a r X i v :h e p -p h /9810551v 1 30 O c t 1998
Di?raction at HERA An Experimentalist’s View
P.Marage
Universit′e Libre de Bruxelles ?CP 230
Boulevard du Triomphe B-1050Brussels Belgium (February 1,2008)
Di?raction studies at HERA are introduced,with reference to other communications to this Conference.Motivations and speci?c features of the experimental approaches are stressed.1
I.INTRODUCTION
Di?ractive scattering of hadrons (see Fig.1)is closely related to elastic scattering and thus to deepest principles of quantum theory,wave-particle duality and unitarity,through the optical theorem and the Froissard and Pumplin bounds (see e.g.
[1,2]).
FIG.1.Di?ractive scattering of hadrons,with double di?ractive dissociation.
In the s -channel approach,di?ractive scattering is explained by the di?erential absorption by the target of the large number of hadronic states which coherently build up the initial state hadron and scatter with di?erent cross sections [3].The implied reorganisation in the outgoing system leads to the production of hadron states with di?erent mass and /or quantum numbers,but obeying de?nite selection rules.Whereas elastic scattering is intimately related to the amount of inelastic scattering (optical theorem)and happens over the full target volume,di?ractive scattering is due to ?uctuations in the inelastic amplitudes.It is of a peripheral character,since the absorption cross sections for the di?erent hadronic states vary more in the outer (“grey”)region of the target than in the center (“black”)core.A limitation of the s -channel approach is that it does not provide ab initio calculations but requires,for any practical purpose,the use of badly known cross sections and of non-diagonal scattering properties.
In the t -channel approach [1],the scattering properties are related to the characteristics of exchanged virtual particles (with t the squared four-momentum of the exchange),using general properties of unitarity,crossing symmetry and analyticity of the amplitudes.In particular,the energy dependence of the cross section is governed by the spin of the exchanged particles.In a generalised form,this leads to the concept of “Regge trajectories”:in the t ?angular momentum plane,real particles (with squared mass t >0)and virtual states (with t <0)are observed to lie on linear trajectories,characterised by a de?nite set of quantum numbers and parameterised as
α(t )=α(0)+α′·t.
(1)
For the exchange of a given trajectory,the cross section depends on the centre of mass energy squared s as
σ∝sα(0)?1.(2)
This approach met tremendous success in the description of total,elastic,single-and double-di?raction scattering cross sections(see e.g.[2,4–6]).In particular,the celebrated Donnachie-Landsho?parameterisation[7]describes the elastic cross section for numerous reactions in terms of the exchange of two main trajectories:the reggeon trajectory, related to theρmeson family,of the form
αI R(t)?0.55+0.9t,(3)
t being measured in GeV2,and the pomeron trajectory,of the form2
αI P(t)?1.08+0.25t,(4)
which carries the quantum numbers of the vacuum and to which no known particle is associated(except maybe for a glueball candidate[9]).At high energy,elastic and di?ractive scattering are dominated by pomeron exchange,which leads to a slow increase of the cross section with s.
In spite of this success,the need of considering multi-reggeon and cut exchange led to intricated mathematics.More fundamentally,questions concerning the nature of the pomeron and the lack of a microscopic theory led in the70’s to“the death of the Reggeon approach”[10].
With the advent of QCD as the theory of strong interactions,models were proposed in order to understand di?raction in this framework.In the simplest form,the pomeron was modelised as a two-gluon system[11],and this approach was actively pursued by several authors.At the end of the80’s,the observation by the UA8experiment of jet production in di?ractive pˉp scattering[12]con?rmed the assumption by Ingelman and Schlein[13]that the pomeron may be built of partons subjected to hard scattering.
The major discovery of the ZEUS and H1experiments in deep inelastic scattering(DIS)was the observation in 1992that the proton structure function F2(Q2,x)is sharply rising for small x values(i.e.high energy).This“hard”behaviour,observed even for low Q2values[14,15]contrasts with the“soft”behaviour of high-energy hadron?hadron cross sections(eq.4).
FIG.2.A typical di?ractive DIS event in the H1detector.The electron is scattered on the right,in the backward electro-magnetic calorimeter.No activity is detected in the forward part of the liquid argon calorimeter nor in the forward detectors, in particular the forward muon detectors,on the left.
A second major result was the “Observation of Events with a
Large Rapidity Gap in Deep Inelastic Scattering at HERA”by ZEUS using a sample of ?25nb ?1accumulated in 1992[16],con?rmed by H1with 300nb ?1of data taken in 1993[17].These large rapidity gap (LRG)events,attributed to di?raction,were observed to make a contribution to the DIS cross section at a level of 8?10%,with a leading twist Q 2dependence.They are characterised (see an example in Fig.2)by the absence of activity in the “forward”part of the detectors.3In contrast,for non-di?ractive “usual”DIS events,a colour string extends through the forward region,connecting the proton remnant and the struck quark,which leads to particle emission.
It is true to say [18]that this observation was a surprise for many experimentalists:few papers dealing with di?raction in DIS were presented at the 1987and 1991Workshops on HERA physics [19],no di?ractive Monte Carlo in DIS was available,and the detectors were not well equipped for di?ractive studies (nor for low-x physics in general).It was also true to state,as written in the ?rst experimental HERA paper on di?raction,that “until recently,Regge theory and perturbative QCD have been subjects without much overlap”[16].
In the last few years,however,considerable progress have been made in both experimental and theoretical research,as testi?ed by the large number of published papers and of workshops devoted to di?raction.In addition to HERA,di?raction has been intensively studied at the Fermilab Tevatron [20].Interactions between experimentalists and theorists have intensively developed,the complexity of the subject making the guidance of experiment important for the progress of theory.
II.INCLUSIVE MEASUREMENTS OF THE DIFFRACTIVE CROSS SECTION
Huge e?orts have been invested by the experimental collaborations to achieve a precise measurement of the inclusive di?raction cross section at https://www.doczj.com/doc/015530050.html,mon de?nitions of the relevant variables have been accepted,the concept of “di?ractive structure functions”has emerged as a useful tool and,most important,experimental procedures and their inter-relations have been discussed and clari?ed (in particular the question of non-di?ractive background subtractions),in order to de?ne precisely and unambiguously the object of the studies.
A.Kinematics;Di?ractive Structure Functions
Y
X
X (M )FIG.3.Deep-inelastic di?ractive interaction.
Di?ractive ep interactions are sketched in Fig.3.The characteristic feature is that the ?nal state hadronic system,
with centre of mass energy W ,4is divided into two subsystems of signi?cantly lower mass,separated by a large gap in rapidity:the system X ,of mass M X ,which corresponds to photon dissociation,and the system Y ,of mass M Y ,which consists in a proton or an excited baryonic state,with small transverse momentum p T ?
3
In the HERA convention,the “forward”(+z )direction is that of the outgoing proton beam;unless stated otherwise,the transverse direction is de?ned here with respect to the beam direction.4
Here,the mass W is always supposed large ,i.e.W ?M p ,M p being the proton mass.Note that the centre of mass hadronic energy is called W in deep-inelastic scattering and √s is the e ?p centre of mass energy.
the hadronisation process for non-di?ractive interactions,and is thus attributed to the exchange of a colour-singlet system,speci?cally reggeon or pomeron.5
In the particular case where the proton remains intact,the di?ractive process
e+p→e+X+p(5) is de?ned,up to an azimuthal angle between the electron and the proton scattering planes,by four kinematical variables.These are conveniently chosen as Q2,x I P,βand t,where Q2is the negative of the squared four-momentum of the photon,t is the squared four-momentum transfer to the proton,and x I P andβare de?ned as
x I P=1?x L?
Q2+M2X
Q2+M2X
,(7)
x L being the fraction of the incident proton energy carried by the scattered proton.
The variable x I P can be interpreted,in the proton in?nite momentum frame,as the fraction of the proton momentum carried by the exchange(reggeon or pomeron)andβis the fraction of the exchanged momentum carried by the quark struck by the photon.These variables are related to the x scaling variable(with W2?Q2/x?Q2)by the relation
x=β·x I P.(8)
Kinematics imply that,at high energy,a large gap in rapidity is created between the system X and the scattered proton when x I P?1,i.e.M X?W.
In analogy with non-di?ractive DIS scattering,the measured cross section is expressed in the form of a four-fold
di?ractive structure function F D(4)
2
(Q2,x I P,β,t):
d4σ(e+p→e+X+p)
βQ4(1?y+
y2
5As will be mentioned below(section III B),approaches have also been proposed for LRG event production which do not refer to di?raction as a speci?c process,but are based on colour reorganisation through soft processes.
6The measurement of R D would be of great interest,since various models make di?erent predictions for the longitudinal cross section(see the review[23]).
7The term di?raction is often used,in a wide sense,for events with a large rapidity gap;strictly speaking,it applies to pomeron exchange.
B.Rapidity Gap Measurement Method;Reggeon Contribution
H1 1994 Data
0.1
P F x I 2
D (3)
00.1
00.1
00.1
00.1
00.1
0.1
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
P
x I FIG.4.H1measurement of x I P ·F D (3)
2(Q 2,x I P ,β)(M Y <1.6GeV,|t |<1GeV 2)as a function of x I P for various Q 2
and βvalues,with the 1994data.The curves show the results of the Regge ?t with interference.The dashed curves show the contributions from the pomeron alone,the dotted curves,the pomeron plus interference,and the continuous curves,the total.
A natural way to study di?raction experimentally is to select events with a large rapidity gap,since the latter is kinematically related to small values of x I P and thus,at high energy,to pomeron exchange.
