1,471 research outputs found
A family of anisotropic integral operators and behaviour of its maximal eigenvalue
We study the family of compact integral operators in
with the kernel K_\beta(x, y) = \frac{1}{\pi}\frac{1}{1 +
(x-y)^2 + \beta^2\Theta(x, y)}, depending on the parameter , where
is a symmetric non-negative homogeneous function of degree
. The main result is the following asymptotic formula for the
maximal eigenvalue of : M_\beta = 1 - \lambda_1
\beta^{\frac{2}{\gamma+1}} + o(\beta^{\frac{2}{\gamma+1}}), \beta\to 0, where
is the lowest eigenvalue of the operator . A central role in the proof is played by the fact that
is positivity improving. The case has been studied earlier in the literature as a simplified model
of high-temperature superconductivity.Comment: 16 page
The quality of gosling meat depending on the level of lithium in mixed fodders
Micronutrients are an important component of a complete poultry feeding. Current detailed feeding standards provide guaranteed feed additives for farm poultry of the microelement complex. Among the normalized microelements there is no lithium, which according to the classification based on biological role for living organisms belongs to the group of conditionally essential elements. The purpose of the study was to investigate the effect of various doses of lithium in compound feed on the chemical composition and toxicological and biological parameters of caterpillar meat. The effect of additives of different doses of lithium (0.05 mg/kg, 0.10 and 0.15 mg/kg) in compound forages on the quality and safety of the products of slaughter of 70-day gosling was studied. The studies were conducted on gosling of the Legart breed. Feeding of gosling from day to 70 days of age was carried out by full-feed compound feeds. The birds of the experimental groups were additionally injected with lithium in the feed, mg/kg: the second group was 0.05; third – 0.10 and fourth – 0.15. The gosling of the control group did not receive lithium. Analysis of the results of the studies revealed differences between the control and experimental groups in the chemical composition of the muscular tissue of the gosling in favor of the latter. It was found that the introduction of lithium compound feed had a positive effect on the deposition of dry matter, protein and fat in the gosling of the experimental groups, which contributed to its increased energy and biological value. The best indicators of meat quality were in young animals, which during the growing period were fed compound feeds enriched with lithium at the rate of 0.1 and 0.15 mg/kg
Sources of Radiation in the Early Universe: The Equation of Radiative Transfer and Optical Distances
We have derived the radiative-transfer equation for a point source with a
specified intensity and spectrum, originating in the early Universe between the
epochs of annihilation and recombination, at redshifts z_\s =10^8\div 10^4.
The direct radiation of the source is separated from the diffuse radiation it
produces. Optical distances from the source for Thomson scattering and
bremsstrahlung absorption at the maximum of the thermal background radiation
are calculated as a function of the redshift z.The distances grow sharply with
decreasing z, approaching asymptotic values, the absorption distance increasing
more slowly and reaching their limiting values at lower z. For the adopted z
values, the optical parameters of the Universe can be described in a flat model
with dusty material and radiation, and radiative transfer can be treated in a
grey approximation.Comment: 14 pages, 2 figure
Molecular hydrogen in the cosmic recombination epoch
The advent of precise measurements of the cosmic microwave background (CMB)
anisotropies has motivated correspondingly precise calculations of the cosmic
recombination history. Cosmic recombination proceeds far out of equilibrium
because of a "bottleneck" at the level of hydrogen: atoms can only reach
the ground state via slow processes: two-photon decay or Lyman-
resonance escape. However, even a small primordial abundance of molecules could
have a large effect on the interline opacity in the recombination epoch and
lead to an additional route for hydrogen recombination. Therefore, this paper
computes the abundance of the H molecule during the cosmic recombination
epoch. Hydrogen molecules in the ground electronic levels X can
either form from the excited H electronic levels B and
C or through the charged particles H, HeH and H. We
follow the transitions among all of these species, resolving the rotational and
vibrational sub-levels. Since the energies of the
X--B (Lyman band) and X-C
(Werner band) transitions are near the Lyman- energy, the distortion of
the CMB spectrum caused by escaped H Lyman-line photons accelerates both the
formation and the destruction of H due to this channel relative to the
thermal rates. This causes the populations of H molecules in
X energy levels to deviate from their thermal equilibrium
abundances. We find that the resulting H abundance is at
and at , which is too small to have any significant
influence on the recombination history.Comment: 13 pages, 10 figures, to be submitted to PR
Two-photon transitions in primordial hydrogen recombination
The subject of cosmological hydrogen recombination has received much
attention recently because of its importance to predictions for and
cosmological constraints from CMB observations. While the central role of the
two-photon decay 2s->1s has been recognized for many decades, high-precision
calculations require us to consider two-photon decays from the higher states
ns,nd->1s (n>=3). Simple attempts to include these processes in recombination
calculations have suffered from physical problems associated with sequences of
one-photon decays, e.g. 3d->2p->1s, that technically also produce two photons.
