Abstract:
Proton linear accelerator is the base Accelerator Driven Power System (ADS). Such ADS are dedicated to various purposes: weapon plutonium conversion, "energy amplifier", transmutation of radionuclear wastes etc. Solution of these tasks requires proton beams with energy 1 GeV and average current up to 30 mA. At the moment there are no problems of fundamental nature in such linac construction. The main problems have economic and technical aspects. Problems of CW linac will be demonstrated on the base beam dynamics requirements. New code package LIDOS.RFQ.Designer makes possible to simulate beam dynamics in RF fields of real vane shape (including gaps between RFQ section) as well as to determine channel parameters tolerances for reliable operation

Abstract:
To follow is the problem on stationary states of an electron in its own gravitational field where the boundary conditions earlier described in [1] are made specific. The simplest approximation provides an assessment of the energy spectrum of stationary states only. Nevertheless, this is enough to confirm the existence of such stationary states and to further elaborate a detailed solution of the problem on stationary states including determination of all the quantum numbers’ spectra and corresponding wave functions. No other matters are discussed here. The case in hand is a purely mathematical problem, further physical interpretation of which is of a fundamental value.

Abstract:
Silicon Photomultipliers (SiPM), also so-called Solid State Photomultipliers (SSPM), are based on Geiger mode avalanche breakdown limited by strong negative feedback. SSPM can detect and resolve single photons due to high gain and ultra-low excess noise of avalanche multiplication in this mode. Crosstalk and afterpulsing processes associated with the high gain introduce specific excess noise and deteriorate photon number resolution of the SSPM. Probabilistic features of these processes are widely studied because of its high importance for the SSPM design, characterization, optimization and application, but the process modeling is mostly based on Monte Carlo simulations and numerical methods. In this study, crosstalk is considered to be a branching Poisson process, and analytical models of probability distribution and excess noise factor (ENF) of SSPM signals based on the Borel distribution as an advance on the geometric distribution models are presented and discussed. The models are found to be in a good agreement with the experimental probability distributions for dark counts and a few photon spectrums in a wide range of fired pixels number as well as with observed super-linear behavior of crosstalk ENF.

Abstract:
In this note we study the growth of \sum_{m=1}^M\frac1{\|m\alpha\|} as a function of M for different classes of \alpha\in[0,1). Hardy and Littlewood showed that for numbers of bounded type, the sum is \simeq M\log M. We give a very simple proof for it. Further we show the following for generic \alpha. For a non-decreasing function \phi tending to infinity, \limsup_{M\to\infty}\frac1{\phi(\log M)}\bigg[\frac1{M\log M}\sum_{m=1}^M\frac1{\|m\alpha\|}\bigg] is zero or infinity according as \sum\frac1{k\phi(k)} converges or diverges.

Abstract:
We describe some natural relations connecting contact geometry, classical Monge-Ampere equations and theory of singularities of solutions to nonlinear PDEs. They reveal the hidden meaning of Monge-Ampere equations and sheds new light on some aspects of contact geometry.

Abstract:
We show that given $n$ normalized intervals on the unit circle, the numbers of visits of $d$ random rotations to these intervals have a joint limiting distribution as lengths of trajectories tend to infinity. If $d$ then tends to infinity, then the numbers of points in different intervals become asymptotically independent unless an arithmetic obstruction arises. This is a generalization of earlier results of J. Marklof.

Abstract:
Let \Gamma<\PSL(2,\C) be a geometrically finite non-elementary discrete subgroup, and let its critical exponent \delta\ be greater than 1. We use representation theory of \PSL(2,\C) to prove an effective bisector counting theorem for \Gamma, which allows counting the number of points of \Gamma\ in general expanding regions in \PSL(2,\C) and provides an explicit error term. We apply this theorem to give power savings in the Apollonian circle packing problem and related counting problems.

Abstract:
We survey recent results beyond equidistribution of sequences modulo one. We focus on the sequence of angles in a Euclidean lattice in $\mathbb R^2$ and on the sequence $\sqrt n\bmod1 $.

Abstract:
In this paper, we propose a flexible and fairness-oriented packet scheduling approach for 3GPP UTRAN long term evolution (LTE) type packet radio systems, building on the ordinary proportional fair (PF) scheduling principle and channel quality indicator (CQI) feedback. Special emphasis is also put on practical feedback reporting mechanisms, including the effects of mobile measurement and estimation errors, reporting delays, and CQI quantization and compression. The performance of the overall scheduling and feedback re-porting process is investigated in details, in terms of cell throughput, coverage and resource allocation fairness, by using extensive quasistatic cellular system simulations in practical OFDMA system environment with frequency reuse of 1. The performance simulations show that by using the proposed modified PF ap-proach, significant coverage improvements in the order of 50% can be obtained at the expense of only 10-15% throughput loss, for all reduced feedback reporting schemes. This reflects highly improved fairness in the radio resource management (RRM) compared to other existing schedulers, without essentially com-promising the cell capacity. Furthermore, we demonstrate the improved functionality increase in radio re-source management for UE’s utilizing multi-antenna diversity receivers.

Abstract:
Surface waters of eutrophic bogs (fens) in the North-Siberian (Taimyr) lowland are characterized by hydrocarbonate, sulfate as well as hydro carbonate-sulfate calcium-magnesium composition. They relate to the type of oxygen waters, mainly, to the class of neutral weakly alkaline and to the family of ultrafresh and fresh waters and to the kind of waters poor with dissolved organic matter. Natural hydrochemical background of bog ecosystems makes in heavy metals in the first approximation: Co–0.16, Pb–0.57, Ni–4.67 and Cu–5.94 mkg/L. In most cases the surface waters are not polluted by heavy metals. Bog waters located in immediate closeness from Norilsk mining and smelting industrial complex are polluted by nickel at mid-level.