21,415 research outputs found
Bounded Projective Functions and Hyperbolic Metrics with Isolated Singularities
We establish a correspondence on a Riemann surface between hyperbolic metrics
with isolated singularities and bounded projective functions whose Schwarzian
derivatives have at most double poles and whose monodromies lie in . As an application, we construct explicitly a new class of
hyperbolic metrics with countably many singularities on the unit disc.Comment: 14 pages. We revised the old version greatly. In particular, we
changed the title a little bit, generalized the main theorem to general
Riemann surface, added a complex analytical definition for cone/cusp
singularity of hyperbolic metric and Example 1.
Multifractal analysis of weighted networks by a modified sandbox algorithm
Complex networks have attracted growing attention in many fields. As a
generalization of fractal analysis, multifractal analysis (MFA) is a useful way
to systematically describe the spatial heterogeneity of both theoretical and
experimental fractal patterns. Some algorithms for MFA of unweighted complex
networks have been proposed in the past a few years, including the sandbox (SB)
algorithm recently employed by our group. In this paper, a modified SB
algorithm (we call it SBw algorithm) is proposed for MFA of weighted
networks.First, we use the SBw algorithm to study the multifractal property of
two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor
dust" WFNs. We also discuss how the fractal dimension and generalized fractal
dimensions change with the edge-weights of the WFN. From the comparison between
the theoretical and numerical fractal dimensions of these networks, we can find
that the proposed SBw algorithm is efficient and feasible for MFA of weighted
networks. Then, we apply the SBw algorithm to study multifractal properties of
some real weighted networks ---collaboration networks. It is found that the
multifractality exists in these weighted networks, and is affected by their
edge-weights.Comment: 15 pages, 6 figures. Accepted for publication by Scientific Report
Cardiovascular Autonomic Dysfunction in Diabetes as a Complication: Cellular and Molecular Mechanisms
Joint resummation for pion wave function and pion transition form factor
We construct an evolution equation for the pion wave function in the
factorization theorem, whose solution sums the mixed logarithm
to all orders, with () being a parton momentum fraction (transverse
momentum). This joint resummation induces strong suppression of the pion wave
function in the small and large regions, being the impact parameter
conjugate to , and improves the applicability of perturbative QCD to hard
exclusive processes. The above effect is similar to those from the conventional
threshold resummation for the double logarithm and the conventional
resummation for . Combining the evolution equation for the
hard kernel, we are able to organize all large logarithms in the scattering, and to establish a scheme-independent
factorization formula. It will be shown that the significance of
next-to-leading-order contributions and saturation behaviors of this process at
high energy differ from those under the conventional resummations. It implies
that QCD logarithmic corrections to a process must be handled appropriately,
before its data are used to extract a hadron wave function. Our predictions for
the involved pion transition form factor, derived under the joint resummation
and the input of a non-asymptotic pion wave function with the second Gegenbauer
moment , match reasonably well the CLEO, BaBar, and Belle data.Comment: 31 pages, 7 figure
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