9,398 research outputs found
Covering collections and a challenge problem of Serre
We answer a challenge of Serre by showing that every rational point on the projective curve X + Y = 17 Z is of the form (1, 2, 1) or (2, 1, 1). Our approach builds on recent ideas from both Nils Bruin and the authors on the application of covering collections and Chabauty arguments to curves of high rank. This is the only value of c81 for which the Fermat quartic X + Y = c Z cannot be solved trivially, either by local considerations or maps to elliptic curves of rank 0, and it seems likely that our approach should give a method of attack for other nontrivial values of c
Finding rational points on bielliptic genus 2 curves
We discuss a technique for trying to find all rational points on curves of the form , where the sextic has nonzero discriminant. This is a bielliptic curve of genus 2. When the rank of the Jacobian is 0 or 1, Chabauty's Theorem may be applied. However, we shall concentrate on the situation when the rank is at least 2. In this case, we shall derive an associated family of elliptic curves, defined over a number field Q(a). If each of these elliptic curves has rank less than the degree of Q(a) : Q, then we shall describe a Chabauty-like technique which may be applied to try to find all the points (x,y) defined over Q(a) on the elliptic curves, for which x is in Q. This in turn allows us to find all Q-rational points on the original genus 2 curve. We apply this to give a solution to a problem of Diophantus (where the sextic in X is irreducible over Q), which simplifies the recent solution of Wetherell. We also present two examples where the sextic in X is reducible over Q
Lattice-Constrained Parametrizations of Form Factors for Semileptonic and Rare Radiative B Decays
We describe the form factors for semileptonic B to rho l nu and radiative B
to K* gamma decays with just two parameters and the two form factors for
semileptonic B to pi l nu decays with three parameters. The parametrizations
are constrained by lattice results and are consistent with heavy quark
symmetry, kinematic constraints and light cone sum rule scaling relations.Comment: 3 pages, latex, 2 eps files, uses epsf.sty and espcrc2.sty, poster
presented at Lattice 97, Edinburgh, 22-26 July 199
A study of trace contaminant identification by microwave double resonance spectroscopy
Trace contaminant identification using microwave double resonance spectroscop
Highly Ionized High-Velocity Clouds toward PKS 2155-304 and Markarian 509
To gain insight into four highly ionized high-velocity clouds (HVCs)
discovered by Sembach et al. (1999), we have analyzed data from the Hubble
Space Telescope (HST) and Far Ultraviolet Spectroscopic Explorer (FUSE) for the
PKS 2155-304 and Mrk 509 sight lines. We measure strong absorption in OVI and
column densities of multiple ionization stages of silicon (SiII/III/IV) and
carbon (CII/III/IV). We interpret this ionization pattern as a multiphase
medium that contains both collisionally ionized and photoionized gas. Toward
PKS 2155-304, for HVCs at -140 and -270 km/s, respectively, we measure
logN(OVI)=13.80+/-0.03 and log N(OVI)=13.56+/-0.06; from Lyman series
absorption, we find log N(HI)=16.37^(+0.22)_(-0.14) and 15.23^(+0.38)_(-0.22).
The presence of high-velocity OVI spread over a broad (100 km/s) profile,
together with large amounts of low-ionization species, is difficult to
reconcile with the low densities, n=5x10^(-6) cm^(-3), in the
collisional/photoionization models of Nicastro et al. (2002), although the HVCs
show a similar relation in N(SiIV)/N(CIV) versus N(CII)/N(CIV) as high-z
intergalactic clouds. Our results suggest that the high-velocity OVI in these
absorbers do not necessarily trace the WHIM, but instead may trace HVCs with
low total hydrogen column density. We propose that the broad high-velocity OVI
absorption arises from shock ionization, at bowshock interfaces produced from
infalling clumps of gas with velocity shear. The similar ratios of high ions
for HVC Complex C and these highly ionized HVCs suggest a common production
mechanism in the Galactic halo.Comment: 38 pages, including 10 figures. ApJ, 10 April, 2004. Replaced with
accepted versio
A New Method for Obtaining Binary Pulsar Distances and its Implications for Tests of General Relativity
We demonstrate how measuring orbital period derivatives can lead to more
accurate distance estimates and transverse velocities for some nearby binary
pulsars. In many cases this method will estimate distances more accurately than
is possible by annual parallax, as the relative error decreases as t^-5/2.
Unfortunately, distance uncertainties limit the degree to which nearby
relativistic binary pulsars can be used for testing the general relativistic
prediction of orbital period decay to a few percent. Nevertheless, the measured
orbital period derivative of PSR B1534+12 agrees within the observational
uncertainties with that predicted by general relativity if the proper-motion
contribution is accounted for.Comment: 4 pages, latex, uuencoded compressed postscript + source, no figures,
uses aaspptwo.sty and dec.sty, accepted for publication in ApJL, omitted
reference now include
Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves
This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. The second of these conjectures relates six quantities associated to a Jacobian over the rational numbers. One of these six quantities is the size of the Shafarevich-Tate group. Unable to compute that, we computed the five other quantities and solved for the last one. In all 32 cases, the result is very close to an integer that is a power of 2. In addition, this power of 2 agrees with the size of the 2-torsion of the Shafarevich-Tate group, which we could compute
Towards a lattice determination of the coupling
The coupling is related to the form factor at zero
momentum of the axial current between - and -states. This form
factor is evaluated on the lattice using static heavy quarks and light quark
propagators determined by a stochastic inversion of the fermionic bilinear. The
\gBBP coupling is related to the coupling between heavy mesons and
low-momentum pions in the effective heavy meson chiral lagrangian. The coupling
of the effective theory can therefore be computed by numerical simulations. We
find the value . Besides its theoretical interest, the
phenomenological implications of such a determination are discussed.Comment: 20 pages, 6 figure
A Kuiper Belt Source for Solar Flare Track-Rich Interplanetary Dust Particles
The presence of solar flare particle tracks in mineral grains within interplanetary dust particles (IDPs) has long been accepted as proof of their extraterrestrial origin [e.g. 1]. The 10-20 micrometers diameter IDPs released by dust producing objects in the solar system (mainly comets and asteroids) spiral in towards the Sun under the influence of Poynting-Robertson (PR) drag forces [2] and accumulate solar flare energetic particle tracks during their journey. The number of IDPs with well-constrained track density measurements is small, owing to the difficulty in the measurements and the lack of appropriatelysized crystals in which to image them. In order to use track densities as a chronometer of space exposure, the track production rate must be known. All previous work relied on track production rates determined by chemical etching techniques [e.g. 3], but tracks in IDPs are measured using TEM imaging. Here we report measurements of track densities in IDPs from both the anhydrous and hydrated IDP groups. Using the track production calibration determined from TEM observations of anorthite and olivine in lunar rock 64455 [4] we estimate space exposure times for these IDPs to constrain their parent body sources
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