5,113 research outputs found
Arithmetic properties of blocks of consecutive integers
This paper provides a survey of results on the greatest prime factor, the
number of distinct prime factors, the greatest squarefree factor and the
greatest m-th powerfree part of a block of consecutive integers, both without
any assumption and under assumption of the abc-conjecture. Finally we prove
that the explicit abc-conjecture implies the Erd\H{o}s-Woods conjecture for
each k>2.Comment: A slightly corrected and extended version of a paper which will
appear in January 2017 in the book From Arithmetic to Zeta-functions
published by Springe
Tagged tiger shark (Galeocerda cuvieri) landed atTuticorin
The shark was caught by a mechanised Tuticorin type boat using hooks and line . The fish was caught at a distance of 40 km from shore southeast of Tuticorin in the 26 fathom depth area The fish weighed 130 kg and was sold by auction for Rupees 916. Morphometric measurements (in mm) of tagged tiger shark Galeocerda cuvieri caught off Tuticorin are Total length 2,050, Fork length 1,680, and detailed morphometry were recorded
Transformation of stimulus correlations by the retina
Redundancies and correlations in the responses of sensory neurons seem to
waste neural resources but can carry cues about structured stimuli and may help
the brain to correct for response errors. To assess how the retina negotiates
this tradeoff, we measured simultaneous responses from populations of ganglion
cells presented with natural and artificial stimuli that varied greatly in
correlation structure. We found that pairwise correlations in the retinal
output remained similar across stimuli with widely different spatio-temporal
correlations including white noise and natural movies. Meanwhile, purely
spatial correlations tended to increase correlations in the retinal response.
Responding to more correlated stimuli, ganglion cells had faster temporal
kernels and tended to have stronger surrounds. These properties of individual
cells, along with gain changes that opposed changes in effective contrast at
the ganglion cell input, largely explained the similarity of pairwise
correlations across stimuli where receptive field measurements were possible.Comment: author list corrected in metadat
Black Hole Statistics from Holography
We study the microstates of the ``small'' black hole in the \half-BPS
sector of AdS, the superstar of Myers and Tafjord, using the
powerful holographic description provided by LLM. The system demonstrates the
inherently statistical nature of black holes, with the geometry of Myer and
Tafjord emerging only after averaging over an ensemble of geometries. The
individual microstate geometries differ in the highly non-trivial topology of a
quantum foam at their core, and the entropy can be understood as a partition of
units of flux among 5-cycles, as required by flux quantization. While the
system offers confirmation of the most controversial aspect of Mathur and
Lunin's recent ``fuzzball'' proposal, we see signs of a discrepancy in
interpreting its details.Comment: 21 pages, 4 figures; References adde
Immunological investigations in tuberculous ascites
Cell mediated immunity was assessed in seven patients with bacteriologically and/or
histologically confirmed tuberculous ascites. Eight non-tuberculous ascites patients were included as
controls. Anti-PPD antibody levels were also estimated by ELISA. Macrophage from tuberculous
ascitic fluid showed increased production of H202 when compared with ascitic fluid macrophages
from controls. Proliferative response of lymphocytes to PPD antigen was greater in ascitic fluid than
in peripheral blood in tuberculous patients, while the responses were reversed in control patients.
Tuberculous ascitic fluid had higher levels of anti-PPD antibodies than ascitic fluid from controls,
though their levels in peripheral blood were similar in the two groups. It is concluded that the
results provide support to the concept of immunologic localization
Deconstruction and Holography
It was recently pointed out that the physics of a single discrete
gravitational extra dimension exhibits a peculiar UV/IR connection relating the
UV scale to the radius of the effective extra dimension. Here we note that this
non-locality is a manifestation of holography, encoding the correct scaling of
the number of fundamental degrees of freedom of the UV theory. This in turn
relates the Wilsonian RG flow in the UV theory to the effective gravitational
dynamics in the extra dimension. The relevant holographic c-function is
determined by the expression for the holographic bound. Holography in this
context is a result of the requirements of unitarity and diffeomorphism
invariance. We comment on the relevance of this observation for the
cosmological constant problem.Comment: 11 pages, LaTe
Finite Action in d5 Gauged Supergravity and Dilatonic Conformal Anomaly for Dual Quantum Field Theory
Gauged supergravity (SG) with single scalar (dilaton) and arbitrary scalar
potential is considered. Such dilatonic gravity describes special RG flows in
extended SG where scalars lie in one-dimensional submanifold of total space.
The surface counterterm and finite action for such gauged SG in three-, four-
and five-dimensional asymptotically AdS space are derived. Using finite action
and consistent gravitational stress tensor (local surface counterterm
prescription) the regularized expressions for free energy, entropy and mass of
d4 dilatonic AdS black hole are found. The same calculation is done within
standard reference background subtraction.
The dilaton-dependent conformal anomaly from d3 and d5 gauged SGs is
calculated using AdS/CFT correspondence. Such anomaly should correspond to two-
and four-dimensional dual quantum field theory which is classically (not
exactly) conformally invariant, respectively. The candidate c-functions from d3
and d5 SGs are suggested. These c-functions which have fixed points in
asymptoticaly AdS region are expressed in terms of dilatonic potential and they
are positively defined and monotonic for number of potentials.Comment: LaTeX file, 46 pages, two appendixes and some clarifications are
adde
Supersymmetry Enhancement of D-p-branes and M-branes
We examine the supersymmetry of classical D-brane and M-brane configurations
and explain the dependence of Killing spinors on coordinates. We find that one
half supersymmetry is broken in the bulk and that supersymmetry near the
D-brane horizon is restored for , for solutions in the stringy frame,
but only for in the10d canonical frame. We study the enhancement for the
case of four intersecting D-3-branes in 10 dimensions and the implication of
this for the size of the infinite throat of the near horizon geometry in
non-compactified theory. We found some indications of universality of near
horizon geometries of various intersecting brane configurations.Comment: 18 pages, late
Towards T1-limited magnetic resonance imaging using Rabi beats
Two proof-of-principle experiments towards T1-limited magnetic resonance
imaging with NV centers in diamond are demonstrated. First, a large number of
Rabi oscillations is measured and it is demonstrated that the hyperfine
interaction due to the NV's 14N can be extracted from the beating oscillations.
Second, the Rabi beats under V-type microwave excitation of the three hyperfine
manifolds is studied experimentally and described theoretically.Comment: 6 pages, 8 figure
A comment on multiple vacua, particle production and the time dependent AdS/CFT correspondence
We give an explicit formulation of the time dependent AdS/CFT correspondence
when there are multiple vacua present in Lorentzian signature. By computing
sample two point functions we show how different amplitudes are related by
cosmological particle production. We illustrate our methods in two example
spacetimes: (a) a ``bubble of nothing'' in AdS space, and (b) an asymptotically
locally AdS spacetime with a bubble of nothing on the boundary. In both cases
the alpha vacua of de Sitter space make an interesting appearance.Comment: 9 page
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