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Journal articles on the topic 'Frenent'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Önder, Mehmet, and Hasan Hüseyin Uğurlu. "Spacelike Regle Yüzeylerin Frenet Çatıları ve Frenet İnvaryantları." Deu Muhendislik Fakultesi Fen ve Muhendislik 19, no. 57 (2017): 712–22. http://dx.doi.org/10.21205/deufmd.2017195764.

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2

El-Ahmady, A. E., and A. T. M-Zidan. "On the Deformation Retractions of Frenet Curves in Minkowski 4 - Space." Modern Applied Science 14, no. 9 (2020): 55. http://dx.doi.org/10.5539/mas.v14n9p55.

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In this paper, the position vector equation of &nbsp;&nbsp;the Frenet curves with constant curvatures in Minkowski 4 -space has been presented. New types for retractions and deformation retracts of Frenet curves in &nbsp;are deduced. The relations between the Frenet apparatus of the Frenet curves before and after the deformation retracts are obtained.

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3

Arreaga, G., R. Capovilla, and J. Guven. "Frenet–Serret dynamics." Classical and Quantum Gravity 18, no. 23 (2001): 5065–83. http://dx.doi.org/10.1088/0264-9381/18/23/304.

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4

Encheva, Radostina P., and Georgi H. Georgiev. "Similar Frenet Curves." Results in Mathematics 55, no. 3-4 (2009): 359–72. http://dx.doi.org/10.1007/s00025-009-0407-8.

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5

Akgun, Muslum Aykut. "Frenet curves in 3-dimensional $ \delta $-Lorentzian trans Sasakian manifolds." AIMS Mathematics 7, no. 1 (2021): 199–211. http://dx.doi.org/10.3934/math.2022012.

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<abstract><p>In this paper, we give some characterizations of Frenet curves in 3-dimensional $ \delta $-Lorentzian trans-Sasakian manifolds. We compute the Frenet equations and Frenet elements of these curves. We also obtain the curvatures of non-geodesic Frenet curves on 3-dimensional $ \delta $-Lorentzian trans-Sasakian manifolds. Finally, we give some results for these curves.</p></abstract>

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6

GÜR MAZLUM, Sümeyye. "On Bishop Frames of Any Regular Curve in Euclidean 3-Space." Afyon Kocatepe University Journal of Sciences and Engineering 24, no. 1 (2024): 23–33. http://dx.doi.org/10.35414/akufemubid.1343172.

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Relationships between type-1 Bishop and Frenet, type-2 Bishop and Frenet, alternative and Frenet, N-Bishop and alternative frames of any regular curve in Euclidean 3-space are known. In this study, relationships between N-Bishop and Frenet frames and relationships between type-1 Bishop, type-2 Bishop and N-Bishop frames of any regular curve in Euclidean 3-space are given. In addition, pole vectors (unit vectors in the direction of Darboux vectors) belonging to these frames are computed. Last, pole and Darboux vectors belonging to these frames are compared with each other.

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7

Şenyurt, Süleyman, Filiz Ertem Kaya, and Davut Canlı. "Pedal curves obtained from Frenet vector of a space curve and Smarandache curves belonging to these curves." AIMS Mathematics 9, no. 8 (2024): 20136–62. http://dx.doi.org/10.3934/math.2024981.

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<abstract><p>In this study, first the pedal curves as the geometric locus of perpendicular projections to the Frenet vectors of a space curve were defined and the Frenet vectors, curvature, and torsion of these pedal curves were calculated. Second, for each pedal curve, Smarandache curves were defined by taking the Frenet vectors as position vectors. Finally, the expressions of Frenet vectors, curvature, and torsion related to the main curves were obtained for each Smarandache curve. Thus, new curves were added to the curve family.</p></abstract>

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8

Bektaş, Özcan, and Salim Yüce. "Serret-Frenet formulas for octonionic curves." Boletim da Sociedade Paranaense de Matemática 38, no. 3 (2019): 47–62. http://dx.doi.org/10.5269/bspm.v38i3.34780.

