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We have carried out a search for galaxies at z [?] 7-10 in [?]14.4 arcmin2 of new NICMOS parallel imaging taken in the Great Observatories Origins Deep Survey (5.9 arcmin2), the Cosmic Origins Survey (7.2 arcmin2), and SSA22 (1.3 arcmin2). These images reach 5s sensitivities of J 110 = 26.0-27.5 (AB), and combined they increase the amount of deep near-infrared data by more than 60% in fields where the investment in deep optical data has already been made. We find no z > 7 candidates in our survey area, consistent with the Bouwens et al. measurements at z [?] 7 and 9 (over 23 arcmin2), which predict 0.7 galaxies at z [?] 7 and <0.03 galaxies at z [?] 9. We estimate that 10%-20% of z > 7 galaxies are missed by this survey, due to incompleteness from foreground contamination by faint sources. For the case of luminosity evolution, assuming a Schecter parameterization with a typical ph* = 10-3 Mpc-3, we find M*> - 20.0 for z [?] 7 and M*> - 20.7 for z [?] 9 (68% confidence). This suggests that the downward luminosity evolution of Lyman break galaxies continues to z [?] 7, although our result is marginally consistent with the z [?] 6 luminosity function of Bouwens et al. In addition, we present newly acquired deep MMT/Megacam imaging of the z [?] 9 candidate JD2325+1433, first presented in Henry et al. The resulting weak but significant detection at i' indicates that this galaxy is most likely an interloper at z [?] 2.7.

We present optical spectroscopy for an X-ray and optical flux-limited sample of 677 XMM-Newton selected targets covering the 2 deg2 Cosmic Evolution Survey field, with a yield of 485 high-confidence redshifts. The majority of the spectra were obtained over three seasons (2005-2007) with the Inamori Magellan Areal Camera and Spectrograph instrument on the Magellan (Baade) telescope. We also include in the sample previously published Sloan Digital Sky Survey spectra and supplemental observations with MMT/Hectospec. We detail the observations and classification analyses. The survey is 90% complete to flux limits of f 0.5-10 keV > 8 x 10-16 erg cm-2 s-1 and i + AB < 22, where over 90% of targets have high-confidence redshifts. Making simple corrections for incompleteness due to redshift and spectral type allows for a description of the complete population to i + AB < 23. The corrected sample includes a 57% broad emission line (Type 1, unobscured) active galactic nucleus (AGN) at 0.13 < z < 4.26, 25% narrow emission line (Type 2, obscured) AGN at 0.07 < z < 1.29, and 18% absorption line (host-dominated, obscured) AGN at 0 < z < 1.22 (excluding the stars that made up 4% of the X-ray targets). We show that the survey's limits in X-ray and optical fluxes include nearly all X-ray AGNs (defined by L 0.5-10 keV > 3 x 1042 erg s-1) to z < 1, of both optically obscured and unobscured types. We find statistically significant evidence that the obscured-to-unobscured AGN ratio at z < 1 increases with redshift and decreases with luminosity.

We present the results of Near-Infrared Camera and Multi-Object Spectrometer (NICMOS) imaging of a sample of 19 high-mass passively evolving galaxies with 1.2 < z < 2, taken primarily from the Gemini Deep Deep Survey (GDDS). Around 80% of galaxies in our GDDS sample have spectra dominated by stars with ages [?]1 Gyr. Our rest-frame R-band images show that most of these objects have compact regular morphologies which follow the classical R 1/4 law. These galaxies scatter along a tight sequence in the size versus surface brightness parameter space which defines the Kormendy relation. Around one-third (3/10) of the massive red objects in the GDDS sample are extraordinarily compact, with effective radii under 1 kpc. Our NICMOS observations allow the detection of such systems more robustly than is possible with optical (rest-frame UV) data, and while similar systems have been seen at z [?] 2, this is the first time such systems have been detected in a rest-frame optical survey at 1.2 < z < 2. We refer to these compact galaxies as "red nuggets," and note that similarly compact massive galaxies are completely absent in the nearby universe. We introduce a new "stellar mass Kormendy relation" (stellar mass density versus size) which we use to single out the effects of size evolution from those of luminosity and color evolution in stellar populations. The 1 < z < 2 passive galaxies have mass densities that are an order of magnitude larger then early-type galaxies today and are comparable to the compact distant red galaxies at 2 < z < 3. We briefly consider mechanisms for size evolution in contemporary models focusing on equal-mass mergers and adiabatic expansion driven by stellar mass loss. Neither of these mechanisms appears to be able to transform the high-redshift Kormendy relation into its local counterpart, leaving the origin and fate of these compact "red nuggets" unresolved.

