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Metric Invariants of Second-Order Surfaces Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 D. Yu. Volkov, K. V. Galunova
Abstract The paper is devoted to the classical problem of analytical geometry in n-dimensional Euclidean space, namely, finding the canonical equation of a quadric from an initial equation. The canonical equation is determined by the invariants of the second-order surface equation, i.e., by quantities that do not change when the space coordinates are changed affinely. S.L. Pevzner found a convenient
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Kindred Diagrams Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 V. M. Nezhinskij
Abstract By a diagram we mean a topological space obtained by gluing to a standard circle a finite number of pairwise non-intersecting closed rectangles along their lateral sides, the glued rectangles being pairwise disjoint. Diagrams are not new objects; they have been used in many areas of low-dimensional topology. Our main goal is to develop the theory of diagrams to a level sufficient for application
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The Transgression Effect in the Problem of Motion of an Almost Holonomic Pendulum Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 A. S. Kuleshov, I. I. Ulyatovskaya
Abstract In 1986, Ya.V. Tatarinov presented the basis of the theory of weakly nonholonomic systems. Mechanical systems with nonholonomic constraints depending on a small parameter are considered. It is assumed that when the value of this parameter is zero, the constraints of such a system become integrable; i.e., in this case, we have a family of holonomic systems depending on several arbitrary integration
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Generation of Records Obtained from Sequences of Independent and Non-Identically Distributed Variables Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 S. A. Petukhov, A. V. Stepanov
Abstract Generation algorithms of record times and values obtained from sequences of independent and non-identically distributed random variables, the distribution functions of which are defined on a common support, are proposed in the present paper. Known algorithms of generation of record times and values are given in Introduction for the case when the initial random variables are independent and
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On Contact Problems with a Deformable Punch and Variable Rheology Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 V. A. Babeshko, O. V. Evdokimova, O. M. Babeshko, M. V. Zaretskaya, V. S. Evdokimov
Abstract 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 used in boundary-value problems for systems of partial differential equations. With its help, solutions
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Construction of Fundamental Solution for an Odd-Order Equation Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 B. Yu. Irgashev
Abstract 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 an odd-order equation with multiple characteristics in a rectangular domain as the sum of these
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Conditions for Local Parameter Identifiability for Systems of Differential Equations with an Infinite-Dimensional Parameter Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 S. Yu. Pilyugin, V. S. Shalgin
Abstract The problem of parametric identification (determining the parameters of a system by observing solutions or functions of them) is one of the main problems in the applied theory of differential equations. When solving this problem, the property of local identifiability plays a crucial role. The presence of this property means that by observing solutions, it is possible to determine unambiguously
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On Thermo-Optically Excited Parametric Oscillations of Microbeam Resonators. II Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 N. F. Morozov, D. A. Indeitsev, A. V. Lukin, I. A. Popov, L. V. Shtukin
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On the Asymptotic Behavior of Probabilities of Moderate Deviations for Combinatorial Sums Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 A. N. Frolov
Abstract In this paper, the asymptotic behavior of probabilities of moderate deviations is investigated for combinatorial sums of independent random variables with moments of order p > 2. The zones are found in which these probabilities are equivalent to the tail of the standard normal law. The width of the zones are expressed in terms of the logarithm of the combinatorial variant of the Lyapunov ratio
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Calculation of Stresses Initiated by an Electrical Explosion of Conductors in a Composite Thick-Walled Cylinder Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 V. M. Kats, V. A. Morozov, Ya. A. Sevastyanov
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Modeling of Imperfect Contacts in Determining the Effective Diffusion Permeability Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 K. P. Frolova, E. N. Vilchevskaya, V. A. Polyanskiy
