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Axioms
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Stability, Approximation, Control and Application
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Stability, Approximation, Control and Application

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 7719

Special Issue Editors

Prof. Dr. Valentyn Sobchuk

E-Mail Website
Guest Editor
Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4E Academician Glushkov Avenue, 03127 Kyiv, Ukraine
Interests: differential equations; information systems; dynamical systems; nonlinear dynamical systems; functional stability
Prof. Dr. Oleksiy V. Kapustyan

E-Mail Website
Guest Editor
Department of Integral and Differential Equations, Taras Shevchenko National University of Kyiv, 4E Glushkov Ave., 03022 Kyiv, Ukraine
Interests: stability theory; control theory; approximation theory; information technologies

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to various advances in stability theory, approximation theory, and control problems, and their multidisciplinary applications.

The recent interest in these topics is a consequence of the increasing complexity of modern mathematical models that require the application of information technologies, computer modeling, and simulations, and, simultaneously, the development of existing and new theoretical approaches in these branches of mathematics. In this Special Issue, we will cover questions regarding Lyapunov stability and robust stability in evolutionary equations describing real-world phenomena, the existence and properties of limit regimes and attracting sets in impulsive dynamical systems with mechanical applications, theoretical and practical aspects of the approximation theory and numerical analysis, and optimal and adaptive control in nonlinear systems. 

Our goal is to gather articles reflecting new trends and approaches in stability theory, approximation theory, control problems, and related topics.

Prof. Dr. Valentyn Sobchuk
Prof. Dr. Oleksiy V. Kapustyan
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlinear system
  • stability
  • perturbation
  • impulsive system
  • approximation
  • numerical methods
  • control

Published Papers (6 papers)

