The classical Poincaré theorem (1907) asserts that the polydisk D^n and the ball B^n in C^n are not biholomorphically equivalent for *n* ≥ 2. Equivalently, this means that the Fréchet algebras O(D^n) and O(B^n) of holomorphic functions are not topologically isomorphic. Our goal is to prove a noncommutative version of the above result. Given a nonzero complex number *q,* we define two noncommutative power series algebras O_q(D^n) and O_q(B^n) which can be viewed as q-analogs of O(D^n) and O(B^n), respectively. Both O_q(D^n) and O_q(B^n) are the completions of the algebraic quantum affine space w.r.t. certain families of seminorms. In the case where 0 < *q* < 1, the algebra O_q(B^n) admits an equivalent definition related to L. L. Vaksman's algebra *C_q(B^n)* of continuous functions on the closed quantum ball. We show that both O_q(D^n) and O_q(B^n) can be interpreted as Fréchet algebra deformations (in a suitable sense) of O(D^n) and O(B^n), respectively. Our main result is that O_q(D^n) and O_q(B^n) are not isomorphic if *n* ≥ 2 and |*q*| = 1, but are isomorphic if |*q*| ≠ 1.

In a metal sample, where at least one of the dimensions is comparable with the de Broglie wavelength of conduction electrons, the quantum size effects (QSE) should be observed. QSEs manifest themselves as non-monotonic dependencies of various material properties as function of relevant dimension. QSE should be particularly noticeable in materials with charge carrier(s) effective mass less than the free electron mass. Bismuth is one of the most suitable semi-metal to observe QSE due to small effective masses and small the Fermi energy. However, bismuth has a high anisotropic energy spectrum. Hence to observe QSE which can be interpreted with reasonable accuracy, it is mandatory to fabricate single-crystal nanostructure with known orientation of crystallographic axes. In this paper several short bismuth nanowires (nanorods) were investigated, and oscillating dependence of electric resistance on effective cross section was found. Theoretical calculations provide a reasonable agreement with experiment. The quantum-size phenomena are important for operation of a wide spectrum of nanolelectronic devices.

Abstract. In a metal sample, where at least one of the dimensions is comparable with the de Broglie wavelength of conduction electrons, the quantum size effects (QSE) should be observed. QSEs manifest themselves as non-monotonic dependencies of various material properties as function of relevant dimension. QSE should be particularly noticeable in materials with charge carrier(s) effective mass less than the free electron mass. Bismuth is one of the most suitable semi-metal to observe QSE due to small effective masses and small the Fermi energy. However, bismuth has a high anisotropic energy spectrum. Hence to observe QSE which can be interpreted with reasonable accuracy, it is mandatory to fabricate singlecrystal nanostructure with known orientation of crystallographic axes. In this paper several short bismuth nanowires (nanorods) were investigated, and oscillating dependence of electric resistance on effective cross section was found. Theoretical calculations provide a reasonable agreement with experiment. The quantum-size phenomena are important for operation of a wide spectrum of nanolelectronic devices.

Quasi-3D model for calculation of radiation leakage currents in modern submicron SOI MOSFET structures is proposed. Instead of the fully 3D modeling is proposed to solve two tasks: 2D modeling of the traditional MOSFET cross-section and 3D modeling of the side parasitic transistor. The radiation-induced leakage current simulation in the 0.35 μm SOI MOSFET structure with taking account ionizing radiation with a dose of up to 500 krad was simulated. The results of the simulation show that in comparison with the traditional fully 3D modeling, which requires 11 hours of computer time, the computer time for the IdVg characteristic was reduced to 71 minutes (i.e. the computer time decreased by 9 times).

We extend concept of local simulation times in parallel discrete event simulation (PDES) in order to take into account architecture of the current hardware and software in high-performance computing. We shortly review previous research on the mapping of PDES on physical problems, and emphasise how physical results may help to predict parallel algorithms behaviour.

Molecular modelling is used to calculate transport properties and to study relaxation of liquid n-triacontane (C30H62). The problem is important in connection with the behavior of liquid isolators in a pre-breakdown state. Two all-atom models and a united-atom model are used. Shear viscosity is calculated using the Green–Kubo formula. The force fields are compared with each other using the following criteria: the required time for one molecular dynamics step, the compliance of the main physical and transport properties with experimental values. The problem of the system equilibration is considered. The united-atom potential is used to model the n-triacontane liquid with an initial directional orientation. The time of relaxation to the disordered state, when all molecules orientations are randomized, are obtained. The influence of the molecules orientations on the shear viscosity value and the shear viscosity relaxation are treated.

