documents, safety data sheets, and even scientific articles for you to read and learn from.One of the best things about Sigma-Aldrich is that they don't just sell stuff, they also help you figure out what you need for your experiments. Their awesome customer service team is always ready to answer your questions and give you expert advice. So if you're ever stuck on a science project, just give Sigma-Aldrich a call and they'll help you out!So if you're a young scientist looking to do some cool experiments or if you're a curious kid who loves learning about science, make sure to check out Sigma-Aldrich. It's like a magical world full of wonders waiting for you to explore. And who knows, maybe one day you'll make a groundbreaking discovery that will change the world, all thanks to Sigma-Aldrich!篇3Title: Sigma Aldrich - The Coolest Science Stuff Ever!Hey guys, have you ever heard of Sigma Aldrich? It's like the ultimate science store where you can find all the coolest stuff for your experiments and projects. They have everything from chemicals to lab equipment to amazing science tools. Let me tell you all about it!First of all, Sigma Aldrich is a super famous company that makes all kinds of high-quality chemicals and materials for scientists and researchers around the world. They have been around for a long time and are known for their top-notch products and excellent customer service.One of the best things about Sigma Aldrich is that they have a huge selection of chemicals for all your science experiments. Whether you need acids, bases, solvents, or specialty chemicals, they have got you covered. And the best part is that everything is super high quality and safe to use, so you don't have to worry about anything going wrong in the lab.But that's not all - Sigma Aldrich also has a ton of awesome lab equipment for all your scientific needs. From glassware to heating equipment to microscopes, they have everything you could ever need to conduct your experiments like a real pro. And the best part is that everything is super affordable, so you won't break the bank stocking up on all your supplies.And let's not forget about all the amazing science tools that Sigma Aldrich has to offer. They have all kinds of cool gadgets and instruments that will help you take your experiments to the next level. Whether you need a pH meter, a spectrophotometer, or a centrifuge, they have it all.So if you're a science lover like me, you definitely need to check out Sigma Aldrich. They have everything you could ever need to conduct your experiments and projects with success. Trust me, you won't be disappointed!篇4Sigma-Aldrich is a super cool company that sells all kinds of science stuff! They have a big name - Sigma-Aldrich Corporation.I know it's a mouthful to say, but they're really famous in the science world. They do all sorts of things like making chemicals, testing materials, and even working with big companies to help them with their science projects.One of the things I like about Sigma-Aldrich is that they have a lot of different products. It's like going to a candy store, but instead of candy, it's all science stuff! They have all sorts of chemicals, lab equipment, and even things like test tubes and beakers. It's like a science lover's dream come true!Not only do they have a ton of awesome products, but Sigma-Aldrich is also really good at helping scientists with their research. They have a team of experts who can answer questions, give advice, and even help you find the right products for your experiments. It's like having your own personal science mentor!One of the things I find the most amazing aboutSigma-Aldrich is that they're always coming up with new and innovative products. They're like the trendsetters of the science world! Whether it's a new chemical compound, a better way to test materials, or a more efficient lab equipment, Sigma-Aldrich is always at the forefront of innovation.I think Sigma-Aldrich is a really awesome company. They're super helpful, have a ton of cool products, and are always pushing the boundaries of science. If you're a science lover like me, you should definitely check them out! Sigma-Aldrich Corporation - it's a name you won't forget!篇5Hey guys! Today I wanna talk to you about something super cool and important for science - Sigma-Aldrich references! Sigma-Aldrich is a big company that makes all kinds of chemicals and materials for scientists to use in their experiments. When we do research or science projects, it's really important to usehigh-quality materials and chemicals, and that's whereSigma-Aldrich comes in.So, what exactly is a Sigma-Aldrich reference? Basically, it's a way for scientists to cite where they got the materials they usedin their research. Just like when we write essays and have to list all the books and articles we used, scientists have to do the same thing when they publish their research. This helps other scientists know where to get the same materials if they want to do similar experiments.When we use Sigma-Aldrich materials in our experiments, we can trust that they are top-notch quality. Sigma-Aldrich is known for making high-purity chemicals and materials that are perfect for scientific research. Plus, they have a huge selection of products to choose from, so we can always find exactly what we need for our experiments.Using Sigma-Aldrich references in our research papers is not only important for giving credit where credit is due, but it also shows that we are using reliable and trustworthy materials in our experiments. It helps to build credibility and trust in the scientific community, which is super important when we are sharing our findings with the world.So next time you're doing a science project or research experiment, remember to check out Sigma-Aldrich for all your chemical and material needs. And don't forget to include Sigma-Aldrich references in your paper to show that you're using the best of the best! Sigma-Aldrich rocks!Sigma-Aldrich is a super cool company that sells lots of fancy science stuff. They have a really long name, it's called Sigma-Aldrich Corporation. Yeah, I know, it's a mouthful!So, what does Sigma-Aldrich do? Well, they sell all kinds of chemicals and materials that scientists use for their experiments. Like, they have stuff for biology, chemistry, and even stuff for making cool things like new medicines or fancy plastics.But Sigma-Aldrich isn't just about selling stuff, they also do research to discover new things and improve the stuff they sell. They have smart scientists who work in labs and come up with new ideas to help other scientists do their experiments better.Oh, and did you know that Sigma-Aldrich is part of a bigger company called Merck Group? Yeah, they're like a big science family working together to make the world a better place with their cool science stuff.I think Sigma-Aldrich is really awesome because they help scientists make new discoveries and inventions that can make our world a better place. So next time you see their name on a bottle in your science class, remember how cool they are and all the amazing things they help scientists do!Sigma-Aldrich is a super cool company that sells all kinds of chemicals and stuff for science experiments. Their full name is Sigma-Aldrich Corporation, and they have lots of labs where they make all the cool chemicals.One time, my science teacher told us about Sigma-Aldrich and how they have this thing called the Sigma-Aldrich Quote. It's like a special way to make sure you're using the right chemicals for your experiments. The Sigma-Aldrich Quote helps scientists know that they're getting good quality chemicals that will work the way they're supposed to.I think it's really cool that Sigma-Aldrich cares so much about making sure scientists have the best stuff to do their experiments. They even have a website where you can go and look up all the chemicals they sell and learn about how to use them safely. It's like a super cool online library for scientists!I heard that Sigma-Aldrich has been around for a really long time, like since 1951. That's older than my grandma! They must be really good at what they do if they've been around for that long. My science teacher said that Sigma-Aldrich is like thesuperhero of the chemical world, always there to save the day with their awesome products.I can't wait to grow up and be a scientist so I can use all the cool chemicals and equipment from Sigma-Aldrich. I bet I'll do some amazing experiments with their stuff and maybe even win a Nobel Prize someday! Sigma-Aldrich is the best!篇8Sigma-Aldrich is a company that sells all kinds of cool science stuff! They have chemicals, lab equipment, and even different types of products for research and development. It's like a science wonderland where scientists can find everything they need to conduct their experiments and studies.One of the coolest things about Sigma-Aldrich is that they have a really big collection of chemicals. They have stuff like acids, bases, solvents, and other chemicals that scientists need for their experiments. The best part is that all of their chemicals are really high quality, so scientists can trust that they are using the best materials for their work.Sigma-Aldrich also sells lab equipment like beakers, test tubes, and microscopes. This equipment is essential for scientists to conduct their experiments and observe their results. WithSigma-Aldrich's high-quality lab equipment, scientists can be confident that they are getting accurate and reliable data.In addition to chemicals and lab equipment, Sigma-Aldrich also offers products for research and development. They have things like antibodies, enzymes, and reagents that scientists can use to further their research projects. These products are essential for scientific advancement and Sigma-Aldrich plays a key role in providing them to the scientific community.Overall, Sigma-Aldrich is a really important company in the world of science. They provide scientists with the tools they need to conduct their research and make important discoveries. Without companies like Sigma-Aldrich, scientific progress would be much slower. So next time you're in the lab conducting experiments, remember to thank Sigma-Aldrich for all the awesome stuff they provide!篇9Once upon a time, there was a super cool company called Sigma-Aldrich. They were like the superheroes of the science world, providing all kinds of fancy chemicals and materials for scientists to use in their experiments.Sigma-Aldrich had a really long name - it was actually called "Sigma-Aldrich Corporation." But nobody really called them that because it was too much of a mouthful. Everyone just called them Sigma-Aldrich for short.Sigma-Aldrich was like a magical store filled with all kinds of potions and powders that scientists could use to make amazing discoveries. They had everything from acids to zwitterions - which is a fancy word for molecules that can be positively or negatively charged.Scientists from all over the world would visit Sigma-Aldrich to buy the special ingredients they needed for their experiments. The scientists would look through the huge catalog that Sigma-Aldrich had and order exactly what they needed. It was like shopping for ingredients to bake a cake, but way more scientific.Sigma-Aldrich also had a website where scientists could order their chemicals online. It was like a magical online store where you could buy all the cool stuff you needed to do your science experiments.One day, a little scientist named Sally went to Sigma-Aldrich to buy some chemicals for her experiment. She needed somespecial enzymes to help her study how plants grow. She looked through the catalog and found exactly what she needed.Sally placed her order online and waited eagerly for her chemicals to arrive. When they did, she couldn't wait to start her experiment. Thanks to Sigma-Aldrich, Sally was able to make a big discovery that helped her win a science fair!From that day on, Sally would always rememberSigma-Aldrich as the place where she got the special ingredients that helped her become a super scientist. Sigma-Aldrich may have a long name, but to Sally, it was like a magical store filled with all the wonders of science.篇10Sigma-Aldrich is like a super cool and helpful store for scientists and researchers. They have all sorts of chemicals and lab supplies that you might need for your experiments and projects. Their official full name is actually Sigma-Aldrich Corporation, but we usually just call them Sigma-Aldrich for short.One of the best things about Sigma-Aldrich is that they have a huge variety of products. They have chemicals for pretty much any experiment you can think of, from basic stuff like acids andbases to more fancy things like reagents and catalysts. They also have lab equipment like beakers, test tubes, and even fancy machines like spectrometers and chromatography systems.But Sigma-Aldrich isn't just about selling stuff – they also do a lot of research and development themselves. They have a team of scientists who work hard to create new and improved products for their customers. They're always coming up with innovative solutions to help make scientific research easier and more efficient.Another cool thing about Sigma-Aldrich is that they have a website where you can easily browse and order products online. It's super convenient – you can just search for what you need, add it to your cart, and check out in a few clicks. And they have really fast shipping, so you can get your stuff delivered right to your lab door in no time.Sigma-Aldrich is like a one-stop shop for all your scientific needs. Whether you're a beginner just starting out in the lab or a seasoned researcher working on cutting-edge projects,Sigma-Aldrich has got you covered. So next time you need supplies for your experiments, remember to check outSigma-Aldrich – they're the best in the biz!。

science公布的全球最前沿的125个科学问题

science公布的全球最前沿的125个科学问题Science公布的全球最前沿的125个科学问题一、数学1. What makes prime numbers so special?什么使素数如此特别？2. Will the Navier–Stokes problem ever be solved?纳维尔-斯托克斯问题会得到解决吗？3. Is the Riemann hypothesis true?黎曼猜想是真的吗？二、化学1. Are there more color pigments to discover?还有更多色彩元素可发现吗？2. Will the periodic table ever be complete?元素周期表会完整吗？3. How can we measure interface phenomena on the microscopic level? 如何在微观层面测量界面现象？4. What is the future for energy storage？能量存储的未来是怎样的？5. Why does life require chirality?为什么生命需要手性？6. How can we better manage the world's plastic waste?我们如何更好地管理世界上的塑料废物？7. Will AI redefine the future of chemistry?AI会重新定义化学的未来吗？8. How can matter be programmed into living materials?物质如何被编码而成为生命材料？9. What drives reproduction in living systems?是什么驱动生命系统的复制？三、医学与健康1. Can we predict the next pandemic?我们可以预测下一次流行病吗？2. Will we ever find a cure for the common cold?我们会找到治疗感冒的方法吗？3. Can we design and manufacture medicines customized for individual people? 我们可以设计和制造出为个人定制的药物吗？4. Can a human tissue or organ be fully regenerated?人体组织或器官可以完全再生吗？5. How is immune homeostasis maintained and regulated?如何维持和调节免疫稳态？6.Is there a scientific basis to the Meridian System in traditional Chinese medicine?中医的经络系统有科学依据吗？7. How will the next generation of vaccines be made?下一代疫苗将如何生产？8. Can we ever overcome antibiotic resistance?我们能否克服抗生素耐药性？9. What is the etiology of autism?自闭症的病因是什么？10. What role does our microbiome play in health and disease?我们的微生物组在健康和疾病中扮演什么角色？11. Can xenotransplantation solve the shortage of donor organs?异种移植能否解决供体器官的短缺问题？四、生命科学1. What could help conservation of the oceans?什么可以帮助保护海洋？2. Can we stop ourselves from aging?我们可以阻止自己衰老吗？3. Why can only some cells become other cells?为什么只有一些细胞会变成其他细胞？4. Why are some genomes so big and others very small?为什么有些基因组非常大而另一些却很小？5. Will it be possible to cure all cancers?有可能治愈所有癌症吗？6. What genes make us uniquely human?哪些基因使我们人类与众不同？7. How do migratory animals know where they're going?迁徙动物如何知道它们要去哪里？8. How many species are there on Earth?地球上有多少物种？9. How do organisms evolve?有机体是如何进化的？10. Why did dinosaurs grow to be so big?为什么恐龙长得如此之大？11. Did ancient humans interbreed with other human-like ancestors? 远古人类是否曾与其他类人祖先杂交？12. Why do humans get so attached to dogs and cats?人类为什么会对猫狗如此着迷？13. Will the world's population keep growing indefinitely?世界人口会无限增长吗？14. Why do we stop growing?我们为什么会停止生长？15. Is de-extinction possible?能否复活灭绝生物？16. Can humans hibernate?人类可以冬眠吗？17. Where do human emotions originate?人类的情感源于何处？18. Will humans look physically different in the future?未来人类的外貌会有所不同吗？19. Why were there species explosions and mass extinction?为什么会发生物种大爆发和大灭绝？20. How might genome editing be used to cure disease?基因组编辑将如何用于治疗疾病？21. Can a cell be artificially synthesized?可以人工合成细胞吗？22. How are biomolecules organized in cells to function orderly and effectively? 细胞内的生物分子是如何组织从而有序有效发挥作用的？五、天文学1. How many dimensions are there in space?空间中有多少个维度？2. What is the shape of the universe?宇宙的形状是怎样的？3. Where did the big bang start?大爆炸从何处开始？4. Why don't the orbits of planets decay and cause them to crash into each other? 为什么行星的轨道不衰减并导致它们相互碰撞？5. When will the universe die? Will it continue to expand?宇宙何时消亡？它会继续膨胀吗？6. Is it possible to live permanently on another planet?我们有可能在另一个星球上长期居住吗？7. Why do black holes exist?为什么存在黑洞？8. What is the universe made of?宇宙是由什么构成的？9. Are we alone in the universe?我们是宇宙中唯一的生命体吗？10. What is the origin of cosmic rays?宇宙射线的起源是什么？11.What is the origin of mass?物质的起源是什么？12. What is the smallest scale of space-time?时空的最小尺度是是多少？13. Is water necessary for all life in the universe, or just on Earth?水是宇宙中所有生命所必需的么，还是仅对地球生命？14. What is preventing humans from carrying out deep-space exploration? 是什么阻止了人类进行深空探测？15. Is Einstein's general theory of relativity correct?爱因斯坦的广义相对论是正确的吗？16. How are pulsars formed?脉冲星是如何形成的？17. Is our Milky Way Galaxy special?我们的银河系特别吗？18. What is the volume, composition, and significance of the deep biosphere? 深层生物圈的规模、组成和意义是什么？19. Will humans one day have to leave the planet (or die trying)?人类有一天会不得不离开地球吗（还是会在尝试中死去）？20. Where do the heavy elements in the universe come from?宇宙中的重元素来自何处？21. Is it possible to understand the structure of compact stars and matter? 有可能了解致密恒星和物质的结构吗？22. What is the origin of the high-energy cosmic neutrinos?高能宇宙中微子的起源是什么？23. What is gravity?什么是重力？六、物理学1. Is there a diffraction limit?有衍射极限吗？2. What is the microscopic mechanism for high-temperature superconductivity?高温超导的微观机理是什么？3. What are the limits of heat transfer in matter?物质传热的极限是什么？4. What are the fundamental principles of collective motion?集体运动的基本原理是什么？5. What are the smallest building blocks of matter?什么是物质的最小组成部分？6. Will we ever travel at the speed of light?我们会以光速行驶吗？7. What is quantum uncertainty and why is it important?什么是量子不确定性，为什么它很重要？8. Will there ever be a "theory of everything"?会有“万有理论”吗？9. Why does time seem to flow in only one direction?为什么时间似乎只朝一个方向流动？10. What is dark matter?什么是暗物质？11. Can we make a real, human-size invisibility cloak?我们可以制作出真人大小的隐形斗篷吗？12.Are there any particles that behave oppositely to the properties or states of photons?是否存在与光子性质或状态相反的粒子？13. Will the Bose-Einstein condensate be widely used in the future?玻色-爱因斯坦冷凝体未来会被广泛使用吗？14. Can humans make intense lasers with incoherence comparable to sunlight? 人类能制造出与太阳光相似的非相干强激光吗？15. What is the maximum speed to which we can accelerate a particle?我们最多可以将粒子加速到多快？16.Is quantum many-body entanglement more fundamental than quantum fields?量子多体纠缠比量子场更基本吗？17. What is the optimum hardware for quantum computers?量子计算机的最佳硬件是什么？18. Can we accurately simulate the macro- and microworld?我们可以精确模拟宏观和微观世界吗？七、信息科学1. Is there an upper limit to computer processing speed?计算机处理速度是否有上限？2. Can AI replace a doctor?AI可以代替医生吗？3. Can topological quantum computing be realized?拓扑量子计算可以实现吗？4. Can DNA act as an information storage medium?DNA可以用作信息存储介质吗？八、工程与材料科学1. What is the ultimate statistical invariances of turbulence?湍流的最终统计不变性是什么？2. How can we break the current limit of energy conversion efficiencies?我们如何突破当前的能量转换效率极限？3. How can we develop manufacturing systems on Mars?我们如何在火星上开发制造系统？4. Is a future of only self-driving cars realistic?纯无人驾驶汽车的未来是否现实？九、神经科学1. What are the coding principles embedded in neuronal spike trains?神经元放电序列的编码准则是什么？2. Where does consciousness lie?意识存在于何处？3.Can human memory be stored, manipulated, and transplanted digitally?能否数字化地存储、操控和移植人类记忆？4. Why do we need sleep?为什么我们需要睡眠？5. What is addiction and how does it work?什么是成瘾？6. Why do we fall in love?为什么我们会坠入爱河？7. How did speech evolve and what parts of the brain control it?言语如何演变形成，大脑的哪些部分对其进行控制？8. How smart are nonhuman animals?除人类以外的其他动物有多聪明？9. Why are most people right-handed?为什么大多数人都是右撇子？10. Can we cure neurodegenerative diseases?我们可以治愈神经退行性疾病吗？11. Is it possible to predict the future?有可能预知未来吗？12. Can we more effectively diagnose and treat complex mental disorders?精神障碍能否有效诊断和治疗？十、生态学1. Can we stop global climate change?我们可以阻止全球气候变化吗？2. Where do we put all the excess carbon dioxide?我们能把过量的二氧化碳存到何处？3. What creates the Earth's magnetic field (and why does it move)?是什么创造了地球的磁场（为什么它会移动）？4.Will we be able to predict catastrophic weather events (tsunami, hurricanes, earthquakes) more accurately?我们是否能够更准确地预测灾害性事件（海啸、飓风、地震）？5. What happens if all the ice on the planet melts?如果地球上所有的冰融化会怎样？6. Can we create an environmentally friendly replacement for plastics?我们可以创造一种环保的塑料替代品吗？7. Can we achieve a situation where essentially every material can be recycled and reused?几乎所有材料都可以回收再利用是否可以实现？8. Will we soon see the end of monocultures like wheat, maize, rice, and soy?我们会很快看到小麦、玉米、大米和大豆等单一作物的终结吗？十一、能源科学1. Could we live in a fossil-fuel-free world?我们可以生活在一个去化石燃料的世界中吗？2. What is the future of hydrogen energy?氢能的未来是怎样的？3. Will cold fusion ever be possible?冷聚变有可能实现吗？十二、人工智能1. Will injectable, disease-fighting nanobots ever be a reality?可注射的抗病纳米机器人会成为现实吗？2. Will it be possible to create sentient robots?是否有可能创建有感知力的机器人？3. Is there a limit to human intelligence?人类智力是否有极限？4. Will artificial intelligence replace humans?人工智能会取代人类吗？5. How does group intelligence emerge?群体智能是如何出现的？6. Can robots or AIs have human creativity?机器人或AI 可以具有人类创造力吗？7.Can quantum artificial intelligence imitate the human brain?量子人工智能可以模仿人脑吗？8. Could we integrate with computers to form a human-machine hybrid species? 我们可以和计算机结合以形成人机混合物种吗？。

