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cosmology and astrophysics 1992 * 



Lawrence M. Krauss
Center for Theoretical Physics and Dept. of Astronomy
Yale University
Sloane Laboratory, 217 Prospect St.
New Haven CT USA 06511






 cosmology and astrophysics 1992 * 
Lawrence M. Krauss
Center for Theoretical Physics and Dept. of Astronomy
Yale University
Sloane Laboratory, 217 Prospect St.
New Haven CT USA 06511
Abstract
I review recent developments in cosmology and astrophysics relevant to particle physics,  focussing on the following questions:  What s new in 1992?, What have we learned since the last ICHEP meeting in 1990?  and, What are the prospects for the future?  Among the topics explicitly discussed are: COBE , Large Scale Structure, and Dark Matter; Big Bang Nucleosynthesis; the Solar Neutrino Problem; and High Energy Gamma Ray Physics.

 introduction
  It was the best of times.  It was the worst of times.  
Charles Dickens 

The subject which I was asked to summarize in one hour spans almost 40 orders of magnitude in energy.  Even in the  worst  of  times this would be difficult.  However, in the times we have been living it is very nearly impossible.  Probably no other area in particle physics has produced as many dramatic results in the last two years as the cosmology-astrophysics interface.  Thus, deciding to attempt to err on the side of incompleteness rather than coherence (the reader can be the final judge), I have chosen to describe here only that subset of results: (a) which are the most topical for this meeting, and (b) which can be combined together into some pseudo-logical fashion.
Nevertheless, to give some idea of both the range of scales and areas of present interest,  I present in figure 1 a graphical view of the field, as a function of energy.   This seems to me an appropriate way to organize my comments, and I will generally, although not universally, work in order of ascending energy.
____________________  
* bitnet: Krauss @Yalehep. Research supported in part by NSF, DOE, and TNRLC
 
Figure 1.  An Overview 

There have been active developments in each of the areas listed above.  I will not have the time, or the space, to describe all of them, however.   Nevertheless, I hope to get to give a flavor of the excitement which has been generated over the past year or two in this field.   


1. COBE, LARGE SCALE STRUCTURE, AND DARK MATTER: OR....                     THE UNIVERSE STRIKES BACK!
(A)  COBE

The popular media reverberated last spring with the news that the Differential Microwave Radiometer (DMR) experiment aboard the COBE (COsmic Background Explorer) satellite had discovered primordial anisotropies in the Cosmic Microwave Background Radiation (CMBR).  Referred to variously as the  holy grail , and  the face of God ,  there was no shortage of hyperbole.  Nevertheless, in spite of the signficance attributed to this discovery by the popular press, it was in fact extremely significant and, I will claim, of great interest for particle physics as well. 
This of course was not the first important observation by the COBE satellite.  Recall that in the first 8 minutes of its flight in 1989 COBE measured1 the spectrum of the CMBR and determined that it was describable by a single black body to better than 1 part in 1000, with a temperature of approx. 2.735 K.  This result alone provided strong support for the Big Bang origin of the CMBR, and also ruled out earlier measurements2 of a high frequency discrepancy with a black body spectrum, which would have required rather exotic sources of energy production during the period 105 sec-100,000 years into the Big Bang expansion. 
As described by George Smoot at this meeting3, the DMR experiment aboard COBE provides a differential  measurement of the CMBR temperature, and not an absolute one.  Thus, it has been able to operate long after the liquid He aboard the satellite, necessary for the sensitivity to the absolute temperature, had evaporated.  The data on which the observed anisotropy is based is the first two years of COBE data.  Another year s data has already been taken and is currently being analyzed.  
The DMR experiment employs two independent microwave antennas sampling the sky at an angular separation of 10o.   Three sets of antennae, operating at 90, 53, and 31 GHz respectively were used, and at each frequency two separate channels were available. 
In searching for CMBR anisotropies, several larger effects must be first removed.  There is a well-known, and well measured, dipole anisotropy in the CMBR signal, at the level of a few parts in a thousand.  This is presumably primarily due to the local motion of the satellite with respect to the frame defined by the surface of last scattering of the CMBR.  This motion is comprised of a sum of several components: the motion of the satellite around the earth, the motion of the earth around the sun, the sun around our galaxy, the infall of our galaxy to the center of our local group of galaxies, and finally, the large scale drift of our local group of galaxies.  The net peculiar motion is on the order of about 600 km/sec, which would be expected to produce a signal of the magnitude observed.  Moreover, COBE has now further supported this interpretation by examining the time dependence of dipole signal.  The yearly variation of the signal can clearly be seen3.
Subtracting the measured dipole from the signal, any analysis of the COBE signal must next concern itself with the chief source of background: our galaxy.  A great deal of effort has gone into both modelling the galactic signal, and verifying that it does not contaminate the observed residuals4.   While the galactic signal is least significant in the 90 GHz band, measurements of the rms temperature deviations at 100 separations in all three bands do not go to zero as one moves away from the plane of our galaxy, but instead approach a constant value of approximately 30  K by a galactic latitude of about 250.  It is this residual signal which is claimed to represent true primordial fluctuations in the CMBR.
With this introduction to the COBE result, I will next address the following 3 issues: (i) What exactly is the COBE result?,  (ii) Why is it interesting?,  (iii) What does it, and what does it not imply?
(i) The COBE Data:
The first COBE result I have already alluded to.  Averaging over the sky at latitudes greater than 300 from the galactic plane, COBE reports an rms temperature deviation:
	DTrms (q >300)  30  K.	(1)
Now of course, there is much more information in the CMBR anisotropy than is obtainable from the rms deviation alone.    Using a formalism with which particle physicists should be comfortable, it is conventional to define a temperature correlation function,  C(a)   <T1T2>, defined crudely as the average over the sky of the product of temperatures in regions separated by an angle q. Specifically,
	 	(2)
where the average is taken with respect to all positions   with   fixed, with a smoothing size of  , the angular response of the detector (a Gaussian FWHM of 70). 
One can also choose to expand the measured temperature fluctuations across the sky in a multipole expansion:
	 	(3)
If we define the rotationally invariant quantity:
	 	(4)
Then one can define the quadrupole anisotropy:
	 	(5)
COBE has measured both the full correlation function of the temperature fluctuations, and has also reported a value for the quadrupole anisotropy Q.    The measured value is
	Q  =  13   4  K.	(6)
However, COBE also reports the value for the quadrupole moment determined in a slightly different way.  If instead, the correlation function is fit assuming a  flat , angle independent spectrum (see below), one infers a slightly larger value of the quadrupole:
	Q rms-PS = 16   4  K. 	(7)
Both values are of use in comparing to theoretical predictions.  
While the quadrupole anisotropy is the most significant numerical result quoted by COBE, the correlation function implicitly contains information on all multipoles.  Specifically,
 	(8)
The quadrupole moment dominates this expansion and is thus easiest to extract.  Hence the use of this value to characterize the observations.  
(ii)  Why the interest ?
The observed CMBR originated at the epoch when the background matter distribution first became neutral, and decoupled from radiation, at a time of   3 x 105 years into the Big Bang explosion.  As we look out to high redshifts, and hence to early times, this time defines a  surface , known as the surface of last scattering. Thus, the CMBR provides a redshifted picture of the distribution of radiation at that time.  As shown on the schematic picture below, the horizon size at that time would correspond today to an observed angle across the sky of about 10. 
   
Figure 2.  A Schematic View of the Universe

Photons travelling from the last scattering surface to a receiver aboard COBE redshift by a factor of 1000 on average.  However, if there are regions of density excess in the dominant energy density at that time, photons leaving such regions at the surface of last scattering will have to  climb up  out of these potential wells, inducing an extra gravitational redshift:
	 	(9)
where F is the gravitational potential.  Thus,  cool  spots in the CMBR represent density excesses which, if gravity governs the formation of structure, will eventually collapse to form galaxies, or clusters of galaxies.   Hot  spots represent regions of under-density, which will eventually form  voids .
Now, the COBE observations, because of their smoothing scale, are only sensitive to fluctuations in temperature on scales of greater than about 100.  However, this is much larger than the scale corresponding the the horizon at the last scattering surface. No causal process since the beginning of the presently observable Big Bang expansion could have moved energy density around on such scales in order to create potential wells!  Thus, if the CMBR has not been further reprocessed since a redshift of z 1000, the anisotropies observed by COBE are primordial, that is, they must represent initial conditions associated with the Big Bang.  Such initial conditions involve the physics appropriate to processes at very high energy, i.e. appropriate to particle physics.  That is why the COBE results are both extremely exciting on general grounds, and are also relevant to this meeting.
(iii)  What does COBE imply?
(a) Does Cosmic Structure Form due to Gravity? 

After the question of what the geometry of the observable universe is, perhaps the central issue in modern cosmology concerns the origin of the observed structures in the universe: galaxies, clusters, and superclusters.  The simplest possibility is that such structures formed out of the gravitational collapse of initially small density excesses in the universe.  Since gravity is universally attractive, if initially one starts with small fluctuations dr/r << 1, gravity will cause these to increase.  Once they exceed unity, they will separate out from the background expansion and collapse to form bound systems.  
After decoupling of matter and radiation at z=1000, matter density perturbations can collapse due to gravity.  Simple perturbation theory5 then implies:
	  	(10)
as long as the perturbations remain in the linear regime.  Here a(t) is the cosmic scale factor at time t.    Because the ratio between the cosmic scale factor at decoupling and today is 1000, this implies that in order for fluctuations on the scale of present day galaxies to have grown sufficiently to become O(1) by today, they would have had to have been at least O(10-3) at the time of last scattering.  Such density fluctuationas would produce a gravitational redshift in the photon gas:
	 	(11)
Now, on small angular scales which entered the horizon before decoupling, a variety of dynamical factors due to the matter-radiation coupling must also be considered in order to determine the remnant fluctuations in the CMBR today.  For example fluctuations in the baryon fluid, which are strongly coupled to radiation before decoupling, cannot collapse due to the pressure of radiation.  Thus, any primordial fluctuations in baryons cannot grow until after decoupling.   Hence, the first scale of fluctuations which can grow immediately after coming inside the horizon is that associated with the horizon scale at decoupling, about 20 on the sky today.  
This argument suggests that if baryons dominated the matter density at the time of decoupling, that their fluctuations should induce an anisotropy at the level given in (11) on scales of about 20 in the CMBR, if they are also responsible for galaxy formation.  Similarly, this suggests that if the spectrum of primordial fluctuations does not vary much as a function of wavelength, that fluctuations in the CMBR on larger scales, those probed at COBE, should not be much smaller. 
The fact that the observed fluctuations in the CMBR are not anywhere near this large is one of the many pieces of indirect evidence that we have that baryonic matter does not dominate the energy density of the universe, at least if galaxy formation is to occur by gravitational collapse.  However, before the present COBE observation the upper limits on the anisotropies in the CMBR were so small as to suggest potential problems for this whole idea.
Arguments of the type I have summarized above for baryonic matter5 suggest that if primordial fluctuations in whatever was the dominant matter in the universe were to grow by gravitational instability to lead to  galaxy and cluster formation by the present time, the remnant signature in the CMBR today at COBE scales should exceed dT/T   few x 10-6.  As the previous COBE upper limit was close to this, the whole gravitational instability picture was perilously close to being ruled out.  Instead, the observation, by COBE of a dT/Tquadrupole   5 x 10-6 is in the range predicted for gravitational instability based models.  Thus COBE observations are consistent  with the standard model of galaxy induced structure formation. 

(b) Nature of Primordial Fluctuations

For gaussian initial fluctuations, all information about the primordial spectrum is contained in the power spectrum, P(k), defined in terms of the Fourier transform of the spatial density fluctuation spectrum:
	 	(12)
The power per logarithmic interval in comoving wavenumber k, or equivalently the rms mass fluctuation on this  scale, can then be written:
	 .	(13)
Under the assumption that there is no preferred primordial scale, one assumes P(k) is of a scale-free form:
	 	(14)
There are at least two conventions for defining the k-dependence of the primordial power spectrum.   A particularly natural way for theorists to describe the spectrum is in terms of the amplitude of each mode at the time that mode enters the  horizon ---the distance over which causal propagation can have taken place since the beginning of the FRW-Big Bang expansion. This is because once the scale of metric perturbations enter the horizon, particle interactions can affect their growth, while before this the evolution of fluctuations on extra-horizon sizes is determined by the equations for the background expansion. Moreover, this is an appropriate scale to discuss the physics responsible for the generation of primordial fluctuations. In inflationary models, for example, the amplitude of primordial fluctuations is fixed as modes are pushed outside the de-Sitter horizon during inflation.   
While it is therefore natural to describe the amplitude of fluctuations at horizon crossing, one should remember that describing the spectrum in this way implies that the amplitude of different modes will be specified at different times.  Alternatively, one can choose to specify the k-dependence of the amplitude of fluctuations at some distinct, fixed, time.  Two commonly chosen examples are: the present time, and the time of decoupling---when the microwave background last scattered. 
In advance of any model of primordial fluctuations, several authors (notably Harrison, Zel dovich, and Peebles and Yu6) suggested that the most reasonable ansatz was a scale-invariant  form.  This is a sensible assumption, since it suggests that there is not arbitrarily large power on either small or large scales.  In the latter case,  this could produce too large an anisotropy in the CMBR, and in the former, it would produce too many small black holes.
If we specify a scale invariant spectrum in its most natural way, as one with constant amplitude at horizon crossing:
	 	(15)
then eq. (13), with each mode measured at its horizon crossing, implies that n=-3.   However, from the observational viewpoint of COBE, we need to translate this into the k-dependence an observer who is probing fluctuations at a specific time: namely the time of last scattering.    
Density fluctuations outside the horizon are not well-defined.  That is, they are gauge dependent.  Fixing the gauge appropriately, however, one finds that during a matter dominated expansion, density fluctuations outside the horizon can also grow according to (10), in order to keep metric perturbations constant.   During a matter dominated expansion a ~t2/3.  Thus, an extra-horizon size mode with wavelength l measured at the time the horizon has size l0 will itself cross the horizon at a time (t/to)   (l/l0)3.  Since during such a time it will grow by a factor (t/to)2/3, this means that for a perturbation on this scale to have the value given in (15) at the time it crosses the horizon, it must have a value at time t0 which is (l0/l)2 smaller.   Thus, since k0~l0-1, one finds
	 	(16)
for modes with k<k0.  From (13), we thus find that P(k) for long wavelength modes in a scale invariant spectrum has index n=1 at time t0.  
From the measured angular temperature correlation function, COBE has extracted the index for primordial temperature fluctuations on extra-horizon sized scales at the time of last scattering.  The best fit value for the spectral index, including cosmic variance in the predicted spectrum is n= ,  consistent with scale invariance. 

