a r X i v :0710.3946v 1 [h e p -e x ] 21 O c t 2007
Fermilab-Pub-07/560-E
Search for Supersymmetry in Di-Photon Final States at
√
S.-J.Park72,S.K.Park31,J.Parsons71,R.Partridge78,N.Parua55,A.Patwa74,G.Pawloski81,B.Penning23, M.Per?lov38,K.Peters45,Y.Peters26,P.P′e tro?16,M.Petteni44,R.Piegaia1,J.Piper66,M.-A.Pleier22, P.L.M.Podesta-Lerma33,c,V.M.Podstavkov51,Y.Pogorelov56,M.-E.Pol2,P.Polozov37,B.G.Pope66,
A.V.Popov39,C.Potter6,W.L.Prado da Silva3,H.
B.Prosper50,S.Protopopescu74,J.Qian65,A.Quadt22,d,
B.Quinn67,A.Rakitine43,M.S.Rangel2,K.Ranjan28,P.N.Rato?43,P.Renkel80,S.Reucroft64,P.Rich45, M.Rijssenbeek73,I.Ripp-Baudot19,F.Rizatdinova77,S.Robinson44,R.F.Rodrigues3,M.Rominsky76,
C.Royon18, P.Rubinov51,R.Ruchti56,G.Safronov37,G.Sajot14,A.S′a nchez-Hern′a ndez33,M.P.Sanders17,A.Santoro3,
G.Savage51,L.Sawyer61,T.Scanlon44,D.Schaile25,R.D.Schamberger73,Y.Scheglov40,H.Schellman54,
P.Schieferdecker25,T.Schliephake26,C.Schwanenberger45,A.Schwartzman69,R.Schwienhorst66,J.Sekaric50,
H.Severini76,E.Shabalina52,M.Shamim60,V.Shary18,A.A.Shchukin39,R.K.Shivpuri28,V.Siccardi19,
V.Simak10,V.Sirotenko51,P.Skubic76,P.Slattery72,D.Smirnov56,J.Snow75,G.R.Snow68,S.Snyder74, S.S¨o ldner-Rembold45,L.Sonnenschein17,A.Sopczak43,M.Sosebee79,K.Soustruznik9,M.Souza2,B.Spurlock79, J.Stark14,J.Steele61,V.Stolin37,D.A.Stoyanova39,J.Strandberg65,S.Strandberg41,M.A.Strang70,
M.Strauss76,E.Strauss73,R.Str¨o hmer25,D.Strom54,L.Stutte51,S.Sumowidagdo50,P.Svoisky56,A.Sznajder3, M.Talby15,P.Tamburello46,A.Tanasijczuk1,W.Taylor6,J.Temple46,B.Tiller25,F.Tissandier13,M.Titov18, V.V.Tokmenin36,T.Toole62,I.Torchiani23,T.Trefzger24,D.Tsybychev73,B.Tuchming18,C.Tully69,P.M.Tuts71, R.Unalan66,S.Uvarov40,L.Uvarov40,S.Uzunyan53,B.Vachon6,P.J.van den Berg34,R.Van Kooten55, W.M.van Leeuwen34,N.Varelas52,E.W.Varnes46,I.A.Vasilyev39,M.Vaupel26,P.Verdier20,L.S.Vertogradov36, M.Verzocchi51,F.Villeneuve-Seguier44,P.Vint44,P.Vokac10,E.Von Toerne60,M.Voutilainen68,e,R.Wagner69,
H.D.Wahl50,L.Wang62,M.H.L.S Wang51,J.Warchol56,G.Watts83,M.Wayne56,M.Weber51,G.Weber24,
A.Wenger23,f,N.Wermes22,M.Wetstein62,A.White79,D.Wicke26,G.W.Wilson59,S.J.Wimpenny49,
M.Wobisch61,D.R.Wood64,T.R.Wyatt45,Y.Xie78,S.Yacoob54,R.Yamada51,M.Yan62,T.Yasuda51, Y.A.Yatsunenko36,K.Yip74,H.D.Yoo78,S.W.Youn54,J.Yu79,A.Zatserklyaniy53,C.Zeitnitz26,T.Zhao83, B.Zhou65,J.Zhu73,M.Zielinski72,D.Zieminska55,A.Zieminski55,L.Zivkovic71,V.Zutshi53,and E.G.Zverev38
(The D?Collaboration)
1Universidad de Buenos Aires,Buenos Aires,Argentina
2LAFEX,Centro Brasileiro de Pesquisas F′?sicas,Rio de Janeiro,Brazil
3Universidade do Estado do Rio de Janeiro,Rio de Janeiro,Brazil
4Universidade Federal do ABC,Santo Andr′e,Brazil
5Instituto de F′?sica Te′o rica,Universidade Estadual Paulista,S?a o Paulo,Brazil
6University of Alberta,Edmonton,Alberta,Canada,
Simon Fraser University,Burnaby,British Columbia,
Canada,York University,Toronto,Ontario,Canada,
and McGill University,Montreal,Quebec,Canada
7University of Science and Technology of China,Hefei,People’s Republic of China
8Universidad de los Andes,Bogot′a,Colombia
9Center for Particle Physics,Charles University,Prague,Czech Republic
10Czech Technical University,Prague,Czech Republic
11Center for Particle Physics,Institute of Physics,
Academy of Sciences of the Czech Republic,Prague,Czech Republic
12Universidad San Francisco de Quito,Quito,Ecuador
13Laboratoire de Physique Corpusculaire,IN2P3-CNRS,
Universit′e Blaise Pascal,Clermont-Ferrand,France
14Laboratoire de Physique Subatomique et de Cosmologie,
IN2P3-CNRS,Universite de Grenoble1,Grenoble,France
15CPPM,IN2P3-CNRS,Universit′e de la M′e diterran′e e,Marseille,France
16Laboratoire de l’Acc′e l′e rateur Lin′e aire,IN2P3-CNRS et Universit′e Paris-Sud,Orsay,France
17LPNHE,IN2P3-CNRS,Universit′e s Paris VI and VII,Paris,France
18DAPNIA/Service de Physique des Particules,CEA,Saclay,France
19IPHC,Universit′e Louis Pasteur et Universit′e de Haute Alsace,CNRS,IN2P3,Strasbourg,France
20IPNL,Universit′e Lyon1,CNRS/IN2P3,Villeurbanne,France and Universit′e de Lyon,Lyon,France
21III.Physikalisches Institut A,RWTH Aachen,Aachen,Germany
22Physikalisches Institut,Universit¨a t Bonn,Bonn,Germany
23Physikalisches Institut,Universit¨a t Freiburg,Freiburg,Germany
24Institut f¨u r Physik,Universit¨a t Mainz,Mainz,Germany
25Ludwig-Maximilians-Universit¨a t M¨u nchen,M¨u nchen,Germany
26Fachbereich Physik,University of Wuppertal,Wuppertal,Germany
27Panjab University,Chandigarh,India
28Delhi University,Delhi,India
29Tata Institute of Fundamental Research,Mumbai,India
30University College Dublin,Dublin,Ireland
31Korea Detector Laboratory,Korea University,Seoul,Korea
32SungKyunKwan University,Suwon,Korea
33CINVESTAV,Mexico City,Mexico
34FOM-Institute NIKHEF and University of Amsterdam/NIKHEF,Amsterdam,The Netherlands 35Radboud University Nijmegen/NIKHEF,Nijmegen,The Netherlands
36Joint Institute for Nuclear Research,Dubna,Russia
37Institute for Theoretical and Experimental Physics,Moscow,Russia
38Moscow State University,Moscow,Russia
39Institute for High Energy Physics,Protvino,Russia
40Petersburg Nuclear Physics Institute,St.Petersburg,Russia
41Lund University,Lund,Sweden,Royal Institute of Technology and Stockholm University,
Stockholm,Sweden,and Uppsala University,Uppsala,Sweden
42Physik Institut der Universit¨a t Z¨u rich,Z¨u rich,Switzerland
43Lancaster University,Lancaster,United Kingdom
44Imperial College,London,United Kingdom