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In this paper, we dene spatial octonionic curves (SOC) in R7 and octonionic curves (OC) in R8 by using octonions. Firstly, we determine Serret-Frenet equations, and curvatures of the SROC in R7. Then, Serret-Frenet equations for the OC in R8 are calculated with the help of Serret-Frenet equations of SOC in R7.

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9

Yılmaz, Süha, and Yasin Unluturk. "On spherical indicatrices of curves in Galilean 4-space G₄." Journal of the Indonesian Mathematical Society 25, no. 2 (2019): 154–70. http://dx.doi.org/10.22342/jims.25.2.473.154-170.

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In this study, we indroduce spherical indicatrices of curves in four dimensional Galilean space. Moreover, we characterize these curves in terms of Frenet-Serret vector fields in four dimensional Galilean space. Frenet-Serret apparatus of these curves are obtained in terms of base curve's Frenet invariants. Additionally, some theorems are given regarding characterizations of spherical indicatrices of curves in four dimensional Galilean space.

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10

ATEŞ, Fatma, Seher KAYA, Yusuf YAYLI, and F. Nejat EKMEKCİ. "Generalized Similar Frenet Curves." Mathematical Sciences and Applications E-Notes 5, no. 2 (2017): 26–36. http://dx.doi.org/10.36753/mathenot.421731.

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11

Capovilla, R., J. Guven, and E. Rojas. "Hamiltonian Frenet–Serret dynamics." Classical and Quantum Gravity 19, no. 8 (2002): 2277–90. http://dx.doi.org/10.1088/0264-9381/19/8/315.

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12

Capovilla, R., J. Guven, and E. Rojas. "Null Frenet-Serret dynamics." General Relativity and Gravitation 38, no. 4 (2006): 689–98. http://dx.doi.org/10.1007/s10714-006-0258-5.

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13

YENEROĞLU, MUSTAFA, and AHMET DUYAN. "ASSOCIATED CURVES ACCORDING TO BISHOP FRAME IN 4-DIMENSIONAL EUCLIDEAN SPACE." Journal of Science and Arts 24, no. 1 (2024): 105–10. http://dx.doi.org/10.46939/j.sci.arts-24.1-a09.

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Many studies have been doneaccording to different frames of the theory of curves in Euclidean Space. Many scientists have studied frames such as the Frenet frame, Bishop frame, and Adapted frame in this theory. These frames help us in the characterization of curves.In this study, associated curves with the Frenet curve according to the Bishop frame in 4-dimensional Euclidean space are investigated. Direction and rectifying curves of the Frenet curve according to this frame are given.

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14

Has, Aykut, and Beyhan Yilmaz. "Alternative planes and the curves on them." Boletim da Sociedade Paranaense de Matemática 42 (May 2, 2024): 1–7. http://dx.doi.org/10.5269/bspm.62928.

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In this study, the planes formed by Frenet elements are defined with a U vector chosen different from T, N and B, which are the elements of the Frenet frame, and the curves on these planes are also characterized. As it is known, the planes formed by Frenet elements between themselves have been defined and investigated many times. In this present article, the plane formed by an arbitrary chosen vector U with T, N and B is defined and the curveslying in this plane are characterized

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15

Saad, M. Khalifa, H. S. Abdel-Aziz, and I. K. Youssef. "Spinor Formulation of Frenet Normal Spherical Image in Euclidean and Pseudo-Euclidean Spaces." International Journal of Analysis and Applications 23 (June 26, 2025): 151. https://doi.org/10.28924/2291-8639-23-2025-151.

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In this paper, we introduce one of the spherical images of a regular curve by translating Frenet frame vectors to the center of the unit sphere (Lorentizian sphere) of the Euclidean 3-space E3 (pseudo-Euclidean 3-space E1,2). Especially, Frenet formulas for the normal spherical image of a regular curve can be obtained in terms of spinors. As a result of this study, we found that Frenet equations for that one can be simplified to a single equation with two complex components. Finally, interesting illustrative examples of the obtained results are given and plotted.

