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ISOTROPIC SMARANDACHE CURVES IN THE COMPLEX 4-SPACE
( Mahmut Ergut ),( Suha Yilmaz ),( Yasin Unluturk ) 호남수학회 2018 호남수학학술지 Vol.40 No.1
We define the e1<sup>a</sup> e3<sup>a</sup> -isotropic Smarandache curves of type-1 and type-2, the e1<sup>a</sup> e2<sup>a</sup> e3<sup>a</sup> -isotropic Smarandache curve, and e1<sup>a</sup> e2<sup>a</sup> e4<sup>a</sup>-isotropic Smarandache curves of type-1 and type-2. Then we examine these kinds of isotropic Smarandache curve according to Cartan frame in the complex 4-space C<sup>4</sup> and give some differential geometric properties of these Samarandache curves.
ISOTROPIC SMARANDACHE CURVES IN THE COMPLEX 4-SPACE
Ergut, Mahmut,Yilmaz, Suha,Unluturk, Yasin The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.1
We define the $e^{\alpha}_1e^{\alpha}_3$-isotropic Smarandache curves of type-1 and type-2, the $e^{\alpha}_1e^{\alpha}_2e^{\alpha}_3$-isotropic Smarandache curve, and the $e^{\alpha}_1e^{\alpha}_2e^{\alpha}_4$-isotropic Smarandache curves of type-1 and type-2. Then we examine these kinds of isotropic Smarandache curve according to Cartan frame in the complex 4-space $\mathbb{C}^4$ and give some differential geometric properties of these Samarandache curves.
( Yasin Unluturk ),( Suha Yilmaz ),( Cumali Ekici ) 호남수학회 2019 호남수학학술지 Vol.41 No.1
In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.
Unluturk, Yasin,Yilmaz, Suha,Ekici, Cumali The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.
Yasin Unluturk,Suha Yilmaz 호남수학회 2022 호남수학학술지 Vol.44 No.1
In this study, we obtain the spherical images of minimal curves in the complex space in $\mathbb{C}^{4}$ which are obtained by translating Cartan frame vector fields to the centre of hypersphere, and present their properties such as becoming isotropic cubic, pseudo helix, and spherical involutes. Also, we examine minimal curves which are characterized by a system of differential equations.
Mustafa Gökhan Vural,Suha Cetin,Murat Yilmaz,Ramazan Akdemir,Huseyin Gunduz 대한뇌졸중학회 2015 Journal of stroke Vol.17 No.3
Background and Purpose To investigate an association between left atrial (LA) structural and P wave dispersion (PWD) during sinus rhythm, and electrical remodeling in cryptogenic stroke (CS) patients. Methods Forty CS patients and 40 age- and sex-matched healthy controls were enrolled. P wave calculations were based on 12-lead electrocardiography (ECG) at a 50-mm/s-paper speed with an amplitude of 10 mm/mV. Difference between the maximum and minimum P wave duration was the P wave dispersion (PWD=Pmax-Pmin). LA deformation was evaluated by speckle tracking echocardiography within 3 days of the acute event. Results PWD was 30.1±7.0 ms and 27.4±3.5 ms in CS and control group (P=0.02), whereas LA maximum volume index [LAVImax] was 20.4±4.5 mL/m2 and 19.9±2.4 mL/m2 in CS and control group, respectively (P=0.04). While global peak LA strain was [pLA-S] (LA reservoir function) 41.4±6.3% and 44.5±7.1% in CS and control group, (P=0.04), global peak late diastolic strain rate values [pLA-SRa] (LA pump function) were 2.5±0.4% and 2.9±0.5% in CS and control group, respectively (P=0.001). A mild and a strong negative correlation between global pLA-S and LAVImax (r=-0.49; P<0.01), and between PWD and global pLA-S (r=-0.52; P<0.01), respectively, was observed in CS. Conclusions Increased PWD is associated with impaired LA mechanical functions and enlargement, and involved in the pathophysiology of AF or an AF-like physiology in CS.