7,790 research outputs found
On the bi-Hamiltonian Geometry of WDVV Equations
We consider the WDVV associativity equations in the four dimensional case.
These nonlinear equations of third order can be written as a pair of six
component commuting two-dimensional non-diagonalizable hydrodynamic type
systems. We prove that these systems possess a compatible pair of local
homogeneous Hamiltonian structures of Dubrovin--Novikov type (of first and
third order, respectively).Comment: 21 pages, revised published version; exposition substantially
improve
Systems of conservation laws with third-order Hamiltonian structures
We investigate -component systems of conservation laws that possess
third-order Hamiltonian structures of differential-geometric type. The
classification of such systems is reduced to the projective classification of
linear congruences of lines in satisfying additional
geometric constraints. Algebraically, the problem can be reformulated as
follows: for a vector space of dimension , classify -tuples of
skew-symmetric 2-forms such that for some non-degenerate symmetric
.Comment: 31 page
Quantum nature of cyclotron harmonics in thermal spectra of neutron stars
Some isolated neutron stars show harmonically spaced absorption features in
their thermal soft X-ray spectra. The interpretation of the features as a
cyclotron line and its harmonics has been suggested, but the usual explanation
of the harmonics as caused by relativistic effects fails because the
relativistic corrections are extremely small in this case. We suggest that the
features correspond to the peaks in the energy dependence of the free-free
opacity in a quantizing magnetic field, known as quantum oscillations. The
peaks arise when the transitions to new Landau levels become allowed with
increasing the photon energy; they are strongly enhanced by the square-root
singularities in the phase-space density of quantum states in the case when the
free (non-quantized) motion is effectively one-dimensional. To explore
observable properties of these quantum oscillations, we calculate models of
hydrogen neutron star atmospheres with B \sim 10^{10} - 10^{11} G (i.e.,
electron cyclotron energy E_{c,e} = 0.1 - 1 keV) and T_{eff} = 1 - 3 MK. Such
conditions are thought to be typical for the so-called central compact objects
in supernova remnants, such as 1E 1207.4-5209 in PKS 1209-51/52. We show that
observable features at the electron cyclotron harmonics form at moderately
large values of the quantization parameter, b_{eff} = E_{c,e}/kT_{eff} = 0.5 -
20. The equivalent widths of the features can reach 100 - 200 eV; they grow
with increasing b_{eff} and are lower for higher harmonics.Comment: 6 pages; shortened, references updated; published in Ap
High energy processes in the vicinity of the Kerr's black hole horizon
Two particle collisions close to the horizon of the rotating nonextremal
black hole are analyzed. It is shown that high energy of the order of the Grand
Unification scale in the centre of mass of colliding particles can be obtained
when there is a multiple collision - the particle from the accretion disc gets
the critical momentum in first collision with the other particle close to the
horizon and then there is a second collision of the critical particle with the
ordinary one. High energy occurs due to a great relative velocity of two
particles and a large Lorentz factor. The dependence of the relative velocity
on the distance to horizon is analyzed, the time of movement from the point in
the accretion disc to the point of scattering with large energy as well as the
time of back movement to the Earth are calculated. It is shown that they have
reasonable order.Comment: 13 pages, 2 figures, added some formulas and one referenc
Polarization of Thermal X-rays from Isolated Neutron Stars
Since the opacity of a magnetized plasma depends on polarization of
radiation, the radiation emergent from atmospheres of neutron stars with strong
magnetic fields is expected to be strongly polarized. The degree of linear
polarization, typically ~10-30%, depends on photon energy, effective
temperature and magnetic field. The spectrum of polarization is more sensitive
to the magnetic field than the spectrum of intensity. Both the degree of
polarization and the position angle vary with the neutron star rotation period
so that the shape of polarization pulse profiles depends on the orientation of
the rotational and magnetic axes. Moreover, as the polarization is
substantially modified by the general relativistic effects, observations of
polarization of X-ray radiation from isolated neutron stars provide a new
method for evaluating the mass-to-radius ratio of these objects, which is
particularly important for elucidating the properties of the superdense matter
in the neutron star interiors.Comment: 7 figures, to be published in Ap
Coronectomy of the mandibular third molar: a prospective study of 20 procedures
Oral surgeon in private practice, Plovdiv, Bulgaria, Oral and maxillofacial surgeon, Department of Oral Surgery, Faculty of Dental Medicine, Medical
University, Plovdiv, BulgariaSummary
Coronectomy is a surgical procedure designed to avoid the risk of iatrogenic neurological injury to the inferior alveolar nerve (IAN).
The aim of this study was to evaluate success rate of coronectomy.
Material and methods: Twenty patients underwent 20 coronectomy procedures of impacted mandibular third molar with close proximity to IAN evaluated
on preoperative radiographs. The procedure was performed under mandibular nerve block. Follow-up appointments were perform at 1 week, 1, 6 months.
Results: No patients developed IAN injury and no cases of root exposure were found. Eighteen wounds healed primary. In two cases the socket opened and
healed secondary. No one root fragments were removed.
Conclusion: Coronectomy of wisdom teeth is a safe technique - effective alternative to extraction, when the wisdom tooth shows radiographic signs of
close proximity of the IAN to the root
Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
We examine the completeness of bi-orthogonal sets of eigenfunctions for
non-Hermitian Hamiltonians possessing a spectral singularity. The correct
resolutions of identity are constructed for delta like and smooth potentials.
Their form and the contribution of a spectral singularity depend on the class
of functions employed for physical states. With this specification there is no
obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde
The X-ray Spectrum of the Vela Pulsar Resolved with Chandra
We report the results of the spectral analysis of two observations of the
Vela pulsar with the Chandra X-ray observatory. The spectrum of the pulsar does
not show statistically significant spectral lines in the observed 0.25-8.0 keV
band. Similar to middle-aged pulsars with detected thermal emission, the
spectrum consists of two distinct components. The softer component can be
modeled as a magnetic hydrogen atmosphere spectrum - for the pulsar magnetic
field G and neutron star mass and radius
km, we obtain \tef^\infty =0.68\pm 0.03 MK, erg s, pc (the
effective temperature, bolometric luminosity, and radius are as measured by a
distant observer). The effective temperature is lower than that predicted by
standard neutron star cooling models. A standard blackbody fit gives MK,
erg s ( is the distance in units of 250 pc); the blackbody
temperature corresponds to a radius, km, much
smaller than realistic neutron star radii. The harder component can be modeled
as a power-law spectrum, with parameters depending on the model adopted for the
soft component - , erg s and , erg s for the hydrogen atmosphere and blackbody soft
component, respectively ( is the photon index, is the luminosity
in the 0.2--8 keV band). The extrapolation of the power-law component of the
former fit towards lower energies matches the optical flux at --1.45.Comment: Submitted to ApJ, three figures; color figure 1 can be found at
http://www.xray.mpe.mpg.de/~zavlin/pub_list.htm
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