低能跑动耦合常数形式对低能常数的影响

低能跑动耦合常数形式对低能常数的影响陈清森;蒋绍周【摘要】[目的]探寻一种理论值与实验值接近的低能跑动耦合常数的形式,比较几种低能跑动耦合常数形式对低能常数的影响.[方法]选取3种低能跑动耦合常数的形式及其变形,利用已有的耦合常数和低能常数的关系,数值计算出低能常数并与实验值作比较.[结果]发现1种与实验符合的低能跑动耦合常数的可能形式,并给出低能常数新的理论预言值.[结论]对于跑动耦合常数低能部分是一个平台的情况,无论其二阶导数是否连续,数值结果对低能常数的影响均较小,并且绝对值都系统地偏大;对于给出的低能耦合常数不是平台的形式,可以通过对参数的调节使得计算的低能常数与实验结果相符.【期刊名称】《广西科学》【年(卷),期】2015(022)001【总页数】4页(P109-112)【关键词】跑动耦合常数;低能常数;夸克自能【作者】陈清森;蒋绍周【作者单位】广西大学物理学院,广西大学-国家天文台天体物理和空间科学研究中心,广西南宁530004;广西大学物理学院,广西大学-国家天文台天体物理和空间科学研究中心,广西南宁530004【正文语种】中文【中图分类】O412.3【研究意义】自然界存在四种相互作用，作用的强弱用耦合常数来描述。

耦合常数会随着动量标度的改变而改变，又称为跑动耦合常数。

对于强相互作用，跑动耦合常数随着动量标度的增加而减小，称为强相互作用的渐进自由效应[1,2]。

对于高能端，理论上已经给出跑动耦合常数到四圈图的结果[3,4]。

然而由于强相互作用在低能端耦合常数比较大，不能使用传统的微扰理论计算，需要采用其他方法近似计算。

赝标介子的手征微扰理论就是其中的一种[5～7]，用于描述低能赝标介子的强相互作用。

但是理论本身并不能给出赝标介子手征有效拉氏量的系数(称为低能常数)。

从量子色动力学的第一原理出发，可以得到夸克自能和低能常数的关系,而夸克自能可以由耦合常数通过Schwinger-Dyson方程给出[8,9]。

super string

THE CONFORMAL BOOTSTRAP AND SUPER W -ALGEBRAS
´ M. Figueroa-O’Farrill Jose
and
Stany Schrans
Instituut voor Theoretische Fysica, Universiteit Leuven Celestijnenlaan 200 D, B–3001 Heverlee, BELGIUM
e-mail: fgbda11@blekul11.BITNET Onderzoeker I.I.K.W., Belgium; e-mail: fgbda31@blekul11.BITNET
§1
Introduction Extended conformal and superconformal algebras have received a great deal
which exist only for speciﬁc values of the central charge, we ﬁnd a new non-linear algebra (super W2 ) generated by a spin 2 superprimary which is associative for all values of the central charge. Furthermore, the spin 3 extension is argued to be the symmetry algebra of the m = 6 super Virasoro unitary minimal model, by exhibiting the (A7 , D4 )-type modular invariant as diagonal in terms of extended characters.