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Rayleigh Waves in an Electroelastic Medium with Prestressed Inhomogeneous Coating Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 T. I. Belyankova, V. V. Kalinchuk
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Specific Features of the Dynamics of the Rectilinear Motion of the Darboux Mechanism Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 S. N. Burian
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Natural Vibrations of Composite Cylindrical Shells Partially Filled with Fluid Vestnik St. Petersb. Univ. Math. Pub Date : 2024-01-24 S. A. Bochkarev, S. V. Lekomtsev, V. P. Matveenko
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Models of Solid Mechanics in the Problems of Ophthalmology Vestnik St. Petersb. Univ. Math. Pub Date : 2023-12-01
Abstract 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 body. The mathematical models describing the process of measuring the true intraocular pressure (IOP)
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Review of Works by V. A. Yakubovich’s Scientific School on Artificial Intelligence and Robotics Vestnik St. Petersb. Univ. Math. Pub Date : 2023-12-01
Abstract 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 development of cybernetics and artificial intelligence is discussed. Special emphasis is put on Yakubovich’s
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Asymptotical Separation of Harmonics by Singular Spectrum Analysis Vestnik St. Petersb. Univ. Math. Pub Date : 2023-12-01
Abstract The paper is devoted to studying the sufficient conditions for the asymptotical separability of distinct terms in the linear combination of harmonics by singular spectrum analysis (SSA). Namely, the series x0, …, \({{x}_{{N - 1}}}\) with xn = \(\sum\nolimits_{i = 1}^r {{{f}_{{i,n}}}} \) , where \({{f}_{{i,n}}}\) = \({{b}_{i}}\cos ({{\omega }_{i}}n + {{\gamma }_{i}})\) and both amplitudes |bi|
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Modeling Problems of Dynamics and Development of Scientific Areas of Mechanics and Applied Mathematics Vestnik St. Petersb. Univ. Math. Pub Date : 2023-12-01
Abstract 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, founder of the scientific school of analytical mechanics, space dynamics, biomechanics, and applied
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Rigid-Body Dynamics from the Euler Equations to the Attitude Control of Spacecraft in the Works of Scientists from Saint Petersburg State University. Part 1 Vestnik St. Petersb. Univ. Math. Pub Date : 2023-09-27 A. A. Tikhonov
Abstract This review, which consists of several works, is dedicated to the 300th anniversary of St. Petersburg State University (SPbSU) and is an attempt to analyze the scientific achievements of the St. Petersburg School of Mathematics and Mechanics in the field of rigid-body dynamics. This work, which is the first part of the review, covers the main achievements of the period from the founding of
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Saint Petersburg School of the Theory of Linear Groups. I. Prehistory Vestnik St. Petersb. Univ. Math. Pub Date : 2023-09-27 N. A. Vavilov
Abstract The present survey describes the contribution of St. Petersburg mathematicians to the development of the theories of linear, classical, and algebraic groups. The first part is dedicated to the prehistory of the studies in the theory of linear groups in St. Petersburg, specifically, to the pedigree of the algebra schools created by Tartakovsky and Faddeev, and to an outline of the origin of
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Stationary Reversible Processes of a Moving Average and Autorepression with Residuals as a Moving Average Vestnik St. Petersb. Univ. Math. Pub Date : 2023-09-27 T. M. Tovstik
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Computer Analysis of a Model of a Synchronous No-Current Electric Motor Vestnik St. Petersb. Univ. Math. Pub Date : 2023-09-27 B. I. Konosevich, Yu. B. Konosevich
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On the MDM Method for Solving the General Quadratic Problem of Mathematical Diagnostics Vestnik St. Petersb. Univ. Math. Pub Date : 2023-09-27 V. N. Malozemov, N. A. Solovyeva
Abstract The term “mathematical diagnostics” was introduced by V. F. Demyanov in the early 2000s. The simplest problem of mathematical diagnostics is to determine the relative position of some point p and the convex hull C of a finite number of given points in n-dimensional Euclidean space. Of interest is the answer to the following questions: does the point p belong to the set C or not? If p does
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Transgression Effect in the Problem of the Motion of a Rod on a Cylinder Vestnik St. Petersb. Univ. Math. Pub Date : 2023-09-27 A. S. Kuleshov, N. M. Vidov
Abstract The motion of a heavy rigid thin rod on the surface of a right circular cylinder is considered. It is assumed that the angle between the generatrix of the cylinder and the direction of gravity is nonzero. The positions of equilibria of the rod on a cylinder form an equilibrium manifold (for all these equilibria the rod rests on the cylinder by its center of mass). The effect of transgression