45University of Manchester,Manchester,United Kingdom
46University of Arizona,Tucson,Arizona85721,USA
47Lawrence Berkeley National Laboratory and University of California,Berkeley,California94720,USA 48California State University,Fresno,California93740,USA
49University of California,Riverside,California92521,USA
50Florida State University,Tallahassee,Florida32306,USA
51Fermi National Accelerator Laboratory,Batavia,Illinois60510,USA
52University of Illinois at Chicago,Chicago,Illinois60607,USA
53Northern Illinois University,DeKalb,Illinois60115,USA
54Northwestern University,Evanston,Illinois60208,USA
55Indiana University,Bloomington,Indiana47405,USA
56University of Notre Dame,Notre Dame,Indiana46556,USA
57Purdue University Calumet,Hammond,Indiana46323,USA
58Iowa State University,Ames,Iowa50011,USA
59University of Kansas,Lawrence,Kansas66045,USA
60Kansas State University,Manhattan,Kansas66506,USA
61Louisiana Tech University,Ruston,Louisiana71272,USA
62University of Maryland,College Park,Maryland20742,USA
63Boston University,Boston,Massachusetts02215,USA
64Northeastern University,Boston,Massachusetts02115,USA
65University of Michigan,Ann Arbor,Michigan48109,USA
66Michigan State University,East Lansing,Michigan48824,USA
67University of Mississippi,University,Mississippi38677,USA
68University of Nebraska,Lincoln,Nebraska68588,USA
69Princeton University,Princeton,New Jersey08544,USA
70State University of New York,Bu?alo,New York14260,USA
71Columbia University,New York,New York10027,USA
72University of Rochester,Rochester,New York14627,USA
73State University of New York,Stony Brook,New York11794,USA
74Brookhaven National Laboratory,Upton,New York11973,USA
75Langston University,Langston,Oklahoma73050,USA
76University of Oklahoma,Norman,Oklahoma73019,USA
77Oklahoma State University,Stillwater,Oklahoma74078,USA
78Brown University,Providence,Rhode Island02912,USA
79University of Texas,Arlington,Texas76019,USA
80Southern Methodist University,Dallas,Texas75275,USA
81Rice University,Houston,Texas77005,USA
82University of Virginia,Charlottesville,Virginia22901,USA and
83University of Washington,Seattle,Washington98195,USA
(Dated:October21,2007)
We report results of a search for supersymmetry(SUSY)with gauge-mediated symmetry breaking in di-photon events collected by the D0experiment at the Fermilab Tevatron Collider in2002–2006.
In1.1fb?1of data,we?nd no signi?cant excess beyond the background expected from the standard model and set the most stringent lower limits to date for a standard benchmark model on the lightest
neutralino and chargino masses of125GeV and229GeV,respectively,at95%con?dence. PACS numbers:14.80.Ly,12.60.Jv,13.85.Rm
Low-scale SUSY is one of the most promising solutions to the hierarchy problem associated with the intrinsic disparity between the electroweak and Planck scales.It postulates that for each known particle there exists a su-perpartner,thereby stabilizing the radiative corrections to the Higgs boson mass.Bosons have fermion super-partners,and vice versa.None of the superpartners have yet been observed,and superpartner masses must there-fore be much larger than those of their partners,i.e., SUSY is a broken symmetry.Experimental signatures of supersymmetry are determined through the manner and scale of SUSY breaking.In models with gauge-mediated supersymmetry breaking(GMSB)[1,2],it is achieved through the introduction of new chiral super-multiplets,called messengers that couple to the ultimate source of supersymmetry breaking and to the SUSY par-ticles.At colliders,assuming R-parity conservation[3], superpartners are produced in pairs(?χ+1?χ?1and?χ±1?χ02 production dominates in most cases)and decay to the standard model particles and next-to-lightest SUSY par-ticle(NLSP),which can be either a neutralino or a slep-ton.In the former case,which is considered in this note,the NLSP decays into a photon and a gravitino (the lightest superpartner in GMSB SUSY models,with mass less than≈1keV).The gravitino is stable,and es-capes detection,creating an apparent imbalance in trans-verse momentum(E/T)in the event.GMSB SUSY?nal states are therefore characterized by two energetic pho-tons and large missing transverse momentum.The dif-ferences in event kinematics between particular GMSB SUSY models result in slightly di?erent experimental sensitivities[1],and to obtain a quantitative measure of limits on SUSY we consider a model referred to as “Snowmass Slope SPS8”[4].This model has only a single dimensioned parameter:an energy scaleΛthat determines the e?ective scale of SUSY breaking.The minimal GMSB parameters correspond to a messenger mass M m=2Λ,the number of messengers N5=1,the ratio of the vacuum expectation values of the two Higgs ?elds tanβ=15,and the sign of the Higgsino mass term μ>0.The neutralino lifetime is not de?ned within the model.For this analysis,it is assumed to be su?ciently short to yield decays with prompt photons.
Searches for GMSB SUSY were carried out by collab-orations at the CERN LEP collider[5]and at the Fer-milab Tevatron collider in both Run I[6]and early in Run II[7,8].The initial limits from CDF and D0for Run II,based on the SPS8model,were combined[9] to yieldΛ>84.6TeV corresponding to the limit on the chargino mass of209GeV,at95%con?https://www.doczj.com/doc/337655348.html,ple-mentary searches for GMSB SUSY with R-parity viola-tion were performed by the H1experiment at HERA[10].
