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On the Dual Quaternionic N̅₃ Slant Helices in D⁴

100%
Tuna Aksoy A., Çöken A.
Acta Physica Polonica A
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2017
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vol. 132
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issue 3
900-904
EN
In this paper, we define the harmonic curvature functions for dual quaternionic curves. Moreover, we also study some characterizations for dual quaternionic slant helices according to dual quaternionic frame.
2
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Null Quaternionic Cartan Helices in ℝ³_{v}

100%
Tuna Aksoy A., Çöken A.
Acta Physica Polonica A
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2017
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vol. 132
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issue 3
896-899
EN
In this study, we define null quaternionic Bertrand curves in ℝ³_{v} for a null quaternionic curve, which has a single non-zero, constant Cartan curvature τ. We also prove that if a null quaternionic curve with non-zero curvatures in ℝ³_{v} is a null quaternionic Bertrand curve, then it is a null quaternionic helix.
3
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Characterizations for the Dual Split Quaternionic Curves

100%
Tuna Aksoy A., Çöken A.
Acta Physica Polonica A
|
2017
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vol. 132
|
issue 3
905-908
EN
We define harmonic curves and inclined curves for dual split quaternionic curves. And then, we give some characterizations for dual split quaternionic inclined curves by means of the harmonic curvatures.
4
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Topological constraints on solar loop plasma instabilities and Alfvén waves

100%
Garcia de Andrade L.
Open Physics
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2009
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vol. 7
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issue 1
130-134
EN
Inhomogeneous plasmas-solar instabilities-are investigated by using the techniques of classical differential geometry for curves, where the Frenet torsion and curvature describe completely the motion of a curve. In our case, the Frenet frame changes in time and also depends upon the other coordinates, taking into account the inhomogeneity of the plasma. The exponential perturbation method, so commonly used to describe cosmological perturbations, is applied to the magnetohydrodynamic (MHD) plasma equations to find modes describing Alfvén wave propagation in the medium of planar loops. Stability is investigated in the imaginary axis of the spectra of complex frequencies ω, i.e. $$ \Im $$ m (ω) ≠ 0. A pratical guide for experimental solar physicists is given by computing the twist of force-free solar loops, which generalizes the Parker formula relating the twist to the Frenet torsion. In our expression the twist of the solar loops also depends on the abnormality of the normal vector of the frame.
5
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Unification Principle and a Geometric Field Theory

52%
Wanas M. I., Osman S. N., El-Kholy R. I.
Open Physics
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2015
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vol. 13
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issue 1
EN
In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.
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