5,620 research outputs found
Asymptotically conical Calabi-Yau manifolds, I
This is the first part in a two-part series on complete Calabi-Yau manifolds
asymptotic to Riemannian cones at infinity. We begin by proving general
existence and uniqueness results. The uniqueness part relaxes the decay
condition needed in earlier work to ,
relying on some new ideas about harmonic functions. We then look at a few
examples: (1) Crepant resolutions of cones. This includes a new class of
Ricci-flat small resolutions associated with flag manifolds. (2) Affine
deformations of cones. One focus here is the question of the precise rate of
decay of the metric to its tangent cone. We prove that the optimal rate for the
Stenzel metric on is .Comment: 27 pages, various corrections, final versio
Women's position and attitudes towards female genital mutilation in Egypt : a secondary analysis of the Egypt demographic and health surveys, 1995-2014
Background: Female genital mutilation (FGM) is still widespread in Egyptian society. It is strongly entrenched in local tradition and culture and has a strong link to the position of women. To eradicate the practice a major attitudinal change is a required for which an improvement in the social position of women is a prerequisite. This study examines the relationship between Egyptian women's social positions and their attitudes towards FGM, and investigates whether the spread of anti-FGM attitudes is related to the observed improvements in the position of women over time.
Methods: Changes in attitudes towards FGM are tracked using data from the Egypt Demographic and Health Surveys from 1995 to 2014. Multilevel logistic regressions are used to estimate 1) the effects of indicators of a woman's social position on her attitude towards FGM, and 2) whether these effects change over time.
Results: Literate, better educated and employed women are more likely to oppose FGM. Initially growing opposition to FGM was related to the expansion of women's education, but lately opposition to FGM also seems to have spread to other segments of Egyptian society.
Conclusions: The improvement of women's social position has certainly contributed to the spread of anti-FGM attitudes in Egyptian society. Better educated and less traditional women were at the heart of this change, and formed the basis from where anti-FGM sentiment has spread over wider segments of Egyptian society
Generalized Ramanujan Primes
In 1845, Bertrand conjectured that for all integers , there exists at
least one prime in . This was proved by Chebyshev in 1860, and then
generalized by Ramanujan in 1919. He showed that for any , there is a
(smallest) prime such that for all .
In 2009 Sondow called the th Ramanujan prime and proved the asymptotic
behavior (where is the th prime). In the present
paper, we generalize the interval of interest by introducing a parameter and defining the th -Ramanujan prime as the smallest integer
such that for all , there are at least primes in
. Using consequences of strengthened versions of the Prime Number
Theorem, we prove that exists for all and all , that as , and that the fraction of primes which
are -Ramanujan converges to . We then study finer questions related to
their distribution among the primes, and see that the -Ramanujan primes
display striking behavior, deviating significantly from a probabilistic model
based on biased coin flipping; this was first observed by Sondow, Nicholson,
and Noe in the case . This model is related to the Cramer model, which
correctly predicts many properties of primes on large scales, but has been
shown to fail in some instances on smaller scales.Comment: 13 pages, 2 tables, to appear in the CANT 2011 Conference
Proceedings. This is version 2.0. Changes: fixed typos, added references to
OEIS sequences, and cited Shevelev's preprin
Conformations of dendrimers in dilute solution
Conformations of isolated homo- dendrimers of G=1-7 generations with D=1-6
spacers have been studied in the good and poor solvents, as well as across the
coil-to-globule transition, by means of a version of the Gaussian
self-consistent (GSC) method and Monte Carlo (MC) simulation in continuous
space based on the same coarse-grained model. The latter includes harmonic
springs between connected monomers and the pair-wise Lennard-Jones potential
with a hard core repulsion. The scaling law for the dendrimer size, the degrees
of bond stretching and steric congestion, as well as the radial density, static
structure factor, and asphericity have been analysed. It is also confirmed that
while smaller dendrimers have a dense core, larger ones develop a hollow domain
at some separation from the centre.Comment: RevTeX, 14 pages, 19 PS figures, Accepted for publication in J. Chem.
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