On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t) in the theory of the Riemann zeta-function.Comment: 11 page

High spatial resolution 100 micron observations of the M83 bar

A program of high spatial resolution far-infrared observations of galaxies using the Kuiper Airborne Observatory (KAO), was conducted to better understand the role of star formation, the general interstellar radiation field, and non-thermal activity in powering the prodigious far-infrared luminosities seen in spiral and interacting galaxies. Here, researchers present observations of the central region of the well-known barred spiral M83 (NGC 5236). The resultant channel 3 scans for M83 and IRC + 10216, after co-addition and smoothing, are shown. These data show that M83 is extended at 100 microns compared to a point source. A simple Gaussian deconvolution of the M83 data with the point source profile from IRC+10216 gives a full width half maximum (FWHM) of about 19 seconds for M83. By comparison with IRC+10216, researchers obtain a flux for the unresolved component in M83 of about 110 Jy. This is about 1/6 the total flux for M83 (Rice et al. 1988) and about 1/2 the PSC flux. The M83 and IRC+10216 profiles in the cross-scan direction (SE-NW) were also compared, and show that M83 is extended in this direction as well, with a width of about 18 seconds. A comparison of the different channel profiles for M83 and IRC+10216 shows that there is an asymmetry in the M83 data, in that the maximum in the profiles shifts from southeast to northwest as channel number increases. This corresponds to the extension in the bar seen in the CO data. Thus the far-infrared emission in the central region of M83 tends to trace the CO bar. The new 100 micron data is also compared with previous H alpha observations from the literature, to determine how well the far-infrared traces the stellar structure, the star formation as measured by H alpha, and the optical colors

Far-infrared photometry of compact extragalactic sources: OJ 187 and BL Lac

The 50 and 100 micron emissions of OJ 287 were detected and upper limits for BL Lac were obtained. These first measurements of two BL Lac objects in the far-infrared show them to be similar to the few quasars previously observed in the far-infrared. In particular, there is no evidence for significant dust emission, and the lambda approximately 100 micron flux density fits on a smooth line joining the near-infrared and millimeter continuum fluxes. The implications of the results for models of the sources are discussed briefly

An infrared study of the bi-polar outflow region GGD 12-15

Infrared observations from 1 to 100 microns are presented for the region associated with a bipolar CO outflow source near the nebulous objects GGD 12 to 15. A luminous far-infrared source was found associated with a radio-continuum source in the area. This object appears to be a compact HII region around a nearly main-sequence BO star. A faint 20 micron source was also discovered at the position of an H2O maser 3O deg northwest of the HII region. This object appears to be associated with but not coincident with a 2 micron reflection nebula. This structure serves as evidence for a non-spherically symmetric, possibly disk-like dust distribution around the exciting star for the maser. This object probably powers the bi-polar CO outflow although its luminosity is less than 10% that of the star which excites the compact HII region. A number of other 2 micron sources found in the area are probably members of a recently formed cluster

Image restoration and superresolution as probes of small scale far-IR structure in star forming regions

Far-infrared continuum studies from the Kuiper Airborne Observatory are described that are designed to fully exploit the small-scale spatial information that this facility can provide. This work gives the clearest picture to data on the structure of galactic and extragalactic star forming regions in the far infrared. Work is presently being done with slit scans taken simultaneously at 50 and 100 microns, yielding one-dimensional data. Scans of sources in different directions have been used to get certain information on two dimensional structure. Planned work with linear arrays will allow us to generalize our techniques to two dimensional image restoration. For faint sources, spatial information at the diffraction limit of the telescope is obtained, while for brighter sources, nonlinear deconvolution techniques have allowed us to improve over the diffraction limit by as much as a factor of four. Information on the details of the color temperature distribution is derived as well. This is made possible by the accuracy with which the instrumental point-source profile (PSP) is determined at both wavelengths. While these two PSPs are different, data at different wavelengths can be compared by proper spatial filtering. Considerable effort has been devoted to implementing deconvolution algorithms. Nonlinear deconvolution methods offer the potential of superresolution -- that is, inference of power at spatial frequencies that exceed D lambda. This potential is made possible by the implicit assumption by the algorithm of positivity of the deconvolved data, a universally justifiable constraint for photon processes. We have tested two nonlinear deconvolution algorithms on our data; the Richardson-Lucy (R-L) method and the Maximum Entropy Method (MEM). The limits of image deconvolution techniques for achieving spatial resolution are addressed

