Papers by Ümit Ziya Savcı
Fen ve mühendislik bilimleri dergisi, Jun 22, 2023
Bu çalışmada, Hamilton operatörlerini kullanarak genelleştirilmiş kuaterniyon cebiri ile gerçel (... more Bu çalışmada, Hamilton operatörlerini kullanarak genelleştirilmiş kuaterniyon cebiri ile gerçel (kompleks) matris cebirleri arasındaki bağlantıyı kurduk. Genelleştirilmiş kuaterniyonların gerçel ve kompleks temeline karşılık gelen gerçel ve kompleks matrisler elde ettik. Ayrıca, gerçel ve kompleks matrislerin temel özelliklerini araştırdık. Genelleştirilmiş kuaterniyonlara karşılık gelen Pauli matrislerini elde ettik. Daha sonra, bu matrisler tarafından üretilen cebirin, genelleştirilmiş 3 uzayı tarafından üretilen Clifford cebiri (3) ile izomorf olduğunu gösterdik. Son olarak, genelleştirilmiş birim kuaterniyonlara karşılık gelen simplektik matrisler grubu, genelleştirilmiş birim matrisler grubu ve genelleştirilmiş ortogonal matrisler grubu arasındaki ilişkileri inceledik.
International Journal of Geometric Methods in Modern Physics, Dec 26, 2020
In this study, we obtained generalized Cayley formula, Rodrigues equation and Euler parameters of... more In this study, we obtained generalized Cayley formula, Rodrigues equation and Euler parameters of an orthogonal matrix in 3-dimensional generalized space [Formula: see text]. It is shown that unit generalized quaternion, which is defined by the generalized Euler parameters, corresponds to a rotation in [Formula: see text] space.We found that the rotation in matrix equation forms using matrix form of the generalized quaternion product. Besides, in [Formula: see text] space, we obtained the rotations determined by the unit quaternions and unit split quaternions, which are special cases of generalized quaternions for [Formula: see text] in 3-dimensional Eulidean space [Formula: see text] in 3-dimensional Lorentzian space [Formula: see text] respectively.
Cumhuriyet Science Journal, 2019
The theory of convex sets is a vibrant and classical field of modern mathematics with rich applic... more The theory of convex sets is a vibrant and classical field of modern mathematics with rich applications. The more geometric aspects of convex sets are developed introducing some notions, but primarily polyhedra. A polyhedra, when it is convex, is an extremely important special solid in . Some examples of convex subsets of Euclidean 3-dimensional space are Platonic Solids, Archimedean Solids and Archimedean Duals or Catalan Solids. There are some relations between metrics and polyhedra. For example, it has been shown that cube, octahedron, deltoidal icositetrahedron are maximum, taxicab, Chinese Checker’s unit sphere, respectively. In this study, we give two new metrics to be their spheres truncated truncated dodecahedron and truncated truncated icosahedron.
International Journal of Geometric Methods in Modern Physics, 2020
In this study, we obtained generalized Cayley formula, Rodrigues equation and Euler parameters of... more In this study, we obtained generalized Cayley formula, Rodrigues equation and Euler parameters of an orthogonal matrix in 3-dimensional generalized space [Formula: see text]. It is shown that unit generalized quaternion, which is defined by the generalized Euler parameters, corresponds to a rotation in [Formula: see text] space.We found that the rotation in matrix equation forms using matrix form of the generalized quaternion product. Besides, in [Formula: see text] space, we obtained the rotations determined by the unit quaternions and unit split quaternions, which are special cases of generalized quaternions for [Formula: see text] in 3-dimensional Eulidean space [Formula: see text] in 3-dimensional Lorentzian space [Formula: see text] respectively.
Symmetry
This paper aims to investigate the screw motion in generalized space. For this purpose, firstly, ... more This paper aims to investigate the screw motion in generalized space. For this purpose, firstly, the change in the screw coordinates is analyzed according to the motion of the reference frames. Moreover, the special cases of this change, such as pure rotation and translation, are discussed. Matrix multiplication and the properties of dual numbers are used to obtain dual orthogonal matrices, which are used to simplify the manipulation of screw motion in generalized space. In addition, the dual angular velocity matrix is calculated and shows that the exponential of this matrix can represent the screw displacement in the generalized space. Finally, to support our results, we give two examples of screw motion, the rotation part of which is elliptical and hyperbolic.
