Izvestiya of Altai State University

Variation of Light Absorption by Yellow Substance in Surface Layer of Continental Reservoir

2018-11-09T21:43:57+07:00

The paper presents experimental data on variation of light absorption by yellow substance in the surface layer of the Novosibirsk reservoir, obtained in August 2017 during hydrological, hydrobiological and hydrochemical investigations. The calculated light absorption index by yellow substance in the spectral range of 400-800 nm varied from 1.0 to 9.7 m

^-1, the light attenuation index — from 2.0 to 14.0 m^-1. Concentration of chlorophyll "a", organic-mineral suspension, and yellow substance was measured. Chlorophyll content in water changed within 7.0-39.3 mg/m³, the average mass concentration of suspended particles made up 14.30 mg/l. Concentration of yellow substance in the reservoir, evaluated by optical method using the rate of light absorption by yellow substance at the wavelength X=450 nm, varied from 17.4 to 30.8 g/m³. To estimate the exponential slope coefficients of the spectral absorption curve of the yellow substance in the Novosibirsk reservoir, the appropriate approximation dependences are constructed. The assessment of spectral contribution of major optically active water components (yellow substance, suspension, chlorophyll, clean water) to the light attenuation is carried out for the surface layer of the reservoir. It is revealed that the most significant contribution at all sites of the reservoir is made by yellow substance.

DOI 10.14258/izvasu(2018)4-01

Formation of interfaces between a semiconductor-sulfur-transition metal

2018-10-08T16:08:31+07:00

Thermodynamic calculations were carried out under standard conditions of chemical reactions occurring during the sulfide passivation of the surface of elementary semiconductors (Si, Ge), gallium, indium, aluminum (GaN, InN, AlN) nitrides. The sulphide passivation of aluminum, silicon and germanium nitride is thermodynamically more probable for the unoxidized surface of semiconductors that is in contact with a gas phase containing sulfur or hydrogen sulphide. There is a thermodynamic probability of sulfidation of the oxidized surface of germanium from the gas phase. The sulfidation of gallium and indium nitrides is spontaneously possible from aqueous solutions of alkali metal sulphides. A comparison of the crystal-chemical parameters of atoms (covalent and atomic radii), the types of symmetry of possible phase compounds at the semiconductor-sulfide-metal and semiconductor-oxide-metal interfaces, showed that the sulfide surface of the semiconductor has a greater structural correspondence than for the oxidized surface of a semiconductor in contact with transition metal. When oxygen atoms are replaced by sulfur atoms in the boundary layer between the transition metal and the semiconductor, a smaller jump in the electronegativity of the elements forming the interface is observed. The formation of a more perfect and stable (by chemical and physical properties) interface with the help of sulphide passivation of the semiconductor surface facilitates the creation of rectifying metal-semiconductor contacts with improved electrophysical parameters.

DOI 10.14258/izvasu(2018)4-02

Using of LAMMPS and OVITO Software Packages to Study the Microkinetics of SH-synthesis of Nickel Aluminides

2018-10-08T16:08:36+07:00

The paper discusses some aspects of the application of the LAMMPS software package, which implements the molecular dynamics (MD) method and by means of MD method simulates the process of propagation of a combustion wave along a sample in the form of a stack of alternating layers of nanoscale crystal lattices of Ni and Al atoms (the atomic system is on the order of a million and more atoms) with the formation of nickel aluminides in the process of SH synthesis. In addition, as the interatomic interaction potential were used two versions of the "embedded atom" model (EAM) for which computational experiments (CEs) were carried out. The second software package OVITO was used to recognize and visualize various types of crystalline, quasi-crystalline and other types of structures. Namely, the OVITO package made it possible to recognize and calculate in the simulated atomic system the percentage of next types of structures: fcc, bcc, hcp and etc. For two varieties of the EAM potential, the results of the CEs include: a family of temperature profiles along the layers of the structure at successive instants of time (up to 12 ns) and a corresponding set of microsections (vertical crosssections along the layers of the atomic system).

