Characteristically Near Stable Vector Fields in the Polar Complex Plane

James F. Peters; Enze Cui

doi:10.33434/cams.1660609

EN

Characteristically Near Stable Vector Fields in the Polar Complex Plane

Abstract

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.

Keywords

Characteristic, Complex Plane, Eigenvalue, Eigenvector, Proximity, Stability

Supporting Institution

University of Manitoba, Canada

Ethical Statement

This paper has not been submitted to any other publication.

Thanks

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

References

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

James F. Peters ^*
0000-0002-1026-4638
Canada

Enze Cui
0009-0008-6856-4570
Canada

Early Pub Date

July 1, 2025

Publication Date

July 1, 2025

Submission Date

March 18, 2025

Acceptance Date

June 29, 2025

Published in Issue

Year 2025 Volume: 8 Number: 2

DOI

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

IZ

https://izlik.org/JA27UE85ZJ

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

1.Peters JF, Cui E. Characteristically Near Stable Vector Fields in the Polar Complex Plane. Communications in Advanced Mathematical Sciences. 2025;8(2):117-124. doi:10.33434/cams.1660609

Chicago

Peters, James F., and Enze Cui. 2025. “Characteristically Near Stable Vector Fields in the Polar Complex Plane”. Communications in Advanced Mathematical Sciences 8 (2): 117-24. https://doi.org/10.33434/cams.1660609.

EndNote

Peters JF, Cui E (July 1, 2025) Characteristically Near Stable Vector Fields in the Polar Complex Plane. Communications in Advanced Mathematical Sciences 8 2 117–124.

IEEE

[1]J. F. Peters and E. Cui, “Characteristically Near Stable Vector Fields in the Polar Complex Plane”, Communications in Advanced Mathematical Sciences, vol. 8, no. 2, pp. 117–124, July 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 (July 1, 2025): 117-124. https://doi.org/10.33434/cams.1660609.

JAMA

1.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., and Enze Cui. “Characteristically Near Stable Vector Fields in the Polar Complex Plane”. Communications in Advanced Mathematical Sciences, vol. 8, no. 2, July 2025, pp. 117-24, doi:10.33434/cams.1660609.

Vancouver

1.James F. Peters, Enze Cui. Characteristically Near Stable Vector Fields in the Polar Complex Plane. Communications in Advanced Mathematical Sciences. 2025 Jul. 1;8(2):117-24. doi:10.33434/cams.1660609

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