(c) Inflation, Dark Matter, and Gravitational Waves:

The COBE results have been claimed to provide support for Inflationary cosmology, with all of its subsequent consequences for dark matter?  To what extent is this claim correct?  COBE clearly has not proved inflation.  However, it is remarkably consistent with all the predictions of inflationary models.
Consider first the nature of the primordial fluctuation spectrum.  The COBE observation is consistent with an n 1 scale invariant spectrum, which is a relatively generic prediction of inflation.  However, is it a unique prediction?  The answer is both yes and no.   As I stated earlier, any sensible model of primordial fluctuations is likely to predict a flat spectrum, and thus models like cosmic strings, Textures, etc., all make this claim.   However, there is one fundamental difference between all these models and inflation.   In the former cases, one must make the unphysical supposition that all truly primordial fluctuations are zero, and then generate them afterwards.  In the latter case any pre-inflationary fluctuation spectrum is erased  by inflation, leaving behind only that spectrum generated during inflation.
Thus, I think it is fair to say that inflation is the only  completely comprehensive model of primordial fluctuations.   In this sense, this one available model is consistent with the COBE observations.   However, this does not preclude that other first principles models may also exist which generate a flat spectrum of primordial fluctuations.  We just don t know of any. 
In a related vein, the uncertainty in the existing COBE limit is sufficiently large as to accomodate significant deviations from scale invariance.  Moreover, it has been increasingly appreciated recently (see below) that inflation allows the possibility that n<1.   Thus, if COBE were eventually to be able to prove that n 1, this might still be compatible with inflationary predictions. 
What about the other  generic  prediction of inflation: that W =1, i.e. we live in a flat universe today?  COBE cannot probe this directly, but it can indirectly.   In the first place,  the fact that the overall magnitude of the observed fluctuations, in the range of 10-6, as expected for gravitational clustering in flat cosmologies dominated by exotic dark matter, provides some support for this whole picture.  Somewhat more quantitatively, it is well known that the growth of perturbations is more efficient in an W=1 flat universe than in open cosmologies with W <1.   The observed small magnitude of the primordial fluctuations in the CMBR are not small enough to require W =1, but it is consistent with this value.  In general, like the direct dynamical determinations, they prefer  W  0.2.
Carrying this line of argument further, one can examine in detail the model predictions for various cosmologies with various different matter contents to see how well the COBE results match onto extrapolations based on observed galaxy clustering and velocities.  This is too complex a subject to discuss  in detail here, and several talks at this meeting were devoted to the beginnings of such investigations7,8.    Suffice it to say that when the predictions of the preferred cosmological model, Cold Dark Matter, W=1, and a flat spectrum of adiabatic primordial fluctuations, normalized to the galaxy-galaxy two point function at about 8 Mpc, is compared to the COBE observations, the predicted values of DT/T are somewhat smaller than those observed9.  At the same time, this normalization of the CDM spectrum tends to predict smaller clustering at the large scales probed by the sample provided by the Infrared Astronomical Satellite (IRAS).  These problems  have lead some to suggest that either: (a) the dark matter distribution is not as biased on small scales as had previously been expected.  In this case the CDM predictions match on better to the large scale observations and the COBE data, but appear to predict too much clustering on small scales, (b) the primordial spectrum is  tilted , i.e. it is n<1, giving more power on large scales, (c) Cold Dark Matter must be supplemented by Hot Dark matter, such as one might get from an O(7 eV) neutrino, (d) Cold Dark Matter is dead.   I shall come back to this issue a little later.  
One factor which was not initially taken into account, but which is now being studied in more detail, is the fact that inflation predicts two   sources of CMBR anisotropies.  In addition to primordial density perturbations, it is predicted that their should also be a primordial spectrum gravitational waves generated during inflation. The heuristic reason for this is that inflation occurs because there is a non-zero vacuum energy density present during the inflationary phase, giving rise to a de Sitter expansion. In such a phase the trace of the energy momentum tensor is non-zero.  It is in fact proportional to the cosmological constant L, which is in turn proporitional to the vacuum energy density:
	 	(15)
 Since gravitational waves couple to the trace of the energy-momentum tensor, they will be generated during any period of expansion when this is non-zero.  Their amplitude will be therefore be proportional to V, the vacuum energy density during inflation10.  
Both primordial density perturbations, and gravitational waves will contribute to the observed COBE anisotropy, and since inflation generates both (as will undoubtedly any other scenario responsible for generating the former), it is necessary to consider both sources when attempting to compare inflationary predictions to the COBE observations11.   This leads to several interesting possibilities.   It is possible, at least in principle that the entire COBE quadrupole signal is due to gravitational waves.  In this case one gets a constraint on the overall scale of inflation.  Because the processes which generate both scalar density perturbations and tensor gravitational waves during inflaton are stochastic, the theoretical predictions themselves involve an inherent uncertainty---the so call  cosmic variance .  Because we happen to live in the actual universe, instead of in all possible universes, the value we observe for the magnitude of these fluctuations is just one of a set of possible values with an intrinsic probability distribution.  The predictions for each of the 5 components of the quadrupole moment generated by each source of fluctuations are independent, leading to a predicted value distributed as a c2 distribution with 5 degrees of freedom.  Comparing the observed value, with the predicted value, assuming the entire contribution is due to gravitational waves, one gets a 95% confidence limit11:
	1.5 x 1016 GeV< V1/4 < 5 x 1016 GeV 	(16)  
This value is remarkably close to the predicted scale of grand unification based on an extrapolation of the measured strong, weak, and electromagnetic couplings at LEP12.   Whether or not this is a coincidence remains to be seen.  
In fact, the idea that at least some of the COBE quadrupole is due to gravitational waves is not outrageous.  If one extrapolates the favored CDM structure formation model predictions based on observed galaxy-galaxy correlations to the COBE scale on tends to predict a quadrupole which is somewhat smaller than COBE sees, as I earlier remarked, and as I will discuss in somewhat more detail soon.   
Of course what one likes, and what one gets may be two different things!  Each inflationary model makes predictions not only for the magnitude of scalar and tensor perturbations, but also for their ratio.  Thus, aside from the cosmic variance, one is not free to independently vary these two components when comparing predictions and observations.
The inflationary predictions for the total quadrupole anisotropy (Q) and the relative contributions have now been addressed in some detail13.   It has been pointed out (i.e see Davis et al in ref 13)that not only are the relative contributions of scalar and tensor perturbations to Q coupled, but so is this ratio and the power law dependence, n, of the primordial spectrum itself.  In order for gravitational waves to contribute significantly to the observed CMBR quadrupole moment, it appears that n<1 is probably required.
Thus, while COBE has provided a remarkable new observable with the potential to shed a great amount of light on our understanding of the cosmology of the early universe, at present it has not allowed any unambiguous tests of models.  In order to unravel the nature of contributions to the quadrupole anisotropy and also determine the nature of the primordial fluctuation spectrum we will have to await the results of a series of new experiments, including South Pole experiments which will anisotropies in the CMBR on very small angular scales.  Among other things, the contribution of gravitational waves is expected to be subdominant on such scales even if they were to dominate at large scales.  COBE is also continuing to take data for a 3rd year, and the analysis of three year s data will hopefully provide tighter limits on all quantities.  

(B) Large Scale Structure

 COBE has filled in one piece of a jigsaw puzzle which we hope will eventually lead to a picture of the origin of structure in the universe.  Meanwhile, over the last two years work on filling in the other pieces has continued apace. 
Most interesting in this regard is new evidence, bolstered by the COBE results described earlier, that gravity is responsible for large scale structure.  As early as two years ago, there was still a wide-spread belief that non-gravitational dynamics,   la hydrodynamics, would be required.  I think it is fair to say that all the evidence which now exists points firmly towards the idea that gravity is at work.
First and foremost is the fact that the long-awaited approach to homogeneity in the distribution of matter in the universe is now apparent in the largest sky surveys.  Prior to these, the overwhelming impression one obtained by looking at the well-known slices of the universe---such as that of the Center for Astrophysics redshift survey with its famous  stick-man ---was that coherent structures persisted on scales as large as the largest survey.  Even surveys on scales as large as  100 Mpc on a side recently provided evidence for coherent structures on this scale14.  
Such structures are embarassing, in part because of the observed isotropy of the microwave background, and also because these structures should, at a certain point, leave a direct imprint on the CMBR which could have been observable.  With this in mind, preliminary results from an ongoing survey are telling.   The Las Companas Southern Sky Redshift survey of Oemler et al15 involves a sparsely sampled set of galaxies in the southern sky with redshifts extending out to 40,000 km/sec (or distances of about 4-800 Mpc, depending upon the value of the Hubble constant).   On this scale structures on characteristic scales of O(100) Mpc and smaller are clearly distinguishable, but no  similar coherent structures are observable on larger scales.  The long-awaited approach to homogeneity in the matter distribution may finally have been observed!
Next, additional dynamical support for the role of gravity in structure formation has been one result of an exciting analytical method, called  POTENT , pioneered by Bertshinger, Deckel, and their collaborators16.   At the same time these studies are providing the first direct evidence that in fact W may actual approach unity on large scales.  
At  the heart of the POTENT analysis is data provided by the IRAS satellite I mentioned earlier.  This satellite provide a relatively unbiased all-sky sample of galaxies which have been used to try and extract statistical information about clustering and large scale velocities by a number of groups.  In particular,  the sample of IRAS galaxies has been systematically probed by other means to measure redshifts.  This allows one to extract from the background Hubble expansion the set of peculiar motions of the individual galaxies which may be in response to the local gravitational attraction of regions of overdensity. 
One of the problems with measuring redshifts, however, is the fact that one can only extract directly the radial, line-of-sight component of velocities in this manner.  At the heart of the POTENT analysis is the recognition that if  gravity is the cause of peculiar velocities, then one would expect the curl of this velocity field to be smaller than its gradient:
	 	(17)
 In this case the peculiar velocity field can be written in terms of a velocity potential:
	 	(18)
The goal of POTENT is to reconstruct both the complete velocity field and the velocity potential from the observed redshifts of IRAS galaxies.    From these, the actual gravitational potentials, and density distributions can be inferred.  These latter distributions can then be compared with the actual distribution of luminous objects on the sky.  If the agreement is good, it provides strong evidence that in fact the observed structures and associated velocity fields resulted from gravitational collapse. 
In practice, since the data are sparse, first the observed radial velocity distribution must be smoothed on the sky.  From this, the velocity potential and peculiar velocity field are determined, and the potential and density distribution are determined16: 
	 	(19)
	 	(20)
Note that both these quantities depend upon the cosmic density parameter W.  Thus, the comparison of potent predictions to observations can not only help distinguish the nature of gravitational collapse, but also can help give evidence on the flatness of the universe. 
The results of POTENT thus far are quite impressive.  The predicted density fields are remarkably similar to the observed distributions of matter.  In addition, of more interest, perhaps, is the fact that the value of W inferred by this analysis is W>0.4,17 substantially larger than that inferred by direct dynamical estimates on smaller scales to date.  
Having obtained some idea of the underlying density distribution, POTENT can also allow us to probe how gaussian the initial conditions which may have led to this distribution were.  Interestingly, POTENT  suggests that these initial conditions could only have been gaussian if W is large.  In particular, assuming gaussian initial conditions gives a bound W > 0.3 at the 6-s level!   All previous dynamical estimates on smaller scales suggested that W < 0.3, which implies that there may need to be significant dark matter on very large scales in order for these two estimates to be consistent.
While these results on large scale structure are preliminary, they are quite exciting.  They not only lend strong support to the conventional notion that gravity causes structure in the universe, but they also support the primary prediction of inflation, namely that W =1.  This is the first time in observational cosmology when firm support for both these ideas has been suggested.  

(C)  Dark Matter

Inextricably tied to both of the issues  I have thus far discussed is the question of the nature and distribution of dark matter in the universe.  COBE, by discovering evidence for primordial fluctuations, allows us to explore the spectrum of these fluctuations, and in turn allows a comparison not only with theoretical predictions, but also with estimates which are derived from observations of large scale structure.  The comparison depends crucially however on the nature of the dominant matter in the universe, which determines how fluctuations grow once they enter the horizon.  
The favored generic model of dark matter, based both on particle theory notions, and on large scale structure modelling, is the so-called  Cold Dark Matter  (CDM) model.  When combined with the simplest prediction from inflation---an adiabatic n=1 spectrum of primordial fluctuations, the CDM model makes definite predictions about the clustering of matter on all scales once it is fit to the observed clustering at one scale.  This is one of its great virtues;  it is testable.  
In the last two years, a full frontal assault on the CDM model has been launched by observational cosmologists.  Recent surveys sensitive to clustering on the scale of  100 Mpc and smaller have confirmed what appears to be a generic problem for the simplest CDM scenario18;  too little power is predicted on large scales compared to that observed, and too much power is predicted on small scales, resulting in predicted peculiar velocity fields which are larger than those which are measured.  
As a result of these results one now hears the cry:  Cold Dark Matter is Dead! shouted from many an ivory tower.  I would suggest that, as in the past, reports of the demise of CDM are premature.   A number of possibilities remain:
(i) n 1:  I have discussed already the potential benefits of a spectrum which is not precisely scale invariant.  In particular, a spectrum with n<1 will result in more large scale power for a fixed power on small scales.  Inflation quite plausibly predicts deviations from scale-invariance, especially if gravitational waves are to contribute to the observed COBE signal.  
(ii) isocurvature fluctuations:  Fluctuations in the density of some material which do not lead to overall metric curvature fluctuations: i.e. they are compensated by corresponding density fluctuations in other species, could easily result in some Cold Dark Matter models19,20.   Such fluctuations would tend to produce more large scale fluctuations than the corresponding adiabatic ones. 
(iii)  Cold Plus Hot:  In vogue recently has been the idea that Cold Dark Matter is not all there is.  Instead, CDM might be supplemented by some material (Hot Dark Matter) which does not cluster so efficiently on small scales.  A  prime candidate is a light,   7 eV neutrino, which may be indicated on numerological grounds by present Solar neutrino experiments (discussed later).   A 70% CDM, 30% HDM universe appears to have several advantages over a purely CDM universe for structure formation.   Perhaps the greatest advantage, in the words of George Smoot is:  Full Employment for All! .  It is also worth noting that many of the advantages of adding HDM can also be obtained by a non-zero cosmological constant, which may be called for on other grounds21,22.
 
It may be that none of these fixes will be required.  In the first place, one exciting result of COBE is that it has caused us to rethink the scale where we chose to normalize density fluctuation predictions.  Previously, small scale clustering observations had been used.  Now, however, it seems to make more sense to normalize them at large scales, where we can observe the primordial fluctuations in the CMBR, instead of fluctuations which have been processed inside the horizon to produce the observed cosmic structures.  
If one normalizes the CDM models to the COBE data, one generally can produce the observed--previously coined  excess -- of power on galaxy cluster-scales.  The only remaining problem is the fact that dramatically more clustering is predicted on galactic scales than is observed.  
This latter problem brings to the fore a point which I think should be kept in the back of our minds when confronting CDM models with data.   All along, and this still persists, the chief problem for CDM scenarios has been from data which is the most suspect.  We must remember that we are only just beginning to map large scale structure in the universe.  Thus inferences made today based on scant data may be changed tomorrow.  Similarly, the present conundrum as I have just described it, is based on some convention for determining how the small scale clustering of dark matter should be reflected in the clustering of luminous galaxies.  The fact that the two need not be the same, now known as  biasing , has been an important ingredient in model building, and in computer simulations of CDM-dominated universes.  Nevertheless, we really do not know the correspondence.  No CDM simulations contain enough physics to unambiguously allow a determinations of which dark matter  clumps  should be associated with galaxies.
To summarize; CDM models make definite predictions about the clustering of matter in the universe which have trouble confronting the simplest interpretation of the existing data.  One of two possibilities ensue: either the models are wrong, or the interpretations are wrong.  Nevertheless, in spite of this potential problem, a CDM-dominated W=1 universe, with an n=1 spectrum of fluctuations from inflation, comes remarkably close to describing the observed universe.  I believe it still remains the best, and simplest testing ground we have.  It remains to be seen if it is right. 

(D)  Conclusions?
 
