Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure

This paper is concerned with the tight closure of an ideal in a commutative Noetherian local ring of prime characteristic . Several authors, including R. Fedder, K-i. Watanabe, K. E. Smith, N. Hara and F. Enescu, have used the natural Frobenius action on the top local cohomology module of such an to good effect in the study of tight closure, and this paper uses that device. The main part of the paper develops a theory of what are here called `special annihilator submodules' of a left module over the Frobenius skew polynomial ring associated to ; this theory is then applied in the later sections of the paper to the top local cohomology module of and used to show that, if is Cohen-Macaulay, then it must have a weak parameter test element, even if it is not excellent.

     

A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium

In a general Sparre Andersen risk model with surplus-dependent premium income, the generalization of Gerber-Shiu function proposed by Cheung et al. (2010a) is studied. A general expression for such Gerber-Shiu function is derived, and it is shown that its determination reduces to the evaluation of a transition function which is independent of the penalty function. Properties of and explicit expressions for such a transition function are derived when the surplus process is subject to (i) constant premium; (ii) a threshold dividend strategy; or (iii) credit interest. Extension of the approach is discussed for an absolute ruin model with debit interest.     

Composition of particles emitted at largep T and medium angles inpp,dd, andαα collisions at the CERN intersecting storage rings

The relative yields of kaons and protons compared with the yield of pions at highp _T and polar angles θ away from 90° (in the range from 10° to 45°) are presented forpp, dd, and αα interactions at a centre-of-mass energy \(\sqrt {s_{NN} } = 31\) GeV per nucleon-nucleon collision. The measured particle ratios depend on the atomic mass numberA of the beam particles and on θ. TheA dependence of the ratios becomes stronger for largerp _T and is more pronounced at smaller polar angles.     

Upgrade of beamline BL08B at Taiwan Light Source from a photon‐BPM to a double‐grating SGM beamline

During the last 20 years, beamline BL08B has been upgraded step by step from a photon beam‐position monitor (BPM) to a testing beamline and a single‐grating beamline that enables experiments to record X‐ray photo‐emission spectra (XPS) and X‐ray absorption spectra (XAS) for research in solar physics, organic semiconductor materials and spinel oxides, with soft X‐ray photon energies in the range 300–1000 eV. Demands for photon energy to extend to the extreme ultraviolet region for applications in nano‐fabrication and topological thin films are increasing. The basic spherical‐grating monochromator beamline was again upgraded by adding a second grating that delivers photons of energy from 80 to 420 eV. Four end‐stations were designed for experiments with XPS, XAS, interstellar photoprocess systems (IPS) and extreme‐ultraviolet lithography (EUVL) in the scheduled beam time. The data from these experiments show a large count rate in core levels probed and excellent statistics on background normalization in the L‐edge adsorption spectrum.     

Spectroscopy of Laser Plumes for Atto‐Mole and ng/g Elemental Analysis

Abstract

Two all‐optical analytical techniques are reviewed. Both are capable of highly sensitive multi‐element analysis. One is by means of resonance‐enhanced plasma spectroscopy. It minimizes the continuum background associated with laser‐induced plasmas. Relative to laser‐induced breakdown spectroscopy, the signal‐to‐noise ratio is improved by orders of magnitude, thus allowing the quantitation of sodium and potassium at the single blood cell level. The other technique utilizes laser‐excited atomic fluorescence. It has been traditionally handicapped by its one wavelength–one transition specificity. We showed, however, that numerous elements could be induced to fluoresce at a single excitation wavelength of 193 nm provided that the analytes were imbedded in dense plumes, such as those produced by pulsed laser ablation. This method eliminates the continuum plasma background and sub‐ppb sensitivity was demonstrated in the analysis of aqueous lead colloids.     

Finite time blowup of the <Emphasis Type="Italic">n</Emphasis>-harmonic flow on <Emphasis Type="Italic">n</Emphasis>-manifolds

In this paper, we generalize the no-neck result of Qing and Tian (in Commun Pure Appl Math 50:295–310, 1997) to show that there is no neck during blowing up for the n-harmonic flow as \(t\rightarrow \infty \). As an application of the no-neck result, we settle a conjecture of Hungerbühler (in Ann Scuola Norm Sup Pisa Cl Sci 4:593–631, 1997) by constructing an example to show that the n-harmonic map flow on an n-dimensional Riemannian manifold blows up in finite time for \(n\ge 3\).     

Assessment of bone calcium and phosphorus content using micro X‐ray fluorescence spectrometry (μ‐EDXRF): effects of long‐term cadmium poisoning

This study assesses whether the concentrations of biologically important elements in bones are altered by long‐term consumption of cadmium (Cd)‐contaminated water. Heavy metal poisoning has significant impact on humans, and pollutants such as Cd are often found at high concentrations in waterways. Twelve Sprague Dawley rats consumed water with 50 p.p.m. Cd (Cd group), and another 12 consumed normal water (control group). Six subjects from each group were sacrificed after 2 weeks and the others after 4 weeks. Spectra were acquired from the femur by using the EDAX Eagle III micro‐XRF setup, and quantitative calculations were performed by using the fundamental parameter method to determine the concentrations of elements. A bone calcium/phosphorus concentration ratio (Ca/P) of 2.07 ± 0.001 is observed in the spectra from control subjects after 2 weeks and 2.07 ± 0.001 after 4 weeks. In Cd subjects, Ca/P after 2 weeks is 2.04 ± 0.001 and after 4 weeks is 1.97 ± 0.003. Statistically significant differences are obtained when comparing controls with Cd subjects at both time points and when comparing Cd subjects at both time points. Cadmium poisoning significantly affects bone Ca and P concentrations, increasing the likelihood of osteoporosis and other bone diseases. Copyright © 2016 John Wiley & Sons, Ltd.