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16

El-Ahmady, A. E., Malak E. Raslan, and A. T. M-Zidan. "On Null Curves in Minkowski 3-Space and Its Fractal Folding." Modern Applied Science 14, no. 4 (2020): 90. http://dx.doi.org/10.5539/mas.v14n4p90.

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In this paper, a form for Frenet equations of all null curves in Minkowski 3-space has been presented. New types of foldings of curves are obtained. The connection between folding, deformation and Frenet equations of curves are also deduced.

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17

Kahveci̇, Derya, and Yusuf Yayli. "Persistent rigid-body motions on slant helices." International Journal of Geometric Methods in Modern Physics 16, no. 12 (2019): 1950193. http://dx.doi.org/10.1142/s0219887819501937.

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This paper reviews the persistent rigid-body motions and examines the geometric conditions of the persistence of some special frame motions on a slant helix. Unlike the Frenet–Serret motion on general helices, the Frenet–Serret motion on slant helices can be persistent. Moreover, even the adapted frame motion on slant helices can be persistent. This paper begins by explaining one-dimensional rigid-body motions and persistent motions. Then, it continues to present persistent frame motions in terms of their instantaneous twists and axode surfaces. Accordingly, the persistence of any frame motion

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18

Kılıçoğlu, Şeyda, and Süleyman Şenyurt. "On the Involute of the Cubic Bezier Curve by Using Matrix Representation in E3." European Journal of Pure and Applied Mathematics 13, no. 2 (2020): 216–26. http://dx.doi.org/10.29020/nybg.ejpam.v13i2.3648.

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In this study we have examined, involute of the cubic Bezier curve based on the control points with matrix form in E3. Frenet vector fields and also curvatures of involute of the cubic Bezier curve are examined based on the Frenet apparatus of the first cubic Bezier curve in E3.

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19

Nesvidomin, Andrii, Serhii Pylypaka, Tetiana Volina, Irina Rybenko, and Alla Rebrii. "Analytical connection between the Frenet trihedron of a direct curve and the Darboux trihedron of the same curve on the surface." Technology audit and production reserves 4, no. 2(78) (2024): 54–59. http://dx.doi.org/10.15587/2706-5448.2024.310524.

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Frenet and Darboux trihedrons are the objects of research. At the current point of the direction curve of the Frenet trihedron, three mutually perpendicular unit orthogonal vectors can be uniquely constructed. The orthogonal vector of the tangent is directed along the tangent to the curve at the current point. The orthogonal vector of the main normal is located in the plane, which is formed by three points of the curve on different sides from the current one when they are maximally close to the current point. It is directed to the center of the curvature of the curve. The orthogonal vector of

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20

Yormaz, Cansel, Simge Simsek, and Serife Naz Elmas. "Quaternionic Serret-Frenet Frames for Fuzzy Split Quaternion Numbers." Advances in Fuzzy Systems 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/7215049.

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We build the concept of fuzzy split quaternion numbers of a natural extension of fuzzy real numbers in this study. Then, we give some differential geometric properties of this fuzzy quaternion. Moreover, we construct the Frenet frame for fuzzy split quaternions. We investigate Serret-Frenet derivation formulas by using fuzzy quaternion numbers.

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21

Iyigün, Esen. "Constant curvature ratios in L6." Filomat 30, no. 3 (2016): 785–89. http://dx.doi.org/10.2298/fil1603785i.

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In this paper, we find a relation between Frenet formulas and harmonic curvatures, and also a relation between Frenet formulas and e-curvature functions of a curve of osculating order 6 in 6 dimensional Lorentzian space L6. Moreover, we give a relation between harmonic curvatures and ccr-curves of a curve in L6.

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22

Alo, Jeta. "Null Hybrid Curves and Some Characterizations of Null Hybrid Bertrand Curves." Symmetry 17, no. 2 (2025): 312. https://doi.org/10.3390/sym17020312.