We show that there has been a dramatic decline in the abundance of massive galaxies with strong Hd stellar absorption lines from z ~ 1.2 to the present. These "Hd-strong" (HDS) galaxies have undergone a recent and rapid break in their star formation activity. Combining data from the Gemini Deep Deep and Sloan Digital Sky surveys to make mass-matched samples (M[?] > 1010.2 M; with 25 and 50,255 galaxies, respectively), we find that the fraction of galaxies in an HDS phase has decreased from about 50% at z = 1.2 to a few percent today. This decrease in fraction is due to an actual decrease in the number density of massive HDS systems by a factor of 2-4, coupled with an increase in the number density of massive galaxies by ~30%. We show that this result depends only weakly on the threshold chosen for the Hd equivalent width (EW) to define HDS systems (if greater than 4 A) and corresponds to a (1 + z)2.5+-0.7 evolution. Spectral synthesis studies of the high-redshift population using the PEGASE code, treating HdA, EW[O II], Dn4000, and rest-frame colors, favor models in which the Balmer absorption features in massive HDS systems are the echoes of intense episodes of star formation that faded [?]1 Gyr prior to the epoch of observation. The z = 1.4-2 epoch appears to correspond to a time at which massive galaxies are in transition from a mode of sustained star formation to a relatively quiescent mode with weak and rare star formation episodes. We argue that the most likely local descendants of the distant massive HDS galaxies are passively evolving massive galaxies in the field and small groups.

We measure the surface density of i'-band dropout galaxies at z ~ 6 through wide-field Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) imaging and ultradeep Keck DEIMOS spectroscopy. Using deep HST ACS SDSS i' (F775W) and SDSS z' (F850LP) imaging from the Great Observatories Origins Deep Survey-North (GOODS-N; 200 arcmin2), we identify nine i'-drops satisfying (i'-z')AB > 1.5 to a depth of zimg1.gif = 25.6 (corresponding to Limg2.gif at z ~ 3). We use HK' imaging data to improve the fidelity of our sample, discriminating against lower redshift red galaxies and cool Galactic stars. Three i'-drops are consistent with M/L/T dwarf stars. We present ultradeep Keck DEIMOS spectroscopy of 10 objects from our combined GOODS-N and GOODS-S i'-drop sample. We detect Lya emission at z = 5.83 from one object in the GOODS-S field, which lies only 8' (i.e., 3 himg3.gif Mpc) away from a previously confirmed z = 5.78 object. One possible Lya emitter at z = 6.24 is found in the GOODS-N field (although identification of this spatially offset emission line is ambiguous). Using the rest-frame UV continuum from our six candidate z ~ 6 galaxies from the GOODS-N field, we determine a lower limit to the unobscured volume-averaged global star formation rate at z ~ 6 of (5.4 +- 2.2) x 10-4 h70 M yr-1 Mpc-3. We find that the cosmic star formation density in Lyman break galaxies (LBGs) with unobscured star formation rates greater than 15 M yr-1 falls by a factor of 8 between z ~ 3 and z ~ 6. Hence, the luminosity function of LBGs must evolve in this redshift interval: a constant integrated star formation density at z > 3 requires a much steeper faint-end slope, or a brighter characteristic luminosity. This result is in agreement with our previous measurement from the GOODS-S field, indicating that cosmic variance is not a dominant source of uncertainty.

