The Littlewood-Gowers problem

We show that if A is a subset of Z/pZ (p a prime) of density bounded away from 0 and 1 then the A(Z/pZ)-norm (that is the l^1-norm of the Fourier transform) of the characterstic function of A is bounded below by an absolute constant times (log p)^{1/2 - \epsilon} as p tends to infinity. This improves on the exponent 1/3 in recent work of Green and Konyagin.Comment: 31 pp. Corrected typos. Updated references

The X-ray Emissions from the M87 Jet: Diagnostics and Physical Interpretation

We reanalyze the deep Chandra observations of the M87 jet, first examined by Wilson & Yang (2002). By employing an analysis chain that includes image deconvolution, knots HST-1 and I are fully separated from adjacent emission. We find slight but significant variations in the spectral shape, with values of $\alpha_x$ ranging from $\sim 1.2-1.6$. We use VLA radio observations, as well as HST imaging and polarimetry data, to examine the jet's broad-band spectrum and inquire as to the nature of particle acceleration in the jet. As shown in previous papers, a simple continuous injection model for synchrotron-emitting knots, in which both the filling factor, $f_{acc}$, of regions within which particles are accelerated and the energy spectrum of the injected particles are constant, cannot account for the X-ray flux or spectrum. Instead, we propose that $f_{acc}$ is a function of position and energy and find that in the inner jet, $f_{acc} \propto E_\gamma^{-0.4 \pm 0.2} \propto E_e^{-0.2 \pm 0.1}$, and in knots A and B, $f_{acc} \propto E_\gamma^{-0.7 \pm 0.2} \propto E_e^{-0.35 \pm 0.1}$, where $E_\gamma$ is the emitted photon energy and and $E_e$ is the emitting electron energy. In this model, the index $p$ of the injected electron energy spectrum ($n(E_{e}) \propto E_{e}^{-p}$) is $p=2.2$ at all locations in the jet, as predicted by models of cosmic ray acceleration by ultrarelativistic shocks. There is a strong correlation between the peaks of X-ray emission and minima of optical percentage polarization, i.e., regions where the jet magnetic field is not ordered. We suggest that the X-ray peaks coincide with shock waves which accelerate the X-ray emitting electrons and cause changes in the direction of the magnetic field; the polarization is thus small because of beam averaging.Comment: Accepted for publication in ApJ; 21 pages, 9 figures, 2 tables; abstract shortened for astro-ph; Figures 1, 7 and 8 at reduced resolutio

MAGIC MOORE-PENROSE INVERSES AND PHILATELIC MAGIC SQUARES WITH SPECIAL EMPHASIS ON THE DANIELS–ZLOBEC MAGIC SQUARE

We study singular magic matrices in which the numbers in the rows and columns and in the two main diagonals all add up to the same sum. Our interest focuses on such magic matrices for which the Moore– Penrose inverse is also magic. Special attention is given to the “Daniels–Zlobec magic square’’ introduced by the British magician and television performer Paul Daniels (b. 1938) and considered by Zlobec (2001); see also Murray (1989, pp. 30–32). We introduce the concept of a “philatelic magic square” as a square arrangement of images of postage stamps so that the associated nominal values form a magic square. Three philatelic magic squares with stamps especially chosen for Sanjo Zlobec are presented in celebration of his 70th birthday; most helpful in identifying these stamps was an Excel checklist by Männikkö (2009)

High Energy Neutrinos: Sources and Fluxes

We discuss briefly the potential sources of high energy astrophysical neutrinos and show estimates of the neutrino fluxes that they can produce. A special attention is paid to the connection between the highest energy cosmic rays and astrophysical neutrinos.Comment: 7 pages, 2 figures, submitted to the Proceedings of TAUP 2005 workshop, corrected left panel of figure

Water Table Management Reduces Tile Nitrate Loss in Continuous Corn and in a Soybean-Corn Rotation

