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## Nonrelativistic Case of Gravitational Lensing by Simple Cosmic String Loops

Cosmic strings are topologically stable, one-dimensional defects in vacuum which can appear during appropriate phase transitions in an adiabatically expanding early Universe which cools down from a very hot initial state. Their discovery would lead to advances in cosmology and fundamental physics. One of the most efficient ways to detect cosmic strings is related to their gravitational lensing signatures which appear to be different from those of standard lenses. We study a simple model of gravitational lensing by symmetric and asymmetric loops. An explicit form of the lens equation is obtained, and the relations for magnification are derived. We also discuss possible observational manifestations of cosmic strings within our model.

The conference was held in the form of lectures by leading scientists, oral and poster presentations of young scientists and students of physical specialties, as well as leaders of innovative structures for the purpose of mutual acquaintance with the new results of fundamental research on a wide range of areas in physics, the prospects and challenges in the expansion of relations between science , education and high technologies. **SECTION (heads):** I. LASERS (Fundam. Probl., Computer ...) (prof. A.A.Ionin) II. OPTICS (quant., And nano materials and new sources) (d.f.m.n.A.V.Masalov) III. Solid state physics, INCLUDING Nanostructures ELEM. BASE UNIT (Corresponding Member of RAS N.N.Sibeldin) IV. Nuclear physics, high energy physics (prof. O.D.Dalkarov, Head: Prof. V.A.Ryabov) V. PLASMA PHYSICS and particle beams (Head: Prof. A.V.Agafonov) VI. Astrophysics (Head: Prof. S.A.Bogachev) VII. PHYSICS IN THE MODERN INSTRUMENT AND TECHNOLOGY (prof. V.N.Nevolin)

The CRAYFIS experiment proposes to use privately owned mobile phones as a ground detector array for Ultra High Energy Cosmic Rays. Upon interacting with Earth’s atmosphere, these events produce extensive particle showers which can be detected by cameras on mobile phones. A typical shower contains minimally-ionizing particles such as muons. As these particles interact with CMOS image sensors, they may leave tracks of faintly-activated pixels that are sometimes hard to distinguish from random detector noise. Triggers that rely on the presence of very bright pixels within an image frame are not efficient in this case. We present a trigger algorithm based on Convolutional Neural Networks which selects images containing such tracks and are evaluated in a lazy manner: the response of each successive layer is computed only if activation of the current layer satisfies a continuation criterion. Usage of neural networks increases the sensitivity considerably comparable with image thresholding, while the lazy evaluation allows for execution of the trigger under the limited computational power of mobile phones.

Today we have the problem of big science data. The information collecting in science experiments, especially in bioinformatics and astrophysics grows in amazing rate. In this paper we consider special program techniques and computer technologies used for work with superlarge volumes of data. Also, we discuss the state of affairs with the big data in the Institute of Mathematical Problems of Biology RAS and in the Pushchino Radio Astronomy Observatory (Astro Space Center of Lebedev Physics Institute RAS).

Thanks to the first mm studies on the territory of the former USSR in the early 1960s and succeeding sub-mm measurements in the 1970s - early 1980s at wavelengths up to 0.34 mm, a completely unique astroclimate was revealed in the Eastern Pamirs, only slightly inferior to the available conditions on the Chajnantor plateau in Chile and Mauna Kea. Due to its high plateau altitude (4300 - 4500 m) surrounded from all sides by big (~7000 m) air-drying icy mountains and remoteness from oceans this area has the lowest relative humidity in the former USSR and extremely high atmospheric stability. In particular, direct measurements of precipitated water vapor in the winter months showed typical pwv=0.8 - 0.9 mm with sometimes of 0.27 mm. To validate previous studies and to compare them with results for other similar regions we performed opacity calculations at mm - sub-mm wavelengths for different sites in the Eastern Pamirs, Tibet, Indian Himalayas, APEX, ALMA, JCM, LMT and many others. To do this we integrate radiative transfer equations using the output of NASA Global Modeling and Assimilation Office model GEOS-FPIT for more than 12 years. We confirm previous conclusions about exceptionally good astroclimate in the Eastern Pamirs. Due to its geographical location, small infrastructure and the absence of any interference in radio and optical bands, this makes the Eastern Pamirs the best place in the Eastern Hemisphere for both optical and sub-mm astronomy.

The ground state of He–HCO+ is investigated using a recently developed double resonance technique, consisting of a rotational transition followed by a vibrational transition into a dissociative state. In order to derive precise predictions for the rotational states, the high resolution infrared predissociation spectroscopy of the v1 C–H stretching mode is revisited. Eleven pure rotational transitions are measured via the double resonance method. A least squares fit of these transitions to a standard linear rotor Hamiltonian reveals that the semirigid rotor model cannot fully describe the loosely bound He–HCO+ complex. The novel double resonance technique is compared with other action spectroscopic schemes, and some potential future applications are presented.

In Proceedings of the conference participants are presented on the following topics: 1) Lasers and Optics 2) Solid State Physics 3) Nuclear Physics 4) The generation and use of X-rays 5) Plasma Physics and particle beams 6) Astrophysics

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.