2304-9782, 2618-8686, 2405-7223 2 242 2016

RAR RUS 9-18 Romanov Nikolay nikromanov.90@gmail.com Peter the Great St. Petersburg Polytechnic University Zakharova Irina zakharova@rhpf.spbstu.ru The composition and the structure of thin films based on metal porphyrin complexes Thin films based on CuTPP, ZnTPP and FeClTPP (ТРР – TetraPhenylPorphyrin) complexes and manufactured by vacuum deposition under quasi-equilibrium conditions have been investigated. The hot-wall epytaxy method was chosen for the preparation of samples. The structure of objects and their composition were examined by scanning electron microscopy (SEM) and energy dispersive microanalysis (EDX). The CuTPP film was established to form whiskers about 20 nm in diameter and 5 μm in length. The structural features and morphology of ZnTPP and FeClTPP films’ surface were revealed. The theoretical interpretation of obtained results was proposed that made possible to relate the film structure with its composition. 10.5862/JPM.242.1 538.951 organic electronics thin film metal-porphyrin complex https://physmath.spbstu.ru/article/2016.32.1/ 01_9_18_2_242_2016.pdf

RAR RUS 19-26 Slutsker Alexander Polykarpov Yuri Peter the Great St. Petersburg Polytechnic University Karov Dmitry dmkarov@yandex.ru Elastic strain energy behavior in the polymer nanocrystals In the paper, the changes in the axial and the contour lengths of skeletal interatomic bonds in the chain molecules of polyethylene nanocrystals have been measured using X-ray diffractometry and Raman spectrometry. In the course of the measurements the samples were subjected to stretching and heating (mechanical and thermal actions). The measured force and temperature dependences were analyzed and the calculated description of the polymer nanocrystal’s strain was inferred from them. In so doing the original results were obtained for the thermal action. The potential energy components related to both the skeletalbond stretching and the chain-molecule bending were determined for the strained polymer crystal. The sharp distinction between the ratios of these components for the object under mechanical and thermal actions was found. 10.5862/JPM.242.2 536.4, 539.3 stretching heating axial length of chain molecule potential energy https://physmath.spbstu.ru/article/2016.32.2/ 02_19_26_2_242_2016.pdf

RAR RUS 27-36 Pankin Dmitry dima-pankin@mail.ru Smirnov Mikhail smirnomb@rambler.ru The applicability of Raman spectroscopy for estimation of interfaces thickness in the AlN/GaN superlattices Polar optical phonons in quaternary nitride-based superlattices have been investigated in the framework of dielectric continuum model. In the considered systems, the superlattice period consisted of two main layers GaN and AlN and two interstitial layers Al0.5Ga0.5N. Such structure simulates binary superlattices with diffuse interfaces. The presence of the finite thickness interface layers was shown to give rise to appearance of several low-intensity additional phonon modes active in Raman scattering; frequency splitting of such modes is sensitive to relative thickness of intermediate layers. The fundamental Raman-intense polar phonon modes were also stated to be independent on the interface thickness, and these modes being very sensitive to the main layer thicknesses. 10.5862/JPM.242.3 538.911 polar phonon dielectric continuum model nitride-based superlattice https://physmath.spbstu.ru/article/2016.32.3/ 03_27_36_2_242_2016.pdf

RAR RUS 37-43 Nelasov Ivan nelasow@bsu.edu.ru Lipnitskii Aleksey lipnitskii@bsu.edu.ru The study of Cu/Nb interface diffusion using molecular dynamics simulation The peculiarities of interfacial boundary diffusion where the boundary goes between nonmiscible metals with body-centered cubic (BCC) and face-centered cubic (FCC)lattices have been studied taking, as a case in point, the Cu/Nb system, and using the molecular dynamics method. The diffusion atomic displacements were shown to occur mainly near the mismatch dislocations and their intersections. The diffusion of the high-melting component was found to be characterized by high anisotropy with the predominant atomic displacement along the dense-packed direction in the interfacial boundary plane being common to FCC and BCC lattices with the Kurdyumov-Sachs mutual orientation. 10.5862/JPM.242.4 539.219.3 interface diffusion copper-niobium. molecular dynamics Kurdyumov-Sachs mutual orientation https://physmath.spbstu.ru/article/2016.32.4/ ph_2_2016.37_43.pdf

