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A NEW APPROACH ON THE CURVATURE DEPENDENT ENERGY FOR ELASTIC CURVES IN A LIE GROUP
Korpinar, Talat,Demirkol, Ridvan Cem The Honam Mathematical Society 2017 호남수학학술지 Vol.39 No.4
Elastica is known as classical curve that is a solution of variational problem, which minimize a thin inextensible wire's bending energy. Studies on elastica has been conducted in Euclidean space firstly, then it has been extended to Riemannian manifold by giving different characterizations. In this paper, we focus on energy of the elastic curve in a Lie group. We attepmt to compute its energy by using geometric description of the curvature and the torsion of the trajectory of the elastic curve of the trajectory of the moving particle in the Lie group. Finally, we also investigate the relation between energy of the elastic curve and energy of the same curve in Frenet vector fields in the Lie group.
ENERGY ON A PARTICLE IN DYNAMICAL AND ELECTRODYNAMICAL FORCE FIELDS IN LIE GROUPS
Korpinar, Talat,Demirkol, Ridvan Cem The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.2
In this study, we firstly define equations of motion based on the traditional model Newtonian mechanics in terms of the Frenet frame adapted to the trajectory of the moving particle in Lie groups. Then, we compute energy on the moving particle in resultant force field by using geometrical description of the curvature and torsion of the trajectory belonging to the particle. We also investigate the relation between energy on the moving particle in different force fields and energy on the particle in Frenet vector fields.
ON NEW FERMI WALKER DERIVATIVE OF BIHARMONIC PARTICLES IN HEISENBERG SPACETIME
Korpinar, Talat The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
In practical applications play an new important role timelike biharmonic particle by Fermi-Walker derivative. In this article, we get a innovative interpretation about timelike biharmonic particle by means of Fermi-Walker derivative and parallelism in Heisenberg spacetime. With this new representation, we derive necessary and sufficient condition of the given particle to be the inextensible flow. Moreover, we provide several characterizations designed for this particles in Heisenberg spacetime.
ENERGY ON A PARTICLE IN DYNAMICAL AND ELECTRODYNAMICAL FORCE FIELDS IN LIE GROUPS
( Talat Korpinar ),( Ridvan Cem Demirkol ) 호남수학회 2018 호남수학학술지 Vol.40 No.2
In this study, we firstly define equations of motion based on the traditional model Newtonian mechanics in terms of the Frenet frame adapted to the trajectory of the moving particle in Lie groups. Then, we compute energy on the moving particle in resultant force field by using geometrical description of the curva-ture and torsion of the trajectory belonging to the particle. We also investigate the relation between energy on the moving particle in different force fields and energy on the particle in Frenet vector fields.
On New Fermi Walker Derivative Of Biharmonic Particles In Heisenberg Spacetime
Talat Korpinar 호남수학회 2019 호남수학학술지 Vol.41 No.1
In practical applications play an new important role timelike biharmonic particle by Fermi-Walker derivative. In this article, we get a innovative interpretation about timelike biharmonic particle by means of Fermi-Walker derivative and parallelism in Heisenberg spacetime. With this new representation, we derive necessary and sufficient condition of the given particle to be the inextensible flow. Moreover, we provide several characterizations designed for this particles in Heisenberg spacetime.
A NEW CONSTRUCTION OF BIENERGY AND BIANGLE IN LORENTZ 5-SPACE
( Talat Korpinar ),( Yasin Unluturk ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
In this study, we firstly compute the energies and the angles of Frenet vector fields in Lorentz 5-space L<sup>5</sup>. Then we obtain the bienergies and biangels of Frenet vector fields in L<sup>5</sup> by using the values of energies and angles. Finally, we present the relations among energies, angles, bienergies, and biangles with graphics.
A New Approach On The Curvature Dependent Energy For Elastic Curves in a Lie Group
Talat Korpinar,Ridvan Cem Demirkol 호남수학회 2017 호남수학학술지 Vol.39 No.4
Elastica is known as classical curve that is a solution of variational problem, which minimize a thin inextensible wire's bending energy. Studies on elastica has been conducted in Euclidean space firstly, then it has been extended to Riemannian manifold by giving different characterizations. In this paper, we focus on energy of the elastic curve in a Lie group. We attepmt to compute its energy by using geometric description of the curvature and the torsion of the trajectory of the elastic curve of the trajectory of the moving particle in the Lie group. Finally, we also investigate the relation between energy of the elastic curve and energy of the same curve in Frenet vector fields in the Lie group.
NEW VERSION OF THE MAGNETIC CURVES ACCORDING TO THE BISHOP FRAME IN E<sup>3</sup>
( Muhammed T. Sariaydin ),( Talat Korpinar ) 호남수학회 2019 호남수학학술지 Vol.41 No.1
In this paper, it is investigated Lorentz force equations for N<sub>1</sub> and N<sub>2</sub>-magnetic curves in 3-Dimensional Euclidean space. We give the Lorentz force in the Bishop frame in E<sup>3</sup>. Then, we obtain a new characterization for a magnetic field V . Also, we also give examples for each curve.
Kenan Akgun,Mehmet Ali Korpinar,Mustafa Tunaya Kalkan,Ulku Akarirmak,Sansin Tuzun,Fikret Tuzun 연세대학교의과대학 2004 Yonsei medical journal Vol.45 No.4
Despite the widespread clinical use of cryotherapy, there is only limited and inconsistent data on application times. The aim of this study was to determine the changes in tissue temperature and the duration of this effect. In this experimental study, five adult dogs were used. A cold gel pack (10×20 cm) was applied transversally over the right leg femoral region. Temperatures were recorded simultaneously: rectal by a mercury thermometer; right leg skin by probe of Nihon Kohden 6000 polygraph; and right leg subcutaneous, intramuscular, and periosteal, and left leg intramuscular temperatures by a fluorooptic biomedical fiber optic (0.6mm diameter) thermometer connected to a computer system. Total system accuracy was 0.01℃. Cold gel packs were applied for 10, 15, 20, 25, and 30 minutes duration. The results can be summarized as cooling and rewarming data. 1) The superficial tissues such as skin and subcutaneous demonstrated the most rapid and profound cooling effect. The deeper tissues such as bone and muscle exhibited a smaller and more gradual decline in temperature. 2) There was a prolonged rewarming period in all tissues after the removal of the cold gel pack but this period was longer in deeper tissues. According to cold gel pack application time, the rewarming time in intramuscular layers to baseline or plateau temperatures was about: 60± 3 minutes for 10 minutes application, 100±4 for 15, 130±5 for 20, 140±7 for 25, and 145±8 for 30. It can be concluded from these results that with increased cold gel pack application time, deep tissue temperature decreased and the duration of cooling effect increased. However, the data indicated that the length of application time and the duration of cooling effect were not linearly related. Especially after 20 minutes of application this ratio decreased progressively. There may be implications of these results for clinical practice.
NEW VERSION OF THE MAGNETIC CURVES ACCORDING TO THE BISHOP FRAME IN 𝔼<sup>3</sup>
Sariaydin, Muhammed T.,Korpinar, Talat The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
In this paper, it is investigated Lorentz force equations for $N_1$ and $N_2$-magnetic curves in 3-Dimensional Euclidean space. We give the Lorentz force in the Bishop frame in ${\mathbb{E}}^3$. Then, we obtain a new characterization for a magnetic field V. Also, we also give examples for each curve.