2,687 research outputs found
Affine extension of noncrystallographic Coxeter groups and quasicrystals
Unique affine extensions H^{\aff}_2, H^{\aff}_3 and H^{\aff}_4 are
determined for the noncrystallographic Coxeter groups , and .
They are used for the construction of new mathematical models for quasicrystal
fragments with 10-fold symmetry. The case of H^{\aff}_2 corresponding to
planar point sets is discussed in detail. In contrast to the cut-and-project
scheme we obtain by construction finite point sets, which grow with a model
specific growth parameter.Comment: (27 pages, to appear in J. Phys. A
The structure of quotients of the Onsager algebra by closed ideals
We study the Onsager algebra from the ideal theoretic point of view. A
complete classification of closed ideals and the structure of quotient algebras
are obtained. We also discuss the solvable algebra aspect of the Onsager
algebra through the use of formal Lie algebras.Comment: 33 pages, Latex, small topos corrected-Journal versio
Recurrence in 2D Inviscid Channel Flow
I will prove a recurrence theorem which says that any () solution
to the 2D inviscid channel flow returns repeatedly to an arbitrarily small
neighborhood. Periodic boundary condition is imposed along the
stream-wise direction. The result is an extension of an early result of the
author [Li, 09] on 2D Euler equation under periodic boundary conditions along
both directions
Quantum Dot Version of Berry's Phase: Half-Integer Orbital Angular Momenta
We show that Berry's geometrical (topological) phase for circular quantum
dots with an odd number of electrons is equal to \pi and that eigenvalues of
the orbital angular momentum run over half-integer values. The non-zero value
of the Berry's phase is provided by axial symmetry and two-dimensionality of
the system. Its particular value (\pi) is fixed by the Pauli exclusion
principle. Our conclusions agree with the experimental results of T. Schmidt
{\it at el}, \PR B {\bf 51}, 5570 (1995), which can be considered as the first
experimental evidence for the existence of a new realization of Berry's phase
and half-integer values of the orbital angular momentum in a system of an odd
number of electrons in circular quantum dots.Comment: 4 pages, 2 figure
Diffractive point sets with entropy
After a brief historical survey, the paper introduces the notion of entropic
model sets (cut and project sets), and, more generally, the notion of
diffractive point sets with entropy. Such sets may be thought of as
generalizations of lattice gases. We show that taking the site occupation of a
model set stochastically results, with probabilistic certainty, in well-defined
diffractive properties augmented by a constant diffuse background. We discuss
both the case of independent, but identically distributed (i.i.d.) random
variables and that of independent, but different (i.e., site dependent) random
variables. Several examples are shown.Comment: 25 pages; dedicated to Hans-Ude Nissen on the occasion of his 65th
birthday; final version, some minor addition
A dimensionally continued Poisson summation formula
We generalize the standard Poisson summation formula for lattices so that it
operates on the level of theta series, allowing us to introduce noninteger
dimension parameters (using the dimensionally continued Fourier transform).
When combined with one of the proofs of the Jacobi imaginary transformation of
theta functions that does not use the Poisson summation formula, our proof of
this generalized Poisson summation formula also provides a new proof of the
standard Poisson summation formula for dimensions greater than 2 (with
appropriate hypotheses on the function being summed). In general, our methods
work to establish the (Voronoi) summation formulae associated with functions
satisfying (modular) transformations of the Jacobi imaginary type by means of a
density argument (as opposed to the usual Mellin transform approach). In
particular, we construct a family of generalized theta series from Jacobi theta
functions from which these summation formulae can be obtained. This family
contains several families of modular forms, but is significantly more general
than any of them. Our result also relaxes several of the hypotheses in the
standard statements of these summation formulae. The density result we prove
for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and
improvement
Education and older adults at the University of the Third Age
This article reports a critical analysis of older adult education in Malta. In educational gerontology, a critical perspective demands the exposure of how relations of power and inequality, in their myriad forms, combinations, and complexities, are manifest in late-life learning initiatives. Fieldwork conducted at the University of the Third Age (UTA) in Malta uncovered the political nature of elder-learning, especially with respect to three intersecting lines of inequality - namely, positive aging, elitism, and gender. A cautionary note is, therefore, warranted at the dominant positive interpretations of UTAs since late-life learning, as any other education activity, is not politically neutral.peer-reviewe
- …