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

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

Studying of stowage massifs formation conditions in deep-laying rich KMA iron oxides developing and efficient stowage composition projection

On the example of Yakovlevsky iron-ore field which is characterized by composite hydro-geological and mining development conditions the natural monitoring technique of intense stowage massif strained state, which is formed in the descending layered dredging system of unstable rich iron oxides is proved and approve

Studies of Sensitivity to Avian Flu Virus A/H5N1 in Chickens

) appear to be highly virulent for chickens. The chance of AFV infection of chickens in case of intranasal challenge is 20 times as great as in the case of peroral one, and 300 times as great as in the case of intragastral one, which bears evidence to higher sensitivity to AFV of the tissues of avian respiratory organs, in comparison with the tissues of gastro-intestinal tract. Therewith, primary target organ for virus in intranasal infected birds is their respiratory channel (mucous membrane of the nasal cavity in particular). Registered is the possibility of existence of fecal-nasal AFV transfer mechanism in chickens

A theoretical model of a wake of a body towed in a stratified fluid at large Reynolds and Froude numbers

International audienceThe objective of the present paper is to develop a theoretical model describing the evolution of a turbulent wake behind a towed sphere in a stably stratified fluid at large Froude and Reynolds numbers. The wake flow is considered as a quasi two-dimensional (2-D) turbulent jet flow whose dynamics is governed by the momentum transfer from the mean flow to a quasi-2-D sinuous mode growing due to hydrodynamic instability. The model employs a quasi-linear approximation to describe this momentum transfer. The model scaling coefficients are defined with the use of available experimental data, and the performance of the model is verified by comparison with the results of a direct numerical simulation of a 2-D turbulent jet flow. The model prediction for the temporal development of the wake axis mean velocity is found to be in good agreement with the experimental data obtained by Spedding (1997)

Dissemination of Influenza A/H5N1 Virus after Intranasal Inoculation of Chickens

Studied was dissemination of avian influenza virus (AIV) in the organism of chickens after intranasal challenge with 10-100 LD50. The primary organ of accumulation of AIV A/H5N1 (A/Chicken/Kurgan/05/2005strain) is the respiratory tract (nasal mucosa), where the virus is registered in 18 hours after challenge. The accumulation of pathogen is observed in many organs and serum of chicken in 30-32 hours after challenge. The animals die in 54 hours, the concentration of virus reaches critical value in all studied samples. The highest AIV loads (7 lg of chicken embryo infective dose - EID50/g or ml) are registered in lungs, blood serum and kidneys of chicken. The results of AIV loads measuring using titration and real time RT-PCR show high degree of correlation (r=0.89)

MACHINE LEARNING INTERATOMIC POTENTIAL FOR AL

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