225 research outputs found
Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains
We establish the resolvent estimates for the Stokes operator in
Lipschitz domains in , for . The result, in particular, implies that the Stokes operator in a
three-dimensional Lipschitz domain generates a bounded analytic semigroup in
for (3/2)-\varep < p< 3+\epsilon. This gives an affirmative answer to a
conjecture of M. Taylor.Comment: 28 page. Minor revision was made regarding the definition of the
Stokes operator in Lipschitz domain
Some genus 3 curves with many points
Using an explicit family of plane quartic curves, we prove the existence of a
genus 3 curve over any finite field of characteristic 3 whose number of
rational points stays within a fixed distance from the Hasse-Weil-Serre upper
bound. We also provide an intrinsic characterization of so-called Legendre
elliptic curves
More Discriminants with the Brezing-Weng Method
The Brezing-Weng method is a general framework to generate families of
pairing-friendly elliptic curves. Here, we introduce an improvement which can
be used to generate more curves with larger discriminants. Apart from the
number of curves this yields, it provides an easy way to avoid endomorphism
rings with small class number
Computing Hilbert Class Polynomials
We present and analyze two algorithms for computing the Hilbert class
polynomial . The first is a p-adic lifting algorithm for inert primes p
in the order of discriminant D < 0. The second is an improved Chinese remainder
algorithm which uses the class group action on CM-curves over finite fields.
Our run time analysis gives tighter bounds for the complexity of all known
algorithms for computing , and we show that all methods have comparable
run times
Predicting melatonin suppression by light in humans:Unifying photoreceptor-based equivalent daylight illuminances, spectral composition, timing and duration of light exposure
Lightâinduced melatonin suppression data from 29 peerâreviewed publications was analysed by means of a machineâlearning approach to establish which light exposure characteristics (ie photopic illuminance, five αâopic equivalent daylight illuminances [EDIs], duration and timing of the light exposure, and the dichotomous variables pharmacological pupil dilation and narrowband light source) are the main determinants of melatonin suppression. Melatonin suppression in the data set was dominated by four light exposure characteristics: (1) melanopic EDI, (2) light exposure duration, (3) pupil dilation and (4) Sâconeâopic EDI. A logistic model was used to evaluate the influence of each of these parameters on the melatonin suppression response. The final logistic model was only based on the first three parameters, since melanopic EDI was the best single (photoreceptor) predictor that was only outperformed by Sâconeâopic EDI for (photopic) illuminances below 21 lux. This confirms and extends findings on the importance of the metric melanopic EDI for predicting biological effects of light in integrative (humanâcentric) lighting applications. The model provides initial and general guidance to lighting practitioners on how to combine spectrum, duration and amount of light exposure when controlling nonâvisual responses to light, especially melatonin suppression. The model is a starting tool for developing hypotheses on photoreceptorsâ contributions to light's nonâvisual responses and helps identifying areas where more data are needed, like on the Sâcone contribution at low illuminances
On the representation ring of the polynomial algebra over a perfect field
We consider the tensor product of modules over the polynomial algebra
corresponding to the usual tensor product of linear operators. We present a
general description of the representation ring in case the ground field k is
perfect. It is made explicit in the special cases when k is real closed
respectively algebraically closed. Furthermore, we discuss the generalisation
of this problem to representations of quivers. In particular the representation
ring of quivers of extended Dynkin type A is provided.Comment: 17 page
On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds
Asymptotic laws for mean multiplicities of lengths of closed geodesics in
arithmetic hyperbolic three-orbifolds are derived. The sharpest results are
obtained for non-compact orbifolds associated with the Bianchi groups SL(2,o)
and some congruence subgroups. Similar results hold for cocompact arithmetic
quaternion groups, if a conjecture on the number of gaps in their length
spectra is true. The results related to the groups above give asymptotic lower
bounds for the mean multiplicities in length spectra of arbitrary arithmetic
hyperbolic three-orbifolds. The investigation of these multiplicities is
motivated by their sensitive effect on the eigenvalue spectrum of the
Laplace-Beltrami operator on a hyperbolic orbifold, which may be interpreted as
the Hamiltonian of a three-dimensional quantum system being strongly chaotic in
the classical limit.Comment: 29 pages, uuencoded ps. Revised version, to appear in NONLINEARIT
Equidistribution of Heegner Points and Ternary Quadratic Forms
We prove new equidistribution results for Galois orbits of Heegner points
with respect to reduction maps at inert primes. The arguments are based on two
different techniques: primitive representations of integers by quadratic forms
and distribution relations for Heegner points. Our results generalize one of
the equidistribution theorems established by Cornut and Vatsal in the sense
that we allow both the fundamental discriminant and the conductor to grow.
Moreover, for fixed fundamental discriminant and variable conductor, we deduce
an effective surjectivity theorem for the reduction map from Heegner points to
supersingular points at a fixed inert prime. Our results are applicable to the
setting considered by Kolyvagin in the construction of the Heegner points Euler
system
Effective equidistribution and the Sato-Tate law for families of elliptic curves
Extending recent work of others, we provide effective bounds on the family of
all elliptic curves and one-parameter families of elliptic curves modulo p (for
p prime tending to infinity) obeying the Sato-Tate Law. We present two methods
of proof. Both use the framework of Murty-Sinha; the first involves only
knowledge of the moments of the Fourier coefficients of the L-functions and
combinatorics, and saves a logarithm, while the second requires a Sato-Tate
law. Our purpose is to illustrate how the caliber of the result depends on the
error terms of the inputs and what combinatorics must be done.Comment: Version 1.1, 24 pages: corrected the interpretation of Birch's moment
calculations, added to the literature review of previous results
What is the potential benefit of pre-hospital extracorporeal cardiopulmonary resuscitation for patients with an out-of-hospital cardiac arrest?:A predictive modelling study
AIM: In this predictive modelling study we aimed to investigate how many patients with an out-of-hospital cardiac arrest (OHCA) would benefit from pre-hospital as opposed to in-hospital initiation of extracorporeal cardiopulmonary resuscitation (ECPR).METHODS: A temporal spatial analysis of Utstein data was performed for all adult patients with a non-traumatic OHCA attended by three emergency medical services (EMS) covering the north of the Netherlands during a one-year period. Patients were considered potentially eligible for ECPR if they had a witnessed arrest with immediate bystander CPR, an initial shockable rhythm (or signs of life during resuscitation) and could be presented in an ECPR-centre within 45 minutes of the arrest. Endpoint of interest was defined as the hypothetical number of ECPR eligible patients after 10, 15 and 20 minutes of conventional CPR and upon (hypothetical) arrival in an ECPR-centre as a fraction of the total number of OHCA patients attended by EMS.RESULTS: During the study period 622 OHCA patients were attended, of which 200 (32%) met ECPR eligibility criteria upon EMS arrival. The optimal transition point between conventional CPR and ECPR was found to be after 15 minutes. Hypothetical intra-arrest transport of all patients in whom no return of spontaneous circulation (ROSC) was obtained after that point (n = 84) would have yielded 16/622 (2.5%) patients being potentially ECPR eligible upon hospital arrival (average low-flow time 52 minutes), whereas on-scene initiation of ECPR would have resulted in 84/622 (13.5%) potential candidates (average estimated low-flow time 24 minutes before cannulation).CONCLUSION: Even in healthcare systems with relatively short transport distances to hospital, consideration should be given to pre-hospital initiation of ECPR for OHCA as it shortens low-flow time and increases the number of potentially eligible patients.</p
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