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In this paper, we investigate null curves in R24, the four-dimensional Minkowski space of index 2, utilizing the concept of hybrid numbers. Hybrid and spatial hybrid-valued functions of a single variable describe a curve in R24. We first derive Frenet formulas for a null curve in R23, the three-dimensional Minkowski space of index 2, by means of spatial hybrid numbers. Next, we apply the Frenet formulas for the associated null spatial hybrid curve corresponding to a null hybrid curve in order to derive the Frenet formulas for this curve in R24. This approach is simpler and more efficient than

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23

Körpınar, Talat, and Ridvan Cem Demirkol. "A new construction on the energy of space curves in unit vector fields in Minkowski space E₂⁴." Boletim da Sociedade Paranaense de Matemática 39, no. 2 (2021): 105–20. http://dx.doi.org/10.5269/bspm.39288.

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In this paper, we firstly introduce kinematics properties of a moving particle lying in Minkowski space E₂⁴. We assume that particles corresponds to different type of space curves such that they are characterized by Frenet frame equations. Guided by these, we present geometrical understanding of an energy and pseudo angle on the particle in each Frenet vector fields depending on the particle corresponds to a spacelike, timelike or lightlike curve in E₂⁴. Then we also determine the bending elastic energy functional for the same particle in E₂⁴ by assuming the particle has a bending feature of e

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24

Körpinar, Talat. "On velocity bimagnetic biharmonic particles with energy on Heisenberg space." Proyecciones (Antofagasta) 37, no. 2 (2018): 379–87. https://doi.org/10.22199/issn.0717-6279-2925.

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In this work, we consider velocity bimagnetic biharmonic particle on 3D Heisenberg space in the magnetic field B and we give the concept of energy. Moreover, we characterize energy conditions of velocity bimagnetic biharmonic particles with Frenet vector field. Therefore, we obtain energy results for bimagnetic particles by Frenet fields in the Heisenberg space.

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25

Şenyurt, Süleyman, and Sümeyye Gür Mazlum. "Some Applications on Spherical Indicatrices of the Helix Curve." Ordu Üniversitesi Bilim ve Teknoloji Dergisi 14, no. 1 (2024): 154–75. http://dx.doi.org/10.54370/ordubtd.1438188.

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In this study, the Frenet elements of the curves that are drawn on the unit sphere by the unit vectors obtained from linear combinations of Frenet vectors of the helix curve are calculated. Moreover, Sabban frames of these curves are created and Smarandache curves are defined. Finally, the geodesic curvatures of each Smarandache curve are calculated.

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26

Tunçer, Yılmaz. "Vectorial moments of curves in Euclidean 3-space." International Journal of Geometric Methods in Modern Physics 14, no. 02 (2017): 1750020. http://dx.doi.org/10.1142/s0219887817500207.

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In this study, we introduced the vectorial moments as a new curves as [Formula: see text]-dual curve, where [Formula: see text], constructed by the Frenet vectors of a regular curve in Euclidean 3-space and we gave the Frenet apparatus of [Formula: see text]-dual curves and also we applied to helices and curve pairs of constant breadth.

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27

Wang, J., and J. Xiao. "Exact Finite Element Formulation of Frenet Formula of Curve in Geospatial Database." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-4 (April 23, 2014): 291–95. http://dx.doi.org/10.5194/isprsarchives-xl-4-291-2014.

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Directly using the difference form of Frenet formula will cause the three basic vectors losing their orthogonal features rapidly. As the analytic form is exact for infinite short length region, for finite length segregation, the omitted items should be retrieved to get high precision. Based on the unit orthogonal transformation in geometrical field theory, the Frenet formula is reformed for finite length region. Then, for given triple at the initial end of curve, using the curve parameters of curvature and torsion, the exact finite element formulation of Frenet formula is obtained to get the t

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28

PARLAK, ESRA, and TEVFİK ŞAHİN. "GEOMETRIC PERSPECTIVE OF BERRY'S PHASE ACCORDING TO ALTERNATIVE ORTHOGONAL MODIFIED FRAME." Journal of Science and Arts 25, no. 1 (2025): 11–24. https://doi.org/10.46939/j.sci.arts-25.1-a02.

