Variation of the first Hilbert coefficients of parameters with a common integral closure

A problem posed by Wolmer V. Vasconcelos on the variation of the first Hilbert coefficients of parameter ideals with a common integral closure in a local ring is studied. Affirmative answers are given and counterexamples are explored as well

Regularized Renormalization Group Reduction of Symplectic Map

By means of the perturbative renormalization group method, we study a long-time behaviour of some symplectic discrete maps near elliptic and hyperbolic fixed points. It is shown that a naive renormalization group (RG) map breaks the symplectic symmetry and fails to describe a long-time behaviour. In order to preserve the symplectic symmetry, we present a regularization procedure, which gives a regularized symplectic RG map describing an approximate long-time behaviour succesfully

Possible Evidence For Axino Dark Matter In The Galactic Bulge

Recently, the SPI spectrometer on the INTEGRAL satellite observed strong 511 keV line emission from the galactic bulge. Although the angular distribution (spherically symmetric with width of \sim 9 degree) of this emission is difficult to account for with traditional astrophysical scenarios, light dark matter particles could account for the observation. In this letter, we consider the possibility that decaying axinos in an R-parity violating model of supersymmetry may be the source of this emission. We find that \sim 1-300 MeV axinos with R-parity violating couplings can naturally produce the observed emission.Comment: 4 pages, 1 figure. Version accepted by Physical Review

Effects of Squark Processes on the Axino CDM Abundance

We investigate the role of an effective dimension-4 axino-quark-squark coupling in the thermal processes producing stable cold axino relics in the early Universe. We find that, while the induced squark and quark scattering processes are always negligible, squark decays become important in the case of low reheat temperature and large gluino mass. The effect can tighten the bounds on the scenario from the requirement that cold dark matter axinos do not overclose the Universe.Comment: 20 pages, 9 figures, uses JHEP3.cl

Nonabelian Gauge Theories on Noncommutative Spaces

In this paper, we describe a method for obtaining the nonabelian Seiberg-Witten map for any gauge group and to any order in theta. The equations defining the Seiberg-Witten map are expressed using a coboundary operator, so that they can be solved by constructing a corresponding homotopy operator. The ambiguities, of both the gauge and covariant type, which arise in this map are manifest in our formalism.Comment: 14 pages, latex, Talk presented at 2001: A Spacetime Odyssey - Michigan Center for Theoretical Physics, some typos correcte

Green's function of fully anharmonic lattice vibration

Motivated by the discovery of superconductivity in beta-pyrochlore oxides, we study property of rattling motion coupled with conduction electrons. We derive the general expression of the Green's function of fully anharmonic lattice vibration within the accuracy of the second order perturbation of electron-ion interaction by introducing self-energy, vertex-correction, and normalization factor for each transition. Using the expression, we discuss the characteristic properties of the spectral function in the entire range from weakly anharmonic potential to double-well case, and calculate NMR relaxation rate due to the two phonon Raman process

Dynamics and thermalization of the nuclear spin bath in the single-molecule magnet Mn12-ac: test for the theory of spin tunneling

The description of the tunneling of a macroscopic variable in the presence of a bath of localized spins is a subject of great fundamental and practical interest, and is relevant for many solid-state qubit designs. Instead of focusing on the the "central spin" (as is most often done), here we present a detailed study of the dynamics of the nuclear spin bath in the Mn12-ac single-molecule magnet, probed by NMR experiments down to very low temperatures (T = 20 mK). We find that the longitudinal relaxation rate of the 55Mn nuclei in Mn12-ac becomes roughly T-independent below T = 0.8 K, and can be strongly suppressed with a longitudinal magnetic field. This is consistent with the nuclear relaxation being caused by quantum tunneling of the molecular spin, and we attribute the tunneling fluctuations to the minority of fast-relaxing molecules present in the sample. The transverse nuclear relaxation is also T-independent for T < 0.8 K, and can be explained qualitatively and quantitatively by the dipolar coupling between like nuclei in neighboring molecules. We also show that the isotopic substitution of 1H by 2H leads to a slower nuclear longitudinal relaxation, consistent with the decreased tunneling probability of the molecular spin. Finally, we demonstrate that, even at the lowest temperatures, the nuclear spins remain in thermal equilibrium with the lattice phonons, and we investigate the timescale for their thermal equilibration. After a review of the theory of macroscopic spin tunneling in the presence of a spin bath, we argue that most of our experimental results are consistent with that theory, but the thermalization of the nuclear spins is not.Comment: 24 pages, 18 figures. Experimental study of the spin bath dynamics in quantum nanomagnets, plus an extensive review and application of the theor

