555 research outputs found
Analysis of the time series in the space maser signals
We analyze the data of the observations of the radio sources frequently found
in space. They are believed to be the sets of molecular condensations each of
which works as a maser, so that the whole set produces a characteristic
spectrum. It turns out that in some cases the intensity of one of the
components of such spectrum corresponding to a single condensation changes
periodically with a period of dozens of minutes or of hours.Comment: 5 pages, 6 figure
A bound for the eigenvalue counting function for Krein--von Neumann and Friedrichs extensions
For an arbitrary open, nonempty, bounded set ,
, and sufficiently smooth coefficients , we consider
the closed, strictly positive, higher-order differential operator in defined on , associated with
the higher-order differential expression and its Krein--von Neumann extension
in . Denoting by , , the eigenvalue counting function
corresponding to the strictly positive eigenvalues of , we derive the bound where (with ) is connected to the eigenfunction expansion of the self-adjoint
operator in defined on
, corresponding to . Here denotes the (Euclidean) volume of the unit ball in
.
Our method of proof relies on variational considerations exploiting the
fundamental link between the Krein--von Neumann extension and an underlying
abstract buckling problem, and on the distorted Fourier transform defined in
terms of the eigenfunction transform of in
.
We also consider the analogous bound for the eigenvalue counting function for
the Friedrichs extension in of
.
No assumptions on the boundary of are made.Comment: 39 pages. arXiv admin note: substantial text overlap with
arXiv:1403.373
Finite lifetime eigenfunctions of coupled systems of harmonic oscillators
We find a Hermite-type basis for which the eigenvalue problem associated to
the operator acting on becomes a three-terms recurrence. Here and are two constant
positive definite matrices with no other restriction. Our main result provides
an explicit characterization of the eigenvectors of that lie in the
span of the first four elements of this basis when .Comment: 11 pages, 1 figure. Some typos where corrected in this new versio
Stability of the magnetic Schr\"odinger operator in a waveguide
The spectrum of the Schr\"odinger operator in a quantum waveguide is known to
be unstable in two and three dimensions. Any enlargement of the waveguide
produces eigenvalues beneath the continuous spectrum. Also if the waveguide is
bent eigenvalues will arise below the continuous spectrum. In this paper a
magnetic field is added into the system. The spectrum of the magnetic
Schr\"odinger operator is proved to be stable under small local deformations
and also under small bending of the waveguide. The proof includes a magnetic
Hardy-type inequality in the waveguide, which is interesting in its own
The BCS gap equation for spin-polarized fermions
We study the BCS gap equation for a Fermi gas with unequal population of
spin-up and spin-down states. For , with the
temperature and the chemical potential difference, the question of
existence of non-trivial solutions can be reduced to spectral properties of a
linear operator, similar to the unpolarized case studied previously in
\cite{FHNS,HHSS,HS}. For the phase diagram is more
complicated, however. We derive upper and lower bounds for the critical
temperature, and study their behavior in the small coupling limit.Comment: 23 pages, 1 figur
Precision determination of absolute neutron flux
A technique for establishing the total neutron rate of a highly-collimated
monochromatic cold neutron beam was demonstrated using a method of an
alpha-gamma counter. The method involves only the counting of measured rates
and is independent of neutron cross sections, decay chain branching ratios, and
neutron beam energy. For the measurement, a target of 10B-enriched boron
carbide totally absorbed the neutrons in a monochromatic beam, and the rate of
absorbed neutrons was determined by counting 478keV gamma rays from neutron
capture on 10B with calibrated high-purity germanium detectors. A second
measurement based on Bragg diffraction from a perfect silicon crystal was
performed to determine the mean de Broglie wavelength of the beam to a
precision of 0.024 %. With these measurements, the detection efficiency of a
neutron monitor based on neutron absorption on 6Li was determined to an overall
uncertainty of 0.058 %. We discuss the principle of the alpha-gamma method and
present details of how the measurement was performed including the systematic
effects. We also describe how this method may be used for applications in
neutron dosimetry and metrology, fundamental neutron physics, and neutron cross
section measurements.Comment: 44 page
ON THE IMPACT OF MONETARY POLICY ON THE ECONOMIC DEVELOPMENT OF RUSSIA
The approaches of various authors to the assessment of the impact of monetary policy on the development of the economy have been considered. The main factors of positive and negative influence of interest rate monetary policy on economic development have been established. Features of influence of monetary policy on development of the developed and developing States have been revealed. It has been defined, that the strength of the influence of individual factors on the effectiveness of monetary policy in individual countries varies, and the appropriateness of using monetary policy to support economic growth is determined by the ratio of the total positive and total negative impact. Recommendations on the construction of monetary policy taking into account its positive and negative impact on the development of the economy have been given. They aim at a gradual transition to the use of monetary policy to support growth, to take into account all the factors of influence and the integrated use of all instruments of monetary and fiscal policy to stimulate growth, the achievement of other strategic objectives
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