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It is very important to determine the Frenet vector fields to obtain the characterizations of curves in 3-dimensional Euclidean space. However, it may not be possible to define Frenet vector fields at some points of the curve, or the Frenet frame may not be sufficient to determine the curve's characterization. New frames can be defined as alternatives to the Frenet frame in these situations. Lots of work has been done for these cases such as Bishop frame, {d_2,C,W}- frame, orthogonal frame, etc. In this study, we produce the magnetic curves related to an alternative modified frame that can be

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29

Nesvidomin, Andrii, Serhiy Pylypaka, Vitaly Babka, and Iryna Zaharova. "AN ANALOGUE OF FRENET FORMULAS FOR THE DARBOUX TRIEDRON CURVE ON THE SURFACE." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 103 (December 23, 2022): 151–61. https://doi.org/10.32347/0131-579x.2022.103.151-161.

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Frenet and Darboux trihedrons are accompanying for the guide curve. The position of the Frenet trihedron on the curve is uniquely determined by its first and second derivatives. The Darboux trihedron is the accompanying to the curve on the surface. Both trihedrons move along the curve so that one of the orthos is tangent to the curve. If in the Frenet trihedron one of the faces is the tangent plane of the curve, then in the Darboux trihedron the corresponding face is tangent to the surface, that is, there is a certain angle between these faces of the trihedrons, which can change when they move

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30

Güven, Ìlkay Arslan, Semra Kaya Nurkan, and Ìpek Agaoglu Tor. "Spherical Images of W-Direction Curves in Euclidean 3-Space." Journal of Mathematics Research 12, no. 3 (2020): 39. http://dx.doi.org/10.5539/jmr.v12n3p39.

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In this paper, we study the spherical indicatrices of W-direction curves in three dimensional Euclidean space which were defined by using the unit Darboux vector field W of a Frenet curve. We obtain the Frenet apparatus of these spherical indicatrices and the characterizations of being general helix and slant helix. Moreover we give some properties between the spherical indicatrices and their associated curves.

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31

Mendonca, Thiago, Jose Alan, and Renato Teixeira. "Smarandache Curves of Natural Curves Pair According to Frenet Frame." Advances in Research 25, no. 5 (2024): 1–13. http://dx.doi.org/10.9734/air/2024/v25i51131.

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Smarandache curves play a significant role in differential geometry. They extend conventional differential geometry concepts and help uncover novel geometric properties. In this work, we define the Smarandache curves of the Natural mate of any given curve \(\alpha\) and calculate their Frenet apparatus. As a particular case, we present the Frenet apparatus when \(\alpha\) is a helix. Additionally, we illustrate an example for the slant helix.

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32

ŞENYURT, Süleyman, Kebire Hilal AYVACI, and Davut CANLI. "Smarandache Curves According to Flc-frame in Euclidean 3-space." Fundamentals of Contemporary Mathematical Sciences 4, no. 1 (2023): 16–30. http://dx.doi.org/10.54974/fcmathsci.1142404.

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The paper investigates some special Smarandache curves according to Flc-frame in Euclidean 3-space. The Frenet and Flc frame vectors, curvature and torsion of the new constructed curves are expressed by means of the initial curve invariants. For the sake of comparison in view, an example for Smarandache curves according to both Frenet and Flc frame is also presented at the end of paper.

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33

CAVASI, ABEL. "The recurrence theorem of Frenet formulae." Creative Mathematics and Informatics 23, no. 2 (2014): 175–82. http://dx.doi.org/10.37193/cmi.2014.02.15.