We present rest-frame, R-band, galaxy luminosity function measurements for three different redshift ranges: 0.5 [?] z [?] 0.75, 0.75 [?] z [?] 1.0, and 1.0 [?] z [?] 1.5. Our measurements are based on photometric redshifts for ~3000 H-band-selected galaxies with apparent magnitudes 17 [?] H [?] 20 from the Las Campanas Infrared Survey. We show that our photometric redshifts are accurate with an rms dispersion between the photometric and spectroscopic redshifts of sz/(1 + z) [?] 0.08. Using galaxies identified in the Hubble Deep Field-South and Chandra Deep Field-South regions, we find, respectively, that 7.3% +- 0.2% and 16.7% +- 0.4% of the H [?] 20 galaxies are at z [?] 1. We first demonstrate that the systematic uncertainty inherent in the luminosity function measurements because of uncertainties in photometric redshifts is nonnegligible and therefore must be accounted for. We then develop a technique to correct for this systematic error by incorporating the redshift error functions of individual galaxies in the luminosity function analysis. The redshift error functions account for the non-Gaussian characteristics of photometric redshift uncertainties. They are the products of a convolution between the corresponding redshift likelihood functions of individual galaxies and a Gaussian distribution function that characterizes template-mismatch variance. We demonstrate, based on a Monte Carlo simulation, that we are able to completely recover the bright end of the intrinsic galaxy luminosity function using this technique. Finally, we calculate the luminosity function separately for the total H-band-selected sample and for a subsample of early-type galaxies that have a best-fit spectral type of E/S0 or Sab from the photometric redshift analysis. The primary results of this analysis are (1) the galaxy luminosity functions are consistent with a Schechter form, (2) the evolution of the comoving luminosity density of H-band-selected galaxies is characterized by D log /D log(1 + z) = 0.6 +- 0.1 at rest frame 6800 A, and (3) R for color-selected, early-type galaxies exhibits moderate evolution from z ~ 1.5 to ~0.3. Specifically, R for these red galaxies brighter than 1.0 (1.6) L* could decrease with increasing redshift by at most a factor of 3 (6) over this redshift range after removing possible stellar brightening according to the most extreme stellar evolution scenario.

Optical spectra of 14 emission-line galaxies representative of the 1999 NICMOS parallel grism Ha survey of McCarthy et al. are presented. Of the 14, 9 have emission lines confirming the redshifts found in the grism survey. The higher resolution of our optical spectra improves the redshift accuracy by a factor of 5. The [O II]/Ha values of our sample are found to be more than 2 times lower than expected from Jansen et al. This [O II]/Ha ratio discrepancy is most likely explained by additional reddening in our Ha-selected sample [on average, as much as an extra E(B-V) = 0.6], as well as by a possible stronger dependence of the [O II]/Ha ratio on galaxy luminosity than is found in local galaxies. The result is that star formation rates (SFRs) calculated from [O II] l3727 emission, uncorrected for extinction, are found to be on average 4 +- 2 times lower than the SFRs calculated from Ha emission. Classification of emission-line galaxies as starburst or Seyfert galaxies based on comparison of the ratios [O II]/Hb and [Ne III] l3869/Hb is discussed. New Seyfert 1 diagnostics using the Ha line luminosity, H-band absolute magnitude, and Ha equivalent widths are also presented. One galaxy is classified as a Seyfert 1 based on its broad emission lines, implying a comoving number density for Seyfert 1 galaxies of 2.5img1.gif x 10-5 Mpc-3. This comoving number density is a factor of 2.4img2.gif times higher than estimated by other surveys.

It is proved that normalised Stiefel manifolds admit a rational parametrisation which generalises Cayley's parametrisation of the unitary groups. Applying (the quaternionic case of) this parametrisation to the Atiyah-Drinfeld-Hitchin-Manin (ADHM) instanton matrix equations, large families of new explicit rational solutions emerge. In particular, new explicit non-'t Hooft solutions are presented.

