A family of anisotropic integral operators and behaviour of its maximal eigenvalue

We study the family of compact integral operators $\mathbf K_\beta$ in $L^2(\mathbb R)$ 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 $\beta >0$, where $\Theta(x, y)$ is a symmetric non-negative homogeneous function of degree $\gamma\ge 1$. The main result is the following asymptotic formula for the maximal eigenvalue $M_\beta$ of $\mathbf K_\beta$: M_\beta = 1 - \lambda_1 \beta^{\frac{2}{\gamma+1}} + o(\beta^{\frac{2}{\gamma+1}}), \beta\to 0, where $\lambda_1$ is the lowest eigenvalue of the operator $\mathbf A = |d/dx| + \Theta(x, x)/2$. A central role in the proof is played by the fact that $\mathbf K_\beta, \beta>0,$ is positivity improving. The case $\Theta(x, y) = (x^2 + y^2)^2$ has been studied earlier in the literature as a simplified model of high-temperature superconductivity.Comment: 16 page

The Remarkable Mid-Infrared Jet of Massive Young Stellar Object G35.20-0.74

The young massive stellar object G35.20-0.74 was observed in the mid-infrared using T-ReCS on Gemini South. Previous observations have shown that the near infrared emission has a fan-like morphology that is consistent with emission from the northern lobe of a bipolar radio jet known to be associated with this source. Mid-infrared observations presented in this paper show a monopolar jet-like morphology as well, and it is argued that the mid-infrared emission observed is dominated by thermal continuum emission from dust. The mid-infrared emission nearest the central stellar source is believed to be directly heated dust on the walls of the outflow cavity. The hydroxyl, water, and methanol masers associated with G35.20-0.74 are spatially located along these mid-infrared cavity walls. Narrow jet or outflow cavities such as this may also be the locations of the linear distribution of methanol masers that are found associated with massive young stellar objects. The fact that G35.20-0.74 has mid-infrared emission that is dominated by the outflow, rather than disk emission, is a caution to those that consider mid-infrared emission from young stellar objects as only coming from circumstellar disks.Comment: Accepted for publication in ApJ Letters; 4 pages; 2 figures; a version with full resolution images is available here: http://www.ctio.noao.edu/~debuizer

On the accuracy of the ALI method for solving the radiative transfer equation

We solve the integral equation describing the propagation of light in an isothermal plane-parallel atmosphere of optical thickness $\tau^*$, adopting a uniform thermalization parameter $\epsilon$. The solution given by the ALI method, widely used in the field of stellar atmospheres modelling, is compared to the exact solution. Graphs are given that illustrate the accuracy of the ALI solution as a function of the parameters $\epsilon$, $\tau^*$ and optical depth variable $\tau$.Comment: 7 pages, 11 figures, A&A, accepted 30 July 2003, minor correction

THE MACROKINETICS PARAMETERS OF THE HYDROCARBONS COMBUSTION IN THE NUMERICAL CALCULATION OF ACCIDENTAL EXPLOSIONS IN MINES

Purpose. Obtaining effective parameters of the macrokinetics of combustion of hydrocarbons in the deflagration and detonation regime for the numerical calculation of emergency explosions in mine workings. Methodology. Mathematical modeling, numerical experiment, kinetics analysis of explosive combustion reaction, analysis and synthesis. Findings. The paper analyzes the parameters of the kinetic equation against experimental data. Obtaining such data in a physical experiment for explosive chemical reactions meets serious difficulties. This is due to the size of the reaction zone not exceeding fractions of a millimeter, the lack of time resolution of experimental techniques and other factors leading to errors in direct measurements and the emergence of multiple solutions. This possibility contributes to obtaining a simultaneous numerical solution of the equations of gas dynamics and chemical kinetics. In the numerical experiment, a direct relationship between the macrokinetic characteristics of the chemical reaction and the parameters of the discontinuous flow of the reacting gas stream is established: velocity, pressure in the front and behind the front of the detonation and deflagration wave. Based on this, Arrhenius characteristics of the reaction – preexponential and effective activation energy for the hydrocarbons under consideration are obtained. Originality. Macrokinetic parameters are established for simulating one-stage ignition and burning of the most probable hydrocarbons of the mine atmosphere in the deflagration and detonation regime. Modeling of explosive combustion of premixed hydrocarbons in stoichiometric concentrations is performed. It is shown that the values of the effective activation energy in explosive combustion reactions are of less importance in contrast to steady-state combustion reactions because of the effect of the gas-dynamical effects of the shock wave on the reaction rate. The Arrhenius characteristics of the reaction – the pre-exponential and the effective activation energy – have been agreed upon, according to the gas dynamic and kinetic parameters of the course of the explosive combustion reaction. Practical value. The obtained parameters of the macrokinetics of the explosive combustion reaction make it possible to apply simple kinetic mechanisms in practical calculations of the processes of deflagration and detonation combustion, and to predict the parameters of emergency explosions in conditions of mine workings with sufficient accuracy. This also makes it possible to solve the problem of accounting for the presence of heavy hydrocarbons in themine atmosphere as products of coal pyrolysis in underground fires as factors of increasing the risk of emergency explosions

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

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

Bethe-Sommerfeld conjecture for periodic operators with strong perturbations

We consider a periodic self-adjoint pseudo-differential operator $H=(-\Delta)^m+B$, $m>0$, in $\R^d$ which satisfies the following conditions: (i) the symbol of $B$ is smooth in \bx, and (ii) the perturbation $B$ has order less than $2m$. Under these assumptions, we prove that the spectrum of $H$ contains a half-line. This, in particular implies the Bethe-Sommerfeld Conjecture for the Schr\"odinger operator with a periodic magnetic potential in all dimensions.Comment: 61 page

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

Buy, sell, or hold? A sense-making account of factors influencing trading decisions

We investigated the effects of news valence, the direction of trends in graphically presented price series, and the culture and personality of traders in a financial trading task. Participants were given 12 virtual shares of financial assets and asked to use price graphs and news items to maximize their returns by buying, selling, or holding each one. In making their decisions, they were influenced by properties of both news items and price series but they relied more on the former. Western participants had lower trading latencies and lower return dispersions than Eastern participants. Those with greater openness to experience had lower trading latencies. Participants bought more shares when they forecast that prices would rise but failed to sell more when they forecast that they would fall. These findings are all consistent with the view that people trading assets try to make sense of information by incorporating it within a coherent narrative