This analysis is an update of that described in Ref.[7], with about a factor of three more data and improved photon identi?cation based on:(i)an electromagnetic (EM)cluster”pointing”algorithm that predicts the ori-gin of a photon with a resolution of about2cm along the beam axis,thereby eliminating the largest instrumental background associated with misreconstruction of the pri-mary interaction vertex,and(ii)an improved track veto requirement that suppresses sources of background with electrons in the?nal state.We also use an improved like-lihood?tter[11]to set limits on the scale parameterΛ. The data in this analysis were recorded using sin-gle EM triggers with the D0detector[12],the main components of which are an inner tracker,liquid-argon/uranium calorimeters,and a muon spectrometer. The inner tracker consists of silicon microstrip and cen-tral scintillating-?ber trackers located in a2T supercon-ducting solenoidal magnet,providing measurements up to pseudorapidities1of|η|≈3.0and|η|≈1.8,respec-tively.The calorimeters are?nely segmented and consist of a central section(CC)covering|η|<1.2and two end-cap calorimeters extending coverage to|η|≈4,all housed in separate cryostats[13].The electromagnetic section of the calorimeter has four longitudinal layers and trans-verse segmentation of0.1×0.1inη?φspace(whereφis the azimuthal angle),except in the third layer,where it is0.05×0.05.The central preshower(CPS)system is placed between the solenoid and the calorimeter cryostat and covers|η|<
～
1.2.The CPS provides precise measure-ment of positions of EM showers.The axes of EM show-ers are reconstructed by?tting straight lines to shower positions measured in the four longitudinal calorimeter layers and the CPS(EM”pointing”).The data for this study were collected between2002and summer2006,us-ing inclusive single EM triggers that are almost100% e?cient to select signal data.The integrated luminos-ity[14]of the sample is1100±70pb?1.
Photons and electrons are identi?ed based on recon-structed EM clusters using calorimetric information and further classi?ed into electron and photon candidates, based on tracking information.The EM clusters are se-lected from calorimeter clusters using the simple cone method(of radius R=
1Pseudorapidity is de?ned as?log(tan(θ
5
ergy in a cone of radius R=0.4,and E EM(0.2)is the EM energy in a cone of radius R=0.2,(iii)the trans-verse,energy-weighted,width of the EM cluster in the third EM calorimeter layer is smaller than0.04rad,and (iv)the scalar sum of the transverse momenta(p T)of all tracks originating from the primary vertex in an an-nulus of0.05 Jets are reconstructed using the iterative,midpoint cone algorithm[15]with a cone size of R=0.5.The missing transverse energy is determined from the energy deposited in the calorimeter for|η|<4and is corrected for the EM and jet energy scales. We selectγγcandidates by requiring events to have two photon candidates,each with transverse energy E T>25GeV identi?ed in the CC with|η|<1.1.We require that at least one of the photon candidates be matched to a CPS cluster,and that the primary vertex be consistent with that of the photon candidate(obtained from the EM pointing).The accuracy of the determina-tion of the photon vertex is measured using photons from ?nal state radiation in Z→eeγdata sample and found to be2.3±0.3cm.The requirement of consistency between the photon and primary vertices ensures correct calcu-lation of the transverse energies and tracking isolation requirements.The accuracy of primary vertex associa-tion is studied in GMSB SUSY Monte Carlo simulated events,where the primary vertex is identi?ed correctly in(98.5±0.1)%of the events while the photon vertex matches the primary vertex in(95.8±0.1)%. To reduce potential bias in the measurement of E/T from mismeasurement of jet transverse momentum, we also require that the jet with the highest E T(if jets are present in the event)be separated from the E/T in az-imuth by no more than2.5radians.This selection yields 2341events(theγγsample). All instrumental backgrounds arise from standard model processes,with either genuine E/T(Wγ,W+jet, and tˉt production)or without inherent E/T(direct pho-ton,multi-jet,and Z→ee production).All these back-grounds are measured using data. The former source always has an electron in the?nal state which is misidenti?ed as a photon.The contribu-tion of this background to the E/T distribution in data can be estimated using an eγsample(selected by re-quiring an electron and a photon candidate and using the same kinematical requirements as for theγγsample) scaled by the probability of an electron-photon misiden-ti?cation