DOI 10.14258/izvasu(2018)4-03

Application of Principal Components Analysis to the Investigation of Acoustic Emission in Plastic Deformation of Lead Alloys

2018-10-08T16:08:40+07:00

A study was made of the dependence of acoustic emission, formed during static deformation of lead alloys, on the stages of strain hardening. An essential change in the informative characteristics of acoustic emission signals during the change in the stages of strain hardening, reflecting the evolution of the physical mechanisms of deformation during loading ofthe material, is established. Quantitative analysis of the effect of stages on acoustic emission signals was carried out using the principal component method. When processing the experimental data, the entire signal recorded during the loading process was divided into small blocks, each of which reflected the behavior of the material in the corresponding portion of the loading curve. Acoustic emission for an individual unit was described using informative signal parameters that reflected its energy and frequency characteristics. The processing of the experimental data made it possible to cluster the signals in accordance with the isolated stages of strain hardening.

The obtained results can be used in the acoustical-emission study of the stagedness of the processes of plastic deformation in materials and for the diagnosis of their deformation behavior.

DOI 10.14258/izvasu(2018)4-04

The Effect of Water Treatment by the Ultrahigh Frequencies Electromagnetic Field on the Relative Viscosity of Aqueous Solutions of Na-Carboxymethylcellulose

2018-10-08T16:08:43+07:00

A significant increase in the relative viscosity of 0.5% solutions of Na-carboxymethylcellulose was found when water, exposed to the electromagnetic field of the radiofrequency band (110-170 MHz), was used as a solvent. It is shown that the efficiency of the electromagnetic action depends on the frequency of the field — the maximum change in the viscosity of the solutions corresponds to the frequencies 130 and 170 MHz. The effect of pH and temperature on the viscosity of these solutions was studied. It is shown that an increase in pH from 3 to 7 is observed. The viscosity is maximal at pH = 7 ... 9, further increase in pH leads to its decrease. The observed dependence is due to conformational changes in polymer macrocoions due to a change in their charge characteristics. The type of dependence on pH is the same for irradiated and nonirradiated systems, however the degree of viscosity increase depends on pH and temperature. Investigations were carried out in the temperature range 278-303 K. As the temperature increases, the viscosity of the solutions decreases, but for solutions prepared in irradiated EMF water, it exceeds the viscosity of the control samples in the studied temperature range. At T = 298 K and pH = 11, it increases by 59% (field frequency 130 MHz) compared to the control sample. The observed phenomena may be caused by the weakening of the solvation of the hydrophilic groups of the polymer in irradiated water and the increase in the rigidity of the chain of macromolecules due to the formation of intra- and intermolecular hydrogen bonds.

DOI 10.14258/izvasu(2018)4-05

Data Interpretation for Weather Extremes on the Basis of Quasiresonance Hypothesis of Blocking Formation

2018-10-08T16:08:49+07:00

The quasiresonance hypothesis is used among other approximations for theoretical study of blocking formation in the recent years. It is propose the magnification of quasistationary waves resulted by thermal and orographic inhomogenities of underlying surface through quasiresonance. In this paper authors perform the interpretation of reanalysis and satellite data for weather extremes situations on the basis of quasiresonance hypothesis that describs mechanism of amplification for amplitudes of quasistationary waves. Base on the analysis of atmospheric waves parameters the situations favorable for realization of this mechanism were selected and described. The spatial distribution of the meridional velocity of atmospheric wind in troposphere was derived to illustrate all considered weather extreme situations. In all cases the conditions necessary for quasiresonance amplification are performed for wave modes with zonal wave numbers. All the considered weather extremes situations exhibit amplitudes for monthly Fourier components that are about 1.5 SD from the 1980-2011 monthly climatology data for the meridional velocity for the corresponding wave numbers.

DOI 10.14258/izvasu(2018)4-06

Development of the Facility and Performance Studies Radio Modules Operating in Unlicensed Frequency Bands

2018-10-08T16:08:45+07:00

The installation is described and the results of the study of some characteristics of the RFM69CW transceiver module operating in the unlicensed frequency range are presented. Controlling the mode of operation of the module and setting its parameters were carried out via a software-implemented SPI interface with the reconfigurable myRI0 I/0 block, and the signals and spectra were recorded using the NI PXIe-5644R vector transceiver. The installation software is developed in the LabVIEW environment. The block diagrams of the programs for configuring the radio module and demodulating FSK and 00K signals are presented.

The change in the waveform and the corresponding changes in the radio signal spectrum are shown when the module settings in the GFSK and 00K signal transmission mode are changed. A nonmonotonicity of the dependence of the output power of the transmitter on the installed power is found. The results obtained can be used to evaluate other characteristics and other types of radio modules, as well as in the educational process as a basis for laboratory work on the course "Signal reception and processing technique".

