3,686 research outputs found
Icosahedral multi-component model sets
A quasiperiodic packing Q of interpenetrating copies of C, most of them only
partially occupied, can be defined in terms of the strip projection method for
any icosahedral cluster C. We show that in the case when the coordinates of the
vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the
superspace can be reduced, namely, Q can be re-defined as a multi-component
model set by using a 6-dimensional superspace.Comment: 7 pages, LaTeX2e in IOP styl
Expression of PEG11 and PEG11AS transcripts in normal and callipyge sheep
BACKGROUND: The callipyge mutation is located within an imprinted gene cluster on ovine chromosome 18. The callipyge trait exhibits polar overdominant inheritance due to the fact that only heterozygotes inheriting a mutant paternal allele (paternal heterozygotes) have a phenotype of muscle hypertrophy, reduced fat and a more compact skeleton. The mutation is a single A to G transition in an intergenic region that results in the increased expression of several genes within the imprinted cluster without changing their parent-of-origin allele-specific expression. RESULTS: There was a significant effect of genotype (p < 0.0001) on the transcript abundance of DLK1, PEG11, and MEG8 in the muscles of lambs with the callipyge allele. DLK1 and PEG11 transcript levels were elevated in the hypertrophied muscles of paternal heterozygous animals relative to animals of the other three genotypes. The PEG11 locus produces a single 6.5 kb transcript and two smaller antisense strand transcripts, referred to as PEG11AS, in skeletal muscle. PEG11AS transcripts were detectable over a 5.5 kb region beginning 1.2 kb upstream of the PEG11 start codon and spanning the entire open reading frame. Analysis of PEG11 expression by quantitative PCR shows a 200-fold induction in the hypertrophied muscles of paternal heterozygous animals and a 13-fold induction in homozygous callipyge animals. PEG11 transcripts were 14-fold more abundant than PEG11AS transcripts in the gluteus medius of paternal heterozygous animals. PEG11AS transcripts were expressed at higher levels than PEG11 transcripts in the gluteus medius of animals of the other three genotypes. CONCLUSIONS: The effect of the callipyge mutation has been to alter the expression of DLK1, GTL2, PEG11 and MEG8 in the hypertrophied skeletal muscles. Transcript abundance of DLK1 and PEG11 was highest in paternal heterozygous animals and exhibited polar overdominant gene expression patterns; therefore, both genes are candidates for causing skeletal muscle hypertrophy. There was unique relationship of PEG11 and PEG11AS transcript abundance in the paternal heterozygous animals that suggests a RNA interference mechanism may have a role in PEG11 gene regulation and polar overdominance in callipyge sheep
Possible contractions of quantum orthogonal groups
Possible contractions of quantum orthogonal groups which correspond to
different choices of primitive elements of Hopf algebra are considered and all
allowed contractions in Cayley--Klein scheme are obtained. Quantum deformations
of kinematical groups have been investigated and have shown that quantum analog
of (complex) Galilei group G(1,3) do not exist in our scheme.Comment: 10 pages, Latex. Report given at XXIII Int. Colloquium on Group
Theoretical Methods in Physics, July 31- August 5, 2000, Dubna (Russia
How model sets can be determined by their two-point and three-point correlations
We show that real model sets with real internal spaces are determined, up to
translation and changes of density zero by their two- and three-point
correlations. We also show that there exist pairs of real (even one
dimensional) aperiodic model sets with internal spaces that are products of
real spaces and finite cyclic groups whose two- and three-point correlations
are identical but which are not related by either translation or inversion of
their windows. All these examples are pure point diffractive.
Placed in the context of ergodic uniformly discrete point processes, the
result is that real point processes of model sets based on real internal
windows are determined by their second and third moments.Comment: 19 page
Multidimensional Binning Techniques for a Two Parameter Trilinear Gauge Coupling Estimation at LEP II
This paper describes two generalization schemes of the Optimal Variables
technique in estimating simultaneously two Trilinear Gauge Couplings. The first
is an iterative procedure to perform a 2-dimensional fit using the linear terms
of the expansion of the probability density function with respect to the
corresponding couplings, whilst the second is a clustering method of
probability distribution representation in five dimensions. The pair production
of W's at 183 GeV center of mass energy, where one W decays leptonically and
the other hadronically, was used to demonstrate the optimal properties of the
proposed estimation techniques.Comment: (25 pages, 11 figures
The rings of n-dimensional polytopes
Points of an orbit of a finite Coxeter group G, generated by n reflections
starting from a single seed point, are considered as vertices of a polytope
(G-polytope) centered at the origin of a real n-dimensional Euclidean space. A
general efficient method is recalled for the geometric description of G-
polytopes, their faces of all dimensions and their adjacencies. Products and
symmetrized powers of G-polytopes are introduced and their decomposition into
the sums of G-polytopes is described. Several invariants of G-polytopes are
found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers
and congruence classes of the polytopes. The definitions apply to
crystallographic and non-crystallographic Coxeter groups. Examples and
applications are shown.Comment: 24 page
Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces
Model sets (or cut and project sets) provide a familiar and commonly used
method of constructing and studying nonperiodic point sets. Here we extend this
method to situations where the internal spaces are no longer Euclidean, but
instead spaces with p-adic topologies or even with mixed Euclidean/p-adic
topologies.
We show that a number of well known tilings precisely fit this form,
including the chair tiling and the Robinson square tilings. Thus the scope of
the cut and project formalism is considerably larger than is usually supposed.
Applying the powerful consequences of model sets we derive the diffractive
nature of these tilings.Comment: 11 pages, 2 figures; dedicated to Peter Kramer on the occasion of his
65th birthda
On contractions of classical basic superalgebras
We define a class of orthosymplectic and unitary
superalgebras which may be obtained from and
by contractions and analytic continuations in a similar way as the
special linear, orthogonal and the symplectic Cayley-Klein algebras are
obtained from the corresponding classical ones. Casimir operators of
Cayley-Klein superalgebras are obtained from the corresponding operators of the
basic superalgebras. Contractions of and are regarded as
an examples.Comment: 15 pages, Late
Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam
We demonstrate experimentally and numerically that the application of a
partially coherent beam (PCB) in combination with time averaging leads to a
significant reduction in the scintillation index. We use a simplified
experimental approach in which the atmospheric turbulence is simulated by a
phase diffuser. The role of the speckle size, the amplitude of the phase
modulation, and the strength of the atmospheric turbulence are examined. We
obtain good agreement between our numerical simulations and our experimental
results. This study provides a useful foundation for future applications of
PCB-based methods of scintillation reduction in physical atmospheres.Comment: 18 pages, 14 figure
Quantum theory of large amplitude collective motion and the Born-Oppenheimer method
We study the quantum foundations of a theory of large amplitude collective
motion for a Hamiltonian expressed in terms of canonical variables. In previous
work the separation into slow and fast (collective and non-collective)
variables was carried out without the explicit intervention of the Born
Oppenheimer approach. The addition of the Born Oppenheimer assumption not only
provides support for the results found previously in leading approximation, but
also facilitates an extension of the theory to include an approximate
description of the fast variables and their interaction with the slow ones.
Among other corrections, one encounters the Berry vector and scalar potential.
The formalism is illustrated with the aid of some simple examples, where the
potentials in question are actually evaluated and where the accuracy of the
Born Oppenheimer approximation is tested. Variational formulations of both
Hamiltonian and Lagrangian type are described for the equations of motion for
the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf
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