Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3
In this paper, we study spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3 . We show that spacelike biharmonic curves are general helices. We characterize position vector of spacelike biharmonic general helices in terms of their curvature and torsion.
Microsoft Word-11. Dr. Asil
In this paper, we study spacelike dual biharmonic curves. We characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the Lorentzian dual Heisenberg group 3 3 Heis D . We give necessary and sufficient conditions for spacelike dual biharmonic curves in the Lorentzian dual Heisenberg group 3 3 Heis D . Therefore, we prove that all spacelike dual biharmonic curves are spacelike dual helix. Moreover, we give their explicit parametrizations of spacelike dual biharmonic curves. Finally, we illustrate our main results in Figs. 1 and 2.
Insanity in Ancient and Modern Life, with Chapters on Its Prevention
be well received by the profession and the public The first eighty-four pages treat of the prevalence of the causes of insanity amongst the nations of antiquity. We know that madness has existed in all the times of which we have any record, and that it had much the same train of symptoms as at present. But it is impossible to find out whether insanity was more or less frequent amongst the Egyptians, Hebrews, Greeks, or liomans. In