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 $\beta$-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 $G$-odometers and the second one is denoted by (QM) and it has been introduced in the framework of tilings associated to Pisot $\beta$-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