N=4 Super-Yang-Mills Theory, QCD and Collider Physics

a rXiv:h ep-th/04121v12O ct24SLAC–PUB–10739,IPPP/04/59,DCPT/04/118,UCLA/04/TEP/40Saclay/SPhT–T04/116,hep-th/0410021October,2004N =4Super-Yang-Mills Theory,QCD and Collider Physics Z.Bern a L.J.Dixon b 1 D.A.Kosower c a Department of Physics &Astronomy,UCLA,Los Angeles,CA 90095-1547,USA b SLAC,Stanford University,Stanford,CA 94309,USA,and IPPP,University of Durham,Durham DH13LE,England c Service de Physique Th´e orique,CEA–Saclay,F-91191Gif-sur-Yvette cedex,France1Introduction and Collider Physics MotivationMaximally supersymmetric (N =4)Yang-Mills theory (MSYM)is unique in many ways.Its properties are uniquely speciﬁed by the gauge group,say SU(N c ),and the value of the gauge coupling g .It is conformally invariant for any value of g .Although gravity is not present in its usual formulation,MSYMis connected to gravity and string theory through the AdS/CFT correspon-dence[1].Because this correspondence is a weak-strong coupling duality,it is diﬃcult to verify quantitatively for general observables.On the other hand, such checks are possible and have been remarkably successful for quantities protected by supersymmetry such as BPS operators[2],or when an additional expansion parameter is available,such as the number ofﬁelds in sequences of composite,large R-charge operators[3,4,5,6,7,8].It is interesting to study even more observables in perturbative MSYM,in order to see how the simplicity of the strong coupling limit is reﬂected in the structure of the weak coupling expansion.The strong coupling limit should be even simpler when the large-N c limit is taken simultaneously,as it corresponds to a weakly-coupled supergravity theory in a background with a large radius of curvature.There are diﬀerent ways to study perturbative MSYM.One approach is via computation of the anomalous dimensions of composite,gauge invariant operators[1,3,4,5,6,7,8].Another possibility[9],discussed here,is to study the scattering amplitudes for(regulated)plane-wave elementaryﬁeld excitations such as gluons and gluinos.One of the virtues of the latter approach is that perturbative MSYM scat-tering amplitudes share many qualitative properties with QCD amplitudes in the regime probed at high-energy colliders.Yet the results and the computa-tions(when organized in the right way)are typically signiﬁcantly simpler.In this way,MSYM serves as a testing ground for many aspects of perturbative QCD.MSYM loop amplitudes can be considered as components of QCD loop amplitudes.Depending on one’s point of view,they can be considered either “the simplest pieces”(in terms of the rank of the loop momentum tensors in the numerator of the amplitude)[10,11],or“the most complicated pieces”in terms of the degree of transcendentality(see section6)of the special functions entering theﬁnal results[12].As discussed in section6,the latter interpreta-tion links recent three-loop anomalous dimension results in QCD[13]to those in the spin-chain approach to MSYM[5].The most direct experimental probes of short-distance physics are collider experiments at the energy frontier.For the next decade,that frontier is at hadron colliders—Run II of the Fermilab Tevatron now,followed by startup of the CERN Large Hadron Collider in2007.New physics at colliders always contends with Standard Model backgrounds.At hadron colliders,all physics processes—signals and backgrounds—are inherently QCD processes.Hence it is important to be able to predict them theoretically as precisely as possi-ble.The cross section for a“hard,”or short-distance-dominated processes,can be factorized[14]into a partonic cross section,which can be computed order by order in perturbative QCD,convoluted with nonperturbative but measur-able parton distribution functions(pdfs).For example,the cross section for producing a pair of jets(plus anything else)in a p¯p collision is given byσp¯p→jjX(s)= a,b1 0dx1dx2f a(x1;µF)¯f b(x2;µF)×ˆσab→jjX(sx1x2;µF,µR;αs(µR)),(1)where s is the squared center-of-mass energy,x1,2are the longitudinal(light-cone)fractions of the p,¯p momentum carried by partons a,b,which may be quarks,anti-quarks or gluons.The experimental deﬁnition of a jet is an in-volved one which need not concern us here.The pdf f a(x,µF)gives the prob-ability forﬁnding parton a with momentum fraction x inside the proton; similarly¯f b is the probability forﬁnding parton b in the antiproton.The pdfs depend logarithmically on the factorization scaleµF,or transverse resolution with which the proton is examined.The Mellin moments of f a(x,µF)are for-ward matrix elements of leading-twist operators in the proton,renormalized at the scaleµF.The quark distribution function q(x,µ),for example,obeys 10dx x j q(x,µ)= p|[¯qγ+∂j+q](µ)|p .2Ingredients for a NNLO CalculationMany hadron collider measurements can beneﬁt from predictions that are accurate to next-to-next-to-leading order(NNLO)in QCD.Three separate ingredients enter such an NNLO computation;only the third depends on the process:(1)The experimental value of the QCD couplingαs(µR)must be determinedat one value of the renormalization scaleµR(for example m Z),and its evolution inµR computed using the3-loopβ-function,which has been known since1980[15].(2)The experimental values for the pdfs f a(x,µF)must be determined,ide-ally using predictions at the NNLO level,as are available for deep-inelastic scattering[16]and more recently Drell-Yan production[17].The evolu-tion of pdfs inµF to NNLO accuracy has very recently been completed, after a multi-year eﬀort by Moch,Vermaseren and Vogt[13](previously, approximations to the NNLO kernel were available[18]).(3)The NNLO terms in the expansion of the partonic cross sections must becomputed for the hadronic process in question.For example,the parton cross sections for jet production has the expansion,ˆσab→jjX=α2s(A+αs B+α2s C+...).(2)The quantities A and B have been known for over a decade[19],but C has not yet been computed.Figure 1.LHC Z production [22].•real ×real:×•virtual ×real:×•virtual ×virtual:×•doubly-virtual ×real:×Figure 2.Purely gluonic contributionsto ˆσgg →jjX at NNLO.Indeed,the NNLO terms are unknown for all but a handful of collider puting a wide range of processes at NNLO is the goal of a large amount of recent eﬀort in perturbative QCD [20].As an example of the im-proved precision that could result from this program,consider the production of a virtual photon,W or Z boson via the Drell-Yan process at the Tevatron or LHC.The total cross section for this process was ﬁrst computed at NNLO in 1991[21].Last year,the rapidity distribution of the vector boson also be-came available at this order [17,22],as shown in ﬁg.1.The rapidity is deﬁned in terms of the energy E and longitudinal momentum p z of the vector boson in the center-of-mass frame,Y ≡1E −p z .It determines where the vector boson decays within the detector,or outside its acceptance.The rapidity is sensitive to the x values of the incoming partons.At leading order in QCD,x 1=e Y m V /√s ,where m V is the vector boson mass.The LHC will produce roughly 100million W s and 10million Z s per year in detectable (leptonic)decay modes.LHC experiments will be able to map out the curve in ﬁg.1with exquisite precision,and use it to constrain the parton distributions —in the same detectors that are being used to search for new physics in other channels,often with similar q ¯q initial states.By taking ratios of the other processes to the “calibration”processes of single W and Z production,many experimental uncertainties,including those associated with the initial state parton distributions,drop out.Thus ﬁg.1plays a role as a “partonic luminosity monitor”[23].To get the full beneﬁt of the remarkable experimental precision,though,the theory uncertainty must approach the 1%level.As seen from the uncertainty bands in the ﬁgure,this precision is only achievable at NNLO.The bands are estimated by varying the arbitrary renormalization and factorization scales µR and µF (set to a common value µ)from m V /2to 2m V .A computation to all orders in αs would have no dependence on µ.Hence the µ-dependence of a ﬁxed order computation is related to the size of the missing higher-order terms in the series.Althoughsub-1%uncertainties may be special to W and Z production at the LHC, similar qualitative improvements in precision will be achieved for many other processes,such as di-jet production,as the NNLO terms are completed.Even within the NNLO terms in the partonic cross section,there are several types of ingredients.This feature is illustrated inﬁg.2for the purely gluonic contributions to di-jet production,ˆσgg→jjX.In theﬁgure,individual Feynman graphs stand for full amplitudes interfered(×)with other amplitudes,in order to produce contributions to a cross section.There may be2,3,or4partons in theﬁnal state.Just as in QED it is impossible to deﬁne an outgoing electron with no accompanying cloud of soft photons,also in QCD sensible observables require sums overﬁnal states with diﬀerent numbers of partons.Jets,for example,are deﬁned by a certain amount of energy into a certain conical region.At leading order,that energy typically comes from a single parton, but at NLO there may be two partons,and at NNLO three partons,within the jet cone.Each line inﬁg.2results in a cross-section contribution containing severe infrared divergences,which are traditionally regulated by dimensional regula-tion with D=4−2ǫ.Note that this regulation breaks the classical conformal invariance of QCD,and the classical and quantum conformal invariance of N=4super-Yang-Mills theory.Each contribution contains poles inǫranging from1/ǫ4to1/ǫ.The poles in the real contributions come from regions ofphase-space where the emitted gluons are soft and/or collinear.The poles in the virtual contributions come from similar regions of virtual loop integra-tion.The virtual×real contribution obviously has a mixture of the two.The Kinoshita-Lee-Nauenberg theorem[24]guarantees that the poles all cancel in the sum,for properly-deﬁned,short-distance observables,after renormal-izing the coupling constant and removing initial-state collinear singularities associated with renormalization of the pdfs.A critical ingredient in any NNLO prediction is the set of two-loop ampli-tudes,which enter the doubly-virtual×real interference inﬁg.2.Such ampli-tudes require dimensionally-regulated all-massless two-loop integrals depend-ing on at least one dimensionless ratio,which were only computed beginning in 1999[25,26,27].They also receive contributions from many Feynman diagrams, with lots of gauge-dependent cancellations between them.It is of interest to develop more eﬃcient,manifestly gauge-invariant methods for combining di-agrams,such as the unitarity or cut-based method successfully applied at one loop[10]and in the initial two-loop computations[28].i,ij+ i iFigure3.Illustration of soft-collinear(left)and pure-collinear(right)one-loop di-vergences.3N=4Super-Yang-Mills Theory as a Testing Ground for QCDN=4super-Yang-Mills theory serves an excellent testing ground for pertur-bative QCD methods.For n-gluon scattering at tree level,the two theories in fact give identical predictions.(The extra fermions and scalars of MSYM can only be produced in pairs;hence they only appear in an n-gluon ampli-tude at loop level.)Therefore any consequence of N=4supersymmetry,such as Ward identities among scattering amplitudes[29],automatically applies to tree-level gluonic scattering in QCD[30].Similarly,at tree level Witten’s topological string[31]produces MSYM,but implies twistor-space localization properties for QCD tree amplitudes.(Amplitudes with quarks can be related to supersymmetric amplitudes with gluinos using simple color manipulations.)3.1Pole Structure at One and Two LoopsAt the loop-level,MSYM becomes progressively more removed from QCD. However,it can still illuminate general properties of scattering amplitudes,in a calculationally simpler arena.Consider the infrared singularities of one-loop massless gauge theory amplitudes.In dimensional regularization,the leading singularity is1/ǫ2,arising from virtual gluons which are both soft and collinear with respect to a second gluon or another massless particle.It can be char-acterized by attaching a gluon to any pair of external legs of the tree-level amplitude,as in the left graph inﬁg.3.Up to color factors,this leading diver-gence is the same for MSYM and QCD.There are also purely collinear terms associated with individual external lines,as shown in the right graph inﬁg.3. The pure-collinear terms have a simpler form than the soft terms,because there is less tangling of color indices,but they do diﬀer from theory to theory.The full result for one-loop divergences can be expressed as an operator I(1)(ǫ) which acts on the color indices of the tree amplitude[32].Treating the L-loop amplitude as a vector in color space,|A(L)n ,the one-loop result is|A(1)n =I(1)(ǫ)|A(0)n +|A(1),ﬁnn ,(3)where |A (1),ﬁn nis ﬁnite as ǫ→0,and I (1)(ǫ)=1Γ(1−ǫ)n i =1n j =i T i ·T j 1T 2i 1−s ij ǫ,(4)where γis Euler’s constant and s ij =(k i +k j )2is a Mandelstam invariant.The color operator T i ·T j =T a i T a j and factor of (µ2R /(−s ij ))ǫarise from softgluons exchanged between legs i and j ,as in the left graph in ﬁg.3.The pure 1/ǫpoles terms proportional to γi have been written in a symmetric fashion,which slightly obscures the fact that the color structure is actually simpler.We can use the equation which represents color conservation in the color-space notation, n j =1T j =0,to simplify the result.At order 1/ǫwe may neglect the (µ2R /(−s ij ))ǫfactor in the γi terms,and we have n j =i T i ·T j γi /T 2i =−γi .So the color structure of the pure 1/ǫterm is actually trivial.For an n -gluon amplitude,the factor γi is set equal to its value for gluons,which turns out to be γg =b 0,the one-loop coeﬃcient in the β-function.Hence the pure-collinear contribution vanishes for MSYM,but not for QCD.The divergences of two-loop amplitudes can be described in the same for-malism [32].The relation to soft-collinear factorization has been made more transparent by Sterman and Tejeda-Yeomans,who also predicted the three-loop behavior [33].Decompose the two-loop amplitude |A (2)n as|A (2)n =I (2)(ǫ)|A (0)n +I (1)(ǫ)|A (1)n +|A (2),ﬁn n,(5)where |A (2),ﬁn n is ﬁnite as ǫ→0and I (2)(ǫ)=−1ǫ+e −ǫγΓ(1−2ǫ)ǫ+K I (1)(2ǫ)+e ǫγT 2i µ22C 2A ,(8)where C A =N c is the adjoint Casimir value.The quantity ˆH(2)has non-trivial,but purely subleading-in-N c ,color structure.It is associated with soft,rather than collinear,momenta [37,33],so it is theory-independent,up to color factors.An ansatz for it for general n has been presented recently [38].3.2Recycling Cuts in MSYMAn eﬃcient way to compute loop amplitudes,particularly in theories with a great deal of supersymmetry,is to use unitarity and reconstruct the am-plitude from its cuts [10,38].For the four-gluon amplitude in MSYM,the two-loop structure,and much of the higher-loop structure,follows from a sim-ple property of the one-loop two-particle cut in this theory.For simplicity,we strip the color indices oﬀof the four-point amplitude A (0)4,by decomposing it into color-ordered amplitudes A (0)4,whose coeﬃcients are traces of SU(N c )generator matrices (Chan-Paton factors),A (0)4(k 1,a 1;k 2,a 2;k 3,a 3;k 4,a 4)=g 2 ρ∈S 4/Z 4Tr(T a ρ(1)T a ρ(2)T a ρ(3)T a ρ(4))×A (0)4(k ρ(1),k ρ(2),k ρ(3),k ρ(4)).(9)The two-particle cut can be written as a product of two four-point color-ordered amplitudes,summed over the pair of intermediate N =4states S,S ′crossing the cut,which evaluates toS,S ′∈N =4A (0)4(k 1,k 2,ℓS ,−ℓ′S ′)×A (0)4(ℓ′S ′,−ℓS ,k 3,k 4)=is 12s 23A (0)4(k 1,k 2,k 3,k 4)×1(ℓ−k 3)2,(10)where ℓ′=ℓ−k 1−k 2.This equation is also shown in ﬁg.4.The scalar propagator factors in eq.(10)are depicted as solid vertical lines in the ﬁgure.The dashed line indicates the cut.Thus the cut reduces to the cut of a scalar box integral,deﬁned byI D =4−2ǫ4≡ d 4−2ǫℓℓ2(ℓ−k 1)2(ℓ−k 1−k 2)2(ℓ+k 4)2.(11)One of the virtues of eq.(10)is that it is valid for arbitrary external states in the N =4multiplet,although only external gluons are shown in ﬁg.4.Therefore it can be re-used at higher loop order,for example by attaching yet another tree to the left.N =41234=i s 12s 231234Figure 4.The one-loop two-particle cuts for the four-point amplitude in MSYM reduce to the tree amplitude multiplied by a cut scalar box integral (for any set of four external states).i 2s 12s121234+s 121234+perms Figure 5.The two-loop gg →gg amplitude in MSYM [11,39].The blob on theright represents the color-ordered tree amplitude A (0)4.(The quantity s 12s 23A (0)4transforms symmetrically under gluon interchange.)In the the brackets,black linesare kinematic 1/p 2propagators,with scalar (φ3)vertices.Green lines are color δab propagators,with structure constant (f abc )vertices.The permutation sum is over the three cyclic permutations of legs 2,3,4,and makes the amplitude Bose symmetric.At two loops,the simplicity of eq.(10)made it possible to compute the two-loop gg →gg scattering amplitude in that theory (in terms of speciﬁc loop integrals)in 1997[11],four years before the analogous computations in QCD [36,37].All of the loop momenta in the numerators of the Feynman di-agrams can be factored out,and only two independent loop integrals appear,the planar and nonplanar scalar double box integrals.The result can be writ-ten in an appealing diagrammatic form,ﬁg.5,where the color algebra has the same form as the kinematics of the loop integrals [39].At higher loops,eq.(10)leads to a “rung rule”[11]for generating a class of (L +1)-loop contributions from L -loop contributions.The rule states that one can insert into a L -loop contribution a rung,i.e.a scalar propagator,transverse to two parallel lines carrying momentum ℓ1+ℓ2,along with a factor of i (ℓ1+ℓ2)2in the numerator,as shown in ﬁing this rule,one can construct recursively the external and loop-momentum-containing numerators factors associated with every φ3-type diagram that can be reduced to trees by a sequence of two-particle cuts,such as the diagram in ﬁg.7a .Such diagrams can be termed “iterated 2-particle cut-constructible,”although a more compact notation might be ‘Mondrian’diagrams,given their resemblance to Mondrian’s paintings.Not all diagrams can be computed in this way.The diagram in ﬁg.7b is not in the ‘Mondrian’class,so it cannot be determined from two-particle cuts.Instead,evaluation of the three-particle cuts shows that it appears with a non-vanishing coeﬃcient in the subleading-color contributions to the three-loop MSYM amplitude.ℓ1ℓ2−→i (ℓ1+ℓ2)2ℓ1ℓ2Figure 6.The rung rule for MSYM.(a)(b)Figure 7.(a)Example of a ‘Mondrian’diagram which can be determined re-cursively from the rung rule.(b)Theﬁrst non-vanishing,non-Mondrian dia-grams appear at three loops in nonplanar,subleading-color contributions.4Iterative Relation in N =4Super-Yang-Mills TheoryAlthough the two-loop gg →gg amplitude in MSYM was expressed in terms of scalar integrals in 1997[11],and the integrals themselves were computed as a Laurent expansion about D =4in 1999[25,26],the expansion of the N =4amplitude was not inspected until last fall [9],considerably after similar investigations for QCD and N =1super-Yang-Mills theory [36,37].It was found to have a quite interesting “iterative”relation,when expressed in terms of the one-loop amplitude and its square.At leading color,the L -loop gg →gg amplitude has the same single-trace color decomposition as the tree amplitude,eq.(9).Let M (L )4be the ratio of this leading-color,color-ordered amplitude to the corresponding tree amplitude,omitting also several conventional factors,A (L ),N =4planar 4= 2e −ǫγg 2N c2 M (1)4(ǫ) 2+f (ǫ)M (1)4(2ǫ)−12(ζ2)2is replaced by approximately sixpages of formulas (!),including a plethora of polylogarithms,logarithms and=+f(ǫ)−12(ζ2)2+O(ǫ)f(ǫ)=−(ζ2+ǫζ3+ǫ2ζ4+...)Figure8.Schematic depiction of the iterative relation(13)between two-loop and one-loop MSYM amplitudes.polynomials in ratios of invariants s/t,s/u and t/u[37].The polylogarithm is deﬁned byLi m(x)=∞i=1x i t Li m−1(t),Li1(x)=−ln(1−x).(14)It appears with degree m up to4at theﬁnite,orderǫ0,level;and up to degree4−i in the O(ǫ−i)terms.In the case of MSYM,identities relating these polylogarithms are needed to establish eq.(13).Although the O(ǫ0)term in eq.(13)is miraculously simple,as noted above the behavior of the pole terms is not a miracle.It is dictated in general terms by the cancellation of infrared divergences between virtual corrections and real emission[24].Roughly speaking,for this cancellation to take place,the virtual terms must resemble lower-loop amplitudes,and the real terms must resemble lower-point amplitudes,in the soft and collinear regions of loop or phase-space integration.At the level of theﬁnite terms,the iterative relation(13)can be understood in the Regge/BFKL limit where s≫t,because it then corresponds to expo-nentiation of large logarithms of s/t[40].For general values of s/t,however, there is no such argument.The relation is special to D=4,where the theory is conformally invariant. That is,the O(ǫ1)remainder terms cannot be simpliﬁed signiﬁcantly.For ex-ample,the two-loop amplitude M(2)4(ǫ)contains at O(ǫ1)all three independent Li5functions,Li5(−s/u),Li5(−t/u)and Li5(−s/t),yet[M(1)4(ǫ)]2has only the ﬁrst two of these[9].The relation is also special to the planar,leading-color limit.The subleading color-components of theﬁnite remainder|A(2),ﬁnn deﬁned by eq.(5)show no signiﬁcant simpliﬁcation at all.For planar amplitudes in the D→4limit,however,there is evidence that an identical relation also holds for an arbitrary number n of external legs, at least for certain“maximally helicity-violating”(MHV)helicity amplitudes. This evidence comes from studying the limits of two-loop amplitudes as two of the n gluon momenta become collinear[9,38,41].(Indeed,it was by analyzing these limits that the relation for n=4wasﬁrst uncovered.)The collinear limits turn out to be consistent with the same eq.(13)with M4replaced by M n everywhere[9],i.e.M(2)n(ǫ)=12(ζ2)2+O(ǫ).(15)The collinear consistency does not constitute a proof of eq.(15),but in light of the remarkable properties of MSYM,it would be surprising if it were not true in the MHV case.Because the direct computation of two-loop amplitudes for n>4seems rather diﬃcult,it would be quite interesting to try to examine the twistor-space properties of eq.(15),along the lines of refs.[31,42].(The right-hand-side of eq.(15)is not completely speciﬁed at order1/ǫandǫ0for n>4.The reason is that the orderǫandǫ2terms in M(1)n(ǫ),which contribute to theﬁrst term in eq.(15)at order1/ǫandǫ0,contain the D=6−2ǫpentagon integral[43],which is not known in closed form.On the other hand, the diﬀerential equations this integral satisﬁes may suﬃce to test the twistor-space behavior.Or one may examine just theﬁnite remainder M(L),ﬁnn deﬁnedvia eq.(5).)It may soon be possible to test whether an iterative relation for planar MSYM amplitudes extends to three loops.An ansatz for the three-loop planar gg→gg amplitude,shown inﬁg.9,was provided at the same time as the two-loop re-sult,in1997[11].The ansatz is based on the“rung-rule”evaluation of the iterated2-particle cuts,plus the3-particle cuts with intermediate states in D=4;the4-particle cuts have not yet been veriﬁed.Two integrals,each be-ginning at O(ǫ−6),are required to evaluate the ansatz in a Laurent expansion about D=4.(The other two integrals are related by s↔t.)The triple ladder integral on the top line ofﬁg.9was evaluated last year by Smirnov,all the way through O(ǫ0)[44].Evaluation of the remaining integral,which contains a factor of(ℓ+k4)2in the numerator,is in progress[45];all the terms through O(ǫ−2)agree with predictions[33],up to a couple of minor corrections.5Signiﬁcance of Iterative Behavior?It is not yet entirely clear why the two-loop four-point amplitude,and prob-ably also the n-point amplitudes,have the iterative structure(15).However, one can speculate that it is from the need for the perturbative series to=i3s12s212+s223+2s12(ℓ+k4)+2s23(ℓ+k1)21Figure9.Graphical representation of the three-loop amplitude for MSYM in the planar limit.be summable into something which becomes“simple”in the planar strong-coupling limit,since that corresponds,via AdS/CFT,to a weakly-coupled supergravity theory.The fact that the relation is special to the conformal limit D→4,and to the planar limit,backs up this speculation.Obviously it would be nice to have some more information at three loops.There have been other hints of an iterative structure in the four-point correlation func-tions of chiral primary(BPS)composite operators[46],but here also the exact structure is not yet clear.Integrability has played a key role in recent higher-loop computations of non-BPS spin-chain anomalous dimensions[4,5,6,8].By imposing regularity of the BMN‘continuum’limit[3],a piece of the anoma-lous dimension matrix has even been summed to all orders in g2N c in terms of hypergeometric functions[7].The quantities we considered here—gauge-invariant,but dimensionally regularized,scattering amplitudes of color non-singlet states—are quite diﬀerent from the composite color-singlet operators usually treated.Yet there should be some underlying connection between the diﬀerent perturbative series.6Aside:Anomalous Dimensions in QCD and MSYMAs mentioned previously,the set of anomalous dimensions for leading-twist operators was recently computed at NNLO in QCD,as the culmination of a multi-year eﬀort[13]which is central to performing precise computations of hadron collider cross sections.Shortly after the Moch,Vermaseren and Vogt computation,the anomalous dimensions in MSYM were extracted from this result by Kotikov,Lipatov,Onishchenko and Velizhanin[12].(The MSYM anomalous dimensions are universal;supersymmetry implies that there is only one independent one for each Mellin moment j.)This extraction was non-trivial,because MSYM contains scalars,interacting through both gauge and Yukawa interactions,whereas QCD does not.However,Kotikov et al.noticed, from comparing NLO computations in both leading-twist anomalous dimen-sions and BFKL evolution,that the“most complicated terms”in the QCDcomputation always coincide with the MSYM result,once the gauge group representation of the fermions is shifted from the fundamental to the adjoint representation.One can deﬁne the“most complicated terms”in the x-space representation of the anomalous dimensions—i.e.the splitting kernels—as follows:Assign a logarithm or factor ofπa transcendentality of1,and a polylogarithm Li m or factor ofζm=Li m(1)a transcendentality of m.Then the most complicated terms are those with leading transcendentality.For the NNLO anomalous dimensions,this turns out to be transcendentality4.(This rule for extracting the MSYM terms from QCD has also been found to hold directly at NNLO,for the doubly-virtual contributions[38].)Strikingly,the NNLO MSYM anomalous dimension obtained for j=4by this procedure agrees with a previous result derived by assuming an integrable structure for the planar three-loop contribution to the dilatation operator[5].7Conclusions and OutlookN=4super-Yang-Mills theory is an excellent testing ground for techniques for computing,and understanding the structure of,QCD scattering amplitudes which are needed for precise theoretical predictions at high-energy colliders. One can even learn something about the structure of N=4super-Yang-Mills theory in the process,although clearly there is much more to be understood. Some open questions include:Is there any AdS/CFT“dictionary”for color non-singlet states,like plane-wave gluons?Can one recover composite operator correlation functions from any limits of multi-point scattering amplitudes?Is there a better way to infrared regulate N=4supersymmetric scattering amplitudes,that might be more convenient for approaching the AdS/CFT correspondence,such as compactiﬁcation on a three-sphere,use of twistor-space,or use of coherent external states?Further investigations of this arena will surely be fruitful.AcknowledgementsWe are grateful to the organizers of Strings04for putting together such a stim-ulating meeting.This research was supported by the US Department of En-ergy under contracts DE-FG03-91ER40662(Z.B.)and DE-AC02-76SF00515 (L.J.D.),and by the Direction des Sciences de la Mati`e re of the Commissariat `a l’Energie Atomique of France(D.A.K.).。

