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B\"{u}lent Nafi \"{O}rnek 대한수학회 2016 대한수학회보 Vol.53 No.2
In this paper, a boundary version of the Schwarz lemma is investigated. We take into consideration a function $f(z)=z+c_{p+1}z^{p+1}+c_{p+2}z^{p+2}+\cdots$ holomorphic in the unit disc and $\left\vert \frac{f(z)}{\lambda f(z)+(1-\lambda )z}-\alpha \right\vert <\alpha $ for $\left\vert z\right\vert <1$, where $\frac{1}{2}<\alpha \leq \frac{1}{1+\lambda }$, $ 0\leq $ $\lambda <1$. If we know the second and the third coefficient in the expansion of the function $f(z)=z+c_{p+1}z^{p+1}+c_{p+2}z^{p+2}+\cdots$, then we can obtain more general results on the angular derivatives of certain holomorphic function on the unit disc at boundary by taking into account $ c_{p+1}$, $c_{p+2}$ and zeros of $f(z)-z$. We obtain a sharp lower bound of $ \left\vert f^{\prime }(b)\right\vert $ at the point $b$, where $\left\vert b\right\vert =1$.
A septic B-spline finite element method for solving the nonlinear Schrödinger equation
Bülent SAKA,Idris Dag 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.3
The septic B-spline collocation algorithm is set up to nd the numerical solution of the nonlinear Schrödinger equation. The e¤ect of use of the higher degree B-spline in the collocation method is searched for getting the numerical solution of the Schrödinger equation. The three test problems are studied to show the robustness of the suggested method.
Estimates for a Certain Subclass of Holomorphic Functions
BÜLENT NAFI ÖRNEK,TUĞBA AKYEL 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.2
In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to N(α) is investigated. For the function f(z) = z + c2z2 + c3z3 + ... which is defined in the unit disc where f(z) ∈ N(α), we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with f(b) = 1 b b ∫ 0 f(t)dt. The sharpness of these inequalities is also proved.
Bülent Çomçalı,Barış Saylam,Buket Altun Özdemir 대한외과학회 2022 Annals of Surgical Treatment and Research(ASRT) Vol.102 No.2
Purpose: The aim of this study was to evaluate the effect of neuromonitoring on the number of lymph nodes (LNs) removed when applied during neck dissection. Methods: A total of 166 patients receiving neck dissection due to papillary thyroid cancer were separated into 2 groups (monitoring group, n = 76; non-monitoring group, n = 90). Results: The number of LNs dissected was observed to be statistically significantly higher in the monitoring group (P = 0.001), and the difference between the groups in the number of positive LNs was significant (P = 0.031). There was seen to be a negative relationship between the number of positive LNs dissected and recurrence (r = –0.404, P = 0.005). Conclusion: Intraoperative neuromonitoring during neck dissection makes a positive contribution to the prevention of the development of recurrence by increasing the number of LNs excised and the number of metastatic LNs.
Bülent Çetinel,Bulent Onal 대한비뇨의학회 2013 Investigative and Clinical Urology Vol.54 No.12
Purpose: Central nervous system (CNS) and cardiovascular system (CVS) side effects of anticholinergic agents used to treat overactive bladder (OAB) are underreported. Hence, this review aimed to focus on the mechanisms of CNS and CVS side effects of anticholinergic drugs used in OAB treatment, which may help urologists in planning the rationale for OAB treatment. Materials and Methods: PubMed/MEDLINE was searched for the key words “OAB,” “anticholinergics,” “muscarinic receptor selectivity,” “blood-brain barrier,” “CNS,” and “CVS side effects.” Additional relevant literature was determined by examining the reference lists of articles identified through the search. Results: CNS and CVS side effects, pharmacodynamic and pharmacokinetic properties, the metabolism of these drugs, and the clinical implications for their use in OAB are presented and discussed in this review. Conclusions: Trospium, 5-hydroxymethyl tolterodine, darifenacin, and solifenacin seem to have favorable pharmacodynamic and pharmacokinetic properties with regard to CNS side effects, whereas the pharmacodynamic features of darifenacin, solifenacin, and oxybutynin appear to have an advantage over the other anticholinergic agents (tolterodine, fesoterodine, propiverine, and trospium) with regard to CVS side effects. To determine the real-life situation, head-to-head studies focusing especially on CNS and CVS side effects of OAB anticholinergic agents are urgently needed.