which is measured using Z→ee data.First, the E/T distribution in the eγsample must be corrected for the contribution from events with no real E/T.The contribution from Drell-Yan events is taken into account by obtaining the E/T distribution for the ee sample(se-lected by requiring two electron candidates and applying the same kinematical requirements as for theγγsample) which is dominated by Drell-Yan events.The Drell-Yan E/T distribution is further normalized to the number of Z boson events in the eγsample(the latter is determined by?tting the eγinvariant mass spectrum to the Z boson mass peak). The contribution from the multi-jet processes is esti-mated from a data sample(referred to as the QCD sam-ple)selected by requiring two EM clusters that(a)sat-isfy all the kinematic selection used to selectγγsample and(b)satisfy all the photon identi?cation criteria but fail the shower shape requirement.The E/T distribution in the QCD sample is normalized to the number of the events in the eγsample with E/T<12GeV after subtrac-tion of the Drell-Yan contribution as determined above. The expected number of Wγ,W+jet,and tˉt events with E/T<12GeV is negligible. After the Drell-Yan and multi-jet contributions to the eγsample are subtracted,the resulting E/T distribution is scaled by(1??trk)/?trk,where?trk is the e?ciency of the track-matching requirement to obtain the estimate of E/T distribution for the background with genuine E/T. The background from events with no inherent E/T is divided into multi-jet events with two real isolated pho-tons and events where one or both photons are misiden-ti?ed jets.Since the E/T resolution for both sources is dominated by the photon energy resolution,the E/T distributions for the two sources are very similar. However,misidenti?ed jets have a di?erent energy re-sponse compared with that of real photons which leads to a slight di?erence in the shapes of the E/T distributions. For the real di-photon events,the E/T is assumed to have the same shape as that of the Drell-Yan events. For misidenti?ed jets,the shape of the E/T distribution is taken from the QCD sample.Relative normaliza-tion of the two sources is obtained using a?t to the E/T distribution in theγγsample.We check that the ?t is not sensitive to possible signal contribution,and cross-check with a method that estimates theγγsam-ple purity using the measured shower shape in the CPS. The relative fraction of di-photons is(60±20)%and this uncertainty is propagated as a systematic uncer-tainty for the limit setting.Absolute normalization of the E/T distributions from both sources is determined so 6 FIG.1:The E/T distribution inγγdata with W/Z+γγback-ground(hatched histogram),instrumental background with no genuine E/T:γγ(solid black line)and multi-jet(?lled histogram),and background from processes with genuine E/T and a misidenti?ed electron(cross-hatched histogram). The expected E/T distributions if GMSB SUSY events were present are shown as dotted and dashed lines. that the number of events with E/T<12GeV matches that in theγγsample. The largest physics backgrounds are from Zγγ→ννγγand Wγγ→?γγνprocesses.Contribu-tions from these backgrounds are estimated as0.15±0.06and0.10±0.04events,respectively,using CompHep[16]Monte Carlo simulation,cross-checked with MadGraph[17].The contribution of these back-grounds to the E/T distribution is taken from Monte Carlo simulation,with number of events normalized to the in-tegrated luminosity of the data sample. The E/T distribution for theγγsample,with contri-butions from physics background(W/Z+γγ),and in-strumental background with genuine E/T(processes with misidenti?ed electrons)and no inherent E/T(γγand multi-jet)is given in Fig 1.We also illustrate the E/T distribution expected from GMSB SUSY for two val-ues ofΛ.The number of observed events,as well as expected background and signal from GMSB SUSY for E/T>30GeV and>60GeV are given in Table I. The expected GMSB signal e?ciency is estimated from Monte Carlo simulation generated for several points on the Snowmass Slope(see Table II),covering the neu-tralino mass range from170GeV to280GeV.Al-though?χ+1?χ?1and?χ±1?χ02processes dominate,we con-sider all GMSB SUSY production channels.We used ISAJET7.58[18]to determine SUSY interaction eigen-state masses and couplings.PYTHIA6.319[19]is used to generate the events after determining the sparticle masses,branching fractions and leading order(LO)pro-duction cross sections using CTEQ6L1parton distribu-tions[20].The generated events are processed through a full GEANT-based[21]detector simulation and the same reconstruction code as used for data.The LO signal cross sections are scaled to match the next-to-leading or-der(NLO)prediction using k-factor values(see Table II), extracted from Ref.