大环多胺

New1H-Pyrazole-Containing Polyamine Receptors Able ToComplex L-Glutamate in Water at Physiological pH ValuesCarlos Miranda,†Francisco Escartı´,‡Laurent Lamarque,†Marı´a J.R.Yunta,§Pilar Navarro,*,†Enrique Garcı´a-Espan˜a,*,‡and M.Luisa Jimeno†Contribution from the Instituto de Quı´mica Me´dica,Centro de Quı´mica Orga´nica Manuel Lora Tamayo,CSIC,C/Juan de la Cier V a3,28006Madrid,Spain,Departamento de Quı´mica Inorga´nica,Facultad de Quı´mica,Uni V ersidad de Valencia,c/Doctor Moliner50, 46100Burjassot(Valencia),Spain,and Departamento de Quı´mica Orga´nica,Facultad deQuı´mica,Uni V ersidad Complutense de Madrid,A V plutense s/n,28040Madrid,SpainReceived April16,2003;E-mail:enrique.garcia-es@uv.esAbstract:The interaction of the pyrazole-containing macrocyclic receptors3,6,9,12,13,16,19,22,25,26-decaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetraene1[L1],13,26-dibenzyl-3,6,9,12,13,16,-19,22,25,26-decaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetraene2[L2],3,9,12,13,16,22,-25,26-octaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetraene3[L3],6,19-dibenzyl-3,6,9,12,13,-16,19,22,25,26-decaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetraene4[L4],6,19-diphenethyl-3,6,9,12,13,16,19,22,25,26-decaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetraene5[L5],and 6,19-dioctyl-3,6,9,12,13,16,19,22,25,26-decaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetra-ene6[L6]with L-glutamate in aqueous solution has been studied by potentiometric techniques.The synthesis of receptors3-6[L3-L6]is described for the first time.The potentiometric results show that4[L4]containing benzyl groups in the central nitrogens of the polyamine side chains is the receptor displaying the larger interaction at pH7.4(K eff)2.04×104).The presence of phenethyl5[L5]or octyl groups6[L6]instead of benzyl groups4[L4]in the central nitrogens of the chains produces a drastic decrease in the stability[K eff )3.51×102(5),K eff)3.64×102(6)].The studies show the relevance of the central polyaminic nitrogen in the interaction with glutamate.1[L1]and2[L2]with secondary nitrogens in this position present significantly larger interactions than3[L3],which lacks an amino group in the center of the chains.The NMR and modeling studies suggest the important contribution of hydrogen bonding andπ-cation interaction to adduct formation.IntroductionThe search for the L-glutamate receptor field has been andcontinues to be in a state of almost explosive development.1 L-Glutamate(Glu)is thought to be the predominant excitatory transmitter in the central nervous system(CNS)acting at a rangeof excitatory amino acid receptors.It is well-known that it playsa vital role mediating a great part of the synaptic transmission.2However,there is an increasing amount of experimentalevidence that metabolic defects and glutamatergic abnormalitiescan exacerbate or induce glutamate-mediated excitotoxic damageand consequently neurological disorders.3,4Overactivation ofionotropic(NMDA,AMPA,and Kainate)receptors(iGluRs)by Glu yields an excessive Ca2+influx that produces irreversible loss of neurons of specific areas of the brain.5There is much evidence that these processes induce,at least in part,neuro-degenerative illnesses such as Parkinson,Alzheimer,Huntington, AIDS,dementia,and amyotrophic lateral sclerosis(ALS).6In particular,ALS is one of the neurodegenerative disorders for which there is more evidence that excitotoxicity due to an increase in Glu concentration may contribute to the pathology of the disease.7Memantine,a drug able to antagonize the pathological effects of sustained,but relatively small,increases in extracellular glutamate concentration,has been recently received for the treatment of Alzheimer disease.8However,there is not an effective treatment for ALS.Therefore,the preparation of adequately functionalized synthetic receptors for L-glutamate seems to be an important target in finding new routes for controlling abnormal excitatory processes.However,effective recognition in water of aminocarboxylic acids is not an easy task due to its zwitterionic character at physiological pH values and to the strong competition that it finds in its own solvent.9†Centro de Quı´mica Orga´nica Manuel Lora Tamayo.‡Universidad de Valencia.§Universidad Complutense de Madrid.(1)Jane,D.E.In Medicinal Chemistry into the Millenium;Campbell,M.M.,Blagbrough,I.S.,Eds.;Royal Society of Chemistry:Cambridge,2001;pp67-84.(2)(a)Standaert,D.G.;Young,A.B.In The Pharmacological Basis ofTherapeutics;Hardman,J.G.,Goodman Gilman,A.,Limbird,L.E.,Eds.;McGraw-Hill:New York,1996;Chapter22,p503.(b)Fletcher,E.J.;Loge,D.In An Introduction to Neurotransmission in Health and Disease;Riederer,P.,Kopp,N.,Pearson,J.,Eds.;Oxford University Press:New York,1990;Chapter7,p79.(3)Michaelis,E.K.Prog.Neurobiol.1998,54,369-415.(4)Olney,J.W.Science1969,164,719-721.(5)Green,J.G.;Greenamyre,J.T.Prog.Neurobiol.1996,48,613-63.(6)Bra¨un-Osborne,H.;Egebjerg,J.;Nielsen,E.O.;Madsen,U.;Krogsgaard-Larsen,P.J.Med.Chem.2000,43,2609-2645and references therein.(7)(a)Shaw,P.J.;Ince,P.G.J.Neurol.1997,244(Suppl2),S3-S14.(b)Plaitakis,A.;Fesdjian,C.O.;Shashidharan,S Drugs1996,5,437-456.(8)Frantz,A.;Smith,A.Nat.Re V.Drug Dico V ery2003,2,9.Published on Web12/30/200310.1021/ja035671m CCC:$27.50©2004American Chemical Society J.AM.CHEM.SOC.2004,126,823-8339823There are many types of receptors able to interact with carboxylic acids and amino acids in organic solvents,10-13yielding selective complexation in some instances.However,the number of reported receptors of glutamate in aqueous solution is very scarce.In this sense,one of the few reports concerns an optical sensor based on a Zn(II)complex of a 2,2′:6′,2′′-terpyridine derivative in which L -aspartate and L -glutamate were efficiently bound as axial ligands (K s )104-105M -1)in 50/50water/methanol mixtures.14Among the receptors employed for carboxylic acid recogni-tion,the polyamine macrocycles I -IV in Chart 1are of particular relevance to this work.In a seminal paper,Lehn et al.15showed that saturated polyamines I and II could exert chain-length discrimination between different R ,ω-dicarboxylic acids as a function of the number of methylene groups between the two triamine units of the receptor.Such compounds were also able to interact with a glutamic acid derivative which has the ammonium group protected with an acyl moiety.15,16Compounds III and IV reported by Gotor and Lehn interact in their protonated forms in aqueous solution with protected N -acetyl-L -glutamate and N -acetyl-D -glutamate,showing a higher stability for the interaction with the D -isomer.17In both reports,the interaction with protected N -acetyl-L -glutamate at physiological pH yields constants of ca.3logarithmic units.Recently,we have shown that 1H -pyrazole-containing mac-rocycles present desirable properties for the binding of dopam-ine.18These polyaza macrocycles,apart from having a highpositive charge at neutral pH values,can form hydrogen bonds not only through the ammonium or amine groups but also through the pyrazole nitrogens that can behave as hydrogen bond donors or acceptors.In fact,Elguero et al.19have recently shown the ability of the pyrazole rings to form hydrogen bonds with carboxylic and carboxylate functions.These features can be used to recognize the functionalities of glutamic acid,the carboxylic and/or carboxylate functions and the ammonium group.Apart from this,the introduction of aromatic donor groups appropriately arranged within the macrocyclic framework or appended to it through arms of adequate length may contribute to the recognition event through π-cation interactions with the ammonium group of L -glutamate.π-Cation interactions are a key feature in many enzymatic centers,a classical example being acetylcholine esterase.20The role of such an interaction in abiotic systems was very well illustrated several years ago in a seminal work carried out by Dougherty and Stauffer.21Since then,many other examples have been reported both in biotic and in abiotic systems.22Taking into account all of these considerations,here we report on the ability of receptors 1[L 1]-6[L 6](Chart 2)to interact with L -glutamic acid.These receptors display structures which differ from one another in only one feature,which helps to obtain clear-cut relations between structure and interaction(9)Rebek,J.,Jr.;Askew,B.;Nemeth,D.;Parris,K.J.Am.Chem.Soc.1987,109,2432-2434.(10)Seel,C.;de Mendoza,J.In Comprehensi V e Supramolecular Chemistry ;Vogtle,F.,Ed.;Elsevier Science:New York,1996;Vol.2,p 519.(11)(a)Sessler,J.L.;Sanson,P.I.;Andrievesky,A.;Kral,V.In SupramolecularChemistry of Anions ;Bianchi,A.,Bowman-James,K.,Garcı´a-Espan ˜a,E.,Eds.;John Wiley &Sons:New York,1997;Chapter 10,pp 369-375.(b)Sessler,J.L.;Andrievsky,A.;Kra ´l,V.;Lynch,V.J.Am.Chem.Soc.1997,119,9385-9392.(12)Fitzmaurice,R.J.;Kyne,G.M.;Douheret,D.;Kilburn,J.D.J.Chem.Soc.,Perkin Trans.12002,7,841-864and references therein.(13)Rossi,S.;Kyne,G.M.;Turner,D.L.;Wells,N.J.;Kilburn,J.D.Angew.Chem.,Int.Ed.2002,41,4233-4236.(14)Aı¨t-Haddou,H.;Wiskur,S.L.;Lynch,V.M.;Anslyn,E.V.J.Am.Chem.Soc.2001,123,11296-11297.(15)Hosseini,M.W.;Lehn,J.-M.J.Am.Chem.Soc.1982,104,3525-3527.(16)(a)Hosseini,M.W.;Lehn,J.-M.Hel V .Chim.Acta 1986,69,587-603.(b)Heyer,D.;Lehn,J.-M.Tetrahedron Lett.1986,27,5869-5872.(17)(a)Alfonso,I.;Dietrich,B.;Rebolledo,F.;Gotor,V.;Lehn,J.-M.Hel V .Chim.Acta 2001,84,280-295.(b)Alfonso,I.;Rebolledo,F.;Gotor,V.Chem.-Eur.J.2000,6,3331-3338.(18)Lamarque,L.;Navarro,P.;Miranda,C.;Ara ´n,V.J.;Ochoa,C.;Escartı´,F.;Garcı´a-Espan ˜a,E.;Latorre,J.;Luis,S.V.;Miravet,J.F.J.Am.Chem.Soc .2001,123,10560-10570.(19)Foces-Foces,C.;Echevarria,A.;Jagerovic,N.;Alkorta,I.;Elguero,J.;Langer,U.;Klein,O.;Minguet-Bonvehı´,H.-H.J.Am.Chem.Soc.2001,123,7898-7906.(20)Sussman,J.L.;Harel,M.;Frolow,F.;Oefner,C.;Goldman,A.;Toker,L.;Silman,I.Science 1991,253,872-879.(21)Dougherty,D.A.;Stauffer,D.A.Science 1990,250,1558-1560.(22)(a)Sutcliffe,M.J.;Smeeton,A.H.;Wo,Z.G.;Oswald,R.E.FaradayDiscuss.1998,111,259-272.(b)Kearney,P.C.;Mizoue,L.S.;Kumpf,R.A.;Forman,J.E.;McCurdy,A.;Dougherty,D.A.J.Am.Chem.Soc.1993,115,9907-9919.(c)Bra ¨uner-Osborne,H.;Egebjerg,J.;Nielsen,E.;Madsen,U.;Krogsgaard-Larsen,P.J.Med.Chem.2000,43,2609-2645.(d)Zacharias,N.;Dougherty,D.A.Trends Pharmacol.Sci.2002,23,281-287.(e)Hu,J.;Barbour,L.J.;Gokel,G.W.J.Am.Chem.Soc.2002,124,10940-10941.Chart 1.Some Receptors Employed for Dicarboxylic Acid and N -AcetylglutamateRecognitionChart 2.New 1H -Pyrazole-Containing Polyamine Receptors Able To Complex L -Glutamate inWaterA R T I C L E SMiranda et al.824J.AM.CHEM.SOC.9VOL.126,NO.3,2004strengths.1[L1]and2[L2]differ in the N-benzylation of the pyrazole moiety,and1[L1]and3[L3]differ in the presence in the center of the polyamine side chains of an amino group or of a methylene group.The receptors4[L4]and5[L5]present the central nitrogens of the chain N-functionalized with benzyl or phenethyl groups,and6[L6]has large hydrophobic octyl groups.Results and DiscussionSynthesis of3-6.Macrocycles3-6have been obtained following the procedure previously reported for the preparation of1and2.23The method includes a first dipodal(2+2) condensation of the1H-pyrazol-3,5-dicarbaldehyde7with the corresponding R,ω-diamine,followed by hydrogenation of the resulting Schiff base imine bonds.In the case of receptor3,the Schiff base formed by condensation with1,5-pentanediamine is a stable solid(8,mp208-210°C)which precipitated in68% yield from the reaction mixture.Further reduction with NaBH4 in absolute ethanol gave the expected tetraazamacrocycle3, which after crystallization from toluene was isolated as a pure compound(mp184-186°C).In the cases of receptors4-6, the precursor R,ω-diamines(11a-11c)(Scheme1B)were obtained,by using a procedure previously described for11a.24 This procedure is based on the previous protection of the primary amino groups of1,5-diamino-3-azapentane by treatment with phthalic anhydride,followed by alkylation of the secondary amino group of1,5-diphthalimido-3-azapentane9with benzyl, phenethyl,or octyl bromide.Finally,the phthalimido groups of the N-alkyl substituted intermediates10a-10c were removed by treatment with hydrazine to afford the desired amines11a-11c,which were obtained in moderate yield(54-63%).In contrast with the behavior previously observed in the synthesis of3,in the(2+2)dipodal condensations of7with 3-benzyl-,3-phenethyl-,and3-octyl-substituted3-aza-1,5-pentanediamine11a,11b,and11c,respectively,there was not precipitation of the expected Schiff bases(Scheme1A). Consequently,the reaction mixtures were directly reduced in situ with NaBH4to obtain the desired hexaamines4-6,which after being carefully purified by chromatography afforded purecolorless oils in51%,63%,and31%yield,respectively.The structures of all of these new cyclic polyamines have been established from the analytical and spectroscopic data(MS(ES+), 1H and13C NMR)of both the free ligands3-6and their corresponding hydrochloride salts[3‚4HCl,4‚6HCl,5‚6HCl, and6‚6HCl],which were obtained as stable solids following the same procedure previously reported18for1‚6HCl and2‚6HCl.As usually occurs for3,5-disubstituted1H-pyrazole deriva-tives,either the free ligands3-6or their hydrochlorides show very simple1H and13C NMR spectra,in which signals indicate that,because of the prototropic equilibrium of the pyrazole ring, all of these compounds present average4-fold symmetry on the NMR scale.The quaternary C3and C5carbons appear together,and the pairs of methylene carbons C6,C7,and C8are magnetically equivalent(see Experimental Section).In the13C NMR spectra registered in CDCl3solution, significant differences can be observed between ligand3,without an amino group in the center of the side chain,and the N-substituted ligands4-6.In3,the C3,5signal appears as a broad singlet.However,in4-6,it almost disappears within the baseline of the spectra,and the methylene carbon atoms C6and C8experience a significant broadening.Additionally,a remark-able line-broadening is also observed in the C1′carbon signals belonging to the phenethyl and octyl groups of L5and L6, respectively.All of these data suggest that as the N-substituents located in the middle of the side chains of4-6are larger,the dynamic exchange rate of the pyrazole prototropic equilibrium is gradually lower,probably due to a relation between proto-tropic and conformational equilibria.Acid-Base Behavior.To follow the complexation of L-glutamate(hereafter abbreviated as Glu2-)and its protonated forms(HGlu-,H2Glu,and H3Glu+)by the receptors L1-L6, the acid-base behavior of L-glutamate has to be revisited under the experimental conditions of this work,298K and0.15mol dm-3.The protonation constants obtained,included in the first column of Table1,agree with the literature25and show that the zwitterionic HGlu-species is the only species present in aqueous solution at physiological pH values(Scheme2and Figure S1of Supporting Information).Therefore,receptors for(23)Ara´n,V.J.;Kumar,M.;Molina,J.;Lamarque,L.;Navarro,P.;Garcı´a-Espan˜a,E.;Ramı´rez,J.A.;Luis,S.V.;Escuder,.Chem.1999, 64,6137-6146.