Star Formation and AGN in the Core of the Shapley Supercluster: A VLA Survey of A3556, A3558, SC1327-312, SC1329-313, and A3562

The core of the Shapley supercluster (A3556, A3558, SC1327-312, SC1329-313, and A3562) is an ideal region in which to study the effects of cluster mergers on the activity of individual galaxies. This paper presents the most comprehensive radio continuum investigation of the region, relying on a 63-pointing mosaic obtained with the Very Large Array yielding an areal coverage of nearly 7 square degrees. The mosaic provides a typical sensitivity of about 80 uJy at a resolution of 16", enabling detection of galaxies with star formation rates as low as 1 solar mass per year. The radio data are complemented by optical imaging in B and R, producing a catalog of 210 radio-detected galaxies with m_R <= 17.36 (M_R <= -19). At least 104 of these radio-detected galaxies are members of the supercluster on the basis of public velocity measurements. Across the entire core of the supercluster, there appears to be a significant deficit of radio galaxies at intermediate optical magnitudes (M_R between -21 and -22). This deficit is offset somewhat by an increase in the frequency with which brighter galaxies (M_R less than -22) host radio sources. More dramatic is the highly significant increase in the probability for fainter galaxies (M_R between -20 and -21) in the vicinity of A3562 and SC1329-313 to be associated with radio emission. The radio and optical data for these sources strongly suggest that these active galaxies are powered by star formation. In conjunction with recent X-ray analysis, this is interpreted as young starbursts related to the recent merger of SC1329-313 with A3562 and the rest of the supercluster.Comment: Accepted by AJ; 50 pages, including 16 figures (for full resolution PDF, see http://mywebpages.comcast.net/nealamiller2/Shapley_pp.pdf

Star formation rate indicators in the Sloan Digital Sky Survey

The Sloan Digital Sky Survey (SDSS) first data release provides a database of 106000 unique galaxies in the main galaxy sample with measured spectra. A sample of star-forming (SF) galaxies are identified from among the 3079 of these having 1.4 GHz luminosities from FIRST, by using optical spectral diagnostics. Using 1.4 GHz luminosities as a reference star formation rate (SFR) estimator insensitive to obscuration effects, the SFRs derived from the measured SDSS Halpha, [OII] and u-band luminosities, as well as far-infrared luminosities from IRAS, are compared. It is established that straightforward corrections for obscuration and aperture effects reliably bring the SDSS emission line and photometric SFR estimates into agreement with those at 1.4 GHz, although considerable scatter (~60%) remains in the relations. It thus appears feasible to perform detailed investigations of star formation for large and varied samples of SF galaxies through the available spectroscopic and photometric measurements from the SDSS. We provide herein exact prescriptions for determining the SFR for SDSS galaxies. The expected strong correlation between [OII] and Halpha line fluxes for SF galaxies is seen, but with a median line flux ratio F_[OII]/F_Halpha=0.23, about a factor of two smaller than that found in the sample of Kennicutt (1992). This correlation, used in deriving the [OII] SFRs, is consistent with the luminosity-dependent relation found by Jansen et al. (2001). The median obscuration for the SDSS SF systems is found to be A_Halpha=1.2 mag, while for the radio detected sample the median obscuration is notably higher, 1.6 mag, and with a broader distribution.Comment: Accepted for publication in ApJ, 40 pages, 26 figure