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Inequalities for the Derivatives of Rational Functions with Prescribed Poles and Restricted Zeros Vestnik St. Petersb. Univ. Math. Pub Date : 2023-09-27 U. M. Ahanger, W. M. Shah
Abstract As a generalization of a result obtained by Dubinin [7], Wali (preprint online) [14] recently proved the following: Let r ∈ \({{\mathcal{R}}_{n}}\), where r has n poles at a1, a2, …, an and all its zeros lie in |z| ≤ 1, with s-fold zeros at the origin, then for |z| = 1 $$\left| {r{\kern 1pt} '(z)} \right| \geqslant \frac{1}{2}\left\{ {\left| {\mathcal{B}{\kern 1pt} '(z)} \right| + (s + m -
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Matrix Representations of Endomorphism Rings for Torsion-Free Abelian Groups Vestnik St. Petersb. Univ. Math. Pub Date : 2023-09-27 E. A. Blagoveshchenskaya, A. V. Mikhalev
Abstract Non-isomorphic direct decompositions of torsion-free Abelian groups are reflected in their endomorphism ring decompositions which admit matrix representations. The set of possible direct decompositions of a special kind matrix rings into direct sums of one-sided indecomposable ideals is described. This leads to the combinatorial constructions of isomorphisms between non-commutative differently
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On the Probabilities of Large Deviations of Combinatorial Sums of Independent Random Variables That Satisfy the Linnik Condition Vestnik St. Petersb. Univ. Math. Pub Date : 2023-09-27 A. N. Frolov
Abstract New results on the asymptotic behavior of the probabilities of large deviations of combinatorial sums of independent random variables satisfying the Linnik condition are obtained. A zone, where these probabilities are equivalent to the tail of the standard normal law, is found. Such results were previously obtained by the author under Bernstein’s condition. The new results are proved by the
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Scientific School of Nonequilibrium Aeromechanics at St. Petersburg State University Vestnik St. Petersb. Univ. Math. Pub Date : 2023-09-27 Yu. N. Voroshilova, V. A. Istomin, O. V. Kunova, E. V. Kustova, E. A. Nagnibeda, M. A. Rydalevskaya
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On the Solution of a Two-Sided Vector Equation in Tropical Algebra Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 N. K. Krivulin
Abstract In the context of tropical mathematics, the problem of solving a vector equation with two given matrices and unknown vectors, each part of which has the form of a product of one of the matrices and an unknown vector, is considered. Such an equation, which has an unknown vector on either side of the equal sign, is often called a two-sided equation. A new procedure for solving two-sided equations
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Separation of Roots of Systems of Nonlinear Equations. Stochastic Approach Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 S. M. Ermakov, S. N. Leora
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On Uniform Consistency of Neyman’s Type Nonparametric Tests Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 M. S. Ermakov, D. Yu. Kapatsa
Abstract The goodness-of-fit problem is explored, when the test statistic is a linear combination of squared Fourier coefficients’ estimates coming from the Fourier decomposition of a probability density. Common examples of such statistics include Neyman’s test statistics and test statistics, generated by L2-norms of kernel estimators. We prove the asymptotic normality of the test statistic for both
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On Generalized Bessel Potentials and Perfect Functional Completions Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 A. L. Dzhabrailov, E. L. Shishkina
Abstract The class of generalized Bessel potentials is the main object of study in this paper. The generalized Bessel potential is a negative real power of the operator (I – ∆γ), where ∆γ = \(\sum\nolimits_{k = 1}^n {\frac{1}{{x_{k}^{{{{\gamma }_{k}}}}}}\frac{\partial }{{\partial {{x}_{k}}}}x_{k}^{{{{\gamma }_{k}}}}\frac{\partial }{{\partial {{x}_{k}}}}} \) is the Laplace–Bessel operator and γ = (γ1
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Stochastic Computational Methods and Experiment Design Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 S. M. Ermakov, V. B. Melas
Abstract The study presents a brief overview of key results of research conducted at the Statistical Modeling Department of St. Petersburg State University. These results include mathematical substantiation of the computer simulation of randomness, stochastic methods for solving equations, stochastic optimization, and study of the stochastic stability and parallelism of Monte Carlo algorithms. In terms
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Numerical Modeling of Hydrodynamic Accidents: Erosion of Dams and Flooding of Territories Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 S. S. Khrapov