The zero rest mass Euclidean Dirac equations in 2 (4) dimensions may be regarded as ‘square roots’ of the second order harmonic equation, and give rise to the crucial integral theorem and integral formula of complex (quaternionic) analysis. Recently discovered ‘2rth root’ equations for the 2rth order ‘harmonic’ equations are here shown to give rise to a similar integral theorem and integral formula.

A Bäcklund transformation between two (sets of) differential equations is strong if the transformation equations already imply the two equations. For each dimension n=2k, k?1, the existence of such strong transformations is proved by constructing a wide variety of them. A simple generalization of a known family of Bäcklund transformations is also given. One such provides a useful analogy for Yang's ‘instanton’ equations.

The two articles which follow, which deal with similar themes in quite different ways, arrived on the editorial table within a short time of each other. Since they are complementary, it seems appropriate to present them here under a common heading.

• One woman (patient 1), aged 27 years, and one man (patient 2), aged 26 years, had pituitary surgery for pituitary-dependent Cushing's syndrome. An adenoma was identified and removed in both patients. Persistence of hypercortisolism characterized the response of patient 2 to surgery; transient hypoadrenalism, the response of patient 1. Patient 1 subsequently underwent a relapse. At the second surgery (total hypophysectomy for both patients), hyperplasia was demonstrated in patient 1, and scattered nests of adrenocorticotropic hormone (ACTH)—secreting cells were demonstrated in patient 2. Postoperatively, Cushing's syndrome persisted in both patients. Inferior petrosal sampling for ACTH during corticotropin releasing hormone stimulation verified a pituitary source of ACTH in patient 1. A decrease in cortisol secretion following hypophysectomy and subsequent cure by pituitary irradiation constitutes the evidence for pituitary origin in patient 2. Dexamethasone suppression and corticotropin releasing hormone—stimulation tests consistently suggested a pituitary cause throughout the clinical course of both patients. Computed tomographic scans after hypophysectomy revealed postoperative changes only. In both patients, panhypopituitarism, except for cortisol and ACTH, followed hypophysectomy. It may be concluded that patients with diffuse pituitary ACTH hyperplasia cannot, at present, be identified preoperatively by conventional clinical testing. Surgery for such patients may not be the therapy of choice.(Arch Intern Med 1988;148:2497-2500)

We report the results of a survey of 1Jy class radio sources in the southern hemisphere. We have identified 20 galaxies with z > 2 and an additional ~16 with 12 appear to be >2 Gyr old, implying large formation redshifts.

Solutionsf:R?R of Feigenbaum's functional equationf(f(x))=a-1f(ax), where a?0 is a fixed real number, account for many of the fascinating properties of the behaviour of successive iterates of (one parameter families of) nonlinear maps. In connection with the phenomenon of intermittency, interesting families of exact solutions have recently been found (for a>0). These solutions can all be derived from continuous bijective solutions which are topologically equivalent to translations. In this paper, thegeneral exact continuous bijective solution is found for any a?0, positive or negative. In particular, it is shown that, forany a?0, there are solutions which areinequivalent to translations. And it is shown that bijective solutions equivalent to translations exist only when 0

It is pointed out that the Bäcklund transformations for a physically interesting class of nonlinear partial differential equations can be interpreted as generalisations of the Cauchy Riemann equations or as nonlinear Dirac equations. The generalisations are inhomogenisations of the Cauchy Riemann equations (or their hyperbolic analogue), whose condensed form makes the transformations easy to remember, which suggests ways to generalise to more than 2 dimensions, and which suggest that complex analysis techniques may be helpful in understanding the transformations.

Dirac's equation is a first-order auto-Bäcklund transformation for the Klein-Gordon equation in 4 variables, this equation being second-order in each of the 4 variables. Here first-order auto-Bäcklund transformations are given for any linear equation of arbitrary (possibly different) order in each of n variables (n arbitrary). This class of equations includes, for example, any of the linearised versions of the KdV hierarchy or equations, and the n-dimensional diffusion equation.