The exciting results of observational cosmology obtained over the past two years have led to an embarrassingly consistent picture.  Many previously discrepant pieces are beginning to come together.  In particular, I believe it is now fair to say that the conventional picture that gravitational collapse is responsible for the observed large scale structure in the universe is now overwhelmingly supported by  the evidence at hand.  Another fact which several years ago seemed to be unsupported but which now is much more firm, is that the universe is likely to have a critical density of matter.   Before the most recent large scale redshift surveys, there was no indication that W might be as large as unity.  Now, the IRAS analyses uniformly suggest this might be the case.  When tied with the COBE observations which support not only the generic predictions of inflation, but also the idea of exotic dark matter, the case for an W=1 universe is now much stronger.  Finally, we have seen proof that when only one sensible idea exists, it is sometimes correct.  COBE has demonstrated that primordial  fluctuations are close to being scale invariant.   Since theoretically that seemed the only reasonable alternative in advance, this discovery is not so surprising as it is reassuring.
In spite of this growing convergence, however, unsettled problems still remain--which is of course good at the very least because it gives us something to do.  The simple Cold Dark Matter dominated universe now has a much greater amount of data to accomodate, and is having a harder time doing it.  I expect that we will have to learn a great deal more before this issue is settled.   Next, an issue I didn t discuss before.  Age estimates, based on models of stellar evolution, consistently  seem to imply that our galaxy is older than the Universe, if the age of the latter is based on the  Hubble age , determined through the measured expansion.  This is more a concern than a problem at present---the uncertainties are still large.  But it does serve as a reminder that we may not yet know it all...
What about the future?  I think without a doubt the central issue in this whole business is the detection of dark matter!  Only then will we have an unambiguous empirical handle on both the early universe, and on the origin of large scale structure.   This issue brings up something that is crucial to remember when attempting to utilize cosmology as a probe of particle physics.  I think the results we have seen over the past few years very strongly support the notion that arguments from cosmology can be  clean  and even testable.  They should be listened to.  However, we must never forget the very important difference between an  observation   and  experiment .   It is only by combining the latter with the former that we can hope to unambiguously probe the universe.   As far as dark matter is concerned, there are ongoing experiments designed to detect various Cold Dark Matter candidates, if they exist, which should be able to report interest limits, if not detections, at the next ICHEP meeting.  The possibility that the tau-neutrino might have a cosmologically interesting mass has now taken on renewed importance.  Both laboratory experiments, based on nm-nt oscillations, and large underground detectors designed to explore the signal from the next supernova, are interesting and useful tools which may shed light on this important issue.
As far as unravelling the spectrum of primordial density fluctuations, new experiments now underway at the South Pole to measure small scale anisotropies will be crucial, as will experiments able to confirm the COBE results.  As far as large scale structure investigations are concerned, besides the new massive redhsift surveys which are essential for mapping the universe, there is much work to be done on numerical simulations.  As I indicated, in order to understand how to label galaxies in a simulation in which the mass being traced is  dark  we must incorporate the physics relevant to baryonic infall and collapse.   Finally,  new technologies are allowing an ever increased sensitivity to trace element abundances in stellar systems.  This will be essential for probing models of stellar evolution which help us date our galaxy, and also for probing primordial nucleosynthesis, my next topic.  
2. big bang nucleosynthesis:                          or ....                                                                    can one have too much of a good thing?
big Bang Nucleosynthesis has been, to date, one of the great success stories of cosmology.  Based on the simplest possible model for an expanding universe, and bolstered by well understood physics, unambiguous predictions were made for the abundance of light elements created in the Big Bang expansion.   These predictions, which vary by over ten orders of magnitude have been, up to the present time, in remarkable qualitative, and where possible quantitative agreement with  observation .  Currently this comparison suggests that the total abundance of baryons in the universe is limited to somewhere between about 1% and 9% of closure density.  At the same time it limits the number of relativistic species present during the formation of primordial helium to less than the equivalent of  3.something light neutrino species, in good agreement with LEP results.  
This is not to suggest that  controversy does not remain.  While the theory of BBN is now quite standard, even allowing for certain uncertainties introduced by possible effects coming from the QCD phase transition, what is by far more uncertain are the measurements and what we can infer from them.    I believe that it is fair to say that in spite of several well publicized potential challenges, at this time BBN remains alive and well.   Nevertheless, we are at the threshold of making several more precise tests which will in any case allow BBN to be an even stronger probe of early universe cosmology.  
The two issues  I want to discuss involve the predicted and observed abundances of He and Li in the universe, the most and least abundant of the observed primordial light elements respectively. 
The fact that approximately 1/4 of the universe, by weight, is He provided the first definitive success of BBN.    Simple arguments, based on the strength of the weak interactions and therefore the abundance of neutrons and protons at the time these interactions freeze out in the early universe immediately pinpointed this as the expected range for primordial He.
This great success has recently become the source of some concern.  Observations suggest, for reasons I will shortly outline, that the primordial abundance of 4He is between 22-24% by weight.  Nevertheless, utilizing limits obtained by a combination of upper limits on observed D and 3He, one finds that BBN predictions are apparently only consistent with observations if the primordial abundance of 4He is greater than 23.5-23.7%23,24,25. (The high value is based on a new investigation of BBN limits incorporating together all theoretical, experimental and observational uncertainties25). This is disturbingly close to the claimed upper limit of 24%.  Moreover, it is well above the  best fit  value which several authors claim is close to, or even below 23%.  
I think that in this case one picture is worth a thousand words.  















Figure 3: Helium Fraction (Y) versus Nitrogen Abundance (from Olive et al26)

In order to determine the actual primordial abundance astronomers try to measure the helium content in stars with smaller and smaller abudances of heavy elements, such as oxygen and nitrogen.  Such stars are presumably older, because the material in them has been less processed.  Based on extrapolating the observed trend in Helium as a function of either oxygen or nitrogen, or some other heavy element, astronomers try and determine the primordial abundance.  Above I display one such set of data, and the statistical fit for a relation between helium and nitrogen abundances. 
I think it is clear from this picture that while a best fit relation may extrapolate, at low metallicity, to a value near or below 23%, it is also clear that systematic errors are at least as important as statistical ones here.  From data like this, it is not clear, to me at least, that a distinction between an upper limit of 24% and 23.7% is meaningful27.  For example, without a first principles understanding of the helium-nitrogen relation one sensible way to estimate the uncertainty in this relation is to examine the uncertainty on the lowest metallicity point. 
While I think the present uncertainties imply that BBN predictions remain safe, these same uncertainties point out more generally the danger in over-interpreting the data.   For example,  the 4He abundance also is central for the argument which gives an upper limit on the number of neutrinos.   Specifically, an upper limit on the sum of primordial D + 3He yields a lower limit on the baryon density of the universe at the time of BBN.  Because the predicted 4He abundance rises monotonically with increasing baryon density, putting a lower limit on this latter quantity also puts a lower limit on the predicted 4He, i.e. the value of 23.7% quoted earlier.  Now the predicted 4He abundance also increases monotonically with the number of relativistic neutrino species present during BBN.  Thus, an observational lower  bound on 4He puts an upper bound on extra neutrinos.   If an upper bound of 24% on 4He is used, a bound of Nn <3.4 has been claimed24.  However, it is very important to recognize that if one raises the upper bound on 4He to  24.2%, this upper bound on Nn increases to  3.6.   If one includes additional possible uncertainties in the D+3He bound this number could increase to  3.7-3.8.  
None of these arguments takes away from the power of BBN to limit the number of new particles in nature.  However, we have seen, with the 17 keV neutrino, that there may be a world of theoretical difference between 3.4 and 3.6 extra effective species in the radiation gas at T  1 MeV.   Before hanging one s theory on the hope of being able to distinguish between the BBN predictions for 3.4 and 3.6 species, some appreciation of the uncertainties in the limits on 4He and the other light elements is warranted.
Finally, what if the actual primordial abundance of 4He were less than 23.7%?  What might the weak link in BBN then be?   My own suspicion is that the D + 3He limit might be revisable upwards.  In this case a lower baryon density would be allowed, and thus a lower abundance of 4He.   I find this particularly attractive because not only would it allow slightly more 7Li to be produced (see below), but it would also make the BBN predictions for the baryon abundance in the universe closer to the observed abundance of luminous matter.  In this case, what you see would be what you get, a possibility I find appealing. 
Next to 4He the element which now appears to provide the most sensitive tests of BBN predictions is 7Li.   In particular, it is the bound on its primordial abundance which now yields one of the stringent upper bounds on the baryon density today, and hence which gives evidence in favor of exotic dark matter. 
	There has been some controversy in the past regarding the comparison of BBN predictions with observations. In particular, BBN predicts that as a function of the baryon density the predicted abundance of 7Li reaches a minimum and then rises again.  The baryon density which is consistent with observed 4He and D+ 3He abundances falls right near the minimum in the predicted 7Li abundance, near about 10-10.   Looking at very old halo stars, Spite and Spite28 observed a plateau in the 7Li abundance near a value of 10-10.  One can derive upper and lower limits on this abundance which are consistent with the BBN predictions,  if one assumes the 7Li abundance in these old objects is indicative of the primordial value, as shown below29.  (The figure below was used because I have the graphics file on disk.  An updated comparison can be obtained in ref 25.)

 
Figure 5: Lithium BBN Predictions and Inferences from Old Halo Stars.
 
At the same time, there has also been a 7Li plateau observed in another set of much younger stars.  The 7Li surface abundance in these stars is an order of magnitude higher than that in the old halo stars.  The question then becomes: Which population yields the true primordial value?  If the old halo stars do, then Li must be produced in the Galaxy.  If the younger stars do, then Li must be destroyed over time in stars.   More important, perhaps, if the younger stars do, then it would be very difficult to explain this value in the context of standard BBN for a range of baryon densities consistent with the other elemental abundances.  
There have been interesting theoretical arguments in favor of both alternatives.  As a result, one would like to have alternate probes of the relevant physics.  One of the most interesting of such probes involves another isotope of lithium, 6Li.  This isotope is much more fragile than 7Li, and is more easily destroyed in stars.  Moreover, BBN estimates suggest that 6Li should be produced primordially at levels far below that of 7Li.   Interestingly, however, alternative BBN scenarios often predict a much larger 6Li/7Li ratio than standard BBN. 
For this reason, there has been great interest recently when the first-ever measurement of 6Li surface abundance in a stellar system was performed30.  Observing an old halo star system, an abundance ratio 6Li/7Li   .05 was reported.  This is an extremely interesting result, if confirmed.  Because 6Li is destroyed much more readily in stars than 7Li, this observation suggests that if this observable remnant 6Li abundance remains in an old halo star, the change in the 7Li abundance, even if the two isotopes were produced initially with equal  abundance, cannot have been great.   This appears to provide strong support for the standard BBN picture.  
However, at the same time focus shifts from the question of how much 6Li was destroyed, to the question of how the 6Li abundance got so large in the first place.  As I said, standard BBN generically predicts the primordial  6Li/7Li ratio to be small.  Is this then a sign of a problem?   Again, the answer at this time seems to be: not yet.  Arguments regarding Li and Be production in the galaxy by cosmic rays31 had earlier been used to predict sufficient 6Li production to lead to a potentially observable 6Li/7Li ratio today.  But it is not yet clear whether, allowing for stellar destruction of Li, whether as large a ratio as has been observed can be accomodated. 
I think observations such as these are leading to the point where precision tests of the BBN picture are possible.  At the present time, not only does the overall qualitative agreement of theoretical prediction and observational evidence persist, but so does the quantitative agreement.   It now appears that the He abundance alone, in spite of the uncertainties I have concentrated on, provides a constraint on not only the number  of neutrino species, but also provides both upper and lower limits on the allowed baryon density in the universe.  The situation in the latter case is so tightly constrained that if the actual primordial He abundance could be reliably estimated to less than 5% one could in principle pinpoint a single value of the baryon density which would be consistent with standard BBN.  At the same time, the Li situation is evolving quite quickly.  It provides an independent probe of both standard and non-standard BBN, and also of models of stellar evolution.  Thus the interest in new observations is very great, and should remain a high priority. I have no doubt that new results in this area will in fact occur between now and the next ICHEP meeting.  

solar neutrinos                                               or....                                                                   THe sun also rises.
Next to COBE, perhaps the most exciting new astrophysical measurements of interest to particle physics have come from two experiments designed to detect the flux of low energy neutrinos from the sun.    Solar neutrinos have been observed for more than two decades now, thanks to Ray Davis and colleagues who have used a Cl detector in the Homestake mine.  This experiment, primarily sensitive to the high energy B solar neutrinos, has observed on average between 1/4 and 1/3 the expected solar neutrino signal since the 1960 s--- establishing the now famous  Solar Neutrino Problem .   Since 1989, the Kamiokande large underground water Cerenkov detector, sensitive to only the high energy B flux, has reported a signal which is about 1/2 that predicted by the most often quoted  standard  solar model32.   This detector has directional information and can therefore unambiguously associate the detected neutrino events with the sun.
Because the high energy B neutrinos are produced in reactions which only contribute marginally to the solar luminosity, there has been great interest in measuring the dominant, low energy pp neutrino flux, with a maximum energy of .42 MeV.   In order to be convinced that the observed paucity of events in Homestake and Kamiokande have their origin in new neutrino physics, it has been clear that an experiment sensitive to this dominant flux of solar neutrinos is required.   While one could remove the reactions which produce the entire B flux by some as of yet unknown astrophysical mechanism without significantly altering solar energetics, one could not remove the pp flux without turning off the sun.
In the last two years, with an anxious physics community chomping at the bit, the Soviet American Galium Experiment (SAGE) and the European GALLEX experiment have come on line and reported their results.  The results have been, at the very least, surprising.  I shall not have time to review the experimental details of these efforts (I think Hamish Robertson has done so in his lecture33) but will only quote the final results here.   
In the table below I list the four operating solar neutrino experiments, their thresholds, and their quoted average rates.  To simplify the table I have symmetrized the quoted statistical and systematic errors and added them in quadrature. 

Experiment Ethreshold
(MeV) Av. Rate/SSM34
 Homestake .81  0.28   0.0435 KamiokandeI-II 7.5 0.46   0.0836 KamiokandeI-III 7.5 0.49   0.0837 SAGE (1st yr) .24 0.15   0.2838 SAGE (2 yrs) .24 0.44   0.2139 GALLEX .24 0.63   0.1640 
Having the results of these 4 experiments, what have we learned after 25 years?

(1) The sun is probably shining:  This is not an entirely facetious remark.  As I have indicated, until the most recent set of  gallium experiments we had not probed the dominant energy producing reaction in the sun.   The first SAGE result was consistent with zero signal, indicating either the sun had turned off, neutrinos were not making it to earth, or the experiment was not detecting the flux.   The GALLEX signal, on the other hand, if interpreted as a solar neutrino signal and not a background related signal, implied that there was indeed a non-zero pp flux from the sun.  Hence the sun is shining.  More recently, after 2 years of running, the SAGE experiment has also quoted a number which is no longer consistent with zero. 
In fact, while it is often stated that the pp flux from the sun is model independent, and should account for at least an 80 SNU (0.6 SSM) signal in the gallium detectors, this is not quite correct.  As has been stressed, for example by Michel Spiro41, if we want to espouse what I would call the  agnostic view , which states that we really don t know anything about the sun, even this seemingly innocuous statement about the pp flux is an overstatement.  I suspect, based on my discussions with many particle physicists, that many are sympathetic to at least a mild agnosticism, coming from their suspicion of all things astrophysical.  
Independent of any solar physics whatsoever, all we really know is the total  neutrino flux from the sun.   This can be immediately calculated from the following facts 
(a) the solar luminosity is 1033 ergs/sec,
(b) 25 MeV is released per 4He formation
(c) 2 n s  are released per 4He formation.
Combining these together fixes the total solar neutrino flux.  If one is willing to ignore all conventional wisdom, one can fix the Be and B neutrino flux by combining the Homestake and Kamiokande results, and therefore fix the expected pp flux to make up the difference.  In this case, one predicts the gallium signal, assuming all neutrinos which are produced in the sun make it to the earth.  The predicted signal is 85 SNU, exactly what GALLEX sees!
One thus might be tempted, and many people have been, to use an argument like this, or else the fact that the GALLEX signal alone is on 2s away from the standard solar model prediction, to argue that there is in fact no solar neutrino problem.   The problem with the above argument is, however, that we do  know something about the sun!   In particular, we know that the Be neutrino flux is much less sensitive to variations in the solar core temperature than is the B flux, and thus it is extremely difficult to imagine varying them in such a way so that the Be flux is more suppressed than the B flux.  This is what is required to reconcile the Homestake and Kamiokande results, as the former, which is sensitive to both Be and B reports a smaller signal than the latter which is only sensitive to B neutrinos42,43.    This leads to my second conclusion:

(2) A neutrino-based solution of the solar neutrino problem remains favored:     There are a number of different, but equivalent ways of expressing this fact.  They all reduce to the following observation:  While the standard solar model prediction is only 2s away from the GALLEX observation, it is much further away  from the other observations.  Neutrino-based solutions, however, lie within 1s of all the observations, for some finite parameter range.    Moreover, even any real or imagined astrophysical variations of the standard solar model do not produce agreement of better than 3-4s with all the experiments.   One graphical demonstration of this which I find particularly appealing (at least in part because I and my collaborators prepared it43) is based on graphing the predictions of various models not in model-parameter space, but rather in experiment vs experiment space.   In this case, one can get an immediate visual idea not only of the agreement between observations and theoretical predictions, but also of the  predictivity  of a model.  For example, if a model can accomodate all points in this space, the fact that it may agree with a particular set of observations is not that significant.  Below I show the predictions of scaling the B, or the B plus Be flux by a variable core temperature, and also the predictions of the favored MSW model for neutrino oscillations, in Homestake-Kamiokande space.  In each case, we have allowed Monte-Carlo variations of all relevant solar neutrino parameters within the 1s uncertainties of the standard solar model43. 

