Analysis of the time series in the space maser signals

We analyze the data of the observations of the radio sources frequently found in space. They are believed to be the sets of molecular condensations each of which works as a maser, so that the whole set produces a characteristic spectrum. It turns out that in some cases the intensity of one of the components of such spectrum corresponding to a single condensation changes periodically with a period of dozens of minutes or of hours.Comment: 5 pages, 6 figure

Two dimensional Berezin-Li-Yau inequalities with a correction term

We improve the Berezin-Li-Yau inequality in dimension two by adding a positive correction term to its right-hand side. It is also shown that the asymptotical behaviour of the correction term is almost optimal. This improves a previous result by Melas.Comment: 6 figure

Precision determination of absolute neutron flux

A technique for establishing the total neutron rate of a highly-collimated monochromatic cold neutron beam was demonstrated using a method of an alpha-gamma counter. The method involves only the counting of measured rates and is independent of neutron cross sections, decay chain branching ratios, and neutron beam energy. For the measurement, a target of 10B-enriched boron carbide totally absorbed the neutrons in a monochromatic beam, and the rate of absorbed neutrons was determined by counting 478keV gamma rays from neutron capture on 10B with calibrated high-purity germanium detectors. A second measurement based on Bragg diffraction from a perfect silicon crystal was performed to determine the mean de Broglie wavelength of the beam to a precision of 0.024 %. With these measurements, the detection efficiency of a neutron monitor based on neutron absorption on 6Li was determined to an overall uncertainty of 0.058 %. We discuss the principle of the alpha-gamma method and present details of how the measurement was performed including the systematic effects. We also describe how this method may be used for applications in neutron dosimetry and metrology, fundamental neutron physics, and neutron cross section measurements.Comment: 44 page

Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics

We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero-Sutherland type.Comment: 17 pages, LaTe

Aperiodically Poled Nonlinear Crystals as Sources of Multi-Frequency Laser Radiation

The new multi-frequency process, which consists of three coupled nonlinear optical interactions: two parametric down-conversions and one up-conversion, in aperiodically poled nonlinear crystal is investigated. The spatial dynamics of wave intensities is studied in detail. The possibility of secondary simplification of coupled equations for correct describing the dynamics of wave interactions is demonstrated. The optimal conditions for parametrical instability of the initial stage of wave interactions are found

The influence of non-vacuum electron-beam facing on the structure of Ti-Ta layers formed on the surface of VT1-0 alloy

The influence of electron-beam facing modes on the structure of Ti-Ta layers formed on the surface of commercially pure titanium VT1-0 has been studied in the paper. The mode of the electron-beam treatment of alloying powder mixture, by which there were no defects in the pad, has been identified. The methods of optical microscopy and scanning electron microscopy have shown that in pads there is dendritic segregation typical for the process of initial crystallisation. At greater magnifications it is possible to observe a structure of the laminar type. The X-ray phase analysis of titanium-tantalum layers justifies the presence of two phases: a hexagonal [alpha]'-phase and a cubic ([beta]-phase of titanium)

Lower order terms in Szego type limit theorems on Zoll manifolds

This is a detailed version of the paper math.FA/0212273. The main motivation for this work was to find an explicit formula for a "Szego-regularized" determinant of a zeroth order pseudodifferential operator (PsDO) on a Zoll manifold. The idea of the Szego-regularization was suggested by V. Guillemin and K. Okikiolu. They have computed the second term in a Szego type expansion on a Zoll manifold of an arbitrary dimension. In the present work we compute the third asymptotic term in any dimension. In the case of dimension 2, our formula gives the above mentioned expression for the Szego-redularized determinant of a zeroth order PsDO. The proof uses a new combinatorial identity, which generalizes a formula due to G.A.Hunt and F.J.Dyson. This identity is related to the distribution of the maximum of a random walk with i.i.d. steps on the real line. The proof of this combinatorial identity together with historical remarks and a discussion of probabilistic and algebraic connections has been published separately.Comment: 39 pages, full version, submitte