DOI 10.14258/izvasu(2018)4-07

The Ground States Diagrams for Adsorption on Nanoclusters, Taking into Account the Interaction of not Nearest Neighbor

2018-10-08T16:08:47+07:00

In connection with the development of nanotechnology and microelectronics, much attention is paid to the study of various adsorption processes. As a rule, adsorption is observed on the surface of a crystal or liquid, but sometimes one-dimensional adsorption takes place. In particular, the question of how the phase distribution passes through adsorption on atomic chains is of particular interest. The paper considers adsorption on an atomic chain of finite size at absolute zero temperatures in the framework of the generalized Ising model. The role of the boundary conditions is fulfilled by the "broken ends" of the atomic chain, which makes it possible to model this physical process on a real chain with free ends. The ground states diagrams are plotted — phase stability diagrams in the coordinate plane of the energy parameters at the absolute zero temperature. This makes it possible to determine possible adsorption transformations and new phases at sufficiently low temperatures. Isotherm of onedimensional adsorption is calculated.

The Delphi programming language has developed a one-dimensional lattice gas model that is tied to the generalized Ising model, taking into account the interaction of the first and second neighbors and the external field. Within the framework of the developed model, adsorption of atoms of one kind on a chain of finite size is considered. The isotherm of one-dimensional adsorption is constructed for absolute zero temperature.

DOI 10.14258/izvasu(2018)4-08

The X-Ray Diffraction Analysis of the Diffusive Boridny Layer of Ct20 on the Basis of Fe+B Coverings after Annealing in the Muffle Furnace

2018-10-08T16:08:51+07:00

The possibility of obtaining diffusion boride coatings on the surface of St20 structural carbon steel in the application of various borating coating compositions and heating in a muffle furnace is considered in the article. The borating paste contained iron and boric acid powder in volume proportions of 25%Fe-75% H₃BO₃, 50%Fe-50% H₃BO₃, 75% Fe-25% H₃BO₃. In addition to these components, liquid glass of Na2SiO3 (concentrate), carbon in the form of graphite powder and ammonium hydroxide NH₄OH were used to prepare the paste. The steel samples in the coating were heat treated in a muffle furnace at 1000 ⁰С for 5 minutes. As a result of thermoactivation of chemical reactions in the coating in the surface layer of steel, redistribution of boron and the formation of Fe and Fe iron borides are observed. A structural-phase analysis of the samples after their paste coating and annealing in a muffle furnace at a high temperature has been carried out. Analysis of the radiographs indicates the diffusion saturation of the surface layer by borides. The crystal lattice B is identified as orthorhombic cubic, the compound FeB has a rhombohedral cubic lattice, the Fe₃B bonded lattice is not identified.

DOI 10.14258/izvasu(2018)4-09

Characteristics of a Two-Layer Flow with Evaporation in a Plane Channel Subjected to Heating from the Bottom

2018-10-08T16:08:52+07:00

Features of convective regimes arising in a twolayer system with a phase transition are investigated. A mathematical model to describe the evaporative convection in an infinite horizontal channel is based on the Oberbeck — Boussinesq approximation of the Navier — Stokes equations and on the relations on the thermocapillary interface. An exact solution of the governing equations is the Ostroumov — Birikh solution analog. It has a group origination and allows one to take into account simultaneous presence of horizontal and vertical temperature gradients and influence of thermodiffusion effects (direct and inverse) both in the gas-vapor mixture and on the interface. Thermal and topological patterns of the joint flows of an evaporating liquid and a mixture of its vapor with an inert gas are described. Characteristics of vapor quality in the upper layer are studied. New results on stability of the exact solution under given consideration are presented in the paper. Typical forms of arising characteristic perturbations are calculated for the case of equal longitudinal temperature gradients on the external channel walls and of nonzero transversal temperature drop. Governing mechanisms responsible for the formation of each type of the structures are described.