 
 
Figure 4: Model Predictions for Rates in Homestake and Kamiokande detectors43

As can be seen from this figure, even allowing the solar core temperature to vary arbitrarily does not bring the predictions, including solar model flux uncertainties anywhere near the 20 year averaged data.  Indeed, as expected this kind of variation inevitably suggests a greater suppression of the Homestake rate than the Kamiokande rate.  The MSW model, for example, on the other hand makes definitive predictions about the relative rates which can be in good agreement with this set of observations.  
It is also enlightening to present the same plot for Gallium versus  Kamiokande for these same models.  I show here the GALLEX and updated SAGE results as well:

 
Figure 5:  Predictions for Rates in Gallium and Kamiokande Detectors for varying Solar Core Temperatures.

Here the MSW locus of predictions is not shown, because it essentially fills almost all the experimental phase space, i.e. any set of experimental predictions for these experiments can be fit by some MSW parameter.  Thus, it is not too surprising that the GALLEX and SAGE data points can be fit.   What is worth noting, however, is that while lowering the solar core temperature can lower the gallium prediction to at least the range observed by GALLEX, even here the model fit is not that good, because significantly lower Kamiokande rates would be predicted than are observed.  The fit is at best about 2s in this case. 
Thus, as advertised, astrophysical variations do not fit the combined data from the 4 experiments well, while neutrino based solutions, of which the MSW solution has been displayed here, do.  It is worth pointing out that the MSW predictions are not unique in this regard.  Essentially all neutrino-based models which could be made consistent with the Cl-Kamiokande results, including vacuum oscillations and neutrino magnetic moment based oscillations can be made consistent with all the data.44   Thus, while a neutrino-based solution of the solar neutrino model remains favored, which  solution is the right one is not yet unambiguous.  This does not stop one from exploring which region of mass-mixing angle space fits the data, and a number of different groups have done just this45,46,47,48.  Below I show again our own analysis, which includes a global fit to all the current data in Table 1, as well as solar model flux uncertainties, and shows the allowed (90% conf.) vacuum and MSW oscillation regions on the same plot48:

 
Figure 6: Allowed Range of Neutrino Mass-Mixing for Global Fit to All Experiments48,

 It is even possible to draw (although impossible to read) the allowed region in 3D parameter space in the case that there are oscillations between all of the known species.  This general non-uniqueness of the possible solutions sets the stage for my third conclusion:

(3)  Gallium experiments have not yet changed the Solar Neutrino Problem..  Specifically, the problem still stands or falls on the Homestake result, even after 25 years:   Sad but true.  The only range in which gallium could not further enlighten us as to the origin of the solar neutrino problem was in the range observed by GALLEX.  Had the number been definitively higher it would have argued strongly in favor of an astrophysical solution.  Had it been definitively lower, as SAGE first indicated, it would have argued strongly in favor of a neutrino-based solution.  Moreover both the gallium results and the Kamiokande results are not sufficiently far from non-exotic variations in the standard solar model as rule out these possibilities.  What was, and still remains damning for these models is the Homestake-Kamiokande combination; specifically the fact that Homestake reports the largest suppression.  If the Homestake result were somehow discredited, and there no evidence at this point that it should be, I think much of the basis of the neutrino solution of the solar neutrino problem would evaporate.

(4)  What we still need are high statistics counting experiments, and eventually experiments sensitive to the full solar neutrino spectrum.    What the current confusion points to, at least in part, is the inadequacy of rare counting experiments.   What one would like is several thousand events/year rather than several events per year.  This is what SNO, Super-Kamiokande, and to some extent BOREXINO promise.   Moreover SNO, with its neutral current capacity, at least in principle, could unambiguously resolve whether neutrino oscillations between the known neutrinos are responsible for the observed signals.   Finally, even if this is the case, determining the neutrino mass parameters will still probably require spectral sensitivity to low energy neutrinos49. 

Thus, while this is probably the 10th  ICHEP review of the solar neutrino problem over the last 20 years or so, we are unfortunately not yet within clear sight of a solution.  Given the probable need for the next generation of detectors, which come on-line around 1996, and given that at least 1 year of running will be required,  I  predict that the problem will remain with us for at least the 1994 and 1996 meetings.  However, the good news is that the answer may appear before the next millenium.

4.  Cosmic rays and Gamma rays:             or.....                                                                       That which is not Forbidden is Required.
Cosmic ray physics has sometimes been a  murky arena.   Yet in the last few years a number of exciting observations have occurred in the field of high energy gamma ray physics which demonstrate exceptionally well the fact that the rationale need not be equated with the mundane.   Moreover, while it is less sexy, another important development has taken place.  High energy detectors around the world have mastered the art of measuring a Gaussian centered at zero with width 1s.   That is, with increasingly unerring accuracy the new generation of cosmic and gamma ray detectors have reported at this meeting seeing nothing where nothing was expected.50  I hope this is not too discouraging to the observers, because it means that the field has achieved a level of maturity where both null results and observations are believable and repeatable.   I shall concentrate here however on three new and exciting results: the isotropy of Gamma Ray Bursters, and the observation of High Energy gamma rays from the CRAB pulsar and a new more exotic object called Markarian 421, because I believe each of these provides an interesting object lesson for particle physicists. 
Before reviewing these areas, however,  I want to begin with a more fundamental issue which I have found is unfortunately not often stressed in the experimental reviews I have read and heard.   That is: why do cosmic ray physics at all?    As far as I can see the central point is the following: Cosmic rays have been observed up to 1020 eV.  They are isotropic, and the charged particles observed with energies greater than 1015 eV are extragalactic.   Thus, their origin is of cosmological interest.  Moreover, we have no idea at the present time of: (a) the source(s), and (b) the acceleration mechanism which produces such incredibly high energies.  It is thus quite likely that when we do learn about these issues, we will learn interesting new physics, or at the very least, discover interesting new objects.  Finally, if we are to do astronomy, that is if we want to associate sources with observed signals we need to detect neutral particles such as photons, or neutrinos.  It is only in this way that we can be sure that we can point back from the signal to the source. 

(a)  Gamma Ray Bursts:  

I learned from Tsvi Piran s talk at this meeting51 that gamma ray bursters were discovered by the VELA system of satellites in 1967.  These were designed to monitor nuclear weapons testing on earth but could also look outwards for more exotic signals.  These objects produce a burst of kev-MeV gamma rays with a duration of between 0.1 and 100 seconds. This time variability suggests that they have a radius less than about 3000 km, making neutron stars prime candidates.  The big surprise of the past year or so, however, was the observation by the COMPTON satellite of over 150 bursts during the course of a year with a distribution which was statistically isotropic.  This is completely unexpected if the sources of these bursts are in our galaxy.  Moreover,  the distribution of intensities follows a canonical -3/2 power law which is characteristic of a cosmological distribution rather than a local one.  
What is so surprising about the possibility that gamma ray bursters are cosmological in origin is the requirements on their net luminosities in order to produce the observed fluences here on earth, which are in the range of 10-5 ergs/cm2.  Assuming isotropic emission one then estimates intrinsic gamma ray luminosities on the order of 1051 -1053 ergs for these objects for redshifts of order unity. 
One explanation for these events, if they are cosmological is particularly intriguing, not merely because of the astrophysical interest, but because it demonstrates that even the most implausible events may happen regularly in the universe.  The prime candidate explanation at present appears to involve coalescing neutron starts which should produce huge amounts of energy.  What is particularly remarkable about this possibility is that such events are predicted, based on estimates of the neutron star binary abundances in typical galaxies, to occur at a rate of about 10-6/yr per galaxy.  However, if one integrates out to a distance of a Hubble length, over which they should be observable, one estimates a predicted event rate of about 1000 events per year.   This is more or less the rate which is seen. 
I have no idea whether this explanation is correct.  If it is, there will no doubt be other interesting signals, including, I would imagine, potential neutrino signals.  However, it should remind us that we should not be timid in imagining what new sources are out there.  

(b)  High Energy Gamma Ray sources and Telescopes:

A new generation of Cerenkov imaging detectors for electromagnetic shower detection52,53has brought forward the discovery of a number of interesting sources.  What is particularly nice about these detections is that they do not involve statistics.  In each case a clear image of the source has been obtained, which can be identified with a known astronomical source.  Because this meeting is near the SSC site, I thought it would be particularly appropriate to review the two most interesting sources, both of which have application to SSC physics.
(i) The first source is the Crab pulsar, located at a distance of about 2200 parsecs.  This is the highest energy known source of gamma rays in the universe.  Gamma rays in the range of 3-15 TeV have been detected at the Whipple observatory52, and based on the observed flux, and assuming isotropic emission one obtains a continuous luminosity of about 1036 ergs, or about 1000 times the solar luminosity , in this energy range.  This must be therefore a truly remarkable accelerator! 
What makes the Crab even more remarkable is the proximity in energy with that of the SSC center of mass energy.  In 1999, when the SSC turns on, it will overtake the Crab and be, barring other discoveries, the highest energy accelerator known not only in Texas, or the US, or the world, but in the Universe!  I hope this fact will prove useful in discussions with politicians.
(ii)  The second source I want to discuss was also first seen in TeV gamma rays at the Whipple Observatory52.  It goes by the name of Markarian 421, and is associated with a known optical source at a distance of about 125 Mpc.  The gamma ray signal is seen with good (0.1o scale) angular resolution and has been observed continuously over a period of months.  Moreover, the image distribution matches exactly the Crab profile.  While the maximum energy of the observed signal is not quite as high as the Crab, rather in 1 TeV range, it is not this maximum energy which makes Markarian 421 so remarkable.   Using the measured flux in TeV gamma rays one determines an estimated luminosity of   3 x 1042 ergs/sec in this energy range!  This is over one billion times the luminosity of the sun, in TeV gammas!   Put another way, this is equivalent to emitting the energy equivalent of about .001 solar masses per year in TeV gamma rays!    Whatever this object is, it is truly remarkable.  More relevant to this meeting, whatever it is, it is a very efficient TeV accelerator.  It may prove very useful to particle physics to understand how and why.
Going further on these lines, consider the following.  Say that Mrk 421 originates with a civilization whose congress was more advanced than ours and approved and funded a working SSC by the present time.  Imagine further that the SSC beam was pointing directly at the earth from a distance of 100 Mpc.  How would it stand up compared to the flux from Markarian 421?    Assuming a beam spread of about 4 x 10-6 radians, which is probably somewhat better than the design specs for the SSC, I derive an observed flux at earth which is approximately 10-8 times the measured Mrk flux.  Thus Markarian 421 has a luminosity in TeV gamma rays, presumably in every possible direction,  of approximately 100 million SSC s!

Moving from these awesome objects, it is perhaps fitting to close this review of cosmic ray physics with an eye to the future.  In particular, one s imagination cannot help being captured by the ultimate cosmic ray array, being promoted by Jim Cronin as an internationally funded device.  This array would have over 2500 detector stations located in a square grid, about 1.5 km apart, communicating with each other by microwave relays.  The beauty of this proposal is that it takes a particle physics approach to the problem of cosmic ray detection.  If we are to ever learn about the origin of the highest energy cosmic rays we have learned from experience that we will probably never do so by detecting 1 or 10 events per year.   The Array 5000 detector system will have a predicted event rate of particles with energy in excess of 1019 ev of 5000 events/year!   This is to be compared with the entire integrated world sample of such events which as present is less than 100 events....  In the words of Shelly Glashow, who said when arguing in favor of a now existing accelerator in Geneva:  Do you want to walk, or do you want to fly? ....

5. Conclusions
Had I more time in this lecture I would certainly have included at least two more topics which I have not been able to treat here.  They are: Electroweak Baryogenesis, and The Curse of the Planck Scale.  The former has shown that even the standard model can be interesting....in spite of LEP.   A great deal of work has been devoted to exploring the possibility that the observed baryon density of the universe, namely all the we can see, was generated dynamically not at the GUT scale, but rather at the electroweak phase transition.  In the process, at the very least, new insights into the nature of the electroweak transition have been gleaned.  I refer interested readers to a recent review volume54.   The latter topic relates to the possibility that the Planck scale might not be impotent, as far as low energy physics is concerned.   First, it has been argued that the quantum theory of gravity, whatever it may be, can lead to measurable violations of global symmetries at low energies55. While this idea has been around for some time56, it has taken on renewed interest with various cosmological proposals which require unbroken global symmetries below the Planck scale.  Second, it has been proposed that physics at the Planck scale might be responsible for ensuring symmetries when nothing else does.  In particular, it might solve the strong CP problem57.  The only problem with these proposals is that we do not have a theory of quantum gravity with which to check them.  In particular, for every argument in favor of the first, having to do with gravitational violation of global symmetries, there exists an equally attractive counter-argument.   Nevertheless, they do open, at least in principle, the possibility that low energy measurements might tell us something about physics at the Planck scale.  
These topics aside, what conclusions can we draw from the developments of the past two years which I have reviewed in depth here?   I think first and foremost, we live in interesting times for cosmology:
(i) We now have further proof that the Big Bang Really  Happened!   
(ii) For the first time, the holy trinity of modern cosmology: inflation, a flat universe, and gravitational clustering as the source of large scale structure, may now finally be consistent with observation.  
(iii) At the same time, Cold Dark Matter may, or may not, finally be inconsistent with observation.   
(iv) Big Bang Nucleosynthesis is still alive and kicking, and at the threshold of several precise tests which can prove it is virus free.
(v) Neutrinos which can prove the sun shines have finally probably been observed.  They have not yet solved the Solar Neutrino puzzle, but they do give us cause for hope in 1998.  He who waits is rewarded. ..
(vi) Cosmic ray physics has spawned a new generation of detectors.  New incredible objects have been discovered, and there is no doubt that more surprises await.  

Perhaps the real lesson of these results is that as far as cosmology and astrophysics are concerned, the 1990 s could well be the Decade of Discovery.   They might do for astophysics what the period 1967-1977 did for particle physics.  Of course, this might be a curse instead of a blessing.    Nevertheless, it is patently clear that the complementarity between particle physics and cosmology not only persists, it is thriving.  


 
Acknowledgements:
This review would not have been possible without the aid of a number of individuals who helped tutor me in various areas, or who informed me of new, late-breaking results.  In particular I want to thank Ren  Ong for his patience and kind explanations of various phenomena in high energy gamma ray physics, which helped clear up many questions I had.  I also want to thank Gary Steigman for discussions of Lithium abundances, George Smoot, Gary Hinshaw, Paul Steinhardt and Martin White for discussions (and in the latter case collaborations) on COBE, and also Martin White and Evalyn Gates for their collaboration on issues related to the solar neutrino problem.  


References
1.	J. C. Mather et al,  A Preliminary Measurement of the Cosmic Microwave Background by the Background Explorer (COBE) Satellite,  Ap. J. 354, pp. L37-L40 (1990).

2. 	T. Matsumoto et al,  The Submillimeter spectrum of the Cosmic Background Radiation,  Ap. J. 329, 567-571 (1988).

3. 	see G. F. Smoot, these proceedings; also G. F. Smoot et al,   COBE Differential Microwave Radiometers: Instrument Design and Implementation,  Ap. J. 360, 685-695 (1990); G. F. Smoot et al,  Structure in the COBE Differential Microwave Radiometer First-Year Maps , Ap. J. 396, L1-L5 (1992).

4. 	C. L. Bennett et al,  Preliminary Separation of Galactic and Cosmic Microwave Emission for the Cobe Differential Microwave Radiometer , Ap. J. 396, L7-L12 (1992).

5.	see for example, P.J. E. Peebles, The Large Scale Structure of the Universe, Princeton: Princeton U. Press, 1980.

6. 	E. R. Harrison,  Fluctuations at the Threshold of Classical Cosmology,  Phys. Rev. D1, 2726-2730 (1970); Ya. B. Zel dovich,  A Hypothesis, Unifying the Structure and the Entropy of the Universe,  MNRAS  160, 1P-3P (1972); P.J. E. Peebles and J. T. Yu,  Primeval Adiabatic Perturbation in an Expanding Universe,  Ap. J. 162, 815 (1970).

7.	see J. Frieman, Inflation , these Proceedings.

8.	see J. Gelb,  N-body Simulations of Cold Dark Mattter , these Proceedings.

9. 	see E. L. Wright et al,  Interpretation of the Cosmic Micreowave Background Radiation Anisotropy Detected by the COBE Differential Microwave Radiometer , Ap. J. 396, L13-L18 (1992).

10. A.A. Starobinsky,  Spectrum of Relic Gravitational Radiation and the Early State of the Universe,  JETP Lett 30, 682-685 (1979).

11. L.M. Krauss and M. White,  Grand Unification, Gravitational Waves, and the Cosmic Microwave Background Anisotropy , Phys. Rev. Lett. 69, 869-872 (1992).

