Abstract:
An approximation of the real line shape of a scintillation detector with a generalized gamma distribution is proposed. The approximation describes the ideal scintillation line shape better than the conventional normal distribution. Two parameters of the proposed function are uniquely defined by the first two moments of the detector response.

Abstract:
We find a new class of algebraic geometric solutions of Heun's equation with the accessory parameter belonging to a hyperelliptic curve. Dependence of these solutions from the accessory parameter as well as their relation to Heun's polynomials is studied. Methods of calculating the algebraic genus of the curve, and its branching points, are suggested. Monodromy group is considered. Numerous examples are given.

Abstract:
We find a new class of the Fuchsian equations, which have an algebraic geometric solutions with the parameter belonging to a hyperelliptic curve. Methods of calculating the algebraic genus of the curve, and its branching points, are suggested. Numerous examples are given.

Abstract:
The development of algorithms of management system’s work by the automated gear-boxes vehicles is considered and the results of their practical use on the example of the KamAZ truck are considered.

Abstract:
During the test measurements of the PMTs to be used in the future Borexino experiment, the data from 2200 PMT were accumulated. The unique timing characteristics of the apparatus used and the large statistics acquired, permit resololution of the fine structure of the ETL9351 PMT time response. A method to obtain the probability density function of the single photoelectron counting from the experimental data is proposed and applied to derive the PMT average characteristics. For the first time, an analytical model of the single photoelectron PMT time response is proposed, describing all the features of the single photoelectron time arrival. The origin of the small amplitude pulses is explained.

Abstract:
We study the possible manifestation of the interference between the effects produced in the atmospheric neutrinos due to oscillation driven by the solar parameters parameters $\Delta m^2_{21}$, $\sin^2 2\theta_{21}$ and due to oscillation driven by $U_{e3}$.

Abstract:
If active to active neutrino transitions are dominant modes of the atmospheric ($\nu_{\mu} \to \nu_{\tau}$) and the solar neutrino oscillations ($\nu_{e}\to \nu_{\mu}/\nu_{\tau}$), as is indicated by recent data, the favoured scheme which accommodates the LSND result - the so called (2+2)-scheme - should be discarded. We introduce the parameters $\eta_s^{atm}$ and $\eta_s^{sun}$ which quantify an involvement of the sterile component in the solar and atmospheric neutrino oscillations. The (2+2)-scheme predicts $\eta_s^{atm} + \eta_s^{sun} = 1$ and the experimental proof of deviation from this equality will discriminate the scheme. In this connection the (3+1)-scheme is revisited in which the fourth (predominantly sterile) neutrino is isolated from a block of three flavour neutrinos by the mass gap $\Delta m^2_{LSND} \sim (0.4-10)$ eV$^2$. We find that in the (3+1)-scheme the LSND result can be reconciled with existing bounds on $\nu_e$- and $\nu_{\mu}$ - disappearance at 95-99 % C.L.. The generic prediction of the scheme is the $\nu_e$- and $\nu_{\mu}$ - disappearance probabilities at the level of present experimental bounds. The possibility to strengthen the bound on $\nu_{\mu}$- disappearance in the KEK - front detector experiment is studied. We consider phenomenology of the (3 + 1)-scheme, in particular, its implications for the atmospheric neutrinos, neutrinoless double beta decay searches, supernova neutrinos and primordial nucleosynthesis.

Abstract:
We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. Recurrence relations following from integration by parts are solved explicitly and any given double box diagram is expressed as a linear combination of two master double boxes and a family of simpler diagrams. The first master double box corresponds to all powers of the propagators equal to one and no numerators, and the second master double box differs from the first one by the second power of the middle propagator. By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms $\Li{a}{-t/s}$, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration.

Abstract:
Neutrino oscillations with parameters relevant for the large mixing solution of the solar neutrino problem ($\Delta m^2_{21} = (2 - 20) \cdot 10^{-5}$ eV$^2$, $\sin^2 2\theta_{12} > 0.65$) can lead to observable (up to 10 - 12 %) excess of the e-like events in the sub-GeV atmospheric neutrino sample. The excess has a weak zenith angle dependence in the low energy part of the sample and strong zenith angle dependence in the high energy part. The effect rapidly decreases with energy of neutrinos, it is suppressed in the multi-GeV sample. These signatures allow to disentangle the effect from other possible explanations of the excess. The possibility of change of the sign of the up-down asymmetry of the excess with energy (positive in the sub-GeV region and negative in the multi-GeV region) is marked. The predicted properties of excess are in agreement with SuperKamiokande data.

Abstract:
There are several new features in production, oscillations and detection of the atmospheric neutrinos of low energies, E<100 MeV. The flavor ratio, r, of muon to electron neutrino fluxes is substantially smaller than 2 and decreases with energy, significant part of events is due to the decay of invisible muons at rest, etc. Oscillations in two-layer medium (atmosphere - earth) should be taken into account. We derive analytical and semi-analytical expressions for the oscillation probabilities of these "sub-subGeV" neutrinos. The energy spectra of the e-like events in water cherenkov detectors are computed and dependence of the spectra on the 2-3 mixing angle, the 1-3 mixing and CP-violation phase are studied. We find that variations of 2-3 mixing angle in the presently allowed region change the number of e-like events by about 15 - 20 % as well as to distortion of the energy spectrum. The 1-3 mixing and CP-violation can lead to ~10% effects. Detailed study of the sub-subGeV neutrinos will be possible in future Megaton-scale detectors.