DOI 10.14258/izvasu(2018)4-10

Numerical Solution of the One-Dimensional Problem of Filtration of an Incompressible Fluid in a Viscous Porous Medium

2018-10-08T16:08:55+07:00

The process of fluid filtration in a deformable porous medium is described by a system of equations consisting of the equations of mass conservation for the liquid and solid phases, the Darcy law, the Maxwell-type rheological relation, and the law of conservation of the balance of forces. It is assumed that the poroelastic medium has predominantly viscous properties and the phase densities are constant. In the case of one spatial variable, the transition to Lagrange variables makes it possible to reduce the initial system of determining equations to one equation for the required porosity. The paper is aimed to study the initial — boundary value problem numerically. In clause 1, the task is set and a brief review of the literature on related work. In paragraph 2, the system of equations is transformed, resulting in a nonlinear third-order equation for porosity. In paragraph 3 we propose an algorithm for the numerical solution of a one-dimensional initial-boundary problem. For numerical realization, we use a homogeneous difference scheme for a second-order equation with variable coefficients and a Runge — Kutta scheme of second-order approximation. The obtained solution satisfies the physical principle of maximum. In paragraph 4, we consider a more general case of reducing the original system to a single equation.

DOI 10.14258/izvasu(2018)4-11

Topic Modeling for Textual Learning Materials on Informatics Using R Language

2018-10-08T16:08:57+07:00

This paper presents results of topic modeling for text learning materials. Learning materials are electronic lecture notes used by teachers to prepare for computer science classes. Topic modeling methods allow users to systematize the content of textual documents without additional manual work. Main topics in documents are highlighted, and the distribution of topics in documents is demonstrated. In other words, the proposed methods provide the framework for the so-called topic model that puts a set of topics that characterize the content of documents in a given collection of documents. The latent Dirichlet allocation (LDA) is used for topic modeling. The implementation is done using the R language. The developed interactive web application provides a set of visual tools for topic modeling to a user (teacher). Visualization techniques gradually improve the ergonomics of a teacher’s work with learning materials and save the time spent on studying, analyzing, and selecting relevant study materials.

DOI 10.14258/izvasu(2018)4-12

Problem of a Moving Load in a Channel Covered with Broken Ice

2018-10-08T16:09:00+07:00

In this paper, the effect of broken ice on the formation of gravitational waves caused by an external load moving along a channel is studied. The external load is modeled by a smooth locally distributed pressure moving along the center line of the channel at a constant speed. The governing equations are the differential equation of oscillations of thin broken ice and the Laplace equation for a flow velocity potential under the broken ice. These equations are closed by the impermeability conditions on the walls and bottom of the channel, and by the kinematic and dynamic conditions at the broken ice-liquid interface. The traveling wave solution that does not depend on time in a coordinate system moving together with the external load is investigated. Using the Fourier transform along the channel the problem under consideration reduces to a two-dimensional problem with respect to the profile of the gravitational wave across the channel, which is solved by the method of separation of variables. The analysis of the formation of gravitational waves in the broken ice is provided. It is shown that for every speed of the load there is a countable number of gravitational waves propagating along the channel with the velocity of the load. Each wave has a given profile across the channel. An example of test calculations for a three-dimensional problem is shown.

DOI 10.14258/izvasu(2018)4-13

Investigation of four-dimensional locally homogeneous (Pseudo)Riemannian Manifolds with an isotropic Schouten — Weyl Tensor

2018-10-08T16:09:02+07:00

Locally homogeneous (pseudo)Riemannian manifolds were studied by many mathematicians. Their generalization is a locally conformally homogeneous (pseudo)Riemannian manifolds on which a conformal transformations act transitively. Such manifolds were previously studied both in the Riemannian case and in the pseudo-Riemannian case.

In the paper of E.D. Rodionov, V.V. Slavsky and L.N. Chibrikova it was proved that a locally homogeneous manifold could be obtained from a locally conformally homogeneous (pseudo)Rieman-nian manifolds by a conformal deformation if the Weyl tensor (or the Schouten — Weyl tensor in the three-dimensional case) has a nonzero squared length. Thus, the problem arises of studying (pseudo)Riemannian locally homogeneous and locally conformally homogeneous manifolds, the Schouten — Weyl tensor of which has zero squared length, and itself is not equal to zero.

In this paper, we present an algorithm that can solve the classification problem of four-dimensional locally homogeneous (pseudo)Riemannian manifolds with a nontrivial isotropy subgroup and an isotropic Schouten — Weyl tensor.

DOI 10.14258/izvasu(2018)4-14

Some Mathematical Approaches to Develop Models for Prediction of Compensation and Decompensation Stages of Diabetes Mellitus among Children and Adolescents

2018-10-08T16:09:04+07:00

The problem of prediction of compensation and decompensation stages of diabetes mellitus among children and adolescents using methods of machine learning is considered in the paper. There are several mathematical models used in the study: logistic regression, decision trees and gradient boosting.

