237 research outputs found
Nonparametric integral statistics ωkn = nk2 ∫∞−∞ [Sn(x) − F(x)]k dF(x): Main properties and applications
AbstractThe main characteristics of nonparametric statistics, ωkn, which can be represented as integrals of the kth degree of the empirical process, are considered. An algebraic form of these statistics, convenient for practical usage, is derived. Tables of percentage points for k = 1,2, …, 5 and small empirical sample sizes n = 1,2, …, 10 are obtained. Goodness-of-fit criteria based on ωkn statistics are constructed, and their main properties are studied. A method for classifying multidimensional data based on these criteria, which was successfully applied in several experiments, is described
Fine structure of Vavilov-Cherenkov radiation near the Cherenkov threshold
We analyze the Vavilov-Cherenkov radiation (VCR) in a dispersive
nontransparent dielectric air-like medium both below and above the Cherenkov
threshold, in the framework of classical electrodynamics. It is shown that the
transition to the subthreshold energies leads to the destruction of
electromagnetic shock waves and to the sharp reduction of the frequency domain
where VCR is emitted. The fine wake-like structure of the Vavilov-Cherenkov
radiation survives and manifests the existence of the subthreshold radiation in
the domain of anomalous dispersion. These domains can approximately be defined
by the two phenomenological parameters of the medium, namely, the effective
frequency of oscillators and the damping describing an interaction with the
other degrees of freedom.Comment: 9 pages, 6 figure
VELOHYBRIDS – A GLANCE IN TO THE FUTURE
Consumer properties and technical characteristics of developed models of electrically operated bycieles are consided
Multivariate data analysis based on the ωkn-criteria and multilayer perceptron
AbstractA comparative study of multidimensional classifiers based on the goodness-of-fit criteria ωkn and multilayer perceptrons (MLP) has been carried out. It is shown that MLP exhibits the “instantaneous” learning effect and improves the quality of recognition in the case of input data represented in the form of variational series. The reasons are analyzed that underlie these effects. Recommendations for joint usage of the ωkn criteria and of MLPs are given
Vacuum Cherenkov radiation
Within the classical Maxwell-Chern-Simons limit of the Standard-Model
Extension (SME), the emission of light by uniformly moving charges is studied
confirming the possibility of a Cherenkov-type effect. In this context, the
exact radiation rate for charged magnetic point dipoles is determined and found
in agreement with a phase-space estimate under certain assumptions.Comment: 4 pages, REVTeX
On Tamm's problem in the Vavilov-Cherenkov radiation theory
We analyse the well-known Tamm problem treating the charge motion on a finite
space interval with the velocity exceeding light velocity in medium. By
comparing Tamm's formulae with the exact ones we prove that former do not
properly describe Cherenkov radiation terms. We also investigate Tamm's formula
cos(theta)=1/(beta n) defining the position of maximum of the field strengths
Fourier components for the infinite uniform motion of a charge. Numerical
analysis of the Fourier components of field strengths shows that they have a
pronounced maximum at cos(theta)=1/(beta n) only for the charge motion on the
infinitely small interval. As the latter grows, many maxima appear. For the
charge motion on an infinite interval there is infinite number of maxima of the
same amplitude. The quantum analysis of Tamm's formula leads to the same
results.Comment: 28 pages, 8 figures, to be published in J.Phys.D:Appl.Phy
Finite temperature Cherenkov radiation in the presence of a magnetodielectric medium
A canonical approach to Cherenkov radiation in the presence of a
magnetodielectric medium is presented in classical, nonrelativistic and
relativistic quantum regimes. The equations of motion for the canonical
variables are solved explicitly for both positive and negative times. Maxwell
and related constitute equations are obtained. In the large-time limit, the
vector potential operator is found and expressed in terms of the medium
operators. The energy loss of a charged particle, emitted in the form of
radiation, in finite temperature is calculated. A Dirac equation concerning the
relativistic motion of the particle in presence of the magnetodielectric medium
is derived and the relativistic Cherenkov radiation at zero and finite
temperature is investigated. Finally, it is shown that the Cherenkov radiation
in nonrelativistic and relativistic quantum regimes, unlike its classical
counterpart, introduces automatically a cutoff for higher frequencies beyond
which the power of radiation emission is zero.Comment: To be appear in PR
Vacuum Cherenkov effect in logarithmic nonlinear quantum theory
We describe the radiation phenomena which can take place in the physical
vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics
- cone angle, flash duration, radiation yield and spectral distribution - are
computed. It turns out that the radiation yield is proportional to the square
of the proper energy scale of the vacuum which serves also as the vacuum
instability threshold and the natural ultraviolet cutoff. While the analysis is
mainly based on the theory engaging the logarithmic nonlinear quantum wave
equation, some of the obtained results must be valid for any
Lorentz-invariance-violating theory describing the vacuum by (effectively)
continuous medium in the long-wavelength approximation.Comment: Updates: v2: changed title, added comments about vacuum instability
and Hawking radiation, added some refs previously missed due to certain
linguistic subtlety, v3 [pub]: removed comments about Hawking radiation
(requested by referees as it requires a separate study), changed title, added
more ref
Self-amplified Cherenkov radiation from a relativistic electron in a waveguide partially filled with a laminated material
The radiation from a relativistic electron uniformly moving along the axis of
cylindrical waveguide filled with laminated material of finite length is
investigated. Expressions for the spectral distribution of radiation passing
throw the transverse section of waveguide at large distances from the laminated
material are derived with no limitations on the amplitude and variation profile
of the layered medium permittivity and permeability. Numerical results for
layered material consisting of dielectric plates alternated with vacuum gaps
are given. It is shown that at a special choice of problem parameters,
Cherenkov radiation generated by the relativistic electron inside the plates is
self-amplified. The visual explanation of this effect is given and a possible
application is discussed.Comment: 8 pages, 4 figures,1 table, the paper is accepted for publication in
the Journal of Physics: Conference Serie
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