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Number of results: 11
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Some algorithms of computer algebra

O. Porkuian A. Timoshyn L. Timoshyna
Teka Commission of Motorization and Power Industry in Agriculture | 2016 | vol. 16 | No 2
Keywords computer algebra Maxima system determinant Bareiss algorithm a quadratic form unitriangular transformation
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Abstract

The article describes one of the methods for computing determinants without using fractions proposed by Bareiss. This problem has a clear algorithmic character in nature and refers to the field of computer algebra. The implementation of this algorithm is proposed in the known Maxima system of symbolic computations. In addition, this method makes it possible to get enough convenient formula for the calculation of the matrix of unitriangular transformation of a quadratic form to a canonical one.
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Authors and Affiliations

O. Porkuian
A. Timoshyn
L. Timoshyna

Art’s Hidden Typology

Marek Kuś Jacek Rogala Joanna Dreszer Beata Bajno
ACADEMIA. The magazine of the Polish Academy of Sciences | 2023 | No 4 (80) Authenticity | 30-34 | DOI: 10.24425/academiaPAS.2023.147631
Keywords artificial intelligence algebraic topology
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Abstract

When we look at works of art, our brain reacts to what we see in subconscious ways. Certain aspects of our perceptions can be captured using algebraic methods.
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Authors and Affiliations

Marek Kuś
1
Jacek Rogala
2
Joanna Dreszer
3
Beata Bajno
4
  1. PAS Center for Theoretical Physics in Warsaw
  2. Center for Research on Culture, Languageand Mind, University of Warsaw
  3. Institute of Psychology Nicolaus CopernicusUniversity in Toruń
  4. Association of Polish Artists and Designers,Warsaw Section

Professor Andrzej Szczepan Białynicki-Birula (1935–2021)

Stefan Jackowski
Nauka | 2021 | No 4 | 187-199 | DOI: 10.24425/nauka.2021.137650
Keywords Andrzej Białynicki-Birula algebraic geometry algebraic topology University of Warsaw
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Abstract

Andrzej Białynicki-Birula, Professor at the University of Warsaw died on April 19, 2021 at the age of 85. He was an outstanding mathematician, who made important contributions to algebra and algebraic geometry. He published many important articles in most prestigious journals such that Annals of Mathematics, Inventiones mathematicae, Topology, American Journal of Mathematics. Professor Białynicki graduated from the University of Warsaw and obtained Ph.D. from the University of California at Berkeley in 1960. After his return to Poland he initiated and played a major role in modernization of research and university curricula in a broad spectrum of mathematical disciplines related to algebra. He has published several textbooks on linear algebra, algebra, algebraic geometry and cryptography, which are currently used at the University of Warsaw and many other Polish universities. Professor Białynicki-Birula served as the dean of the Faculty of Mathematics, Informatics and Mechanics (1977–1981) and as the vice-rector of the University of Warsaw (1985–1987). He was an ordinary member of the Polish Academy of Sciences, and a member of the Academia Europea. In recognition of his achievements Professor Białynicki-Birula received several prizes and distinctions, among them the Officers Cross of the Order Polonia Restituta. Professor Białynicki-Birula was also an art collector, particularly interested in a gothic sculpture, on which he was an expert. In his summerhouse near Belorussian border he was renovating and collecting ethnographic objects related to everyday life and work of peasants. He left a wife, Magdalena Borsuk-Białynicka, a professor of palaeontology, two daughters, a son and 11 grandchildren.
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Authors and Affiliations

Stefan Jackowski

Automated Linearization of a System of Nonlinear Ordinary Differential Equations

Aigerim Mazakova Sholpan Jomartova Waldemar Wójcik Talgat Mazakov Gulzat Ziyatbekova
International Journal of Electronics and Telecommunications | 2023 | vol. 69 | No 4 | 655-600 | DOI: 10.24425/ijet.2023.147684
Keywords Ordinary differential equation Computer algebra stability controllability MatLab
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Abstract

This paper investigates the possibility of automatically linearizing nonlinear models. Constructing a linearised model for a nonlinear system is quite labor-intensive and practically unrealistic when the dimension is greater than 3. Therefore, it is important to automate the process of linearisation of the original nonlinear model. Based on the application of computer algebra, a constructive algorithm for the linearisation of a system of non-linear ordinary differential equations was developed. A software was developed on MatLab. The effectiveness of the proposed algorithm has been demonstrated on applied problems: an unmanned aerial vehicle dynamics model and a twolink robot model. The obtained linearized models were then used to test the stability of the original models. In order to account for possible inaccuracies in the measurements of the technical parameters of the model, an interval linearized model is adopted. For such a model, the procedure for constructing the corresponding interval characteristic polynomial and the corresponding Hurwitz matrix is automated. On the basis of the analysis of the properties of the main minors of the Hurwitz matrix, the stability of the studied system was analyzed.
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Authors and Affiliations

