8,768 research outputs found
Distributional versions of Littlewood's Tauberian theorem
We provide several general versions of Littlewood's Tauberian theorem. These
versions are applicable to Laplace transforms of Schwartz distributions. We
apply these Tauberian results to deduce a number of Tauberian theorems for
power series where Ces\`{a}ro summability follows from Abel summability. We
also use our general results to give a new simple proof of the classical
Littlewood one-sided Tauberian theorem for power series.Comment: 15 page
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
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
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
Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism
Three decades of work on the quantum field equations of pure Yang-Mills
theory have distilled two families of solutions in Landau gauge. Both coincide
for high (Euclidean) momentum with known perturbation theory, and both predict
an infrared suppressed transverse gluon propagator, but whereas the solution
known as "scaling" features an infrared power law for the gluon and ghost
propagators, the "massive" solution rather describes the gluon as a vector
boson that features a finite Debye screening mass.
In this work we examine the gauge dependence of these solutions by adopting
stochastic quantization. What we find, in four dimensions and in a rainbow
approximation, is that stochastic quantization supports both solutions in
Landau gauge but the scaling solution abruptly disappears when the parameter
controlling the drift force is separated from zero (soft gauge-fixing),
recovering only the perturbative propagators; the massive solution seems to
survive the extension outside Landau gauge. These results are consistent with
the scaling solution being related to the existence of a Gribov horizon, with
the massive one being more general.
We also examine the effective action in Faddeev-Popov quantization that
generates the rainbow and we find, for a bare vertex approximation, that the
the massive-type solutions minimise the quantum effective action.Comment: 13 pages, 7 figures. Change of title to reflect version accepted for
publicatio
On fermionic tilde conjugation rules and thermal bosonization. Hot and cold thermofields
A generalization of Ojima tilde conjugation rules is suggested, which reveals
the coherent state properties of thermal vacuum state and is useful for the
thermofield bosonization. The notion of hot and cold thermofields is introduced
to distinguish different thermofield representations giving the correct normal
form of thermofield solution for finite temperature Thirring model with correct
renormalization and anticommutation properties.Comment: 13 page
Temperature dependence of the anomalous effective action of fermions in two and four dimensions
The temperature dependence of the anomalous sector of the effective action of
fermions coupled to external gauge and pseudo-scalar fields is computed at
leading order in an expansion in the number of Lorentz indices in two and four
dimensions. The calculation preserves chiral symmetry and confirms that a
temperature dependence is compatible with axial anomaly saturation. The result
checks soft-pions theorems at zero temperature as well as recent results in the
literature for the pionic decay amplitude into static photons in the chirally
symmetric phase. The case of chiral fermions is also considered.Comment: RevTex, 19 pages, no figures. References adde
A corresponding states approach to Small-Angle-Scattering for polydisperse ionic colloidal fluids
Approximate scattering functions for polydisperse ionic colloidal fluids are
obtained by a corresponding states approach. This assumes that all pair
correlation functions of a polydisperse fluid are
conformal to those of an appropriate monodisperse binary fluid (reference
system) and can be generated from them by scaling transformations. The
correspondence law extends to ionic fluids a {\it scaling approximation} (SA)
successfully proposed for nonionic colloids in a recent paper. For the
primitive model of charged hard spheres in a continuum solvent, the partial
structure factors of the monodisperse binary reference system are evaluated by
solving the Orstein-Zernike (OZ) integral equations coupled with an approximate
closure. The SA is first tested within the mean spherical approximation (MSA)
closure, which allows analytical solutions. The results are found in good
overall agreement with exact MSA predictions up to relevant polidispersity. The
SA is shown to be an improvement over the ``decoupling approximation'' extended
to the ionic case. The simplicity of the SA scheme allows its application also
when the OZ equations can be solved only numerically. An example is then given
by using the hypernetted chain (HNC) closure. Shortcomings of the SA approach,
its possible use in the analysis of experimental scattering data and other
related points are also briefly addressed.Comment: 29 pages, 7 postscript figures (included), Latex 3.0, uses aps.sty,
to appear in Phys. Rev. E (1999
Grande Queimado numa Unidade de Cuidados Intensivos PediĂĄtricos â ExperiĂȘncia de 20 Anos
Introdução: A abordagem inicial do grande queimado atĂ© Ă sua estabilização hemodinĂąmica e hidroeletrolĂtica Ă© fundamental para diminuir a morbimortalidade.
Material e MĂ©todos: Estudo retrospectivo, descritivo e analĂtico, de todos os internamentos por queimadura numa Unidade
de Cuidados Intensivos PediĂĄtricos durante o perĂodo de 20 anos (Abril/1991 a Dezembro/2010). Avaliaram -se parĂąmetros nosodemogrĂĄficos, agente causal, gravidade e extensĂŁo da queimadura, procedimentos, terapĂȘutica, complicaçÔes e resultados.
Resultados: Ocorreram 137 internamentos por queimadura correspondentes a 123 doentes e a 1,8% do total de internamentos
na UCIP. A mediana de idade foi 3,6 anos e 62,4% era do sexo masculino. Verificou -se maior incidĂȘncia em Agosto (13,0%). Foram agentes da queimadura: lĂquido fervente
(38,1%), fogo (38,1%) e eletricidade (23,9%). A mediana da superfĂcie
corporal queimada foi de 30% (0,5 -92,0%), com queimaduras do terceiro grau em 59,0% dos doentes. Necessitaram de ventilação mecĂąnica 45,5% e de cateter venoso central 64,2% dos doentes. As complicaçÔes incluĂram: sĂ©psis (29,2%), falĂȘncia
respiratĂłria (21,1%), falĂȘncia cardiovascular (16,5%) e falĂȘncia
multiorgĂąnica (18,8%). Verificou -se melhoria em 88,6% dos casos e ocorreram 10 Ăłbitos (8,1%), nove dos quais nos primeiros 10 anos do estudo e nove devido a causa infeciosa. No entanto, o score avaliador do risco de mortalidade (PRISM), Ăndice de intervenção terapĂȘutica (TISS) e o risco de probabilidade de morte (RPM) foram mais elevados no segundo decĂ©nio.
ConclusĂ”es: Nos Ășltimos anos do estudo, apesar do maior nĂșmero de admissĂ”es e da sua maior gravidade, verificou -se
uma diminuição do nĂșmero de mortes, o que poderĂĄ dever-se Ă melhoria dos cuidados prestados
To what extent is Gluon Confinement an empirical fact?
Experimental verifications of Confinement in hadron physics have established
the absence of charges with a fraction of the electron's charge by studying the
energy deposited in ionization tracks at high energies, and performing Millikan
experiments with charged droplets at rest. These experiments test only the
absence of particles with fractional charge in the asymptotic spectrum, and
thus "Quark" Confinement. However what theory suggests is that Color is
confined, that is, all asymptotic particles are color singlets. Since QCD is a
non-Abelian theory, the gluon force carriers (indirectly revealed in hadron
jets) are colored. We empirically examine what can be said about Gluon
Confinement based on the lack of detection of appropriate events, aiming at an
upper bound for high-energy free-gluon production.Comment: 14 pages, 12 figures, version accepted at Few Body Physic
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