(24)(a)Yuen Ng,C.;Motekaitis,R.J.;Martell,A.E.Inorg.Chem.1979,18,2982-2986.(b)Anelli,P.L.;Lunazzi,L.;Montanari,F.;Quici,.Chem.1984,49,4197-4203.Scheme1.Synthesis of the Pyrazole-Containing MacrocyclicReceptorsNew1H-Pyrazole-Containing Polyamine Receptors A R T I C L E SJ.AM.CHEM.SOC.9VOL.126,NO.3,2004825glutamate recognition able to address both the negative charges of the carboxylate groups and the positive charge of ammonium are highly relevant.The protonation constants of L 3-L 6are included in Table 1,together with those we have previously reported for receptors L 1and L 2.23A comparison of the constants of L 4-L 6with those of the nonfunctionalized receptor L 1shows a reduced basicity of the receptors L 4-L 6with tertiary nitrogens at the middle of the polyamine bridges.Such a reduction in basicity prevented the potentiometric detection of the last protonation for these ligands in aqueous solution.A similar reduction in basicity was previously reported for the macrocycle with the N -benzylated pyrazole spacers (L 2).23These diminished basicities are related to the lower probability of the tertiary nitrogens for stabilizing the positive charges through hydrogen bond formation either with adjacent nonprotonated amino groups of the molecule or with water molecules.Also,the increase in the hydrophobicity of these molecules will contribute to their lower basicity.The stepwise basicity constants are relatively high for the first four protonation steps,which is attributable to the fact that these protons can bind to the nitrogen atoms adjacent to the pyrazole groups leaving the central nitrogen free,the electrostatic repulsions between them being therefore of little significance.The remaining protonation steps will occur in the central nitrogen atom,which will produce an important increase in the electrostatic repulsion in the molecule and therefore a reduction in basicity.As stated above,the tertiary nitrogen atoms present in L 4-L 6will also contribute to this diminished basicity.To analyze the interaction with glutamic acid,it is important to know the protonation degree of the ligands at physiological pH values.In Table 2,we have calculated the percentages ofthe different protonated species existing in solution at pH 7.4for receptors L 1-L 6.As can be seen,except for the receptor with the pentamethylenic chains L 3in which the tetraprotonated species prevails,all of the other systems show that the di-and triprotonated species prevail,although to different extents.Interaction with Glutamate.The stepwise constants for the interaction of the receptors L 1-L 6with glutamate are shown in Table 3,and selected distribution diagrams are plotted in Figure 1A -C.All of the studied receptors interact with glutamate forming adduct species with protonation degrees (j )which vary between 8and 0depending on the system (see Table 3).The stepwise constants have been derived from the overall association constants (L +Glu 2-+j H +)H j LGlu (j -2)+,log j )provided by the fitting of the pH-metric titration curves.This takes into account the basicities of the receptors and glutamate (vide supra)and the pH range in which a given species prevails in solution.In this respect,except below pH ca.4and above pH 9,HGlu -can be chosen as the protonated form of glutamate involved in the formation of the different adducts.Below pH 4,the participation of H 2Glu in the equilibria has also to be considered (entries 9and 10in Table 3).For instance,the formation of the H 6LGlu 4+species can proceed through the equilibria HGlu -+H 5L 5+)H 6LGlu 4+(entry 8,Table 3),and H 2Glu +H 4L 4+)H 6LGlu 4(entry 9Table 3),with percentages of participation that depend on pH.One of the effects of the interaction is to render somewhat more basic the receptor,and somewhat more acidic glutamic acid,facilitating the attraction between op-positely charged partners.A first inspection of Table 3and of the diagrams A,B,and C in Figure 1shows that the interaction strengths differ markedly from one system to another depending on the structural features of the receptors involved.L 4is the receptor that presents the highest capacity for interacting with glutamate throughout all of the pH range explored.It must also be remarked that there are not clear-cut trends in the values of the stepwise constants as a function of the protonation degree of the receptors.This suggests that charge -charge attractions do not play the most(25)(a)Martell,E.;Smith,R.M.Critical Stability Constants ;Plenum:NewYork,1975.(b)Motekaitis,R.J.NIST Critically Selected Stability Constants of Metal Complexes Database ;NIST Standard Reference Database,version 4,1997.Table 1.Protonation Constants of Glutamic Acid and Receptors L 1-L 6Determined in NaCl 0.15mol dm -3at 298.1KreactionGluL 1aL 2aL 3bL 4L 5L 6L +H )L H c 9.574(2)d 9.74(2)8.90(3)9.56(1)9.25(3)9.49(4)9.34(5)L H +H )L H 2 4.165(3)8.86(2)8.27(2)8.939(7)8.38(3)8.11(5)8.13(5)L H 2+H )L H 3 2.18(2)7.96(2) 6.62(3)8.02(1) 6.89(5)7.17(6)7.46(7)L H 3+H )L H 4 6.83(2) 5.85(4)7.63(1) 6.32(5) 6.35(6) 5.97(8)L H 4+H )L H 5 4.57(3) 3.37(4) 2.72(8) 2.84(9) 3.23(9)L H 5+H )L H 6 3.18(3) 2.27(6)∑log K H n L41.135.334.233.634.034.1aTaken from ref 23.b These data were previously cited in a short communication (ref 26).c Charges omitted for clarity.d Values in parentheses are the standard deviations in the last significant figure.Scheme 2.L -Glutamate Acid -BaseBehaviorTable 2.Percentages of the Different Protonated Species at pH 7.4H 1L aH 2LH 3LH 4LL 11186417L 21077130L 3083458L 4083458L 51154323L 6842482aCharges omitted for clarity.A R T I C L E SMiranda et al.826J.AM.CHEM.SOC.9VOL.126,NO.3,2004outstanding role and that other forces contribute very importantly to these processes.26However,in systems such as these,which present overlapping equilibria,it is convenient to use conditional constants because they provide a clearer picture of the selectivity trends.27These constants are defined as the quotient between the overall amounts of complexed species and those of free receptor and substrate at a given pH[eq1].In Figure2are presented the logarithms of the effective constants versus pH for all of the studied systems.Receptors L1and L2with a nonfunctionalized secondary amino group in the side chains display opposite trend from all other receptors. While the stability of the L1and L2adducts tends to increase with pH,the other ligands show a decreasing interaction. Additionally,L1and L2present a close interaction over the entire pH range under study.The tetraaminic macrocycle L3is a better(26)Escartı´,F.;Miranda,C.;Lamarque,L.;Latorre,J.;Garcı´a-Espan˜a,E.;Kumar,M.;Ara´n,V.J.;Navarro,mun.2002,9,936-937.(27)(a)Bianchi,A.;Garcı´a-Espan˜a,c.1999,12,1725-1732.(b)Aguilar,J.A.;Celda,B.;Garcı´a-Espan˜a,E.;Luis,S.V.;Martı´nez,M.;Ramı´rez,J.A.;Soriano,C.;Tejero,B.J.Chem.Soc.,Perkin Trans.22000, 7,1323-1328.Table3.Stability Constants for the Interaction of L1-L6with the Different Protonated Forms of Glutamate(Glu) entry reaction a L1L2L3L4L5L6 1Glu+L)Glu L 3.30(2)b 4.11(1)2HGlu+L)HGlu L 3.65(2) 4.11(1) 3.68(2) 3.38(4) 3Glu+H L)HGlu L 3.89(2) 4.48(1) 3.96(2) 3.57(4) 4HGlu+H L)H2Glu L 3.49(2) 3.89(1) 2.37(4) 3.71(2)5HGlu+H2L)H3Glu L 3.44(2) 3.73(1) 2.34(3) 4.14(2) 2.46(4) 2.61(7) 6HGlu+H3L)H4Glu L 3.33(2) 3.56(2) 2.66(3) 4.65(2) 2.74(3) 2.55(7) 7HGlu+H4L)H5Glu L 3.02(2) 3.26(2) 2.58(3) 4.77(2) 2.87(3) 2.91(5) 8HGlu+H5L)H6Glu L 3.11(3) 3.54(2) 6.76(3) 4.96(3) 4.47(3) 9H2Glu+H4L)H6Glu L 2.54(3) 3.05(2) 3.88(2) 5.35(3) 3.66(4) 3.56(3) 10H2Glu+H5L)H7Glu L 2.61(6) 2.73(4) 5.51(3) 3.57(4) 3.22(8) 11H3Glu+H4L)H7Glu L 4.82(2) 4.12(9)a Charges omitted for clarity.b Values in parentheses are standard deviations in the last significantfigure.Figure1.Distribution diagrams for the systems(A)L1-glutamic acid, (B)L4-glutamic acid,and(C)L5-glutamicacid.Figure2.Representation of the variation of K cond(M-1)for the interaction of glutamic acid with(A)L1and L3,(B)L2,L4,L5,and L6.Initial concentrations of glutamate and receptors are10-3mol dm-3.Kcond)∑[(H i L)‚(H j Glu)]/{∑[H i L]∑[H j Glu]}(1)New1H-Pyrazole-Containing Polyamine Receptors A R T I C L E SJ.AM.CHEM.SOC.9VOL.126,NO.3,2004827receptor at acidic pH,but its interaction markedly decreases on raising the pH.These results strongly suggest the implication of the central nitrogens of the lateral polyamine chains in the stabilization of the adducts.Among the N-functionalized receptors,L4presents the largest interaction with glutamate.Interestingly enough,L5,which differs from L4only in having a phenethyl group instead of a benzyl one,presents much lower stability of its adducts.Since the basicity and thereby the protonation states that L4and L5 present with pH are very close,the reason for the larger stability of the L4adducts could reside on a better spatial disposition for formingπ-cation interactions with the ammonium group of the amino acid.In addition,as already pointed out,L4presents the highest affinity for glutamic acid in a wide pH range,being overcome only by L1and L2at pH values over9.This observation again supports the contribution ofπ-cation inter-actions in the system L4-glutamic because at these pH values the ammonium functionality will start to deprotonate(see Scheme2and Figure1B).Table4gathers the percentages of the species existing in equilibria at pH7.4together with the values of the conditional constant at this pH.In correspondence with Figure1A,1C and Figure S2(Supporting Information),it can be seen that for L1, L2,L5,and L6the prevailing species are[H2L‚HGlu]+and[H3L‚HGlu]2+(protonation degrees3and4,respectively),while for L3the main species are[H3L‚HGlu]+and[H4L‚HGlu]2+ (protonation degrees4and5,respectively).The most effective receptor at this pH would be L4which joins hydrogen bonding, charge-charge,andπ-cation contributions for the stabilization of the adducts.To check the selectivity of this receptor,we have also studied its interaction with L-aspartate,which is a competitor of L-glutamate in the biologic receptors.The conditional constant at pH7.4has a value of3.1logarithmic units for the system Asp-L4.Therefore,the selectivity of L4 for glutamate over aspartate(K cond(L4-glu)/K cond(L4-asp))will be of ca.15.It is interesting to remark that the affinity of L4 for zwiterionic L-glutamate at pH7.4is even larger than that displayed by receptors III and IV(Chart1)with the protected dianion N-acetyl-L-glutamate lacking the zwitterionic charac-teristics.Applying eq1and the stability constants reported in ref17,conditional constants at pH7.4of 3.24and 2.96 logarithmic units can be derived for the systems III-L-Glu and IV-L-Glu,respectively.Molecular Modeling Studies.Molecular mechanics-based methods involving docking studies have been used to study the binding orientations and affinities for the complexation of glutamate by L1-L6receptors.The quality of a computer simulation depends on two factors:accuracy of the force field that describes intra-and intermolecular interactions,and an adequate sampling of the conformational and configuration space of the system.28The additive AMBER force field is appropriate for describing the complexation processes of our compounds,as it is one of the best methods29in reproducing H-bonding and stacking stabiliza-tion energies.The experimental data show that at pH7.4,L1-L6exist in different protonation states.So,a theoretical study of the protonation of these ligands was done,including all of the species shown in5%or more abundance in the potentiometric measurements(Table4).In each case,the more favored positions of protons were calculated for mono-,di-,tri-,and tetraprotonated species.Molecular dynamics studies were performed to find the minimum energy conformations with simulated solvent effects.Molecular modeling studies were carried out using the AMBER30method implemented in the Hyperchem6.0pack-age,31modified by the inclusion of appropriate parameters. Where available,the parameters came from analogous ones used in the literature.32All others were developed following Koll-man33and Hopfinger34procedures.The equilibrium bond length and angle values came from experimental values of reasonable reference compounds.All of the compounds were constructed using standard geometry and standard bond lengths.To develop suitable parameters for NH‚‚‚N hydrogen bonding,ab initio calculations at the STO-3G level35were used to calculate atomic charges compatible with the AMBER force field charges,as they gave excellent results,and,at the same time,this method allows the study of aryl-amine interactions.In all cases,full geometry optimizations with the Polak-Ribiere algorithm were carried out,with no restraints.Ions are separated far away and well solvated in water due to the fact that water has a high dielectric constant and hydrogen bond network.Consequently,there is no need to use counteri-ons36in the modelization studies.In the absence of explicit solvent molecules,a distance-dependent dielectric factor quali-tatively simulates the presence of water,as it takes into account the fact that the intermolecular electrostatic interactions should vanish more rapidly with distance than in the gas phase.The same results can be obtained using a constant dielectric factor greater than1.We have chosen to use a distance-dependent dielectric constant( )4R ij)as this was the method used by Weiner et al.37to develop the AMBER force field.Table8 shows the theoretical differences in protonation energy(∆E p) of mono-,bi-,and triprotonated hexaamine ligands,for the (28)Urban,J.J.;Cronin,C.W.;Roberts,R.R.;Famini,G.R.J.Am.Chem.Soc.1997,119,12292-12299.(29)Hobza,P.;Kabelac,M.;Sponer,J.;Mejzlik,P.;Vondrasek,put.Chem.1997,18,1136-1150.(30)Cornell,W.D.;Cieplak,P.;Bayly,C.I.;Gould,I.R.;Merz,K.M.,Jr.;Ferguson,D.M.;Spelmeyer,D.C.;Fox,T.;Caldwell,J.W.;Kollman,P.A.J.Am.Chem.Soc.1995,117,5179-5197.(31)Hyperchem6.0(Hypercube Inc.).(32)(a)Fox,T.;Scanlan,T.S.;Kollman,P.A.J.Am.Chem.Soc.1997,119,11571-11577.(b)Grootenhuis,P.D.;Kollman,P.A.J.Am.Chem.Soc.1989,111,2152-2158.(c)Moyna,G.;Hernandez,G.;Williams,H.J.;Nachman,R.J.;Scott,put.Sci.1997,37,951-956.(d)Boden,C.D.J.;Patenden,put.-Aided Mol.Des.1999, 13,153-166.(33)/amber.(34)Hopfinger,A.J.;Pearlstein,put.Chem.1984,5,486-499.(35)Glennon,T.M.;Zheng,Y.-J.;Le Grand,S.M.;Shutzberg,B.A.;Merz,K.M.,put.Chem.1994,15,1019-1040.(36)Wang,J.;Kollman,P.A.J.Am.Chem.Soc.1998,120,11106-11114.Table4.Percentages of the Different Protonated Adducts[HGlu‚H j L](j-1)+,Overall Percentages of Complexation,andConditional Constants(K Cond)at pH7.4for the Interaction ofGlutamate(HGlu-)with Receptors L1-L6at Physiological pH[H n L‚HGlu]an)1n)2n)3n)4∑{[H n L‚HGlu]}K cond(M-1)L13272353 2.44×103L2947763 4.12×103L31101324 3.99×102L423737581 2.04×104L51010222 3.51×102L6121224 3.64×102a Charges omitted for clarity.A R T I C L E S Miranda et al. 828J.AM.CHEM.SOC.9VOL.126,NO.3,2004。

