Yazar "Gundogan, Halit" seçeneğine göre listele

Listeleniyor 1 - 11 / 11
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    The derivative and tangent operators of a motion in Lorentzian space
    (World Scientific Publ Co Pte Ltd, 2017) Durmaz, Olgun; Aktas, Busra; Gundogan, Halit
    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. L-Tangent operators are related to vectors. Some illustrative examples for applications of L-Tangent operators are also presented.
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    Dual Split Quaternions and Screw Motion in 3-Dimensional Lorentzian Space
    (Birkhauser Verlag Ag, 2011) Ozkaldi, Siddika; Gundogan, Halit
    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 are obtained by replacing the L-Euler parameters with their split dual versions.
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    GENERALIZED MATRIX MULTIPLICATION AND ITS SOME APPLICATION
    (Univ Nis, 2017) Kecilioglu, Osman; Gundogan, Halit
    In this paper, a generalized matrix multiplication is defined in R-m,R-n x R-n,R-p by using any scalar product in R-n, where R-m,R-n denotes set of matrices of m rows and n columns. With this multiplication it has been shown that R-n,R-n is an algebra with unit. By considering this new multiplication we define eigenvalues and eigenvectors of square n x n matrix A. A special case is considered and generalized diagonalization is also introduced.
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    New Approaches On Dual Space
    (UNIV NIS, 2020) Durmaz, Olgun; Aktas, Busra; Gundogan, Halit
    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, the dual analytic functions defined by Dimentberg have been examined in detail, and by using the derivative of the these functions, dual directional derivatives and dual tangent maps have been introduced.
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    On Interpretation of Hyperbolic Angle
    (KYUNGPOOK NATL UNIV, DEPT MATHEMATICS, 2020) Aktas, Busra; Gundogan, Halit; Durmaz, Olgun
    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] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.
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    On Parallelizable Spheres in Semi Euclidean Space
    (SOUTHEAST ASIAN MATHEMATICAL SOC-SEAMS, 2020) Durmaz, Olgun; Aktas, Busra; Gundogan, Halit
    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 numbers. In this paper, a theorem and the proof of this theorem about parallelization of spheres in semi-Euclidean space is given. It is presented that some spheres are parallelizable with respect to specific number systems.
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    On The Basic Structures Of Dual Space
    (UNIV NIS, 2020) Aktas, Busra; Durmaz, Olgun; Gundogan, Halit
    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 space is topology. There exists little information on the expression of the basis and topology on dual space. The main point of the research is to explain how to define the basis and topology on dual space D-n. Then, we will study the geometric constructions corresponding to the open balls in D and D-2, respectively.
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    Pseudo Matrix Multiplication
    (Ankara Univ, Fac Sci, 2017) Kecilioglu, Osman; Gundogan, Halit
    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 is an algebra with unit. By considering this new multiplication we define eigenvalues and eigenvectors of square n x n matrix A and also present some applications.
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    Rodrigues parameters on dual hyperbolic unit sphere H20
    (Taylor & Francis Ltd, 2018) Aktas, Busra; Durmaz, Olgun; Gundogan, Halit
    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 straight lines in R-3. In this paper, we give Cayley's formula for the dual hyperbolic spherical motion and explain 3x3 type L-Dual skew symmetric matrices by using properties of this formula. Then, we obtain Rodrigues parameters of dual Hyperbolic unit sphere and show that Rodrigues parameters contain the hyperbolic rotation angle which is being between timelike lines and distance which is the minimal Lorentzian distance between the timelike lines of R-1(3)
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    Rotations and Screw Motion with Timelike Vector in 3-Dimensional Lorentzian Space
    (Springer Basel Ag, 2012) Kecilioglu, Osman; Ozkaldi, Siddika; Gundogan, Halit
    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 given rotation in a split quaternion formulation, we produce split quaternion equation of a rotation motion in L-3. Moreover the components of a dual split quaternion are obtained by replacing the timelike L-Euler parameters with their split dual versions.
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    Structure equations and constraint manifolds on Lorentz plane
    (Wiley, 2019) Durmaz, Olgun; Aktas, Busra; Gundogan, Halit
    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 manifold satisfies to make geometric interpretations about the form that is obtained. What is more, the constraint forced on the positions of the end link by the rest of the chain is represented by the manifold. In Lorentz space, the structure equations change according to the causal characters of the first link. In this paper, we attain the structure equations of a planar open chain in terms of the causal character of the first link in this space. Later, the constraint manifolds of the chain by using these equations are given. Some geometric comments about these manifolds are explained.