[22]. The systematic error on the expected number of signal events comes from the uncertainties in photon identi?-cation e?ciency(10%),statistics in MC samples(5%), track veto requirement(3%),and trigger e?ciency(4%). These were obtained using Z→e+e?and Z→e+e?γdecays in data and in MC simulation.Variation of par-ton distribution functions and uncertainty in the total integrated luminosity result in additional4%and6.1% errors in signal yield respectively.The total uncertainty on the background is dominated by statistics. As the observed number of events for all values of E/T is in good agreement with the standard model pre-diction,we conclude that there is no evidence for GMSB SUSY in the data.We set limits on the production cross section by utilizing a likelihood?tter[11]that incorpo-rates a log-likelihood ratio(LLR)test statistic method. This method utilizes binned E/T distributions rather than a single-bin(fully-integrated)value,and therefore ac-counts for the shapes of the distributions,leading to greater sensitivity.The value of the con?dence level for the signal CL s is de?ned as CL s=CL s+b/CL b,where CL s+b and CL b are the con?dence levels for the sig-nal plus background hypothesis and the background-only (null)hypothesis,respectively.These con?dence levels are evaluated by integrating corresponding LLR distri-butions populated by simulating outcomes via Poisson statistics.Systematic uncertainties are treated as un-certainties on the expected numbers of signal and back-ground events,not the outcomes of the limit calculations. The degrading e?ects of systematic uncertainties are re-duced by introducing a maximum likelihood?t to the missing transverse energy distribution.A separate?t is performed for both the background-only and signal-plus-background hypotheses for each data or pseudo-data dis-tribution. The limits are shown in Fig.2together with expected signal cross sections.The observed limits are statistically compatible with the expected limits.The observed upper limit on the signal cross section is below the prediction of the Snowmass Slope model forΛ<91.5TeV,or in terms of gaugino masses,m?χ0 1 <125GeV and m ?χ+ 1 < 229GeV.These represent the most stringent limits on this particular GMSB SUSY model to date. We thank the sta?s at Fermilab and collaborating in-stitutions,and acknowledge support from the DOE and NSF(USA);CEA and CNRS/IN2P3(France);FASI, Rosatom and RFBR(Russia);CAPES,CNPq,FAPERJ, FAPESP and FUNDUNESP(Brazil);DAE and DST (India);Colciencias(Colombia);CONACyT(Mexico); KRF and KOSEF(Korea);CONICET and UBACyT (Argentina);FOM(The Netherlands);Science and Tech- 7 Background events Expected signal events Observed events Genuine E/T No E/T Physics TotalΛ=75TeVΛ=90TeV 7093.7168.2215 1.210.17±0.03 75101.0182.3148 1.200.18±0.03 80108.5198.197.5 1.190.18±0.03 85115.8212.065.4 1.180.19±0.03 90123.0225.841.8 1.170.19±0.03 95130.2239.729.5 1.160.20±0.03 100137.4253.420.6 1.150.20±0.03 105144.5267.014.4 1.140.18±0.03 110151.7280.710.3 1.130.19±0.03 TABLE II:Points on the GMSB Snowmass Slope model: neutralino and chargino masses,cross sections predicted by PYTHIA,k-factors,and reconstruction e?ciencies with total uncertainty. FIG.2:Predicted cross section for the Snowmass Slope model versusΛ.The observed and expected95%C.L.limits are shown in solid and dash-dotted lines,respectively. nology Facilities Council(United Kingdom);MSMT and GACR(Czech Republic);CRC Program,CFI,NSERC and WestGrid Project(Canada);BMBF and DFG(Ger-many);SFI(Ireland);The Swedish Research Council (Sweden);CAS and CNSF(China);Alexander von Hum-boldt Foundation;and the Marie Curie Program. [a]Visitor from Augustana College,Sioux Falls,SD,USA. [b]Visitor from The University of Liverpool,Liverpool,UK. [c]Visitor from ICN-UNAM,Mexico City,Mexico. [d]Visitor from II.Physikalisches Institut,Georg-August- University G¨o ttingen,Germany. [e]Visitor from Helsinki Institute of Physics,Helsinki,Fin- land. [f]Visitor from Universit¨a t Z¨u rich,Z¨u rich,Switzerland. [?]Fermilab International Fellow. [?]Deceased. [1]P.Fayet,Phys.Lett.B70,461(1977);ibid.86,272 (1979);ibid.175,471(1986). [2]M.Dine,A.E.Nelson,Y.Nir,and Y.Shirman,Phys. 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[22]W.Beenakker et al.,Phys.Rev.Lett.83,3780(1999). 函数大全一、数据库函数（13条） 二、日期与时间函数（20条） 三、外部函数（2条） 四、工程函数（39条） 五、财务函数（52条） 六、信息函数（9条） 七、逻辑运算符（6条） 八、查找和引用函数（17条） 九、数学和三角函数（60条） 十、统计函数（80条） 十一、文本和数据函数（28条） 一、数据库函数（13条） 1.DAVERAGE 【用途】返回数据库或数据清单中满足指定条件的列中数值的平均值。 