Vestnik St Petersburg University Mathematics

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Journal Article

On the Anniversary of Alexander Konstantinovich Belyaev

2023 Vestnik St Petersburg University Mathematics

doi:10.1134/s1063454123040064

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Journal Article

On Contact Problems with a Deformable Punch and Variable Rheology

Babeshko, V. A.; Evdokimova, O. V.; Babeshko, O. M.; Zaretskaya, M. V.; Evdokimov, V. S.

2023 Vestnik St Petersburg University Mathematics

doi:10.1134/s1063454123040027

The paper presents for the first time one of the methods for studying and solving contact problems with a deformed stamp for those cases when there is a need to change the rheology of the stamp material. It is based on a new universal modeling method previously published by the authors, which is...

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Journal Article

Rayleigh Waves in an Electroelastic Medium with Prestressed Inhomogeneous Coating

Belyankova, T. I.; Kalinchuk, V. V.

2023 Vestnik St Petersburg University Mathematics

doi:10.1134/s1063454123040040

An approach to studying the influence of initial mechanical stresses and an electrostatic field on the structure and behavior of Rayleigh waves in piezoelectric media with nonhomogeneous coatings is proposed. This paper considers two-component coatings made of functionally graded piezoelectric...

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Journal Article

Natural Vibrations of Composite Cylindrical Shells Partially Filled with Fluid

Bochkarev, S. A.; Lekomtsev, S. V.; Matveenko, V. P.

2023 Vestnik St Petersburg University Mathematics

doi:10.1134/s1063454123040052

The paper presents the results of studies of natural vibrations of circular vertical layered cylindrical shells completely or partially filled with a quiescent compressible fluid and subjected to hydrostatic load. The behavior of the elastic structure and the fluid medium is described using the...

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Journal Article

On Thermo-Optically Excited Parametric Oscillations of Microbeam Resonators. II

Morozov, N. F.; Indeitsev, D. A.; Lukin, A. V.; Popov, I. A.; Shtukin, L. V.

2023 Vestnik St Petersburg University Mathematics

doi:10.1134/s1063454123040106

The present article is the second part of our study of the nonlinear dynamics of parametrically excited bending vibrations of a microbeam fixed at both ends, a basic sensitive element of a promising class of microsensors of various physical quantities, under laser thermo-optical action in the...

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Journal Article

Modeling of Imperfect Contacts in Determining the Effective Diffusion Permeability

Frolova, K. P.; Vilchevskaya, E. N.; Polyanskiy, V. A.

2023 Vestnik St Petersburg University Mathematics

doi:10.1134/s1063454123040088

The work develops a universal approach to accounting for imperfect contacts in determining effective properties of various nature, namely, effective diffusivity and thermal and electrical conductivity. Imperfect contacts appear when fields at the microlevel are not continuous. The possibility of...

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Journal Article

Modeling Problems of Dynamics and Development of Scientific Areas of Mechanics and Applied Mathematics

Alferov, G. V.; Korolev, V. S.; Polyakhova, E. N.; Kholshevnikov, K. V.

2023 Vestnik St Petersburg University Mathematics

doi:10.1134/s1063454123040167

The paper discusses the development of scientific areas of mechanics in the research by the honorary professor of St. Petersburg State University, Honored Worker of Science and Technology of the Russian Federation, and Doctor of Physical and Mathematical Sciences Viktor Sergeevich Novoselov,...

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Journal Article

Review of Works by V. A. Yakubovich’s Scientific School on Artificial Intelligence and Robotics

Matveev, A. S.; Fradkov, A. L.; Shepeljavyi, A. I.

2023 Vestnik St Petersburg University Mathematics

doi:10.1134/s106345412304009x

This is a review of the works of the research school of V.A. Yakubovich in the field of artificial intelligence, machine learning, adaptive systems, and robotics. The method of recurrent objective inequalities is considered in detail. The significance of the presented results for the further...

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Journal Article

Models of Solid Mechanics in the Problems of Ophthalmology

Bauer, S. M.; Venatovskaya, L. A.; Voronkova, E. B.

2023 Vestnik St Petersburg University Mathematics

doi:10.1134/s1063454123040039

This paper presents a very brief review of models constructed in cooperation with ophthalmologists, namely, for the change in the stress-strain state of the eye membrane after vision-correction operations and the change in the intraocular pressure after the injection of drugs into the vitreous...

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Journal Article

Construction of Fundamental Solution for an Odd-Order Equation

Irgashev, B. Yu.

2023 Vestnik St Petersburg University Mathematics

doi:10.1134/s1063454123040180

In previous papers, we obtained some delta-shaped partial solutions of odd-order equations with multiple characteristics and studied some of their properties. In this paper, we first obtain the necessary estimates at infinity for these solutions, and then construct a fundamental solution (FS) of...

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