12.	i.e. see M. Peskin,  Beyond the Standard Model , these proceedings.

13.	R. L. Davis et al,  Cosmic Microwave Background Probes Models of Inflation ,  Phys. Rev. Lett. 69, 1856-1859 (1992); D.S. Salopek,  Consequence of the COBE Satellite for the Inflationary Scenario , DAMTP preprint,  submitted to Phys. Rev. Lett. ;  L. M. Krauss,  COBE, Inflation, and Inflation Scalars , Yale preprint, submitted to Phys. Rev. Lett.

14.	W. Saunders et al.,  The Density Field of the Local Universe,  Nature  349, 32-38 (1991).

15. A. Oemler, D.L. Tucker, R.P. Kirshner, H. Lin, S.A. Shectman, P.L. Schechter,  The Las Campanas Deep Redshift Survey" to be published in Observational Cosmology, A.S.P. Conference Series, 1993.

16. see A. Dekel,  Large Scale Structure: Dynamics  and references therein, to appear in Proceedings of Rencontres de Blois, Particle Astrophysics, June 1992, Editions Frontieres, to appear; see also, A. Dekel, E. Bertshinger, A. Yahil, M. Strauss, M. Davis, and J. Huchra, to appear.

17.  see A. Yahil,  Extra Galactic Dark Matter  and references therein, to appear in Proceedings of Rencontres de Blois, Particle Astrophysics, June 1992, Editions Frontieres,  to appear.

18. see J. Gelb,  N-body Simulations of Cold Dark Mattter , these proceedings; also J. Gelb, MIT Ph.D thesis;  M.A. Strauss and M. Davis,  in Large Scale Motions in the Universe, Princeton: Princeton U. Press (1990).

19.  D. Seckel and M. S. Turner,  Isothermal  Density Perturbations in an Axion-dominated Inflationary Universe,  Phys. Rev.  D32, 3178-3183 (1985).

20. L. M. Krauss,  COBE, Inflation, and Inflation Scalars , Yale preprint, submitted to Phys. Rev. Lett.

21. see L.M. Krauss,  Non Baryonic Dark Matter  and references therein, to appear in Proceedings of Rencontres de Blois, Particle Astrophysics, June 1992, Editions Frontieres,  to appear.

22. G. P. E. Efstathiou, W. Sutherland, S.J. Maddox,  The Cosmological Constant and Cold Dark Matter,  Nature  348, 705-707 (1990).

23. L. M. Krauss and P. Romanelli,  Big Bang Nucleosynthesis: Predictions and Uncertainties , Ap. J. 358, 47-59 (1990).

24. T. P. Walker et al,  Primordial Nucleosynthesis Redux , Ap. J.  376, 51-69 (1991).

25. M. Smith, L. H. Kawano, and R. A. Malaney,  Experimental, Computational, and Observational Analysis of Primordial Nucleosynthesis ,  Caltech preprint OAP-716, submitted to Ap. J.   May 1991.

26.  K. A. Olive, G. Steigman and T.P. Walker,  The Upper Bound to the Primordial Abundance of Helium and the Consistency of the Hot Big Bang Model , Ap.  J.  380, L1-L4 (1991).

27. see ref. 26, and also B.E.J. Pagel, A. Kazlauskas,  Primordial Helium: The Third Decimal Place , Nordita preprint, 92/24A, submitted to MNRAS. 1992.

28. F. Spite and M. Spite,  Lithium Abundance in the Nitrogen-rich Halo Dwarfs,  Astron. Astrophys. 163, 140-144 (1986).

29. L. M. Krauss and P. Romanelli,  Big Bang Nucleosynthesis: Predictions and Uncertainties , Ap. J. 358, 47-59 (1990).

30. V. Smith et al, U. Texas preprint, 1992.

31. G. Steigman and Terry P. Walker,  Production of Li, Be, and B in the Early Galaxy,  Ap.J. 385, L13-L16 (1992).

32. for a further discussion see J. Bahcall,  Solar Neutrino Predictions , these proceedings.

33. see H. Robertson,  Non-Accelerator Physics , these proceedings.

34. J. Bahcall, Neutrino Astrophysics,  Cambridge: Cambridge University Press, 1989.

35.  see ref. 34;  also R. Davis Jr. in Proceedings of the Seventh Workshop on Grand Unification, Toyama, Japan 1986, ed. by J. Arafune, Singapore: World Scientific 1986.

36. K. Hirata et al.,  Constraints on Neutrino-Oscillation Parameters from the Kamiokande-II Solar-Neutrino Data,  Phys. Rev.  Lett. 65 1301-1304 (1990);  Search for Day-Night and Semiannual Variations in the Solar Neutrino Flux Observed int he Kamiokande-II Detector,  Phys. Rev. Lett. 66, 9-12 (1991).

37.  see T. Kajita,  Solar and Atmospheric Neutrinos , these proceedings.

38. A. I. Abazov et al,  Search for Neutrinos from the Sun Using the Reaction 71Ga(ne,e-) 71Ge,  Phys. Rev. Lett.  67, 3332-3335, (1991).

39.  A. Gavrin,  Summary of the Soviet American Gallium Experiment , these proceedings. 

40.  D Vignaud,  Report on GALLEX , these proceedings.

41.  M. Spiro and D. Vignaud,  Solar Model Independent Neutrino Oscillation Signals in the Forthcoming Solar Neutrino Experiments,  Phys. Lett. B242, 279-284 (1990).

42.  J.N. Bahcall and H. A. Bethe,  A Solution of the Solar Neutrino Problem,  Phys. Rev. Lett. 65, 2233-2235 (1990)

43. see. M. White, L.M. Krauss and E. Gates,  A New Look at the Solar Neutrino Problem ,  Yale preprint YCTP-P14-92 April 1992, submitted to Phys. Rev. Lett. 

44.  see for example C. S. Lim et al,  Correlation Between Solar Neutrino Flux and Solar Magnetic Activity for Majorana Neutrinos,  Phys. Lett. B243, 389-395 (1990); P. I. Krastev and S.T. Petcov,  Neutrino Oscillatiosn in Vacuum as a Possible Solution of the Solar Neutrino Problem,  Phys. Lett. B285, 85-90 (1992);  E. Gates, L.M. Krauss, and M. White,  Solar Neutrino Data and Their Implications , Phys. Rev. D46, 1263-1273 (1992).

45.   X. Shi,D.N. Schramm, and J.N. Bahcall,  Monte Carlo Exploration of Mikheyev-Smirnov-Wolfenstein solutions to the Solar Neutrino Problem , Phys. Rev. Lett.  69, 717-720 (1992).

46. S. Bludman et al, Penn preprint, July 1992.

47.  P. I. Krastev and S.T. Petcov,  Neutrino Oscillatiosn in Vacuum as a Possible Solution of the Solar Neutrino Problem, , Phys. Lett. B285, 85-90 (1992).

48. L.M. Krauss, E. Gates, and M. White,  Solar Neutrino Data, Solar Model Uncertainties, and Neutrino Oscillations , Yale preprint YCTP-P38-92, Sept 1992, submitted to Phys. Lett. B. 

49.  see for example,  ref. 43, and J. M. Gelb, W. Kwong and S. P. Rosen,  Implications of new GALLEX results for the MSW solution of the solar neutrino problem , Phys. Rev. Lett.  69, 1864-1866 (1992)

50.  see D. Williams,  Results from the CYGNUS expt and Plans for MILAGRO ,  T. McKay,  Search for Astrophysical Gamma Rays above 100 TeV , C. Akerlof,  TeV gamma rays from Markarian 421 , P. Baillon,  Detection of Very High Energy Gamma Rays from the Crab Nebula , M. Longo,  Muon and Neutrino Astronomy (MACRO) , these proceedings. 

51. see T. Piran,  Gamma Ray Bursters , these proceedings.

52. see C. Akerlof,  TeV gamma rays from Markarian 421 , these proceedings.

53. see P. Baillon,  Detection of Very High Energy Gamma Rays from the Crab Nebula 

54.  see Baryon Number Violation at the Electroweak Scale,  ed. L.M. Krauss and S.J. Rey, Singapore: World Scientific, 1992, to appear. 

55.  eg. see M. Kamionkowski and J. March Russell,  Planck-scale Physics and the Peccei-Quinn Mechanism,  Phys. Lett. B282, 137-141 (1992); R. Holman et al,  Solutions to the Strong-CP Problem in a World with Gravity,  Phys. Lett. B282, 132-136 (1992).

56.  i.e. see. H. Georgi, L.J. Hall, M. B. Wise,  Grand Unified Models with an Automatic Peccei-Quinn Symmetry, Nucl. Phys. B192, 409-416 (1981).

57.  eg. see M. Dine et al,  CP and Other Gauge Symmetries in String Theory , Phys. Rev. Lett.  69, 2030-2032 (1992); K. Choi, D. Kaplan, and A. Nelson, UCSD preprint PTH 92-11, 1992. 

*  Plenary Lecture delivered at the XXVI International Conference on High Energy Physics, Dallas, August 1992.   To appear in the Proceedings (AIP).






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(q) t
279 47 /Times-Roman 0 0 0 38 T
(21) t
316 34 /Times-Roman 0 0 0 50 T
(\)) t
 
 
 R( x 	" # 
 	+ 1 
 ( ) x" # 
 	+ 2
 ( (=)
 cos ) q 
 	+ 21
 ( L ) d Ex r ]|Expr|[#>`b___}()$^<c$5Q^" *~: ;bP8&c55*x}(" 1}_"!Symbol^:!&c0  /7$^<c$5Q^: &c55*x}(" 2}_,H,] cos $^:!&c0  q(!: &c55*21}_,I}]|[ 	 
 v 	 
 f d xpr Ex r Gr ph bj 
 , 	 Symbol 
 . +

   " 
currentpoint  " ~translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 21 /Symbol 0 1 0 50 T
(s) t
 
 ( s d /Ex r ]|Expr|[#>`b___}^" Symbol^: ;bP8&c552s]|[ d xpr Ex r Gr ph bj 
 ! , Times 
 . +

   )  , 	 Symbol )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 46 /Symbol 0 0 0 50 T
(d) t
25 46 /Times-Italic 0 0 0 50 T
(T) t
69 46 /Times-Roman 0 0 0 50 T
(\() t
86 46 /Symbol 0 0 0 50 T
(q) t
112 46 /Times-Roman 0 0 0 50 T
(,) t
125 46 /Symbol 0 0 0 50 T
(j) t
155 46 /Times-Roman 0 0 0 50 T
(\)) t
184 46 /Times-Roman 0 0 0 50 T
(=) t
283 46 /Times-Italic 0 0 0 50 T
(a) t
318 59 /Times-Italic 0 0 0 38 T
(lm) t
367 46 /Times-Italic 0 0 0 50 T
(Y) t
405 59  b/Times-Italic 0 0 0 38 T
(lm) t
442 46 /Times-Roman 0 0 0 50 T
(\() t
459 46 /Symbol 0 0 0 50 T
(q) t
485 46 /Times-Roman 0 0 0 50 T
(,) t
498 46 /Symbol 0 0 0 50 T
(j) t
528 46 /Times-Roman 0 0 0 50 T
(\)) t
225 52 /Symbol 0 0 0 75 T
(S) t
224 80 /Times-Italic 0 0 0 38 T
(l) t
235 80 /Times-Roman 0 0 0 38 T
(,) t
244 80 /Times-Italic 0 0 0 38 T
(m) t
 
 ( d ) T ) ( ) q ) , ) j ) )) = ) a
 	+ lm
 ( X Y
 	+	 lm 
 ( j ( ) q ) , ) j ) ) 
 ( 
 6 S 
 	* l ) , ) m d Ex r ]|Expr|[#>`b___}),# b(<" Symbol^: ;bP8&c0  d"!*~:!&c55*T ,H: &c0  q:!&c55*,L: &c0  j:!&c55*,I ,] <c%#D(($^a(" lm}_ $^Y(" lm}_,H: &c0  q:!&c55*,L: &c0  j:!&c55*,I}^: &c55"S(#:!&c55*l,Lm}_}}# b D b!( b!L!WW}]|[ L L J d xpr Ex r JGr ph bj 
 b, 	 Symbol 
 . +

  , Times 
 	)   
 )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 46 /Times-Italic 0 0 0 50 T
(a) t
35 59 /Times-Italic 0 0 0 38 T
(l) t
27 31 /Times-Roman 0 0 0 38 T
(2) t
58 46 /Times-Roman 0 0 0 50 T
(=) t
168 46 /Times-Italic 0 0 0 50 T
(a) t
203 59 /Times-Italic 0 0 0 38 T
(lm) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
 /L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
155 8 M
155 57 L
S
263 8 M
263 57 L
S
268 23 /Times-Roman 0 0 0 38 T
(2) t
98 52 /Symbol 0 0 0 75 T
(S) t
106 72 /Times-Italic 0 0 0 38 T
(m) t
 
 J( a
 	+ l ( 2
 + = ) a
 	+	 lm 	" & 
" > 
 ( @ 2 
 ( 
 S 
 	+ m d Ex r ]|Expr|[#>`b___})%# b(<$^" *~: ;bP8&c55*a(" l}^2 ,] <c%#D("$^<c!1!("$^a(" lm}_ }}_^2 }^"!Symbol^:!&c55"S^: &c55*m_}}# b D b!( b!L!WW}]|[ # H H F d xpr Ex r FGr ph bj 
 ], 	 Symbol 
 . +

  , Times )   )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 46 /Times-Italic 0 0 0 50 T
(Q) t
48 46 /Times-Roman 0 0 0 50 T
(=) t
101 46 /Times-Italic 0 0 0 50 T
(a) t
136 59 /Times-Roman 0 0 0 38 T
(2) t
137 31 /Times-Roman 0 0 0 38 T
(2) t
156 46 /Times-Roman 0 0 0 50 T
(/4) t
195 46 /Symbol 0 0 0 50 T
(p) t
/H {newpath moveto 2 copy curveto 2 copy curveto fill} bind def
89 7 89 33 92 7 100 7 92 33 H
89 59 89 33 92 59 100 59 92 33 H
234 7 234 33 231 7 223 7 231 33 H
 L234 59 234 33 231 59 223 59 231 33 H
237 23 /Times-Roman 0 0 0 38 T
(1/2) t
 
 F( Q ) = ) a 
 	+	 2( ! 2
 + /4 )
 p ` Zh Z` 1 7 Zh Z Z 
 	( 9 1/2 d Ex r ]|Expr|[#>`b___})%# b(<" *~: ;bP8&c55*Q ,] $^<c!$1(#$^a(" 2}(" 2},O4"!Symbol^:!&c0  p}}_(!: &c55*1,O2}}# b D b!( b!L!WW}]|[ ' 	 d xpr 
 Ex r 
 Gr ph bj 
 $ , 	 Symbol 
 . +

  , Times )   )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 63 /Times-Italic 0 0 0 50 T
(C) t
46 63 /Times-Roman 0 0 0 50 T
(\() t
64 63 /Times-Italic 0 0 0 50 T
(x) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
71 35 M
77 29 L
84 35 L
S
95 76 /Times-Roman 0 0 0 38 T
(1) t
114 63  /Symbol 0 0 0 50 T
(\327) t
128 63 /Times-Italic 0 0 0 50 T
(x) t
135 35 M
141 29 L
148 35 L
S
159 76 /Times-Roman 0 0 0 38 T
(2) t
190 63 /Times-Roman 0 0 0 50 T
(:) t
204 63 /Symbol 0 0 0 50 T
(s) t
235 63 /Times-Roman 0 0 0 50 T
(\)) t
264 63 /Times-Roman 0 0 0 50 T
(=) t
310 43 /Times-Roman 0 0 0 50 T
(1) t
297 90 /Times-Roman 0 0 0 50 T
(4) t
322 90 /Symbol 0 0 0 50 T
(p) t
294 49 M
350 49 L
S
435 63 /Times-Italic 0 0 0 50 T
(a) t
461 76 /Times-Italic 0 0 0 38 T
(l) t
471 48 /Times-Roman 0 0 0 38 T
(2) t
490 63 /Times-Italic 0 0 0 50 T
(P) t
517 76 /Times-Italic 0 0 0 38 T
(l) t
540 63 /Times-Roman 0 0 0 50 T
(\() t
558 63 /Times-Italic 0 0 0 50 T
(x) t
565 35 M
571 29 L
578 35 L
S
589 76 /Times-Roman 0 0 0 38 T
(1) t
608 63 /Symbol 0 0 0 50 T
(\327) t
622 63 /Times-Italic 0 0 0 50 T
(x) t
629 35 M
635 29 L
642 35 L
S
653 76 /Times-Roman 0 0 0 38 T
(2) t
672 63 /Times-Roman 0 0 0 50 T
(\)) t
701 63 /Times-Roman 0 0 0 50 T
(e) t
725 48 /Times-Roman 0 0 0 38 T
(\261) t
754 48 /Times-Italic 0 0 0 38 T
(l) t 
774 48 /Times-Roman 0 0 0 38 T
(+1/2) t
/H {newpath moveto 2 copy curveto 2 copy curveto fill} bind def
745 19 745 38 747 19 753 19 747 38 H
745 57 745 38 747 57 753 57 747 38 H
851 19 851 38 849 19 843 19 849 38 H
851 57 851 38 849 57 843 57 849 38 H
853 29 /Times-Roman 0 0 0 25 T
(2) t
866 48 /Symbol 0 0 0 38 T
(s) t
889 35 /Times-Roman 0 0 0 25 T
(2) t
366 69 /Symbol 0 0 0 75 T
(S) t
354 97 /Times-Italic 0 0 0 38 T
(l) t
374 97 /Times-Roman 0 0 0 38 T
(=) t
404 97 /Times-Roman 0 0 0 38 T
(0) t
375 16 /Symbol 0 0 0 38 T
(\245) t
 