Prespacetime Journal, 2018
In this work, we characterize certain special curves in the four-dimensional Galilean space in te... more In this work, we characterize certain special curves in the four-dimensional Galilean space in terms of Frenet-Serret vector fields. We investigate an explicit characterization of general helices of the Galilean space G4. We express position vector of an arbitrary helix and, introduce type-1, type-2 and type-3 slant helices by aid of the second, third and fourth vector fields of the Frenet-Serret tetrad. A number of differential and integral characterizations of the mentioned curves are expressed using classical differential geometry methods.
In this work, differential equations characterizing curves of constant breadth have been given in... more In this work, differential equations characterizing curves of constant breadth have been given in pseudo-Galilean space G¹₃. The special cases related to these differential equations have been studied in G¹₃.Publisher's Versio
New Trends in Mathematical Sciences, 2015
In this work, dual spacelike curves of constant breadth are defined in dual Lorentzian space D0³.... more In this work, dual spacelike curves of constant breadth are defined in dual Lorentzian space D0³. Some characterizations of closed dual spacelike curves of constant breadth are presented in dual Lorentzian space D0³ . These characterizations are made by obtaining special solutions of differential equations which is related to dual spacelike curves of constant breadth.
Ölçeği uygulanmıştır. Sonuç olarak, formasyon eğitimine katılan öğretmen adaylarının bilgisayar d... more Ölçeği uygulanmıştır. Sonuç olarak, formasyon eğitimine katılan öğretmen adaylarının bilgisayar destekli öğretime yönelik tutumlarının olumlu yönde olduğu, adayların bilgisayar destekli öğretim yapmaya yönelik tutumlarında cinsiyete veya öğretmenlik deneyimlerine bağlı anlamlı farklılık olmadığı; ancak, yaşa bağlı olarak bilgisayar destekli öğretim yapmaya ilişkin tutumlar incelendiğinde 30 yaş üstü öğretmen adaylarının 25 yaş altı adaylara göre pozitif yönde anlamlı derecede olumlu tutumda oldukları görülmüştür. Ayrıca, İlahiyat alanından mezun öğretmen adaylarının tutumlarında Fizik, Kimya, Matematik ve Türk Dili ve Edebiyatı alanlarından mezun adaylara göre pozitif yönde anlamlı farklılık gözlenmiştir. Son olarak Bilgisayar Destekli Öğretim/Eğitim derslerinin uygulamalı olarak yapılması gerektiği önerilmiştir.
viXra, 2016
In this paper, we investigate Smarandache curves according to type-2 Bishop frame in Euclidean 3-... more In this paper, we investigate Smarandache curves according to type-2 Bishop frame in Euclidean 3- space and we give some differential geometric properties of Smarandache curves. Also, some characterizations of Smarandache breadth curves in Euclidean 3-space are presented. Besides, we illustrate examples of our results.
Mathematical Sciences Letters
In this work, curves of constant breadth are defined and some characterizations of closed dual cu... more In this work, curves of constant breadth are defined and some characterizations of closed dual curves of constant breadth according to Bishop frame are presented in dual Euclidean space. Also, it has been obtained that a third order vectorial differential equation in dual Euclidean 3-space.
Mathematical Sciences Letters
In this work, curves of constant breadth are defined and some characterizations of closed dual cu... more In this work, curves of constant breadth are defined and some characterizations of closed dual curves of constant breadth according to Bishop frame are presented in dual Euclidean space. Also, it has been obtained that a third order vectorial differential equation in dual Euclidean 3-space.
Mathematical Sciences Letters
In this work, curves of constant breadth are defined and some characterizations of closed dual cu... more In this work, curves of constant breadth are defined and some characterizations of closed dual curves of constant breadth according to Bishop frame are presented in dual Euclidean space. Also, it has been obtained that a third order vectorial differential equation in dual Euclidean 3-space.
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences
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Papers by Ümit Ziya Savcı