2,598 research outputs found
Spectral spaces and ultrafilters
Let be the prime spectrum of a ring. In [arXiv:0707.1525] the authors
define a topology on by using ultrafilters and they show that this topology
is precisely the constructible topology. In this paper we generalize the
construction given in [arXiv:0707.1525] and, starting from a set and a
collection of subsets of , we define by using ultrafilters a
topology on in which is a collection of clopen sets. We use
this construction for giving a new characterization of spectral spaces and
several new examples of spectral spaces.Comment: 16 pages. To appear in Communications in Algebr
Pr\"ufer-like conditions on an amalgamated algebra along an ideal
Let be a ring homomorphism and let be an
ideal of . In this paper we study Pr\"ufer like conditions in the
amalgamation of with along , with respect to , a ring
construction introduced in 2009 by D'Anna, Finocchiaro and Fontana.Comment: 17 pages. To appear in Houston Journal of Mathematic
Magnetic-field and chemical-potential effects on the low-energy separation
We show that in the presence of a magnetic field the usual low-energy
separation of the Hubbard chain is replaced by a ``'' and ``''
separation. Here and refer to small-momentum and low-energy independent
excitation modes which couple both to charge and spin. Importantly, we find the
exact generators of these excitations both in the electronic and pseudoparticle
basis. In the limit of zero magnetic field these generators become the usual
charge and spin fluctuation operators. The and elementary excitations
are associated with the and pseudoparticles, respectively. We also
study the separate pseudoparticle left and right conservation laws. In the
presence of the magnetic field the small-momentum and low-energy excitations
can be bosonized. However, the suitable bosonization corresponds to the and
pseudoparticle modes and not to the usual charge and spin fluctuations. We
evaluate exactly the commutator between the electronic-density operators. Its
spin-dependent factor is in general non diagonal and depends on the
interaction. The associate bosonic commutation relations characterize the
present unconventional low-energy separation.Comment: 29 pages, latex, submitted to Phys. Rev.
A variational justification of the assumed natural strain formulation of finite elements
The objective is to study the assumed natural strain (ANS) formulation of finite elements from a variational standpoint. The study is based on two hybrid extensions of the Reissner-type functional that uses strains and displacements as independent fields. One of the forms is a genuine variational principle that contains an independent boundary traction field, whereas the other one represents a restricted variational principle. Two procedures for element level elimination of the strain field are discussed, and one of them is shown to be equivalent to the inclusion of incompatible displacement modes. Also, the 4-node C(exp 0) plate bending quadrilateral element is used to illustrate applications of this theory
A topological version of Hilbert's Nullstellensatz
We prove that the space of radical ideals of a ring , endowed with the
hull-kernel topology, is a spectral space, and that it is canonically
homeomorphic to the space of the nonempty Zariski closed subspaces of
Spec, endowed with a Zariski-like topology.Comment: J. Algebra (to appear
Topological properties of semigroup primes of a commutative ring
A semigroup prime of a commutative ring is a prime ideal of the semigroup
. One of the purposes of this paper is to study, from a topological
point of view, the space \scal(R) of prime semigroups of . We show that,
under a natural topology introduced by B. Olberding in 2010, \scal(R) is a
spectral space (after Hochster), spectral extension of \Spec(R), and that the
assignment R\mapsto\scal(R) induces a contravariant functor. We then relate
-- in the case is an integral domain -- the topology on \scal(R) with the
Zariski topology on the set of overrings of . Furthermore, we investigate
the relationship between \scal(R) and the space
consisting of all nonempty inverse-closed subspaces of \spec(R), which has
been introduced and studied in C.A. Finocchiaro, M. Fontana and D. Spirito,
"The space of inverse-closed subsets of a spectral space is spectral"
(submitted). In this context, we show that \scal( R) is a spectral retract of
and we characterize when \scal( R) is
canonically homeomorphic to , both in general and
when \spec(R) is a Noetherian space. In particular, we obtain that, when
is a B\'ezout domain, \scal( R) is canonically homeomorphic both to
and to the space \overr(R) of the overrings of
(endowed with the Zariski topology). Finally, we compare the space
with the space \scal(R(T)) of semigroup primes