 ( C ) ( ) x 	" # 
 	+ 1 
 ( ) x" " # 
 	+ 2
 ( . : ) s ) )) =( 
 J 1( G 4 ) p" G ( h a
 	+ l ( q 2 
 + P
 	+ l 
 ( ( ) x" # 
 	+ 1 
 ( ) x" # 
 	+ 2
 ( )) e
 	( ) l ) +1/2 ` Zh Z` Zh Z Z
 ( 2 
 	+ s 
 ( 2 
 ( X S 
 	( U l ) =) 0 ( Z d mEx r ]|Expr|[#>`b___}).# b(<" *~: ;bP8&c55*C ,H$^<c$5Q^x}(" 1}_"!Symbol^:!&c0  /7$^<c$5Q^: &c55*x}(" 2}_ ,Z:!&c0  s: &c55*,I ,]<2^1("4:!&c0  p}}<c%#D)*# b(<$^: &c55*a^l(" 2}$^P^l_ ,H$^<c$5Q^x}(" 1}_:!&c0  /7$^<c$5Q^: &c55*x}(" 2}_,I $^&c55"e_(#/0$^<c!$1(#&c55*l ,K1,O2}}_^2$^:!&c0  s_^: &c55*2}}# b D b!( b!L!WW}^:!&c55"S(%: &c55*l ,] 0}^:!.E}}# b D b!( b!L!WW}]|[ S 6 \ \ d WORD \ 
 \` Q V  ` h ~ Z` g T k uX` Z` T X` Z` T XP " "   " , Times 
 . ( ' z = 0; 
* 
t = 10   yrs
* 
T =2.735 K ( 	z = 0.2;
* 
t   10   yrs
* T   15 K " 
 ` Q [   
 \h ( } 	z =1000;
* t   3 x 10  yrs
* T .3 eV a ^ x ; 0" d X + a 0" R 5 a 0" c * ( K r last scattering surface  
 
+ 10 ( 	 9 ( ! 5 " W D 	" L ] 	" [ I a I K c e 1 0" Q U ` & O N S , 	 Symbol 
 ( 9 K l ( 8 U =ct ;  + q ( 8 u 1 ( 4 0 	 : : 8 d xpr 	 Ex r 	 8Gr ph bj 
 ! K, 	 Symbol 
 . +

  , Times )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
5 34 /Times-Roman 0 0 0 50 T
(\261) t
30 34 /Symbol 0 0 0 50 T
(Dn) t
33 71 /Symbol 0 0 0 50 T
(n) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
2 41 M
88 41 L
S
92 55 /Symbol 0 0 0 50 T
(\273) t
124 35  x/Times-Roman 0 0 0 50 T
(1) t
124 82 /Times-Roman 0 0 0 50 T
(3) t
121 41 M
150 41 L
S
154 55 /Symbol 0 0 0 50 T
(DF) t
 
 8( ) Dn+ 	 n 	" 
 ( 
 ( 1* 3" 
 ( 
 % DF d vEx r ]|Expr|[#>`b___})$# b(<<2("" *~: ;bP8&c55*/0"!Symbol^:!&c0  Dn}^n}.[<2^: &c55*1^3}:!&c0  DF}# b D b!( b!L!WW}]|[  Wi 	 h 	 h f d xpr Ex r fGr ph bj 
 ( , Times 
 . +

  , 	 Symbol )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
5 34 /Symbol 0 0 0 50 T
(dr) t
57 34 /Times-Roman 0 0 0 50 T
(\() t
74 34 /Times-Roman 0 0 0 50 T
(t) t
90 47 /Times-Roman 0 0 0 38 T
(f) t
115 34 /Times-Roman 0 0 0 50 T
(\)) t
55 83 /Symbol 0 0 0 50 T
(r) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
 /L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
2 53 M
133 53 L
S
149 67 /Times-Roman 0 0 0 50 T
(=) t
194 34 /Times-Roman 0 0 0 50 T
(a) t
216 34 /Times-Roman 0 0 0 50 T
(\() t
233 34 /Times-Roman 0 0 0 50 T
(t) t
249 47 /Times-Roman 0 0 0 38 T
(f) t
262 34 /Times-Roman 0 0 0 50 T
(\)) t
195 94 /Times-Roman 0 0 0 50 T
(a) t
217 94 /Times-Roman 0 0 0 50 T
(\() t
234 94 /Times-Roman 0 0 0 50 T
(t) t
250 107 /Times-Roman 0 0 0 38 T
(i) t
260 94 /Times-Roman 0 0 0 50 T
(\)) t
191 53 M
280 53 L
S
301 34 /Symbol 0 0 0 50 T
(dr) t
353 34 /Times-Roman 0 0 0 50 T
(\() t
370 34 /Times-Roman 0 0 0 50 T
(t) t
386 47 /Times-Roman 0 0 0 38 T
(i) t
396 34 /Times-Roman 0 0 0 50 T
(\)) t
343 83 /Symbol 0 0 0 50 T
(r) t
298 53 M
414 53 L
S
 
 f( dr )
 () t
 	+ f
 ( ) ( 
 r 	" 
 ( $ =( / a) () t
 	+ f
 ( ? )( / a) () t
 	+ i
 ( > )" 
 . ( H dr )
 () t
 	+ i
 ( _ ) ( R r" 
 H d Ex r ]|Expr|[#>`b___})'# b(<<2(%" Symbol^: ;bP8&c55"dr"!*~:!,H$^t^f_ ,I}^: r}:! ,] <2($a,H$^t^f_,I}($a,H$^t^i_,I}} <2($: dr:!,H$^t^i_,I}^: r}}# b D b!( b!L!WW}]|[ / S 7 ] ) ] [ d xpr 	 Ex r 	 [Gr ph bj 
 # w, Times 
 . +

   )  , 	 Symbol )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
5 43 /Symbol 0 0 0 50 T
(d) t
30 43 /Times-Italic 0 0 0 50 T
(T) t
17 90 /Times-Italic 0 0 0 50 T
(T) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
2 49 M
63 49 L
S
79 63 /Symbol 0 0 0 50 T
(\273) t
123 43  0/Times-Roman 0 0 0 50 T
(1) t
123 90 /Times-Roman 0 0 0 50 T
(3) t
120 49 M
149 49 L
S
158 32 /Symbol 0 0 0 50 T
(dr) t
170 79 /Symbol 0 0 0 50 T
(r) t
155 49 M
211 49 L
S
227 63 /Symbol 0 0 0 50 T
(\263) t
302 43 /Times-Roman 0 0 0 50 T
(1) t
265 90 /Times-Roman 0 0 0 50 T
(3000) t
262 49 M
366 49 L
S
 
 [( 
 d ) T( T 	" 
 ( ( 
 1* 3" ( & dr+ r" & ( 6 ( 
 H 1( @ 3000" ? d Ex r ]|Expr|[#>`b___})+# b(<<2("" Symbol^: ;bP8&c0  d"!*~:!&c55*T}^T} : &c0  .[:!&c55* <2^1^3}<2(!: &c0  dr}^r}:!&c55* : &c0  .S:!&c55*!!<2^1(!3000}}}# b D b!( b!L!WW}]|[ 	L 	> 	. d xpr Ex r Gr ph bj 
 ' , Times 
 . +

  , 	 Symbol )   )   )   )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 67 /Times-Italic 0 0 0 50 T
(P) t
43 67 /Times-Roman 0 0 0 50 T
(\() t
60 67 /Times-Italic 0 0 0 50 T
(k) t
107 67 /Times-Roman 0 0 0 50 T
(\)) t
136 67 /Times-Roman 0 0 0 50 T
(~) t
238 67 /Symbol 0 0 0 50 T
(Dr) t
308 67 /Times-Roman 0 0 0 50 T
(\() t
325 67 /Times-BoldItalic 0 0 0 50 T
(x) t
374 67 /Times-Roman 0 0 0 50 T
(\)) t
403 67 /Times-Roman 0 0 0 50 T
(e) t
427 52 /Times-Roman 0 0 0 38 T
(i) t
437  52 /Times-BoldItalic 0 0 0 38 T
(k) t
457 52 /Symbol 1 0 0 38 T
(\327) t
466 52 /Times-BoldItalic 0 0 0 38 T
(x) t
497 67 /Times-Italic 0 0 0 50 T
(d) t
523 67 /Times-BoldItalic 0 0 0 50 T
(x) t
216 4 moveto
230 4 216 19 216 6 curveto
207 6 209 17 209 54 curveto
209 91 203 104 196 104 curveto
182 104 196 89 196 102 curveto
205 102 203 91 203 54 curveto
203 17 209 4 216 4 curveto
fill
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
176 4 M
176 102 L
S
571 4 M
571 102 L
S
576 23 /Times-Roman 0 0 0 38 T
(2) t
 
 ( P )
 ( ) k ) )) ~ ) Dr ) ( ) x ) )) e
 	( f i ) k ) ) x 
 + d ) x ` 1 9 Z` + 3 Z ZQ 4 6Q . 0 	" + " 
 	( 2 d Ex r ]|Expr|[#>`b___})+# b(<" *~: ;bP8&c55*P ,Hk&c55) &c55* ,I -^ $^<c!1!^<c" #(-"!Symbol^:!&c0  Dr: &c55* ,H&c55)x  &c55*,I $^&c55"e_($i&c55)k:!&c55!/7: &c55)x}&c55* d&c55)x }__}}_^&c55*2}# b D b!( b!L!WW}]|[ Y Y W d xpr 	 Ex r 	 WGr ph bj 
 & r, Times 
 	. +

   )  , 	 Symbol 
 )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
20 40 /Symbol 0 0 0 50 T
(dr) t
32 87 /Symbol 0 0 0 50 T
(r) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
17 57 M
73 57 L
S
/H {newpath moveto 2 copy curveto 2 copy curveto fill} bind def
1 6 1 52 4 6 14 6 4 52 H
1 98 1  52 4 98 14 98 4 52 H
91 6 91 52 88 6 78 6 88 52 H
91 98 91 52 88 98 78 98 88 52 H
94 100 /Times-Italic 0 0 0 38 T
(k) t
94 25 /Times-Roman 0 0 0 38 T
(2) t
125 71 /Times-Roman 0 0 0 50 T
(~) t
164 71 /Times-Italic 0 0 0 50 T
(k) t
198 50 /Times-Roman 0 0 0 38 T
(3) t
229 71 /Times-Italic 0 0 0 50 T
(P) t
272 71 /Times-Roman 0 0 0 50 T
(\() t
289 71 /Times-Italic 0 0 0 50 T
(k) t
336 71 /Times-Roman 0 0 0 50 T
(\)) t
 
 W( 	 dr+ r 	" ` 	 Zh Z` 
 Zh Z Z 
 	+ k ( 2
 + ~ )	 k 
 	( 0 3 
 + P )
 ( ) k ) ) d Ex r ]|Expr|[#>`b___})-# b(<$^<c!$1^<2(!" Symbol^: ;bP8&c0  dr}^r}}^"!*~:!&c55*k^2 -^ $^k_(" 3} P ,Hk  ,I}# b D b!( b!L!WW}]|[ ; ; 9 d xpr Ex r 9Gr ph bj 
 L, Times 
 . +

   )   " 
currentpoint  " etranslate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 42 /Times-Italic 0 0 0 50 T
(P) t
43 42 /Times-Roman 0 0 0 50 T
(\() t
72 42 /Times-Italic 0 0 0 50 T
(k) t
107 42 /Times-Roman 0 0 0 50 T
(\)) t
136 42 /Times-Roman 0 0 0 50 T
(~) t
175 42 /Times-Italic 0 0 0 50 T
(k) t
209 21 /Times-Italic 0 0 0 38 T
(n) t
 
 9( 
 P )
 ( ) k )	 )) ~ )	 k
 	( 2 n d WEx r ]|Expr|[#>`b___})+# b(<" *~: ;bP8&c55*P ,H k ,I -^ $^k_(" n}}# b D b!( b!L!WW}]|[ P P N d xpr 	 Ex r 	 NGr ph bj 
 # g, Times 
 . +

   
 	)  , 	 Symbol 
 )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
20 32 /Symbol 0 0 0 50 T
(dr) t
32 79 /Symbol 0 0 0 50 T
(r) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
17 49 M
73 49 L
S
/H {newpath moveto 2 copy curveto 2 copy curveto fill} bind def
1 -2 1 44 4 -2 14 -2 4 44 H
1 90  1 44 4 90 14 90 4 44 H
91 -2 91 44 88 -2 78 -2 88 44 H
91 90 91 44 88 90 78 90 88 44 H
94 92 /Times-Italic 0 0 0 38 T
(hor) t
157 63 /Times-Roman 0 0 0 50 T
(=) t
197 63 /Times-Italic 0 0 0 50 T
(const) t
304 63 /Times-Roman 0 0 0 50 T
(.) t
 
 N( dr+ r 	" ` 	 Zh Z` 
 Zh Z Z 
 	+ hor 
 ( & = )	 const ) . d vEx r ]|Expr|[#>`b___})&# b(<$^<c!$1^<2(!" Symbol^: ;bP8&c0  dr}^r}}(!"!*~:!&c55*hor}_ ,] const,N}# b D b!( b!L!WW}]|[ 	L 	> 	. } d xpr Ex r }Gr ph bj 
 ) , Times 
 . +

   
 	)  , 	 Symbol 
 )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
20 40 /Symbol 0 0 0 50 T
(dr) t
32 87 /Symbol 0 0 0 50 T
(r) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
17 57 M
73 57 L
S
/H {newpath moveto 2 copy curveto 2 copy curveto fill} bind def
1 6 1 52 4 6 14 6 4 52 H
1 98 1  52 4 98 14 98 4 52 H
91 6 91 52 88 6 78 6 88 52 H
91 98 91 52 88 98 78 98 88 52 H
94 100 /Times-Italic 0 0 0 38 T
(t) t
112 108 /Times-Roman 0 0 0 25 T
(0) t
94 25 /Times-Roman 0 0 0 38 T
(2) t
137 71 /Times-Roman 0 0 0 50 T
(=) t
177 71 /Times-Italic 0 0 0 50 T
(const) t
284 71 /Times-Roman 0 0 0 50 T
(.) t
299 61 /Times-Roman 0 0 0 38 T
(2) t
330 71 /Symbol 0 0 0 50 T
(\264) t
409 51 /Times-Italic 0 0 0 50 T
(k) t
389 99 /Times-Italic 0 0 0 50 T
(k) t
433 112 /Times-Roman 0 0 0 38 T
(0) t
386 57 M
453 57 L
S
370 17 370 64 373 17 383 17 373 64 H
370 111 370 64 373 111 383 111 373 64 H
471 17 471 64 468 17 458 17 468 64 H
471 111 471 64 468 111 458 111 468 64 H
492 36 /Times-Roman 0 0 0 38 T
(4) t
 
 }( 	 dr+ r 	" ` 	 Zh Z` 
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 + 0
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 +
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 <, Times 
 . +