【语法】DAVERAGE(database，field，criteria) 【参数】Database构成列表或数据库的单元格区域。Field指定函数所使用的数据列。Criteria为一组包含给定条件的单元格区域。 2.DCOUNT 【用途】返回数据库或数据清单的指定字段中，满足给定条件并且包含数字的单元格数目。 【语法】DCOUNT(database，field，criteria) 【参数】Database构成列表或数据库的单元格区域。Field指定函数所使用的数据列。Criteria为一组包含给定条件的单元格区域。 3.DCOUNTA 【用途】返回数据库或数据清单指定字段中满足给定条件的非空单元格数目。 【语法】DCOUNTA(database，field，criteria) 【参数】Database构成列表或数据库的单元格区域。Field指定函数所使用的数据列。Criteria为一组包含给定条件的单元格区域。 4.DGET 【用途】从数据清单或数据库中提取符合指定条件的单个值。 【语法】DGET(database，field，criteria) 【参数】Database构成列表或数据库的单元格区域。Field指定函数所使用的数据列。Criteria为一组包含给定条件的单元格区域。 5.DMAX 【用途】返回数据清单或数据库的指定列中，满足给定条件单元格中的最大数值。 【语法】DMAX(database，field，criteria) 【参数】Database构成列表或数据库的单元格区域。Field指定函数所使用的数据列。Criteria为一组包含给定条件的单元格区域。 6.DMIN 【用途】返回数据清单或数据库的指定列中满足给定条件的单元格中的最小数字。 【语法】DMIN(database，field，criteria) 【参数】Database构成列表或数据库的单元格区域。Field指定函数所使用的数据列。Criteria为一组包含给定条件的单元格区域。 7.DPRODUCT 【用途】返回数据清单或数据库的指定列中，满足给定条件单元格中数值乘积。 【语法】DPRODUCT(database，field，criteria) 【参数】同上 excel常用函数及使用方法 一、数字处理 （一）取绝对值：=ABS(数字) （二）数字取整：=INT(数字) （三）数字四舍五入：=ROUND(数字,小数位数) 二、判断公式 （一）把公式返回的错误值显示为空： 1、公式：C2=IFERROR(A2/B2,"") 2、说明：如果是错误值则显示为空，否则正常显示。 （二）IF的多条件判断 1、公式：C2=IF(AND(A2<500,B2="未到期"),"补款","") 2、说明：两个条件同时成立用AND,任一个成立用OR函数。 三、统计公式 （一）统计两表重复 1、公式:B2=COUNTIF(Sheet15!A:A,A2) 2、说明：如果返回值大于0说明在另一个表中存在，0则不存在。 （二）统计年龄在30~40之间的员工个数 公式=FREQUENCY(D2:D8,{40,29} （三）统计不重复的总人数 1、公式：C2=SUMPRODUCT(1/COUNTIF(A2:A8,A2:A8)) 2、说明：用COUNTIF统计出每人的出现次数，用1除的方式把出现次数变成分母，然后相加。 （四）按多条件统计平均值 =AVERAGEIFS(D:D,B:B,"财务",C:C,"大专") （五）中国式排名公式 =SUMPRODUCT(($D$4:$D$9>=D4)*(1/COUNTIF(D$4:D$9,D$4:D$9))) 四、求和公式 （一）隔列求和 1、公式：H3=SUMIF($A$2:$G$2,H$2,A3:G3) 或=SUMPRODUCT((MOD(COLUMN(B3:G3),2)=0)*B3:G3) 2、说明：如果标题行没有规则用第2个公式 （二）单条件求和 1、公式：F2=SUMIF(A:A,E2,C:C) 2、说明：SUMIF函数的基本用法 （三）单条件模糊求和 说明：如果需要进行模糊求和，就需要掌握通配符的使用，其中星号是表示任意多个字符，如"*A*"就表示a前和后有任意多个字符，即包含A。 （四）多条求模糊求和 1、公式：=SUMIFS(C2:C7,A2:A7,A11&"*",B2:B7,B11) 2、说明：在sumifs中可以使用通配符* （五）多表相同位置求和 1、公式：=SUM(Sheet1:Sheet19!B2) 2、说明：在表中间删除或添加表后，公式结果会自动更新。 英语单词惯用法集锦 习惯接动词不定式的动词（V to inf) adore(vi极喜欢) dread （vt.不愿做，厌恶）plan 计划 afford（+to,vt有条件，能承担）endeavour （vt，竭力做到，试图或力图）prefer（vt.宁可；宁愿(选择)；更喜欢）agree 同意endure(忍受.cannot ~ to) prepare准备 aim (vi[口语]打算：) engage (vi.保证，担保；) presume(vt.冒昧；敢于[用于第一人称时为客套话]：) appear (vi.似乎；显得) essay(vt.尝试，试图) pretend(vt.自命；自称；敢于；妄为) apply （申请）expect（期望，希望）proceed（开始，着手，）arrange （vi.做安排，(事先)筹划）fail （vt.未做…；疏忽)promise(许诺，保证做 ask （要求）forget （vt. 忘记）purpose （vt.决心，打算） beg （vt.正式场合的礼貌用语]请(原谅)，请(允许)：I beg to differ.恕我不能赞同）guarantee（保证，担保）refuse（拒绝）bear 承受，忍受hate（[口语]不喜欢；不愿意；）regret （vt. 抱歉；遗憾）begin help （有助于，促进）remember（记住） bother （vi.通常用于否定句]麻烦，费心）hesitate（vi.犹豫；有疑虑，不愿）scheme（策划做）care （vt.想要；希望；欲望[后接不定式，常用于否定、疑问及条件句中]）hope （vt.希望，盼望，期待）seek（vt.谋求，图谋[后接不定式]） cease （停止; 不再(做某事)[正式] intend （打算；想要）seem（似乎，好像[后接不定式或从句]；觉得像是，以为[ choose （意愿；选定；决定）itch start开始claim （vt. 主张；断言；宣称） continue （继续）like 喜欢swear（vt.起誓保证；立誓要做(或遵守） dare （vt.敢，敢于，勇于，胆敢）long（vi.渴望；热望；极想） decline（vt.拒绝，拒不(做、进入、考虑等) manage（设法完成某事）threaten（vt.威胁，恐吓，恫吓）deign （屈尊做）mean（有意[不用进行时）trouble（vi.费心，费神；麻烦）demand（vi.要求，请求：）need （需要）try（设法做） deserve (应得) neglect (疏忽) undertake(承诺,答应，保证) desire （希望渴望）offer（表示愿意(做某事)，自愿；）venture（冒险(做某事））determine（vi.决心，决意，决定，）omit （疏忽，忘记）want 想要 die （誓死做）pine （渴望）wish （希望） 习惯接“疑问词+动词不定式”的动词（有时也包括VN wh-+to do) advise 建议explain 解释perceive 觉察，发觉 answer 答复find 得知，察觉persuade 说服，劝说；使某人相信 ask 询问，问forget 忘记phone 打电话 assure 保证guess 臆测，猜度pray 祈祷 beg 请求，恳求hear 小心聆听（法庭案件）promise 允诺 conceive 想象，设想imagine 以为，假象remember记得 consider 考虑，思考indicate 暗示remind 提醒，使想起 convince 使相信inform告知通知instruct告知，教导 see 看看，考虑，注意decide 解决，决定know 学得，得知 show 给人解释；示范；叙述；discover发现；知道learn 得知，获悉 signal以信号表示doubt 怀疑，不相信look 察看；检查；探明 strike 使想起；使突然想到；使认为suggest 提议，建议tell 显示，表明；看出，晓得；warn 警告，告诫think 想出；记忆，回忆；想出，明白wonder 纳闷，想知道 wire 打电报telegraph 打电报 习惯接动名词的动词（包括v+one’s/one+v+ing) acknowledge 认知，承认…之事实escape免除，避免omit疏忽，忽略 admit 承认，供认excuse 原谅overlook 放任，宽容，忽视adore （非正式）极为喜欢fancy 构想，幻想，想想postpone 延期，搁置 advise 劝告，建议finish完成prefer较喜欢 appreciate 为…表示感激(或感谢)forbid 不许，禁止prevent预防 avoid 逃避forget 忘记prohibit 禁止，妨碍 The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because EXCEL的文本函数REPLACE、FIND和SEARCH 文本中的LEFT、MID、RIGHT、LEN、LENB、SUBSTITUTE有印象不？最后一个类似于替换，你也用过替换命令的，很多时候需要对某个文本中的部分内容进行替换,除了EXCEL原本具有的查找替换功能以外还可以用文本替换函数，而SUBSTITUTE 就是替换函数之一，如果你知道要替换的字符是什么但不知道该字符在文本中的具体位置就可以使用该函数，比如:你好你们好你好，要把你好替换成你不好，条件是被替换的字符串是你好，要替换成你不好，文本中我不确定具体位置就用SUBSTITUTE公式=SUBSTITUTE(A1,"你好","你不好")，字符串:你好你们好你好中,我要把第二个你好替换成你不好呢?也就是说第一个你好我不替换，只替换第二个出现的你好，还是使用SUBSTITUTE,因为我不知道第二个你好的位置在哪 =SUBSTITUTE(A1,"你好","你不好",2)后面的数字2是该函数的第四个参数,代 表替换位置，也就是替换第二个你好，通过组合我们可以完成一些小应用，所以SUBSTITUTE的替换作用还是挺实用的，但我们如何知道一个文本中有几个指定 的字符?这是一个小应用 比如这一串文本中有几个好字?如果知道这个文本中有几个好字? 比如里面有三个好,如果用公式算出来?如何用公式来 整出来?比如原来的字符宽是多少?再判断替换掉好字的文本的宽度，再相减,不就是结果了?