Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain C_c^\infty(\Omega) where the self-adjointness is defined relative to L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E. Segal and B. Fuglede, and is difficult in general. In this paper, we provide a representation-theoretic answer in the special case when \Omega=I\times\Omega_2 and I is an open interval. We then apply the results to the case when \Omega is a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that {e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km, 02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt, 61.44.B

Ages, metallicities and α\alpha-element enhancement for galaxies in Hickson compact groups

Central velocity dispersions and eight line-strength Lick indices have been determined from 1.3${\rm \AA}$ resolution long-slit spectra of 16 elliptical galaxies in Hickson compact groups. These data were used to determine galaxy properties (ages, metallicities and $\alpha$-element enhancements) and allowed a comparison with the parameters determined for a sample of galaxies in lower density environments, studied by Gonz\'alez (1993). The stellar population parameters were derived by comparison to single stellar population models of Thomas et al. (2003) and to a new set of SSP models for the indices Mg$_2$, Fe5270 and Fe5335 based on synthetic spetra. These models, based on an update version of the fitting functions presented in Barbuy et al. (2003), are fully described here. Our main results are: (1) the two samples have similar mean values for the metallicities and [$\alpha$/Fe] ratios, (2) the majority of the galaxies in compact groups seem to be old (median age of 14 Gyr for eight galaxies for which ages could be derived), in agreement with recent work by Proctor et al. (2004). These findings support two possible scenarios: compact groups are either young systems whose members have recently assembled and had not enough time to experience any merging yet or, instead, they are old systems that have avoided merging since their time of formation.Comment: Accepted for publication in A

Relation between TMAOase activity and content of formaldehyde in fillet minces and bellyflap minces from gadoid fishes

Minced fish is a significant component of a number of frozen fishery products like fish fingers, cakes and patties. Predominately minced fish is produced from gadoid species (Alaska pollack, cod, saithe, hake and others) possessing the enzyme trimethylamine oxide demethylase (TMAOase, E.C. 4.1.2.32) (Rehbein and Schreiber 1984). TMAOase catalyses the degradation of trimethylamine oxide (TMAO) to formaldehyde (FA) and dimethylamine (DMA), preferentially during frozen storage of products (Hultin 1992). In most gadoid species light muscle contains only low activity of TMAOase, the activity of red muscle and bellyflaps being somewhat higher. In contrast, the TMAOase activity in blood, kidney and other tissues, residues of which may contaminate minced fish flesh, may be higher for several orders of magnitude (Rehbein and Schreiber 1984)

The Fundamental Plane of Gravitational Lens Galaxies and The Evolution of Early-Type Galaxies in Low Density Environments

Most gravitational lenses are early-type galaxies in relatively low density environments -- a ``field'' rather than a ``cluster'' population. We show that field early-type galaxies with 0 < z < 1, as represented by the lens galaxies, lie on the same fundamental plane as those in rich clusters at similar redshifts. We then use the fundamental plane to measure the combined evolutionary and K-corrections for early-type galaxies in the V, I and H bands. Only for passively evolving stellar populations formed at z > 2 (H_0=65 km/s Mpc, Omega_0=0.3, Lambda_0=0.7) can the lens galaxies be matched to the local fundamental plane. The high formation epoch and the lack of significant differences between the field and cluster populations contradict many current models of the formation history of early-type galaxies. Lens galaxy colors and the fundamental plane provide good photometric redshift estimates with an empirical accuracy of -0.03 +/- 0.11 for the 17 lenses with known redshifts. A mass model dominated by dark matter is more consistent with the data than either an isotropic or radially anisotropic constant M/L mass model, and a radially anisotropic model is better than an isotropic model.Comment: 36 pages, 9 figures, 6 tables. ApJ in press. Final version contains more observational dat

The Possible z=0.83 Precursors of z=0 M* Early-type Cluster Galaxies

We examine the distribution of stellar masses of galaxies in MS 1054-03 and RX J0152.7-1357, two X-ray selected clusters of galaxies at z=0.83. Our stellar mass estimates, from spectral energy distribution fitting, reproduce the dynamical masses as measured from velocity dispersions and half-light radii with a scatter of 0.2 dex in the mass for early-type galaxies. When we restrict our sample of members to high stellar masses, > 1e11.1 Msun (M* in the Schechter mass function for cluster galaxies), we find that the fraction of early-type galaxies is 79 +/- 6% at z=0.83 and 87 +/- 6% at z=0.023 for the Coma cluster, consistent with no evolution. Previous work with luminosity-selected samples finds that the early-type fraction in rich clusters declines from =~80% at z=0 to =~60% at z=0.8. The observed evolution in the early-type fraction from luminosity-selected samples must predominately occur among sub-M* galaxies. As M* for field and group galaxies, especially late-types, is below M* for clusters galaxies, infall could explain most of the recent early-type fraction growth. Future surveys could determine the morphological distributions of lower mass systems which will confirm or refute this explanation.Comment: 5 pages in emulate ApJ format with three color figures. Accepted for publication in ApJ Letters, v642n2. Updated to correct grammatical and typographic errors found by the journa

RXJ0142.0+2131: I. The galaxy content of an X-ray-luminous galaxy cluster at z=0.28