of the Nagata ring , providing a canonical spectral embedding
\xcal(R)\hookrightarrow\scal(R(T)) which makes \xcal(R) a spectral retract
of \scal(R(T)).Comment: 21 page
The first ANDES elements: 9-DOF plate bending triangles
New elements are derived to validate and assess the assumed natural deviatoric strain (ANDES) formulation. This is a brand new variant of the assumed natural strain (ANS) formulation of finite elements, which has recently attracted attention as an effective method for constructing high-performance elements for linear and nonlinear analysis. The ANDES formulation is based on an extended parametrized variational principle developed in recent publications. The key concept is that only the deviatoric part of the strains is assumed over the element whereas the mean strain part is discarded in favor of a constant stress assumption. Unlike conventional ANS elements, ANDES elements satisfy the individual element test (a stringent form of the patch test) a priori while retaining the favorable distortion-insensitivity properties of ANS elements. The first application of this formulation is the development of several Kirchhoff plate bending triangular elements with the standard nine degrees of freedom. Linear curvature variations are sampled along the three sides with the corners as gage reading points. These sample values are interpolated over the triangle using three schemes. Two schemes merge back to conventional ANS elements, one being identical to the Discrete Kirchhoff Triangle (DKT), whereas the third one produces two new ANDES elements. Numerical experiments indicate that one of the ANDES element is relatively insensitive to distortion compared to previously derived high-performance plate-bending elements, while retaining accuracy for nondistorted elements
Ground states of integrable quantum liquids
Based on a recently introduced operator algebra for the description of a
class of integrable quantum liquids we define the ground states for all
canonical ensembles of these systems. We consider the particular case of the
Hubbard chain in a magnetic field and chemical potential. The ground states of
all canonical ensembles of the model can be generated by acting onto the
electron vacuum (densities ), suitable
pseudoparticle creation operators. We also evaluate the energy gaps of the
non-lowest-weight states (non - LWS's) and non-highest-weight states (non -
HWS's) of the eta-spin and spin algebras relative to the corresponding ground
states. For all sectors of parameter space and symmetries the {\it exact ground
state} of the many-electron problem is in the pseudoparticle basis the
non-interacting pseudoparticle ground state. This plays a central role in the
pseudoparticle perturbation theory.Comment: RevteX 3.0, 43 pages, preprint Univ.Evora, Portuga
Electrons, pseudoparticles, and quasiparticles in the one-dimensional many-electron problem
We generalize the concept of quasiparticle for one-dimensional (1D)
interacting electronic systems. The and
quasiparticles recombine the pseudoparticle colors and (charge and spin
at zero magnetic field) and are constituted by one many-pseudoparticle {\it
topological momenton} and one or two pseudoparticles. These excitations cannot
be separated. We consider the case of the Hubbard chain. We show that the
low-energy electron -- quasiparticle transformation has a singular charater
which justifies the perturbative and non-perturbative nature of the quantum
problem in the pseudoparticle and electronic basis, respectively. This follows
from the absence of zero-energy electron -- quasiparticle overlap in 1D. The
existence of Fermi-surface quasiparticles both in 1D and three dimensional (3D)
many-electron systems suggests there existence in quantum liquids in dimensions
1D3. However, whether the electron -- quasiparticle overlap can vanish in
D1 or whether it becomes finite as soon as we leave 1D remains an unsolved
question.Comment: 43 pages, latex, no figures, submitted to Physical Review
Superconductivity Driven by Chain Coupling and Electronic Correlations
We present an analysis of a system of weakly coupled Hubbard chains based on
combining an exact study of spectral functions of the uncoupled chain system
with a renormalization group method for the coupled chains. For low values of
the onsite repulsion and of the doping , the leading instability is
towards a superconducting state. The process includes excited states above a
small correlation pseudogap. Similar features appear in extended Hubbard models
in the vicinity of commensurate fillings. Our theoretical predictions are
consistent with the phase diagram observed in the (TMTTF)X and (TMTSF)X
series of organic compounds.Comment: 7 pages, 2 figure
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