This procedure is used by the H1experiment,which takes advantage of a good coverture of the forward region.Speci?cally,events are selected,for which hadronic activity is observed in the central detectors,whereas the pseu-dorapidity 8of the most forward track or energy deposit in the central calorimeter is ηmax =3.2and no activity is registered in the “forward detectors”,i.e.the “plug”calorimeter,the forward muon detectors and the proton remnant tagger.These detectors overlap in acceptance and are sensitive to primary particles emitted at small angle and to secondaries due to rescatterings in the beam pipe wall or adjacent collimators.For these events,no hadron emission is thus observed in the large rapidity region 3.2<η<7.5.The selected sample is consequently restricted to events with an elastically scattered proton or a low mass (M Y ～<1.6GeV)proton dissociation system (the latter contribute
a few %of the selected events),with |t |～<1GeV 2
.
The ZEUS experiment has similarly selected,in the 1993data sample,events with ηmax =2.5,using only the main calorimeter.The implied relatively small gap in rapidity (the calorimeter extends up to η?3.8)required the use of Monte Carlo simulations to estimate the contamination of non-di?ractive events with a gap due to particle density ?uctuation during hadronisation and of events with proton dissociation.
With the integrated luminosity of 300?500nb ?1accumulated in 1993,the H1and ZEUS experiments could present
a ?rst measurement of the di?ractive structure function F D (3)2as a function of x I P ,for di?erent bins in Q 2
and β[21,24].Within the measurement precision,factorisation in the sense of eqs.10and 11was observed.
The integrated luminosity of 2pb ?1accumulated in 1994by the H1experiment allowed the measurement of F D (3)
2in a total of 47bins in βand Q 2(0.04<β<0.9and 4.5 accessible x I P range varying from bin to bin (see Fig.4)[25].This measurement has been extended by H1to low Q 2 values (0.4 With the increased precision of these measurements,presented in the sensitive form of the x I P ·F D (3) 2 distribution,the apparent factorisation of eq.10was broken.This feature was explained as due to the superposition of two contributions,corresponding respectively to pomeron and reggeon exchange: F D (3) 2 (Q 2,x I P ,β)=ΦI P (x I P )·F I P 2(Q 2,β)+ΦI R (x I P )·F I R 2(Q 2 ,β)+interf . =x 2· αI P ?1 I P ·F I P 2(Q 2,β)+x 2· αI R ?1 I P ·F I R 2(Q 2,β)+interf . (13) H1 1994 Data 0.020.040.060.080.10.1210 10 P F 2 D (3)x I P x I 10 10 P x I FIG.5.H1measurement of x I P ·F D (3) 2(Q 2,x I P ,β)as a function of x I P for two Q 2 and βvalues,with the 1994data.The lower curves correspond to the reggeon contribution only,the upper curves to the summed reggeon and pomeron contributions. From a Regge ?t of the data to eq.13,the reggeon trajectory intercept is found to be αI R (0)=0.50±0.18,in agreement with the expected value (eq.3),and the pomeron intercept is measured to be αI P (0)=1.20±0.04,higher than for soft interactions (see discussion in section II E).In the case of an incoming virtual state,the strength of the interference between pomeron and reggeon exchange is not known [27];the data are compatible with maximum as well as with no interference [25]. The detailed contributions of pomeron and reggeon exchange are illustrated on Fig.5.The reggeon contribution is larger for larger values of x I P ,which correspond to smaller energy (for given Q 2and βvalues,x I P =x/β?Q 2/[β·W 2 ]).It is also larger for small values of β,which is consistent with the expected decrease with βof the reggeon structure function,following the meson example,whereas the pomeron structure function is observed to be approximately ?at in β(see Fig.12below). Within the precision of the measurement,no evidence is found for factorisation breaking of the pomeron term itself,also when the lower Q 2data are included [26]. C.The ln M 2 X Measurement Method The ZEUS experiment [28–30]has also exploited the fact that di?ractive interactions are characterised by a non-exponentially suppressed rapidity gap.For ?xed values of the hadronic centre of mass energy W ,this corresponds to a non-exponentially suppressed contribution to the M X mass distribution at amall M X ,as reconstructed in the central detector.9The di?ractive contribution is observed in Fig.6for small values of M X ,whereas for large M X the distribution can be parameterised as a single exponential (the falling ?ange at largest M X values is due to detector acceptance). ZEUS 1994 Q 2 =8 G e V 2 Q 2 =27 G e V 2Q =8 G e V Q =27 G e V FIG.6.Distribution of M X (left)and ln M 2 X (right)for the ZEUS 1994data.The shaded histograms show the distribution of events with ηmax <1.5.The straight lines in the right-hand side ?gures give the non-di?ractive contributions as obtained from an exponential ?t to the data. The di?ractive cross section is thus extracted for several Q 2and W intervals (see Fig.7),after subtraction of the exponentially falling non-di?ractive background.The ZEUS detector acceptance implies that events are selected with M Y <5.5GeV.For the selected (M X ,W ,Q 2)bins,x I P is e?ectively kept below 0.01,leading to a negligible contribution of reggeon exchange. d σ/d M X (n b /G e V ) Q 2 = 8 G e V 2 ZEUS 1994 Q 2 = 14 G e V 2Q 2 = 27 G e V 2Q 2 = 60 G e V 2W(GeV) 010******* 05010001020304002468FIG.7.ZEUS measurement of the di?erential cross section d σdif f γ?p →XY /d M X with M Y <5.5GeV as a function of W for several M X and Q 2 values.The solide curves show the result of ?tting the di?ractive cross section for each (W ,Q 2)bin separately as a power of W ;the dashed curves show the result of the ?t when the power of W is assumed to be the same for all bins. D.LPS Measurement;the t Slope Finally,the ZEUS collaboration has also measured the di?ractive structure function,using their leading proton spectrometer (LPS)[31]. The use of proton spectrometers,which detect protons with energy close to the beam energy,provides a clean mea-surement of the di?ractive cross section since the scattered proton is unambiguously tagged,avoiding contaminations due to proton dissociation events and to particle density ?uctuations in the central detector.Another advantage of the LPS is that the proton momentum measurement leads to a direct determination of x I P (see eq.6).However,the drawbacks of the present ZEUS and H1proton spectrometers are the limited statistics (the acceptance is 5?7%)and the limited range in t (0.1～<|t |～<0.4GeV 2 for x I P <0.03),which implies that the cross section estimate requires an extrapolation in t of the measurement. The di?ractive structure function measured by ZEUS with the LPS is presented in Fig.8,together with the ZEUS ln M 2X and a subsample of the H1measurements.Given the large errors,the LPS measurement is in agreement with the other results. x I P F 2D (3) Q 2 = 7.5 G e V 2 ZEUS (Mx) 1994 M N < 5.5 GeV Q 2 = 9 G e V 2 Q 2 = 12 G e V 2 Q 2 = 28 G e V 2 Q 2 = 75 G e V 2 x IP 0.05 0.1 0.05 0.05 0.05 00.05 10 10 10 10 10 10 10 10 10 10 -1 FIG.8.Measurement of x I P ·F D (3) 2(Q 2,x I P ,β)as a function of x I P for various Q 2 and βvalues with the 1994data:ZEUS LPS data (stars),ZEUS data with the ln M 2 X method (solid points),and a subsample of the H1measurements (open squares). Proton spectrometers have also the unique ability of providing a measurement of the t distribution for inclusive events.The ZEUS LPS has been used to measure the t distribution both in photo-and electroproduction [31–33].For 3 ,the t distribution has been measured with the ZEUS LPS to be exponential,with a slope b =7.1±1.0(stat .)±1.2(syst .)GeV ?2. (14) | t | (GeV 2) d N /d |t | (G e V -2) FIG.9.Di?erential t distribution of di?ractive interactions with 3 No Q 2 dependence of the slope is observed in the electroproduction data.A photoproduction measurement gives a very similar value [32].This has to be contrasted with the strong dependence with Q 2of the ρmeson production slope. E.