368 research outputs found
A superintegrable finite oscillator in two dimensions with SU(2) symmetry
A superintegrable finite model of the quantum isotropic oscillator in two
dimensions is introduced. It is defined on a uniform lattice of triangular
shape. The constants of the motion for the model form an SU(2) symmetry
algebra. It is found that the dynamical difference eigenvalue equation can be
written in terms of creation and annihilation operators. The wavefunctions of
the Hamiltonian are expressed in terms of two known families of bivariate
Krawtchouk polynomials; those of Rahman and those of Tratnik. These polynomials
form bases for SU(2) irreducible representations. It is further shown that the
pair of eigenvalue equations for each of these families are related to each
other by an SU(2) automorphism. A finite model of the anisotropic oscillator
that has wavefunctions expressed in terms of the same Rahman polynomials is
also introduced. In the continuum limit, when the number of grid points goes to
infinity, standard two-dimensional harmonic oscillators are obtained. The
analysis provides the limit of the bivariate Krawtchouk
polynomials as a product of one-variable Hermite polynomials
The Ammann-Beenker tilings revisited
This paper introduces two tiles whose tilings form a one-parameter family of
tilings which can all be seen as digitization of two-dimensional planes in the
four-dimensional Euclidean space. This family contains the Ammann-Beenker
tilings as the solution of a simple optimization problem.Comment: 7 pages, 4 figure
Birth and death processes and quantum spin chains
This papers underscores the intimate connection between the quantum walks
generated by certain spin chain Hamiltonians and classical birth and death
processes. It is observed that transition amplitudes between single excitation
states of the spin chains have an expression in terms of orthogonal polynomials
which is analogous to the Karlin-McGregor representation formula of the
transition probability functions for classes of birth and death processes. As
an application, we present a characterization of spin systems for which the
probability to return to the point of origin at some time is 1 or almost 1.Comment: 14 page
Spectral Difference Equations Satisfied by KP Soliton Wavefunctions
The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the
KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring
of translational operators in the spectral parameter. In the rational limit,
these translational operators converge to the differential operators in the
spectral parameter previously discussed as part of the theory of
"bispectrality". Consequently, these translational operators can be seen as
demonstrating a form of bispectrality for the non-rational solitons as well.Comment: to appear in "Inverse Problems
A topological central point theorem
In this paper a generalized topological central point theorem is proved for
maps of a simplex to finite-dimensional metric spaces. Similar generalizations
of the Tverberg theorem are considered.Comment: In this version some typos were corrected after the official
publicatio
Køb af B-t-B-serviceydelser - Konceptualisering af industriel købsadfærd i forbindelse med hr-konsulentydelser
I den tidlige B-t-B-købsadfærdslitteratur har man lagt megen vægt på, at købsadfærden i forbindelse med B-t-B-serviceydelser er meget rationel præget. Gennem en større eksplorativ undersøgelse af danske virksomheders indkøb af konsulentydelser inden for hr, har forfatterne fået indblik i de faktorer, som bestemmer danske virksomheders valg af leverandør inden for konsulentydelser. På grundlag af et litteratur review er der udviklet fem hypoteser. Resultaterne viser, at købsadfærden er langt mindre rationel end hidtil antaget. Det viser sig f.eks., at konsulentens personlige relationer til kunderne ofte kan kompensere for mangler i konsulentens faglige viden. Dette betyder bl.a., at konsulenternes udvikling af langvarige personlige relationer til kunderne er en af de vigtigste nøglesuccesfaktorer i konsulentbranchen. Et andet vigtigt resultat af undersøgelsen er kundernes specifikke ønske om at deltage aktivt i produktionen af konsulentserviceydelserne
Analogues of the central point theorem for families with -intersection property in
In this paper we consider families of compact convex sets in
such that any subfamily of size at most has a nonempty intersection. We
prove some analogues of the central point theorem and Tverberg's theorem for
such families
Construction and Analysis of Projected Deformed Products
We introduce a deformed product construction for simple polytopes in terms of
lower-triangular block matrix representations. We further show how Gale duality
can be employed for the construction and for the analysis of deformed products
such that specified faces (e.g. all the k-faces) are ``strictly preserved''
under projection. Thus, starting from an arbitrary neighborly simplicial
(d-2)-polytope Q on n-1 vertices we construct a deformed n-cube, whose
projection to the last dcoordinates yields a neighborly cubical d-polytope. As
an extension of thecubical case, we construct matrix representations of
deformed products of(even) polygons (DPPs), which have a projection to d-space
that retains the complete (\lfloor \tfrac{d}{2} \rfloor - 1)-skeleton. In both
cases the combinatorial structure of the images under projection is completely
determined by the neighborly polytope Q: Our analysis provides explicit
combinatorial descriptions. This yields a multitude of combinatorially
different neighborly cubical polytopes and DPPs. As a special case, we obtain
simplified descriptions of the neighborly cubical polytopes of Joswig & Ziegler
(2000) as well as of the ``projected deformed products of polygons'' that were
announced by Ziegler (2004), a family of 4-polytopes whose ``fatness'' gets
arbitrarily close to 9.Comment: 20 pages, 5 figure
Formation of dodecagonal quasicrystals in two-dimensional systems of patchy particles
The behaviour of two-dimensional patchy particles with 5 and 7
regularly-arranged patches is investigated by computer simulation. For higher
pressures and wider patch widths, hexagonal crystals have the lowest enthalpy,
whereas at lower pressures and for narrower patches, lower-density crystals
with five nearest neighbours and that are based on the (3^2,4,3,4) tiling of
squares and triangles become lower in enthalpy. Interestingly, in regions of
parameter space near to that where the hexagonal crystals become stable,
quasicrystalline structures with dodecagonal symmetry form on cooling from high
temperature. These quasicrystals can be considered as tilings of squares and
triangles, and are probably stabilized by the large configurational entropy
associated with all the different possible such tilings. The potential for
experimentally realizing such structures using DNA multi-arm motifs are
discussed.Comment: 12 pages, 12 figure
Coloring translates and homothets of a convex body
We obtain improved upper bounds and new lower bounds on the chromatic number
as a linear function of the clique number, for the intersection graphs (and
their complements) of finite families of translates and homothets of a convex
body in \RR^n.Comment: 11 pages, 2 figure
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