APPLICATIONS OF THE JACK'S LEMMA FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMA
( Bülent Nafi Örnek ) 한국수학교육학회 2021 純粹 및 應用數學 Vol.28 No.3
In this study, a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions, is considered. The results of Rogosinskis lemma and Jacks lemma have been utilized to derive novel inequalities. Also, these inequalities have been strengthened by considering the critical points which are different from zero.
On a Class of Analytic Function related to Schwarz Lemma
Bülent Nafi ÖRNEK 한국수학교육학회 2022 純粹 및 應用數學 Vol.29 No.1
In this paper, we plan to introduce the class of the analytic functions called $\mathcal{P}\left( b\right) $ and to investigate the various properties of the functions belonging this class. The modulus of the second coefficient $c_{2}$ in the expansion of $f(z)=z+c_{2}z^{2}+...$ belonging to the given class will be estimated from above. Also, we estimate a modulus of the second angular derivative of $f(z)$ function at the boundary point $% \alpha $ with $f^{\prime }(\alpha )=1-b$, $b\in %TCIMACRO{\U{2102} }% %BeginExpansion \mathbb{C} %EndExpansion $, by taking into account their first nonzero two Maclaurin coefficients.
APPLICATIONS OF THE SCHWARZ LEMMA RELATED TO BOUNDARY POINTS
( Bülent Nafi Örnek ) 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.3
Different versions of the boundary Schwarz lemma for the N (ρ) class are discussed in this study. Also, for the function g(z) = z+b<sub>2</sub>z<sup>2</sup>+b<sub>3</sub>z<sup>3</sup>+... defined in the unit disc D such that g ∈ N (ρ), we estimate a modulus of the angular derivative of g(z) function at the boundary point 1 ∈ ∂D with g′(1) = 1 + σ(1 - ρ), where ρ = 1/n∑<sup>n</sup><sub>i=1</sub> g(ci) = g′(c1)+g′(c2)+:::+g′(c<sub>n</sub>)/n ∈ g′(D) and ρ ≠ 1, σ > 1 and c1; c2, ..., c<sub>n</sub> ∈ ∂D. That is, we shall give an estimate below |g′′(1)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and z<sub>1</sub> ≠ 0. Estimating is made by using the arithmetic average of n different derivatives g′(c<sub>1</sub>), g′(c<sub>2</sub>), ..., g′(c<sub>n</sub>).
CARATHÉODORY'S INEQUALITY ON THE BOUNDARY
BÜlent Nafi Örnek 한국수학교육학회 2015 純粹 및 應用數學 Vol.22 No.2
In this paper, a boundary version of Carathéodory's inequality is in- vestigated. Also, new inequalities of the Carathéodory's inequality at boundary are obtained and the sharpness of these inequalities is proved.
Bülent Çetin,Hakan Özer,Ahmet Cakir,Tas¸kin Polat,Atilla Dursun,Ebru Mete,Erdog˘an O¨ ztu¨rk,Melek Ekinci 한국식품영양과학회 2010 Journal of medicinal food Vol.13 No.1
The objective of this study was to determine the chemical compositions of the essential oil and hexane extract isolated from the inflorescence, leaf stems, and aerial parts of Florence fennel and the antimicrobial activities of the essential oil, hexane extract, and their major component, anethole, against a large variety of foodborne microorganisms. Gas chromatography and gas chromatography-mass spectrometry analysis showed that the essential oils obtained from inflorescence, leaf stems, and whole aerial parts contained (E)-anethole (59.28–71.69%), limonene (8.30–10.73%), apiole (trace to 9.23%), β-fenchyl acetate (3.02–4.80%), and perillene (2.16–3.29%) as the main components. Likewise, the hexane extract of the plant sample exhibited a similar chemical composition, and it contained (E)-anethole (53.00%), limonene (27.16%), γ-terpinene (4.09%), and perillene (3.78%). However, the hexane extract also contained less volatile components such as n-hexadecanoic acid (1.62%), methyl palmitate (1.17%), and linoleic acid (1.15%). The in vitro antimicrobial assays showed that the essential oil, anethole, and hexane extract were effective against most of the foodborne pathogenic, saprophytic, probiotic, and mycotoxigenic microorganisms tested. The results of the present study revealed that (E)-anethole, the main component of Florence fennel essential oil, is responsible for the antimicrobial activity and that the essential oils as well as the hexane extract can be used as a food preservative. This study is the first report showing the antimicrobial activities of essential oil and hexane extract of Florence fennel against probiotic bacteria.