“Soft”and “Hard”Inclusive Di?raction Although “soft”di?raction may be only an “e?ective”concept,it will be used here as referring to a mild energy dependence in the parameterisation of eq.2,typical of hadron ?hadron scattering at high energy (cf.eq.4),in contrast with the stronger energy dependence characterised by a pomeron intercept of the order of 1.2?1.3,as observed in inclusive DIS [14,15]and in di?ractive J/ψproduction [34,35]. In photoproduction,measurements of the inclusive di?ractive cross section have been performed by the H1[36]and ZEUS [37]experiments.In both cases,the energy dependence was found to be consistent with “soft”di?raction.A triple-Regge analysis was performed of the W and M X dependences of the H1data,complemented with lower energy data.While this analysis indicates the presence of a sizeable non-di?ractive contribution,the ?tted pomeron intercept is αI P (0)=1.07±0.05. (15) The description of the ZEUS data in the range 8 the pomeron intercept αI P (0)=1.12±0.09; (16) a substantial non-di?ractive contribution is found to be necessary at low mass. In contrast,in DIS di?ractive scattering,the pomeron intercept αI P (0)is inconsistent with a “soft”value (see Fig.10).The H1measurement is αI P (0)=1.20±0.02(stat .)±0.01(syst .)±0.03(model), (17) with no signi?cant βor Q 2dependence over the range 0.4 similar,also with no signi?cant Q 2dependence over the measured range [29,30](see Fig.10).Both measurements lie signi?cantly above the “soft”pomeron values,although they seem to be below the “hard”values measured in inclusive DIS.This suggests that inclusive di?raction may be putting the stage for interplay between soft and hard processes. Q 2(GeV 2)αI P (0)Q 2(GeV 2) αI P (0) 1 10 10 1 10 10 FIG.10.Measurement of αI P (0)for H1(the measurement limits are indicated as the dotted lines)and for ZEUS (dots). III.PARTONIC STRUCTURE OF DIFFRACTION Given the fundamental aspect of di?raction in hadron ?hadron interactions,its understanding in terms of partons is a major challenge for QCD.This understanding is helped by the use of two complementary pictures:photon hadronic ?uctuations and pomeron structure function.The parton densities in the pomeron extracted from the study of scaling violations can then be extended,under the assumption of factorisation,to the study of inclusive ?nal states and semi-inclusive processes. A.Two Complementary Pictures In a traditional approach of di?raction,LRG events are attributed to the exchange in the t-channel of a colourless object,the pomeron,which is sensitive to hard interactions,is?avour blind and carries the quantum numbers J P C I G=0++0+of the vacuum.In this context,di?ractive interactions can be conveniently visualised in two di?erent Lorentz frames. In the proton rest frame(see Fig.11a,c),or any fast moving frame with respect to the photon,relativistic time dilatation implies that photon?uctuations into hadronic systems(qˉq,qˉq g,etc.),taking place at a long distance from the proton,appear as“frozen”during the(much shorter)interaction time with the proton.In this approach,the di?ractive cross section is thus calculated as the convolution of three factors,corresponding respectively to the(long-lived)photon hadronic structure,the(short time)di?ractive interaction between the photon hadronic components and the proton,and the(long-time)hadronisation and?nal state parton recombination: σD(γ+p→X+Y)= qˉq,qˉq g,... d2b TΨ(γ→qˉq,...)·σ(qˉq,...+p→qˉq,...+p)·Ψ(qˉq,...→hadrons).(18) These calculations are usually performed in the impact parameter space(b T),and only the?rst Fock states(qˉq,qˉq g) are considered.The pomeron is parameterised as a two gluon sytem or a Lipatov ladder,which meets the requirements of colour neutrality and?avour blindness. The pomeron structure function approach is developed in the pomeron(or proton)in?nite momentum frame,and views the pomeron as a colour singlet partonic object emitted from the proton.In this approach,if the concept of ?ux factorisation`a la Ingelman-Schlein[13]holds,the virtual photon probes the pomeron structure similarly to the probing of the proton structure by the photon in“normal”DIS.10The DGLAP equations may then describe the QCD C). evolution of the pomeron structure function(see however below,section III FIG.11.Photon-proton di?ractive interaction:a,c)visualised in a frame moving fast with respect to the photon:the photon ?uctuates in a qˉq(a)or a qˉq g Fock state(c),wich subsequently di?ractively scatters on the proton(here,the pomeron is modelised as a two-gluon system,and only one of the relevant diagrams is shown);b,d)visualised in the Breit frame,the pomeron being parameterised as a qˉq system,with direct photon?quark coupling(b),or as a gg system,with photon-gluon fusion(d). These two complementary pictures of di?raction have of course to be consistent with each other.In a semiclassical approach,they have been shown to be equivalent in the case of soft gluon emission o?the photon(a qˉq+soft g Fock state)[41]. B.Alternative Approaches In recent years,models have been proposed to explain the production of LRG events in excess over expectations for particle ?uctuation,without reference to the speci?c concepts of di?raction or pomeron exchange.Here,the formation of LRG events is seen as a two-step process.The ?rst step is similar to “normal”DIS events,a quark being ejectecd o?the proton by the photon.In a second stage,soft colour interactions (SCI)modify the colour properties of the outgoing system,leading to the formation of two colour-neutral systems separated by a gap in rapidity. In a semi-classical approach [42],the propagation of the struck parton through the proton colour ?eld is accompanied by soft colour rotation which leads,for a fraction of the events,to colour neutralisation. The concept of SCI has also been implemented into the LEPTO Monte Carlo calculation [43]where,before hadroni-sation,parton reconnection takes place through the exchange of soft gluons,leading to the formation of colour neutral systems. C.Parton Distributions in the Pomeron Fig.12presents the 1994H1measurement of x I P ·F D (3) 2(Q 2,x I P ,β)interpolated to x I P =0.003, 11 as a function of βfor several Q 2 values.In strong contrast to the hadron structure function at high x ,the pomeron structure function is large for high βvalues,even for relatively large Q 2.In Fig.13,the H1measurement is shown as a function of Q 2for several βvalues.Scaling violations with a positive slope are observed up to large βvalues,which suggests that the pomeron is dominated by hard gluons. H1 1994 x I P F 2D (3)(x I P =0.003) x I P F 2D (3)(x I P =0.003) β β 00.0500.05 00.0500.0500.0500.0500.0500.0500.0500.0500.0500.0500.0500.050 0.050 0.05FIG.12.H1measurement (1994data)of x I P ·F D (3) 2 (Q 2,x I P ,β)interpolated to x I P =0.003,as a function of βfor several Q 2values.The superimposed curves represent a)a DGLAP ?t with quarks only at the starting scale Q 20=3GeV 2;b)the preferred QCD ?t with quarks and gluons at the starting scale. H1 1994 x I P F 2D (3)(x I P =0.003) x I P F 2D (3)(x I P =0.003) Q 2 / GeV 2 (a)Q 2 / GeV 2 (b)0 0.050 0.0500.0500.0500.0500.0500.0500.0500.0500.050 0.0510 102 0.0510 10 2 FIG.13.H1measurement (1994data)of x I P ·F D (3) 2(Q 2,x I P ,β)interpolated to x I P =0.003,as a function of Q 2 for several βvalues.The superimposed curves represent a)a DGLAP ?t with quarks only at the starting scale Q 20=3GeV 2 ;b)the preferred QCD ?t with quarks and gluons at the starting scale. To analyse quantitatively the pomeron structure,DGLAP ?ts to the 1994di?ractive structure function presented in Fig.4have been performed by H1for the two contributions of eq.13,thus assuming factorisation [25].12The reggeon contribution is parameterised using the pion structure function [44],and two cases are considered for the pomeron structure function.In the ?rst case,only quarks are allowed to contribute at the starting scale Q 20=3GeV 2 (“?t 1”in [25]);this gives a poor χ2:314for 159d.o.f.?see the curves superimposed on Figs.12a,13a.In the second case,gluons are also allowed to contribute at the starting scale,and a good description of the data is obtained:χ2/d .o .f .