In order that the high friction fluid seal and

专利名称：In order that the high friction fluid seal and 发明人：井元智可至,塚本修民,中田悦郎
申请号：JP2007294013
申请日：20071113
公开号：JP5209940B2
公开日：
20130612
专利内容由知识产权出版社提供
摘要：A high-friction fluid seal used for high-friction sealing, comprising a fluid seal lip provided on the working fluid filling side to intercept a working fluid; and a dust lip provided on the working fluid non-filling side (the outer side) of the fluid seal lip to intercept dust coming from the outside, wherein the thickness of a working fluid film formed on the extension stroke by the dust lip is smaller than the thickness of a working fluid film formed on the extension stroke by the fluid seal lip.
申请人：カヤバ工業株式会社
地址：東京都港区浜松町２丁目４番１号世界貿易センタービル
国籍：JP
代理人：特許業務法人広江アソシエイツ特許事務所
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2023届高考英语外刊阅读模拟强化训练：七选五专题二十七

高考英语外刊阅读模拟强化训练七选五专题二十七①Scientists have called for a major clinical trial of a substance added to many energy drinks after studies in animals showed that supplementation might slow the ageing process and promote healthier lives.Researchers found that levels of the micronutrient taurine（牛磺酸）fell substantially with age. _____1___It is unclear whether humans might benefit in the same way–--or whether the required high doses are even safe. ____2____ Particularly it is a fact that taurine occurs naturally in the body and is already used as a supplement at lower doses.____3______ “It will probably be very difficult to look at whether they live longer, but at least we can check if they live healthier for longer,” added the molecular exercise physiologist. Scientists homed in on taurine as a potential driver of the ageing process in 2012 when an analysis of blood compounds found that levels of the amino acid(氨基酸) dropped dramatically with age in mice, monkeys and humans. __4_______Without a major trial to demonstrate the safety or any benefits of taurine supplements, the scientists are not recommending people boost their intake through pills, energy drinks or dietary changes. ___5____ Some energy drinks contain taurine, but the scientists warned that they also contained other substances that might not be safe to consume at high levels.【The Guardian (June 9, 2023)】A. By the age of 60, taurine levels in a typical person had slumped to one-third that seen in five-year-olds, they found.B. What the scientists really need now is a human intervention study.C. However, topping them up to more youthful levels boosted the health of mice and monkeys and even extended mouse lifespans.D. Taurine abundance declines with age and reversal of this decline makes animals live longer and healthier lives.E. Prof Henning said a trial would compare how humans fared after taking daily taurine or placebo supplements.F. But scientists believe the evidence is strong enough to warrant a large-scale trial.G. Taurine is made naturally in the body and is found in meat and shellfish diets, but the healthiest diets are largely plant-based.②Restrictions should be put on bottled water advertising and a 10p tax should be added to shrink-wrapped packs to curb the UK’s 10m bottles-a-day habit, according to campaigners hoping to tackle the plastic pollution crisis.Despite the supposed plastics backlash inspired by TV shows such as the BBC’s Blue Planet, big water brands are forecast to report growth of more than 10% over the next four years, equivalent to an extra 280m bottles. ___1____The creation of dedicated brands has seen annual bottled water consumption in the UK increase from just one 300ml can a head in the mid-1970s to 37 litres a head in 2021.Britons spent £1.6bn on branded and supermarket own-label bottled water in 2021. This used about 3.5bn bottles, or 10m a day. ___2____ Buoyed by advertising, this footprint could be 2.8bnbottles by 2026.While carrying a reusable water bottle has become the norm for many people, the study found that just over-half, or 51%, drink bottled water once a week or more. ____3___“Plastic bottled water is a scar on our society,” said David Hall, the UK managing director of Brita. “Plastic bottled water takes about five seconds to make, five minutes to use, and a staggering 500 years to break down in landfill. ______4___The report recommends the government should treat bottled water in the same way as foods sold in England that are high in fat, salt or sugar, removing them from prominent positioning in shops. On packaging, it says wrappers on multipacks are “tantamount to a plastic bag” and should be treated like them. ____5_____【The Guardian (June 12, 2023)】A. It suggests a 10p charge under existing plastic bag levies or, as with plastic straws and stirrers, a ban.B. The public recommends restricting advertising and promotions and putting environmental labels on bottles.C. With brands the driving force behind the growth, they account for £1bn of sales and 2.5bn bottles.D. Any restrictions on advertising for the category would risk inadvertently driving consumers towards less healthy beverage options.E. The report argued that brand advertising played a “critical” role in burnishing the “desirability” of bottled water.F. It’s one of the main culprits of the worldwide plastic pollution crisis.”G. The research established that more than half of all bottled water was being drunk at home or at work, places where tap water is available.③Welcome to float therapy. Neuroscientists say that it’s one of the most effective ways to recharge the nervous system. And in our hyper-stimulated world, an hour without light, sound or external sensations may be the ultimate luxury. ____1____ They’re dark and quiet inside. The water is so salty. With nothing external to process, the brain has no choice but to power down. You may think of float tanks as a wacky, fringe idea. ___2_____ Researchers are finding that regularly spending time in a float tank can help restore physical and mental health. Studies show it can reduce stress, anxiety and depression, as well as physical pain and blood pressure. It can improve sleep.Neuroscientists began studying the effects of floating in the 1950s, submerging astronauts in upright vats of water while they wore masks with breathing tubes. ____3____ Yet the practice never caught on widely.Now it’s having a revival. ____4____ Prices vary, from $60 an hour at a flotation center in Des Moines to $99 for half an hour at a high-end spa in Miami. Navy SEALs float. So do athletes, cancer patients, veterans with PTSD and business executives.Floating isn’t a silver bullet—and it isn’t for everyone. ____5____ Others find it boring. You don’t necessarily need a tank. You can reap some of the benefits by floating quietly in a pool, pond or lake, researchers say.【The Wall Street Journal (June 15, 2023)】A. And I had the oddly pleasant sensation that I was floating away, down a dark passageway.B. Companies are popping up, offering roomy pods, 7-foot-tall chambers and even open rooms.C. Float tanks are designed to relieve our brain of all auditory, visual or tactile sensations.D. This experience was consistent with a study published this month that shows that the positive effects of a float can last at least 48 hours.E. But floating is actually a growing area of serious study.F. Recreational floating enjoyed a moment in the early 1980s with celebrities and New Agey types.G. Some people are turned off by the idea of being in a constricted space, or worry that sensory deprivation will make them hallucinate.答案CFEAGECGFACEFBG。

Supercritical-extract(超临界)

polymers; • (5) unsaturated fatty acids from fish oils.
Hops(啤酒花 )
unsaturated fatty acids
Properties of supercritical fluids
• A supercritical fluid is any substance above its critical temperature and critical pressure. In the supercritical area there is only one state-of-the-fluid and it possesses both gas- and liquid-like properties.
1）无毒，无腐蚀性，不可燃烧，纯度高且价格低。
2）有优良旳传质性能，扩散系数大，粘度低
3）与其他用作超临界流体旳溶剂相比，CO2 具有相对较低旳临界压力和临界温度，适合于处理某些热敏性生物制品和天然物产品。
在超临界区内，一般将1 ≤ Tr ≤ 1.4， 1 < Pr < 5 旳区域作为超临界CO2旳工作区。在这个区域内，密度对压力及温度都比较敏感，符合萃取对溶剂旳要求。
超临界流体萃取旳热力学基础简介（一）、固体溶质在超临界流体中旳溶解度
y2 = (ps2/p)E
lnE＝(Vs2－2B12)/V
（二）、液体溶质在超临界流体中旳溶解度
x2r2f02 ＝ y2φ2p
超临界流体旳选择性
• 超临界萃取剂旳临界温度越接近操作温度，则溶解度越大。临界温度相同旳萃取剂，与被萃取溶质化学性质越相同，溶解能力越大。所以应该选用与被萃取溶质相近旳超临界流体作为萃取剂。

