Completion of a Prüfer domain

AbstractLet V (resp. D) be a valuation domain (resp. SFT Prüfer domain), I a proper ideal, and V̂ (resp. D̂) be the I-adic completion of V (resp. D). We show that (1) V̂ is a valuation domain, (2) Krull dimension of V̂=dimV/I+1 if I is not idempotent, V̂≅V/I if I is idempotent, (3) dimD̂=dimD/I+1, (4) D̂ is an SFT Prüfer ring, and (5) D̂ is a catenarian ring

The Krull dimension of power series rings over non-SFT rings

AbstractLet R be a commutative ring with identity. We show that the Krull dimension of the power series ring R〚X〛 can be uncountably infinite, i.e., there exists an uncountably infinite chain of prime ideals in R〚X〛, even if dimR is finite. In fact, we show that dimR〚X〛 is uncountably infinite if R is a non-SFT ring, which is an improvement of Arnold’s result

Cholesterol granuloma in the wall of a mandibular dentigerous cyst: a rare case report

Cholesterol granuloma is an inflammatory reaction to cholesterol crystals deposition. It may develop in a variety of sites including the middle ear, mastoid process or even paranasal sinuses. Very few cases of cholesterol granuloma occurring in the jaws were reported. This report presents a rare case of cholesterol granuloma that developed in the wall of a large mandibular dentigerous cyst. The condition was treated with hemimandibulectomy followed by reconstruction with a free fibular flap

Single-filament Composite MgB2/SUS Ribbons by Powder-In-Tube Process

We report the successful fabrication of single-filament composite MgB2/SUS ribbons, as an ultra-robust conductor type, employing the powder-in-tube (PIT) process, by swaging and cold rolling only. The remarkable transport critical current (Ic) of the non-sintered MgB2/SUS ribbon has observed, as an unexpected result. Transport critical currents Ic ~ 316 A at T = 4.2 K and Ic ~ 82 A at T = 20 K were observed at self-field, for the non-sintered composite MgB2/SUS ribbon. In addition, the persistent current density Jp values, that were estimated by Bean formula, were more than ~ 7  105 A/cm2 at T = 5 K, and ~ 1.2  105 A/cm2 at T = 30 K, for the sintered composite MgB2/SUS ribbon, at H = 0 G.Comment: 10 pages, 4 figure

Is the brick-wall model unstable for a rotating background?

The stability of the brick wall model is analyzed in a rotating background. It is shown that in the Kerr background without horizon but with an inner boundary a scalar field has complex-frequency modes and that, however, the imaginary part of the complex frequency can be small enough compared with the Hawking temperature if the inner boundary is sufficiently close to the horizon, say at a proper altitude of Planck scale. Hence, the time scale of the instability due to the complex frequencies is much longer than the relaxation time scale of the thermal state with the Hawking temperature. Since ambient fields should settle in the thermal state in the latter time scale, the instability is not so catastrophic. Thus, the brick wall model is well defined even in a rotating background if the inner boundary is sufficiently close to the horizon.Comment: Latex, 17 pages, 1 figure, accepted for publication in Phys. Rev.

Exact soliton solutions of coupled nonlinear Schr\"odinger equations: Shape changing collisions, logic gates and partially coherent solitons

The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{\"o}dinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by explicitly constructing multisoliton solutions (upto four-soliton solutions) for two coupled and arbitrary $N$-coupled nonlinear Schr{\"o}dinger equations using the Hirota bilinearization method, we bring out clearly the various features underlying the fascinating shape changing (intensity redistribution) collisions of solitons, including changes in amplitudes, phases and relative separation distances, and the very many possibilities of energy redistributions among the modes of solitons. However in this multisoliton collision process the pair-wise collision nature is shown to be preserved in spite of the changes in the amplitudes and phases of the solitons. Detailed asymptotic analysis also shows that when solitons undergo multiple collisions, there exists the exciting possibility of shape restoration of atleast one soliton during interactions of more than two solitons represented by three and higher order soliton solutions. From application point of view, we have shown from the asymptotic expressions how the amplitude (intensity) redistribution can be written as a generalized linear fractional transformation for the $N$-component case. Also we indicate how the multisolitons can be reinterpreted as various logic gates for suitable choices of the soliton parameters, leading to possible multistate logic. In addition, we point out that the various recently studied partially coherent solitons are just special cases of the bright soliton solutions exhibiting shape changing collisions, thereby explaining their variable profile and shape variation in collision process.Comment: 50 Pages, 13 .jpg figures. To appear in PR

The random disc thrower problem

We describe a number of approaches to a question posed by Philips Research, described as the "random disc thrower" problem. Given a square grid of points in the plane, we cover the points by equal-sized planar discs according to the following random process. At each step, a random point of the grid is chosen from the set of uncovered points as the centre of a new disc. This is an abstract model of spatial reuse in wireless networks. A question of Philips Research asks what, as a function of the grid length, is the expected number of discs chosen before the process can no longer continue? Our main results concern the one-dimensional variant of this problem, which can be solved reasonably well, though we also provide a number of approaches towards an approximate solution of the original two-dimensional problem. The two-dimensional problem is related to an old, unresolved conjecture ([6]) that has been the object of close study in both probability theory and statistical physics. Keywords: generating functions, Markov random fields, random sequential adsorption, Rényi’s parking problem, wireless network

Neutron beam test of CsI crystal for dark matter search

We have studied the response of Tl-doped and Na-doped CsI crystals to nuclear recoils and $\gamma$'s below 10 keV. The response of CsI crystals to nuclear recoil was studied with mono-energetic neutrons produced by the $^3$H(p,n)$^3$He reaction. This was compared to the response to Compton electrons scattered by 662 keV $\gamma$-ray. Pulse shape discrimination between the response to these $\gamma$'s and nuclear recoils was studied, and quality factors were estimated. The quenching factors for nuclear recoils were derived for both CsI(Na) and CsI(Tl) crystals.Comment: 21pages, 14figures, submitted to NIM

Influence of the starting composition on the structural and superconducting properties of MgB2 phase

We report the preparation of Mg$_{1-x}$B$_{2}$ (0$\le$x$\le$0.5) compounds with the nominal compositions. Single phase MgB$_{2}$ was obtained for x=0 sample. For 0$<$x$\le$0.5, MgB$_{4}$ coexists with "MgB$_{2}$" and the amount of MgB$_{4}$ increases with x. With the increase of x, the lattice parameter ${\it c}$ of "MgB$_{2}$" increases and the lattice parameter ${\it a}$ decreases, correspondingly T$_{c}$ of Mg$_{1-x}$B$_{2}$ decreases. The results were discussed in terms of the presence of Mg vacancies or B interstitials in the MgB$_{2}$ structure. This work is helpful to the understanding of the MgB$_{2}$ films with different T$_{c}$, as well as the Mg site doping effect for MgB$_{2}$.Comment: 11 pages, 4 figure