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( Furkan Birol ),( Ozden Koruoglu ),( Recep Sahin ),( Bilal Demir ) 호남수학회 2019 호남수학학술지 Vol.41 No.1
We consider the extended generalized Hecke groups H<sub>3;q</sub> generated by X(z) = -(z - 1)<sup>-1</sup>, Y (z) = -(z + λ<sub>q</sub>)<sup>-1</sup> with λ<sub>q</sub> =2 cos(π/q) where q ≥ 3 an integer. In this work, we study the generalized Pell sequences in H<sub>3;q</sub> : Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group H<sub>3;3</sub> can be written by using Pell, Pell-Lucas and modified-Pell numbers.
Relationships between cusp points in the extended modular group and Fibonacci numbers
¨Ozden Koruo˘glu,Sule Kaymak Sarica,Bilal Demir,A. Furkan Kaymak 호남수학회 2019 호남수학학술지 Vol.41 No.3
Cusp (parabolic) points in the extended modular group $\overline{\Gamma}$ are basically the images of infinity under the group elements. This implies that the cusp points of $\overline{\Gamma}$ are just rational numbers and the set of cusp points is $Q_{\infty}=Q\cup\left\{ \infty\right\} .$The Farey graph $F$ is the graph whose set of vertices is $Q_{\infty}$ and whose edges join each pair of Farey neighbours. Each rational number $x$ has an integer continued fraction expansion (ICF) $x=[b_{1},...,b_{n}].$ We get a path from $\infty$ to $x$ in $F$ as \TEXTsymbol{<}$\infty,C_{1},...,C_{n}>$ for each ICF. In this study, we investigate relationships between Fibonacci numbers, Farey graph, extended modular group and ICF. Also, we give a computer program that computes the geodesics, block forms and matrix represantations.
Birol, Furkan,Koruoglu, Ozden,Sahin, Recep,Demir, Bilal The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
We consider the extended generalized Hecke groups ${\bar{H}}_{3,q}$ generated by $X(z)=-(z-1)^{-1}$, $Y(z)=-(z+{\lambda}_q)^{-1}$ with ${\lambda}_q=2\;cos({\frac{\pi}{q}})$ where $q{\geq}3$ an integer. In this work, we study the generalized Pell sequences in ${\bar{H}}_{3,q}$. Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group ${\bar{H}}_{3,3}$ can be written by using Pell, Pell-Lucas and modified-Pell numbers.
RELATIONSHIPS BETWEEN CUSP POINTS IN THE EXTENDED MODULAR GROUP AND FIBONACCI NUMBERS
Koruoglu, Ozden,Sarica, Sule Kaymak,Demir, Bilal,Kaymak, A. Furkan The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.3
Cusp (parabolic) points in the extended modular group ${\bar{\Gamma}}$ are basically the images of infinity under the group elements. This implies that the cusp points of ${\bar{\Gamma}}$ are just rational numbers and the set of cusp points is $Q_{\infty}=Q{\cup}\{{\infty}\}$.The Farey graph F is the graph whose set of vertices is $Q_{\infty}$ and whose edges join each pair of Farey neighbours. Each rational number x has an integer continued fraction expansion (ICF) $x=[b_1,{\cdots},b_n]$. We get a path from ${\infty}$ to x in F as $<{\infty},C_1,{\cdots},C_n>$ for each ICF. In this study, we investigate relationships between Fibonacci numbers, Farey graph, extended modular group and ICF. Also, we give a computer program that computes the geodesics, block forms and matrix represantations.
¨Ozden Koruo˘glu,Furkan Birol,Recep Sahin,Bilal Demir 호남수학회 2019 호남수학학술지 Vol.41 No.1
We consider the extended generalized Hecke groups $\overline{H}_{3,q}$ generated by $X(z)=-(z-1)^{-1}$, $Y(z)=-(z+\lambda _{q})^{-1}$ with $\lambda _{q}=2\cos (\frac{\pi }{q})$ where $q\geq 3$ an integer.\ In this work, we study the generalized Pell sequences in $\overline{H}_{3,q}.$ Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group $\overline{H}_{3,3}$ can be written by using Pell, Pell-Lucas and modified-Pell numbers.
Yaylaci, Selcuk,Tosun, Onder,Sahin, Orhan,Genc, Ahmet Bilal,Aydin, Ercan,Demiral, Gokhan,Karahalil, Fatma,Olt, Serdar,Ergenc, Hasan,Varim, Ceyhun Asian Pacific Journal of Cancer Prevention 2016 Asian Pacific journal of cancer prevention Vol.17 No.4
Background: Inflammatory hematological parameters like the neutrophil/lymphocyte (N/L) ratio have been investigated in many cancer types and significant relationships found with prognosis, for example. The aim of this present study was to investigate the impact of hematological parameters notably on N/L ratio and mean platelet volume (MPV) in papillary thyroid cancer cases. Materials and Methods: A total of 79 patients who underwent a thyroidectomy operation in Findikli, Goiter Research and Treatment Center during 2011-2015 period were enrolled in the study, 41 with papillary thyroid cancer and 38 with benign goiter confirmed by pathological examination. We collected clinical and laboratory data for the patients from hospital records retrospectively. Blood samples taken at admission were assessed for parameters compared between the groups. Results: No significant differences between papillary thyroid cancer and benign goiter groups were apparent in terms of age, the N/L ratio, MPV, white blood cell count (WBC), red blood cell count (RBC), hemoglobin, hematocrit, platelet, neutrophil, lymphocyte, red blood cell distribution width (RDW) and platelet crit (PCT) levels (p>0.05). Only the level of platelet distribution width (PDW) significantly differed, being lower in the papillary cancer group (p<0.05). Conclusions: No significant relationship between papillary thyroid cancer and inflammatory hematological parameters including in particular the N/L ratio and MPV. The relevance of the PDW values remains unclear.