=176/154?see the curves on Figs.12b,13b. From this DGLAP analysis,parton distributions are extracted.The distributions corresponding to the best ?t to the H1data (“?t 3”in [25])are presented in Fig.14as a function of z ,the pomeron momentum fraction carried by the parton entering the hard interaction (note that β=z for quarks but β≤z for gluons).This distribution shows an enhancement of the gluon contribution at high z for small Q 2values (the turn-over at high z was forced into the ?t in order to avoid a singular behaviour of the gluon distribution).A nearly equally good ?t (“?t 2”in [25]),also presented in Fig.14,is obtained with a gluon distribution ?at in z at the starting scale.In both cases,the gluons amount to ≥80%of the pomeron partonic content in the present Q 2range,and the parton distribution functions are dominated by hard gluons. Similar studies were performed by the ZEUS collaboration [45](see also [46]).In this case,simultaneous ?ts were performed to the F D (3) 2(Q 2,x I P ,β)distributions in DIS and to the jet di?ractive photoprodution cross section.These analyses also lead to the conclusion that gluons dominate the pomeron structure:at a scale of 4GeV 2,the ZEUS analysis indicates that the fraction of the pomeron momentum carried by gluons lies between 0.64and 0.94.Note however that in such a simultaneous ?t,possible factorisation breaking e?ects (e.g.related to secondary interactions of photon remnants with the proton in the resolved regime of photoproduction)are not taken into account,nor a possibly di?erent interplay between “hard”and “soft”di?raction for the two processes. From an empirical point of view,a major merit of these DGLAP analyses is that they provide good ?ts to the data,based on simple assumptions,and that the results can easily be implemented in Monte Carlo simulations in order to test in various semi-inclusive analyses,the universality of the extracted parton distributions. H1 1994 (a) Q 2=4.5 GeV 2 Gluon, fit 3Gluon, fit 2 Light Quarks, fit 3Light Quarks, fit 2 (b) Q 2=12 GeV 2 (c) Q 2=75 GeV 2 00.511.500.511.50 0.511.500.10.20.30.40.50.60.70.80.9 1 FIG.14.Parton distributions for three Q 2values,as obtained from DGLAP ?ts to the 1994H1measurement of x I P ·F D (3)2(Q 2,x I P ,β),as a function of z ,the pomeron momentum fraction carried by the parton entering the hard interaction.The curves represent the gluon contributions for the best ?t (“?t 3”,dashed-dotted curves)and for the case of a ?at gluon contribution at the starting scale (“?t 2”,dashed curves);the lower curves correspond to the light quark contributions. It is important to note however that the use of the DGLAP evolution equation may not be valid over the whole βrange.It has been stressed (see e.g.[38,47])that three di?erent contributions,with di?erent Q 2evolutions,may dominate di?erent βregions:q ˉq g at small β(large M X masses);transversely polarised q ˉq systems in the central β region (0.2～<β～<0.8);longitudinally polarised q ˉq systems for large βvalues,giving a higher twist contribution.The importance of the longitudinal contribution at high βis supported by the observation of a dominant longitudinal cross section for vector meson production (following eq.7,low mass vector mesons are generally produced with large βvalues).A simple DGLAP analysis through the whole kinematic domain can thus be dubious,especially since the superposition of the three contributions could mimic the distributions in Fig.12(see Fig.15,taken from [47]).However,it should be noted that the H1conclusions are basically una?ected if the ?t domain is restricted to β<0.65.13 FIG.15.Shape of the three contributions expected to contribute to inclusive DIS di?raction:qˉq g Fock states at smallβvalues(dashed line,F c);transversely polarised qˉq states at mediumβvalues(dotted line,F a);longitudinally polarised qˉq g states at largeβ,with a higher twist behaviour(dash-dotted line,F b). D.Monte-Carlo Programs:RAPGAP and LEPTO Monte-Carlo programs provide basic tools for experimental studies:they are used to correct the raw data for acceptance,e?ciency and smearing e?ects,and modelise theoretical predictions in a form directly comparable to the measurements. In the?eld of di?raction,two main Monte-Carlo simulations are available for DIS interactions:the RAPGAP and LEPTO programs. The RAPGAP program[52],based on a factorisable pomeron?ux,uses parton distribution functions in the pomeron evolved following the DGLAP equations.At the starting scale,the distributions can be modelised as a qˉq system, following the results of the?ts to the F D(3) 2scaling violations,or any other form.The photon interaction thus takes place directly on a quark in the pomeron(Fig.11b),or via boson-gluon fusion(Fig.11d).In both cases,a“pomeron remnant”is present(a quark in the?rst case,a gluon in the second case).Higher order contributions(e.g.the QCD-Compton diagram),hadronisation processes and QED radiation are incorporated. The LEPTO5.1Monte Carlo program[43]is the implementation of the concept of SCI in the framework of the Lund model.LRG event are produced as for“normal”deep-inelastic scattering,using standard parameterisations of the parton densities in the proton,but parton reconnection by soft gluons,with pure colour exchange and no kine-matics modi?cation,generates neutral partonic https://www.doczj.com/doc/015530050.html,pared to“normal”DIS interactions,the only adjustable parameter in LEPTO5.1is the amount of soft colour interactions,and the program is thus highly constrained. For photoproduction,the POMPYT program[53]is a di?ractive-speci?c extension to PYTHIA,containing both direct and resolved photon interactions. IV.INCLUSIVE AND SEMI-INCLUSIVE FINAL STATE STUDIES The H1and ZEUS collaborations have performed numerous studies of the features of inclusive and semi-inclusive di?ractive?nal states(the photon dissociation system X).The most inclusive studies concern the event shape (thrust and sphericity),charged particle multiplicities(total multiplicity,rapidity distributions,forward-backward correlations),energy?ow and single particle properties(x F distributions,transverse momentum spectra,the“sea-gull”plot).Semi-inclusive studies have been performed of jet and of charm production.These measurements are reviewed in detail in separate contributions to this Conference[54–56],and only motivations and general features of the analyses will be presented in this introduction. Although de?nite theoretical predictions are presently lacking,especially for the overall features of di?ractive?nal states,an experimental study of the data has provided useful informations on the structure of di?raction.This information was gained both through model independent comparisons of the characteristics of di?ractive events with those of other processes,and through the confrontation to the data of Monte Carlo predictions.In particular, RAPGAP calculations are used to test the sensitivity of the?nal state features to the input parton distributions,as obtained from DGLAP?ts to the total inclusive di?ractive cross section(see section III C).The pomeron modelisation as a qˉq system,although inconsistent with the?ts to the structure function measurements,is often used for comparison. A.Expected Qualitative Features of Di?ractive Final States It is useful to contrast,as a?rst order approach,the implications for the hadronic?nal