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The article presents new applications of bent crystals in accelerator science, which can stimulate new experiments in high-energy physics: particle channels of new type made for positive secondary particles and production of high-energy neutrino beams and a crystalline muon collider. Proposals were formulated for the use of crystals in large hadron colliders, which were confirmed by experimental studies both at CERN accelerators and at the domestic U-70 accelerator.

The article is devoted to the study of the suppression of multiple scattering of positively charged particles with momenta of 180 GeV/c and 400 GeV/c passing through bent single crystals of silicon at small angles to the plane (111) both in channeling mode and in the above-barrier state. For the first time, the suppression of the effect of multiple scattering of non-channeling particles passing at a small angle to one of the planes of a silicon single crystal was observed. In addition, the asymmetry was observed in the multiple scattering of over-barrier particles with respect to their zero angle of entry into the single crystal.

We present the experimental observation of the reduction of multiple scattering of high-energy positively charged particles during channeling in single crystals. According to our measurements the rms angle of multiple scattering in the plane orthogonal to the plane of the channeling is less than half that for non-channeled particles moving in the same crystal. In the experiment we use focusing bent single crystals. Such crystals have a variable thickness in the direction of beam propagation. This allows us to measure rms angles of scattering as a function of thickness for channeled and non-channeled particles. The behaviour with thickness of non-channeled particles is in agreement with expectations whereas the behaviour of channeled particles has unexpected features.

The Multi-Purpose Detector (MPD) is constructing to study the properties of the hot and dense matter created in heavy-ion collisions in the energy range of 4-11 A*GeV where the maximum baryonic density is expected. The crucial detector in the new experimental setup is a large-sized barrel electromagnetic calorimeter (ECal), designed for precise spatial and energy measurements for photons and electrons. Taking into account the requirements of high energy resolution, dense active medium with the small Moliere radius, and high segmentation of ECal, the Shashlyk-type electromagnetic calorimeter with projective geometry has been selected. The mass production of ECal modules has been started. In this talk, we report about methods and technologies for the quality control of ECal modules and their components.

Recently studies are started on the application of volume reflection of particles in crystals for the steering beams (for extraction and collimation of a circulating beam in accelerators). Volume reflection is more efficient than channeling, but requires amplification of the deflection angle by applying multicrystals. The report discusses two new applications of multicrystals made like multistrip structures: (i) the property of effective deflection of particle beam was used to protect the septum magnets of the U-70 in the process of extraction of the proton beam with energy of 50 GeV; (ii) the possibility of generation of gamma radiation was studied in the secondary electron beam with energy of 7 GeV. In both cases, promising preliminary data were obtained.

This article is devoted to the problem of construction of Hermite interpolation formulas with knots of the second multiplicity for second order partial differential operators given in the space of continuously differentiable functions of two variables. The obtained formulas contain the Gateaux differentials of a given operator. The construction of operator interpolation formulas is based on interpolation polynomials for scalar functions with respect to an arbitrary Chebyshev system of functions. An explicit representation of the interpolation error has been obtained.

The work is concerned with calculations and analysis of the maximum wind speed in Tomsk city. The data for analysis were taken from the TOR-station located in the north-eastern part of the city. The TOR-station sensors to measure a speed and a direction of wind are installed on the 10-meter meteorological mast. Wind is measured by M-63, which uses the standard approach and the program with one-minute averaging for wind gusts recording as well. According to the measured results in the research performed, the estimation of the dynamic and wind load on different types of antenna systems was performed. The work shows the calculations of wind load on ten types of antenna systems, distinguished by their different constructions and antenna areas. For implementation of calculations, we used methods developed in the Central Research and Development Institute of Building Constructions named after V.A. Kucherenko. The research results could be used for design engineering of the static antenna systems and mobile tracking systems for the distant objects.

For the work with polynomials such data representations as lists of terms, geobuckets, and heaps are usually used. In this paper, an attempt to give a new look on the representation of polynomials for computing involutive and Gröbner bases of systems of nonlinear polynomial equations is made. The proposed approach makes it possible to execute a part of this computational task on the GPU, which opens prospects for solving more complicated problems.

In the computation of involutive and Gröbner bases with rational coefficients, the major part of the memory is occupied by precision numbers; however, in the case of modular operations (especially, in the computation of Gröbner bases), of most importance is the problem of compact representation of monomials composing polynomials of the system. For this purpose, for example, ZDD diagrams and other structures are used, which make execution of typical operations—multiplication by a monomial and reduction of polynomials—more complicated. In this paper, an attempt is made to develop convenient (in the sense of computation of bases) and compact representation of polynomials that is based on hash-tables. Results of test runs are presented.

The carbon ion +6C beam with energy 25 GeV nucleon was extracted by bent crystal from the U-70 ring. The bent angle of silicon crystal was 85 mrad. About 2×105 particles for 109 circulated ions in the ring were observed in beam line 4a after bent crystal. Geometrical parameters, time structure and ion beam structure were measured. The ability of the bent monocrystal to extract and generate ion beam with necessary parameters for regular usage in physical experiments is shown in the first time.