Aigerim Mazakova
3
Sholpan Jomartova
3
Waldemar Wójcik
2
Talgat Mazakov
1
Gulzat Ziyatbekova
1
  1. Institute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, Kazakhstan
  2. Lublin Technical University, Poland
  3. Al-Farabi Kazakh NationalUniversity, Kazakhstan

Sub-optimal motion planning of one-chained, two-input nonholonomic systems

Ignacy Duleba Iwona Karcz-Duleba
Bulletin of the Polish Academy of Sciences Technical Sciences | 2023 | 71 | 3 | e145684 | DOI: 10.24425/bpasts.2023.145684
Keywords nonholonomic systems chained form optimization algorithm Lie algebraic method
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Abstract

In this paper three algorithms of motion planning for two-input, one-chained nonholonomic systems are presented. The classical Murray-Sastry algorithm is compared with two original algorithms aimed at optimizing energy of controls. Based on the generalized Campbell- Baker-Hausdorff-Dynkin formula applied to the systems, some observations are made concerning the optimal relationship between amplitudes and phases of harmonic controls. The observations help to optimize a selection of controls and to design new algorithms for planning a sub- optimal trajectory between given boundary configurations. It was also shown that for those particular systems the generalized C-B-H-D formula is valid not only locally (as in a typical case) but also globally. Simulations performed on the five-dimensional chain system facilitate distinguishing the proposed algorithms from the Murray-Sastry algorithm and to illustrate their features. Systems in a chained form are important from a practical point of view as they are canonical for a class of systems transformable into this form. The most prominent among them are mobile robots with or without trailers.
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Authors and Affiliations

Ignacy Duleba
1
ORCID: ORCID
Iwona Karcz-Duleba
2
ORCID: ORCID
  1. Department of Cybernetics and Robotics
  2. Department of Control Systems and Mechatronics Wroclaw University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Matrix black box algorithms - a survey

Jerzy Respondek
Bulletin of the Polish Academy of Sciences Technical Sciences | 2022 | 70 | 2 | e140535 | DOI: 10.24425/bpasts.2022.140535
Keywords matrix algebra matrix multiplication algorithm numerical recipes recursion
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Abstract

The implementations of matrix multiplication on contemporary, vector-oriented, and multicore-oriented computer hardware are very carefully designed and optimized with respect to their efficiency, due to the essential significance of that operation in other science and engineering domains. Consequently, the available implementations are very fast and it is a natural desire to take advantage of the efficiency of those implementations in other problems, both matrix and nonmatrix. Such an approach is often called a black box matrix computation paradigm in the literature on the subject. In this article, we gathered a broad series of algorithms taking advantage of the efficiency of fast matrix multiplication algorithms in other mathematical and computer science operations.
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Authors and Affiliations

Jerzy Respondek
1
  1. Silesian University of Technology, Faculty of Automatic Control, Electronics and Computer Science, ul. Akademicka 16, 44-100 Gliwice, Poland

Novel solutions on model-based and model-free robotic-assisted ankle rehabilitation

Juan Carlos Arceo Jorge Álvarez Carlos Armenta Jimmy Lauber Sylvain Cremoux Emilie Simoneau-Buessinger Miguel Bernal
Archives of Control Sciences | 2021 | vol. 31 | No 1 | 5-27 | DOI: 10.24425/acs.2021.136878
Keywords active disturbance rejection computed torque control differential algebraic equations parallel rehabilitation robot real-time implementation system identification
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Abstract

In this report, ankle rehabilitation routines currently approved by physicians are implemented via novel control algorithms on a recently appeared robotic device known as the motoBOTTE. The physician specifications for gait cycles are translated into robotic trajectories whose tracking is performed twofold depending on the availability of a model: (1) if obtained via the Euler-Lagrange approach along with identification of unknown plant parameters, a new computed-torque control law is proposed; it takes into account the parallel-robot characteristics; (2) if not available, a variation of the active disturbance rejection control technique whose parameters need to be tuned, is employed. A detailed discussion on the advantages and disadvantages of the model-based and model-free results, from the continuous-time simulation to the discrete-time implementation, is included.
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Authors and Affiliations

Juan Carlos Arceo
1
Jorge Álvarez
2
Carlos Armenta
1
Jimmy Lauber
1
Sylvain Cremoux
3
Emilie Simoneau-Buessinger
1
Miguel Bernal
2
  1. Université Polytechnique Hauts-de-France, LAMIH UMR CNRS 8201, F-59313 Valenciennes, France
  2. Sonora Institute of Technology, 5 de Febrero 818 Sur, Ciudad Obregon, Sonora, Mexico
  3. Centre de Recherche Cerveau et Cognition, CNRS UMR 5549, Université de Toulouse, Toulouse 31052, France

On an episode in academic contacts of Jacek Hawranek and Jan Zygmunt with Professor Bogusław Wolniewicz

Jan Zygmunt
Przegląd Filozoficzny. Nowa Seria | 2018 | No 3 | 149-162 | DOI: 10.24425/pfns.2018.125458
Keywords semilattice formal ontology of situations algebraic logic history of Polish logic Bogusław Wolniewicz
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Abstract

