2,674 research outputs found
The QCD analysis of xF_3 structure function based on the analytic approach
We apply analytic perturbation theory to the QCD analysis of the xF_3
structure function data of the CCFR collaboration. We use different approaches
for the leading order Q^2 evolution of the xF_3 structure function and compare
the extracted values of the parameter Lambda_QCD and the shape of the higher
twistcontribution. Our consideration is based on the Jacobi polynomial
expansion method of the unpolarized structure function. The analysis shows that
the analytic approach provides reasonable results in the leading order QCD
analysis.Comment: 7 pages, 5 figure
Supercritical holes for the doubling map
For a map and an open connected set ( a hole) we
define to be the set of points in whose -orbit avoids
. We say that a hole is supercritical if (i) for any hole such
that the set is either empty or contains
only fixed points of ; (ii) for any hole such that \barH\subset H_0
the Hausdorff dimension of is positive.
The purpose of this note to completely characterize all supercritical holes
for the doubling map .Comment: This is a new version, where a full characterization of supercritical
holes for the doubling map is obtaine
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An investigation into using news analytics data in GARCH type volatility models
This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.In the work we study different dynamic volatility models. We consider the family of ARCH and GARCH models to compare the performance of the models using both unconditional coverage Kupiec’s test and the test of conditional coverage proposed by Christoffersen. In-sample estimation procedure and out-of-sample evaluation will be based on General Electric stock market closing daily prices (January 2, 2008 - December 31, 2010). We consider different volatility models augmented with news analytics data to examine the impact of news intensity on stock volatility. First we consider two types of GARCH models: augmented with volume and augmented with news intensity. Based on empirical evidences for some of FTSE100 companies it will be shown that the GARCH(1,1) model augmented with volume does remove GARCH and ARCH effects for the most of the companies, while the GARCH(1,1) model augmented with news intensity has difficulties in removing the impact of log return on volatility. Then we compare GARCH model with jumps and GARCH–Jumps model augmented with news intensity using likelihood ratio test. The study shows that the problem of examining the impact of news intensity on volatility is far more sophisticated than it might seem at first sight. Some hypothesists and suggestions for future work are proposed in the final chapter.This work was funded by the Russian
Government Programme ”National Research University”
Effect of Magnetization Inhomogeneity on Magnetic Microtraps for Atoms
We report on the origin of fragmentation of ultracold atoms observed on a
permanent magnetic film atom chip. A novel technique is used to characterize
small spatial variations of the magnetic field near the film surface using
radio frequency spectroscopy of the trapped atoms. Direct observations indicate
the fragmentation is due to a corrugation of the magnetic potential caused by
long range inhomogeneity in the film magnetization. A model which takes into
account two-dimensional variations of the film magnetization is consistent with
the observations.Comment: 4 pages, 4 figure
Precision measurements of s-wave scattering lengths in a two-component Bose-Einstein condensate
We use collective oscillations of a two-component Bose-Einstein condensate
(2CBEC) of \Rb atoms prepared in the internal states and for the precision measurement of
the interspecies scattering length with a relative uncertainty of
. We show that in a cigar-shaped trap the three-dimensional
(3D) dynamics of a component with a small relative population can be
conveniently described by a one-dimensional (1D) Schr\"{o}dinger equation for
an effective harmonic oscillator. The frequency of the collective oscillations
is defined by the axial trap frequency and the ratio , where
is the intra-species scattering length of a highly populated component
1, and is largely decoupled from the scattering length , the total atom
number and loss terms. By fitting numerical simulations of the coupled
Gross-Pitaevskii equations to the recorded temporal evolution of the axial
width we obtain the value , where is the Bohr
radius. Our reported value is in a reasonable agreement with the theoretical
prediction but deviates significantly from the
previously measured value \cite{Mertes07} which is commonly
used in the characterisation of spin dynamics in degenerate \Rb atoms. Using
Ramsey interferometry of the 2CBEC we measure the scattering length
which also deviates from the previously reported value
\cite{Mertes07}. We characterise two-body losses for the
component 2 and obtain the loss coefficients
and
.Comment: 11 pages, 8 figure
Combinatorics of linear iterated function systems with overlaps
Let be points in , and let
be a one-parameter family of similitudes of : where
is our parameter. Then, as is well known, there exists a
unique self-similar attractor satisfying
. Each has
at least one address , i.e.,
.
We show that for sufficiently close to 1, each has different
addresses. If is not too close to 1, then we can still have an
overlap, but there exist 's which have a unique address. However, we
prove that almost every has addresses,
provided contains no holes and at least one proper overlap. We
apply these results to the case of expansions with deleted digits.
Furthermore, we give sharp sufficient conditions for the Open Set Condition
to fail and for the attractor to have no holes.
These results are generalisations of the corresponding one-dimensional
results, however most proofs are different.Comment: Accepted for publication in Nonlinearit
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