140 research outputs found
Condensation of the roots of real random polynomials on the real axis
We introduce a family of real random polynomials of degree n whose
coefficients a_k are symmetric independent Gaussian variables with variance
= e^{-k^\alpha}, indexed by a real \alpha \geq 0. We compute exactly
the mean number of real roots for large n. As \alpha is varied, one finds
three different phases. First, for 0 \leq \alpha \sim
(\frac{2}{\pi}) \log{n}. For 1 < \alpha < 2, there is an intermediate phase
where grows algebraically with a continuously varying exponent,
\sim \frac{2}{\pi} \sqrt{\frac{\alpha-1}{\alpha}} n^{\alpha/2}. And finally for
\alpha > 2, one finds a third phase where \sim n. This family of real
random polynomials thus exhibits a condensation of their roots on the real line
in the sense that, for large n, a finite fraction of their roots /n are
real. This condensation occurs via a localization of the real roots around the
values \pm \exp{[\frac{\alpha}{2}(k+{1/2})^{\alpha-1} ]}, 1 \ll k \leq n.Comment: 13 pages, 2 figure
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
Boundedness, compactness and Schatten-class membership of weighted composition operators
The boundedness and compactness of weighted composition operators on the
Hardy space of the unit disc is analysed. Particular reference
is made to the case when the self-map of the disc is an inner function.
Schatten-class membership is also considered; as a result, stronger forms of
the two main results of a recent paper of Gunatillake are derived. Finally,
weighted composition operators on weighted Bergman spaces are considered, and the results of Harper and Smith,
linking their properties to those of Carleson embeddings, are extended to this
situation.Comment: 12 page
Magnetic and pair correlations of the Hubbard model with next-nearest-neighbor hopping
A combination of analytical approaches and quantum Monte Carlo simulations is
used to study both magnetic and pairing correlations for a version of the
Hubbard model that includes second-neighbor hopping as a
model for high-temperature superconductors. Magnetic properties are analyzed
using the Two-Particle Self-Consistent approach. The maximum in magnetic
susceptibility as a function of doping appears both at finite
and at but for two totally different physical reasons. When
, it is induced by antiferromagnetic correlations while at
it is a band structure effect amplified by interactions.
Finally, pairing fluctuations are compared with -matrix results to
disentangle the effects of van Hove singularity and of nesting on
superconducting correlations. The addition of antiferromagnetic fluctuations
increases slightly the -wave superconducting correlations despite the
presence of a van Hove singularity which tends to decrease them in the
repulsive model. Some aspects of the phase diagram and some subtleties of
finite-size scaling in Monte Carlo simulations, such as inverted finite-size
dependence, are also discussed.Comment: Revtex, 8 pages + 15 uuencoded postcript figure
Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories
We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus
system by considering a planar secular model, that can be regarded as a major
refinement of the approach first introduced by Lagrange. Indeed, concerning the
planetary orbital revolutions, we improve the classical circular approximation
by replacing it with a solution that is invariant up to order two in the
masses; therefore, we investigate the stability of the secular system for
rather small values of the eccentricities. First, we explicitly construct a
Kolmogorov normal form, so as to find an invariant KAM torus which approximates
very well the secular orbits. Finally, we adapt the approach that is at basis
of the analytic part of the Nekhoroshev's theorem, so as to show that there is
a neighborhood of that torus for which the estimated stability time is larger
than the lifetime of the Solar System. The size of such a neighborhood,
compared with the uncertainties of the astronomical observations, is about ten
times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1010.260
q-Newton binomial: from Euler to Gauss
A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made
less mysterious by virtue of being generalized through the introduction of an
additional parameter
Diminished Superoxide Generation Is Associated With Respiratory Chain Dysfunction and Changes in the Mitochondrial Proteome of Sensory Neurons From Diabetic Rats
Readers may use this article as long as the work is properly cited, the use is educational and not for profit, and the work is not altered. See http://creativecommons.org/licenses/by-nc-nd/3.0/ for details.OBJECTIVE Impairments in mitochondrial function have been proposed to play a role in the etiology of diabetic sensory neuropathy. We tested the hypothesis that mitochondrial dysfunction in axons of sensory neurons in type 1 diabetes is due to abnormal activity of the respiratory chain and an altered mitochondrial proteome.
RESEARCH DESIGN AND METHODS Proteomic analysis using stable isotope labeling with amino acids in cell culture (SILAC) determined expression of proteins in mitochondria from dorsal root ganglia (DRG) of control, 22-week-old streptozotocin (STZ)-diabetic rats, and diabetic rats treated with insulin. Rates of oxygen consumption and complex activities in mitochondria from DRG were measured. Fluorescence imaging of axons of cultured sensory neurons determined the effect of diabetes on mitochondrial polarization status, oxidative stress, and mitochondrial matrix-specific reactive oxygen species (ROS).
