Diurnal variations of cosmic ray geomagnetic cut-off threshold rigidities

The spectrographic global survey method was used to investigate the rigidity variations Rc of geomagnetic cut-off as a function of local time and the level of geomagnetic disturbance for a number of stations of the world wide network. It is shown that geomagnetic cut-off threshold rigidities undergo diurnal variations. The diurnal wave amplitude decreases with increasing threshold rigidity Rc, and the wave maximum occurs at 2 to 4 hr LT. The amplitude of diurnal variations increases with increasing geomagnetic activity. The results agree with those from trajectory calculations made for an asymmetric model of the magnetosphere during different geomagnetic disturbance conditions

Superanalogs of the Calogero operators and Jack polynomials

A depending on a complex parameter $k$ superanalog ${\mathcal S}{\mathcal L}$ of Calogero operator is constructed; it is related with the root system of the Lie superalgebra ${\mathfrak{gl}}(n|m)$. For $m=0$ we obtain the usual Calogero operator; for $m=1$ we obtain, up to a change of indeterminates and parameter $k$ the operator constructed by Veselov, Chalykh and Feigin [2,3]. For $k=1, \frac12$ the operator ${\mathcal S}{\mathcal L}$ is the radial part of the 2nd order Laplace operator for the symmetric superspaces corresponding to pairs $(GL(V)\times GL(V), GL(V))$ and $(GL(V), OSp(V))$, respectively. We will show that for the generic $m$ and $n$ the superanalogs of the Jack polynomials constructed by Kerov, Okunkov and Olshanskii [5] are eigenfunctions of ${\mathcal S}{\mathcal L}$; for $k=1, \frac12$ they coinside with the spherical functions corresponding to the above mentioned symmetric superspaces. We also study the inner product induced by Berezin's integral on these superspaces

On generalisations of Calogero-Moser-Sutherland quantum problem and WDVV equations

It is proved that if the Schr\"odinger equation $L \psi = \lambda \psi$ of Calogero-Moser-Sutherland type with $$L = -\Delta + \sum\limits_{\alpha\in{\cal A}_{+}} \frac{m_{\alpha}(m_{\alpha}+1) (\alpha,\alpha)}{\sin^{2}(\alpha,x)}$$ has a solution of the product form $\psi_0 = \prod_{\alpha \in {\cal {A}_+}} \sin^{-m_{\alpha}}(\alpha,x),$ then the function $F(x) =\sum\limits_{\alpha \in \cal {A}_{+}} m_{\alpha} (\alpha,x)^2 {\rm log} (\alpha,x)^2$ satisfies the generalised WDVV equations.Comment: 10 page

Thermodynamic properties of methyl 4-(4-methoxyphenyl)-6-methyl-2-oxo-1,2,3,4-tetrahydropyrimidine-5-carboxylate in organic solutions

The enthalpy and the entropy of dissolution of methyl 4-(4-methoxyphenyl)-6-methyl-2-oxo-1,2,3,4-tetrahydropyrimidine-5-carboxylate in 2-propanol, ethyl acetate, acetonitrile, 2-propanone and benzene were determined from the temperature dependence of its solubility.The enthalpies and the entropies of mixing at 298 K were calculated taking into account the enthalpy of melting of the compound, determined via differential thermal analysis.The influence of the solvent on the solubility of the compound and on the corresponding enthalpy and entropy of mixing values was shown

Study (301)-(000) D2O band in 10200 - 10450 cm-1 spectral region

Measurements of D2O absorption spectra in the visible spectral region near 0.98 μm are performed using FT-spectrometer IFS-125M and Light-emitting diode (LED) as source of radiation. Water vapor spectrum has been obtained by averaging over 17136 scans recorded at 24 m optical path length, temperature 24 С and pressure of sample 27 mBar. Due to strong emission of LED source it was possible to achieve signal-to-noise ratio about 104 and to record weak lines with intensities of 6 10-27 cm/molecule. Comparisons with results of early works are made. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

Influence of ion-beam treatment on structure and defor-mation resistance of 12Cr1MoV steel under static, cyclic and dynamic loading

Features of modification of structure and properties of 12Cr1MoV steel subjected to ion-beam irradiation by zirconium ion beam have been investigated with the use of optical and electron microscopy, and microhardness measurement. It was shown that after the treat-ment the modification occurs across the entire cross-section of specimens with the thickness of 1 mm. Changes in mechanical properties of these specimens under static, cyclic and impact loading were interpreted in terms of identified structure modifications