A derivation of two quadratic transformations contiguous to that of Gauss via a differential equation approach

The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach

On a new class of summation formulae involving the Laguerre polynomial

By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummer’s first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie et al. [Generalizations of Whipple’s theorem on the sum of a 3 F 2, J. Comput. Appl. Math. 72 (1996), pp. 293–300] are then applied to obtain a new class of summation formulae involving the Laguerre polynomial, which have not previously appeared in the literature. Several related results due to Exton have also been given in a corrected form

An extension of Saalschütz's summation theorem for the series _<i>r</i>+3F_<i>r</i>+2

The aim in this research note is to provide an extension of Saalschütz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear]

On two Thomae-type transformations for hypergeometric series with integral parameter differences

We obtain two new Thomae-type transformations for hypergeometric series with r pairs of numeratorial and denominatorial parameters differing by positive integers. This is achieved by application of the so-called Beta integral method developed by Krattenthaler and Rao [Symposium on Symmetries in Science (ed. B. Gruber), Kluwer (2004)] to two recently obtained Euler-type transformations. Some special cases are given

Galilean invariance and homogeneous anisotropic randomly stirred flows

The Ward-Takahashi (WT) identities for incompressible flow implied by Galilean invariance are derived for the randomly forced Navier-Stokes equation (NSE), in which both the mean and fluctuating velocity components are explicitly present. The consequences of Galilean invariance for the vertex renormalization are drawn from this identity.Comment: REVTeX 4, 4 pages, no figures. To appear as a Brief Report in the Physical Review

High contrast imaging and thickness determination of graphene with in-column secondary electron microscopy

We report a new method for quantitative estimation of graphene layer thicknesses using high contrast imaging of graphene films on insulating substrates with a scanning electron microscope. By detecting the attenuation of secondary electrons emitted from the substrate with an in-column low-energy electron detector, we have achieved very high thickness-dependent contrast that allows quantitative estimation of thickness up to several graphene layers. The nanometer scale spatial resolution of the electron micrographs also allows a simple structural characterization scheme for graphene, which has been applied to identify faults, wrinkles, voids, and patches of multilayer growth in large-area chemical vapor deposited graphene. We have discussed the factors, such as differential surface charging and electron beam induced current, that affect the contrast of graphene images in detail.Comment: 5 pages, 4 figure

Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids

The path integral for randomly forced incompressible fluids is shown to have an underlying Becchi-Rouet-Stora (BRS) symmetry as a consequence of Galilean invariance. This symmetry must be respected to have a consistent generating functional, free from both an overall infinite factor and spurious relations amongst correlation functions. We present a procedure for respecting this BRS symmetry, akin to gauge fixing in quantum field theory. Relations are derived between correlation functions of this gauge fixed, BRS symmetric theory, analogous to the Slavnov-Taylor identities of quantum field theory.Comment: 5 pages, no figures, In Press Physical Review Letters, 200

The Spectral Energy Distribution and Infrared Luminosities of z ≈ 2 Dust-obscured Galaxies from Herschel and Spitzer

Dust-obscured galaxies (DOGs) are a subset of high-redshift (z ≈ 2) optically-faint ultra-luminous infrared galaxies (ULIRGs, e.g., L_(IR) > 10^(12) L_☉). We present new far-infrared photometry, at 250, 350, and 500 μm (observed-frame), from the Herschel Space Telescope for a large sample of 113 DOGs with spectroscopically measured redshifts. Approximately 60% of the sample are detected in the far-IR. The Herschel photometry allows the first robust determinations of the total infrared luminosities of a large sample of DOGs, confirming their high IR luminosities, which range from 10^(11.6) L_☉ 10^(13) L_☉. The rest-frame near-IR (1-3 μm) spectral energy distributions (SEDs) of the Herschel-detected DOGs are predictors of their SEDs at longer wavelengths. DOGs with "power-law" SEDs in the rest-frame near-IR show observed-frame 250/24 μm flux density ratios similar to the QSO-like local ULIRG, Mrk 231. DOGs with a stellar "bump" in their rest-frame near-IR show observed-frame 250/24 μm flux density ratios similar to local star-bursting ULIRGs like NGC 6240. None show 250/24 μm flux density ratios similar to extreme local ULIRG, Arp 220; though three show 350/24 μm flux density ratios similar to Arp 220. For the Herschel-detected DOGs, accurate estimates (within ~25%) of total IR luminosity can be predicted from their rest-frame mid-IR data alone (e.g., from Spitzer observed-frame 24 μm luminosities). Herschel-detected DOGs tend to have a high ratio of infrared luminosity to rest-frame 8 μm luminosity (the IR8 = L_(IR)(8-1000 μm)/νL_ν(8 μm) parameter of Elbaz et al.). Instead of lying on the z = 1-2 "infrared main sequence" of star-forming galaxies (like typical LIRGs and ULIRGs at those epochs) the DOGs, especially large fractions of the bump sources, tend to lie in the starburst sequence. While, Herschel-detected DOGs are similar to scaled up versions of local ULIRGs in terms of 250/24 μm flux density ratio, and IR8, they tend to have cooler far-IR dust temperatures (20-40 K for DOGs versus 40-50 K for local ULIRGs) as measured by the rest-frame 80/115 μm flux density ratios (e.g., observed-frame 250/350 μm ratios at z = 2). DOGs that are not detected by Herschel appear to have lower observed-frame 250/24 μm ratios than the detected sample, either because of warmer dust temperatures, lower IR luminosities, or both

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