9,774 research outputs found
Curves of every genus with many points, I: Abelian and toric families
Let N_q(g) denote the maximal number of F_q-rational points on any curve of
genus g over the finite field F_q. Ihara (for square q) and Serre (for general
q) proved that limsup_{g-->infinity} N_q(g)/g > 0 for any fixed q. In their
proofs they constructed curves with many points in infinitely many genera;
however, their sequences of genera are somewhat sparse. In this paper, we prove
that lim_{g-->infinity} N_q(g) = infinity. More precisely, we use abelian
covers of P^1 to prove that liminf_{g-->infinity} N_q(g)/(g/log g) > 0, and we
use curves on toric surfaces to prove that liminf_{g-->infty} N_q(g)/g^{1/3} >
0; we also show that these results are the best possible that can be proved
with these families of curves.Comment: LaTeX, 20 page
Quasi-shuffle products revisited
Quasi-shuffle products, introduced by the first author, have been useful in
studying multiple zeta values and some of their analogues and generalizations.
The second author, together with Kajikawa, Ohno, and Okuda, significantly
extended the definition of quasi-shuffle algebras so it could be applied to
multiple zeta q-values. This article extends some of the algebraic machinery of
the first author's original paper to the more general definition, and uses this
extension to obtain various algebraic formulas in the quasi-shuffle algebra in
a transparent way. Some applications to multiple zeta values, interpolated
multiple zeta values, multiple q-zeta values, and multiple polylogarithms are
given.Comment: This is an extensively revised and expanded version of the Max Planck
Institute preprint (MPIM 2012-16) with the same title. 27 Oct 16: minor
revision and corrections 3 Apr 17: additional revision and correction
Explosive fragmentation of thin ceramic tube using pulsed power
This study experimentally examined the explosive fragmentation of thin
ceramic tubes using pulsed power. A thin ceramic tube was threaded on a thin
copper wire, and high voltage was applied to the wire using a pulsed power
generator. This melted the wire and the resulting vapor put pressure on the
ceramic tube, causing it to fragment. We examined the statistical properties of
the fragment mass distribution. The cumulative fragment mass distribution
obeyed the double exponential or power-law with exponential decay. Both
distributions agreed well with the experimental data. We also found that the
weighted mean fragment mass was scaled by the multiplicity. This result was
similar to impact fragmentation, except for the crossover point. Finally, we
obtained universal scaling for fragmentation, which is applicable to both
impact and explosive fragmentation.Comment: 5 pages, 6 figure
Microscopic observation of superconducting fluctuations in -(BEDT-TTF)Cu[N(CN)]Br by C NMR spectroscopy
We performed C-NMR experiment and measured spin-lattice relaxation
rate divided by temperature near the superconducting (SC) transition
temperature in -(BEDT-TTF)Cu[N(CN)]Br (-Br
salt), and -(BEDT-TTF)Cu(NCS) (-NCS salt). We
observed the reduction of starting at the temperature higher than
in -Br salt. Microscopic observation of quasi-particle density of
states in the fluctuating SC state revealed the effects of short-range Cooper
pairs induced in the normal state to the quasi-particle density of states. We
also performed systematic measurements in the fields both parallel and
perpendicular to the conduction plane in -Br and -NCS salts,
and confirmed that the reduction of above is observed only
in -Br salt regardless of the external field orientation.Comment: Accepted for publication in PR
- âŠ