Standard noncommuting and commuting dilations of commuting tuples

We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction there are two commonly used dilations in multivariable operator theory. Firstly there is the minimal isometric dilation consisting of isometries with orthogonal ranges and hence it is a noncommuting tuple. There is also a commuting dilation related with a standard commuting tuple on Boson Fock space. We show that this commuting dilation is the maximal commuting piece of the minimal isometric dilation. We use this result to classify all representations of Cuntz algebra O_n coming from dilations of commuting tuples.Comment: 18 pages, Latex, 1 commuting diagra

Snow cover, snowmelt and runoff in the Himalayan River basins

Not withstanding the seasonal vagaries of both rainfall amount and snowcover extent, the Himalayan rivers retain their basic perennial character. However, it is the component of snowmelt yield that accounts for some 60 to 70 percent of the total annual flow volumes from Hamilayan watersheds. On this large hydropotential predominantly depends the temporal performance of hydropower generation and major irrigation projects. The large scale effects of Himalayan snowcover on the hydrologic responses of a few selected catchments in western Himalayas was studied. The antecedent effects of snowcover area on long and short term meltwater yields can best be analyzed by developing appropriate hydrologic models forecasting the pattern of snowmelt as a function of variations in snowcover area. It is hoped that these models would be of practical value in the management of water resources. The predictability of meltwater for the entire snowmelt season was studied, as was the concurrent flow variation in adjacent watersheds, and their hydrologic significance. And the applicability of the Snowmelt-Runoff Model for real time forecast of daily discharges during the major part of the snowmelt season is examined

Spin liquid behaviour in Jeff=1/2 triangular lattice Ba3IrTi2O9

Ba3IrTi2O9 crystallizes in a hexagonal structure consisting of a layered triangular arrangement of Ir4+ (Jeff=1/2). Magnetic susceptibility and heat capacity data show no magnetic ordering down to 0.35K inspite of a strong magnetic coupling as evidenced by a large Curie-Weiss temperature=-130K. The magnetic heat capacity follows a power law at low temperature. Our measurements suggest that Ba3IrTi2O9 is a 5d, Ir-based (Jeff=1/2), quantum spin liquid on a 2D triangular lattice.Comment: 10 pages including supplemental material, to be published in Phys. Rev. B (Rapid Comm.

Possible spin-orbit driven spin-liquid ground state in the double perovskite phase of Ba3YIr2O9

We report the structural transformation of hexagonal Ba3YIr2O9 to a cubic double perovskite form (stable in ambient conditions) under an applied pressure of 8GPa at 1273K. While the ambient pressure (AP) synthesized sample undergoes long-range magnetic ordering at 4K, the high pressure(HP) synthesized sample does not order down to 2K as evidenced from our susceptibility, heat capacity and nuclear magnetic resonance (NMR) measurements. Further, for the HP sample, our heat capacity data have the form gamma*T+beta*T3 in the temperature (T) range of 2-10K with the Sommerfeld coefficient gamma=10mJ/mol-Ir K2. The 89Y NMR shift has no T-dependence in the range of 4-120K and its spin-lattice relaxation rate varies linearly with T in the range of 8-45K (above which it is T-independent). Resistance measurements of both the samples confirm that they are semiconducting. Our data provide evidence for the formation of a 5d based, gapless, quantum spin-liquid (QSL) in the cubic (HP) phase of Ba3YIr2O9. In this picture, the T term in the heat capacity and the linear variation of 89Y 1/T1 arises from excitations out of a spinon Fermi surface. Our findings lend credence to the theoretical suggestion [G. Chen, R. Pereira, and L. Balents, Phys. Rev. B 82, 174440 (2010)] that strong spin-orbit coupling can enhance quantum fluctuations and lead to a QSL state in the double perovskite lattice.Comment: 6 pages 5 figure

High-Redshift Dust Obscured Galaxies: A Morphology-Spectral Energy Distribution Connection Revealed by Keck Adaptive Optics

A simple optical to mid-IR color selection, R – [24]>14, i.e., f_ν(24 μm)/f_ν(R) ≳ 1000, identifies highly dust obscured galaxies (DOGs) with typical redshifts of z ~ 2 ± 0.5. Extreme mid-IR luminosities (L_(IR) > 10^(12-14)) suggest that DOGs are powered by a combination of active galactic nuclei (AGNs) and star formation, possibly driven by mergers. In an effort to compare their photometric properties with their rest-frame optical morphologies, we obtained high-spatial resolution (0."05-0."1) Keck Adaptive Optics K'-band images of 15 DOGs. The images reveal a wide range of morphologies, including small exponential disks (eight of 15), small ellipticals (four of 15), and unresolved sources (two of 15). One particularly diffuse source could not be classified because of low signal-to-noise ratio. We find a statistically significant correlation between galaxy concentration and mid-IR luminosity, with the most luminous DOGs exhibiting higher concentration and smaller physical size. DOGs with high concentration also tend to have spectral energy distributions (SEDs) suggestive of AGN activity. Thus, central AGN light may be biasing the morphologies of the more luminous DOGs to higher concentration. Conversely, more diffuse DOGs tend to show an SED shape suggestive of star formation. Two of 15 in the sample show multiple resolved components with separations of ~1 kpc, circumstantial evidence for ongoing mergers

The Star Formation Histories of z ~ 2 Dust-obscured Galaxies and Submillimeter-selected Galaxies

The Spitzer Space Telescope has identified a population of ultraluminous infrared galaxies (ULIRGs) at z ~ 2 that may play an important role in the evolution of massive galaxies. We measure the stellar masses (M_*) of two populations of Spitzer-selected ULIRGs that have extremely red R – [24] colors (dust-obscured galaxies, or DOGs) and compare our results with submillimeter-selected galaxies (SMGs). One set of 39 DOGs has a local maximum in their mid-infrared (mid-IR) spectral energy distribution (SED) at rest frame 1.6 μm associated with stellar emission ("bump DOGs"), while the other set of 51 DOGs have power-law mid-IR SEDs that are typical of obscured active galactic nuclei ("power-law DOGs"). We measure M_* by applying Charlot & Bruzual stellar population synthesis models to broadband photometry in the rest-frame ultraviolet, optical, and near-infrared of each of these populations. Assuming a simple stellar population and a Chabrier initial mass function, we find that power-law DOGs and bump DOGs are on average a factor of 2 and 1.5 more massive than SMGs, respectively (median and inter-quartile M_* values for SMGs, bump DOGs, and power-law DOGs are log(M_*/M_☉) = 10.42^(+0.42)_(–0.36), 10.62^(+0.36)_(–0.32), and 10.71^(+0.40)_(–0.34), respectively). More realistic star formation histories drawn from two competing theories for the nature of ULIRGs at z ~ 2 (major merger versus smooth accretion) can increase these mass estimates by up to 0.5 dex. A comparison of our stellar masses with the instantaneous star formation rate (SFR) in these z ~ 2 ULIRGs provides a preliminary indication supporting high SFRs for a given M_*, a situation that arises more naturally in major mergers than in smooth accretion-powered systems