Covers of acts over monoids II

In 1981 Edgar Enochs conjectured that every module has a flat cover and finally proved this in 2001. Since then a great deal of effort has been spent on studying different types of covers, for example injective and torsion free covers. In 2008, Mahmoudi and Renshaw initiated the study of flat covers of acts over monoids but their definition of cover was slightly different from that of Enochs. Recently, Bailey and Renshaw produced some preliminary results on the `other' type of cover and it is this work that is extended in this paper. We consider free, divisible, torsion free and injective covers and demonstrate that in some cases the results are quite different from the module case

The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line

In this paper we find explicit formulas for: (1) Green's function for a system of one-dimensional bosons interacting via a delta-function potential with particles confined to the positive half-line; and (2) the transition probability for the one-dimensional asymmetric simple exclusion process (ASEP) with particles confined to the nonnegative integers. These are both for systems with a finite number of particles. The formulas are analogous to ones obtained earlier for the Bose gas and ASEP on the line and integers, respectively. We use coordinate Bethe Ansatz appropriately modified to account for confinement of the particles to the half-line. As in the earlier work, the proof for the ASEP is less straightforward than for the Bose gas.Comment: 14 Page

On the nature of Bose-Einstein condensation in disordered systems

We study the perfect Bose gas in random external potentials and show that there is generalized Bose-Einstein condensation in the random eigenstates if and only if the same occurs in the one-particle kinetic-energy eigenstates, which corresponds to the generalized condensation of the free Bose gas. Moreover, we prove that the amounts of both condensate densities are equal. Our method is based on the derivation of an explicit formula for the occupation measure in the one-body kinetic-energy eigenstates which describes the repartition of particles among these non-random states. This technique can be adapted to re-examine the properties of the perfect Bose gas in the presence of weak (scaled) non-random potentials, for which we establish similar results

Properties of baryon resonances from a multichannel partial wave analysis

Properties of nucleon and $\Delta$ resonances are derived from a multichannel partial wave analysis. The statistical significance of pion and photo-induced inelastic reactions off protons are studied in a multichannel partial-wave analysis.Comment: 12 pages, 8 Table

Refraction contrast imaging and edge effects in neutron radiography

This paper reports on the edge enhancement and refraction scattering effects in neutron radiography measured at thermal and cold neutron beams with a high resolution 55 mm microchannel plate neutron counting detector. These effects in some cases can enhance the contrast of certain features in the neutron radiographic images. At the same time, the edge effects introduce image distortions, as in case of tomographic reconstructions. The edge effects in radiographies of several steel and aluminum objects are shown for different beam divergences and sample orientations relative to the beam. It is also demonstrated how novel microcapillary neutron collimators can enable refraction and scattering contrast imaging in some cases, where the refraction and scattering angles are relatively large. These collimators can also be used to reduce some refraction artifacts, namely remove bright edges in the transmission image