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Characteristically Near Stable Vector Fields in the Polar Complex Plane

Yıl 2025, , 117 - 124, 01.07.2025

James F. Peters , Enze Cui

https://doi.org/10.33434/cams.1660609

Öz

This paper introduces results for characteristically proximal vector fields that are stable or non-stable in the polar complex plane $\mathbb{C}$. All characteristic vectors (aka eigenvectors) emanate from the same fixed point in $\mathbb{C}$, namely, 0. Stable characteristic vector fields satisfy an extension of the Krantz stability condition, namely, the maximal eigenvalue of a stable system lies within or on the boundary of the unit circle in $\mathbb{C}$. An application is given for stable vector fields detected in motion waveforms in infrared video frames. AI is used to separate the changing from the unchanging parts of each video frame.

Anahtar Kelimeler

Characteristic Complex Plane Eigenvalue Eigenvector Proximity Stability

Etik Beyan

This paper has not been submitted to any other publication.

Destekleyen Kurum

University of Manitoba, Canada

Teşekkür

Many thanks for considering this paper for publication in the CAMS journal.

Kaynakça

  • [1] S. G. Krantz, Essentials of topology with applications, CRC Press, New York, 2009. http://dx.doi.org/10.1201/b12333
  • [2] H. Poincaré, Sur les équations de la dynamique et le probl`eme des trois corps, Acta Math., 13 (1890), 1-272.
  • [3] R. De Leo, J. A. Yorke, Streams and graphs of dynamical systems, Qual. Theory Dyn. Syst., 24 (2024), Article ID 1, 53 pages. https://doi.org/10.1007/s12346-024-01112-x
  • [4] M. Feldman, Hilbert Transform Applications in Mechanical Vibration, John Wiley and Sons, 2011. http://doi.org/10.1002/9781119991656
  • [5] P. Pokorny, A. Klic, Dynamical systems generated by two alternating vector fields, Eur. Phys. J. Special Top., 165 (2008), 61-71. https://doi.org/10.1140/epjst/e2008-00849-9
  • [6] R. Forman, Combinatorial vector fields and dynamical systems, Mathematische Zeitschrift, 228 (1998), 629–681. https://doi.org/10.1007/PL00004638
  • [7] S. Tiwari, J. F. Peters, Proximal groups: Extension of topological groups. Application in the concise representation of Hilbert envelopes on oscillatory motion waveforms, Comm. Algebra, 52(9) (2024), 3904–3914. https://doi.org/10.1080/00927872.2024.2334895
  • [8] M. S. Haider, J. F. Peters, Temporal proximities: Self-similar temporally close shapes, Chaos Solitons Fractals, 151 (2021), Article ID 111237, 10 pages. https://doi.org/10.1016/j.chaos.2021.111237
  • [9] J. F. Peters, T. Vergili, Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan curve theorems, Appl. Gen. Topol., 24(1) (2023), 25–45. https://doi.org/10.4995/agt.2023.17046
  • [10] E. Ozkan, B. Kuloglu, J. F. Peters, k-Narayana sequence self-similarity. Flip graph views of k-Narayana self-similarity, Chaos Solitons Fractals, 153(2) (2021), Article ID 111473. https://doi.org/10.1016/j.chaos.2021.111473
  • [11] E. Erdag, J. F. Peters, O. Deveci, The Jacobsthal-Padovan-Fibonacci p-sequence and its application in the concise representation of vibrating systems with dual proximal groups, J. Supercomput., 81 (2025), Article ID 197. https://doi.org/10.1007/s11227-024-06608-6
  • [12] L. Euler, Introductio in Analysin Infinitorum. (Latin), Sociedad Andaluza de Educacion Matematica Thales, Springer, New York, 1748.
  • [13] J. F. Peters, T. Vergili, F. Ucan, D. Vakeesan, Indefinite descriptive proximities inherent in dynamical systems. An Axiomatic Approach, arXiv, (2025). https://doi.org/10.48550/arXiv.2501.02585
  • [14] D. G. Magiros, On stability definitions of dynamical systems, Proc. Nat. Acad. Sci. U.S.A., 53(6) (1965), 1288–1294,
  • [15] Z. Pawlak, J. F. Peters, Jak bliski? [Polish] (How near?). In: Systemy Wspomagania Decyzji, vol. I, 2007, pp. 57–109, University of Silesia, Katowice, ISBN 83-920730-4-5.
  • [16] J. F. Peters, T. U. Liyanage, Energy Dissipation in Hilbert Envelopes on Motion Waveforms Detected in Vibrating Systems: An Axiomatic Approach, Commun. Adv. Math. Sci., 7(4) (2024), 178–186. https://doi.org/10.33434/cams.1549815

