20,490 research outputs found
On the etale cohomology of algebraic varieties with totally degenerate reduction over p-adic fields
Let K be a finite extension of Q_p and X a smooth projective variety over K.
We define the notion of totally degenerate reduction of such an X and the
associated Chow complexes of the special fibre of a suitable regular proper
model of X over the ring of integers of K. If X has such reduction, we then
show that for all l, the Q_l-adic etale cohomology of X has a filtration whose
graded quotients are isomorphic, as Galois modules, to the tensor product of a
finite dimensional Q-vector space (with a finite unramified action of Galois)
with twists of Q_l by the cyclotomic character.Comment: 29 pages This and math.AG/0601401 replace math.AG/030612
Some determinants of path generating functions
We evaluate four families of determinants of matrices, where the entries are
sums or differences of generating functions for paths consisting of up-steps,
down-steps and level steps. By specialisation, these determinant evaluations
have numerous corollaries. In particular, they cover numerous determinant
evaluations of combinatorial numbers - most notably of Catalan, ballot, and of
Motzkin numbers - that appeared previously in the literature.Comment: 35 pages, AmS-TeX; minor corrections; final version to appear in Adv.
Appl. Mat
Differential Galois Approach to the Non-integrability of the Heavy Top Problem
We study integrability of the Euler-Poisson equations describing the motion
of a rigid body with one fixed point in a constant gravity field. Using the
Morales-Ramis theory and tools of differential algebra we prove that a
symmetric heavy top is integrable only in the classical cases of Euler,
Lagrange, and Kovalevskaya and is partially integrable only in the
Goryachev-Chaplygin case. Our proof is alternative to that given by Ziglin
({\em Funktsional. Anal. i Prilozhen.}, 17(1):8--23, 1983; {\em Funktsional.
Anal. i Prilozhen.}, 31(1):3--11, 95, 1997).Comment: 31 pages, 1 figur
Maharam's problem
We construct an exhaustive submeasure that is not equivalent to a measure.
This solves problems of J. von Neumann (1937) and D. Maharam (1947)
Perfect countably infinite Steiner triple systems
We use a free construction to prove the existence of perfect Steiner triple systems on a countably infinite point set. We use a specific countably infinite family of partial Steiner triple systems to start the construction, thus yielding 2ℵ0 non-isomorphic perfect systems
Thermal evolution and structure models of the transiting super-Earth GJ 1214b
The planet GJ 1214b is the second known super-Earth with a measured mass and
radius. Orbiting a quiet M-star, it receives considerably less mass-loss
driving X-ray and UV radiation than CoRoT-7b, so that the interior may be quite
dissimilar in composition, including the possibility of a large fraction of
water. We model the interior of GJ 1214b assuming a two-layer (envelope+rock
core) structure where the envelope material is either H/He, pure water, or a
mixture of H/He and H2O. Within this framework we perform models of the thermal
evolution and contraction of the planet. We discuss possible compositions that
are consistent with Mp=6.55 ME, Rp=2.678 RE, an age tau=3-10 Gyr, and the
irradiation level of the atmosphere. These conditions require that if water
exists in the interior, it must remain in a fluid state, with important
consequences for magnetic field generation. These conditions also require the
atmosphere to have a deep isothermal region extending down to 80-800 bar,
depending on composition. Our results bolster the suggestion of a
metal-enriched H/He atmosphere for the planet, as we find water-world models
that lack an H/He atmosphere to require an implausibly large water-to-rock
ratio of more than 6:1. We instead favor a H/He/H2O envelope with high water
mass fraction (~0.5-0.85), similar to recent models of the deep envelope of
Uranus and Neptune. Even with these high water mass fractions in the H/He
envelope, generally the bulk composition of the planet can have subsolar
water:rock ratios. Dry, water-enriched, and pure water envelope models differ
to an observationally significant level in their tidal Love numbers k2 of
respectively ~0.018, 0.15, and 0.7.Comment: 11 pages, 6 figures, 1 table, accepted to Ap
Microscopic Investigation of Vortex Breakdown in a Dividing T-Junction Flow
3D-printed microfluidic devices offer new ways to study fluid dynamics. We
present the first clear visualization of vortex breakdown in a dividing
T-junction flow. By individual control of the inflow and two outflows, we
decouple the effects of swirl and rate of vorticity decay. We show that even
slight outflow imbalances can greatly alter the structure of vortex breakdown,
by creating a net pressure difference across the junction. Our results are
summarized in a dimensionless phase diagram, which will guide the use of vortex
breakdown in T-junctions to achieve specific flow manipulation.Comment: 5 pages, 5 figure
Liquid oxygen/liquid hydrogen boost/vane pump for the advanced orbit transfer vehicles auxiliary propulsion system
A rotating, positive displacement vane pump with an integral boost stage was designed to pump saturated liquid oxygen and liquid hydrogen for auxiliary propulsion system of orbit transfer vehicle. This unit is designed to ingest 10% vapor by volume, contamination free liquid oxygen and liquid hydrogen. The final pump configuration and the predicted performance are included
Regular graphs with four eigenvalues
AbstractWe study the connected regular graphs with four distinct eigenvalues. Properties and feasibility conditions of the eigenvalues are found. Several examples, constructions and characterizations are given, as well as some uniqueness and nonexistence results
- …