Wiener-Hopf operators in higher dimensions: the Widom conjecture for piece-wise smooth domains

We prove a two-term quasi-classical trace asymptotic formula for the functions of multi-dimensional Wiener-Hopf operators with discontinuous symbols. The discontinuities occur on the surfaces which are assumed to be piece-wise smooth. Such a two-term formula was conjectured by H. Widom in 1982, and proved by A. V Sobolev for smooth surfaces in 2009.Comment: 15 page

On a coefficient in trace formulas for Wiener-Hopf operators

Let $a = a(\xi), \xi\in\mathbb R,$ be a smooth function quickly decreasing at infinity. For the Wiener-Hopf operator $W(a)$ with the symbol $a$, and a smooth function $g:\mathbb C\to~\mathbb C$, H. Widom in 1982 established the following trace formula: $${\rm tr}\bigl(g\bigl(W(a)\bigr) - W(g\circ a)\bigr) = \mathcal B(a; g),$$ where $\mathcal B(a; g)$ is given explicitly in terms of the functions $a$ and $g$. The paper analyses the coefficient $\mathcal B(a; g)$ for a class of non-smooth functions $g$ assuming that $a$ is real-valued. A representative example of one such function is $g(t) = |t|^{\gamma}$ with some $\gamma\in (0, 1]$.Comment: 21 page

On the Class II Methanol Maser Periodic Variability due to the Rotating Spiral Shocks in the Gaps of Disks Around Young Binary Stars

We argue that the periodic variability of Class II methanol masers can be explained by variations of the dust temperature in the accretion disk around proto-binary star with at least one massive component. The dust temperature variations are caused by rotation of hot and dense material of the spiral shock wave in the disk central gap. The aim of this work is to show how different can be the Class II methanol maser brightness in the disk during the Moment of Maximum Illumination by the Spiral Shock material (hereafter MMISS) and the Moment when the disk is Illuminated by the Stars Only (MISO). We used the code CLOUDY (v13.02) to estimate physical conditions in the flat disk in the MISO and the MMISS. Model physical parameters of the disk were then used to estimate the brightness of 6.7, 9.9, 12.1 and 107 GHz masers at different impact parameters $p$ using LVG approximation. It was shown that the strong masers experience considerable brightness increase during the MMISS with respect to MISO. There can happen both flares and dips of the 107 GHz maser brightness under the MMISS conditions, depending on the properties of the system. The brightest 9.9 GHz masers in the MMISS are situated at the greater $p$ than the strong 6.7, 12.1 and 107 GHz masers that are situated at $p<200$ AU. The brightness of 9.9 GHz maser in the MMISS suppressed at $p<200$ AU and increase at $p>200$ AU.Comment: Accepted for publication in MNRAS, 9 figure

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

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 Spectral Type of the Ionizing Stars and the Infrared Fluxes of HII Regions

The 20 cm radio continuum fluxes of 91 HII regions in a previously compiled catalog have been determined. The spectral types of the ionizing stars in 42 regions with known distances are estimated. These spectral types range from B0.5 to O7, corresponding to effective temperatures of 29 000-37 000 K. The dependences of the infrared (IR) fluxes at 8, 24, and 160 $\mu$m on the 20 cm flux are considered. The IR fluxes are used as a diagnostic of heating of the matter, and the radio fluxes as measurements of the number of ionizing photons. It is established that the IR fluxes grow approximately linearly with the radio flux. This growth of the IR fluxes probably indicates a growth of the mass of heated material in the envelope surrounding the HII region with increasing effective temperature of the star.Comment: 16, pages, 10 figures, published in Astronomy Report

Database of Molecular Masers and Variable Stars

We present the database of maser sources in H2O, OH and SiO lines that can be used to identify and study variable stars at evolved stages. Detecting the maser emission in H2O, OH and SiO molecules toward infrared-excess objects is one of the methods of identification long-period variables (LPVs, including Miras and Semi-Regular), because these stars exhibit maser activity in their circumstellar shells. Our sample contains 1803 known LPV objects. 46% of these stars (832 objects) manifest maser emission in the line of at least one molecule: H2O, OH or SiO. We use the database of circumstellar masers in order to search for long-periodic variables which are not included in the General Catalogue of Variable Stars (GCVS). Our database contains 4806 objects (3866 objects without associations in GCVS catalog) with maser detection in at least one molecule. Therefore it is possible to use the database in order to locate and study the large sample of long-period variable stars. Entry to the database at http://maserdb.netComment: Accepted for publication in RA