state of two basic underlying parton topologies:two-and three-body?nal states,as illustrated in Fig.11. The left-hand side diagrams(a,c)of Fig.11correspond to the photon?uctuation picture(the strong interaction between the proton and the photon hadronic?uctuations,modelised in the simplest case as two-gluon exchange,is illustrated by one of the relevant diagrams).The right-hand side diagrams(b,d)illustrate the pomeron structure function approach. The upper two?gures correspond to two-body?nal states:the qˉq Fock state of the photon(a),and the qˉq contribution to the pomeron(b). The lower two?gures correspond to three-body?nal states.The left-hand side diagram(c)corresponds to the qˉq g Fock state of the photon.In the right-hand side picture(d),the pomeron is a two-gluon object,which interacts with the photon through boson-gluon fusion(BGF). The characteristic feature of the two-body case is a jetty structure of the X system,aligned with the photon-pomeron direction.Photon?uctuations into qˉq pairs with large transverse momenta(Fig.11a)have small interaction cross section with the proton because this topology corresponds,through the uncertainty principle,to a small transverse distance between the quarks,which thus screen each other and form a nearly colour neutral system when seen from the proton.This screening e?ect damps the large p T contributions,and favours an aligned jet topology.Note that,in the structure function approach for a qˉq pomeron(Fig.11b),QCD-Compton emission can induce an increase of the ?nal state sphericity and the generation of large transverse momenta,but this process is suppressed by an additional power ofαs. Three-body?nal states are characterised by a dominant e?ective colour octet-octet interaction[47].In the qˉq g Fock state picture of Fig.11c,both the fast qˉq system and the soft gluon are colour octets.The topology is similar for Fig.11d,with a forward going qˉq system and a pomeron remnant.The octet-octet interaction between the forward and backward regions in Fig.11c,d leads to an increased activity(energy?ow,particle multiplicity)in the central region,compared to the triplet-triplet case of the two body qˉq?nal states of Fig.11a,b,expected to be close to the e+e?case. B.Inclusive Final States The event shape of di?ractive events has been studied by H1[57]and ZEUS[58,59].The X system is mostly aligned with the photon-pomeron direction.However,a signi?cant fraction of the events have a large P t,the component of the thrust jet momentum transverse to the photon direction in the X system rest frame(see Fig.16a).In addition, for the same kinematic domain,the average thrust value is smaller than for e+e?interactions,and the sphericity is larger(see Fig.16b).14These features suggest that,compared to a basic aligned jet two-parton topology,which is expected to be close to the topology observed in e+e?interactions,higher parton multiplicities are also at work in di?raction.This is con?rmed by the comparison with RAPGAP predictions:thrust values for a purely qˉq pomeron are signi?cantly higher than observed,whereas the gross features of the data are reasonably reproduced by a gluon dominated pomeron,following the parton distributions obtained from the inclusive cross section measurement. FIG.16.H1measurement with the1994data of a)the normalised thrust jet P2t distributions for six M X intervals;b)the average thrust,as a function of1/M X(solid circles);the open squares are for e+e?data,with s(e+e?)=M2X. Both HERA experiments have also measured the momentum distributions of charged particles in the forward (photon)and backward(pomeron)hemispheres of di?ractive events[59,60].These spectra have been compared by H1to those obtained in?xed target non-di?ractive DIS lepton-proton interactions in the same kinematic range (W DIS?M LRG X ).Whereas in DIS a strong asymmetry is observed between the photon hemisphere and the proton remnant region,characterised by a reduced particle emission,the momentum spectra are similar for both hemispheres of LRG events(see Fig.17,left[60]),and they are softer than for DIS.The distribution of the average transverse momentum squared(with respect to the photon direction in the X system rest frame)as a function of x F(“sea-gull”plots?Fig.17,right),show that charged particles in LRG events have larger transverse momentum than in DIS events.These features point towards a signi?cant role of photon?uctuation topologies of the type qˉq g or,equivalently, towards a gluonic pomeron. Multiplicity[61]and energy?ow[60]studies reinforce these conclusions.The central charged particle multiplicity for di?ractive events is signi?cantly higher than for e+e?events(see Fig.18,left),which is attributed to stronger parton radiation in the e?ective octet-octet structure of di?raction than for the triplet-triplet interactions of e+e?data.The role of gluons is con?rmed by the comparison of the data with predictions of the RAPGAP model:the central activity,both for particle multiplicity and energy?ow,is well described by the RAPGAP Monte Carlo when using the parton distributions as obtained from the DGLAP?t to the inclusive cross section measurement,whereas the prediction is signi?cantly too low for a hypothetic qˉq pomeron.Finally,the correlations in the multiplicity distributions between the backward and forward hemispheres in di?ractive DIS(Fig.18,right)are stronger than for e+e?or non-di?ractive lepton hadron interactions,which correspond to triplet-triplet topologies.In contrast,they are of comparable strength to those in soft hadron interactions,where the strong correlations are attributed to the number of overlapping strings in phase space. It must be noted that most features of the di?ractive?nal states are not only well reproduced by a gluon dominated pomeron as implemented in RAPGAP,but also by the LEPTO SCI model.This is consistent with the major role attributed to gluons in di?raction,since the low x parton distribution functions,with an important gluon contribution, are input to the LEPTO model. (left) and , √s?, W (GeV) y M X FIG.18.Left:charged particle multiplicity distribution of DIS LRG events,measured by H1for three intervals of M X, compared to non-di?ractive lepton?proton data and to e+e?interactions,represented by the JETSET calculation.Right: correlations between the backward and forward hemispheres for H1LRG events,compared to non-di?ractive lepton?proton and meson?proton data and to e+e?interactions,represented by the JETSET calculation.The curves are predictions of several Monte Carlo models:RAPGAP with the parton distributions extracted from a DGLAP?t to the inclusive di?ractive cross section(“?t3”)or with quarks only at the starting scale(“?t1”),LEPTO,JETSET. C.Jet and Charm Production The studies of inclusive properties of the di?ractive?nal state are complemented by semi-inclusive studies of the characteristics of jet and charm production in di?raction. The particular interest of these processes is in the presence of a well de?ned hard scale(jet p t or charm mass),which provides an access to perturbative QCD calculations.Unfortunately,the cross section for jet production is small,and stringent experimental selection procedures have to be imposed to select open charm events.The full potential of these processes for understanding hard di?raction has thus not been exploited yet. Jets with transverse momenta larger than5(H1)or6GeV(ZEUS),de?ned with respect to the photon direction in the rest frame of the system X,have been studied in photoproduction both by H1[62]and ZEUS[63],and in DIS by H1[62]. In photoproduction,the distribution of the xγvariable,which describes the fraction of the photon momentum entering the hard interaction,requires the presence of both a direct(xγ?1)and a resolved(xγ<1)contribution (see Fig.19,left). Both for photoproduction and DIS jet production,a sizeable contribution is observed of events where a large fraction z of the pomeron momentum enters the hard interaction;however,the cross section increases as z decreases, suggesting the presence of pomeron remnants(see Fig.19b,right).This supports the hypothesis of a small jet cross section for a qˉq Fock state,due to screening e?ects(see section IV A),as demonstrated by the fact that the predictions of a relevant model[64]and of the RAPGAP Monte Carlo with a qˉq pomeron at the starting scale are signi?cantly too small.The bulk of the data is thus explained by qˉq g states,as expected both in perturbative QCD calculations (see e.g.