13,119 research outputs found
A note on the theorems of M. G. Krein and L. A. Sakhnovich on continuous analogs of orthogonal polynomials on the circle
Continuous analogs of orthogonal polynomials on the circle are solutions of a
canonical system of differential equations, introduced and studied by M.G.Krein
and recently generalized to matrix systems by L.A.Sakhnovich. We prove that the
continuous analog of the adjoint polynomials converges in the upper half-plane
in the case of L^2 coefficients, but in general the limit can be defined only
up to a constant multiple even when the coefficients are in L^p for any p>2,
the spectral measure is absolutely continuous and the Szego-Kolmogorov-Krein
condition is satisfied. Thus we point out that Krein's and Sakhnovich's papers
contain an inaccuracy, which does not undermine known implications from these
results
Collective Current Rectification
We consider a network of coupled underdamped ac-driven dynamical units
exposed to a heat bath. The topology of connections defines the
absence/presence of certain spatial symmetries, which in turn cause
nonzero/zero value of a mean dc-output. We discuss dynamical mechanisms of the
rectification and identify dc-current reversals with
synchronization/desynchronization transitions in the network dynamics.Comment: 3 fig
Superheavy element production, nucleus-nucleus potential and mu-catalysis
The semi-microscopic potential between heavy nuclei is evaluated for various
colliding ions in the approach of frozen densities in the framework of the
extended Thomas-Fermi approximation with hbar^2 correction terms in the kinetic
energy density functional. The proton and neutron densities of each nucleus are
obtained in the Hartree-Fock-BCS approximation with SkM* parameter set of the
Skyrme force. A simple expression for the nuclear interaction potential between
spherical nuclei is presented. It is shown that muon bound with light
projectile induces the superheavy elements production in nucleus-nucleus
collisions.Comment: 9 pages, 4 figures, RevTex, Tours 5 Symposium on Nuclear Physics,
Tours, August 200
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