1,112 research outputs found
Completion of a PrĂŒfer domain
AbstractLet V (resp. D) be a valuation domain (resp. SFT PrĂŒfer domain), I a proper ideal, and VÌ (resp. DÌ) be the I-adic completion of V (resp. D). We show that (1) VÌ is a valuation domain, (2) Krull dimension of VÌ=dimV/I+1 if I is not idempotent, VÌâ
V/I if I is idempotent, (3) dimDÌ=dimD/I+1, (4) DÌ is an SFT PrĂŒfer ring, and (5) DÌ 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 RăXă can be uncountably infinite, i.e., there exists an uncountably infinite chain of prime ideals in RăXă, even if dimR is finite. In fact, we show that dimRăXă is uncountably infinite if R is a non-SFT ring, which is an improvement of Arnoldâs 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 -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
-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
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 's below 10 keV. The response of CsI crystals to nuclear
recoil was studied with mono-energetic neutrons produced by the
H(p,n)He reaction. This was compared to the response to Compton
electrons scattered by 662 keV -ray. Pulse shape discrimination between
the response to these '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
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, RĂ©nyiâs parking problem, wireless network
Influence of the starting composition on the structural and superconducting properties of MgB2 phase
We report the preparation of MgB (0x0.5) compounds
with the nominal compositions. Single phase MgB was obtained for x=0
sample. For 0x0.5, MgB coexists with "MgB" and the amount
of MgB increases with x. With the increase of x, the lattice parameter
of "MgB" increases and the lattice parameter
decreases, correspondingly T of MgB decreases. The results
were discussed in terms of the presence of Mg vacancies or B interstitials in
the MgB structure. This work is helpful to the understanding of the
MgB films with different T, as well as the Mg site doping effect
for MgB.Comment: 11 pages, 4 figure
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