1,248 research outputs found
Additive unit representations in global fields - A survey
We give an overview on recent results concerning additive unit
representations. Furthermore the solutions of some open questions are included.
The central problem is whether and how certain rings are (additively) generated
by their units. This has been investigated for several types of rings related
to global fields, most importantly rings of algebraic integers. We also state
some open problems and conjectures which we consider to be important in this
field.Comment: 13 page
Highly parallel computation
Highly parallel computing architectures are the only means to achieve the computation rates demanded by advanced scientific problems. A decade of research has demonstrated the feasibility of such machines and current research focuses on which architectures designated as multiple instruction multiple datastream (MIMD) and single instruction multiple datastream (SIMD) have produced the best results to date; neither shows a decisive advantage for most near-homogeneous scientific problems. For scientific problems with many dissimilar parts, more speculative architectures such as neural networks or data flow may be needed
Modula-2*: An extension of Modula-2 for highly parallel programs
Parallel programs should be machine-independent, i.e., independent of properties that are likely to differ from one parallel computer to the next. Extensions are described of Modula-2 for writing highly parallel, portable programs meeting these requirements. The extensions are: synchronous and asynchronous forms of forall statement; and control of the allocation of data to processors. Sample programs written with the extensions demonstrate the clarity of parallel programs when machine-dependent details are omitted. The principles of efficiently implementing the extensions on SIMD, MIMD, and MSIMD machines are discussed. The extensions are small enough to be integrated easily into other imperative languages
Linear recursive odometers and beta-expansions
The aim of this paper is to study the connection between different properties
related to -expansions. In particular, the relation between two
conditions, both ensuring pure discrete spectrum of the odometer, is analysed.
The first one is the so-called Hypothesis B for the -odometers and the
second one is denoted by (QM) and it has been introduced in the framework of
tilings associated to Pisot -numerations
Dynamical effects of exchange symmetry breaking in mixtures of interacting bosons
In a double-well potential, a Bose-Einstein condensate exhibits Josephson
oscillations or self-trapping, depending on its initial preparation and on the
ratio of inter-particle interaction to inter-well tunneling. Here, we elucidate
the role of the exchange symmetry for the dynamics with a mixture of two
distinguishable species with identical physical properties, i.e. which are
governed by an isospecific interaction and external potential. In the
mean-field limit, the spatial population imbalance of the mixture can be
described by the dynamics of a single species in an effective potential with
modified properties or, equivalently, with an effective total particle number.
The oscillation behavior can be tuned by populating the second species while
maintaining the spatial population imbalance and all other parameters constant.
In the corresponding many-body approach, the single-species description
approximates the full counting statistics well also outside the realm of
spin-coherent states. The method is extended to general Bose-Hubbard systems
and to their classical mean-field limits, which suggests an effective
single-species description of multicomponent Bose gases with weakly
an-isospecific interactions.Comment: amended and expanded, accepted for Phys. Rev. A, 14 pages, 7 figure
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