   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 46 /Times-Roman 0 0 0 50 T
(1.15) t
90 59 /Times-Roman 0 0 0 38 T
(\2610.65) t
90 25 /Times-Roman 0 0 0 38 T
(+0.45) t
 
 ,( 1.15
 	+ 0.65( +0.45 d ^Ex r ]|Expr|[#>`b___})!# b(<$(!" *~: ;bP8&c55*1,N15}(!/00,N65}(!,K0,N45}}# b D b!( b!L!WW}]|[ ing 4 F & F D d xpr Ex r DGr ph bj 
 Z, 	 Symbol 
 	. +

  , Times 
 )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
15 38 /Times-Roman 0 0 0 50 T
(T) t
48 18 /Symbol 0 0 0 38 T
(m) t
69 51 /Symbol 0 0 0 38 T
(m) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
12 0 M
1 28 L
12 57 L
S
91 0 M
102 28 L
91 57 L
S
117 38 /Times-Roman 0 0 0 50 T
 p(~) t
156 38 /Symbol 0 0 0 50 T
(L) t
202 38 /Times-Roman 0 0 0 50 T
(~) t
241 38 /Times-Roman 0 0 0 50 T
(V) t
 
 D( 	 T 
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 {, Times 
 . +

   )  , 	 Symbol )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
14 46 /Symbol 0 0 0 50 T
(\321) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
18 4 M
44 4 L
40 0 M
44 4 L
40 8 L
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62 46 /Symbol 0 0 0 50 T
(\264) t
101 46 /Times-Italic 0 0 0 50 T
(v) t
135 46 /Times-Roman 0 0 0 50 T
(') t ~
106 4 M
137 4 L
133 0 M
137 4 L
133 8 L
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1 0 M
1 56 L
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155 0 M
155 56 L
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170 46 /Times-Roman 0 0 0 50 T
(<<) t
252 46 /Symbol 0 0 0 50 T
(\321) t
256 4 M
282 4 L
278 0 M
282 4 L
278 8 L
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300 46 /Symbol 0 0 0 50 T
(\327) t
325 46 /Times-Italic 0 0 0 50 T
(v) t
359 46 /Times-Roman 0 0 0 50 T
(') t
330 4 M
361 4 L
357 0 M
361 4 L
357 8 L
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239 0 M
239 56 L
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379 0 M
379 56 L
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currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 46 /Times-Italic 0 0 0 50 T
(v) t
34 46 /Times-Roman 0 0 0 50 T
(') t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
5 4 M
36 4 L
32 0 M
36 4 L
32 8 L
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55 46 /Times-Roman 0 0 0 50 T
(=) t
95 46 /Times-Roman 0 0 0 50 T
(\261 G) t
120 46 /Symbol 0 0 0 50 T
(\321) t
156 46 /Symbol 0 0 0 50 T
(j) t
 
 /( v ) ' 	" " # ) =)
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 ! P, Times 
 . +

  , 	 Symbol )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 55 /Symbol 0 0 0 50 T
(F) t
50 55 /Symbol 0 0 0 50 T
(\273) t
94 35 /Times-Roman 0 0 0 50 T
(3) t
94 82 /Times-Roman 0 0 0 50 T
(2) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
/L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
91 41 M
120 41 L
S
124 55  `/Symbol 0 0 0 50 T
(W) t
164 34 /Times-Roman 0 0 0 38 T
(0.4) t
211 55 /Symbol 0 0 0 50 T
(j) t
 
 <( 
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 	( ' 0.4 
 + j d Ex r ]|Expr|[#>`b___})'# b(<" Symbol^: ;bP8&c0  F"!*~:!&c55* : &c0  .[:!&c55* <2^3^2}$^: &c0  W_(!:!&c55*0,N4}: &c0  j}# b D b!( b!L!WW}]|[ J J H d xpr Ex r HGr ph bj 
 _, Times 
 . +