不用替换成空格，替换成空 第一步替换好为无=SUBSTITUTE(A1,"好",)，第二步判断已替换的字符长 =len(SUBSTITUTE(A1,"好",))第三步用原来的字符长去减 =len(a1)-len(SUBSTITUTE(A1,"好",))得到最后的答案，len是判断字符长度的，这上次已讲过了,赫赫。=len("abc")结果为3代表abc文本中有三个字符len("中华人民共和国")结果是7代表有7个字符，上次讲了LEFT、MID、RIGHT、LEN、LENB、SUBSTITUTE，len是判断字符长度的,一个字母,一个数字,一个汉字都是 一个字符，lenb是判断字节长的,一个半角字母或数字为一个字节,一个汉字是 两个字节，这个可以看上次的聊天记录吧。现在我来讲一个REPLACE，REPLACE 也是替换函数，他的参数描述是replace(原文本,第几个字符,宽度,替换成的新文本)比如A1="abcde"我要把A1的第2和第3个字符变成x，也就是我要把abcde 变成axde，用replace函数就是=replace(a1,2,2,"x")从a1的第2个位置开始,向右截2个字符宽度,以x来替换，replace一般用在已知道具体的替换位置的 应用 SUMIF 函数的公式语法和用法。 说明 使用SUMIF函数可以对区域中符合指定条件的值求和。例如，假设在含有数字的某一列中，需要让大于5 的数值相加，请使用以下公式： =SUMIF(B2:B25,">5") 在本例中，应用条件的值即要求和的值。如果需要，可以将条件应用于某个单元格区域，但却对另一个单元格区域中的对应值求和。例如，使用公式=SUMIF(B2:B5, "John", C2:C5)时，该函数仅对单元格区域C2:C5 中与单元格区域B2:B5 中等于“John”的单元格对应的单元格中的值求和。注释若要根据多个条件对若干单元格求和，请参阅SUMIFS 函数。 语法 SUMIF(range, criteria, [sum_range]) SUMIF函数语法具有以下参数： range必需。用于条件计算的单元格区域。每个区域中的单元格都必须是数字或名称、数组或包含数字的引用。空值和文本值将被忽略。 criteria必需。用于确定对哪些单元格求和的条件，其形式可以为数字、表达式、单元格 引用、文本或函数。例如，条件可以表示为32、">32"、B5、32、"32"、"苹果" 或TODAY()。 要点任何文本条件或任何含有逻辑或数学符号的条件都必须使用双引号(") 括起来。如果条件为数字，则无需使用双引号。 sum_range可选。要求和的实际单元格（如果要对未在range 参数中指定的单元格求和）。 如果sum_range参数被省略，Excel 会对在range参数中指定的单元格（即应用条件的单元格）求和。 注释 sum_range 参数与range参数的大小和形状可以不同。求和的实际单元格通过以下方法确定：使用sum_range参数中左上角的单元格作为起始单元格，然后包括与range参数大小和形状相对应的单元格。例如： 如果区域是并且sum_range 是则需要求和的实际单元格是 A1:A5 B1:B5 B1:B5 A1:A5 B1:B3 B1:B5 A1:B4 C1:D4 C1:D4 A1:B4 C1:C2 C1:D4 可以在criteria参数中使用通配符（包括问号(?) 和星号(*)）。问号匹配任意单个字符； 星号匹配任意一串字符。如果要查找实际的问号或星号，请在该字符前键入波形符(~)。示例 示例1 如果将示例复制到一个空白工作表中，可能会更容易理解该示例。 如何复制示例？ 1.选择本文中的示例。 1、keep ①keep + 形容词表示“保持” Please keep quite. 请保持安静。 ②keep + 宾语+ 形容词（或介词短语）表示“把……保持在某一状态” We must do everything we can to keep the air clean. 我们必须尽一切所能保持空气清洁。 ③keep sb doing sth 表示“让某人做某事” ——只能用现在分词作宾语补足语，不能用不定式。 He kept us waiting for two hours. 他让我们等了两个小时。 He kept us to wait for two hours. (错误) ④keep on doing sth和keep doing sth 表示“继续做某事，反复做某事”，可换用。 但keep on doing 更强调动作的反复性或做事人的决心。 He keeps on phoning me, but I don’t want to talk to him. Though he failed 3 times, he kept on trying. 他老是给我打电话，但我不想同他讲话。虽然他已失败了3次，但他仍继续干下去。 keep doing sth 经常用于静态动词。 He kept lying in bed all day long. 他整天都躺在床上。 ⑤keep …from doing sth 表示“阻止，使免于” He kept them from fishing in the lake. 他不让他们在那个湖里捕鱼。 2、may not / mustn’t / needn’t / wouldn’t ①may not be 是may be的否定式，意为“可能不是，也许不是” He may be there.他可能在那里。He may not be there.他可能不在那里。 ②must 意为“必须”，mustn’t 意为“千万不可，绝对不可” 所以Must we/I ……?的否定回答要用needn’t—意为“不必” -Must we get there before 11 o’clock？ -No, we needn’t. ③wouldn’t = would not 意为“不会，不愿” I wouldn’t say no. 3、do ①do表示“做”，做某事，常指某种不具体的活动；make表示“制作”，指做出某种具体的东西。 The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中 一动词加-ing 的情况 consider, suggest/advise,look forward to, excuse/pardon admit,delay/put off,fancy avoid,miss,keep/keep on,practise deny,finish,enjoy/appreciate forbid,imagine,risk can't help,mind,allow/permit,escape 考虑建议盼原谅, 承认推迟没得想. 避免错过继续练, 否认完成就欣赏. 禁止想象才冒险, 不禁介意准逃亡. 如：建议：advise,suggest,冒险:risk,献身:devote oneself to 二动词后加doing 和加to do sth. 意思不一样的情况 ①remember doing指记住过去做过的事，remember to do指记住将来要做的事，表示“不要忘记”。 ②forget doing表示忘记过去做过的事，forget to do表示“没有想起做某事”。 ③mean doing表示“意味着做某事”，mean to do表示“打算做某事”。 ④regret doing表示对已做过的事感到后悔，regret to do表示对将要做的事表示遗憾。 ⑤stop doing表示“停止做某事”，stop to do是停止做正在做的事以便去做另外一件事，这里的to do不是stop的宾语而是stop的目的状语。 ⑥try doing表示“尝试做某事”，try to do表示“设法、试图做某事”。 ⑦go on doing表示继续做同一件事，go on to do表示做完一件事后，接下去做另外一件事。 三动词后加to do sth. afford负担得起agree同意appear似乎，显得arrange安排 ask问attempt企图beg请求begin开始 choose选择claim要求decide决定demand要求 desire愿望determine决定expect期望fail不能 forget忘记happen碰巧hate憎恨，厌恶hesitate犹豫 hope希望intend想要learn学习long渴望 love爱manage设法mean意欲，打算need需要 neglect忽视offer提供omit忽略，漏other扰乱；烦恼 定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way... pretend三种易混淆不定式的用法 今天给大家带来了pretend三种易混淆不定式的用法，我们一起来学习吧，下面就和大家分享，来欣赏一下吧。 pretend三种易混淆不定式的用法 1. pretend to do sth .这个短语的意思是假装(将要)去做什么事情，适用于将来时态动作将来假装要去做但不一定去做的状态。 举例: If youpretend to know what you dont know，youll only make afool of yourself.不懂装懂就会闹笑话。(suri的回答) Child pretend to be mother and father in kindergarten.孩子在幼稚园里面假扮父亲和母亲(表将来)(JasoOon的回答) 2. pretend to have done sth .这个短语的意思是假装已经做过了某事，强调事情的一个完成的状态，侧重于假装的事情已经做好了。 举例:I pretend tohave seen nothing，but I cant.我假装自己没有看到任何东西，但是我做不到(侧重于一个完成时态，已经试图去假装没有看到) she pretended to have finished the homeworkwhen she went out and played.当她出门玩的时候她假装自己已经完成了家庭作业。(假装做作业这个动作已经在出门玩之前做完了)(JasoOon的回答)以及怀陌的回答:When the teacher came in，he pretended to havefinished the homework.当老师进来的时候他假装自己已经完成家庭作业了，两者有异曲同工之妙。 3. pretendtobe doing sth 这个短语的意思是假装正在做某事，强调动作的一个进行时态。 举例:They pretend to be reading books when the teacher sneakingly stands at the back door.当老师偷偷地站在后门的时候他们假装正在读书(读书与老师站在后门都是过去进行时 态)(JasoOon的回答) Asmanypeople do，youoftenpretend to be doingwork when actuallyyou arejust wasting time online.