8,047 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
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
"Clumpiness" Mixing in Complex Networks
Three measures of clumpiness of complex networks are introduced. The measures
quantify how most central nodes of a network are clumped together. The
assortativity coefficient defined in a previous study measures a similar
characteristic, but accounts only for the clumpiness of the central nodes that
are directly connected to each other. The clumpiness coefficient defined in the
present paper also takes into account the cases where central nodes are
separated by a few links. The definition is based on the node degrees and the
distances between pairs of nodes. The clumpiness coefficient together with the
assortativity coefficient can define four classes of network. Numerical
calculations demonstrate that the classification scheme successfully
categorizes 30 real-world networks into the four classes: clumped assortative,
clumped disassortative, loose assortative and loose disassortative networks.
The clumpiness coefficient also differentiates the Erdos-Renyi model from the
Barabasi-Albert model, which the assortativity coefficient could not
differentiate. In addition, the bounds of the clumpiness coefficient as well as
the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure
Dynamic communicability predicts infectiousness
Using real, time-dependent social interaction data, we look at correlations between some recently proposed dynamic centrality measures and summaries from large-scale epidemic simulations. The evolving network arises from email exchanges. The centrality measures, which are relatively inexpensive to compute, assign rankings to individual nodes based on their ability to broadcast information over the dynamic topology. We compare these with node rankings based on infectiousness that arise when a full stochastic SI simulation is performed over the dynamic network. More precisely, we look at the proportion of the network that a node is able to infect over a fixed time period, and the length of time that it takes for a node to infect half the network.We find that the dynamic centrality measures are an excellent, and inexpensive, proxy for the full simulation-based measures
"Clumpiness" Mixing in Complex Networks
Three measures of clumpiness of complex networks are introduced. The measures
quantify how most central nodes of a network are clumped together. The
assortativity coefficient defined in a previous study measures a similar
characteristic, but accounts only for the clumpiness of the central nodes that
are directly connected to each other. The clumpiness coefficient defined in the
present paper also takes into account the cases where central nodes are
separated by a few links. The definition is based on the node degrees and the
distances between pairs of nodes. The clumpiness coefficient together with the
assortativity coefficient can define four classes of network. Numerical
calculations demonstrate that the classification scheme successfully
categorizes 30 real-world networks into the four classes: clumped assortative,
clumped disassortative, loose assortative and loose disassortative networks.
The clumpiness coefficient also differentiates the Erdos-Renyi model from the
Barabasi-Albert model, which the assortativity coefficient could not
differentiate. In addition, the bounds of the clumpiness coefficient as well as
the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure
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 Łojasiewicz, 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. Cesàro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesàro 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
Analytical approach to chiral symmetry breaking in Minkowsky space
The mass gap equation for spontaneous chiral symmetry breaking is studied
directly in Minkowsky space. In hadronic physics, spontaneous chiral symmetry
breaking is crucial to generate a constituent mass for the quarks, and to
produce the Partially Conserved Axial Current theorems, including a small mass
for the pion. Here a class of finite kernels is used, expanded in Yukawa
interactions. The Schwinger-Dyson equation is solved with an analytical
approach. This improves the state of the art of solving the mass gap equation,
which is usually solved with the equal-time approximation or with the Euclidean
approximation. The mapping from the Euclidean space to the Minkowsky space is
also illustrated.Comment: 7 pages, 3 figure
Differences in results and related factors between hospital-at-home modalities in Catalonia: a cross-sectional study
This is the final version. Available on open access from MDPI via the DOI in this record. Hospital-at-home (HaH) is a healthcare modality that provides active treatment by healthcare staff in the patient's home for a condition that would otherwise require hospitalization. The aims were to describe the characteristics of different types of hospital-at-home (HaH), assess their results, and examine which factors could be related to these results. A cross-sectional study based on data from all 2014 HaH contacts from Catalonia was designed. The following HaH modalities were considered-admission avoidance (n = 7,214; 75.1%) and early assisted discharge (n = 2,387; 24.9%). The main outcome indicators were readmission, mortality, and length of stay (days). Multivariable models were fitted to assess the association between explanatory factors and outcomes. Hospital admission avoidance is a scheme in which, instead of being admitted to acute care hospitals, patients are directly treated in their own homes. Early assisted discharge is a scheme in which hospital in-care patients continue their treatment at home. In the hospital avoidance modality, there were 8.3% readmissions, 0.9% mortality, and a mean length of stay (SD) of 9.6 (10.6) days. In the early assisted discharge modality, these figures were 7.9%, 0.5%, and 9.8 (11.1), respectively. In both modalities, readmission and mean length of stay were related to comorbidity and type of hospital, and mortality with age. The results of HaH in Catalonia are similar to those observed in other contexts. The factors related to these results identified might help to improve the effectiveness and efficiency of the different HaH modalities
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
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