RAR RUS 44-54 Kartamyshev Andrey andrei_kart@mail.ru Dat Duy duydat_bel@yahoo.com Lipnitskii Aleksey lipnitskii@bsu.edu.ru The interactions between some impurity atoms and vacancies in titanium and aluminum metals: an ab initio study In this paper, we present binding energies between an atom of hydrogen (H), carbon (C), nitrogen (N) and oxygen (O) with a vacancy in the hexagonal closedpacked (HCP) lattice of titanium (Ti) and the face centered cubic (FCC) lattice of aluminum (Al), calculated using the density functional theory (DFT). We have also investigated the trapping of up to five hydrogen atoms by a vacancy and the reduction of the vacancy formation energy, due to the formation of a hydrogen–vacancy complex. We used the molecular-dynamics modeling with consecutive relaxation at 0 K to obtain an atomic configuration of the vacancy–impurity complex, corresponding to the global energy minimum. According to our calculations, C–V, H–V, C–(H–V), N–(H–V) complexes are stable in the Al lattice with only H–V complex being stable in Ti. The formation of C–(H–V) and N–(H–V) complexes in the Al lattice results in the negative vacancy formation energy. The formation of H–V complex decreases the vacancy formation energy by 0.26 eV in the Ti lattice. A vacancy in the Ti lattice can trap up to four hydrogen atoms. 10.5862/JPM.242.5 538.9 titanium aluminium vacancy impurity density functional theory https://physmath.spbstu.ru/article/2016.32.5/ ph_2_2016.44_54.pdf

RAR RUS 55-64 Pavlov Vladimir vova-gt@yandex.ru 0000-0002-6162-9481 Peter the Great St. Petersburg Polytechnic University Krasnova Nadezhda n.k.krasnova@mail.ru Synthesis of electrostatic fields for transportation of charged particle beams In the article, an approach to creation of corpuscular-optical devices for transportation and transformation of charged particle beams has been elucidated. These devices are able to optimize and create the most convenient configuration of ionic or electron path. The approach relies upon the inverse dynamics problem formulated on a basis of the Hamilton-Jacobi equation. The motion in the symmetry plane of a threedimensional (3D) field was considered. The problem was solved by analytical methods. An algorithm for construction electric fields providing the particle motion on the desired trajectories was described. А key to this algorithm lies with a concept of conformal transformation from complex variable theory. This procedure was illustrated by examples. Quadratic potential was chosen as a basis. Three functions of conformal transformation were considered, they providing the rotation of the focused charged particle beam at fixed angle, the transformation of divergent flow to parallel one. The calculated two-dimensional potentials were extended into 3D-space by power series expansion on transverse coordinate. Device embodiments were suggested on a basis of the calculated field structures. 10.5862/JPM.242.6 537.533.3:537.291 inverse dynamics problem charged particle optics conformal transformation ideal focusing https://physmath.spbstu.ru/article/2016.32.6/ ph_2_2016.55_64.pdf

RAR RUS 65-71 0000-0002-4363-9352 Peter the Great St. Petersburg Polytechnic University Korablev Vadim korablev@spbstu.ru 57193675419 Peter the Great St. Petersburg Polytechnic University Dubov Victor dubov@spbstu.ru The formation of the angular dependences of the inelastically scattered electrons by their quantum transport near the surface of a solid Features of the formation of angular dependences of electrons emitted from a disordered solid and experienced inelastic scattering have been considered. Such fine details of the dependences are formed by the processes of the quantum transport of emitted particles. We took the cases of two-particle and multi-particle inelastic processes. Qualitative and quantitative assessments of the relative contributions of the different groups of particles were carried out. The effects related to quantum electron transport were shown to be generally more pronounced in the case of registration of electrons, generated inside the solid in the inelastic scattering of particles of the primary beam. This is true both to the electrons generated by ionization processes and Auger electrons. The obtained results point up the possibility of using this effect in the applied electron spectroscopy. 10.5862/JPM.242.7 530.145+539.1 electron scattering quantum transport weak localization surface of a solid https://physmath.spbstu.ru/article/2016.32.7/ ph_2_2016.65_71.pdf

RAR RUS 72-81 Egorova Polina bio_polya@mail.ru Peter the Great St. Petersburg Polytechnic University Vlasova Olga olvlasova@yandex.ru O-7971-2016 7006214225 0000-0001-7006-6951 UT Southwestern Med Ctr, Dept Physiol Bezprozvanny Ilya mnlabspb@gmail.com