We present a photometric and spectroscopic study of stellar populations in the X-ray-luminous cluster of galaxies RXJ0142.0+2131 at z=0.280. This paper analyses the results of high signal-to-noise spectroscopy, as well as g'-, r'-, and i'-band imaging, using the Gemini Multi-Object Spectrograph on Gemini North. Of 43 spectroscopic targets, we find 30 cluster members over a range in color. Central velocity dispersions and absorption-line strengths for lines in the range 3700A < lambda_rest < 5800A are derived for cluster members, and are compared with a low-redshift sample of cluster galaxies, and single stellar population (SSP) models. We use a combination of these indicators to estimate luminosity-weighted mean ages, metallicities ([M/H]), and alpha-element abundance ratios ([alpha/Fe]). RXJ0142.0+2131 is a relatively poor cluster and lacks galaxies with high central velocity dispersions. Although the red sequence and the Faber-Jackson relation are consistent with pure passive evolution of the early-type population with a formation redshift of z_form = 2, the strengths of the 4000A break and scaling relations between metal line indices and velocity dispersion reject this model with high significance. By inverting SSP models for the Hbeta_G, Mgb, and line indices, we calculate that, at a given velocity dispersion and metallicity, galaxies in RXJ0142.0+2131 have luminosity-weighted mean ages 0.14 +- 0.07 dex older than the low-redshift sample. We also find that [alpha/Fe] in stellar populations in RXJ0142.0+2131 is 0.14 +- 0.03 greater than at low redshift. All scaling relations are consistent with these estimated offsets. (abridged)Comment: AJ, accepted. 31 pages, 13 figures, uses emulateapj.cls. High-resolution figures available on request from first autho

The Star Formation Epoch of the Most Massive Early-Type Galaxies

We present new Keck spectroscopy of early-type galaxies in three galaxy clusters at z~0.5. We focus on the fundamental plane (FP) relation, and combine the kinematics with structural parameters determined from HST images. The galaxies obey clear FP relations, which are offset from the FP of the nearby Coma cluster due to passive evolution of the stellar populations. The z~0.5 data are combined with published data for 11 additional clusters at 0.18<z<1.28, to determine the evolution of the mean M/L(B) ratio of cluster galaxies with masses M>10^11 M_sun, as implied by the FP. We find dlog(M/L(B))/dz = -0.555+-0.042, stronger evolution than was previously inferred from smaller samples. The observed evolution depends on the luminosity-weighted mean age of the stars in the galaxies, the initial mass function (IMF), selection effects due to progenitor bias, and other parameters. Assuming a normal IMF but allowing for various other sources of uncertainty we find z* = 2.01+-0.20 for the luminosity-weighted mean star formation epoch. The main uncertainty is the slope of the IMF in the range 1-2 Solar masses: we find z* = 4.0 for a top-heavy IMF with slope x=0. The M/L(B) ratios of the cluster galaxies are compared to those of recently published samples of field early-type galaxies at 0.32<z<1.14. Assuming that progenitor bias and the IMF do not depend on environment we find that the present-day age of stars in massive field galaxies is 4.1 +- 2.0 % (~0.4 Gyr) less than that of stars in massive cluster galaxies, consistent with most, but not all, previous studies of local and distant early-type galaxies. This relatively small age difference is surprising in the context of expectations from ``standard'' hierarchical galaxy formation models. [ABRIDGED]Comment: Accepted for publication in ApJ. Minor corrections to match published versio

Tuning of magnetic and electronic states by control of oxygen content in lanthanum strontium cobaltites

We report on the magnetic, resistive, and structural studies of perovskite La$_{1/3}$Sr$_{2/3}$CoO$_{3-\delta}$. By using the relation of synthesis temperature and oxygen partial pressure to oxygen stoichiometry obtained from thermogravimetric analysis, we have synthesized a series of samples with precisely controlled $\delta=0.00-0.49$. These samples show three structural phases at $\delta=0.00-0.15$, $\approx0.25$, $\approx0.5$, and two-phase behavior for other oxygen contents. The stoichiometric material with $\delta=0.00$ is a cubic ferromagnetic metal with the Curie temperature $T_{\rm C}=274$ K. The increase of $\delta$ to 0.15 is followed by a linear decrease of $T_{\rm C}$ to $\approx$ 160 K and a metal-insulator transition near the boundary of the cubic structure range. Further increase of $\delta$ results in formation of a tetragonal $2a_p\times 2a_p \times 4a_p$ phase for $\delta\approx 0.25$ and a brownmillerite phase for $\delta\approx0.5$. At low temperatures, these are weak ferromagnetic insulators (canted antiferromagnets) with magnetic transitions at $T_{\rm m}\approx230$ and 120 K, respectively. At higher temperatures, the $2a_p\times 2a_p \times 4a_p$ phase is $G$-type antiferromagnetic between 230 K and $\approx$360 K. Low temperature magnetic properties of this system for $\delta<1/3$ can be described in terms of a mixture of Co$^{3+}$ ions in the low-spin state and Co$^{4+}$ ions in the intermediate-spin state and a possible spin transition of Co$^{3+}$ to the intermediate-spin state above $T_{\rm C}$. For $\delta>1/3$, there appears to be a combination of Co$^{2+}$ and Co$^{3+}$ ions, both in the high-spin state with dominating antiferromagnetic interactions.Comment: RevTeX, 9 pages, 7 figures, to be published in Physical Review

Harmonic analysis of iterated function systems with overlap

In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.Comment: 37 page