coca 词频1000英语单词

coca 词频1000英语单词全文共10篇示例，供读者参考篇1Coca-Cola is a super duper yummy drink that lots of people like to drink! Do you know what makes it taste so good? It's because of the secret recipe that the Coca-Cola company keeps super duper top secret!Coca-Cola was invented a long time ago, way back in 1886 by a dude named John Pemberton. He came up with the recipe in his kitchen in Atlanta, Georgia. And guess what? The original Coca-Cola had a little bit of cocaine in it! But don't worry, they took that out a long time ago.Nowadays, Coca-Cola is made with a super special mixture of ingredients including carbonated water, high fructose corn syrup, caramel color, caffeine, and natural flavors. And did you know that Coca-Cola is sold in over 200 countries around the world? That's a whole lot of Coca-Cola!People love to drink Coca-Cola because it's so refreshing, especially on a hot day. Some people even like to mix it with other drinks like rum or whiskey to make yummy cocktails. Andthere are lots of different flavors of Coca-Cola too, like Vanilla Coke, Cherry Coke, and even Coca-Cola Zero for those who want to watch their sugar intake.So next time you're feeling thirsty, grab yourself a nice cold Coca-Cola and enjoy the fizzy, tasty goodness! Cheers toCoca-Cola, the best drink ever!篇2Hi everyone! Today I want to talk to you about Coca-Cola! Have you ever tried this yummy drink before? It's so tasty and refreshing, I love drinking it on a hot summer day.Did you know that Coca-Cola was invented in the United States in 1886? That's over 100 years ago! It was originally made as a medicine, but then people started drinking it just for fun.Coca-Cola is made from a secret recipe that includes carbonated water, sugar, and a special ingredient called "cola nut extract." That's what gives it that unique flavor that we all love.You can find Coca-Cola in almost every country in the world. It's so popular that it's even sold in tiny villages in Africa and remote islands in the Pacific Ocean. Everywhere you go, you can always find a cold can of Coca-Cola waiting for you.Some people say that Coca-Cola is bad for you because it has a lot of sugar in it. But as long as you drink it in moderation, it's just fine. You can even use it to make yummy treats like Coca-Cola floats or Coca-Cola cake.So next time you're thirsty and looking for something delicious to drink, why not reach for a bottle of Coca-Cola? You won't regret it! Cheers!篇3Title: My Favorite Coca-ColaHi everyone! Today I want to talk about my favorite drink –Coca-Cola! Coca-Cola is so yummy and refreshing, I could drink it all day long!First of all, let me tell you about the taste of Coca-Cola. It’s like a party in my mouth! It’s sweet and fizzy, and it makes me feel so happy when I take a sip. I love the way it bubbles in my mouth and tickles my tongue. It’s the best feeling ever!Another reason why I love Coca-Cola is because it comes in so many different flavors. My favorite is the classic Coke, but I also like Cherry Coke and Vanilla Coke. They all taste so good, I can’t decide which one I like the most!I also love the packaging of Coca-Cola. The red and white colors are so bright and cheerful, and the logo is so iconic. Whenever I see a Coca-Cola bottle or can, it makes me smile because I know I’m about to have a great time drinking it.In addition to being delicious, Coca-Cola also reminds me of fun times with my friends and family. Whether we’re having a picnic in the park or watching a movie at home, Coca-Cola always makes the moment even better. It’s like a magic potion that brings everyone together.Overall, Coca-Cola is my absolute favorite drink in the whole wide world. I love everything about it – the taste, the variety of f lavors, the packaging, and the memories it brings. I can’t imagine my life without Coca-Cola, and I hope I never have to!So, do you love Coca-Cola as much as I do? Let me know in the comments below! Cheers to Coca-Cola!篇4Hi everyone! Today, I want to talk about Coca-Cola with you. Have you ever heard of Coca-Cola before? It's a super popular soda drink that people love to drink all around the world.First of all, let me tell you a little bit about the history of Coca-Cola. It was created by a man named John Pemberton in 1886. He made the drink by mixing together a syrup made from sugar, water, caffeine, and some secret ingredients. People loved the taste of Coca-Cola and it quickly became a hit.One of the best things about Coca-Cola is that it comes in so many different flavors. There's regular Coca-Cola, Diet Coke for those who want to watch their sugar intake, and even special flavors like Cherry Coke and Vanilla Coke. You can choose whichever one you like best!Another fun fact about Coca-Cola is that it's not just a drink – it's also a symbol of happiness and friendship. Have you ever seen a Coca-Cola commercial where people are sharing a Coke and having a good time? That's because Coca-Cola wants to spread happiness and bring people together.In conclusion, Coca-Cola is a delicious soda drink that has been enjoyed by people for over a hundred years. Whether you like it cold on a hot day or mixed with ice cream for a special treat, there's a Coca-Cola flavor out there for everyone. So next time you're thirsty, why not crack open a Coke and enjoy a little sip of happiness?篇5Hey guys, today I want to talk to you all about Coca Cola! Do you guys like Coca Cola? My mom always says it's not good for me, but it's so tasty!Did you know that Coca Cola has over 1000 English words written on the label? It's true! There are words like "refreshing," "delicious," and "fun" on the label. These words are supposed to make us feel happy and excited when we drink Coca Cola.But did you know that Coca Cola also has a lot of sugar in it? That's why my mom doesn't want me to drink too much of it. She says it's not good for my teeth and my health. She's right, we should always listen to our parents when it comes to our health.Even though Coca Cola has a lot of sugar, it's still okay to have it once in a while as a treat. Just remember to drink water most of the time to keep yourself healthy and hydrated.So next time you see a bottle of Coca Cola with all those cool English words on it, remember to drink it in moderation and enjoy it as a special treat. And don't forget to brush your teeth afterwards!That's all for today, guys. Thanks for listening to my talk about Coca Cola! Have a great day!篇6Title: My Adventure with Coca-ColaHey guys! Today I want to tell you all about my amazing adventure with Coca-Cola! It all started when I was at the store with my mom and saw a huge display of Coca-Cola bottles. I begged my mom to buy one for me and she finally gave in.As soon as I opened the bottle, I heard a little voice coming from inside. It was the Coca-Cola genie! He told me that I had won a special prize - a trip to the Coca-Cola factory. I was so excited!When I arrived at the factory, I was greeted by a friendly tour guide who showed me all around. I saw how the Coca-Cola is made from start to finish - from mixing the secret recipe to bottling the delicious drink.The best part of the tour was when I got to taste test all the different flavors of Coca-Cola. There were so many to choose from, but my favorite was the classic Coca-Cola. It was so refreshing and fizzy!After the tour, the genie gave me a special Coca-Cola backpack filled with goodies like t-shirts, hats, and my very own Coca-Cola bottle opener. I was so happy and grateful for the amazing experience.I will never forget my adventure with Coca-Cola. It was a day full of fun, laughter, and of course, lots of delicious Coca-Cola. I can't wait to go back again soon and make even more memories with this awesome drink!So, if you ever get the chance to visit a Coca-Cola factory, don't hesitate - you won't regret it! Coca-Cola is not just a drink, it's a whole adventure waiting to happen. Cheers to Coca-Cola, the best drink in the world!篇7Hello everyone! Today I want to talk about Coca-Cola! Have you ever tried this delicious and fizzy drink? It's one of the most popular sodas in the world!Coca-Cola was invented by a guy named John Pemberton in 1886. He mixed together some ingredients like sugar, water, and cola nuts to create this yummy drink. And did you know that the original Coca-Cola recipe actually contained cocaine? Crazy, right?Nowadays, Coca-Cola is sold in over 200 countries around the world. You can find it in almost every grocery store, restaurant, and vending machine. It comes in different flavors like Coca-Cola Classic, Diet Coke, and Coca-Cola Zero Sugar. My favorite is the classic one because it's so refreshing and tasty!But do you know how much sugar is in a can of Coca-Cola? It's a lot! That's why it's not a good idea to drink too much of it. It's okay to have it as a treat once in a while, but you should try to drink more water and other healthy beverages instead.Did you know that Coca-Cola has a secret recipe? It's kept in a vault in Atlanta, Georgia, and only a few people know what it is. Some say it contains special ingredients like vanilla, cinnamon, and orange oils. I wonder what it tastes like!I hope you enjoyed learning some fun facts about Coca-Cola. Remember to drink it in moderation and stay healthy! See you next time!篇8Hey guys, do you know what Coca Cola is? Well, let me tell you all about it! Coca Cola is a super popular drink all around the world. It’s fizzy and sweet and comes in a bunch of different flavors like Coke, Diet Coke, and Coke Zero.Did you know that Coca Cola was first made way back in 1886 by a guy named John Pemberton? He made it in a soda fountain in Atlanta, Georgia. Back then, Coca Cola had a secret ingredient called coca leaves, which gave it a special flavor. But do n’t worry, they took out the coca leaves a long time ago!Nowadays, Coca Cola is sold in over 200 countries and people drink billions of cans and bottles of it every day. It’s so famous that you can find it pretty much anywhere, like at restaurants, movie theaters, and even in vending machines.Some people say that Coca Cola is bad for you because it has a lot of sugar in it. But as long as you don’t drink too much of it, it’s okay to have it as a treat once in a while.So there you have it, the scoop on Coca Cola! It’s a tasty drink that’s been around for a long time and is loved by people all over the world. Just remember, everything in moderation, including Coca Cola!篇9Hello everyone! Today I'm going to talk about Coca-Cola, which is one of the most popular drinks in the world! Have you ever tried Coca-Cola before? It tastes so yummy and refreshing!Coca-Cola was invented by Dr. John Pemberton in 1886. He created the delicious and fizzy drink in Atlanta, Georgia, and it quickly became a hit! Over the years, Coca-Cola has become a household name and is loved by people all around the world.Did you know that Coca-Cola used to contain cocaine in the original recipe? But don't worry, they took it out a long time ago! Now, Coca-Cola is made with carbonated water, sugar, caffeine, phosphoric acid, caramel color, and natural flavorings. It's the perfect drink to enjoy on a hot day or with a tasty meal.Coca-Cola is also famous for its catchy slogans and advertising campaigns. Do you remember the slogan "I'd like to buy the world a Coke" or the Christmas commercials with the polar bears? They always make us smile and feel happy!In addition to the original Coca-Cola, there are many other flavors and variations to choose from. Have you tried Coca-Cola Cherry, Coca-Cola Vanilla, or Coca-Cola Zero Sugar? They all have their own unique taste and are just as delicious as the original.Next time you're thirsty, grab a cold Coca-Cola and enjoy the fizzy goodness! It's the perfect pick-me-up and always puts a smile on your face. Cheers to Coca-Cola, the world's favorite drink!篇10Hey guys, today I want to tell you all about Coca-Cola! Have you ever wondered why it's called Coca-Cola? Well, let me tell you all about it.Coca-Cola was invented way back in 1886 by a guy named John Pemberton. He was a pharmacist and he created this fizzy drink with a special secret recipe. The drink was originally made with coca leaf extract and cola nut extract, which is where the name Coca-Cola comes from.And did you know that Coca-Cola used to contain a little bit of cocaine in it? That's right, back in the old days, they used to put some cocaine in the drink to give it an extra kick. But don't worry, they took the cocaine out a long time ago and now it's just a tasty soda.Coca-Cola became super popular and now you can find it all over the world. It's sold in over 200 countries and people drink billions of bottles and cans of Coca-Cola every day. That's a lot of soda!But it's not just about the drink itself, Coca-Cola is also famous for their advertising. They have all kinds of catchy slogans and commercials that make you want to grab a Coke andshare it with a friend. One of their most famous slogans is "I'd like to buy the world a Coke and keep it company."So next time you see a bottle of Coca-Cola, remember all the history and fun facts behind this iconic drink. And maybe even share a Coke with a friend and enjoy it together. Cheers to Coca-Cola!。

残余SYNTAX评分对左主干病变经皮冠状动脉介入治疗患者预后的影响

中网心血哲病研究 2021 什•3 13第 19 卷 3 Chinese Journal of C ardiovascular Research, March 2021, Vol.l9,No.3•224.临床研究残余SYNTAX评分对左主干病变经皮冠状动脉介入治疗患者预后的影响郭超王心宇许浩博滕浩波袁建松崔锦钢杨伟宪胡奉环吴元乔树宾作者单位:100037北京市，中国医学科学院北京协和医学院国家心血管病中心阜外医院冠心病中心通信作者：乔树资，E-mail:***************【摘要】目的探讨残余SYNTAX评分（residua丨SYNTAX score,rSS)对左主干病变（left main lesion,LM L)接受经皮冠状动脉介入治疗（percutaneous coronary intervention，PC丨）的患5•远期预后的影响方法回顾性分析我院接受LMLCI治疗的患者，收集其临床资料、实验室检查、冠状动脉造影及介人操作资料，并计算其基线SYNTAX评分(baseline SYNTAX score,bSS)和rSS,根据rSS分值进行分为rSS<8、rSS>8两组，所有患荇接受3年随丨方结果高rSS组患荇LM+ T i；病变比例迟高，LM钙化比例电0，左心室射血分数更低、肌酐清除率更低、操作并发症发生率及IABP支持比例更高，预后方面，高rSS与更高的心源性死亡(1.13% 比0.51%，P=0.0458)、支架内血栓(2.36% 比丨.35%,P=0.0440)、所有血运重建（12.43% 比 8.09%,/"=0.0002)、全因死亡+所有心肌梗死+所有的血运重建复合终点（丨9.丨1%比13.29%，/"<0.000丨）和心源性死亡+靶血管相义心肌梗死+靶血管血运重建的M合终点（4.28%比2.789K/MJ.0286)发生率相关回归分析表明，rSSM分、年龄、左心室射血分数是全因死亡+所有心肌梗死+所有的血运®建复合终点发生的独立危险因素结论在接受LM介入治疗的患？[•人群，较巧的残余SYNTAX评分是3年复介终点发生的浊、危险因素【关键词】左主干；经皮冠状动脉介人治疗；预后；SYNTAX评分；残余SYNTAX评分doi ： 10.3969/j.issn. 1672-5301.2021.03.007中图分类号R541.4文献标识码A 文章编号1672-5301(2021)03-0224-07Impact of residual SYNTAX score on prognosis of patients with left main coronary artery diseaseundergoing percutaneous coronary interventionGUO Chao, WANG Xin-yu, XU Hao-bo, TENG Hao-bo, YUAN Jian-song, CU1 Jin-gang, YANG IVei-xian, HUFetig-huan, WLJ Yuan, QIAO S/w-bin. Center o f Coroncny Heart Disease, Fuwai Hospital, National Center forCardiovascular Diseases, Chinese Academy o f Medical Sciences and Peking Union Medical College, Beijing100037, ChinaCorresponding author ： QIAO Shu-bin, E-mail：****************【Abstract】Objective To investigate the impact of residual SYNTAX score on long term prognosis ofpatients with left main coronary artery lesion and received percutaneous coronary intervention. Methods Theclinical data, laboratory examination and characteristics of coronary angiography and intervention of the patientswith left main lesion and received percutaneous coronary intervention were collected and the residual SYNTAXscore were calculated, grouped as rSS<8 and rSS^8. All the patients received follow-up of 3 years. Results Atotal of 3960 cases with LML; and received PCI in our hospital were enrolled in the study. A higher rSS wasrelated with higher incidence of LM and three vessel disease, calcification of LM, procedural complication andIABP support and lower creatinine clearance and LVEF. On long-tenn prognosis, higher rSS was associated withhigher incidences of cardiogenic death ( 1.139f vs. 0.5\c/r,/J=0.0458) , stent thrombosis (2.36^ vs. 1.359f, P=0.0440), any revascularization (12.43% vs. 8.099^, /J=0.0002) and the composite endpoint of all-cause mortality+myocardial infarction + any revascularization (19.1 lCf vs. 13.297r, /)<0.0001 )and the composite endpoint ofcardiovascular mortaIity+ target vessel myocardial infarction +target vessel revascularization (4.289f vs. 2.78%,/,=0.0286). According to multiple regression analysis, rSS^8 and higher age, LVEF were the independent riskfactors of the composite endpoint of all-cause mortality+myocardial infarction+any revascularization. ConclusionI1闺心血管病研究 2021 年3 月第 19 卷第3 朗Chinese Journal o f C ardiovascular Research March 202/ . loU9,No.3In patients with LML and received PCI, a higher residual Syntax Score is an independent risk factor of the 3-year- composite.【Key w o rds】Left main; Percutaneous coronary intervention；Prognosis；SYNTAX score；Residual SYNTAX scoreSYNTAX评分诞生于SYNTAX研究丨丨丨，是基于冠状动脉病变影像学特征而计算得出的评分，可反映病变的范围和复杂程度，作为一种量化工具，有助于血运电建治疗策略的制定，研究证实可较好地预测接受经皮冠状动脉成形术（percutaneous coronary intervention，PCI)患者的远期预后 ;进而衍生出了残余 SYTNAX评分（residual SYNTAX score, rSS)的概念，定义该评分>0为+完全血运重建，rSS n J■客观并量化地体现未经处理的冠状动脉病变程度及复杂性，并反映不完全血运軍:建带来的心肌缺血负担，Li被证实可作为PC丨患者临床预后的预测因素,但目前对左主干(left main,LM)病变人群尚缺少关于rSS对远期预G的相关研究。