Data analysis in fundamental sciences nowadays is an essential process that pushes frontiers of our knowledge and leads to new discoveries. At the same time we can see that complexity of those analyses increases fast due to a) enormous volumes of datasets being analyzed, b) variety of techniques and algorithms one have to check inside a single analysis, c) distributed nature of research teams that requires special communication media for knowledge and information exchange between individual researchers. There is a lot of resemblance between techniques and problems arising in the areas of industrial information retrieval and particle physics. To address those problems we propose Reproducible Experiment Platform (REP), a software infrastructure to support collaborative ecosystem for computational science. It is a Python based solution for research teams that allows running computational experiments on shared datasets, obtaining repeatable results, and consistent comparisons of the obtained results. We present some key features of REP based on case studies which include trigger optimization and physics analysis studies at the LHCb experiment.

The paper considers programs and devices of augmented reality, examines the general environments and methods of software development and the rationale for their selection. The work describes in detail the operating principle of the software, the pattern recognition algorithm, the UML class diagram, the UML usage diagram, and the architecture of the 3D rendering engine and a description of its operation. An example of practical application of software with pattern recognition is offered. The paper examines the impact of virtual reality on human health, as well as the problem of assimilation of educational material in preschool education. To solve the problem, various algorithms for the program are proposed. Based on the conducted studies, it was decided to create the software for the experiment on the basis of developed algorithms for preschool education. The results of the work can be used for further research in the field of expanded reality, for new developments in this field and improvement of the quality of education.

The aim of this work is the software implementation of three image scaling

algorithms using parallel computations, as well as the development of an application with a

graphical user interface for the Windows operating system to demonstrate the operation of

algorithms and to study the relationship between system performance, algorithm execution

time and the degree of parallelization of computations. Three methods of interpolation were

studied, formalized and adapted to scale images. The result of the work is a program for

scaling images by different methods. Comparison of the quality of scaling by different methods

is given.

In this work we study influence of various factors on stability of ionizing radiation detectors installed in the cosmic ray spectrometer (SCR) based on diamond detectors of ionization radiation (DDIR). Diamond detectors for SCR are made of single crystals of synthetic diamond type IIa. Diamond detectors were studied successively in three different experiments. Checking detector stability with ambient temperature increased up to 70 degrees Celsius was the first experiment. At next we change the geometry of detector irradiation by rotating nuclear source around it and measuring changes in detector count rate. And last one experiment was about checking the phenomenon of polarization by prolonged detector irradiation by ionizing radiation of various types and energies. The study revealed the presence of the strong influence of the polarization effect on the work of diamond detectors for registration of ionizing particles with short mean free path (in our experiment they were the alfa-particles of 238Pu). In this work correspondence of the experimental results of the "rotation" the source around the detector with the data obtained by simulation in GEANT-4 was shown.

Reservoir Computing (RC) is taking attention of neural networks structures developers because of machine learning algorithms are simple at the high level of generalization of the models. The approaches are numerous. RC can be applied to different architectures including recurrent neural networks with irregular connections that are called Echo State Networks (ESN). However, the existence of successful examples of chaotic sequences predictions does not provide successful method of multiple attribute objects classification.

In this paper the binary ESN classifiers are researched. We show that the reason of low precision of classification is the existence of unbalanced classes. Then the method to solve the problem is proposed. It is possible to use randomizing algorithm of learning data set balancing and method of data temporalization. The resulting errors matrixes have pretty good numbers. The proposed method is illustrated by the usage on synthetic data set. The features of ESN classifier are demonstrated in the case of rare events detection such as transaction attributes fraud detection.

One of the mechanisms of energy transfer between degrees of freedom of dusty plasma system is based on parametric resonance. Initial stage of this process can de described by equation similar to Mathieu equation. Such equation is studied by analytical and numerical approach. The numerical solution of the extended Mathieu equation is obtained for a wide range of parameter values. Boundaries of resonance regions, growth rates of amplitudes and times of onset are obtained. The energy transfer between the degrees of freedom of dusty plasma system can occur over a wide range of frequencies.

Molecular dynamics is applied to calculate diffusion coefficients of n-triacontane C30H62 using Einstein-Smoluchowski and Green-Kubo relations. The displacement 〈Δr2〉(*t*) has a subdiffusive part 〈Δr2〉 ~ *t* α, caused by molecular crowding at low temperatures. Longtime asymptotes of 〈v(0)v(t)〉 are collated with the hydrodynamic tail t-3/2 demonstrated for atomic liquids. The influence of these asymptotes on the compliance of Einstein-Smoluchowski and Green-Kubo methods is analyzed. The effects of the force field parameters on the diffusion process are treated. The results are compared with experimental data.

The development of multi-core processor systems is a demanded branch of science and technology. The appearance of processors with dozens and hundreds of cores poses to the developers the question of choosing the optimal topology capable to provide efficient routing in a network with a large number of nodes. In this paper, we consider the possibility of using multiplicative circulants as a topology for networks-on-chip. A specialized routing algorithm for networks with multiplicative circulant topology, taking into account topology features and having a high scalability, has been developed.