The “de-identified” data of medical examination of children and adolescents of the Altai region suffering from diabetes mellitus are used to train the models in this study.

The output parameter of the models is the stage of diabetes mellitus compensation encoded with the following values: 0 — compensation of diabetes mellitus, 1 — decompensation of diabetes mellitus. This way, the prediction is the problem of binary classification.

The results of the conducted research are the following: models to predict the stages of compensation and decompensation of diabetes mellitus among children and adolescents are developed using the high-level Python programming language; optimal parameters are obtained for each model; prediction quality is estimated for each model using the following metrics: accuracy, completeness, F-measure, sensitivity, and specificity.

Professionals can use the obtained results for the supplementary diagnosis of children and adolescents of the Altay region who suffer from diabetes mellitus.

DOI 10.14258/izvasu(2018)4-15

On a Change in the Curvature of a Conformally Flat Metric under the Legendre Transformation

2018-10-08T16:09:05+07:00

It is known that the theory of conformally flat Riemannian metric is closely associated with pseudo-Euclidean geometry, due to the existence of the canonical isometric embedding conformally flat metric in pseudo-isotropic cone space. This fact was first noticed by H. Brinkmann, and later was used in the works of N. Kuyper. The geometry of homogeneous Riemannian manifolds with a conformally flat Riemannian metric was studied in the papers of A.D. Alekseevsky and B.N. Kimel’feld, in which their classification was given. In the inhomogeneous case such a classification does not exist, therefore, in the study of conformally flat Riemannian manifolds restrictions of various types are used: either on the dimension of the manifold, or on a topological structure, or on different types of Riemannian manifold curvatures of the conformally flat metric. In the last case, theorems on homogeneous Riemannian manifolds with a conformally flat metric of bounded one-dimensional curvature are well known, which were obtained by V.V. Slavsky and E.D. Rodionov. In this paper, we study the behavior of a one-dimensional curvature and the Ricci curvature under Legendre Transform of the conformally flat Riemannian metric.

10.14258/izvasu(2018)4-16

On the Uniqueness of the Classical Solution of the Initial-boundary Value Problem for a Viscoelastic Maxwell Medium Flow with Zero Velocities at the Boundary

2018-10-08T16:09:06+07:00

A system of equations with a rotational Jaumann derivative describing the motion of a viscoelastic incompressible Maxwell medium in a bounded region of three-dimensional space in the Stokes approximation (without convective terms in both the equation of motion and the rheological relation) is under consideration. The choice of the objective derivative of Jaumann type in the rheological ratio is due to the presence of an energy identity, the validity of which cannot be proved for the cases of using the upper and lower convective derivatives as objective derivatives. The uniqueness of the classical solution of the initial-boundary value problem with the adherence condition on the boundary of the flow domain in the class of sufficiently smooth functions under the assumption that the system has four distinct real sound characteristics is proved. The proof is based on the application of integral estimates and the use of the hyperbolicity condition of the system. For the sake of clarity, the calculations are carried out for the two-dimensional case, however, nowhere does it use the properties of two-dimensionality. Differences from the three-dimensional case are purely technical in nature. It is noted that the presence of convective terms in the equations of motion does not prevent the proof of uniqueness. Uniqueness is initially proved for a small interval of time, then in the standard way, the statement is extended to an interval of arbitrary length.

DOI 10.14258/izvasu(2018)4-17

A Method of Searching for Extreme Observations in a Problem of Fuzzy Regression

2018-10-08T16:09:08+07:00

The study of statistical data for outliers is an urgent task of modern mathematics. The reliability of these methods directly affects the quality of the subsequent processing of statistical data sets and the adequacy of the resulting conclusions. In general, all available observations should be checked and compared with a certain numerical indicator. The further conclusion should be made by comparing these indicators among themselves.

In this paper, a technique to search for statistical outliers for one of the possible regression models based on the Chebyshev norm is considered. The proposed approach is based on the Legendre transformation, one of the known transformations used in the convex analysis. This algorithm allows us to refer to the group of statistical outliers for a set of observations and not for individual observations. This key point distinguishes this algorithm from the most of the commonly used algorithms. This way, the task can be solved in one pass with less required time. An example of the study of a sample for outliers is presented. The possibility to compare the obtained characteristics provides the opportunity to solve the problem for a different number of assumed extreme values.

