20,940 research outputs found
Statistical analysis of bound companions in the Coma cluster
The rich and nearby Coma cluster of galaxies is known to have substructure.
We aim to create a more detailed picture of this substructure by searching
directly for bound companions around individual giant members. We have used two
catalogs of Coma galaxies, one covering the cluster core for a detailed
morphological analysis, another covering the outskirts. The separation limit
between possible companions (secondaries) and giants (primaries) is chosen as
M_B = -19 and M_R = -20, respectively for the two catalogs. We have created
pseudo-clusters by shuffling positions or velocities of the primaries and
search for significant over-densities of possible companions around giants by
comparison with the data. This method was developed and applied first to the
Virgo cluster by Ferguson (1992). In a second approach we introduced a modified
nearest neighbor analysis using several interaction parameters for all
galaxies. We find evidence for some excesses due to possible companions for
both catalogs. Satellites are typically found among the faintest dwarfs (M_B <
-16) around high-luminosity primaries. The most significant excesses are found
around very luminous late-type giants (spirals) in the outskirts, which is
expected in an infall scenario of cluster evolution. A rough estimate for an
upper limit of bound galaxies within Coma is 2 - 4 percent, to be compared with
ca. 7 percent for Virgo. The results agree well with the expected low frequency
of bound companions in a regular cluster such as Coma.Comment: Astronomy & Astrophysics, in press; 17 pages, 13 figure
On the non-vanishing of certain Dirichlet series
Given , we study the vanishing of the Dirichlet series
at the point , where is a
periodic function modulo a prime . We show that if or
and , then there are no odd rational-valued
functions such that , whereas in all other cases
there are examples of odd functions such that .
As a consequence, we obtain, for example, that the set of values
, where ranges over odd characters mod , are linearly
independent over .Comment: 16 page
On the Smoothness of Value Functions
We prove that under standard Lipschitz and growth conditions, the value function of all optimal control problems for one-dimensional diffusions is twice continuously differentiable, as long as the control space is compact and the volatility is uniformly bounded below, away from zero. Under similar conditions, the value function of any optimal stopping problem is continuously differentiable. For the first problem, we provide sufficient conditions for the existence of an optimal control, which is also shown to be Markov. These conditions are based on the theory of monotone comparative statics.Super Contact; Smooth Pasting; HJB Equation; Optimal Control; Markov Control; Comparative Statics; Supermodularity; Single-Crossing; Interval Dominance Order
Multiplier phenomenology in random multiplicative cascade processes
We demonstrate that the correlations observed in conditioned multiplier
distributions of the energy dissipation in fully developed turbulence can be
understood as an unavoidable artefact of the observation procedure. Taking the
latter into account, all reported properties of both unconditioned and
conditioned multiplier distributions can be reproduced by cascade models with
uncorrelated random weights if their bivariate splitting function is non-energy
conserving. For the alpha-model we show that the simulated multiplier
distributions converge to a limiting form, which is very close to the
experimentally observed one. If random translations of the observation window
are accounted for, also the subtle effects found in conditioned multiplier
distributions are precisely reproduced.Comment: 4 pages, 3 figure
On the centralizer of vector fields: criteria of triviality and genericity results
In this paper, we investigate the question of whether a typical vector field
on a compact connected Riemannian manifold has a `small' centralizer. In
the case, we give two criteria, one of which is -generic, which
guarantees that the centralizer of a -generic vector field is indeed
small, namely \textit{collinear}. The other criterion states that a
\textit{separating} flow has a collinear -centralizer. When all the
singularities are hyperbolic, we prove that the collinearity property can
actually be promoted to a stronger one, refered as \textit{quasi-triviality}.
In particular, the -centralizer of a -generic vector field is
quasi-trivial. In certain cases, we obtain the triviality of the centralizer of
a -generic vector field, which includes -generic Axiom A (or
sectional Axiom A) vector fields and -generic vector fields with countably
many chain recurrent classes. For sufficiently regular vector fields, we also
obtain various criteria which ensure that the centralizer is \textit{trivial}
(as small as it can be), and we show that in higher regularity, collinearity
and triviality of the -centralizer are equivalent properties for a generic
vector field in the topology. We also obtain that in the non-uniformly
hyperbolic scenario, with regularity , the -centralizer is trivial.Comment: This is the final version, accepted in Mathematische Zeitschrift. New
introduction and some proofs where rewritten and/or expanded, according to
referee's suggestion. Also, a new appendix was adde
On Algorithms and Complexity for Sets with Cardinality Constraints
Typestate systems ensure many desirable properties of imperative programs,
including initialization of object fields and correct use of stateful library
interfaces. Abstract sets with cardinality constraints naturally generalize
typestate properties: relationships between the typestates of objects can be
expressed as subset and disjointness relations on sets, and elements of sets
can be represented as sets of cardinality one. Motivated by these applications,
this paper presents new algorithms and new complexity results for constraints
on sets and their cardinalities. We study several classes of constraints and
demonstrate a trade-off between their expressive power and their complexity.
Our first result concerns a quantifier-free fragment of Boolean Algebra with
Presburger Arithmetic. We give a nondeterministic polynomial-time algorithm for
reducing the satisfiability of sets with symbolic cardinalities to constraints
on constant cardinalities, and give a polynomial-space algorithm for the
resulting problem.
In a quest for more efficient fragments, we identify several subclasses of
sets with cardinality constraints whose satisfiability is NP-hard. Finally, we
identify a class of constraints that has polynomial-time satisfiability and
entailment problems and can serve as a foundation for efficient program
analysis.Comment: 20 pages. 12 figure
Pulsed source of spectrally uncorrelated and indistinguishable photons at telecom wavelengths
We report on the generation of indistinguishable photon pairs at telecom
wavelengths based on a type-II parametric down conversion process in a
periodically poled potassium titanyl phosphate (PPKTP) crystal. The phase
matching, pump laser characteristics and coupling geometry are optimised to
obtain spectrally uncorrelated photons with high coupling efficiencies. Four
photons are generated by a counter- propagating pump in the same crystal and
anlysed via two photon interference experiments between photons from each pair
source as well as joint spectral and g^(2) measurements. We obtain a spectral
purity of 0.91 and coupling efficiencies around 90% for all four photons
without any filtering. These pure indistinguishable photon sources at telecom
wavelengths are perfectly adapted for quantum network demonstrations and other
multi-photon protocols
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