[38,47])and in a semi-classical approach of soft colour interactions[65]. The results of both experiments support models where the partonic structure of the pomeron is dominated by hard gluons.This is shown by ZEUS using a simultaneous?t of the inclusive di?ractive DIS cross section and of the jet production cross section,and by H1by implementing in the RAPGAP calculation the parton densities obtained from the?ts to the scaling violations in inclusive DIS.H1observes that parton distributions in which the pomeron gluon structure is relatively?at(“?t2”in[25])describe the data better than those in which the gluon distribution is peaked at large z(“?t3”).In resolved photoproduction,a possible underlying interaction between the proton and the photon remnant can be parameterised as a“survival probability”[66].The best description of the combined DIS and photoproduction data is obtained when a rapidity gap survival probability of0.6is applied to the“?at”gluon distribution,but the measurements are a?ected by large uncertainties. 50 100 150 200 250 300 350 400 450 x γ OBS d σ / d x γ O B S [ p b ] 200 400 600 800 1000 1200 1400 1600 z IP jets d σ / d z I P j e t s [ p b ] 10 1 10 10 d σ / d z I P j e t s [ p b ] FIG.19.Left:ZEUS measurement of the cross section of and ?1.5<ηjet<1,as a function of xγ,the fraction of the photon momentum entering the hard interaction;the shaded area represents a systematic uncertainty due to the absolute energy scale of the jets;the curves represent the resolved(dot-dashed line),the direct(dashed line)and the resolved+direct contributions,based on the pomeron parton distribution parameterised as hard quarks and hard gluons,in a joint QCD?t of the inclusive DIS di?ractive cross section and the dijet di?ractive pho-toproduction.Right:H1measurements of the cross section of di?ractive dijet photoproduction(top)and of DIS production (bottom)for p jet T >5GeV and?1<ηjet<2,as a function of z,the fraction of the pomeron momentum entering the hard interaction;the shaded bands show the overall normalisation uncertainties;the data are compared to the predictions of the POMPYT(photoproduction)and RAPGAP(DIS)Monte Carlo models with parton densities dominated by a“?at”(“?t2”) or“peaked”(“?t3”)gluon distribution at the starting scale;in the photoproduction case,the POMPYT prediction for the “?at”distribution is also shown for a survival probability of0.6;in the DIS case,the prediction of a qˉq Fock state calculation is shown as well. 1 2 3 4 5 6 x 10 -2events separated by the interval ?ηin rapidity, with no hadronic activity between the jets,as a function of ?η;the distribution is ?tted as the sum of an exponentially falling contribution (dotted line),attributed to events with “usual”colour exchange properties,and of a constant contribution (dashed line),attributed to colour-singlet exchange between the jets.Right:H1measurement of the cross section,di?erential in x I P , of photoproduction events with four-momentum transfer squared |t |>20GeV 2 ;the solid line is the prediction of a standard photoproduction Monte Carlo;the dashed line is the prediction of a model based on perturbative QCD calculations (with well de?ned slope but uncertain absolute normalisation). Di?ractive exchange is also manifest in a class of events containing jets,and characterised by the absence of hadronic activity between the jets.In photoproduction,both ZEUS and H1have observed a signal for such events, in excess over the exponential fall-o?expected from “usual”colour exchange and hadronisation properties (see Fig.20,left).This signal is attributed to the exchange between the hard partons producing the jets of a coulour-singlet object,presumably the pomeron. Following a suggestion to relax the requirement of observing the two jets in the main detector [69],the H1collab-oration has selected photoproduction events characterised by the presence of a gap in rapidity of at least 1.5units between two systems,X and Y ,of masses M X ,M Y ?W ,with |t |=p 2tX >20GeV 2 [70].In the selected kinematics range,a signi?cant excess of events is observed above the expectation for standard photoproduction processes (see Fig.20,right).The measurement is performed di?erentially in x I P ,and allows direct comparison with predictions based on perturbative QCD calculations [69]:although the absolute nor;alisation is uncertain,the slope is well described,in contrast with the case of “standard”Monte Carlo simulations. ?M / GeV E v e n t s p e r M e V 5101520253035W (GeV) 0.02 0.040.060.080.1 0.12FIG.21.Left:H1measurement of the mass di?erence ?M =M (K ?π+π+ s )?M (K ?π+),exhibiting a clear signal for di?ractive DIS charm production,of 38±10±4events.Right:ZEUS measurement of the fraction of di?ractively produced D ?±mesons,as a function of Q 2and W . Both experiments have also reported the observation of a signal for di?ractive production of open charm in DIS, in the channel D ?+→D 0π+s →(K ?π+)π+s (and the charge conjugate),where the particle noted π+ s is a slow pion [71,72](see Fig.21,left).The fraction of di?ractively produced D ?± mesons is measured by ZEUS to be of 漏斗实验(Funnel Experiment) 在戴明博士四日谈中，以漏斗实验来解释管理与干预问题。管理人员常因缺乏对系统变异的统计思考方式而对系统进行干预，造成问题越变越离谱。譬如，厂内的管理阶层在品质会议中要 求不良率最高的单位提出改善计划或业务会议中要求营业额退步的营业员提出对策。以前国中的 导师每周对学生评分排名，对退步的学生给与严厉的指责警告(现在应该还是一样)。但是以长期 来看不良率依然有高有低；营业额每月仍是有好有坏；学生的排名每周还是有进有退，这些数据 的变异很多是系统的正常变异，也就是所谓共同原因的变异。但是，管理人员对这些变异进行干 预，采取矫正措施，使得系统越变越复杂。例如，制程管理人员隐藏不良品使不良率好看；营业 人员虚报营业额使得帐面上好看；学生到补习班先练习考试题目使得排名进步。以上这些现象在 我们所处的工作或生活环境中屡见不鲜，我们应该先了解系统的变异是来自特殊原因或是共同原 因，再采取适当的行动。 所谓，就是假想我们有一漏斗，装在桌上约半公尺高的架上，桌上有个靶。假设我 们把一颗弹珠放入漏斗，不论我们放下的方式如何，弹珠就会以随机的方式滚下漏斗，然后由漏 斗底部掉下到靶上，再用铅笔在落点做个记号。我们利用一些简单的规则来使漏斗瞄准目标，这 些规则相当于我们在使用设备、流程或系统中作的一些决策规则。 [编辑] 漏斗实验的四种规则： 规则一：每次都不调整漏斗位置(结果：弹珠落点随机分布在目标值两侧) 规则二：根据上一次落点，调整漏斗位置(结果：弹珠落点范围较规则一大了约41%) 规则三：调整前先归回目标值(结果：弹珠落点由两侧大幅散开) 规则四：瞄准上一次的落点(结果：弹珠落点呈随机漫步到天边) 将四个规则仿真的结果绘在同张图上，可以一目了然地比较四种规则的结果。 ：一个漏斗、一粒可以很容易通过漏斗的弹珠、一张桌子，最好铺上桌布。 第一次实验：规则为漏斗位置不变。首先在桌布上标出一点作为目标，开始实验。将漏斗口 瞄准目标点。保持这种状态，将弹珠由漏斗口落下50次，在弹珠每次落下的静止位置作标记。 暴力行为是否属于侵犯行为呢？在判断某行为是否是侵犯行为时，有三个标准：一是个体外在的行为，二是看该行为是否违反社会主流规范，三是个体的内在动机或意图如何。显而易见地，看守的行为动机就是对罪犯进行报复，是故意的，而且也有外在的暴力动作，但是否能将这种暴力行为归于侵犯，我仍有一丝疑虑，因为在实验之初就已经说过，囚犯会丧失部分人权，所以这样的行为有没有违反社会主流规范仍旧存在疑虑，因为“看守看管囚犯，即使他运用了怎样的手段，也是可以理解的”这种思想没有经过调查，不好判断它是否属于社会主流思想。侵犯行为是否与生俱来也是社会心理学界争论的问题。霍尔提出过“挫折——侵犯理论”，他认为挫折是指当一个人为实现某种目标而努力时遭受干扰或破坏，致使需求不能得到满足时的情绪状态，人的侵犯行为是因为个体遭受挫折而引起的。从这个实验来看，如果证实了“看守”的行为的确属于侵犯行为的话，那么可见侵犯行为确实不是与生俱来的。因为在实验之前，他们都是正常人，而是在实验过程中，由于17号的挑战对于监狱管理产生困难与挫折，看守才最终选择了暴力侵犯行为。 关于群体压力。群体借助规范的力量形成的对其成员心理上的强迫力量，就是群体压力，群体借助这种力量达到对群体成员行为的约束作用。看守将17号关入黑屋子的惩罚就是为了造成对囚犯的群体压力。然而群体压力也有积极的意义：增强群体团结，有助于群体任务的完成，对多数成员内心安全感的形成起很大作用。这点明见于最后的囚犯群体大逃亡。但群体心理对于群体内固执己见的少数人 1 ? 陈强,《高级计量经济学及 Stata 应用》课件，第二版，2014 年，高等教育出版社。 第 18 章 随机实验与自然实验 18.1 实 验 数 据 假设研究x 1 是否导致 y 。假定{x 1, x 2 , , x K }包含所有影响 y 的因素。 不同学科采用不同的实验方法，大致分为以下几类。 (1) 控制实验(controlled experiment)：在理想的物理实验中，控制 {x 2 , , x K }全部不变，单独让x 1 变化，观察 y 的变化。 (2) 随机(控制)实验(randomized controlled experiment)： 【例】医学上对新药x 疗效的实验。由于参加实验者的体质与生活 1 方式不同，不可能完全控制所有其他因素{x2 , , x K }。 随机实验将实验人群(或个体)随机地分为两组，其中“实验组”或“处理组”(treatment group)服用真药，而“控制组”(control group，也称“对照组”)服用“安慰药”(placebo)。 被试者不知道自己分在哪一组，避免心理干扰。有时科研人员也不知道被试者在哪一组，称为“双盲法”(double blind)。 【例】农学中将地块随机地分成三组(很难找到土壤条件完全一样的地块)，分别给予不同的施肥量，然后考察施肥的效果。 