Water table management systems can be designed to alleviate soil water excesses and deficits, as well as reduce nitrate leaching losses in tile discharge. With this in mind, a standard tile drainage (DR) system was compared over 8 years (1991 to 1999) to a controlled tile drainage/subirrigation (CDS) system on a low-slope (0.05 to 0.1%) Brookston clay loam soil (Typic Argiaquoll) in southwestern Ontario, Canada. In the CDS system, tile discharge was controlled to prevent excessive drainage, and water was pumped back up the tile lines (subirrigation) to replenish the crop root zone during water deficit periods. In the first phase of the study (1991 to 1994), continuous corn (Zea mays, L.) was grown with annual nitrogen (N) fertilizer inputs as per local soil test recommendations. In the second phase (1995 to 1999), a soybean (Glycine max L., Merr.)-corn rotation was used with N fertilizer added only during the two corn years. In Phase 1 when continuous corn was grown, CDS reduced total tile discharge by 26% and total nitrate loss in tile discharge by 55%, compared to DR. In addition, the 4-year flow weighted mean (FWM) nitrate concentration in tile discharge exceeded the Canadian drinking water guideline (10 mg N l–1) under DR (11.4 mg N l–1), but not under CDS (7.0 mg N l–1). In Phase 2 during the soybean-corn rotation, CDS reduced total tile discharge by 38% and total nitrate loss in tile discharge by 66%, relative to DR. The 4-year FWM nitrate concentration during Phase 2 in tile discharge was below the drinking water guideline for both DR (7.3 mg N l–1) and CDS (4.0 mg N l–1). During both phases of the experiment, the CDS treatment caused only minor increases in nitrate loss in surface runoff relative to DR. Hence CDS decreased FWM nitrate concentrations, total drainage water loss, and total nitrate loss in tile discharge relative to DR. In addition, soybean-corn rotation reduced FWM nitrate concentrations and total nitrate loss in tile discharge relative to continuous corn. CDS and crop rotations with reduced N fertilizer inputs can thus improve the quality of tile discharge water substantially

Rayleigh-Taylor Instabilities in Young Supernova Remnants Undergoing Efficient Particle Acceleration

We employ hydrodynamic simulations to study the effects of high shock compression ratios, as expected for fast shocks with efficient particle acceleration, on the convective instability of driven waves in supernova remnants. We find that the instability itself does not depend significantly on the compression ratio, but because the width of the interaction region between the forward and reverse shocks can shrink significantly with increasing shock compression, we find that convective instabilities can reach all the way to the forward shock front if compression ratios are high enough.Comment: Submitted to The Astrophysical Journa

Nonthermal Emission from a Supernova Remnant in a Molecular Cloud

In evolved supernova remnants (SNRs) interacting with molecular clouds, such as IC 443, W44, and 3C391, a highly inhomogeneous structure consisting of a forward shock of moderate Mach number, a cooling layer, a dense radiative shell and an interior region filled with hot tenuous plasma is expected. We present a kinetic model of nonthermal electron injection, acceleration and propagation in that environment and find that these SNRs are efficient electron accelerators and sources of hard X- and gamma-ray emission. The energy spectrum of the nonthermal electrons is shaped by the joint action of first and second order Fermi acceleration in a turbulent plasma with substantial Coulomb losses. Bremsstrahlung, synchrotron, and inverse Compton radiation of the nonthermal electrons produce multiwavelength photon spectra in quantitative agreement with the radio and the hard emission observed by ASCA and EGRET from IC 443. We distinguish interclump shock wave emission from molecular clump shock wave emission accounting for a complex structure of molecular cloud. Spatially resolved X- and gamma- ray spectra from the supernova remnants IC 443, W44, and 3C391 as might be observed with BeppoSAX, Chandra XRO, XMM, INTEGRAL and GLAST would distinguish the contribution of the energetic lepton component to the gamma-rays observed by EGRET.Comment: 14 pages, 4 figure, Astrophysical Journal, v.538, 2000 (in press

The Contribution of Different Supernova Populations to the Galactic Gamma-Ray Background

The contribution of Source Cosmic Rays (SCRs), accelerated and still confined in Supernova Remnants (SNRs), to the diffuse high energy \gr emission above 1 GeV from the Galactic disk is studied. The \grs produced by the SCRs have a much harder spectrum than those generated by the Galactic Cosmic Rays (GCRs). Extending a previous paper, a simple SNR population synthesis is considered and the Inverse Compton emission from the SCR electrons is evaluated in greater detail. Then the combined spectrum of \gr emission from the Galactic Supernova Remnant population is calculated and this emission at low Galactic latitudes is compared with the diffuse \gr emission observed by the EGRET and ground based instruments. The average contribution of SCRs is comparable to the GCR contribution already at GeV energies, due to Supernovae of types II and Ib exploding into the wind bubbles of quite massive progenitor stars, and becomes dominant at \gr energies above 100 GeV. At TeV energies the dominant contribution is from SCRs in SNRs that expand into a uniform interstellar medium. In fact, the sum of hadronic and Inverse Compton \grs would exceed the limits given by the existing experimental data, unless the confinement time $T_{SN}$, i.e. the time until which SNRs confine the main fraction of accelerated SCRs, is as small as $T_{SN}\sim 10^4$ yr and the typical magnetic field strength in SNRs as large as 30 $\mu$G. Both situations are however possible as a result of field amplification through CR backreaction in the acceleration process. It is pointed out that accurate measurements of the low-latitude diffuse Galactic \gr spectrum at TeV-energies can serve as a unique consistency test for CR origin from the Supernova Remnant population as a whole.Comment: To appear in Astrophysical Journa