Expression patterns of chondrocyte genes cloned by differential display in tibial dyschondroplasia

AbstractTibial dyschondroplasia (TD) appears to involve a failure of the growth plate chondrocytes within growing long bones to differentiate fully to the hypertrophic stage, resulting in a mass of prehypertrophic chondrocytes which form the avascular TD lesion. Many biochemical and molecular markers of chondrocyte hypertrophy are absent from the lesion, or show reduced expression, but the cause of the disorder remains to be identified. As differentiation to the hypertrophic state is impaired in TD, we hypothesised that chondrocyte genes that are differentially expressed in the growth plate should show altered expression in TD. Using differential display, four genes, B-cadherin, EF2, HT7 and Ex-FABP were cloned from chondrocytes stimulated to differentiate to the hypertrophic stage in vitro, and their differential expression confirmed in vivo. Using semi-quantitative RT-PCR, the expression patterns of these genes were compared in chondrocytes from normal and TD growth plates. Surprisingly, none of these genes showed the pattern of expression that might be expected in TD lesion chondrocytes, and two of them, B-cadherin and Ex-FABP, were upregulated in the lesion. This indicates that the TD phenotype does not merely reflect the absence of hypertrophic marker genes, but may be influenced by more complex developmental mechanisms/defects than previously thought

SUSY and Dark Matter Constraints from the LHC

The ability of the LHC to make statements about the dark matter problem is considered, with a specific focus on supersymmetry. After reviewing the current strategies for supersymmetry searches at the LHC (in both CMS and ATLAS), some key ATLAS studies are used to demonstrate how one could establish that SUSY exists before going on to measure the relic density of a neutralino WIMP candidate. Finally, the general prospects for success at the LHC are investigated by looking at different points in the MSSM parameter space.Comment: Talk given at the XLIrst Rencontres de Moriond session devoted to Electroweak Interactions And Unified Theories in March 2006, to be published in the associated proceedings. 10 pages, 8 figure

Regions of beta 2 and beta 4 responsible for differences between the steady state dose-response relationships of the alpha 3 beta 2 and alpha 3 beta 4 neuronal nicotinic receptors

We constructed chimeras of the rat beta 2 and beta 4 neuronal nicotinic subunits to locate the regions that contribute to differences between the acetylcholine (ACh) dose-response relationships of the alpha 3 beta 2 and alpha 3 beta 4 receptors. Expressed in Xenopus oocytes, the alpha 3 beta 2 receptor displays an EC50 for ACh approximately 20-fold less than the EC50 of the alpha 3 beta 4 receptor. The apparent Hill slope (n(app)) of alpha 3 beta 2 is near one whereas the alpha 3 beta 4 receptor displays an n(app) near two. Substitutions within the first 120 residues convert the EC50 for ACh from one wild-type value to the other. Exchanging just beta 2:104-120 for the corresponding region of beta 4 shifts the EC50 of ACh dose-response relationship in the expected direction but does not completely convert the EC50 of the dose- response relationship from one wild-type value to the other. However, substitutions in the beta 2:104-120 region do account for the relative sensitivity of the alpha 3 beta 2 receptor to cytisine, tetramethylammonium, and ACh. The expression of beta 4-like (strong) cooperativity requires an extensive region of beta 4 (beta 4:1-301). Relatively short beta 2 substitutions (beta 2:104-120) can reduce cooperativity to beta 2-like values. The results suggest that amino acids within the first 120 residues of beta 2 and the corresponding region of beta 4 contribute to an agonist binding site that bridges the alpha and beta subunits in neuronal nicotinic receptors