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Fixed Point Theorem via Measure of Non-Compactness for a New Kind of Contractions Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 Youssef Touail, Amine Jaid, Driss El Moutawakil
Abstract In this paper, we will use the notion of \(\alpha \)-admissible mappings in Banach spaces, to introduce the concept of \({{T}_{\beta }}\)-contractive mappings and establish a fixed point theorem for this type of contractions. Our theorems generalize and improve many results in the literature. Moreover, we apply the main result to prove the existence of a solution for Volterra-integral equation
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On Opto-Thermally Excited Parametric Oscillations of Microbeam Resonators. I Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 N. F. Morozov, D. A. Indeitsev, A. V. Lukin, I. A. Popov, L. V. Shtukin
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Finite Deformations of a Bilayer Dielectric Nonlinear-Elastic Anisotropic Tube under the Action of an Electric Field Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 A. M. Kolesnikov, D. A. Letunova
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Free Vibrations of a Cylindrical Shell with a Cap. II. Analysis of the Spectrum Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 G. A. Nesterchuk, A. L. Smirnov, S. B. Filippov
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Modeling of Nonequilibrium Processes behind a Shock Wave in a Mixture of Carbon Dioxide and Argon Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 S. A. Batalov, E. V. Kustova
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Approximation of Hölder Functions in the Lp Norm by Harmonic Functions on Some Multidimensional Compact Sets Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 D. A. Pavlov
Abstract In this paper, the class of Hölder functions in the sense of the Lp norm on certain compacts in \({{\mathbb{R}}^{m}}\) (m \( \geqslant \) 3) is analyzed, and theorems of the approximation by functions being harmonic in the neighborhoods of these compacts are proved. These compacts represent a generalization of the concept of a chord-arc curve in \({{\mathbb{R}}^{3}}\) to higher dimensions
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Differential Resonant MEMS Accelerometer: Synchronization Characteristics of Weakly Coupled Microbeam Sensing Elements Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 D. A. Indeitsev, V. S. Igumnova, A. V. Lukin, I. A. Popov, L. V. Shtukin
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Control of Composite-Wing Oscillation Coupling Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 V. M. Ryabov, B. A. Yartsev
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On the Asymptotic Power of a Method for Testing Hypotheses on the Equality of Distributions Vestnik St. Petersb. Univ. Math. Pub Date : 2023-06-08 V. B. Melas
Abstract In this paper, the asymptotic power of a method for testing hypotheses on the equality of two distributions is investigated; it can be regarded as a generalization of the Wilcoxon–Mann–Whitney test. We consider a class of distributions such that the mathematical expectation of the square of some auxiliary function is finite. For the case where the alternative distribution differs from the
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On Some Probability Distributions Related to the Classical Bernoulli Scheme. II Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 S. M. Ananjevskii, V. B. Nevzorov
Abstract The classical scheme of independent Bernoulli trials has been one of the most popular topics in probability theory for more than three centuries (starting with the works of Jacob Bernoulli). This scheme is ideal for formulating and solving various practical problems. Many results have been obtained using modifications of this scheme; however, new situations and new problems appear, and they
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Fourier-Transform Method for Partial Differential Equations. Part 2. Existence and Uniqueness of Solutions to the Cauchy Problem for Linear Equations Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 V. I. Gishlarkaev
Abstract The work proposes a method for analyzing the Cauchy problem for a wide class of linear evolution partial differential equations with variable coefficients. By applying the (inverse) Fourier transform, the original equation is reduced to an integrodifferential equation, which can be considered as an ordinary differential equation in an appropriate Banach space. The latter space is chosen so
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Location of Zeros of Lacunary-Type Polynomials Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 Irfan Ahmad Wani, Mohammad Ibrahim Mir, Ishfaq Nazir
Abstract In this paper, by relaxing the hypothesis of well-known Eneström–Kakeya theorem, we obtain a result which is applicable to the lacunary-type of polynomials and generalizes several well-known results concerning the location of zeros of polynomials. In addition to this, we show by examples that our results presents better information about the bounds of zeros of polynomials than some known results