These correspond to resonances in the two-photon spectrum that are optically
thick, necessitating a radiative transfer calculation. We derive the
appropriate equations, develop a numerical code to solve them, and verify the
results by finding agreement with analytic approximations to the radiative
transfer equation. The related processes of Raman scattering and two-photon
recombination are included using similar machinery. Our results show that early
in recombination the two-photon decays act to speed up recombination, reducing
the free electron abundance by 1.3% relative to the standard calculation at
z=1300. However we find that some photons between Ly-alpha and Ly-beta are
produced, mainly by 3d->1s two-photon decay and 2s->1s Raman scattering. At
later times these photons redshift down to Ly-alpha, excite hydrogen atoms, and
act to slow recombination. Thus the free electron abundance is increased by
1.3% relative to the standard calculation at z=900. The implied correction to
the CMB power spectrum is neligible for the recently released WMAP and ACBAR
data, but at Fisher matrix level will be 7 sigma for Planck. [ABRIDGED]Comment: Matches PRD accepted version. 28 pages, 12 figure
How do methanol masers manage to appear in the youngest star vicinities and isolated molecular clumps?
General characteristics of methanol (CH3OH) maser emission are summarized. It
is shown that methanol maser sources are concentrated in the spiral arms. Most
of the methanol maser sources from the Perseus arm are associated with embedded
stellar clusters and a considerable portion is situated close to compact HII
regions. Almost 1/3 of the Perseus Arm sources lie at the edges of optically
identified HII regions which means that massive star formation in the Perseus
Arm is to a great extent triggered by local phenomena. A multiline analysis of
the methanol masers allows us to determine the physical parameters in the
regions of maser formation. Maser modelling shows that class II methanol masers
can be pumped by the radiation of the warm dust as well as by free-free
emission of a hypercompact region hcHII with a turnover frequency exceeding 100
GHz. Methanol masers of both classes can reside in the vicinity of hcHIIs.
Modelling shows that periodic changes of maser fluxes can be reproduced by
variations of the dust temperature by a few percent which may be caused by
variations in the brightness of the central young stellar object reflecting the
character of the accretion process. Sensitive observations have shown that the
masers with low flux densities can still have considerable amplification
factors. The analysis of class I maser surveys allows us to identify four
distinct regimes that differ by the series of their brightest lines.Comment: 8 pages, 4 figures, invited presentation at IAU242 "Astrophysical
Masers and their environments
Methanol in W3(H2O) and Surrounding Regions
We present the results of an interferometric study of 38 millimeter-wave
lines of CH3OH in the region around the water maser source W3(H2O) and a region
extending about 30" to the south and west of the hydroxyl maser source W3(OH).
The methanol emitting region around W3(H2O) has an extent of 2.0" x 1.2"
(4400 x 2600 AU). The density is of order 1.e7 cm-3, sufficient to thermalize
most of the methanol lines. The kinetic temperature is approximately 140 K and
the methanol fractional abundance greater than 1.e-6, indicative of a high
degree of grain mantle evaporation. The W3(H2O) source contains sub-structure,
with peaks corresponding to the TW source and Wyrowski's B/C, separated by 2500
AU in projection. The kinematics are consistent with these being distinct
protostellar cores in a wide binary orbit and a dynamical mass for the region
of a few tens of Mo.
The extended methanol emission to the southwest of W3(OH) is seen strongly
only from the lowest excitation lines and from lines known elsewhere to be
class I methanol masers, namely the 84.5 GHz 5(-1)-4(0)E and 95.2 GHz
8(0)-7(1)A+ lines. Within this region there are two compact clumps, which we
denote as swA and swB, each about 15" (0.16 pc projected distance) away from
W3(OH). Excitation analysis of these clumps indicates the presence of lines
with inverted populations but only weak amplification. The sources swA and swB
appear to have kinetic temperatures of order 50-100 K and densities of order
1.e5 - 1.e6 cm-3. The methanol fractional abundance for the warmer clump is of
order 1.e-7, suggestive of partial grain mantle evaporation. The clumping
occurs on mass scales of order 1 Mo.Comment: 28 pages including 6 figures and 4 tables, accepted by Ap
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