Particles interaction and value of the screening length in dusty plasma systems are of great interest in dusty plasma area. Three inter-particle potentials (Debye potential, Gurevich potential and interaction potential in the weakly collisional regime) are used to solve equilibrium equations for two dusty particles suspended in a parabolic trap. The inter-particle distance dependence on screening length, trap parameter and particle charge is obtained. The functional form of inter-particle distance dependence on ion temperature is investigated and compared with experimental data at 200–300 K in order to test used potentials applicability to dusty plasma systems at room temperatures. The preference is given to the Yukawa-type potential including effective values of particle charge and screening length. The estimated effective value of the screening length is 5–15 times larger than the Debye length.

The article describes the device for selective registration of electrons, protons and heavy ions fluxes from the solar and galactic cosmic rays in the twelve energy ranges, built on a base of diamond detector. The use of the diamond detectors allowed for the creation a device for registration of cosmic particles fluxes at the external spacecraft surface with the resource not less than 20 years. Selective detector is aimed for continuous monitoring of radiation situation on board the spacecrafts, in order to predict the residual life of their work and prompt measures to actively protect the spacecraft when the flow of cosmic particles is sharply increased.

Here we present an integrated nanophotonic circuit for on-chip spontaneous four-wave mixing. The fabricated device includes an O-ring resonator, a Bragg noch-filter as well as a nine-channel arrayed waveguide gratings (AWG) operated in the C-band wavelength range (1550 nm). The measured optical losses of the device (-6.8 dB) as well as a high Q-factor (> 1.2× 10 5) shows a good potential for realizing the spontaneous four-wave mixing on the silicon nitride chip.

Simulation of electron, ion and metastable excited atom motion and interactions in a low-current discharge between the flat electrodes of a gas- discharge device in argon-mercury mixture is fulfilled. Also influence of gas temperature on both densities and fluxes of particles has been investigated. Distributions of the particle densities along the discharge gap under different mixture temperatures are obtained. It has been demonstrated that the principal mechanism of mercury ion generation was the Penning ionization of mercury atoms by argon metastables, which contribution grows sharply with the mixture temperature due to mercury density increase. Calculations showed that both mercury and argon ion flow densities near the cathode where of the same order already under the relative mercury content of about 10^{-4} corresponding at the argon pressure 10^{3} Pa to the mixture temperature 30 C. Because the mean path length of a mercury ion in the mixture between the resonant charge exchanges on parent gas atoms is much more than that of an argon ion, the energies of mercury ions exceed considerably the energies of argon ions, and they make the main contribution to the physical electrode sputtering. which reduces the service time of the gas- discharge device.

**Abstract**. The article considers the features of super-scalar processors, their way of performing several operations on several pairs of operands simultaneously. The research focuses on the organization of processor pipeline execution operation of several machine instructions in one processor core. The simulating kit was developed for better understanding of a processor core microarchitecture. It includes two parts: program and methodical recommendations with multiple task options. The simulating kit demonstrates the pipeline architecture consisting of two clusters: front-end and back-end and the principle of translating complex multi-cycle CISC-like instructions into simpler RISC-like micro-operations. The main types of machine instructions are considered: data transfer between registers and memory cells (four variations), data processing of couple of operands from registers and memory cells (four variations), conditional jump to the specified address. The program-simulator makes it possible to conduct a more detailed simulation of one of the three mechanisms for calculations accelerating in the processor core: multi-functional (super-scalar) processing, out-of-order processing, speculative instructions execution after the branch prediction. The simulating kit is used in educational process when training masters of Higher School of Economics National Research University.

Object of this research are macroeconomic indicators, which are important to

descript economic situation in a country. Purpose of this work is to identify these indicators

and to analyze how the state can affect these figures with available instruments. Here was

constructed a model where the targets can be calculated from raw data – tools in the field of

economic policy. Software code that implements all relations among the indicators and allows

to analyze with high accuracy, sufficiently successful economic policies and with the help of

some tools, you can achieve better results. This model can be used to forecast macroeconomic

scenarios. The corresponding values of the objective (outcome) variables are set as a

consequence of the configuration data of the previous period, subject to external influences and

depend on the instrumental variables. The results may be useful in economical predictions. The

results were successfully checked on real scenarios of Russian, European and Chinese

economics. Moreover, the results can be applied in the field of education. Program is available

to use as “economical game” the educational process of the University, in which you can

virtually implement various macroeconomic scenarios, draw conclusions about their success.

We study an optimal control problem for a nonlinear spherical inverted pendulum on a movable base. As the cost functional, the mean-squared deviation of the pendulum from the upper equilibrium is considered, so optimal controls stabilize the pendulum at the unstable upper position. We show that the problem under consideration posses a singular point of the second order and there are spiral-similar solution which attains the singular point in finite time.