Yazar "Aktas, Busra" seçeneğine göre listele

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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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    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 Constraint Manifolds of Lorentz Sphere
    (OVIDIUS UNIV PRESS, 2020) Aktas, Busra; Durmaz, Olgun; Gundogan, Hal't
    The expression of the structure equation of a mechanism is significant to present the last position of the mechanism. Moreover, in order to attain the constraint manifold of a chain, we need to constitute the structure equation. In this paper, we determine the structure equations and the constraint manifolds of a spherical open-chain in the Lorentz space. The structure equations of spherical open chain with reference to the causal character of the first link are obtained. Later, the constraint manifolds of the mechanism are determined by means of these equations. The geometric constructions corresponding to these manifolds are studied.
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    On constraint manifolds of planar and spherical mechanisms in Lorentzian space
    (Pergamon-Elsevier Science Ltd, 2025) Aktas, Busra
    This study aims to investigate the algebraic forms of the constraint manifolds of 4 R and 6 R planar and spherical closed chains in Lorentzian space. For this purpose, firstly, the structure equations of closed chains are obtained by using the structure equations of planar and spherical open chains in Lorentzian space. Then, using these equations, the algebraic forms of the constraint manifolds of 4 R and 6 R planar and spherical closed chains in spacelike and timelike mechanisms are constructed and it is shown which curves these manifolds correspond to.
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    On constraint manifolds of spatial closed chains in Lorentzian space
    (World Scientific Publ Co Pte Ltd, 2024) Aktas, Busra; Durmaz, Olgun; Aydin, Oeznur
    The objective of this paper is to explore the unexplored algebraic representations of the constraint manifolds associated with 4C and 6C spatial closed chains in Lorentzian space. Initially, we establish the structure equations of spatial closed chains by utilizing the structure equations for spatial open chains in Lorentzian space. Subsequently, we employ these structure equations to derive the algebraic expressions defining the constraint manifolds of 4C and 6C spatial closed chains in Lorentzian space, considering factors such as the causal character of the first link and the rotational axis of the cylindrical joint. This study will finalize all algebraic representations of constraint manifolds for spacelike and timelike mechanisms in Lorentzian space.
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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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    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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    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.