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Impact of a Rigid Sphere with an Infinite Kirchhoff–Love Plate Taking into Account Bulk and Shear Relaxation Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 M. V. Shitikova
Abstract The problem of the low-velocity normal impact of a rigid sphere with an infinite viscoelastic Kirchhoff–Love plate is considered. The dynamic behavior of a viscoelastic plate is described by a fractional-derivative standard linear solid model. The fractional parameter, which determines the order of the fractional derivative, takes into account the change in the viscosity of the plate material
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On the Properties of Some Inversion Methods of the Laplace Transform Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 A. V. Lebedeva, V. M. Ryabov
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Discontinuous Mappings and the Limit Load in Boundary Value Problems of Nonlinear Elasticity Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 I. A. Brigadnov
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Approximation by Polynomials Composed of Weierstrass Doubly Periodic Functions Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 K. A. Sintsova, N. A. Shirokov
Abstract The approximation-theory problem to describe classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, and splines arose over 100 years ago; it still remains topical. Among many problems related to approximation, we consider the two-variable polynomial approximation problem for a function defined on the continuum of an elliptic curve
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Remark on the Accuracy of Recurrent Forecasting in Singular Spectrum Analysis Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 V. V. Nekrutkin
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On the Ellipticity of Static Equations of Strain Gradient Elasticity and Infinitesimal Stability Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 V. A. Eremeyev
Abstract Conditions for the strong ellipticity of equilibrium equations are formulated within strain gradient elasticity under finite deformations. In this model, the strain energy density is a function of the first and second gradients of the position vector (deformation gradient). Ellipticity imposes certain constraints on the tangent elastic moduli. It is also closely related to infinitesimal stability
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Optimization of Oscillation Damping Modes of a Spatial Double Pendulum: 2. Solution of the Problem and Analysis of the Results Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 A. S. Smirnov, B. A. Smolnikov
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Natural Vibrations of a Cylindrical Shell with an End Cap. I. Asymptotic Analysis Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 S. B. Filippov, A. L. Smirnov, G. A. Nesterchuk
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On the Extension of a Family of Projections to a Positive Operator-Valued Measure Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 A. O. Alekseev, G. G. Amosov
Abstract In this paper, the problem of constructing a measure which accepts values within a positive cone of bounded operators in a Hilbert space is considered. The assumption is made that a projection-valued function defined on a subset X0 of the original set X is initially given. The goal of this paper is to find such a scalar measure μ on set X as well as the extension of a projection-valued function
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Zero-Velocity Surface in the General Three-Body-Problem Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 V. B. Titov
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Isosceles Tetrahedron and an Equimomental System of a Rigid Body Vestnik St. Petersb. Univ. Math. Pub Date : 2023-04-19 E. A. Nikonova
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Algebraic Solution to Optimal Scheduling Problems Taking into Account the Scheduled Start Time of Jobs in Projects Vestnik St. Petersb. Univ. Math. Pub Date : 2022-12-19 S. A. Gubanov
Abstract A direct analytical solution is proposed for problems of the optimal scheduling of jobs within a project, which is based on the models and methods of tropical (idempotent) optimization. Optimal scheduling problems are reduced to the problems of tropical optimization, which consist in minimizing the objective function under given strict constraints on the start and finish times of jobs. The
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Solution of a Two-Facility Location Problem in a Space with Chebyshev Distance Vestnik St. Petersb. Univ. Math. Pub Date : 2022-12-19 N. K. Krivulin, M. A. Bryushinin
Abstract The work considers a minimax two-facility location problem in a multidimensional space with Chebyshev distance under interval constraints on the feasible location area. The problem involves two groups of facilities with known coordinates and the objective to select optimal location coordinates for two new facilities under given constraints. The location of the new facilities is considered