113,149 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
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
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
Rigorous theory of nuclear fusion rates in a plasma
Real-time thermal field theory is used to reveal the structure of plasma
corrections to nuclear reactions. Previous results are recovered in a fashion
that clarifies their nature, and new extensions are made. Brown and Yaffe have
introduced the methods of effective quantum field theory into plasma physics.
They are used here to treat the interesting limiting case of dilute but very
highly charged particles reacting in a dilute, one-component plasma. The highly
charged particles are very strongly coupled to this background plasma. The
effective field theory proves that this mean field solution plus the one-loop
term dominate; higher loop corrections are negligible even though the problem
involves strong coupling. Such analytic results for very strong coupling are
rarely available, and they can serve as benchmarks for testing computer models.Comment: 4 pages and 2 figures, presented at SCCS 2005, June 20-25, Moscow,
Russi
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