1,512 research outputs found
Asymptotic formula for the moments of Minkowski question mark function in the interval [0,1]
In this paper we prove the asymptotic formula for the moments of Minkowski
question mark function, which describes the distribution of rationals in the
Farey tree. The main idea is to demonstrate that certain a variation of a
Laplace method is applicable in this problem, hence the task reduces to a
number of technical calculations.Comment: 11 pages, 1 figure (final version). Lithuanian Math. J. (to appear
Perturbations in electromagnetic dark energy
It has been recently proposed that the presence of a temporal electromagnetic
field on cosmological scales could explain the phase of accelerated expansion
that the universe is currently undergoing. The field contributes as a
cosmological constant and therefore, the homogeneous cosmology produced by such
a model is exactly the same as that of CDM. However, unlike a
cosmological constant term, electromagnetic fields can acquire perturbations
which in principle could affect CMB anisotropies and structure formation. In
this work, we study the evolution of inhomogeneous scalar perturbations in this
model. We show that provided the initial electromagnetic fluctuations generated
during inflation are small, the model is perfectly compatible with both CMB and
large scale structure observations at the same level of accuracy as
CDM.Comment: 12 pages, 3 figures. Added new comments to match the published
versio
Cosmological constraints on the generalized holographic dark energy
We use the Markov ChainMonte Carlo method to investigate global constraints
on the generalized holographic (GH) dark energy with flat and non-flat universe
from the current observed data: the Union2 dataset of type supernovae Ia
(SNIa), high-redshift Gamma-Ray Bursts (GRBs), the observational Hubble data
(OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation
(BAO), and the cosmic microwave background (CMB) data. The most stringent
constraints on the GH model parameter are obtained. In addition, it is found
that the equation of state for this generalized holographic dark energy can
cross over the phantom boundary wde =-1.Comment: 14 pages, 5 figures. arXiv admin note: significant text overlap with
arXiv:1105.186
Hypertrophic cardiomyopathy in South African Blacks
Hypertrophic cardiomyopathy (HCM) has been considered rare among the Black population of southern Africa. We report 7 patients with the disease who presented during a 14-month period. Current concepts in the approach to the diagnosis and treatment of HCM are discussed. It is possible that with greater awareness of the occurrence of the condition in Blacks the diagnosis of HCM will be made in more members of this population group
Counting matrices over finite fields with support on skew Young diagrams and complements of Rothe diagrams
We consider the problem of finding the number of matrices over a finite field
with a certain rank and with support that avoids a subset of the entries. These
matrices are a q-analogue of permutations with restricted positions (i.e., rook
placements). For general sets of entries these numbers of matrices are not
polynomials in q (Stembridge 98); however, when the set of entries is a Young
diagram, the numbers, up to a power of q-1, are polynomials with nonnegative
coefficients (Haglund 98).
In this paper, we give a number of conditions under which these numbers are
polynomials in q, or even polynomials with nonnegative integer coefficients. We
extend Haglund's result to complements of skew Young diagrams, and we apply
this result to the case when the set of entries is the Rothe diagram of a
permutation. In particular, we give a necessary and sufficient condition on the
permutation for its Rothe diagram to be the complement of a skew Young diagram
up to rearrangement of rows and columns. We end by giving conjectures
connecting invertible matrices whose support avoids a Rothe diagram and
Poincar\'e polynomials of the strong Bruhat order.Comment: 24 pages, 9 figures, 1 tabl
Reflection factorizations of Singer cycles
The number of shortest factorizations into reflections for a Singer cycle in is shown to be . Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given
Heritability of specific language impairment depends on diagnostic criteria
Heritability estimates for specific language impairment (SLI) have been inconsistent. Four twin studies reported heritability of 0.5 or more, but a recent report from the Twins Early Development Study found negligible genetic influence in 4-year-olds. We considered whether the method of ascertainment influenced results and found substantially higher heritability if SLI was defined in terms of referral to speech and language pathology services than if defined by language test scores. Further analysis showed that presence of speech difficulties played a major role in determining whether a child had contact with services. Childhood language disorders that are identified by population screening are likely to have a different phenotype and different etiology from clinically referred cases. Genetic studies are more likely to find high heritability if they focus on cases who have speech difficulties and who have been referred for intervention
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