7,278 research outputs found
Riesz-Jacobi transforms as principal value integrals
We establish an integral representation for the Riesz transforms naturally
associated with classical Jacobi expansions. We prove that the Riesz-Jacobi
transforms of odd orders express as principal value integrals against kernels
having non-integrable singularities on the diagonal. On the other hand, we show
that the Riesz-Jacobi transforms of even orders are not singular operators. In
fact they are given as usual integrals against integrable kernels plus or
minus, depending on the order, the identity operator. Our analysis indicates
that similar results, existing in the literature and corresponding to several
other settings related to classical discrete and continuous orthogonal
expansions, should be reinvestigated so as to be refined and in some cases also
corrected.Comment: 30 page
Topological enslavement in evolutionary games on correlated multiplex networks
Governments and enterprises strongly rely on incentives to generate favorable
outcomes from social and strategic interactions between individuals. The
incentives are usually modeled by payoffs in evolutionary games, such as the
prisoner's dilemma or the harmony game, with imitation dynamics. Adjusting the
incentives by changing the payoff parameters can favor cooperation, as found in
the harmony game, over defection, which prevails in the prisoner's dilemma.
Here, we show that this is not always the case if individuals engage in
strategic interactions in multiple domains. In particular, we investigate
evolutionary games on multiplex networks where individuals obtain an aggregate
payoff. We explicitly control the strength of degree correlations between nodes
in the different layers of the multiplex. We find that if the multiplex is
composed of many layers and degree correlations are strong, the topology of the
system enslaves the dynamics and the final outcome, cooperation or defection,
becomes independent of the payoff parameters. The fate of the system is then
determined by the initial conditions
Radiative decays of the strange-bottom mesons
In this article, we assume that the strange-bottom mesons are the
conventional mesons, and calculate the electromagnetic coupling
constants , , and using the light-cone QCD sum rules. Then
we study the radiative decays , ,
and , and observe that the
widths are rather narrow. We can search for the strange-bottom
mesons in the invariant and mass distributions in the
strong decays or in the invariant and mass
distributions in the radiative decays.Comment: 16 pages, 4 figures, revised versio
Signal from noise retrieval from one and two-point Green's function - comparison
We compare two methods of eigen-inference from large sets of data, based on
the analysis of one-point and two-point Green's functions, respectively. Our
analysis points at the superiority of eigen-inference based on one-point
Green's function. First, the applied by us method based on Pad?e approximants
is orders of magnitude faster comparing to the eigen-inference based on
uctuations (two-point Green's functions). Second, we have identified the source
of potential instability of the two-point Green's function method, as arising
from the spurious zero and negative modes of the estimator for a variance
operator of the certain multidimensional Gaussian distribution, inherent for
the two-point Green's function eigen-inference method. Third, we have presented
the cases of eigen-inference based on negative spectral moments, for strictly
positive spectra. Finally, we have compared the cases of eigen-inference of
real-valued and complex-valued correlated Wishart distributions, reinforcing
our conclusions on an advantage of the one-point Green's function method.Comment: 14 pages, 8 figures, 3 table
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