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In this paper we generalize Frenet trihedron and we provide some other classes of trihedrons, called Frenet trihedrons of order n, n ≥ 1. Moreover we prove that those trihedrons can be defined recurrently and we emphasize their role in the study of the generalized helices of order n. As practical applications we present the influence of the recurrence theorem in some interdisciplinary domains like physics, chemistry and biology.

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34

Viana, Thiago Mariano, and Fernando Pereira Souza. "CURVAS REGULARES E EQUAÇÕES DE FRENET." Colloquium Exactarum 4, Especial (2013): 01–09. http://dx.doi.org/10.5747/ce.2013.v05.nesp.000046.

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35

Ali, Md Showkat, and Md Abu Hanif Sarkar. "Serret-Frenet Equations in Minkowski Space." Dhaka University Journal of Science 61, no. 1 (2013): 87–92. http://dx.doi.org/10.3329/dujs.v61i1.15102.

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In this paper we established the Serret-Frenet equations in Minkowski space. These equations originally formulated in Euclidean space in R3, constitute a beautiful set of vector differential equations which contains all intrinsic properties of parameterized curve. From the local theory of curves in R3 states that a curve lies in a plane if and only if its torsion vanishes, which gives us clear geometrical insight in the notion of torsion. This theorem has two counterparts in Minkowski space that has been focused. Dhaka Univ. J. Sci. 61(1): 87-92, 2013 (January) DOI: http://dx.doi.org/10.3329/d

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36

DESHMUKH, Sharief, İbrahim AL-DAYEL, and Kazım İLARSLAN. "Frenet Curves in Euclidean 4-Space." International Electronic Journal of Geometry 10, no. 2 (2017): 56–66. http://dx.doi.org/10.36890/iejg.545050.

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37

Avanzini, Giulio. "Frenet-Based Algorithm for Trajectory Prediction." Journal of Guidance, Control, and Dynamics 27, no. 1 (2004): 127–35. http://dx.doi.org/10.2514/1.9338.

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38

Tjahjana, R. H., and R. H. S. Utomo. "Multi agent through serret-frenet system." Journal of Physics: Conference Series 1321 (October 2019): 022071. http://dx.doi.org/10.1088/1742-6596/1321/2/022071.

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39

UNDERWOOD, MICHAEL S., and KARL-PETER MARZLIN. "FERMI–FRENET COORDINATES FOR SPACELIKE CURVES." International Journal of Modern Physics A 25, no. 06 (2010): 1147–54. http://dx.doi.org/10.1142/s0217751x10047841.

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We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's worldline, to the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are fixed using a covariant Frenet triad so that the metric can be expressed using the curvature and torsion of the spatial curve. As an application of Fermi–Frenet coordinates, we show that they allow covariant inertial forces to be expressed in a simple and physically intuitive way.

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40

Wagner, Michael G., and Bahram Ravani. "Curves with rational Frenet-Serret motion." Computer Aided Geometric Design 15, no. 1 (1997): 79–101. http://dx.doi.org/10.1016/s0167-8396(97)81786-4.

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41

Iyer, B. R., and C. V. Vishveshwara. "Frenet-Serret description of gyroscopic precession." Physical Review D 48, no. 12 (1993): 5706–20. http://dx.doi.org/10.1103/physrevd.48.5706.

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42

Ogrenmis, Meltem, and Alper Osman Ogrenmis. "Curves in Multiplicative Equiaffine Space." Mathematics 13, no. 7 (2025): 1107. https://doi.org/10.3390/math13071107.

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In this study, the geometric properties of curves in multiplicative equiaffine space are investigated using multiplicative calculus. Fundamental geometric concepts such as multiplicative arc length, multiplicative equiaffine curvature, and torsion are introduced. This study derives the multiplicative Frenet frame and associated Frenet equations, providing a systematic framework for describing the geometric behavior of multiplicative equiaffine curves. Additionally, curves with constant multiplicative curvature and torsion are characterized and supported with illustrative examples.