2 (3)自然实验或准实验(natural experiment or quasi experiment)： 由于某些并非为了实验目的而发生的外部突发事件，使得当事人仿佛被随机地分在了实验组或控制组。 【例】一个州通过某法律，但相邻州未通过此法律。两州民众事先不知道哪个州会通过此法律，故无法自我选择住在哪个州。从考察法律的效果而言，可近似认为民众随机选择住在哪个州，或被随机分为实验组(通过法律)与控制组(没通过法律)。 (4)思想实验(thought experiment)： Milton Friedman 曾设想在小岛上通过空投货币，考察该岛的宏观经济的变化。 3 东北农业大学本科课程教学大纲 课程名称：田间试验与统计方法 英文名称：Field Experiment and Statistic-method 课程编号：01600008j 适用专业：草业科学、植物生产类 总学时数：40 总学分：2.5 大纲主撰人：李文霞 内容简介 《试验设计与统计分析》是一门收集整理数据、分析数据, 并根据数据进行推断的科学。本课程为高等农业院校农学类专业的专业基础课，主要讲授有关田间试验的基本知识和统计分析的基本方法和技能，为学习专业课程奠定基础，使学生具备承担科学试验，正确分析和评价科学试验结果及其可靠性的能力。 教学大纲 一、课堂讲授部分 （一）分章节列出标题、各章节要点及授课时数（务必将要点写清楚） 第1章绪论 一、基本内容 1.1 农业科学试验的任务和要求1学时 1.1.1 农业科学试验和田间试验 1.1.2 农业科学试验的任务和来源 1.1.3 农业科学试验的基本要求 1.2 试验误差及其控制2学时 1.2.1 试验误差 1.2.2 试验误差的来源 1.2.3试验误差的控制 1.3 生物统计学与农业科学试验1学时 1.3.1 部分生物统计学基本概念 1.3.2 生物统计学的形成与发展 1.3.3 生物统计学在农业科学试验中的作用和注意问题 二、教学目的与要求 要求学生掌握农业科学试验的基本要求、试验误差的概念、来源和控制、部分生物统计学的概念，了解农业科学试验的任务和来源、生物统计学在农业科学试验中的作用和注意问题。 三、重点与难点 重点：农业科学试验的基本要求、试验误差的概念、来源和控制、部分生物统计学的概念 难点：试验误差的概念和生物统计学的基本概念的理解 第2章试验的设计和实施 一、基本内容 2.1 试验方案1学时 2.1.1 试验方案的概念和类别 2.1.2 处理效应 2.1.3 试验方案的设计要点 2.2 试验设计原则 1.5学时 2.2.1 重复 2.2.2 随机排列 2.2.3 局部控制 2.3 小区技术0.5学时 2.3.1 小区 2.3.2 区组和小区的排列 2.3.3 保护行 2.4 常用的试验设计1学时 2.4.1 对比法设计 2.4.2 间比法设计 2.4.3 完全随机设计 2.4.4 随机区组设计 2.4.5 拉丁方设计 2.4.6 裂区设计 2.5 试验的实施（学生自学） 2.6 田间抽样（学生自学） 二、教学目的与要求 要求学生掌握试验方案、试验设计原则、小区技术和常用的试验设计，自学试验的实施和田间抽样。 三、重点与难点 重点：试验方案、试验设计原则、小区技术和常用的试验设计。 难点：试验设计原则、小区技术、试验方案的设计要点的理解。 第3章描述性统计 一、基本内容 3.1 次数分布 1.5学时 3.1.1次数分布表 定量资料、定性资料 3.1.2次数分布图 柱形图、多边形图 3.1.3其它常用统计图 结合Excel的作图向导讲解，重点柱形图和折线图 3.2 平均数1.5学时 熱傳導實驗（Heat Conduction Experiment） 目的：測定各種金屬之『熱傳導係數』，並探討物質具有不同大小之熱傳導係數要如何應用。實驗設備：自己填寫 實驗方式：分別以沿『軸向』及『徑向』之熱傳導試件進行實驗，以試件內之溫度達到穩定狀態時為準，來計算金屬之熱傳導係數。 操作步驟： （1）將金屬試件（不鏽鋼或黃銅、 不鏽鋼或鋁）安裝到要進行實 驗的座位台上 （2）打開電源，選擇溫度顯示相近 的RTD測溫棒插入試件的測 溫孔，並確定測溫棒與測溫孔 緊密接觸 （3）選擇『軸向』或『徑向』之加 熱源，並調整熱率輸入視窗之 數值為20W （4）每隔5分鐘讀取每支測溫棒 之溫度，每個試件至少記錄六次共30分鐘，歸納結果時要將各個測溫點的『溫度-時間圖』畫出，並以溫度達到穩定狀態時為準，來計算金屬之熱傳導係數。 （5）更換試件重複步驟（1）~（4） 實驗數據記錄： 試件名稱：軸向熱傳導 T1（℃） T2（℃） T3（℃） T4（℃） T5（℃）測溫點 時間 5（min） 10（min） 15（min） 20（min） 25（min） 30（min） 試件名稱：軸向熱傳導 T1（℃） T2（℃） T3（℃） T4（℃） T5（℃）測溫點 時間 5（min） 10（min） 15（min） 20（min） 25（min） 30（min） 試件名稱： 徑向熱傳導 測溫點 時間 T1（℃） T2（℃） T3（℃） T4（℃） T5（℃） 5（min ） 10（min ） 15（min ） 20（min ） 25（min ） 30（min ） 試件名稱： 徑向熱傳導 測溫點 時間 T1（℃） T2（℃） T3（℃） T4（℃） T5（℃） 5（min ） 10（min ） 15（min ） 20（min ） 25（min ） 30（min ） 實驗數據圖示： （1） 用Excell 畫出各個測溫點的『溫度-時間』圖 （2） 依據（1）之圖，估計各個測溫點達到穩定狀態時的溫度，依此溫度，畫出各試件在各個 測溫點達到穩定狀態的『溫度-位置』圖（在『軸向』實驗中應有兩試件之線；在『徑向』實驗中也應有兩試件之線） 實驗數據計算： （1） 依據穩定狀態的『溫度-位置』圖，將各點連成擬合直線（不是折線），依據此直線之斜 率（『軸向』為 X T ΔΔ）（『徑向』為)ln(i o o i r r T T ?）來 計算『熱傳導係數K 』。 （2） 『軸向』公式為X T KA Q ΔΔ=；Q ：輸入熱率（A ：試件截面積（m 2）；△T ：直線上兩點之溫度差（℃）；△X ：直線上兩點之位置差（m ） （3） 『徑向』公式為)ln(2i o o i r r T T KL Q ?=π；L=試件厚度（m ），T i =靠近圓心處之溫度（℃），r i =靠近圓心處之半徑（m ），T o =靠外側處之溫度（℃），r o =靠外側處之半徑（m ） 結果與討論： （1） 書本上不鏽鋼的『熱傳導係數K 』約為20W/m ℃；黃銅約為100W/m ℃；鋁約為200W/m ℃，為何實驗計算出的值比書本提供的值為大？ 教学用PPT ，《高级计量经济学及Stata 应用》，陈强编著，高等教育出版社，2010年 第15章 随机实验与自然实验 15.1实验数据 不同学科可能依条件的不同而采用不同的实验方法。 （1）控制实验（controlled experiment ）：在理想的物理实验中，对除1x 以外的因素{}2,,K x x "全部控制不变，单独让 x变化，然后观察y变化的情况。 1 （2）随机（控制）实验（randomized controlled experiment）：通常将实验人群随机地分为两组，其中“实验组”（treatment group）服用真药，而“控制组”（control group，也称“对照组”）服用“安慰药”（placebo）。 （3）自然实验或准实验（natural experiment or quasi experiment）：由于某些并非为了实验目的而发生的外部突 发事件，使得当事人仿佛 ．．被随机分在了实验组或控制组。 15.2 理想的随机实验 在理想的随机实验（ideal randomized experiment）中，实验组与控制组的成员决定完全随机，比如，通过抛硬币或电脑随机数来决定。故个体究竟被分在哪一组或得到多大的实验“剂量水平”（treatment level），与个体的特征或其他可能影响实验结果的因素是完全独立的。这就避免了遗漏变量偏差（omitted variable bias）。 考虑以下回归模型， i i i y x αβε=++ (15.1) 其中，i x 是完全随机地决定的。由于i x 与i ε相互独立，故 Cov(,)0i i x ε=，因此OLS 是一致的。由于i x 与i ε相互独立，故1E(|,,)0i n x x ε="，故OLS 也是无偏的。 在理想的随机实验中，X 对y 的因果效应表现在条件期望的差别，即E(|)E(|0)y X x y X =?=，也称为“实验效应” E UROPEAN S YNCHROTRON R ADIATION F ACILITY INSTALLATION EUROPEENNE DE RAYONNEMENT SYNCHROTRON EXPERIMENT RISK ANALYSIS Experimental Number:Beamline: Main Proposer: Title of the Experiment: 1EXPERIMENT (only if changes since the proposal) Classification of the sample: Radioactive Contaminant Corrosive Oxidising Explosive Biological Other: Sample Description: Crystal Powder Polycrystalline Multilayer Liquid Gas Nanoparticles Other: Container: Capillaries Flat plate Pressure cell – Type: Other: ESRF equipment to be used: Furnace Magnet Cryostat Cryogenic gas stream Refrigerator Laser High pressure Fixed temperature Other: The Safety Group must immediately be informed of all modifications made and which differ from the original proposal and this at least two weeks before your arrival on site. Your equipment has been tested by your home institute. No changes can be made before your arrival at the ESRF and until your experiment has started. Page 1 / 12- Analyse des risques de l’expérience 实验一 电位、电压的测量和叠加定理的研究 一、实验目的 1．熟悉实验台的整体布置及交、直流电源和交、直流仪表的使用。 2．学会测量电路中各点的电位和电压的方法。 3．掌握线性电路的叠加定理。 二、实验设备 实验箱（EEL-51）(EEL-53)、恒压源、直流电压表、直流电流表 三、实验内容 1．熟悉实验台的整体布局、记录实验台的主要设备和仪表的参数。要求记录：设备的名称、规格、量程及精度。 2．熟悉直流恒压源、恒流源和直流电压表、电流表的使用。 (a)自行设计一个电路，以某点为参考点，测量电路各点的电位和两点之间的电压。具体要求： ①用三个电阻和一个电源（电压不超过8V ）组成一个简单电路； ②由附录中实验箱选择电阻元件的阻值，并画出电路； ③选择参考点计算各点的电位和两点之间的电压，自行设计一个表格，将所计算的数据填入表格中。然后实际连接电路，测量电位和电压。 (b)叠加定理的研究 使用EEL-53实验箱，按叠加原理图1-1进行实验，测量每个电源（V U S 121 =，V U S 62 =） 单独作用时和共同作用时各支路电流值，填入表1-1中。 表1-1 图1-1 4 5 四、实验注意事项 1．测量直流电压应并联在被测元件上，注意正负极性。测量直流电流时应串联在被测支路中，要注意电流的方向。 2．选择测量仪表的量程，根据估算选择稍大的量程，如电流偏小，再降低量程，以保证测量的精度。注意测量仪表报警铃响时，应关闭仪表的电源，检查原因，改正后重新合上仪表的电源。 3．正确使用可调直流恒压源和恒流源，正确读数（读数以电压表测量为准，而不以电源表盘指示值为准）。 4．使用电流插头测量时应注意仪表的极性的正确连接，以及读数时"",""-+号的记录。 5．叠加定理实验中，每个电源单独作用时，去掉另一个电源，是由开关S 1 ，S 2 操作完成，而不能将直流电源短路。 五、预习思考题 1．叠加定理实验中1 S U ，2 S U 分别单独作用时实验中应如何操作？ 2．如将叠加定理中电阻R 3改为二极管D 时，叠加定理是否成立？ 3．电路中各点电位与选择的参考点有什么关系？任意两点之间的电压与参考点的选择有关系吗？ 六、实验报告要求 1．预习报告内容的要求：实验目的、实验设备（写出具体实验箱的型号和测量仪表的型号）、实验内容及步骤、根据实验内容，具体画出线路及实验参数，计算结果，以及设计出测量用的记录表格。 2．总结报告内容的要求：除预习报告内容之外，再增加数据的误差分析或曲线比较，理论分析，故障分析和心得体会。 Reynolds experiment Aim of the experiment 1.Observe the laminar and turbulent flow, and the process of transition from one state to the other. 2.Measure the critical Reynolds number and develop the skills on how to distinguish the pipe flow state. 3.Study the dimensional analysis method to analyze the experiment, confirming the criterion number of flow state for a non-circular pipe. Experimental apparatus 1. The figure of the apparatus Figure 1 shows the experimental apparatus and the name of each part. Figure 1. 1: Self-circulating water supply, 2: Hydraulic bench, 3: Speed controller, 4: Constant head water tank, 5: Coloured water pipe, 6: Perforated plate, 7: Overflow, 8: Experiment pipe, 9: Flow rate control valve DOE 出自 MBA智库百科(https://www.doczj.com/doc/015530050.html,/) DOE（Design of Experiment,试验设计） 目录 [隐藏] ? 1 什么是DOE ? 2 为什么需要DOE ? 3 DOE的基本原理 ? 4 DOE实验的基本策略 ? 5 DOE的步骤 ? 6 DOE的作用 ?7 DOE的方法 [编辑] 什么是DOE DOE（Design of Experiment）试验设计，一种安排实验和分析实验数据的数理统计方法；试验设计主要对试验进行合理安排，以较小的试验规模(试验次数)、较短的试验周期和较低的试验成本，获得理想的试验结果以及得出科学的结论。 试验设计源于1920年代研究育种的科学家Dr.Fisher的研究, Dr. Fisher 是大家一致公认的此方法策略的创始者, 但后续努力集其大成, 而使DOE在工业界得以普及且发扬光大者, 则非Dr. Taguchi (田口玄一博士) 莫属。 [编辑] 为什么需要DOE ?要为原料选择最合理的配方时（原料及其含 量）； ?要对生产过程选择最合理的工艺参数时； ?要解决那些久经未决的“顽固”品质问题 时； ?要缩短新产品之开发周期时； ?要提高现有产品的产量和质量时； ?要为新或现有生产设备或检测设备选择最 合理的参数时等。 另一方面，过程通过数据表现出来的变异，实际上来源于二部分：一部分来源于过程本身的变异，一部分来源于测量过程中产生的变差，如何知道过程表现出来的变异有多接近过程本身真实的变异呢？这就需要进行MSA测量系统分析。 [编辑] DOE的基本原理 试验设计的三个基本原理是重复，随机化，以及区组化。 所谓重复，意思是基本试验的重复进行。重复有两条重要的性质。第一，允许试验者得到试验误差的一个估计量。这个误差的估计量成为确定数据的观察差是否是统计上的试验差的基本度量单位。第二，如果样本均值用作为试验中一个因素的效应的估计量，则重复允许试验者求得这一效应的更为精确的估计量。如 s2是数据的方差，而有n次重复，则样本均值的方差是。这一点的实际含义是，如果n=1，如果2个处理的y1 = 145，和y2 = 147，这时我们可能不能作出2个 处理之间有没有差异的推断，也就是说，观察差147-145=2可能是试验误差的结果。但如果n合理的大，试验误差足够小，则当我们观察得y1随机化是试验设计使用统计方法的基石。 所谓随机化，是指试验材料的分配和试验的各个试验进行的次序，都是随机地确定的。统计方法要求观察值（或误差）是独立分布的随机变量。随机化通常能使这一假定有效。把试验进行适当的随机化亦有助于“均匀”可能出现的外来因素的效应。 区组化是用来提高试验的精确度的一种方法。一个区组就是试验材料的一个部分，相比于试验材料全体它们本身的性质应该更为类似。区组化牵涉到在每个区组内部对感兴趣的试验条件进行比较。 [编辑] DOE实验的基本策略 策略一：筛选主要因子（X型问题化成A型问题） Project 1 Technology Enhanced Presentations Choice 1. To begin a presentation: a.choose the New menu, then choose New. b.choose the File menu, then choose New Presentation. c.choose the File menu, then choose New. d.click the New Slide button on the toolbar. 