Dallas, USA

The limitation of the Purkinje cell’s impulse activity in the laboratory mice’s vermis by in vivo activation of SK channels This study tested the effect of intravenous injections of CyPPA [the activator of small conductance calcium-activated potassium channels of types 2 and 3 (SK2/SK3)] on the firing frequency of cerebellar Purkinje cells of laboratory male mice at the age of 6 months via the method of extracellular in vivo recordings from Purkinje cells. This method revealed that 1 mM CyPPA tail vein injections lead to progressive reduction of Purkinje cells firing frequency. Thus, simple spike’s firing frequency decreases by 16% in one hour after injection, by 49% in two hours after injection, and by 61% in three hours. The obtained results confirmed the hypothesis about the important role of SK channels in the maintenance of Purkinje cells spontaneous activity in vivo. Since deterioration of biophysical and physiological functions is observed in many cerebellar ataxias, SK channels can serve as a potential target for the treatment of such disorders. 10.5862/JPM.242/8 577.35 ataxia cerebellum purkinje cells SK channels cyppa https://physmath.spbstu.ru/article/2016.32.8/ ph_2_2016.72_81.pdf

RAR RUS 82-86 Oktyabrskiy Valeriy vokt@yandex.ru A new opinion of the greenhouse effect The article analyzes the correspondence between actually occurring physical and chemical processes and the concept of the greenhouse effect. The absorption of the solar radiation by the gases existing in the Earth atmosphere has been examined. It was demonstrated that, despite the absorption of radiation from the Earth’s surface in the middle and long-wave infrared (IR) regions, there is a strong absorption of the overtones and combined frequencies of water vapor in the solar radiation (visible and near IR regions), i.e. the transmittance bandwidth of ‘the glass greenhouse’. Thus, the Earth atmosphere does not really function as a greenhouse, and the terms ‘greenhouse effect’ and ‘greenhouse gases’ lost their original meaning and have remained symbolical. 10.5862/JPM.242.9 535-1/3 absorption spectrum greenhouse effect greenhouse gas water vapor overtone https://physmath.spbstu.ru/article/2016.32.9/ ph_2_2016.82_86.pdf

RAR RUS 87-94 Khokhlyuk Vitaly Principles for constructing the disjunctive cuts This article focuses on solving the disjunctive problem. Various methods of constructing the disjunctive cuts (DC) from the logical limitations on the linear inequalities have been presented. A general principle of DC and a principle making possible to strengthen these cuts were stated. By virtue of the stated principles, solving the problems of optimization with a great number of limitations can be simplified. Two theorems were formulated and proved. Four examples illustrated various theoretical statements. The suggested principles and procedures on their basis provide the theoretical background to the elaboration of algorithms intended for the software implementation in solving the practical problems. 10.5862/JPM.242.10 519.854 mathematical logic disjunctive problem convex hull closure of set strengthening of cut https://physmath.spbstu.ru/article/2016.32.10/ ph_2_2016.87_94.pdf

RAR RUS 95-107 Pastukhov Alexey pastuhov1992@gmail.com Prokofiev Alexander aaprokof@yandex.ru Kohonen self-organizing map application to representative sample formation in the training of the multilayer perceptron In this paper, we have considered an item of effective formation of a representative sample for training the neural network of the multilayer perceptron (MLP) type. The main problems arising in the process of the factor space division into the test, verification and training sets were formulated. An approach based on the use of clustering, that allowed one to increase the entropy of the training set was put forward. Kohonen selforganizing maps (SOM) were examined as an effective procedure of a clustering. Based on such maps, the clustering of factor spaces of different dimensions was carried out, and a representative sample was formed. To verify our approach we synthesized the MLP neural network and trained it. The training technique was performed with the sets formed both using the clustering and no doing it. The approach under consideration was concluded to have an influence on the increase in the entropy of the training set and (as a result) to lead to the quality improvement of training of MLP with the small dimensionality of the factor space. 10.5862/JPM.242.11 004.032.26 artificial neural network Kohonen self-organizing map clustering sample formation https://physmath.spbstu.ru/article/2016.32.11/ ph_2_2016.95_107.pdf

