Top

Published in:

2024 | OriginalPaper | Chapter

Some Applications of the Dickson Polynomials of Higher Kind for Modeling Radiation Diagrams

Authors : Maria Vasileva, Vesselin Kyurkchiev, Anton Iliev, Asen Rahnev, Nikolay Kyurkchiev

Published in: New Trends in the Applications of Differential Equations in Sciences

Publisher: Springer Nature Switzerland

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper we consider the Dickson polynomials \(D_{m+1,n}(x,a)\) of the sixth and seven kind (i.e. \(m=5\) and \(m=6\), respectively). First, a model with Dickson polynomials as corrections in the Lienard system is presented and “level curves” are studied. In the second place, we will note that some specifics of the amplitudes of these high-degree polynomials open up the possibility of modeling signals from the field of antenna-feeder technology. So, for example, changing the variable t by \(t=b\cos \theta +c\) (\(\theta \) is the azimuthal angle and c is the phase difference) in the y(t)-component of the solution of Lienard differential system results in the generation of radiation diagrams. Numerical examples, illustrating our results using CAS MATHEMATICA are given.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Special Lattice and Digital Sequences for Multidimensional Air Pollution Modelling

next chapter Novel Stochastic Method for Multidimensional Fredholm Integral Equations

Wang, Q., Yucas, J.: Dickson polynomials over finite fields. Finite Fields Appl. 18 (4), 814–831 (2013). https://doi.org/10.1016/j.ffa.2012.02.001

Dickson, L. E. : The analytic representation of substitutions on a power of a prime number of letters with a discussion of the linear group. Ann. of Math. 11, 65–120 (1896). https://doi.org/10.2307/1967217

Lidl, R., Mullen, G. L., Turnwald, G.: Dickson polynomials, Longman Scientific and Technical, Essex, United Kingdom, 1993.

Cipu, M.: Dickson polynomials that are permutations. Serdica Math. J. 30, 177–194 (2004).

Stoll, T.: Complete decomposition of Dickson-type polynomials and related Diophantine equations. Journal of Number Theory 128(5), 1157–1181 (2008). https://doi.org/10.1016/j.jnt.2007.02.004

Fernando, N., Manukure, S.: A note on Dickson polynomials of the third kind and Legendre functions. J. of Inequalities and Special Functions 10(1), 151–160 (2019).

Lienard, A.: Etude des oscillations entretenues. Revue generale de e’electricite 23, 901–912 and 946–954 (1828).

Kyurkchiev, V., Iliev, A., Rahnev, A., Kyurkchiev, N.: Simulations on the Lienard polynomial system with Dickson-type polynomial corrections. The level curves. Int. J. of Differ. Equ. and Appl. 21(2), 31–44 (2022). https://doi.org/10.12732/ijdea.v21i2.3

Kyurkchiev, V., Iliev, A., Rahnev, A., Kyurkchiev, N.: A note on the extended Lienard system with Dickson polynomials of the third kind as corrections. The level curves. Int. J. of Differ. Equ. and Appl. 21(2), 73–87 (2022). https://doi.org/10.12732/ijdea.v21i2.6

10.

Kyurkchiev, V., Kyurkchiev, N.: On an extended relaxation oscillator model: number of limit cycles, simulations. I. Commun. Appl. Anal. 26(1), 19–42 (2022). https://doi.org/10.12732/caa.v26i1.3

11.

Kyurkchiev, V., Iliev, A., Rahnev, A., Kyurkchiev, N.: A technique for simulating the dynamics of some extended relaxation oscillator models. II. Commun. Appl. Anal. 26(1), 43–59 (2022). https://doi.org/10.12732/caa.v26i1.4

12.

Kyurkchiev, V., Iliev, A., Rahnev, A., Kyurkchiev, N.: Another extended polynomial Lienard systems: simulations and applications. III. Int. J. Pure Appl. Math. 16(1), 55–65 (2022). https://doi.org/10.12732/iejpam.v16i1.6

13.

Kyurkchiev, V., Iliev, A., Rahnev, A., Kyurkchiev, N.: Investigations on some polynomial Lienard-type systems: number of limit cycles, simulations. Int. J. of Differ. Equ. and Appl. 21 (1), 117–126 (2022). https://doi.org/10.12732/ijdea.v21i1.10

14.

Kyurkchiev, V., Kyurkchiev, N., Iliev, A., Rahnev, A.: On some extended oscillator models: a technique for simulating and studying their dynamics. Plovdiv, Plovdiv University Press (2022), ISBN: 978-619-7663-13-6.

15.

Kyurkchiev, N., Iliev, A.: On the hypothetical oscillator model with second kind Chebyshev’s polynomial–correction: number and type of limit cycles, simulations and possible applications. Algorithms 15(12), 462 (2022). https://doi.org/10.3390/a15120462

16.

Kyurkchiev, V., Iliev, A., Rahnev, A., Kyurkchiev, N.: Lienard system with first kind Chebyshev’s polynomial–correction in the light of Melnikov’s approach. Simulations and possible applications. In: International Scientific Conference IMEA’2022, pp. 105–112. Plovdiv University Press, Bulgaria, (2022). ISBN: 978-619-7663-33-4.

17.

Angelova, E., Arnaudova, V., Terzieva, T., Malinova, A.: Investigations on a differential system with correction of Zernike-type radial polynomials. Simulations. In: International Scientific Conference IMEA’2022, pp. 87–92. Plovdiv University Press, Bulgaria, (2022). ISBN: 978-619-7663-33-4.

18.

Kyurkchiev, N.: The effects on the dynamics of Lienard equation with Morse–type corrections: level curves. Int. J. of Differ. Equ. and Appl. (2), 59–72 (2022). https://doi.org/10.12732/ijdea.v21i2.5

19.

Malinova, A., Terzieva, T., Rahneva, O., Angelova, E.: Legendre polynomials as ”correction factors” in the Lienard differential system. Simulations. Commun. Appl. Anal. 26(1), 75–88 (2022). https://doi.org/10.12732/caa.v26i1.6

20.

Malinova, A., Terzieva, T., Rahneva, O., Angelova, E., Golev, A.: Associated Legendre polynomials as corrections in the classical Lienard system. Commun. Appl. Anal. 26(1), 89–97 (2022). https://doi.org/10.12732/caa.v26i1.7

21.

Golev, A., Arnaudova, V.: Lienard system with ”correcting factors” of the type of interpolating polynomials of some basic functions. Int. J. Pure Appl. Math. 16(1), 67–80 (2022). https://doi.org/10.12732/iejpam.v16i1.7

22.

Golev, A., Arnaudova, V.: Higher-kind Chebyshev polynomials and their applications to dynamic model studies. Int. J. of Differ. Equ. and Appl. 21(2), 101–108 (2022). https://doi.org/10.12732/ijdea.v21i2.8

23.

Kyurkchiev, V., Iliev, A., Rahnev, A., Kyurkchiev, N.: Gegenbauer polynomials as correction in the Lienard planar system: Melnikov’s approach. Int. J. of Differ. Equ. and Appl. 21(2), 45–57 (2022). https://doi.org/10.12732/ijdea.v21i2.4

24.

Kyurkchiev, V., Kyurkchiev, N., Iliev, A., Rahnev, A.: On the Lienard System with Some "Corrections of Polynomial-type": Number of limit cycles, simulations and possible applications. Part II. Plovdiv, Plovdiv University Press (2022). ISBN: 978-619-7663-41-9.

25.

Kyurkchiev, V., Iliev, A., Rahnev, A., Kyurkchiev, N.: Dynamics of the Lienard polynomial system using Dickson polynomials of the (M + 1)-th kind. The level curves. Int. J. of Differ. Equ. and Appl. 21(2), 109–120 (2022). https://doi.org/10.12732/ijdea.v21i2.9

26.

Kyurkchiev, V., Iliev, A., Rahnev, A., Kyurkchiev, N.: Chebyshev polynomials of the fifth kind and their application to study the dynamics of Lienard-type equations. Commun. Appl. Anal. 26(1), 111–123 (2022). https://doi.org/10.12732/caa.v26i1.9

27.

Kyurkchiev, N., Andreev, A.: Approximation and antenna and filter synthesis: Some moduli in programming environment Mathematica. LAP LAMBERT Academic Publishing: Saarbrucken, Germany, (2014). ISBN: 978-3-659-53322-8.

28.

Kyurkchiev, N.: Some intrinsic properties of Tadmor-Tanner functions: Related problems and possible applications. Mathematics 8(11), 1963 (2020). https://doi.org/10.3390/math8111963

Title: Some Applications of the Dickson Polynomials of Higher Kind for Modeling Radiation Diagrams
Authors: Maria Vasileva
Vesselin Kyurkchiev
Anton Iliev
Asen Rahnev
Nikolay Kyurkchiev
Publisher: Springer Nature Switzerland
Book: New Trends in the Applications of Differential Equations in Sciences
Print ISBN: 978-3-031-53211-5

Electronic ISBN: 978-3-031-53212-2

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-53212-2_42

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"