143,058 research outputs found
Averages and moments associated to class numbers of imaginary quadratic fields
For any odd prime , let denote the -part of the
class number of the imaginary quadratic field .
Nontrivial pointwise upper bounds are known only for ; nontrivial
upper bounds for averages of have previously been known only for
. In this paper we prove nontrivial upper bounds for the average of
for all primes , as well as nontrivial upper bounds
for certain higher moments for all primes .Comment: 26 pages; minor edits to exposition and notation, to agree with
published versio
A documentation of two- and three-dimensional shock-separated turbulent boundary layers
A shock-related separation of a turbulent boundary layer has been studied and documented. The flow was that of an axisymmetric turbulent boundary layer over a 5.02-cm-diam cylinder that was aligned with the wind tunnel axis. The boundary layer was compressed by a 30 deg half-angle conical flare, with the cone axis inclined at an angle alpha to the cylinder axis. Nominal test conditions were P sub tau equals 1.7 atm and M sub infinity equals 2.85. Measurements were confined to the upper-symmetry, phi equals 0 deg, plane. Data are presented for the cases of alpha equal to 0. 5. and 10 deg and include mean surface pressures, streamwise and normal mean velocities, kinematic turbulent stresses and kinetic energies, as well as reverse-flow intermittencies. All data are given in tabular form; pressures, streamwise velocities, turbulent shear stresses, and kinetic energies are also presented graphically
The energy partitioning of non-thermal particles in a plasma: or the Coulomb logarithm revisited
The charged particle stopping power in a highly ionized and weakly to
moderately coupled plasma has been calculated to leading and next-to-leading
order by Brown, Preston, and Singleton (BPS). After reviewing the main ideas
behind this calculation, we use a Fokker-Planck equation derived by BPS to
compute the electron-ion energy partitioning of a charged particle traversing a
plasma. The motivation for this application is ignition for inertial
confinement fusion -- more energy delivered to the ions means a better chance
of ignition, and conversely. It is therefore important to calculate the
fractional energy loss to electrons and ions as accurately as possible, as this
could have implications for the Laser Megajoule (LMJ) facility in France and
the National Ignition Facility (NIF) in the United States. The traditional
method by which one calculates the electron-ion energy splitting of a charged
particle traversing a plasma involves integrating the stopping power dE/dx.
However, as the charged particle slows down and becomes thermalized into the
background plasma, this method of calculating the electron-ion energy splitting
breaks down. As a result, the method suffers a systematic error of order T/E0,
where T is the plasma temperature and E0 is the initial energy of the charged
particle. In the case of DT fusion, for example, this can lead to uncertainties
as high as 10% or so. The formalism presented here is designed to account for
the thermalization process, and in contrast, it provides results that are
near-exact.Comment: 10 pages, 3 figures, invited talk at the 35th European Physical
Society meeting on plasma physic
Simultaneous Integer Values of Pairs of Quadratic Forms
We prove that a pair of integral quadratic forms in 5 or more variables will
simultaneously represent "almost all" pairs of integers that satisfy the
necessary local conditions, provided that the forms satisfy a suitable
nonsingularity condition. In particular such forms simultaneously attain prime
values if the obvious local conditions hold. The proof uses the circle method,
and in particular pioneers a two-dimensional version of a Kloosterman
refinement.Comment: 63 page
Positive psychology and romantic scientism: Reply to comments on Brown, Sokal, & Friedman (2013)
This is a response to five comments [American Psychologist 69, 626-629 and
632-635 (2014)] on our article arXiv:1307.7006.Comment: PDF, 9 page
The persistence of wishful thinking: Response to "Updated thinking on positivity ratios"
This is a response to Barbara Fredrickson's comment [American Psychologist
68, 814-822 (2013)] on our article arXiv:1307.7006.
We analyze critically the renewed claims made by Fredrickson (2013)
concerning positivity ratios and "flourishing", and attempt to disentangle some
conceptual confusions; we also address the alleged empirical evidence for
nonlinear effects. We conclude that there is no evidence whatsoever for the
existence of any "tipping points", and only weak evidence for the existence of
any nonlinearity of any kind. Our original concern, that the application of
advanced mathematical techniques in psychology and related disciplines may not
always be appropriate, remains undiminished.Comment: LaTeX2e, 10 pages including 6 Postscript figure
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