   )  , 	 Symbol )   " 
currentpoint  " translate currentpoint scale 
1 setlinecap 0 setlinejoin  2 setmiterlimit
6 array currentmatrix aload pop pop pop abs exch abs add exch abs add exch abs add 2 exch div /onepx exch def
[ 0.238806 0 0 0.238806 2 2 ] concat
/T {/fsize exch def /funder exch 0 ne def /fital exch fsize mul 4 div def /fbold exch 0 ne def
/fmat [ fsize 0 fital fsize neg 0 0 ] def findfont fmat makefont setfont moveto} bind def
/t {funder {currentpoint 0 fsize 12 div rmoveto 2 index stringwidth rlineto fsize 24 div setlinewidth stroke moveto} if
fbold {currentpoint fsize 24 div 0 rmoveto 2 index show moveto} if show} bind def
0 46 /Symbol 0 0 0 50 T
(d) t
37 46 /Symbol 0 0 0 50 T
(\273) t
76 46 /Times-Roman 0 0 0 50 T
(\261) t
101 46 /Symbol 0 0 0 50 T
(W) t
141 25 /Times-Roman 0 0 0 38 T
(0.6) t
187 46 /Symbol 0 0 0 50 T
(\321) t
/Lw {onepx sub setlinewidth} bind def
2 Lw /S /stroke load def
/M {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch moveto} bind def
 /L {currentlinewidth .5 mul add exch currentlinewidth .5 mul add exch lineto} bind def
191 4 M
217 4 L
213 0 M
217 4 L
213 8 L
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223 46 /Symbol 0 0 0 50 T
(\327) t
248 46 /Times-Italic 0 0 0 50 T
(v) t
282 46 /Times-Roman 0 0 0 50 T
(') t
253 4 M
284 4 L
280 0 M
284 4 L
280 8 L
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 H( d)	 )	 ) W 
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 + 	" . " 1 # )	 ) v ) '" = " B # d Ex r ]|Expr|[#>`b___})*# b(<" Symbol^: ;bP8&c0  d"!*~:!&c55* : &c0  .[:!&c55* /0$^: &c0  W_(!:!&c55*0,N6}<c$%!^: &c0  /1}/7:!&c55* <c$%!(#v ,G}}}# b D b!( b!L!WW}]|[ d P 	 B 	 2 ) ) 
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 ( w 2 " t " t " t " t " t E D D E B " d 
SPNT d SPNT E B " 
 E B "	 U U U U" % P2-v16 - Copyright 1991 Silicon Beach Software, Inc.
userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d
begin}bind def/P2_d 33 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup
/mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md
/setTxMode known}{false}ifelse/sk exch def mk{md/xl known}{false}ifelse/xk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp
concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload
pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl
{lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be
{grestore}b/p{/gf false def}b p/g{/gf true def}b pk{/_pat/pat load def/_gr/gr load def}{/_gr
{64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{mk{av 68 gt
{false}if}if}b/bps 8 string def/bpm[8 0 0 8 0 0]def/bpp{bps}def/obp{gsave setrgbcolor bps copy pop
dup 0 get 8 div floor cvi 8 mul 1 index 2 get 8 div floor cvi 8 mul 2 index 1 get 8 div floor cvi 8 mul 
8 4 index 3 get 8 div floor cvi 8 mul{2 index 8 3 index{1 index gsave translate 8 8 scale 8 8 false bpm/bpp
load imagemask grestore}for pop}for pop pop pop grestore}b end P2_b pk end{/pat{P2_b gf{end pop sg
P2_b mk end{av 68 gt{pop}if}if}{/_pat load end exec}ifelse}bind def}{/pat{P2_b pop _gr end}bind
def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg dup 0 ge{/_gr load end exec}
{pop end}ifelse}bind def}{/setTxMode{pop P2_b tg dup 0 ge{/_gr load end exec}{pop end}ifelse}bind
def}ifelse P2_b xk end{P2_d/_xl/xl load put/xl{P2_b 2 copy P2_tp 4 get add P2_tp 4 3 -1 roll put
P2_tp 5 get add P2_tp 5 3 -1 roll put/_xl load end exec}bind def}if}if
 " F f21 69 1 index neg 1 index neg matrix translate 3 1 roll
currentpoint 2 copy matrix translate 6 1 roll
" A ! 546 578 currentpoint 1 index 6 index sub 4 index 9 index sub div
1 index 6 index sub 4 index 9 index sub div
matrix scale 11 1 roll
 o[ 9 1 roll cleartomark
3 2 roll matrix concatmatrix
exch matrix concatmatrix
/P2_tp exch def
P2_b mk end{bn}if
 " d 
SPNT 	 d SPNT v J f . ^[ a t O d2 	 { ]E NH Im s la 7w 
 ~=i j 6 / T0? i af v J f . ^[ P2_b  496 102 bb
 0504.1821 94.35867 511.94727 97.80853 494 116 bc
 3402.84886 208.39139 284.61906 349.27168 197 433 bc
 3165.30579 463.28682 153.58551 486.73665 115 488 bc
 >108.38277 488.21666 126.23988 484.69775 154.6666 461.90787 bc
 ?183.09328 439.11801 222.08955 397.05664 273.75072 340.18846 bc
 3361.69469 243.38046 417.52133 175.29181 496 102 bc
 bx
 'g x6 end 48 <8822882288228822>pat P2_b
 bp
 &p x6 end 0 <FFFFFFFFFFFFFFFF>pat P2_b
 1 1 bf
 be end
 P2_b g end
 	 " " " "q b q f d c b b b c d f i j l n p r t w z } | y u r o l h e b _ [ X U R   N $ K ( H + E / B 2 > 6 ; 9 8 = 5 @ 1 D . G + K ( N % R " U X \ _ c f i l p s v y } ~ | z x u s q q r t v z { ~ | y v s o l i e b _ [ X T Q N K H E B " ? % = ' : * 7 , 4 / 1 1 . 4 , 6 ) 9 & ; # > ! @ C E G J L O Q S 	 V X Z \ _ a c f h j l n q s u w z | ~ } { x v t q o m k h f P2_b p end
 	 p b q f d c b b b c d f i j l n p r t w z } | y u r o l h e b _ [ X U R   N $ K ( H + E / B 2 > 6 ; 9 8 = 5 @ 1 D . G + K ( N % R " U X \ _ c f i l p s v y } ~ | z x u s q q r t v z { ~ | y v s o l i e b _ [ X T Q N K H E B " ? % = ' : * 7 , 4 / 1 1 . 4 , 6 ) 9 & ; # > ! @ C E G J L O Q S 	 V X Z \ _ a c f h j l n q s u w z | ~ } { x v t q o m k h f d 
SPNT 	 d SPNT ] % J D # N e   r r! 9 3 O .SF Y? DJS > 	 c5 O ] * K 	 | h c c f A L ] % J D # N e   P2_b  324 291 bb
 2268.3085 357.62158 114.90582 533.44582 179 482 bc
 ?183.22647 478.60757 232.68047 429.04417 302.32529 345.24861 bc
 ?324.29033 318.82062 355.20709 280.31071 389.51704 238.16418 bc
 1430.29681 188.0701 508.67377 104.74178 506 99 bc
 1506 99 483.76974 102.67018 420.25435 182.9668 bc
 2385.5587 226.82928 349.67244 260.28906 324 291 bc
 bx
 'g x6 end 60 <8000080080000800>pat P2_b
 bp
 &p x6 end 0 <FFFFFFFFFFFFFFFF>pat P2_b
 1 1 bf
 be end
 P2_b g end
 	 q c # D % B ' @ * ? , = . ; 1 8 3 6 6 4 8 2 ; 0 > . @ + C ) F & I $ L ! O R U X [ ^ a d 
 g 
 j n q t w z ~ 	 
 ~ | y w u r p m k i " f $ d & a ( ^ * \ , Y . V 1 R 4 O 7 K : G = C @ A B ? D = E ; G 9 I 7 K 5 L 3 N 0 P . R , S * U ' W % Y # [   ] _ a c e g h j 
 m 
 o q s u w y { } ~ | y v t r p n l j i f d c c c e f g h j l o p r s u w y { } } { y w u s q o m k i g e c a _ ] 	 [ Y 
 W U S R P N K G # D P2_b p end
 	 p c # D % B ' @ * ? , = . ; 1 8 3 6 6 4 8 2 ; 0 > . @ + C ) F & I $ L ! O R U X [ ^ a d 
 g 
 j n q t w z ~ 	 
 ~ | y w u r p m k i " f $ d & a ( ^ * \ , Y . V 1 R 4 O 7 K : G = C @ A B ? D = E ; G 9 I 7 K 5 L 3 N 0 P . R , S * U ' W % Y # [   ] _ a c e g h j 
 m 
 o q s u w y { } ~ | y v t r p n l j i f d c c c e f g h j l o p r s u w y { } } { y w u s q o m k i g e c a _ ] 	 [ Y 
 W U S R P N K G # D d 
SPNT d SPNT & M + d 
SPNT , Times 
 . ( " RN0.0         0.2          0.4          0.6         0.8         1.0          1.2 d 
SPNT d SPNT & 1 d 
SPNT ( 6 0.0 d 
SPNT d SPNT & 1 d 
SPNT ( 6 0.2 d 
SPNT d SPNT & Z 1 u d 
SPNT ( l 6 0.4 d 
SPNT d SPNT & 1 4 d 
SPNT ( + 6 0.6 d 
SPNT d SPNT & 1 d 
SPNT ( 6 0.8 d 
SPNT d SPNT & 1   d 
SPNT ( 6 1.0 d 
SPNT d SPNT & S 1 n " d 
SPNT ( e 6 1.2 d 
SPNT P2_b g end
	 1 c p p P2_b p end
	 8 d 
SPNT P2_b g end
	 " " " "1 x p P2_b p end
	 8 d 
SPNT d SPNT & ` t d 
SPNT 
 +T &B Flux Reduction Only (68% Confidence) d 
SPNT d SPNT & u d 
SPNT * 3B and Be Flux Reduction Scaled by Temp. (68% Conf.) d 
SPNT d SPNT & ' B d 
SPNT 
 ( 9 Homestake Prediction d 
SPNT   d SPNT & u 0 d &SPNT d 
SPNT b 
 ( Kamiokande Prediction 
 E B " u 0 u 0 u 0 @ ?  @   @ ? @ 0  @  @ 0 @ ? ? @  @   8  @  @ 0 @ ? ? @   ! 
 $ $ % 0 0  @ ? @ @ @ 
 $ $ %   ! @ ?  @   @ ? @ @ ? $ "@ 3 @   ! 3@ . @ @ 0  @  @ 0 @ ? ? @ @ ?  @   @ ?  @   @ ? @ @ ? $ "@ 3 @ @ @ F , @ @ d 
SPNT   S d 
SPNT d 
SPNT 	 	" ] d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " 3 d 
SPNT d 
SPNT 	 " V d 
SPNT d 
SPNT 	 " z d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " 	 d 
SPNT d 
SPNT 	   E S E d 
SPNT d 
SPNT 	 " E ] d 
SPNT d 
SPNT 	 " E d 
SPNT d 
SPNT 	 " E d 
SPNT d 
SPNT 	 " E d 
SPNT d 
SPNT 	 " E d 
SPNT d 
SPNT 	 " E d 
SPNT d 
SPNT 	 " E 3 d 
SPNT d 
SPNT 	 " E V d 
SPNT d 
SPNT 	 " E z d 
SPNT d 
SPNT 	 " E d 
SPNT d 
SPNT 	 " E d 
SPNT d 
SPNT 	 " E d 
SPNT d 
SPNT 	 " E 	 d 
SPNT d 
SPNT 	   S E S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " e S d 
SPNT d 
SPNT 	 " D S d 
SPNT d 
SPNT 	 " $ S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " _ S d 
SPNT d 
SPNT 	   E d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " e d 
SPNT d 
SPNT 	 " D d 
SPNT d 
SPNT 	 " $ d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " d 
SPNT d 
SPNT 	 " _ d 
SPNT P2_b g end
 	 U U U U1 p P2_b p end
	 8 d 
SPNT d SPNT & d 
SPNT 
 ( MSW Prediction (68% Confidence) d 
SPNT 	 # d SPNT G r	 G r	 > 
 K-=   ;PW Xr i w d 6 zq  J n k x P_ ![ - /;7 A Q {I h0 ~ 	 ! 5& { ]Y fY c7 c7 G r	 G r	 > d &SPNT 7 7 + s v P2_b  451.84093 127.44545 bb
 =391.7861 160.75267 331.17671 197.01552 285.8006 250.51611 bc
 >230.84293 315.31383 88.44534 412.58034 105.01031 438.46523 bc
 ?100.51765 450.80942 122.44189 446.04721 127.85931 440.29269 bc
 ?199.92746 363.74011 249.88707 336.37488 274.13029 301.01213 bc
 ?303.23131 258.56349 337.00275 233.48158 360.19092 220.70686 bc
 >382.54288 213.02701 384.0591 252.20761 412.85901 209.48351 bc
 ;417.36464 202.7995 513.71346 102.3481 501.50775 99.2186 bc
 451.84093 127.44545 bl
 bx
 'g x6 end 32 <AA55AA55AA55AA55>pat P2_b
 bp
 &p x6 end 0 <FFFFFFFFFFFFFFFF>pat P2_b
 1 1 bf
 be end
 P2_b g end
 	 U U U Uq c h } z v r o k h d a ] Z V S P L I F B ? < 9 6 3 / , ) & $ ! 	 
 " $ & ) + - 0 2 4 7 9 ; > @ B E G I L N P S U W Z \ ^ ` c e g i l n p r t v x { } } z w t q o m k j i h h h h i h h j k n q t w y | } z w t q n k h f c a ^ \ Y W T R P N K I G E C @ > < : 8 
 6 4 
 1 / - * ( % #   ! # % ' ) * , 
 . 0 2 4 8 < ? C G J N R U X \ _ b e h k m p r t v z } } z w u r p n l j i f d c P2_b p end
 	 p c h } z v r o k h d a ] Z V S P L I F B ? < 9 6 3 / , ) & $ ! 	 
 " $ & ) + - 0 2 4 7 9 ; > @ B E G I L N P S U W Z \ ^ ` c e g i l n p r t v x { } } z w t q o m k j i h h h h i h h j k n q t w y | } z w t q n k h f c a ^ \ Y W T R P N K I G E C @ > < : 8 
 6 4 
 1 / - * ( % #   ! # % ' ) * , 
 . 0 2 4 8 < ? C G J N R U X \ _ b e h k m p r t v z } } z w u r p n l j i f d c d 
SPNT p n 8 l 8 P Q P Q R R R S T S T l T S T S R R R Q P Q P 8 d 
SPNT p n 8 l 8 P Q P Q R R R S T S T l T S T S R R R Q P Q P 8 d 
SPNT d SPNT & & : d 
SPNT ( 3 
20yr weighted d 
SPNT d SPNT & ' d 
SPNT (   20 yr unwt. d 
SPNT " 8 4 d 
SPNT " R d 
SPNT " R d 
SPNT p n 8 l 8 P Q P Q R R R S T S T l T S T S R R R Q P Q P 8 d 
SPNT d SPNT & d 
SPNT ( 	3 yr unwt d SPNT mbo 1 1 1 i b , d 
SPNT d SPNT i b , 
 i b ," % P2-v16 - Copyright 1991 Silicon Beach Software, Inc.
userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d
begin}bind def/P2_d 33 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup
/mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md
/setTxMode known}{false}ifelse/sk exch def mk{md/xl known}{false}ifelse/xk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp
concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload
pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl
{lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be
{grestore}b/p{/gf false def}b p/g{/gf true def}b pk{/_pat/pat load def/_gr/gr load def}{/_gr
{64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{mk{av 68 gt
{false}if}if}b/bps 8 string def/bpm[8 0 0 8 0 0]def/bpp{bps}def/obp{gsave setrgbcolor bps copy pop
dup 0 get 8 div floor cvi 8 mul 1 index 2 get 8 div floor cvi 8 mul 2 index 1 get 8 div floor cvi 8 mul 
8 4 index 3 get 8 div floor cvi 8 mul{2 index 8 3 index{1 index gsave translate 8 8 scale 8 8 false bpm/bpp
load imagemask grestore}for pop}for pop pop pop grestore}b end P2_b pk end{/pat{P2_b gf{end pop sg
P2_b mk end{av 68 gt{pop}if}if}{/_pat load end exec}ifelse}bind def}{/pat{P2_b pop _gr end}bind
def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg dup 0 ge{/_gr load end exec}
{pop end}ifelse}bind def}{/setTxMode{pop P2_b tg dup 0 ge{/_gr load end exec}{pop end}ifelse}bind
def}ifelse P2_b xk end{P2_d/_xl/xl load put/xl{P2_b 2 copy P2_tp 4 get add P2_tp 4 3 -1 roll put
P2_tp 5 get add P2_tp 5 3 -1 roll put/_xl load end exec}bind def}if}if
 " j g22 105 1 index neg 1 index neg matrix translate 3 1 roll
currentpoint 2 copy matrix translate 6 1 roll
" a + 556 610 currentpoint 1 index 6 index sub 4 index 9 index sub div
1 index 6 index sub 4 index 9 index sub div
matrix scale 11 1 roll
 o[ 9 1 roll cleartomark
3 2 roll matrix concatmatrix
exch matrix concatmatrix
/P2_tp exch def
P2_b mk end{bn}if
 " d 
SPNT d SPNT & u d 
SPNT , Times 
 . + "B Flux Reduction Only (68% Conf.)
* 3B and Be Flux Reduction Scaled by Temp (68% Conf.)
 d 
SPNT 	 d SPNT } r r q ( q ( pP 2 v { K 3
7 | ## |/ x 
 P2_b  519 135 bb
 &402 157 286.1003 187.77586 175 234 bc
 '148.98386 244.82422 125 252 114 280 bc
 113 296 bl
 ?112.31453 306.96664 123.88396 307.05162 124.00584 291.14021 bc
 3124.18398 267.88605 159.69324 255.88695 167 252 bc
 '264.94516 199.89651 455 183 513 135 bc
 519 135 bl
 bx
 'g x6 end 48 <8822882288228822>pat P2_b
 bp
 &p x6 end 0 <FFFFFFFFFFFFFFFF>pat P2_b
 1 1 bf
 be end
 P2_b g end
 	 " " " "q q 0 } y v r n k g d ` \ Y U R N J G C @ < 9 5 1 . * ' #   
 } 	 z x w u s r ( q + q - q . r / s 0 u 0 v / x . y , z * { ' | # |   | } ~ 
 $ ( , 0 4 9 = A E J N R V [ _ c g k o t x | P2_b p end
 	 p q 0 } y v r n k g d ` \ Y U R N J G C @ < 9 5 1 . * ' #   
 } 	 z x w u s r ( q + q - q . r / s 0 u 0 v / x . y , z * { ' | # |   | } ~ 
 $ ( , 0 4 9 = A E J N R V [ _ c g k o t x | d 
SPNT 	 d SPNT g$) / p tY ) 7 1{  d * 0 g$) / p tY ) P2_b  112 202 bb
 '116.35072 218.69203 179 197 209 201 bc
 311 185 423 187 523 145 bc
 519 135 bl
 5518.5 135 408.07063 153.50623 305.48096 161.75934 bc
 3200.89127 182.01245 103.14125 168.01244 112 202 bc
 bx
 'g x6 end 60 <8000080080000800>pat P2_b
 bp
 &p x6 end 0 <FFFFFFFFFFFFFFFF>pat P2_b
 1 1 bf
 be end
 P2_b g end
 	 q o p q r t v y } " & ) , 0 3 6 : = @ C G J M Q T W [ ^ a e h k o r u y | ~ { x u r n k h e b _ [ X U R N K H E B > ; 8 5 1 . + ( $ ! ~ | y w v t r q p p p o o p P2_b p end
 	 p o p q r t v y } " & ) , 0 3 6 : = @ C G J M Q T W [ ^ a e h k o r u y | ~ { x u r n k h e b _ [ X U R N K H E B > ; 8 5 1 . + ( $ ! ~ | y w v t r q p p p o o p d 
SPNT d SPNT & + \ F * d 
SPNT 
 ( = aL 0.0         0.2         0.4         0.6         0.8         1.0         1.2 d 
SPNT d SPNT & 0 d 
SPNT ( 5 0.0 d 
SPNT d SPNT & 0 d 
SPNT ( 5 0.2 d 
SPNT d SPNT & n 0 d 
SPNT ( 5 0.4 d 
SPNT d SPNT & # 1 > d 
SPNT ( 5 6 0.6 d 
SPNT d SPNT & 1 d 
SPNT ( 6 0.8 d 
SPNT d SPNT & 2 ! d 
SPNT ( 7 1.0 d 
SPNT   ( S ( + d 
SPNT d 
SPNT 	 	" ( r d 
SPNT d 
SPNT 	 " ( d 
SPNT d 
SPNT 	 " ( d 
SPNT d 
SPNT 	 " ( d 
SPNT d 
SPNT 	 " ( d 
SPNT d 
SPNT 	 " ( d 
SPNT d 
SPNT 	 " ( @ d 
SPNT d 
SPNT 	 " ( c d 
SPNT d 
SPNT 	 " ( d 
SPNT d 
SPNT 	 " ( d 
SPNT d 
SPNT 	 " ( d 
SPNT d 
SPNT 	 " ( d 
SPNT d 
SPNT 	 " ( d 
SPNT d 
SPNT 	   i S i + d 
SPNT d 
SPNT 	 " i r d 
SPNT d 
SPNT 	 " i d 
SPNT d 
SPNT 	 " i d 
SPNT d 
SPNT 	 " i d 
SPNT d 
SPNT 	 " i d 
SPNT d 
SPNT 	 " i d 
SPNT d 
SPNT 	 " i @ d 
SPNT d 
SPNT 	 " i c d 
SPNT d 
SPNT 	 " i d 
SPNT d 
SPNT 	 " i d 
SPNT d 
SPNT 	 " i d 
SPNT d 
SPNT 	 " i d 
SPNT d 
SPNT 	 " i d 
SPNT d 
SPNT 	   ( S i S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " z S d 
SPNT d 
SPNT 	 " U S d 
SPNT d 
SPNT 	 " 0 S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " S d 
SPNT d 
SPNT 	 " w S d 
SPNT d 
SPNT 	   ( + i + d 
SPNT d 
SPNT 	 " + d 
SPNT d 
SPNT 	 " + d 
SPNT d 
SPNT 	 " + d 
SPNT d 
SPNT 	 " + d 
SPNT d 
SPNT 	 " z + d 
SPNT d 
SPNT 	 " U + d 
SPNT d 
SPNT 	 " 0 + d 
SPNT d 
SPNT 	 " + d 
SPNT d 
SPNT 	 " + d 
SPNT d 
SPNT 	 " + d 
SPNT d 
SPNT 	 " + d 
SPNT d 
SPNT 	 " w + d 
SPNT d SPNT & G b d 
SPNT ( Y Kamiokande Prediction d 
SPNT   d SPNT & 1 d &SPNT d 
SPNT R 
 ( / Gallium Prediction 
 i b , 1 1 1 @ ?  @   @ ? @ 0  @  @ 0 @ ? ? @  @   8  @  @ 0 @ ? ? @   ! 
 $ $ % 0 0  @ ? @ @ @ @ ?  @   @ ?  @   @ ? @ ? ?   @ @ ? ?   @ ? ? @ @ @ @ @ @ ? $ "@ 3 @ @ @ @ < d 
SPNT P2_b g end
 	 " " " "1 v P2_b p end
	 8 d 
SPNT P2_b g end
	 1 y v P2_b p end
	 8 d 
SPNT " % 7 d 
SPNT Q # ) X d 
SPNT " % d 
SPNT " ^ d 
SPNT " _ 
 d 
SPNT " d 
SPNT " < d 
SPNT d SPNT & / 4 d 
SPNT ( + 4 GALLEX d 
SPNT d SPNT & b 9 }   d 
SPNT +
I SAGE d 
SPNT " d 
SPNT " , d 
SPNT   " d 
SPNT " m 8 d 
SPNT Q l p X d 
SPNT " " d 
SPNT " d 
SPNT " i d 
SPNT " i - d SPNT G G G 5 d 
SPNT d SPNT 5 
 5" % P2-v16 - Copyright 1991 Silicon Beach Software, Inc.
userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d
begin}bind def/P2_d 33 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup
/mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md
/setTxMode known}{false}ifelse/sk exch def mk{md/xl known}{false}ifelse/xk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp
concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload
pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl
{lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be
{grestore}b/p{/gf false def}b p/g{/gf true def}b pk{/_pat/pat load def/_gr/gr load def}{/_gr
{64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{mk{av 68 gt
{false}if}if}b/bps 8 string def/bpm[8 0 0 8 0 0]def/bpp{bps}def/obp{gsave setrgbcolor bps copy pop
dup 0 get 8 div floor cvi 8 mul 1 index 2 get 8 div floor cvi 8 mul 2 index 1 get 8 div floor cvi 8 mul 
8 4 index 3 get 8 div floor cvi 8 mul{2 index 8 3 index{1 index gsave translate 8 8 scale 8 8 false bpm/bpp
load imagemask grestore}for pop}for pop pop pop grestore}b end P2_b pk end{/pat{P2_b gf{end pop sg
P2_b mk end{av 68 gt{pop}if}if}{/_pat load end exec}ifelse}bind def}{/pat{P2_b pop _gr end}bind
def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg dup 0 ge{/_gr load end exec}
{pop end}ifelse}bind def}{/setTxMode{pop P2_b tg dup 0 ge{/_gr load end exec}{pop end}ifelse}bind
def}ifelse P2_b xk end{P2_d/_xl/xl load put/xl{P2_b 2 copy P2_tp 4 get add P2_tp 4 3 -1 roll put
P2_tp 5 get add P2_tp 5 3 -1 roll put/_xl load end exec}bind def}if}if
 " f6 386 1 index neg 1 index neg matrix translate 3 1 roll
currentpoint 2 copy matrix translate 6 1 roll
" 4 565 744 currentpoint 1 index 6 index sub 4 index 9 index sub div
1 index 6 index sub 4 index 9 index sub div
matrix scale 11 1 roll
 o[ 9 1 roll cleartomark
3 2 roll matrix concatmatrix
exch matrix concatmatrix
/P2_tp exch def
P2_b mk end{bn}if
 " d 
SPNT 	 d SPNT 
 
 &	 0 ( P2_b  532 434 bb
 517 432 486 431 484 440 bc
 502 451 522 465 515 489 bc
 495 490 510 540 483 525 bc
 '479 519 445.09288 524.91789 463 527 bc
 '488.14857 529.92409 513 560 534 552 bc
 535 513 538 444 532 434 bc
 bx
 'g x6 end 32 <AA55AA55AA55AA55>pat P2_b
 bp
 &p x6 end 0 <FFFFFFFFFFFFFFFF>pat P2_b
 1 1 bf
 be end
 P2_b g end
 	 U U U Uq r ) 	 
 
 
 
 
 
 
   ! # $ & ' ( ) ) ) ) ) ( & #   
 
 P2_b p end
 	 p r ) 	 
 
 
 
 
 
 
   ! # $ & ' ( ) ) ) ) ) ( & #   
 
 d 
SPNT 	 d SPNT ! 7 
 ! 7 P2_b  538 677 bb
 '545.64928 665.52596 511 674 517 682 bc
 522 687 540 694 538 680 bc
 536 680 bl
 538 677 bl
 bx
 n64 <0000000000000000>32 <AA55AA55AA55AA55>32 <AA55AA55AA55AA55>64 <0000000000000000>32 <AA55AA55AA55AA55>cpat
 bp
 &p x6 end 0 <FFFFFFFFFFFFFFFF>pat P2_b
 1 1 bf
 be end
 P2_b g end
 	 U U U Uq v 
 	 
 P2_b p end
 !	 p v 
 	 
 d 
SPNT   D # d 
SPNT d 
SPNT 	 	" d 
SPNT d SPNT & p d 
SPNT 
 5, Times 
 . ( u 10 d 
SPNT d SPNT & d 
SPNT 
 5( -3 d 
SPNT d 
SPNT 	 
 5" 
 d 
SPNT d SPNT & d 
SPNT 
 5+s 10 d 
SPNT d SPNT & # d 
SPNT 
 5( 
 -2 d 
SPNT d 
SPNT 	 
 5" d 
SPNT d SPNT & } d 
SPNT 
 5+u 10 d 
SPNT d SPNT & d 
SPNT 
 5( -1 d 
SPNT d 
SPNT 	 
 5" d 
SPNT d SPNT & " d 
SPNT 
 5+x 10 d 
SPNT d SPNT & 5 d 
SPNT 
 5( 0 d 
SPNT d 
SPNT 	 
 5" N d 
SPNT d 
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