4,849 research outputs found
Finite groups of units of finite characteristic rings
In \cite[Problem 72]{Fuchs60} Fuchs asked the following question: which
groups can be the group of units of a commutative ring? In the following years,
some partial answers have been given to this question in particular cases. The
aim of the present paper is to address Fuchs' question when is a {\it
finite characteristic ring}. The result is a pretty good description of the
groups which can occur as group of units in this case, equipped with examples
showing that there are obstacles to a "short" complete classification. As a
byproduct, we are able to classify all possible cardinalities of the group of
units of a finite characteristic ring, so to answer Ditor's question
\cite{ditor}
On wild extensions of a p-adic field
In this paper we consider the problem of classifying the isomorphism classes
of extensions of degree pk of a p-adic field, restricting to the case of
extensions without intermediate fields. We establish a correspondence between
the isomorphism classes of these extensions and some Kummer extensions of a
suitable field F containing K. We then describe such classes in terms of the
representations of Gal(F/K). Finally, for k = 2 and for each possible Galois
group G, we count the number of isomorphism classes of the extensions whose
normal closure has a Galois group isomorphic to G. As a byproduct, we get the
total number of isomorphism classes
An equivalent formulation of 0-closed sesquilinear forms
In 1970, McIntosh introduced the so-called 0-closed sesquilinear forms and proved a corresponding representation theorem. In this paper, we give a simple equivalent formulation of 0-closed sesquilinear forms. The main underlying idea is to consider minimal pairs of non-negative dominating forms
Separatrix Reconnections in Chaotic Regimes
In this paper we extend the concept of separatrix reconnection into chaotic
regimes. We show that even under chaotic conditions one can still understand
abrupt jumps of diffusive-like processes in the relevant phase-space in terms
of relatively smooth realignments of stable and unstable manifolds of unstable
fixed points.Comment: 4 pages, 5 figures, submitted do Phys. Rev. E (1998
Ab-initio calculations for the beta-tin diamond transition in Silicon: comparing theories with experiments
We investigate the pressure-induced metal-insulator transition from diamond
to beta-tin in bulk Silicon, using quantum Monte Carlo (QMC) and density
functional theory (DFT) approaches. We show that it is possible to efficiently
describe many-body effects, using a variational wave function with an optimized
Jastrow factor and a Slater determinant. Variational results are obtained with
a small computational cost and are further improved by performing diffusion
Monte Carlo calculations and an explicit optimization of molecular orbitals in
the determinant. Finite temperature corrections and zero point motion effects
are included by calculating phonon dispersions in both phases at the DFT level.
Our results indicate that the theoretical QMC (DFT) transition pressure is
significantly larger (smaller) than the accepted experimental value. We discuss
the limitation of DFT approaches due to the choice of the exchange and
correlation functionals and the difficulty to determine consistent
pseudopotentials within the QMC framework, a limitation that may significantly
affect the accuracy of the technique.Comment: 13 pages, 9 figures, submitted to the Physical Review B on October 2
Anisotropy and percolation threshold in a multifractal support
Recently a multifractal object, , was proposed to study percolation
properties in a multifractal support. The area and the number of neighbors of
the blocks of show a non-trivial behavior. The value of the
probability of occupation at the percolation threshold, , is a function
of , a parameter of which is related to its anisotropy. We
investigate the relation between and the average number of neighbors of
the blocks as well as the anisotropy of
Mechanical Mixing in Nonlinear Nanomechanical Resonators
Nanomechanical resonators, machined out of Silicon-on-Insulator wafers, are
operated in the nonlinear regime to investigate higher-order mechanical mixing
at radio frequencies, relevant to signal processing and nonlinear dynamics on
nanometer scales. Driven by two neighboring frequencies the resonators generate
rich power spectra exhibiting a multitude of satellite peaks. This nonlinear
response is studied and compared to -order perturbation theory and
nonperturbative numerical calculations.Comment: 5 pages, 7 figure
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