877 research outputs found
On almost universal mixed sums of squares and triangular numbers
In 1997 K. Ono and K. Soundararajan [Invent. Math. 130(1997)] proved that
under the generalized Riemann hypothesis any positive odd integer greater than
2719 can be represented by the famous Ramanujan form ,
equivalently the form represents all integers greater than
1359, where denotes the triangular number . Given positive
integers we employ modular forms and the theory of quadratic forms to
determine completely when the general form represents
sufficiently large integers and establish similar results for the forms
and . Here are some consequences of our main
theorems: (i) All sufficiently large odd numbers have the form
if and only if all prime divisors of are congruent to 1 modulo 4. (ii) The
form is almost universal (i.e., it represents sufficiently large
integers) if and only if each odd prime divisor of is congruent to 1 or 3
modulo 8. (iii) is almost universal if and only if all odd prime
divisors of are congruent to 1 modulo 4. (iv) When , the form
is almost universal if and only if all odd prime divisors of
are congruent to 1 modulo 4 and , where is the
2-adic order of .Comment: 35 page
Quantifying jet transport properties via large hadron production
Nuclear modification factor for large single hadron is studied
in a next-to-leading order (NLO) perturbative QCD (pQCD) parton model with
medium-modified fragmentation functions (mFFs) due to jet quenching in
high-energy heavy-ion collisions. The energy loss of the hard partons in the
QGP is incorporated in the mFFs which utilize two most important parameters to
characterize the transport properties of the hard parton jets: the jet
transport parameter and the mean free path , both at
the initial time . A phenomenological study of the experimental data
for is performed to constrain the two parameters with
simultaneous fits to RHIC as well as LHC data. We obtain
for energetic quarks GeV/fm and
fm in central collisions at
GeV, while GeV/fm, and
fm in central collisions at
TeV. Numerical analysis shows that the best fit favors a
multiple scattering picture for the energetic jets propagating through the bulk
medium, with a moderate averaged number of gluon emissions. Based on the best
constraints for and , the estimated value for the
mean-squared transverse momentum broadening is moderate which implies that the
hard jets go through the medium with small reflection.Comment: 8 pages, 6 figures, revised versio
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On modeling subgrid-scale macro-structures in narrow twisted channels
Low Concentrations of Bisphenol A Induce Mouse Spermatogonial Cell Proliferation by G Protein–Coupled Receptor 30 and Estrogen Receptor-α
Background: Bisphenol A (BPA) is one of the most prevalent chemicals in daily-use materials; therefore, human exposure to BPA is ubiquitous. The estrogenicity of BPA is generally mediated by nuclear estrogen receptors (ERs). However, low concentrations of BPA stimulate seminoma cell proliferation by an uncertain mechanism that does not involve activation of ERs
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