Sounds of Planet EXs 177 Saxophones for Kronos 商品说

© 2012-2018 by SOP - All Rights Reserved This document is protected by EU copyright andother intellectual property laws and may not be reproduced, rewritten, distributed, re-disseminated, transmitted, displayed, published or broadcast, directly or indirectly, in any medium without the prior written permission of SoP.Executive Producer/Editor: Grzegorz MarciakSounds of Planet would like to thank you for purchase of sound set called EXs 177 Saxophones for Kronos.Sounds of Planet prepared the sound library EXs 177 Saxophones.This is the library, which offers the highest quality samples of extraordinary instruments, as the saxophones are, and more :- alto saxophone – two different instruments were recorded by two various musicians,- tenor saxophone - two different instruments were recorded by two various musicians,- soprano saxophone- baritone saxophone- trumpetAll samples have been processed in 24-bit technology at 48000 Hz.Ex’s 177 Saxophone s from Sounds of Planet offers the set of sounds consisting of- 128 programs- 32 wave sequences- 393 MB multisamplesSaxophone came into existence in Belgium and its artificer was Antoine Joseph Sax known as Adolphe, who was born era of Napoleon and Beethoven. He was fascinated by the way, in which from ordinary piece of metal the real music is born. He created an instrument, which until today has been fascinating for people and has so irresistible charm. Mr. Sax created the instrument, which allows to freely shape the tone and pitch of the sound, from gentle whisper to loud scream and anything in between. Saxophone combines the best features of orchestral instruments . It has quickly turned out that , that this instrument fits into any kind of music and because of that it has been so popular until now. Programs of EXs 177 Saxophones require the factory preload sounds.Make a copy of all own files in the instrument performing SAVE ALL function- see manualKRONOS_Quick_Starts or KRONOS_Param_Guide.The following instructions are copied from the Kronos Parameter Guide for your convenience:To install an EX s:1. If you downloaded the EXs data, un‐zip the downloaded file. Un‐zipping thearchive will result in a folder containing several different files. Note: Depending on yourbrowser settings, the downloaded file may be unzipped automatically. One of the files in theresulting folder has a name which ends with “tar.gz.” Please do not un‐zip this tar.gz file.2. Copy the un‐zipped folder to a USB storage device.3. Safely disconnect the USB storage device from your computer.4. Connect the USB storage device to the KRONOS.5. Go to the Disk Utility page.6. Using the Drive Select menu at the bottom of the page, select the USB storagedevice. You may need to wait a few seconds after connecting the device before it isrecognized.7. Open the folder containing the EXs data from step 2.8. Select the file whose name ends in .exsins. The “exsins” suffix stands for “EXSIns taller.” For instance, an installer file might be named “EXs177.exsins.” When an .exsins fileis selected, the Load button changes to read Install. Only one EX s can be installed at a time.If Multiple Select is On, Install will be disabled.9. Select Install EXs from the menu, or press the Install button. The system will checkto confirm that the installation files are valid, and that there is sufficient space on the SSD to install the EX s. Next, a dialog box will appear:Found installer for: [EX s name]Space required: [nnn] MBSSD1: [disk name] [nnn] GB available10. Press Install to continue with the installation, or press Cancel to stop without installing. An “are you sure?” message will appear to confirm the installation.11. Press OK to continue with the installation, or press Cancel to stop withoutinstalling. The installation will then begin. This may take a while; a progress bar shows the installation as it proceeds. Next, the newly installed files will be verified. After the verification has completed successfully, the progress bar will disappear, and the installation is complete. The EX s sample data itself is installed on an invisible, protected part of the disk. To use the EX s, you’ll lo ad its associated files (.KSC, PCG etc.); for the location of these files, see the documentation of the specific EX s.Using the newly installed EXsTo use the new EX s:1. Load the newly installed .PCG and .KSC files. Make sure to back up any sounds before over‐writing them in memory.As default, programs EXs177 Saxophone will load to the bank U-FF.Programs of EXs 177 Saxophones require the factory preload sounds.Global “0–3: KSC Auto‐Load”Global “0–4: Sample Management”Disk mode menu command “Load .PCG”Disk mode menu command “Load .KSC”AuthorizationIf an authorization code is required, the EX s will work in demo mode, fading in and out, until the code is purchased and entered into the KRONOS. For more information, see “Global P6: Options Info”.New programs are installed in bank U-FF. Program & Multisample List:Short description of abbreviations used in name of programs reflecting the nature or type of sound :FF (fortissimo) very loud – for example : Alto FFMF (mezzo forte) medium loud - for example : Alto MFPP (pianissimo) very quietly - for example : Alto PPOther examples of used abbreviations:Alto 1 Layer (-Y)Growl P – “P ” on the end means PolyAlto 1 Layer (-Y)Growl M – “M ” on the end means MonoNew WaveSequence are installed in bank U-FF.The following instructions are copied from the Kronos Parameter Guide for your convenience:Uninstall EXsOptional EXs may be uninstalled to reclaim space on the internal disk(s). To do so:1. Go to the Global P6: Options Info page.2. In the list of Installed Options, select the EXs thatyou’d like to remove.3. Select the Uninstall EXs command from the menu.A dialog box will appear: Uninstall [EXs name and number]Delete all of the option’s EXs Samples and Multisamples?4. Press OK to continue. Another dialog box will appear, showing that the uninstall isin progress. After the uninstall is complete, a third dialog box will appear:[EXs name and number] sample data deleted.Related PCG, KSC etc. may remain; delete manually if desired. Only the EXs Multisamples and Drum Samples are removed from the disk. KSC and PCG files can be edited, and so they might contain your personal data; to avoid inadvertently affecting your data, these files are left untouched.5. Press OK to continue.6. If you like, delete the related PCG and KSC filesmanually in Disk mode.。

神奇的精灵一号英语作文

神奇的精灵一号英语作文The Enchanting Wonder of Aurora Borealis.In the celestial realm, amidst the vast expanse of the cosmos, there exists a breathtaking phenomenon that has captivated hearts and minds for centuries: the aurora borealis. This ethereal display of nature's artistry paints the night sky with a kaleidoscope of vibrant hues, creating a celestial masterpiece that leaves stargazers spellbound.The Northern Lights, as they are affectionately known, occur when charged particles from the sun collide with atoms and molecules in the Earth's atmosphere. These particles, primarily electrons and protons, interact with the elements present in the upper atmosphere, causing them to emit photons of light.The specific colors observed in the aurora depend on the type of gas encountered by the particles. Nitrogen, the most abundant element in the atmosphere, produces vibrantshades of green and red. Oxygen, though less common, emits a breathtaking blue or purple hue. The altitude at which the collisions occur also plays a role in the color spectrum, with higher altitudes yielding more intense blues and purples.Aurorae typically occur in the regions surrounding the Earth's magnetic poles, where the magnetic field lines are strongest. This is why they are most commonly observed in the northernmost and southernmost latitudes, forming an auroral oval around the poles. However, during periods of increased solar activity, such as solar storms, the aurora can expand to lower latitudes, offering a rare glimpse of this celestial wonder from unexpected locations.The beauty of the aurora is not solely confined to its vibrant colors. Its dynamic and ever-changing nature adds to its allure. Aurorae can take on various forms, from ethereal curtains of light that shimmer and dance across the sky to pulsating orbs that glow with an otherworldly intensity. This continuous transformation makes each aurora unique and unforgettable.While the aurora borealis is predominantly associated with cold, winter months, its occurrence is not strictly seasonal. Aurorae can be observed throughout the year, but they are more likely to occur during periods of increased solar activity, which peaks around the equinoxes in March and September.Observing the aurora is an experience that combines awe and wonder. For those who have witnessed this natural spectacle firsthand, the memory of its ethereal beauty remains etched in their minds forever. The Northern Lights have inspired countless works of art, literature, and music, captivating imaginations and sparking a sense of awe in people of all ages.Whether you are a seasoned aurora enthusiast or an aspiring stargazer, chasing the aurora can be anexhilarating and rewarding adventure. There are numerous destinations around the world that offer optimal viewing conditions, including Alaska, Canada, Norway, Iceland, and Finland.To enhance your aurora viewing experience, it is essential to choose a location far from artificial light pollution. Dark skies allow for a clearer and more vivid display of the aurora. Additionally, being patient and persistent is key. Aurorae can be unpredictable, and sometimes waiting several nights can be necessary to catch a glimpse of this celestial wonder.When the aurora finally graces the night sky, take a moment to appreciate its breathtaking beauty. Let the vibrant colors and ethereal forms fill you with a sense of awe and wonder. Embrace the magic of the Northern Lights, and allow it to become an unforgettable memory that you will cherish forever.。

高能量断奶指南说明书

High energy weaning – a guide to increasing calories and protein in your baby’s dietThe current guidelines from the Department of Health England recommend weaning from 6 months and onwards. In certain circumstances, it may be appropriate for your child to be weaned before these recommendations. This should only be agreed and supervised by your dietitian. Your child should never be weaned before 17 weeks of age. High energy weaning helps provide extra calorie’s in your child’s food to promote weight gain.Weaning should not be delayed past 6 months of age as babies grow very quickly and require good sources of energy, as well as nutrients such as iron which are not provided in sufficient amounts by breast milk or formula. Biting, chewing and swallowing will also help your baby to develop the muscles that are needed for speech. Your baby may already be on a high energy formula such as SMA High Energy®, Infatrini® or Similac High Energy®. This formula should be continued during weaning, and quantities should NOT be reduced as it is providing essential calories.Signs your baby is ready to weanBabies develop at different rates, and some babies will be ready to wean before others. There are three key signs which indicate your baby is ready for weaning:1. They can stay in a sitting position and are able to hold their head steady2. They can pick up food and put it in their mouths by themselves (this demonstrateshand / eye / mouth coordination).3. They can swallow solids (this will take a little practice).Source: Nutrition & DieteticsReference No: 6683-1Chewing fists, waking in the night or wanting extra milk feeds are not signs of being ready to wean. These are just normal baby behaviours.How to start weaning•Aim to give one teaspoon at one mealtime and build this up to a few teaspoons over a few days.•Start with one meal time per day and increase this to two meal times and then three after a few days or weeks, depending on how well your baby takes toweaning.•Try to use a highchair which they can be strapped into.•Initially, offer baby rice mixed with formula or breast milk.•After a couple of days, move onto pureed fruit or vegetables.•From 6 months, you can give mashed foods and finger foods.Early stage weaning foods (from 17 weeks)Until now, your baby will only have had milk and they will need to develop the skills needed to move food around their mouth and to swallow it.First foods should be purees which are smooth and runny. To start, offer powdered baby rice mixed with breast milk or their usual formula. You can also offer purees made from well cooked vegetables, potatoes or stewed fruits all mixed with breast milk or formula to make them runny. Try offering one new fruit or vegetable per day.Once your child is accepting a few spoons of these foods, start to add higher calorie foods into the puree. Butter, cream, avocado and full fat cream cheese are helpful foods and will add good sources of energy and calories but only need to be added in small amounts. Some foods are naturally higher in energy, such as potato, sweet potato, banana, avocado, lentils, beans, full fat natural yoghurt and dried fruits which have been soaked in water or milk and pureed.Foods to avoid until your baby is 6 months oldHowever, some foods are best avoided until your baby is 6 months old. These include: •Salt: do not add salt to any foods.•Sugar: do not add sugar to any foods.•Eggs should not be given under 6 months. They can be given after 6 months but should be lion-stamped and well cooked.•Nuts and peanuts (unless you have been specifically told to give these by your dietitian). Whole nuts are a choking risk. Nut butters and ground nuts can be given from 6 months onwards.•Meat and fish should not be given until 6 months.These foods should not be given to your baby until they are one year old:•Honey: This should not be given until one year old as it can cause botulism. •Raw or lightly cooked shellfish should be avoided for babies due to the risk of food poisoning.•Shark, swordfish or marlin should be avoided for the first year as they are high in mercury and can affect the development of your baby’s nervous system.These foods should be avoided for longer:•Rice milk or rice drinks should not be given until four and a half years old: these contain arsenic.•Whole or chopped nuts: These are a choking risk, avoid until the age of 5 years old.How to add more calories to your baby’s food➢Add ½ to 1 teaspoons of butter / cheese / cream or oil to 1 - 2 tablespoons of potatoes or vegetables.➢Add 1 teaspoon butter to savoury homemade baby meals or to half a jar of baby food.➢Add 1 teaspoon double cream to sweet homemade baby meals or half a jar of dessert.➢Try to use cheese sauces made with your baby’s usual milk and cheese, and add to pasta, rice or vegetables.➢If they are having a high energy formula, use this to make up cereals, baby rice, milk puddings or dried baby food.➢If you are giving fruit puree, add 1 - 2 tablespoons double cream or full fat custard.➢Always use full fat products.➢After the first couple of weeks, try to offer 2 courses at each meal, even if they only eat a small amount. Give rice pudding, fruit and custard, fruit and yoghurt, or fruit and cream after each meal.RecipesMashed banana with coconut cream¼ banana1 teaspoons coconut creamMash the banana and add the coconut cream. Serve straight away.Mashed avocado¼ avocadoMash until smooth and serveSweet potato with cinnamon1 sweet potato, peeled and cut into chunksA generous pinch of ground cinnamon2 -3 tablespoons single cream or coconut creamBoil the sweet potato until soft. Mash/puree with the cinnamon and add the coconut cream.Peas, potato and mint20g frozen peas70g potato10ml (2 teaspoons) coconut cream2 -3 mint leavesPeel the potatoes and place in a pan of cold unsalted water. Bring to the boil and cook until tender. Drain potatoes and leave to one side. Cook peas in hot water for 2 minutes. Drain and mash the peas through a sieve to get rid of the skins. Add the pea puree and mint leaves to the potatoes and using a stick blender, blend until smooth. If the puree is a little thick, add a small amount of your baby’s usual milk. Put into ice cube trays for portion control and/or freezing for use on another day.Peaches, sultanas and baby rice75g tinned peaches15g sultanas20g baby rice10ml (2 teaspoons) single creamPlace the tinned peaches and sultanas in a pan and simmer on a low heat for 5 minutes. Add in 20g baby rice. Using a stick blender puree until smooth. Add the 2 teaspoons of cream and mix well. Put into ice cube trays for portion control and/or freezing for use on another day.Weaning from 6 months of ageIf you have started weaning earlier than 6 months, your baby will be ready to quickly move to soft mashed foods with a thicker consistency and some small, soft lumps. They may also be able to have soft finger foods.If you are starting to wean at 6 months, you should start with runny purees but quickly move onto lumpier textures at around 7 months of age.From 6 months, there is a wider range of foods which can be introduced to your baby which will provide necessary energy and minerals such as iron:* Meats which are minced or cooked until very soft, such as beef, chicken, pork and lamb.* Boneless fish and seafood, mashed or flaked.* Soft cooked rice, pasta, and noodles.* Bread, toast, chapatti, naan, pitta.* Weetabix®, Shreddies®, porridge and other cereals.* Lentils, beans and chickpeas, blended until smooth.* Eggs: can be soft cooked if stamped with the British Lion, otherwise well-cooked. * Nut or seed butters or pastes. No whole or chopped nuts before the age of five years old.* Full fat dairy such as cheese, yoghurt, fromage frais, custard, rice pudding. Milk in sauces or on cereal, but not as a main drink.* Butter, oils and oil-based spreads.After a few weeks, each meal should have a carbohydrate, protein and a fruit or vegetable portion.Adding extra energy to baby foods from 6 monthsThe latest advice on nuts encourages you to give your baby nuts from 6 months as long as there is no family history of nut allergies. Ensure they are finely ground or smooth nut butters to avoid choking.•If you are using ready-made baby meals, add ½ teaspoon of smooth nut butter to each meal, including baby porridge.•Add a teaspoon of smooth nut butters, coconut cream or plain cream cheese (full fat) or a small pinch of grated cheese to any savoury dishes.From 7 - 8 months, start to increase the lumpiness of textures and offer finger foods as well as puree at mealtimes so babies can feed themselves. Let them play and get messy!RecipesWhite fish, kale, butternut and potato15g white fish30g carrots60g kale35g butternut squash60g potatoChop carrots, butternut, kale and fish. Add them to a pan along with the olive oil and cook on a low heat until soft. Take out a couple of pieces of carrot and fish to be used as finger foods during the meal. Mash or puree the rest. You can loosen the mixture a little if it is too thick by using a little full fat milk or cream.Lentil and vegetables½ small onion100g carrot15g celery2 tablespoons vegetable oil200g sweet potato400ml waterFry the onion, carrot and celery in the oil for 5 minutes until softened. Add lentils and sweet potato and pour over the water. Bring to the boil, turn down the heat and simmer covered for 20 minutes. Puree with a stick blender.Bolognese sauce1 tablespoons olive oil1 small onion1 garlic clove1 carrot100g lean minced beef½ tin tomatoes½ teaspoons tomato puree150ml unsalted chicken stock2 tablespoons tiny pasta shapesFry the chopped onion, garlic, carrot for 5 minutes. Add the minced beef and brown for 5 minutes, stirring occasionally. Stir in the tomatoes, tomato puree and chicken stock. Simmer for 15 minutes. Cook a little pasta, drain and mix with the sauce and puree. Cheesy potato cakes400g mashed potato (fortified with butter and whole milk)40 - 50g of all-purpose flour1 medium egg75g grated cheese50g feta cheese crumbled3 spring onionHandful of spinachMix all the ingredients in a bowl. Divide mixture into 8 portions, to form small cakes. Heat frying pan with a drizzle of oil and teaspoon of butter. Cook on a medium heat until golden brown and flip over, then puree or fork mash.Chocolate and chia seed pudding1 ripe banana80 – 85mls coconut milk2 tablespoons chia seeds1 teaspoons of cocoa powderBlend the banana and coconut milk together as if you were making a smoothie. Add the chia seeds and cocoa powder and blend for a few seconds, you can mix by hand if you prefer. Pour into serving jar and rest in the fridge for 20 - 30 minutes until mixture is custard like in texture. You could prepare this well in advance and keep refrigerated overnight.Are vitamin supplements needed?The Department of Health recommends that all babies, are given a daily supplement containing 8.5 to 10 micrograms of Vitamin D to protect their bone health. Infant formulas are fortified with added Vitamin D, so additional supplements are not required for formula fed babies unless they are consuming less than 500mls (17floz) of formula each day. Vitamin D supplements should be continued until at least 5 years of age.© West Suffolk NHS Foundation Trust。