1,221 research outputs found
Positive solutions of Schr\"odinger equations and fine regularity of boundary points
Given a Lipschitz domain in and a nonnegative
potential in such that is bounded
in we study the fine regularity of boundary points with respect to
the Schr\"odinger operator in . Using potential
theoretic methods, several conditions equivalent to the fine regularity of are established. The main result is a simple (explicit if
is smooth) necessary and sufficient condition involving the size of
for to be finely regular. An essential intermediate result consists in
a majorization of for
positive harmonic in and . Conditions for
almost everywhere regularity in a subset of are also
given as well as an extension of the main results to a notion of fine
-regularity, if , being two potentials, with and a second order elliptic operator.Comment: version 1. 23 pages version 3. 28 pages. Mainly a typo in Theorem 1.1
is correcte
Paper Session III-D - Elements of Space Flight Project: A Partnership for Space Education
A unique partnership for space education was formed to facilitate greater understanding of space technology and issues for K12 students world-wide. The Elements of Space Flight Project brought school children and teachers together with experts from government and industry, using the Internet, to create a one-of-a-kind learning experience. This four-week project involved thirty-one classes from all corners of the globe -- led by teachers who want to explore the universe with their students, and expand their horizons so they can take their place in the world of the future. 128 others were turned down due to a lack of funds and personnel to assist. Internet-monitored projects for the students included: construction of a space shuttle glider; rocket cars; and paper rockets. Students are tasked to conduct test flights, to analyze data and form conclusions concerning their work. They were also tasked to conduct research on a variety of space topics and answer challenge questions via e-mail. Each class was provided e-mail Experts from whom they could gather additional information or pose questions about their projects. Questions and results could also be posted to the general project membership for consideration and review. This model program, in its first year of existence, was made possible by the efforts of Ms Joan Berger of the Roslyn Public Schools, Roslyn, New York, the US Air Force Academy (USAFA), Air Force Space Command (AFSPC), NASA and the US Space Foundation (USSF). Results are presented from this first experience, as well as recommendations for changes to next year\u27s program
Bottom quark electroproduction in variable flavor number schemes
Two variable flavor number schemes are used to describe bottom quark
production in deep inelastic electron-proton scattering. In these schemes the
coefficient functions are derived from mass factorization of the heavy quark
coefficient functions presented in a fixed flavor number scheme. Also one has
to construct a parton density set with five light flavors (u,d,s,c,b) out of a
set which only contains four light flavors (u,d,s,c). In order the
two sets are discontinuous at which follows from mass factorization
of the heavy quark coefficient functions when it is carried out in the -scheme. Both variable flavor number schemes give almost identical
predictions for the bottom structure functions and . Also
they both agree well with the corresponding results based on fixed order
four-flavor perturbation theory over a wide range in and .Comment: Latex with seventeen PostScript figure
Neural signals predict information sharing across cultures
Information sharing influences which messages spread and shape beliefs, behavior, and culture. In a preregistered neuroimaging study conducted in the United States and the Netherlands, we demonstrate replicability, predictive validity, and generalizability of a brain-based prediction model of information sharing. Replicating findings in Scholz et al., Proc. Natl. Acad. Sci. U.S.A. 114, 2881â2886 (2017), self-, social-, and value-related neural signals in a group of individuals tracked the population sharing of US news articles. Preregistered brain-based prediction models trained on Scholz et al. (2017) data proved generalizable to the new data, explaining more variance in population sharing than self-report ratings alone. Neural signals (versus self-reports) more reliably predicted sharing cross-culturally, suggesting that they capture more universal psychological mechanisms underlying sharing behavior. These findings highlight key neurocognitive foundations of sharing, suggest potential target mechanisms for interventions to increase message effectiveness, and advance brain-as-predictor research
Comparison between variable flavor number schemes for charm quark electroproduction
Where appropriate, the abbreviation 'VFNS' is replaced by 'CSN' to indicate
the scheme using massive heavy quark coefficient functions proposed in this
paper. The text below Eq. (2.13) and between Eqs. (2.33) and (2.36) has been
considerably changed.Comment: 64 pages, LaTeX, 16 Postscript figure
The universal Glivenko-Cantelli property
Let F be a separable uniformly bounded family of measurable functions on a
standard measurable space, and let N_{[]}(F,\epsilon,\mu) be the smallest
number of \epsilon-brackets in L^1(\mu) needed to cover F. The following are
equivalent:
1. F is a universal Glivenko-Cantelli class.
2. N_{[]}(F,\epsilon,\mu)0 and every probability
measure \mu.
3. F is totally bounded in L^1(\mu) for every probability measure \mu.
4. F does not contain a Boolean \sigma-independent sequence.
It follows that universal Glivenko-Cantelli classes are uniformity classes
for general sequences of almost surely convergent random measures.Comment: 26 page
The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation
The relation between the bulk correlation length and the decay length of
thermodynamic Casimir forces is investigated microscopically in two
three-dimensional systems undergoing Bose-Einstein condensation: the perfect
Bose gas and the imperfect mean-field Bose gas. For each of these systems, both
lengths diverge upon approaching the corresponding condensation point from the
one-phase side, and are proportional to each other. We determine the
proportionality factors and discuss their dependence on the boundary
conditions. The values of the corresponding critical exponents for the decay
length and the correlation length are the same, equal to 1/2 for the perfect
gas, and 1 for the imperfect gas
Passing through the bounce in the ekpyrotic models
By considering a simplified but exact model for realizing the ekpyrotic
scenario, we clarify various assumptions that have been used in the literature.
In particular, we discuss the new ekpyrotic prescription for passing the
perturbations through the singularity which we show to provide a spectrum
depending on a non physical normalization function. We also show that this
prescription does not reproduce the exact result for a sharp transition. Then,
more generally, we demonstrate that, in the only case where a bounce can be
obtained in Einstein General Relativity without facing singularities and/or
violation of the standard energy conditions, the bounce cannot be made
arbitrarily short. This contrasts with the standard (inflationary) situation
where the transition between two eras with different values of the equation of
state can be considered as instantaneous. We then argue that the usually
conserved quantities are not constant on a typical bounce time scale. Finally,
we also examine the case of a test scalar field (or gravitational waves) where
similar results are obtained. We conclude that the full dynamical equations of
the underlying theory should be solved in a non singular case before any
conclusion can be drawn.Comment: 17 pages, ReVTeX 4, 13 figures, minor corrections, conclusions
unchange
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