10,143 research outputs found
Hadamard Regularization
Motivated by the problem of the dynamics of point-particles in high
post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a
certain class of functions which are smooth except at some isolated points
around which they admit a power-like singular expansion. We review the concepts
of (i) Hadamard ``partie finie'' of such functions at the location of singular
points, (ii) the partie finie of their divergent integral. We present and
investigate different expressions, useful in applications, for the latter
partie finie. To each singular function, we associate a partie-finie (Pf)
pseudo-function. The multiplication of pseudo-functions is defined by the
ordinary (pointwise) product. We construct a delta-pseudo-function on the class
of singular functions, which reduces to the usual notion of Dirac distribution
when applied on smooth functions with compact support. We introduce and analyse
a new derivative operator acting on pseudo-functions, and generalizing, in this
context, the Schwartz distributional derivative. This operator is uniquely
defined up to an arbitrary numerical constant. Time derivatives and partial
derivatives with respect to the singular points are also investigated. In the
course of the paper, all the formulas needed in the application to the physical
problem are derived.Comment: 50 pages, to appear in Journal of Mathematical Physic
Diacritical study of light, electrons, and sound scattering by particles and holes
We discuss the differences and similarities in the interaction of scalar and
vector wave-fields with particles and holes. Analytical results are provided
for the transmission of isolated and arrayed small holes as well as surface
modes in hole arrays for light, electrons, and sound. In contrast to the
optical case, small-hole arrays in perforated perfect screens cannot produce
acoustic or electronic surface-bound states. However, unlike electrons and
light, sound is transmitted through individual holes approximately in
proportion to their area, regardless their size. We discuss these issues with a
systematic analysis that allows exploring both common properties and unique
behavior in wave phenomena for different material realizations.Comment: 3 figure
Lorentzian regularization and the problem of point-like particles in general relativity
The two purposes of the paper are (1) to present a regularization of the
self-field of point-like particles, based on Hadamard's concept of ``partie
finie'', that permits in principle to maintain the Lorentz covariance of a
relativistic field theory, (2) to use this regularization for defining a model
of stress-energy tensor that describes point-particles in post-Newtonian
expansions (e.g. 3PN) of general relativity. We consider specifically the case
of a system of two point-particles. We first perform a Lorentz transformation
of the system's variables which carries one of the particles to its rest frame,
next implement the Hadamard regularization within that frame, and finally come
back to the original variables with the help of the inverse Lorentz
transformation. The Lorentzian regularization is defined in this way up to any
order in the relativistic parameter 1/c^2. Following a previous work of ours,
we then construct the delta-pseudo-functions associated with this
regularization. Using an action principle, we derive the stress-energy tensor,
made of delta-pseudo-functions, of point-like particles. The equations of
motion take the same form as the geodesic equations of test particles on a
fixed background, but the role of the background is now played by the
regularized metric.Comment: 34 pages, to appear in J. Math. Phy
Correlation, Network and Multifractal Analysis of Global Financial Indices
We apply RMT, Network and MF-DFA methods to investigate correlation, network
and multifractal properties of 20 global financial indices. We compare results
before and during the financial crisis of 2008 respectively. We find that the
network method gives more useful information about the formation of clusters as
compared to results obtained from eigenvectors corresponding to second largest
eigenvalue and these sectors are formed on the basis of geographical location
of indices. At threshold 0.6, indices corresponding to Americas, Europe and
Asia/Pacific disconnect and form different clusters before the crisis but
during the crisis, indices corresponding to Americas and Europe are combined
together to form a cluster while the Asia/Pacific indices forms another
cluster. By further increasing the value of threshold to 0.9, European
countries France, Germany and UK constitute the most tightly linked markets. We
study multifractal properties of global financial indices and find that
financial indices corresponding to Americas and Europe almost lie in the same
range of degree of multifractality as compared to other indices. India, South
Korea, Hong Kong are found to be near the degree of multifractality of indices
corresponding to Americas and Europe. A large variation in the degree of
multifractality in Egypt, Indonesia, Malaysia, Taiwan and Singapore may be a
reason that when we increase the threshold in financial network these countries
first start getting disconnected at low threshold from the correlation network
of financial indices. We fit Binomial Multifractal Model (BMFM) to these
financial markets.Comment: 32 pages, 25 figures, 1 tabl
Measuring public perceptions of sex offenders: reimagining the Community Attitudes Toward Sex Offenders (CATSO) scale
The Community Attitudes Toward Sex Offenders (CATSO) scale is an 18-item self-report questionnaire designed to measure respondentsâ attitudes toward sex offenders. Its original factor structure has been questioned by a number of previous studies, and so this paper sought to reimagine the scale as an outcome measure, as opposed to a scale of attitudes. A face validity analysis produced a provisional three-factor structure underlying the CATSO: âpunitiveness,â âstereotype endorsement,â and ârisk perception.â A sample of 400 British members of the public completed a modified version of the CATSO, the Attitudes Toward Sex Offenders scale, the General Punitiveness Scale, and the Rational-Experiential Inventory. A three-factor structure of a 22-item modified CATSO was supported using half of the sample, with factors being labeled âsentencing and management,â âstereotype endorsement,â and ârisk perception.â Confirmatory factor analysis on data from the other half of the sample endorsed the three-factor structure; however, two items were removed in order to improve ratings of model fit. This new 20-item âPerceptions of Sex Offenders scaleâ has practical utility beyond the measurement of attitudes, and suggestions for its future use are provided
The BES f_0(1810): a new glueball candidate
We analyze the f_0(1810) state recently observed by the BES collaboration via
radiative J/\psi decay to a resonant \phi\omega spectrum and confront it with
DM2 data and glueball theory. The DM2 group only measured \omega\omega decays
and reported a pseudoscalar but no scalar resonance in this mass region. A
rescattering mechanism from the open flavored KKbar decay channel is considered
to explain why the resonance is only seen in the flavor asymmetric \omega\phi
branch along with a discussion of positive C parity charmonia decays to
strengthen the case for preferred open flavor glueball decays. We also
calculate the total glueball decay width to be roughly 100 MeV, in agreement
with the narrow, newly found f_0, and smaller than the expected estimate of
200-400 MeV. We conclude that this discovered scalar hadron is a solid glueball
candidate and deserves further experimental investigation, especially in the
K-Kbar channel. Finally we comment on other, but less likely, possible
assignments for this state.Comment: 11 pages, 4 figures. Major substantive additions, including an
ab-initio, QCD-based computation of the glueball inclusive decay width,
evaluation of final state effects, and enhanced discussion of several
alternative possibilities. Our conclusions are unchanged: the BES f_0(1810)
is a promising glueball candidat
Atlas versus range maps: robustness of chorological relationships to distribution data types in European mammals
Aim Chorological relationships describe the patterns of distributional overlap
among species. In addition to revealing biogeographical structure, the resulting
clusters of species with similar geographical distributions can serve as natural
units in conservation planning. Here, we assess the extent to which temporal,
methodological and taxonomical differences in the source of speciesâ distribution
data can affect the relationships that are found
On the order of summability of the Fourier inversion formula
In this article we show that the order of the point value, in the sense of Ćojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. CesĂ ro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. CesĂ ro summable of order k, then the distribution is the (k+1)-th derivative of a locally integrable function, and the distribution has a distributional point value of order k+2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems
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