RESULTS Proteins associated with mitochondrial dysfunction, oxidative phosphorylation, ubiquinone biosynthesis, and the citric acid cycle were downregulated in diabetic samples. For example, cytochrome c oxidase subunit IV (COX IV; a complex IV protein) and NADH dehydrogenase Fe-S protein 3 (NDUFS3; a complex I protein) were reduced by 29 and 36% (P < 0.05), respectively, in diabetes and confirmed previous Western blot studies. Respiration and mitochondrial complex activity was significantly decreased by 15 to 32% compared with control. The axons of diabetic neurons exhibited oxidative stress and depolarized mitochondria, an aberrant adaption to oligomycin-induced mitochondrial membrane hyperpolarization, but reduced levels of intramitochondrial superoxide compared with control.
CONCLUSIONS Abnormal mitochondrial function correlated with a downregulation of mitochondrial proteins, with components of the respiratory chain targeted in lumbar DRG in diabetes. The reduced activity of the respiratory chain was associated with diminished superoxide generation within the mitochondrial matrix and did not contribute to oxidative stress in axons of diabetic neurons. Alternative pathways involving polyol pathway activity appear to contribute to raised ROS in axons of diabetic neurons under high glucose concentration.This work was supported by grants from the Juvenile Diabetes Research Foundation (#1-2008-280) and the National Institutes of Health to R.T.D. (grants NS-054847 and DK-073594). E.A. was supported by a grant from the National Science and Engineering Research Council (#3311686-06) to P.F. and subsequently by a postgraduate scholarship from the Manitoba Health Research Council. S.K.R.C. and E.Z. were supported by grants to P.F. from the Canadian Institutes for Health Research (#MOP-84214) and the Juvenile Diabetes Research Foundation (#1-2008-193). D.R.S. was supported by a grant to P.F. from the Manitoba Health Research Council. This work was also funded by the St. Boniface General Hospital and Research Foundation
Exponential sums with multiplicative coefficients
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46603/1/222_2005_Article_BF01390204.pd
First Measurement of Z/gamma* Production in Compton Scattering of Quasi-real Photons
We report the first observation of Z/gamma* production in Compton scattering
of quasi-real photons. This is a subprocess of the reaction e+e- to
e+e-Z/gamma*, where one of the final state electrons is undetected.
Approximately 55 pb-1 of data collected in the year 1997 at an e+e-
centre-of-mass energy of 183 GeV with the OPAL detector at LEP have been
analysed. The Z/gamma* from Compton scattering has been detected in the
hadronic decay channel. Within well defined kinematic bounds, we measure the
product of cross-section and Z/gamma* branching ratio to hadrons to be
(0.9+-0.3+-0.1) pb for events with a hadronic mass larger than 60 GeV,
dominated by (e)eZ production. In the hadronic mass region between 5 GeV and 60
GeV, dominated by (e)egamma* production, this product is found to be
(4.1+-1.6+-0.6) pb. Our results agree with the predictions of two Monte Carlo
event generators, grc4f and PYTHIA.Comment: 18 pages, LaTeX, 5 eps figures included, submitted to Physics Letters
Search for Higgs Bosons in e+e- Collisions at 183 GeV
The data collected by the OPAL experiment at sqrts=183 GeV were used to
search for Higgs bosons which are predicted by the Standard Model and various
extensions, such as general models with two Higgs field doublets and the
Minimal Supersymmetric Standard Model (MSSM). The data correspond to an
integrated luminosity of approximately 54pb-1. None of the searches for neutral
and charged Higgs bosons have revealed an excess of events beyond the expected
background. This negative outcome, in combination with similar results from
searches at lower energies, leads to new limits for the Higgs boson masses and
other model parameters. In particular, the 95% confidence level lower limit for
the mass of the Standard Model Higgs boson is 88.3 GeV. Charged Higgs bosons
can be excluded for masses up to 59.5 GeV. In the MSSM, mh > 70.5 GeV and mA >
72.0 GeV are obtained for tan{beta}>1, no and maximal scalar top mixing and
soft SUSY-breaking masses of 1 TeV. The range 0.8 < tanb < 1.9 is excluded for
minimal scalar top mixing and m{top} < 175 GeV. More general scans of the MSSM
parameter space are also considered.Comment: 49 pages. LaTeX, including 33 eps figures, submitted to European
Physical Journal
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