像很多人一样，你经常假装正在工作，其实是在上网。 群主补充：昨天和今天已提交作业的同学，做得都很好，全部授予小红花。希望你们再接再厉，不要松懈哟。所以下周一出题者为所有已提交作业的同学或者你们选出的代表。 “tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法 不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke. 江西省南昌市2015-2016学年度第一学期期末试卷 （江西师大附中使用）高三理科数学分析 一、整体解读 试卷紧扣教材和考试说明，从考生熟悉的基础知识入手，多角度、多层次地考查了学生的数学理性思维能力及对数学本质的理解能力，立足基础，先易后难，难易适中，强调应用，不偏不怪，达到了“考基础、考能力、考素质”的目标。试卷所涉及的知识内容都在考试大纲的范围内，几乎覆盖了高中所学知识的全部重要内容，体现了“重点知识重点考查”的原则。 1．回归教材，注重基础 试卷遵循了考查基础知识为主体的原则，尤其是考试说明中的大部分知识点均有涉及，其中应用题与抗战胜利70周年为背景，把爱国主义教育渗透到试题当中，使学生感受到了数学的育才价值，所有这些题目的设计都回归教材和中学教学实际，操作性强。 2．适当设置题目难度与区分度 选择题第12题和填空题第16题以及解答题的第21题，都是综合性问题，难度较大，学生不仅要有较强的分析问题和解决问题的能力，以及扎实深厚的数学基本功，而且还要掌握必须的数学思想与方法，否则在有限的时间内，很难完成。 3．布局合理，考查全面，着重数学方法和数学思想的考察 在选择题，填空题，解答题和三选一问题中，试卷均对高中数学中的重点内容进行了反复考查。包括函数，三角函数，数列、立体几何、概率统计、解析几何、导数等几大版块问题。这些问题都是以知识为载体，立意于能力，让数学思想方法和数学思维方式贯穿于整个试题的解答过程之中。 二、亮点试题分析 1．【试卷原题】11.已知,,A B C 是单位圆上互不相同的三点，且满足AB AC → → =，则A BA C →→ ?的最小值为（ ） A ．1 4- B ．12- C ．34- D ．1- s u m i f s函数多条件求和实 例 Prepared on 22 November 2020 sumifs函数多条件求和实例 内容提要：文章首先介绍sumifs函数基本用法，然后以一个综合的实例来剖析sumifs函数的详细深入使用。 第一部分，sumifs函数用法介绍 excel中sumifs函数是2007以后版本新增的多条件求和函数。 sumifs函数的语法是：SUMIFS(求和区域,条件区域1,条件1,[条件区域2,条件2],...) 说明：[]以内的条件区域2、条件2为可选参数。最多允许127个区域/条件对。 第二部分，sumifs函数实例介绍 项目一：客户A的销售额 =SUMIFS(C2:C10,A2:A10,A2) 项目二：客户A的1月份销售额 =SUMIFS(C2:C10,A2:A10,A2,B2:B10,B2) 项目三：客户A的1月份和3月份销售额 =SUM(SUMIFS(C2:C10,A2:A10,A2,B2:B10,{1,3})) 项目四：客户A和C的销售额 =SUM(SUMIFS(C2:C10,A2:A10,{"A","C"})) 项目五：客户A和C的1月份销售额合计 =SUM(SUMIFS(C2:C10,A2:A10,{"A","C"},B2:B10,B2)) 项目六：客户A的1月份和客户C的3月份销售额合计 =SUM(SUMIFS(C2:C10,A2:A10,{"A","C"},B2:B10,{1,3})) 项目七：客户A和客户C的1月份\3月份\4月份销售额合计 =SUM(SUMIFS(C2:C10,A2:A10,{"A","C"},B2:B10,{1;3;4})) 表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法 【优质文档】sumif函数的使用方法word版本 本文部分内容来自网络整理，本司不为其真实性负责，如有异议或侵权请及时联系，本司将立即删除！ == 本文为word格式，下载后可方便编辑和修改！ == sumif函数的使用方法 sumif函数的使用方法 使用SUMIF函数可以对区域（区域:工作表上的两个或多个单元格。区域中的单元格可以相邻或不相邻。）中符合指定条件的值求和。例如，假设在含有数字 的某一列中，需要让大于5的数值相加，请使用以下公式： =SUMIF(B2:B25,">5") 在本例中，应用条件的值即要求和的值。如果需要，可以将条件应用于某个单 元格区域，但却对另一个单元格区域中的对应值求和。例如，使用公式 =SUMIF(B2:B5,"俊元",C2:C5)时，该函数仅对单元格区域C2:C5中与单元格区 域B2:B5中等于“俊元”的单元格对应的单元格中的值求和。 注释若要根据多个条件对若干单元格求和，请参阅SUMIFS函数。语法 SUMIF(range,criteria,[sum_range]) SUMIF函数语法具有以下参数（参数:为操作、事件、方法、属性、函数或过程 提供信息的值。）：range必需。用于条件计算的单元格区域。每个区域中的 单元格都必须是数字或名称、数组或包含数字的引用。空值和文本值将被忽略。criteria必需。用于确定对哪些单元格求和的条件，其形式可以为数字、表达式、单元格引用、文本或函数。例如，条件可以表示为32、">32"、B5、32、"32"、"苹果"或TODAY()。 要点任何文本条件或任何含有逻辑或数学符号的条件都必须使用双引号(")括起来。如果条件为数字，则无需使用双引号。sum_range可眩要求和的实际单元 格（如果要对未在range参数中指定的单元格求和）。如果sum_range参数被 省略，Excel会对在range参数中指定的单元格（即应用条件的单元格）求和。 注释sum_range参数与range参数的大小和形状可以不同。求和的实际单元格 通过以下方法确定：使用sum_range参数中左上角的单元格作为起始单元格， 然后包括与range参数大小和形状相对应的单元格。例如：如果区域是并且 sum_range是则需要求和的实际单元格是 A1:A5B1:B5B1:B5A1:A5B1:B3B1:B5A1:B4C1:D4C1:D4A1:B4C1:C2C1:D4可以在criteria参数中使用通配符（包括问号(?)和星号(*)）。问号匹配任意单个字符；星号匹配任意一串字符。如果要查找实际的问号或星号，请在该字符前键 入波形符(~)。注解使用SUMIF函数匹配超过255个字符的字符串时，将返回不正确的结果#VALUE!。示例示例1 英语语法顺口溜(巧记). 英语学习 动词为纲“滚雪球” 难易编组抓循环 同类归纳印象深图示介词最直观 混淆多因形音义反义词语成对念 构词方法不可忘习惯用语集中练 词不离句法最好课外阅读莫间断 be 的用法口诀 我用am，你用are，is连着他，她，它； 单数名词用is，复数名词全用are。 变疑问，往前提，句末问号莫丢弃。 变否定，更容易，be后not莫忘记。 疑问否定任你变，句首大写莫迟疑。 时间名词前所用介词的速记歌 年月周前要用in，日子前面却不行。 遇到几号要用on，上午下午又是in。 要说某日上下午，用on换in才能行。 午夜黄昏须用at，黎明用它也不错。 at也用在明分前，说“差”可要用上to， 说“过”只可使用past，多说多练牢牢记， 莫让岁月空蹉跎。 记住f(e)结尾的名词复数 妻子持刀去宰狼，小偷吓得发了慌； 躲在架后保己命，半片树叶遮目光。 巧记48个国际音标 单元音共十二，四二六前中后。 双元音也好背，合口集中八个整。 辅音共计二十八，八对一清又七浊， 四个连对也包括。有气无声清辅音， 有声无气浊辅音，发音特点应掌握。 非谓语动词的一些特殊用法后只接不定式作宾语的一些常用特殊谓语动词动词后，不定式，want, hope和wish， agree, decide, mean, manage, promise, expect, pretend,且说两位算在此， 要记牢，要记住，掌握它们靠自己。 英语学习小窍门 后接动词不定式做宾语补足语省略不定式符号“to”的一些常用特殊动词 一些动词要掌握，have, let和make, 此三动词是使役，“注意”“观察”“听到”see， 还有feel和watch，使用它们要仔细， 后接“宾补”略去“to”，此点千万要牢记 除此之外，还可以掌握“八字言”， 一感feel,二听hear, listen to, 三让have, let, make,四看see, look at, observe, watch 后只接动名词做宾语的一些常用特殊动词 特殊动词接“动名”，使用它们要记清， “放弃”“享受”可“后悔”， “坚持”“练习”必“完成”， “延期”“避免”非“介意” 掌握它们今必行。 动名词在句中的功能及其它 “动名”语法其功能，名词特征有动、形，主宾表定都可作，“动名”、“现分”要认清，“现分”不作“宾”和“主”， 动名作“状”可不行。二词皆可作定语，混为一谈不允许，主谓关系视分词，“动名”一词无此义。 现在分词形式及在句子中的作用（包括过去分词的作用）： 现在分词真好记，动词后面ING。它的作用真不小，可以充当定状表。 还有宾语补足语，忘记此项不可以。 分词做定语的位置及其它 “定分”位置有二条，词前词后定分晓。 单个分词在词前，有时此规有颠倒。 分词短语在词后，“定从”和它互对照。 “现分”动作进行时，“过分”动作完成了。 （注：“定分”：做定语的分词；“定从”：定语从句；“现分”：现在分词；“过分”：过去分词。） 分词做状语在句子中所表示的意义 分词做状语，概有七意义。“ 时间”和“原因”，“结果”与“目的”。 “方式”加“伴随”，“条件”常出席。 且谈其主语，谓语头前的*。 欲要记住它，必须常练习。（*指句子的主语）EXCEL函数表(最全的函数大全)
Excel常用函数及使用方法
英语单词惯用法集锦解析
The way常见用法
EXCEL的文本函数REPLACE、FIND和SEARCH
excel 函数的公式语法和用法
常见动词用法
The way的用法及其含义(二)
动词以及动词短语的用法(动词后加to do 还是doing)
(完整版)the的用法
pretend三种易混淆不定式的用法
“the way+从句”结构的意义及用法
Excel函数之Search函数
sumifs函数多条件求和实例
way 用法
【优质文档】sumif函数的使用方法word版本 (2页)
英语语法用法顺口溜(巧记)
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