2. To insert footer into the slide presentation: a.click the Header/Footer button on the toolbar. b.choose the View menu, choose Master, then choose Slide Master. c.choose the Edit menu, then choose Header/Footer. d.choose the View menu, then choose Header/Footer. 3. The type of animation that is caused by the change from one slide to another is a(n): a.action setting. b.custom animation. c.slide transition. d.preset animation. 4. To set a transition: a.choose the Slide Show menu, then choose Transition. b.choose the Slide Show menu, then choose Slide Transition. c.click the Transition button on the toolbar. d.choose the Format menu, then choose Transition. 5. What is the first step in setting a custom animation? a.Clicking the Animation button on the toolbar. b.Choosing the Slide Show menu. c.Clicking the mouse on a part of the text to be animate d. d.Clicking the Add Effect button on the toolbar. Essay Questions What is the purpose of having a clear beginning and ending to a presentation? 实验2 存储管理 1. 实验目的 存储管理的主要功能之一是合理地分配空间，请求页式管理式一种常用的虚拟存储管理技术。本实验的目的是通过请求页式管理中页面置换算法的模拟设计，了解虚拟存储技术的特点，掌握请求页式存储管理的页面置换算法。 2. 实验内容 (1) 通过随机数产生一个指令序列，共320条指令，指令地址按下述原则生成 ①50%的指令是顺序执行； ②25%的指令是均匀分布在前地址部分； ③25%的指令是均匀分布在后地址部分； 具体的实施方法是 ①在[0, 319] 的指令地址之间随机选取一起点m ； ②顺序执行一条指令，即执行地址为m+1 的指令； ③在前地址[0, m+1] 中随机选取一条指令并执行，该指令的地址是m’； ④顺序执行一条指令，其地址为m’+1 ； ⑤在后地址[m’+2, 319] 中随机选取一条指令并执行； ⑥重复上述步骤①～⑤，直到执行320次指令。 (2) 将指令序列变为页地址流 设：①页面大小为1K ； ②用户页面内存容量为4页到32页； ③用户虚存容量为32K 。 在用户虚存中，按每K 存放10条指令排列虚存地址，即320条指令在虚存中的存放方式为： 第0条～第9条指令为第0页（对应虚存地址为[0, 9]）； 第10条～第19条指令为第1页（对应虚存地址为[10, 19]）； …… …… 第310条～第319条指令为第31页（对应虚存地址为[310, 319]）； 按以上方式，用户指令可组成32页。 (3) 计算并输出下述各种算法在不同内存容量下的命中率 ①First-In-First-out (FIFO) Page Replacement ②Least-Recently-Used (LRU) Page Replacement ③Optimal Page Replacement 其中③和④为选择内容 Ambiguity and Uncertainty in Dr. Heidegger's Experiment Nathaniel Hawthorne's short story, Dr. Heidegger's Experiment, reveals that people have a futile and self-destructive desire to relive their pasts instead of moving onward and accepting their fates. In Dr. Heidegger's Experiment, Hawthorne uses a point of view that allows ambiguity to enter the narration. The unnamed narrator opens many aspects of the story to more than one interpretation and enhances the revelation of the theme through uncertainty as he tells of the reactions of four old people to the water of the Fountain of Youth. The narrator himself seems unsure whether the events he is relating have even occurred. "Was it delusion?" he asks, "Even while the draught was passing down their throats, it seemed to have wrought a change on their whole systems." Commenting on the many tales that have sprung up around the mysterious Dr. Heidegger, the narrator even admits his own unreliability, stating, "Some of these fables, to my shame be it spoken, might possibly be traced back to mine own veracious self; and if any passages of the present tale should startle the reader's faith, I must be content to bear the stigma of a fiction-monger." These uncertainties divorce the story's happenings from reality, enhancing the allegorical meaning of the tale. The narrator is uncertain whether Dr. Heidegger's four old subjects have attained a second youth. As they drink the water, their actions become those of youths, but have their bodies changed too? "...the three gentlemen behaved in such a manner, as proved that the water of the Fountain of Youth possessed some intoxicating qualities; unless, indeed, their exhilaration of spirits were merely a lightsome dizziness, caused by the sudden removal of the weight of years." When they lose their newfound "youth," the same doubts are shown: "A strange chillness, whether of body or spirit they could not tell, was creeping gradually over them all. They ... fancied that each fleeting moment snatched away a charm, and left a deepening furrow where none had been before. Was it an illusion? Had the changes of a life-time been crowded into so brief a space... In truth, they had [grown old]. The Water of Youth possessed merely a virtue more transient than that of wine." The Elixir of Youth is likened to an alcoholic drink, yet the effects of an actual loss of age, and later a loss of their new-found youth, are felt in the four subjects. The narrator, and thus the reader, does not know the true extent of Dr. Heidegger's "experiment." This does not obscure the truths that the subjects reactions reveal; whatever interpretation the reader chooses, the theme remains. This uncertainty also highlights the multiple meanings of certain lines. When the four old 以下所有实验完成的环境： OS: Windows XP IDE: Eclipse Database: MySQL或SQL Server 实验一 实验名称：JAV A中循环结构 实验目的：熟悉循环结构，熟悉JA V A类的定义以及参数的传递。 实验时间：（2学时） 实验内容： 1.金字塔：Pyramid.java 在屏幕上显示一个由星型符号“*”组成的金字塔图案，示例如下： * *** ***** 实验二 实验名称：封装，继承与多态 实验目的：熟悉JA V A面向对象的三大特性。 实验时间：（4学时） 实验内容： 1.定义一个形状类（Shape）方法：计算周长，计算面积 子类： 矩形类（Rect）：额外的方法：cha（）计算长宽差 圆形类（Circle） 正方形类（Square）矩形的子类 生成几个不同的形状对象，放在一个Shape类型的数组里，分别求每个形状的周长和面积。如果形状对象是一个矩形，且不是正方形，则计算长宽差。 实验三 实验名称：集合 实验目的：熟悉JA V A的集合框架，熟练掌握以下接口和类的使用，Collection, Map, List,Set, SortedSet, ArrayList, LinkedList, Vector, HashMap, Hashtable等。 实验时间：（2学时） 实验内容： 1. 数组拷贝CopyArray.java 定义数组int[] a = { 1，2，3，4，5，6，7，8，9，10 }和b。 （1）将数组a中的所以元素拷贝到数组b中,打印b中元素。（用循环实现） 结果参考： 1，2，3，4，5，6，7，8，9， （2）将数组a中从第3个元素起连续5个元素拷贝到数组b中,打印b中的元素（用api中提供的数组拷贝方法实现） 1 ? 陈 强,《高级计量经济学及S t a t a 应用》课件，第二版，2014年，高等教育出版社。 第1 8章 随机 实验与自然实验 18.1 实 验 数 据 假设研 究1x 是否导致y 。假定{}12,,,K x x x 包含所有影响y 的因素。 不同学科采用不同的实验方法，大致分为以下几类。 (1) 控制实验(c o n t r o l l e d e x p e r i m e n t )：在理想的物理实验中，控制{}2,,K x x 全部不变，单独让1x 变化，观察y 的变化。 (2) 随机(控制)实验(r a n d o m i z e d c o n t r o l l e d e x p e r i m e n t )： 2 【例】 医学 上对 新药 1x 疗效的 实验。 由于 参加实验者的体质 与生 活 方式不同 ，不 可能 完全 控制 所有 其他因 素 {} 2, , K x x 。 随机实 验将实验人群(或个体)随机地分为两组，其中“实验组”或“处理组” (t r e a t m e n t g r o u p )服用真药，而“控制组”(c o n t r o l g r o u p ，也称“对照组”)服用“安慰药”(p l a c e b o )。 被试 者不知道自己分在哪一组，避免心理干扰。有时科研人员也不知道被试者 在哪一组，称为“双盲法”(d o u b l e b l i n d )。 【例 】农学中将地块随机地分成三组(很难找到土壤条件完全一样的地块 )，分 别给予不同的施肥量，然后考察施肥的效果。 3 (3) 自然实验或 准实验 (n a t u r a l e x p e r i m e n t o r q u a s i e x p e r i m e n t )： 由于某些 并非 为 了实 验 目的而发生的外部突发事件，使得当事 人 仿佛被随机 地分在 了实验 组或控制组。 【例】一个州通过某法律，但相邻州未通过此法律。两州民众事先不知道哪个州会通过此法律，故无法自我选择住在哪个州。从考察法律的效果而言，可近似认为民众随机选择住在哪个州，或被随机分为实验组(通过法律)与控制组(没通过法律)。 (4) 思想实验(t h o u g h t e x p e r i m e n t )： M i l t o n F r i e d m a n 曾设想在小岛上通过空投货币，考察该岛的宏观经济的变化。 Experiment Report (实验报告) Experiment Name(实验名称) The first Experiment（第 1 次实验） Experiment Date（日期） 2014-06-17 Teacher(老师) Student ID（学号） Name(姓名) Class（班级） Score(成绩) 一．Aim and Requirement（目的和要求） Define a Class containing an overloaded method area(), which calculates area of a Square, Rectangle, and a Circle depending on the type and number of arguments passed to it. 二． Experiment Content（实验内容） 1、Write an overloaded method area(), which calculates area of a Square, Rectangle, and a Circle. 2、Write the main function to test the method. 三．Experimental Procedures（实验步骤） 1、Write an overloaded method area() to calculate area of a Circle. 2、Overload the method area() again to calculate area of a Square or a Rectangle. 3、Write the main function to test the method. 4、Run the project file, the result shows that: 四．Experimental Summary（实验小结）2GeV and 0.073<|t |<0.40GeV 2
2,as measured by the ZEUS collaboration using the Leading Proton Spectrometer.
漏斗实验(Funnel Experiment)
死亡实验(the experiment)观后感
第18章-随机实验与自然实验
完全随机设计试验资料的方差分析-东北农业大学植物科学与技术实验
热传导实验(Heat Conduction Experiment)
15章随机实验与自然实验-ShandongUniversity
实验安全风险分析EXPERIMENT RISK ANALYSIS
experiment1
Reynolds_experiment雷诺实验(英文版)
DOE(Design of Experiment,试验设计)
experiment
操作系统experiment3
Dr. Heidegger's Experiment读后感
JAVA Experiment
第18章-随机实验与自然实验(优选.)
Experiment_Report
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