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Research

11 pages, 644 KiB  
Article
Optimizing Energy Conversion in a Piezo Disk Using a Controlled Supply of Electrical Load
by Oleksandr Boryseiko, Oleksandr Laptiev, Oleh Perehuda and Anton Ryzhov
Axioms 2023, 12(12), 1074; https://doi.org/10.3390/axioms12121074 - 23 Nov 2023
Viewed by 797
Abstract
Piezoceramic products are actively used in modern technical devices and appliances. Disk piezoelectric devices are widely used in elements of information systems: in wireless communication, elements of satellite communication, global positioning systems. Among such devices, microwave piezo motors on traveling waves of various [...] Read more.
Piezoceramic products are actively used in modern technical devices and appliances. Disk piezoelectric devices are widely used in elements of information systems: in wireless communication, elements of satellite communication, global positioning systems. Among such devices, microwave piezo motors on traveling waves of various types are distinguished, including a motor built on an electromechanical disk converter, which performs non-axisymmetric oscillations under the action of a harmonic electric load. In this study, we perform separation of the electrode coating of the plate with thin diametrical dielectric sections and introduce a time-varying electric potential difference of different amplitude or phase to individual parts of the plate. We study the problem of non-axisymmetric planar oscillations of a piezoceramic disk with thickness polarization and the problem of optimization of the electromechanical coupling coefficient (EMCO) value as a function of an infinite number of parameters in space l2 of square summable sequences. Full article
(This article belongs to the Special Issue Stability, Approximation, Control and Application)
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22 pages, 399 KiB  
Article
Optimal Sparse Control Formulation for Reconstruction of Noise-Affected Images
by Peter Kogut and Yaroslav Kohut
Axioms 2023, 12(12), 1073; https://doi.org/10.3390/axioms12121073 - 23 Nov 2023
Viewed by 3079
Abstract
We discuss the optimal control formulation for enhancement and denoising of satellite multiband images and propose to take it in the form of an L1 control problem for a quasi-linear parabolic equation with a nonlocal p[u] Laplacian and with [...] Read more.
We discuss the optimal control formulation for enhancement and denoising of satellite multiband images and propose to take it in the form of an L1 control problem for a quasi-linear parabolic equation with a nonlocal p[u] Laplacian and with a cost functional of a tracking type. The main characteristic features of the considered parabolic problem is that the variable exponent p(t,x) and the diffusion anisotropic tensor D(t,x) are not predefined well a priori; instead, these characteristics nonlocally depend on the form of the solution of this problem (i.e., pu=p(t,x,u) and Du=D(t,x,u)). We prove the existence of optimal pairs with sparse L1 controls used for the indirect approach and a special family of approximation problems. Full article
(This article belongs to the Special Issue Stability, Approximation, Control and Application)
13 pages, 307 KiB  
Article
On Kemeny Optimization Scheme for Fuzzy Set of Relations
by Serhii O. Mashchenko, Olena A. Kapustian and Bruno Rubino
Axioms 2023, 12(12), 1067; https://doi.org/10.3390/axioms12121067 - 21 Nov 2023
Viewed by 718
Abstract
The present paper investigated the aggregation of individual preferences into a group fuzzy preference relation for a fuzzy set of decision-makers (DMs). This aggregation is based on the Kemeny optimization scheme. It was proven that this group relation is a Type-2 fuzzy relation [...] Read more.
The present paper investigated the aggregation of individual preferences into a group fuzzy preference relation for a fuzzy set of decision-makers (DMs). This aggregation is based on the Kemeny optimization scheme. It was proven that this group relation is a Type-2 fuzzy relation (T2FR). The decomposition approach was used to analyze the group T2FR. It is shown that the group T2FR can be decomposed according to secondary membership grades into a finite collection of Type-1 fuzzy relations. Each of them is a group fuzzy relation for a crisp set of DMs, which is the corresponding α-cut of the original fuzzy set of DMs. Illustrative examples are given. Full article
(This article belongs to the Special Issue Stability, Approximation, Control and Application)
14 pages, 1340 KiB  
Article
On the Acoustic Radiation Force Affecting Two Liquid Drops Located in the Wave Field
by Oleksandr P. Zhuk, Yaroslav Zhuk and Taras Klimchuk
Axioms 2023, 12(10), 940; https://doi.org/10.3390/axioms12100940 - 29 Sep 2023
Viewed by 619
Abstract
A system of initially immobile spherical liquid drops placed in another liquid in the field of a propagating acoustic wave is considered. The acoustic radiation force acting on each spherical liquid drop is determined as the function of the incident wave frequency, making [...] Read more.
A system of initially immobile spherical liquid drops placed in another liquid in the field of a propagating acoustic wave is considered. The acoustic radiation force acting on each spherical liquid drop is determined as the function of the incident wave frequency, making use of the solution of a problem of plane harmonic wave scattering on a system of two spherical bodies. The problem is solved by the variable separation method. To satisfy the boundary conditions on spherical surfaces, the expansion of the incident and reflected wave potentials over the spherical wave functions are used. Required constants in the solution are calculated from an infinite system of the algebraic equations, which is solved by a truncation method. It is established that the value of the acoustic radiation force affecting each liquid drop depends significantly on the densities, speed of sound in the outer and internal liquid, as well as on the distance between drops. It is also found that the acoustic radiation force has the same or opposite direction as the incident sound wave depending on its frequency. As result, at different frequencies, the liquid drops can start moving towards or further away from each other. Full article
(This article belongs to the Special Issue Stability, Approximation, Control and Application)
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14 pages, 336 KiB  
Article
ω-Limit Sets of Impulsive Semigroups for Hyperbolic Equations
by Petro Feketa, Juliya Fedorenko, Dmytro Bezushchak and Anna Sukretna
Axioms 2023, 12(10), 918; https://doi.org/10.3390/axioms12100918 - 27 Sep 2023
Viewed by 641
Abstract
In this paper, we investigate the qualitative behavior of an evolutionary problem consisting of a hyperbolic dissipative equation whose trajectories undergo instantaneous impulsive discontinuities at the moments when the energy functional reaches a certain threshold value. The novelty of the current study is [...] Read more.
In this paper, we investigate the qualitative behavior of an evolutionary problem consisting of a hyperbolic dissipative equation whose trajectories undergo instantaneous impulsive discontinuities at the moments when the energy functional reaches a certain threshold value. The novelty of the current study is that we consider the case in which the entire infinite-dimensional phase vector undergoes an impulsive disturbance. This substantially broadens the existing results, which admit discontinuities for only a finite subset of phase coordinates. Under fairly general conditions on the system parameters, we prove that such a problem generates an impulsive dynamical system in the natural phase space, and its trajectories have nonempty compact ω-limit sets. Full article
(This article belongs to the Special Issue Stability, Approximation, Control and Application)
9 pages, 274 KiB  
Article
Zeroes of Multifunctions with Noncompact Image Sets
by Pavlo O. Kasyanov, Liudmyla B. Levenchuk and Angela V. Piatova
Axioms 2023, 12(9), 879; https://doi.org/10.3390/axioms12090879 - 14 Sep 2023
Viewed by 866
Abstract
In this article we consider zeroes for multifunctions with possibly noncompact image sets. We introduce the notion of multifunction with K-inf-compact support. We also establish three types of applications: the Bayesian approach for analysis of financial operational risk under certain constraints, occupational [...] Read more.
In this article we consider zeroes for multifunctions with possibly noncompact image sets. We introduce the notion of multifunction with K-inf-compact support. We also establish three types of applications: the Bayesian approach for analysis of financial operational risk under certain constraints, occupational health and safety measures optimization, and transfer of space innovations and technologies. Full article
(This article belongs to the Special Issue Stability, Approximation, Control and Application)
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