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Some Remarks on Positive Real Functions and Their Circuit Applications

Year 2019, Volume: 8 Issue: 2, 617 - 627, 28.06.2019
https://doi.org/10.17798/bitlisfen.492656

Abstract

In this paper, a boundary version of the Schwarz lemma has been considered for driving point impedance functions at s=0 point of the imaginary axis. Accordingly, under Z(0)=0condition, the modulus of the derivative of the Z(s)  function has been considered from below. Here, Z(alfa), c1 and c2 coefficients of the Taylor expansion of the Z(s)=beta+c1(s-alfa)+...  function have been used in the obtained inequalities. The sharpness of these inequalities has also been proved.

References

  • Sharma A., Soni, T. 2017. A Review on Passive Network Synthesis Using Cauer Form, World Journal of Wireless Devices and Engineering, 1 (1): 39–46.
  • Bakshi M., Sule V., Baghini M. S. 2016. Stabilization Theory for Active Multi Port Networks, arXiv preprint (aXiv:1606.03194).
  • Reza F. 1962. A Bound for the Derivative of Positive Real Functions, SIAM Review, 4 (1): 40–42.
  • Richards P. I. 1947. A Special Class of Functions with Positive Real Part in a Half-Plane. Duke Mathematical Journal 1947, 14 (3): 777–786. DOI: 10.1215/S0012-7094-47-01461-0.
  • Osserman R. 2000. A Sharp Schwarz Inequality on the Boundary. Proceedings of the American Mathematical Society, 128 (12): 3513–3517.
  • Dubinin V. 2004. The Schwarz Inequality on the Boundary for Functions Regular in the Disk, Journal of Mathematical Sciences, 122 (6): 3623–3629.
  • Azeroğlu T. A., Örnek B. N. (2013). A Refined Schwarz Inequality on the Boundary, Complex Variables and Elliptic Equations, 58 (4): 571–577.
  • Örnek B. N. 2013. Sharpened Forms of the Schwarz Lemma on the Boundary, Bulletin of the Korean Mathematical Society, 50 (6): 2053–2059.

Pozitif Reel Fonksiyonlar ve Devre Uygulamaları Üzerine Bazı Sonuçlar

Year 2019, Volume: 8 Issue: 2, 617 - 627, 28.06.2019
https://doi.org/10.17798/bitlisfen.492656

Abstract



Bu çalışmada, Schwarz lemmasının bir sınır versiyonu,
süren nokta empedans fonksiyonları için sanal eksen üzerindeki s=0
 noktasında
değerlendirilmiştir. Buna göre, Z(0)=0 koşulu altında, Z(s) fonksiyonunun
türevinin modülü aşağıdan değerlendirilmiştir. Burada, elde edilen
eşitsizliklerde, Z(s)=beta+c1(s-alfa)+....  fonksiyonunun Taylor
açılımındaki ,  Z(alfa), c1 ve c2 katsayıları
kullanılmıştır. Aynı zamanda, bu eşitsizliklerin keskinliği ispatlanmıştır.



References

  • Sharma A., Soni, T. 2017. A Review on Passive Network Synthesis Using Cauer Form, World Journal of Wireless Devices and Engineering, 1 (1): 39–46.
  • Bakshi M., Sule V., Baghini M. S. 2016. Stabilization Theory for Active Multi Port Networks, arXiv preprint (aXiv:1606.03194).
  • Reza F. 1962. A Bound for the Derivative of Positive Real Functions, SIAM Review, 4 (1): 40–42.
  • Richards P. I. 1947. A Special Class of Functions with Positive Real Part in a Half-Plane. Duke Mathematical Journal 1947, 14 (3): 777–786. DOI: 10.1215/S0012-7094-47-01461-0.
  • Osserman R. 2000. A Sharp Schwarz Inequality on the Boundary. Proceedings of the American Mathematical Society, 128 (12): 3513–3517.
  • Dubinin V. 2004. The Schwarz Inequality on the Boundary for Functions Regular in the Disk, Journal of Mathematical Sciences, 122 (6): 3623–3629.
  • Azeroğlu T. A., Örnek B. N. (2013). A Refined Schwarz Inequality on the Boundary, Complex Variables and Elliptic Equations, 58 (4): 571–577.
  • Örnek B. N. 2013. Sharpened Forms of the Schwarz Lemma on the Boundary, Bulletin of the Korean Mathematical Society, 50 (6): 2053–2059.
There are 8 citations in total.

Details

Primary Language English
Journal Section Araştırma Makalesi
Authors

Bülent Nafi Örnek 0000-0001-7109-230X

Timur Düzenli 0000-0003-0210-5626

Publication Date June 28, 2019
Submission Date December 5, 2018
Acceptance Date May 20, 2019
Published in Issue Year 2019 Volume: 8 Issue: 2

Cite

IEEE B. N. Örnek and T. Düzenli, “Some Remarks on Positive Real Functions and Their Circuit Applications”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 8, no. 2, pp. 617–627, 2019, doi: 10.17798/bitlisfen.492656.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS