21,269 research outputs found
Contact, the feature pool and the speech community : The emergence of Multicultural London English.
In Northern Europe’s major cities, new varieties of the host languages are emerging in the multilingual inner cities. While some analyse these ‘multiethnolects’ as youth styles, we take a variationist approach to an emerging ‘Multicultural London English’ (MLE), asking: (1) what features characterise MLE? (2) at what age(s) are they acquired? (3) is MLE vernacularised? (4) when did MLE emerge, and what factors enabled its emergence? We argue that innovations in the diphthongs and the quotative system are generated from the specific sociolinguistics of inner-city London, where at least half the population is undergoing group second-language acquisition and where high linguistic diversity leads to a feature pool to select from. We look for incrementation (Labov) in the acquisition of the features, but find this only for two ‘global’ changes, BE LIKE and GOOSE-fronting, for which adolescents show the highest usage. Community-internal factors explain the age-related variation in the remaining features
Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops
We consider two coupled quantum tops with angular momentum vectors
and . The coupling Hamiltonian defines the
Feinberg-Peres model which is a known paradigm of quantum chaos. We show that
this model has a nonstandard symmetry with respect to the Altland-Zirnbauer
tenfold symmetry classification of quantum systems which extends the well-known
threefold way of Wigner and Dyson (referred to as `standard' symmetry classes
here). We identify that the nonstandard symmetry classes BD (chiral
orthogonal class with no zero modes), BD (chiral orthogonal class with one
zero mode) and C (antichiral orthogonal class) as well as the standard
symmetry class A (orthogonal class). We numerically analyze the specific
spectral quantum signatures of chaos related to the nonstandard symmetries. In
the microscopic density of states and in the distribution of the lowest
positive energy eigenvalue we show that the Feinberg-Peres model follows the
predictions of the Gaussian ensembles of random-matrix theory in the
appropriate symmetry class if the corresponding classical dynamics is chaotic.
In a crossover to mixed and near-integrable classical dynamics we show that
these signatures disappear or strongly change.Comment: 15 page
Axiomatics for the external numbers of nonstandard analysis
Neutrices are additive subgroups of a nonstandard model of the real numbers.
An external number is the algebraic sum of a nonstandard real number and a
neutrix. Due to the stability by some shifts, external numbers may be seen as
mathematical models for orders of magnitude. The algebraic properties of
external numbers gave rise to the so-called solids, which are extensions of
ordered fields, having a restricted distributivity law. However, necessary and
sufficient conditions can be given for distributivity to hold. In this article
we develop an axiomatics for the external numbers. The axioms are similar to,
but mostly somewhat weaker than the axioms for the real numbers and deal with
algebraic rules, Dedekind completeness and the Archimedean property. A
structure satisfying these axioms is called a complete arithmetical solid. We
show that the external numbers form a complete arithmetical solid, implying the
consistency of the axioms presented. We also show that the set of precise
elements (elements with minimal magnitude) has a built-in nonstandard model of
the rationals. Indeed the set of precise elements is situated between the
nonstandard rationals and the nonstandard reals whereas the set of non-precise
numbers is completely determined
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