564 research outputs found
Bounded operators on weighted spaces of holomorphic functions on the polydisk
We consider the weighted and spaces of
holomorphic functions on the polydisk (in the case of ).
We prove some theorems about the boundedness of Toeplitz operators on
weighted Besov spaces and about the boundedness of generalized
little Hankel and Berezin- type operators on .Comment: 1
A principal possibility for computer investigation of evolution of dynamical systems with independent on time accuracy
Extensive N-body simulations are among the key means for the study of
numerous astrophysical and cosmological phenomena, so various schemes are
developed for possibly higher accuracy computations. We demonstrate the
principal possibility for revealing the evolution of a perturbed Hamiltonian
system with an accuracy independent on time. The method is based on the Laplace
transform and the derivation and analytical solution of an evolution equation
in the phase space for the resolvent and using computer algebra.Comment: Eur Phys Journ C (in press), to match the version to appear, 7 pages,
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High frequency homogenization for travelling waves in periodic media
We consider high frequency homogenization in periodic media for travelling
waves of several different equations: the wave equation for scalar-valued waves
such as acoustics; the wave equation for vector-valued waves such as
electromagnetism and elasticity; and a system that encompasses the
Schr{\"o}dinger equation. This homogenization applies when the wavelength is of
the order of the size of the medium periodicity cell. The travelling wave is
assumed to be the sum of two waves: a modulated Bloch carrier wave having
crystal wave vector \Bk and frequency plus a modulated Bloch
carrier wave having crystal wave vector \Bm and frequency . We
derive effective equations for the modulating functions, and then prove that
there is no coupling in the effective equations between the two different waves
both in the scalar and the system cases. To be precise, we prove that there is
no coupling unless and (\Bk-\Bm)\odot\Lambda \in 2\pi
\mathbb Z^d, where is the
periodicity cell of the medium and for any two vectors the product is defined to be
the vector This last condition forces the
carrier waves to be equivalent Bloch waves meaning that the coupling constants
in the system of effective equations vanish.
We use two-scale analysis and some new weak-convergence type lemmas. The
analysis is not at the same level of rigor as that of Allaire and coworkers who
use two-scale convergence theory to treat the problem, but has the advantage of
simplicity which will allow it to be easily extended to the case where there is
degeneracy of the Bloch eigenvalue.Comment: 30 pages, Proceedings of the Royal Society A, 201
Holomorphic Bloch spaces on the unit ball in
summary:This work is an introduction to anisotropic spaces of holomorphic functions, which have -weight and are generalizations of Bloch spaces on a unit ball. We describe the holomorphic Bloch space in terms of the corresponding space. We establish a description of via the Bloch classes for all
A new exactly integrable hypergeometric potential for the Schr\"odinger equation
We introduce a new exactly integrable potential for the Schr\"odinger
equation for which the solution of the problem may be expressed in terms of the
Gauss hypergeometric functions. This is a potential step with variable height
and steepness. We present the general solution of the problem, discuss the
transmission of a quantum particle above the barrier, and derive explicit
expressions for the reflection and transmission coefficients
Electrical conductivity of warm neutron star crust in magnetic fields: Neutron-drip regime
We compute the anisotropic electrical conductivity tensor of the inner crust
of a compact star at non-zero temperature by extending a previous work on the
conductivity of the outer crust. The physical scenarios, where such crust is
formed, involve proto-neutron stars born in supernova explosions, binary
neutron star mergers and accreting neutron stars. The temperature-density range
studied covers the transition from a non-degenerate to a highly degenerate
electron gas and assumes that the nuclei form a liquid, i.e., the temperature
is above the melting temperature of the lattice of nuclei. The electronic
transition probabilities include (a) the dynamical screening of electron-ion
interaction in the hard-thermal-loop approximation for the QED plasma, (b) the
correlations of the ionic component in a one-component plasma, and (c) finite
nuclear size effects. The conductivity tensor is obtained from the Boltzmann
kinetic equation in relaxation time approximation accounting for the
anisotropies introduced by a magnetic field. The sensitivity of the results
towards the matter composition of the inner crust is explored by using several
compositions of the inner crust which were obtained using different nuclear
interactions and methods of solving the many-body problem. The standard
deviation of relaxation time and components of the conductivity tensor from the
average are below except close to crust-core transition, where
non-spherical nuclear structures are expected. Our results can be used in
dissipative magneto-hydrodynamics (MHD) simulations of warm compact stars
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