759,693 research outputs found
The Newman--Shapiro problem
We give a negative answer to the Newman--Shapiro problem on weighted
approximation for entire functions formulated in 1966 and motivated by the
theory of operators on the Fock space. There exists a function in the Fock
space such that its exponential multiples do not approximate some entire
multiples in the space. Furthermore, we establish several positive results
under different restrictions on the function in question.Comment: 28 page
Shift of Shapiro Step in High-Temperature Superconductor
Influence of the charge imbalance effect on the system of intrinsic Josephson
junctions of high temperature superconductors under external electromagnetic
radiation are investigated. We demonstrate that the charge imbalance is
responsible for a slope in the Shapiro step in the IV-characteristic. The
nonperiodic boundary conditions shift the Shapiro step from the canonical
position which determined by a frequency of external radiation. We also
demonstrate how the system parameters affect on the shift of Shapiro step.Comment: arXiv admin note: text overlap with arXiv:1601.0445
Half-Integer Shapiro Steps in a Short Ballistic InAs Nanowire Josephson Junction
We report on half-integer Shapiro steps observed in an InAs nanowire
Josephson junction. We observed the Shapiro steps of the short ballistic InAs
nanowire Josephson junction and found anomalous half-integer steps in addition
to the conventional integer steps. The half-integer steps disappear as the
temperature increases or transmission of the junction decreases. These
experimental results agree closely with numerical calculation of the Shapiro
response for the skewed current phase relation in a short ballistic Josephson
junction
Shapiro steps in Josephson junctions with alternating critical current density
We treat theoretically Shapiro steps in tunnel Josephson junctions with
spatially alternating critical current density. Explicit analytical formulas
for the width of the first integer (normal) and half-integer (anomalous)
Shapiro steps are derived for short junctions. We develop coarse-graining
approach, which describes Shapiro steps in the voltage-current curves of the
asymmetric grain boundaries in YBCO thin films and different
superconductor-ferromagnet-superconductor Josephson-type heterostructures.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev.
The Mahler measure of the Rudin-Shapiro polynomials
Littlewood polynomials are polynomials with each of their coefficients in
{-1,1}. A sequence of Littlewood polynomials that satisfies a remarkable
flatness property on the unit circle of the complex plane is given by the
Rudin-Shapiro polynomials. It is shown in this paper that the Mahler measure
and the maximum modulus of the Rudin-Shapiro polynomials on the unit circle of
the complex plane have the same size. It is also shown that the Mahler measure
and the maximum norm of the Rudin-Shapiro polynomials have the same size even
on not too small subarcs of the unit circle of the complex plane. Not even
nontrivial lower bounds for the Mahler measure of the Rudin Shapiro polynomials
have been known before
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