37,765 research outputs found
Noncommutative Geometry and a Discretized Version of Kaluza-Klein Theory with a Finite Field Content
We consider a four-dimensional space-time supplemented by two discrete points
assigned to a algebraic structure and develop the formalism of
noncommutative geometry. By setting up a generalised vielbein, we study the
metric structure. Metric compatible torsion free connection defines a unique
finite field content in the model and leads to a discretized version of
Kaluza-Klein theory. We study some special cases of this model that illustrate
the rich and complex structure with massive modes and the possible presence of
a cosmological constant.Comment: 21 pages, LATEX fil
A Discretized Version of Kaluza-Klein Theory with Torsion and Massive Fields
We consider an internal space of two discrete points in the fifth dimension
of the Kaluza-Klein theory by using the formalism of noncommutative geometry
developed in a previous paper \cite{VIWA} of a spacetime supplemented by two
discrete points. With the nonvanishing internal torsion 2-form there are no
constraints implied on the vielbeins. The theory contains a pair of tensor, a
pair of vector and a pair of scalar fields. Using the generalized Cartan
structure equation we are able not only to determine uniquely the hermitian and
metric compatible connection 1-forms, but also the nonvanishing internal
torsion 2-form in terms of vielbeins. The resulting action has a rich and
complex structure, a particular feature being the existence of massive modes.
Thus the nonvanishing internal torsion generates a Kaluza-Klein type model with
zero and massive modes.Comment: 24 page
Delocalization and scaling properties of low-dimensional quasiperiodic systems
In this paper, we explore the localization transition and the scaling
properties of both quasi-one-dimensional and two-dimensional quasiperiodic
systems, which are constituted from coupling several Aubry-Andr\'{e} (AA)
chains along the transverse direction, in the presence of next-nearest-neighbor
(NNN) hopping. The localization length, two-terminal conductance, and
participation ratio are calculated within the tight-binding Hamiltonian. Our
results reveal that a metal-insulator transition could be driven in these
systems not only by changing the NNN hopping integral but also by the
dimensionality effects. These results are general and hold by coupling distinct
AA chains with various model parameters. Furthermore, we show from finite-size
scaling that the transport properties of the two-dimensional quasiperiodic
system can be described by a single parameter and the scaling function can
reach the value 1, contrary to the scaling theory of localization of disordered
systems. The underlying physical mechanism is discussed.Comment: 9 pages, 8 figure
Gold(I)-catalysed one-pot synthesis of chromans using allylic alcohols and phenols
A gold(I)-catalysed reaction of allylic alcohols and phenols produces chromans regioselectively via a one-pot Friedel–Crafts allylation/intramolecular hydroalkoxylation sequence. The reaction is mild, practical and tolerant of a wide variety of substituents on the phenol
Construction of nested space-filling designs
New types of designs called nested space-filling designs have been proposed
for conducting multiple computer experiments with different levels of accuracy.
In this article, we develop several approaches to constructing such designs.
The development of these methods also leads to the introduction of several new
discrete mathematics concepts, including nested orthogonal arrays and nested
difference matrices.Comment: Published in at http://dx.doi.org/10.1214/09-AOS690 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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