Selected scientific contacts of Jacek Hawranek and Jan Zygmunt with Professor Bogusław Wolniewicz in the period from the end of the 1980s to the beginning of the 21st century are presented in this essay. They concerned the algebraic aspects of the ontology of situations and from one moment – one only question that was posed by Wolniewicz in his note A question about join-semilattices (Bulletin of the Section of Logic, 19/3, 1990, pp. 108–108), and resulted in the Hawranek & Zygmunt paper Wokół pewnego zagadnienia z dziedziny półkrat górnych z jednością (“Some comments on a question about semilattices with unit”) (Acta Universitatis Wratislaviensis 1445, Logika 15 (1993), pp. 59–68) containing an answer to Wolniewicz’s question. The Hawranek & Zygmunt paper is reprinted below, and the essay might be also treated as a kind of an analytical and historical introduction to it. The story of contacts Wolniewicz – Hawranek & Zygmunt has been told with the help of the preserved correspondence between the three persons. In his letters Professor Wolniewicz appears as a passionate researcher, open to discussion, ready to share his research successes and difficulties with others.

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Authors and Affiliations

Jan Zygmunt

Distributed controllability of one-dimensional heat equation in unbounded domains: The Green’s function approach

Asatur Zh. Khurshudyan
Archives of Control Sciences | 2019 | vol. 29 | No 1 | 57-71 | DOI: 10.24425/acs.2019.127523
Keywords lack of controllability exact controllability approximate controllability null controllability Green’s function heuristic method infinite system of algebraic equations regularity fully regularity
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Abstract

We derive exact and approximate controllability conditions for the linear one-dimensional heat equation in an infinite and a semi-infinite domains. The control is carried out by means of the time-dependent intensity of a point heat source localized at an internal (finite) point of the domain. By the Green’s function approach and the method of heuristic determination of resolving controls, exact controllability analysis is reduced to an infinite system of linear algebraic equations, the regularity of which is sufficient for the existence of exactly resolvable controls. In the case of a semi-infinite domain, as the source approaches the boundary, a lack of L2-null-controllability occurs, which is observed earlier by Micu and Zuazua. On the other hand, in the case of infinite domain, sufficient conditions for the regularity of the reduced infinite system of equations are derived in terms of control time, initial and terminal temperatures. A sufficient condition on the control time, heat source concentration point and initial and terminal temperatures is derived for the existence of approximately resolving controls. In the particular case of a semi-infinite domain when the heat source approaches the boundary, a sufficient condition on the control time and initial temperature providing approximate controllability with required precision is derived.

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Authors and Affiliations

Asatur Zh. Khurshudyan

Some comments on a question about semilattices with a unit

Jacek Hawranek Jan Zygmunt
Przegląd Filozoficzny. Nowa Seria | 2018 | No 3 | 163-174 | DOI: 10.24425/pfns.2018.125459
Keywords join-semilattice minimal element B. Wolniewicz’s question formal ontology of situations topological space dense set Boolean algebra filter consequence operation independent set
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Abstract

Bogusław Wolniewicz, inspired by his formal ontology of situations, has put forward a question on semilattices with a unit (A question about joinsemilattices, Bulletin of the Section of Logic 19/3, 1990). The present paper is entirely devoted to this problem in the formulation given by Wolniewicz. First, the meaning of the question is analyzed and its lattice-theoretical and Boolean algebraic contents are exhibited. Second, set-theoretical and topological counterparts of the question are formulated and commented upon.

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Authors and Affiliations

Jacek Hawranek
Jan Zygmunt

Construction of Generalized Rademacher Functions in Terms of Ternary Logic: Solving the Problem of Visibility of Using Galois Fields for Digital Signal Processing

Elizaveta S. Vitulyova Dinara K. Matrassulova Ibragim E. Suleimenov
International Journal of Electronics and Telecommunications | 2022 | vol. 68 | No 2 | 237-244 | DOI: 10.24425/ijet.2022.139873
Keywords digital signal processing non-binary Galois fields Fourier transform Rademacher functions Walsh function multivalued logic visibility problem algebraic extensions ternary representation of a number
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Abstract

Generalized Rademacher functions, constructed as a sequence of elements of Galois fields are intended to find the spectral representation of signals with levels. These functions form a complete basis on the interval corresponding to -1 discrete time intervals and for passing into the classical Rademacher functions. The advantage of such spectra obtained using Galois Fields Fourier Transform is that the range of variation of the spectrum amplitudes remains the same as the range of variation of the original signal, which is modeled on discrete time functions taking values in the Galois field.
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Authors and Affiliations

Elizaveta S. Vitulyova
1
Dinara K. Matrassulova
2
Ibragim E. Suleimenov
3
  1. Almaty University of Power Engineering and Telecommunications named after Gumarbek Daukeyev, Almaty, Republic of Kazakhstan
  2. Almaty Universityof Power Engineering and Telecommunications named after GumarbekDaukeyev, Almaty, Republic of Kazakhstan
  3. National Engineering Academy of Republic of Kazakhstan, Almaty, Kazakhstan

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