DOI 10.14258/izvasu(2018)4-18

The Trace Theorem for Anisotropic Sobolev — Slobodetskii Spaces with Applications to Nonhomogeneous Elliptic BVPs

2018-10-08T16:09:09+07:00

In this paper, anisotropic Sobolev — Slobodetskii spaces in poly-cylindrical domains of any dimension N are considered. In the first part of the paper we revisit the well-known Lions — Magenes Trace Theorem (1961) and, naturally, extend regularity results for the trace and lift operators onto the anisotropic case. As a byproduct, we build a generalization of the Kruzhkov — Korolev Trace Theorem for the first-order Sobolev Spaces (1985). In the second part of the paper we observe the nonhomogeneous Dirichlet, Neumann, and Robin problems for p-elliptic equations. The well-posedness theory for these problems can be successfully constructed using isotropic theory, and the corresponding results are outlined in the paper. Clearly, in such a unilateral approach, the anisotropic features are ignored and the results are far beyond the critical regularity. In the paper, the refinement of the trace theorem is done by the constructed extension.

DOI 10.14258/izvasu(2018)4-19

On the Solvability of the Problem of Fluid Filtration in a Deformable Porous Medium in the Gravitational Field

2018-10-08T16:09:10+07:00

The paper deals with the model of filtration of a viscous compressible fluid in a deformable medium, which has predominantly viscous properties with respect to elastic media. In contrast to the earlier works devoted to the substantiation of this model, the present paper gives a justification for a model that takes into account the influence of gravity. A theorem on local solvability of the problem in the field of gravity is proved. In § 1 we give a brief statement of the problem and formulate the main result of the paper. The initial system of equations describing the process consists of the equations of mass conservation for the solid and liquid phases, the law of conservation of momentum for the liquid, which is taken in the form of Darcy’s law and takes into account the motion of the skeleton, the conservation of the momentum of the system as a whole, and the equation linking the effective pressure and porosity, which determines the rheology. After the transition to the Lagrange variables, this system reduces to two equations for finding the porosity functions and the density of the liquid phase. In § 2 we give a proof of the theorem for the system obtained, and we also establish the physical maximum principle for the porosity and density functions of the liquid phase. The proof of the theorem is based on the Tikhonov-Schauder theorem on a fixed point. In paragraph 3 we give a generalization to the case of a complete equation of the balance of forces.

DOI 10.14258/izvasu(2018)4-20

Irreversible Deformations of a Rotating Cylinder

2018-10-08T16:09:11+07:00

The problem of acceleration of a cylindrical medium with consideration of irreversible deformation of creep and plasticity is investigated. For comparison, the problem of a rotating cylinder without creep deformation is considered. The problem of elastic deformation is solved analytically for the case of viscoplastic deformation and numerically -for the case of creep deformation. The Norton power low with continuous Mises type potential is used for modeling a process of creep deformation. The viscoplasticity model with Mises type stress potential is used for plastic deformation. When plastic flow occurs, it is assumed that the processes of accumulation of irreversible deformations of plasticity and creep take place together. The conclusions are made about the influence of creep deformation on the final distribution of stress. The significant decrease of stress intensity is observed for cylindrical mediums with rigid inclusion. However, the decrease is less significant for the hollow cylindrical medium. Also, the redistribution of stress intensity without decreasing is observed for the cylindrical medium with two free boundaries.

DOI 10.14258/izvasu(2018)4-21

Construction of Surfaces with Constant Mean Curvature

2018-11-16T09:23:21+07:00

The paper studies surfaces with constant mean curvature (CMC) H. If H = 0 then the surfaces are minimal. CMC tori were studied by H. Wente. U. Abresz proved that Wente tori have one family of planar lines of curvature and characterized them with elliptic integrals.

A.I. Bobenko in his studies considered the problem of constructing CMC tori E³, S³, H³. In this paper, CMC surfaces of revolution are investigated. For a surface in E³ the Bonnet’s theorem states that for any surface having constant positive Gaussian curvature, there exists a surface parallel to it with a constant mean curvature.

According to this statement, for surfaces of revolution with constant positive Gaussian curvature, CMC surfaces are constructed using the Bonnet’s theorem. It is proved that constructed surfaces are also surfaces of revolution. A family of plane curvature lines (meridians) is described by elliptic integrals, and surfaces with Gaussian curvature are also described by elliptic integrals. These surfaces are constructed using the mathematical software package.

DOI 10.14258/izvasu(2018)4-22