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Journals / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2026 / Volume: 8 Issue: 2

Some Remarks on Positive Real Functions and Their Circuit Applications

Pozitif Reel Fonksiyonlar ve Devre Uygulamaları Üzerine Bazı Sonuçlar

Bülent Nafi Örnek(AMASYA UNIVERSITY)0000-0001-7109-230X
Timur Düzenli(AMASYA UNIVERSITY)0000-0003-0210-5626
Pages
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Publication Date
2019-06-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The sharpness of these inequalities has also been proved.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
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Key Findings & Data:Accordingly, under Z(0)=0 condition, the modulus of the derivative of the Z(s) function has been considered from below.
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Conclusion & Impact:The sharpness of these inequalities has also been proved.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Extremal function · Schwarz lemma · Positive real function

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)=0 condition, 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.

Özet

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.

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Cite This Article

Örnek, B. N., Düzenli, T. (2019). Some Remarks on Positive Real Functions and Their Circuit Applications. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Volume: 8 Issue: 2. https://doi.org/10.17798/bitlisfen.492656

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References (8)

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