Yıl 2025, , 117 - 124, 01.07.2025

James F. Peters , Enze Cui

https://doi.org/10.33434/cams.1660609

Öz

Kaynakça

  • [1] S. G. Krantz, Essentials of topology with applications, CRC Press, New York, 2009. http://dx.doi.org/10.1201/b12333
  • [2] H. Poincaré, Sur les équations de la dynamique et le probl`eme des trois corps, Acta Math., 13 (1890), 1-272.
  • [3] R. De Leo, J. A. Yorke, Streams and graphs of dynamical systems, Qual. Theory Dyn. Syst., 24 (2024), Article ID 1, 53 pages. https://doi.org/10.1007/s12346-024-01112-x
  • [4] M. Feldman, Hilbert Transform Applications in Mechanical Vibration, John Wiley and Sons, 2011. http://doi.org/10.1002/9781119991656
  • [5] P. Pokorny, A. Klic, Dynamical systems generated by two alternating vector fields, Eur. Phys. J. Special Top., 165 (2008), 61-71. https://doi.org/10.1140/epjst/e2008-00849-9
  • [6] R. Forman, Combinatorial vector fields and dynamical systems, Mathematische Zeitschrift, 228 (1998), 629–681. https://doi.org/10.1007/PL00004638
  • [7] S. Tiwari, J. F. Peters, Proximal groups: Extension of topological groups. Application in the concise representation of Hilbert envelopes on oscillatory motion waveforms, Comm. Algebra, 52(9) (2024), 3904–3914. https://doi.org/10.1080/00927872.2024.2334895
  • [8] M. S. Haider, J. F. Peters, Temporal proximities: Self-similar temporally close shapes, Chaos Solitons Fractals, 151 (2021), Article ID 111237, 10 pages. https://doi.org/10.1016/j.chaos.2021.111237
  • [9] J. F. Peters, T. Vergili, Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan curve theorems, Appl. Gen. Topol., 24(1) (2023), 25–45. https://doi.org/10.4995/agt.2023.17046
  • [10] E. Ozkan, B. Kuloglu, J. F. Peters, k-Narayana sequence self-similarity. Flip graph views of k-Narayana self-similarity, Chaos Solitons Fractals, 153(2) (2021), Article ID 111473. https://doi.org/10.1016/j.chaos.2021.111473
  • [11] E. Erdag, J. F. Peters, O. Deveci, The Jacobsthal-Padovan-Fibonacci p-sequence and its application in the concise representation of vibrating systems with dual proximal groups, J. Supercomput., 81 (2025), Article ID 197. https://doi.org/10.1007/s11227-024-06608-6
  • [12] L. Euler, Introductio in Analysin Infinitorum. (Latin), Sociedad Andaluza de Educacion Matematica Thales, Springer, New York, 1748.
  • [13] J. F. Peters, T. Vergili, F. Ucan, D. Vakeesan, Indefinite descriptive proximities inherent in dynamical systems. An Axiomatic Approach, arXiv, (2025). https://doi.org/10.48550/arXiv.2501.02585
  • [14] D. G. Magiros, On stability definitions of dynamical systems, Proc. Nat. Acad. Sci. U.S.A., 53(6) (1965), 1288–1294,
  • [15] Z. Pawlak, J. F. Peters, Jak bliski? [Polish] (How near?). In: Systemy Wspomagania Decyzji, vol. I, 2007, pp. 57–109, University of Silesia, Katowice, ISBN 83-920730-4-5.
  • [16] J. F. Peters, T. U. Liyanage, Energy Dissipation in Hilbert Envelopes on Motion Waveforms Detected in Vibrating Systems: An Axiomatic Approach, Commun. Adv. Math. Sci., 7(4) (2024), 178–186. https://doi.org/10.33434/cams.1549815
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik (Diğer)
Bölüm Makaleler
Yazarlar

James F. Peters 0000-0002-1026-4638

Enze Cui 0009-0008-6856-4570

Erken Görünüm Tarihi 1 Temmuz 2025
Yayımlanma Tarihi 1 Temmuz 2025
Gönderilme Tarihi 18 Mart 2025
Kabul Tarihi 29 Haziran 2025
Yayımlandığı Sayı Yıl 2025

Kaynak Göster

APA Peters, J. F., & Cui, E. (2025). Characteristically Near Stable Vector Fields in the Polar Complex Plane. Communications in Advanced Mathematical Sciences, 8(2), 117-124. https://doi.org/10.33434/cams.1660609
AMA Peters JF, Cui E. Characteristically Near Stable Vector Fields in the Polar Complex Plane. Communications in Advanced Mathematical Sciences. Temmuz 2025;8(2):117-124. doi:10.33434/cams.1660609
Chicago Peters, James F., ve Enze Cui. “Characteristically Near Stable Vector Fields in the Polar Complex Plane”. Communications in Advanced Mathematical Sciences 8, sy. 2 (Temmuz 2025): 117-24. https://doi.org/10.33434/cams.1660609.
EndNote Peters JF, Cui E (01 Temmuz 2025) Characteristically Near Stable Vector Fields in the Polar Complex Plane. Communications in Advanced Mathematical Sciences 8 2 117–124.
IEEE J. F. Peters ve E. Cui, “Characteristically Near Stable Vector Fields in the Polar Complex Plane”, Communications in Advanced Mathematical Sciences, c. 8, sy. 2, ss. 117–124, 2025, doi: 10.33434/cams.1660609.
ISNAD Peters, James F. - Cui, Enze. “Characteristically Near Stable Vector Fields in the Polar Complex Plane”. Communications in Advanced Mathematical Sciences 8/2 (Temmuz 2025), 117-124. https://doi.org/10.33434/cams.1660609.
JAMA Peters JF, Cui E. Characteristically Near Stable Vector Fields in the Polar Complex Plane. Communications in Advanced Mathematical Sciences. 2025;8:117–124.
MLA Peters, James F. ve Enze Cui. “Characteristically Near Stable Vector Fields in the Polar Complex Plane”. Communications in Advanced Mathematical Sciences, c. 8, sy. 2, 2025, ss. 117-24, doi:10.33434/cams.1660609.
Vancouver Peters JF, Cui E. Characteristically Near Stable Vector Fields in the Polar Complex Plane. Communications in Advanced Mathematical Sciences. 2025;8(2):117-24.

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