306 research outputs found
Variable Stars: which Nyquist Frequency ?
In the analysis of variable stars, the problem of sampling is central. This
article focusses on the determination of the Nyquist frequency. It is well
defined in the case of regular sampling. However, the time series of variable
stars observations are generally unevenly sampled. Fourier analysis using the
spectral window furnishes some clues about the equivalent Nyquist frequency in
the irregular case. Often it is pushed very high, and thus very short periods
can be detected. A specific example is shown, drawn from MACHO databases.Comment: 4 pages, 5 figures, submitted to A&
A Mealy machine with polynomial growth of irrational degree
We consider a very simple Mealy machine (three states over a two-symbol
alphabet), and derive some properties of the semigroup it generates. In
particular, this is an infinite, finitely generated semigroup; we show that the
growth function of its balls behaves asymptotically like n^2.4401..., where
this constant is 1 + log(2)/log((1+sqrt(5))/2); that the semigroup satisfies
the identity g^6=g^4; and that its lattice of two-sided ideals is a chain.Comment: 20 pages, 1 diagra
Branch Rings, Thinned Rings, Tree Enveloping Rings
We develop the theory of ``branch algebras'', which are infinite-dimensional
associative algebras that are isomorphic, up to taking subrings of finite
codimension, to a matrix ring over themselves. The main examples come from
groups acting on trees.
In particular, for every field k we construct a k-algebra K which (1) is
finitely generated and infinite-dimensional, but has only finite-dimensional
quotients;
(2) has a subalgebra of finite codimension, isomorphic to ;
(3) is prime;
(4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2;
(5) is recursively presented;
(6) satisfies no identity;
(7) contains a transcendental, invertible element;
(8) is semiprimitive if k has characteristic ;
(9) is graded if k has characteristic 2;
(10) is primitive if k is a non-algebraic extension of GF(2);
(11) is graded nil and Jacobson radical if k is an algebraic extension of
GF(2).Comment: 35 pages; small changes wrt previous versio
From self-similar groups to self-similar sets and spectra
The survey presents developments in the theory of self-similar groups leading
to applications to the study of fractal sets and graphs, and their associated
spectra
On abstract commensurators of groups
We prove that the abstract commensurator of a nonabelian free group, an
infinite surface group, or more generally of a group that splits appropriately
over a cyclic subgroup, is not finitely generated.
This applies in particular to all torsion-free word-hyperbolic groups with
infinite outer automorphism group and abelianization of rank at least 2.
We also construct a finitely generated, torsion-free group which can be
mapped onto Z and which has a finitely generated commensurator.Comment: 13 pages, no figur
Influence of flowering and fruiting upon vegetative growth and tuber yield in the potato
This archival publication may not reflect current scientific knowledge or recommendations
On Property (FA) for wreath products
We characterize permutational wreath products with Property (FA). For
instance, the standard wreath product A wr B of two nontrivial countable groups
A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely
generated group with finite abelianisation. We also prove an analogous result
for hereditary Property (FA). On the other hand, we prove that many wreath
products with hereditary Property (FA) are not quotients of finitely presented
groups with the same property.Comment: 12 pages, 0 figur
On abstract commensurators of groups
Abstract We prove that the abstract commensurator of a nontrivial free group, an infinite surface group, or more generally a group that splits appropriately over a cyclic subgroup is not finitely generated. This applies in particular to all torsion-free word-hyperbolic groups with infinite outer automorphism group and abelianization of rank at least 2. We also construct a finitely generated group which can be mapped onto Z and which has a finitely generated commensurator
Search for high-amplitude Delta Scuti and RR Lyrae stars in Sloan Digital Sky Survey Stripe 82 using principal component analysis
We propose a robust principal component analysis (PCA) framework for the
exploitation of multi-band photometric measurements in large surveys. Period
search results are improved using the time series of the first principal
component due to its optimized signal-to-noise ratio.The presence of correlated
excess variations in the multivariate time series enables the detection of
weaker variability. Furthermore, the direction of the largest variance differs
for certain types of variable stars. This can be used as an efficient attribute
for classification. The application of the method to a subsample of Sloan
Digital Sky Survey Stripe 82 data yielded 132 high-amplitude Delta Scuti
variables. We found also 129 new RR Lyrae variables, complementary to the
catalogue of Sesar et al., 2010, extending the halo area mapped by Stripe 82 RR
Lyrae stars towards the Galactic bulge. The sample comprises also 25
multiperiodic or Blazhko RR Lyrae stars.Comment: 23 pages, 17 figure
Representing Terrain With Mathematical Operators
This work describes a mathematical representation of terrain data consisting of a novel operation, the “drill”. It facilitates the representation of legal terrains, capturing the richness of the physics of the terrain’s generation by digging channels in the surface. Given our current reliance on digital map data, hand-held devices, and GPS navigation systems, the accuracy and compactness of terrain data representations are becoming increasingly important. Representing a terrain as a series of operations that can procedurally regenerate the terrains allows for compact representation that retains more information than height fields, TINs, and other popular representations. Our model relies on the hydrography information extracted from the terrain, and so drainage information is retained during encoding. To determine the shape of the drill along each channel in the channel network, a cross section of the channel is extracted, and a quadratic polynomial is fit to it. We extract the drill representation from a mountainous dataset, using a series of parameters (including size and area of influence of the drill, as well as the density of the hydrography data), and present the accuracy calculated using a series of metrics. We demonstrate that the drill operator provides a viable and accurate terrain representation that captures both the terrain shape and the richness of its generation
- …