Yazar "Gundogan, Halit" için listeleme
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Clifford Product and Lorentzian Plane Displacements In 3-Dimensional Lorentzian Space
Gundogan, Halit; Ozkaldi, Siddika (Springer Basel Ag, 2009)In this paper, by defining Clifford algebra product in 3-dimensional Lorentz space, L (3), it is shown that even Clifford algebra of L (3) corresponds to split quaternion algebra. Then, by using Lorentzian matrix multiplication, ... -
The derivative and tangent operators of a motion in Lorentzian space
Durmaz, Olgun; Aktas, Busra; Gundogan, Halit (World Scientific Publ Co Pte Ltd, 2017)In this paper, by using Lorentzian matrix multiplication, L-Tangent operator is obtained in Lorentzian space. The L-Tangent operators related with planar, spherical and spatial motion are computed via special matrix groups. ... -
Dual Split Quaternions and Screw Motion in 3-Dimensional Lorentzian Space
Ozkaldi, Siddika; Gundogan, Halit (Birkhauser Verlag Ag, 2011)In this paper we obtain screw axis of a displacement in L(3). Then by using the L-screw axis, L-Rodrigues equation for a spatial displacement is obtained in the space L(3). Moreover, the components of a dual split quaternion ... -
New Approaches On Dual Space
Durmaz, Olgun; Aktas, Busra; Gundogan, Halit (UNIV NIS, 2020)In this paper, we have explained how to define the basic concepts of differential geometry on Dual space. To support this, dual tangent vectors that have (p) over bar as dual point of application have been defined. Then, ... -
On Interpretation of Hyperbolic Angle
Aktas, Busra; Gundogan, Halit; Durmaz, Olgun (KYUNGPOOK NATL UNIV, DEPT MATHEMATICS, 2020)Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] ... -
On Parallelizable Spheres in Semi Euclidean Space
Durmaz, Olgun; Aktas, Busra; Gundogan, Halit (SOUTHEAST ASIAN MATHEMATICAL SOC-SEAMS, 2020)In Euclidean space, there exist four theorems which show that S-n sphere is not parallelizable for n not equal 1, 3, 7. While three of them are shown by using Bott theorem, the last one is shown by using Hurwitz-Radon ... -
On The Basic Structures Of Dual Space
Aktas, Busra; Durmaz, Olgun; Gundogan, Halit (UNIV NIS, 2020)Topology studies the properties of spaces that are invariant under any continuous deformation. Topology is needed to examine the properties of the space. Fundamentally, the most basic structure required to do math in the ... -
Pseudo Matrix Multiplication
Kecilioglu, Osman; Gundogan, Halit (Ankara Univ, Fac Sci, 2017)In this paper, a new matrix multiplication is defined in R-m,R-n x R-n,R-p by using scalar product in R-n, where R-m,R-n is set of matrices of m rows and n columns. With this multiplication it has been shown that R-n,R-n ... -
Rodrigues parameters on dual hyperbolic unit sphere H20
Aktas, Busra; Durmaz, Olgun; Gundogan, Halit (Taylor & Francis Ltd, 2018)Rodrigues parameters depend on the tangent of the half rotation angle in Euclidean space but in Dual space, dual Rodrigues parameters contain both rotation angle and distance corresponding the shortest distance between the ... -
Rotations and Screw Motion with Timelike Vector in 3-Dimensional Lorentzian Space
Kecilioglu, Osman; Ozkaldi, Siddika; Gundogan, Halit (Springer Basel Ag, 2012)In the present paper we obtain the timelike Euler parameters of a Lorentzian orthogonal matrix in Lorentz space L-3 = R-2,R-1 by using Lorentzian matrix multiplication. Then, by using the timelike Euler parameters of a ... -
Structure equations and constraint manifolds on Lorentz plane
Durmaz, Olgun; Aktas, Busra; Gundogan, Halit (Wiley, 2019)Calculating the structure equation of a chain is important to represent the position of the end link on the chain. Furthermore, the structure equation helps to determine the constraint manifold of the chain. The constraint ...