RAR RUS 108-115 Berezin Sergey servberezin@yandex.ru On analytic characteristic functions and processes governed by SDEs We study analyticity of the characteristic function of a process defined by means of SDEs. Namely, starting with the simple case of a scalar Ito SDE we show that the corresponding characteristic function is entire. The proof is based on the Gröenwall’s inequality technique and the classic analyticity criterion in terms of moments. Further, we extend this criterion and derive a handy sufficient condition of analyticity in the multidimensional case. This condition is used to prove the corresponding general result of analyticity. We assume that the drift vector obeys the linear growth condition, and the diffusion matrix is time-onlydependent, but possibly degenerate. The approach used in the article can be extended to more general types of SDEs. 10.5862/JPM.242.12 519.213.2:519.217.4 stochastic differential equation complex analytic function holomorphic function multivariate holomorphic function https://physmath.spbstu.ru/article/2016.32.12/ ph_2_2016.108_115.pdf

RAR RUS 116-125 Sharifulin Albert Poludnitsin Anatoliy panam.48@mail.ru The borders of existence of anomalous convection flow in the inclined square cylinder: numerical determination The article is devoted to the study of bifurcations of stationary convection regimes in a closed, heated from below and tilted square cylinder filled with air for cases of heat-insulated and perfectly heat-conducting sidewalls. The temperature and velocity fields were obtained using grid method for inclinations from a horizontal position up to 30 degrees in the range of Rayleigh numbers up to 20-fold excess of its critical value. The limit angle of anomalous-flow existence in the cylinder with the heat-insulated walls was established to be about 3 times greater than that in the cylinder with the heat-conducting ones. In the case of the heatconducting walls the maximum angle of the anomalous-flow existence reached 7.7 degrees at a 3.3-fold excess of the critical value of Rayleigh number. 10.5862/JPM.242.13 532.5.013.4.536.25+519.6 thermal convection inclination of the cavity anomalous flow numerical simulation https://physmath.spbstu.ru/article/2016.32.13/ ph_2_2016.116_125.pdf

RAR RUS 126-135 Peter the Great St. Petersburg Polytechnic University Tikhomirov Victor victikh@mail.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

A semi-infinite crack of mode III in the bimaterial wedge An exact solution of the antiplane problem for a semi-infinite interface crack in a piecewise-homogeneous wedge under a self-balanced load on its sides has been obtained. Three types of boundary conditions on the wedge sides were examined: the both sides being stress-free; both sides being clamped, and one side being stress-free with the second one clamped. As a result of using the Wiener-Hopf method, the solution was represented in quadratures. The Green’s functions were obtained for stress intensity factors; in the case of a geometrically symmetrical wedge structure simple formulae were found for these functions. The stress singularity in the apex of the wedge was studied. In contrast to the homogeneous wedge structure the asymptotic of the stresses near the apex was established to have sometimes two singular terms for some values of the composite parameters. 10.5862/JPM.242.14 539.3 interfacial mode III crack bimaterial wedge stress intensity factor stress singularity https://physmath.spbstu.ru/article/2016.32.14/ 14_126-135_2(242)2016.pdf

RAR RUS 136-140 Lobanov Ivan lobanov.111@yandex.ru Denisov Alexander A.V.Denisov@inbox.ru The exact analytical solution of the problem on the average number of spikes of the narrowband Gaussian stoсhastic process     In this article, the problem of the number of spikes (level crossings) of the stationary narrowband Gaussian process has been considered. The process was specified by the exponentially-cosine autocorrelation function. The problem had been solved earlier by S. Rice in terms of the joint probabilities’ density of the process and its derivative with respect to time, but in our article we obtained the solution using the functional of probabilities’ density (the functional was obtained by I.N. Amiantov), as well as an expansion of the canonical stochastic process. In this article, the optimal canonical expansion of narrowband stochastic process based on the work of A.P. Filimonov and A.V. Denisov was also considered to solve the problem. The application of all these resources allowed obtaining an exact analytical solution of the problem on spikes of stationary narrowband Gaussian process. The obtained formulae one could use to solve, for example, some problems about the residual resource of some radiotechnical products, about the breaking sea waves and others. 10.5862/JPM.242.15 519.21(075) emission of stoсhastic process density functional of probability canonical expansion https://physmath.spbstu.ru/article/2016.32.15/ ph_2_2016.136_140.pdf

SCO RUS 141-144 Without author Vadim K. Ivanov (on the occasion of his 70th birthday) https://physmath.spbstu.ru/article/2016.32.16/ ph_2_2016.141_144.pdf