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43

Nesvidomin, Andrii. "ANALYTICAL RELATION BETWEEN THE FRENET TRIHEDRON OF A DIRECT CURVE AND THE DARBOUX TRIHEDRON OF THE SAME CURVE ON A SURFACE." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 107 (February 26, 2025): 136–49. https://doi.org/10.32347/0131-579x.2024.107.136-149.

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The Frenet trihedron plays an extremely important role in the theory of differential geometry. It concerns curved lines, which we will call direction lines. At the current point of the direction curve, three mutually perpendicular unit orthogonals of this trihedron can be uniquely constructed. The tangent ort is directed along the tangent to the curve at the current point. The ort of main normal is located in the plane formed by three points of the curve on different sides of the current one when they approach the current point as close as possible. It is directed towards the center of curvatu

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44

ÖNDER, Mehmet. "Direction curves of generalized Bertrand curves and involute-evolute curves in $E^{4}$." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 2 (2022): 326–38. http://dx.doi.org/10.31801/cfsuasmas.950707.

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In this study, we define (1,3)-Bertrand-direction curve and (1,3)-Bertrand-donor curve in the 4-dimensional Euclidean space $E^{4}$. We introduce necessary and sufficient conditions for a special Frenet curve to have a (1,3)-Bertrand-direction curve. We introduce the relations between Frenet vectors and curvatures of these direction curves. Furthermore, we investigate whether (1,3)-evolute-donor curves in $E^{4}$ exist and show that there is no (1,3)-evolute-donor curve in $E^{4}$ .

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Uçar, Ayşenur, Fatma Karakuş, and Yusuf Yaylı. "Generalized Fermi–Walker derivative and non-rotating frame." International Journal of Geometric Methods in Modern Physics 14, no. 09 (2017): 1750131. http://dx.doi.org/10.1142/s0219887817501316.

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In this paper, generalized Fermi–Walker derivative, generalized Fermi–Walker parallelism and generalized non-rotating frame concepts are given for Frenet frame, Darboux frame and Bishop frame for any curve in Euclidean space. Being generalized, non-rotating frame conditions are analyzed for each frames along the curve. Then we show that Frenet and Darboux frames are generalized non-rotating frames along all curves and also Bishop frame is generalized non-rotating frame along planar curves in Euclidean space.

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Auzias, A., C. Bollet, R. Ayari, M. Drancourt, and D. Raoult. "Corynebacterium freneyi Bacteremia." Journal of Clinical Microbiology 41, no. 6 (2003): 2777–78. http://dx.doi.org/10.1128/jcm.41.6.2777-2778.2003.

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Di Fátima, Branco. "Depois do frenesi." Revista FAMECOS 30, no. 1 (2023): e41773. http://dx.doi.org/10.15448/1980-3729.2023.1.41773.

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Dez anos depois do frenesi gerado por obras como Snow Fall e NSA files, chega o momento de problematizar a resiliência da reportagem na internet. Este artigo apresenta uma proposta historiográfica do gênero na web. O seu desenvolvimento é organizado em três períodos, marcados pela introdução de aparatos tecnológicos nas rotinas produtivas da redação: Transposição (1996-2001) examina os primeiros anos da reportagem na rede; Renovação (2002-2011) explora rupturas iniciais e como linguagens informáticas foram absorvidas; e Estabilização (2012-2021) analisa o quadro mais atual das práticas do gêne

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José, Adonai Pereira Seixas, and Isaac Barbosa Isnaldo. "On Frenet Apparatus of Curves in Rn." Latin American Journal of Mathematics 01, no. 01 (2022): 40–76. https://doi.org/10.5281/zenodo.7922410.

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In this paper, we present new explicit and nonrecursive formulas for the curvatures and the frame of Frenet of a regular curve with an arbitrary parameter in the Euclidean space Rn, n >2, expressed only in terms of its derivatives.

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İşbilir, Zehra, and Murat Tosun. "On generalized osculating-type curves in Myller configuration." Analele Universitatii "Ovidius" Constanta - Seria Matematica 32, no. 2 (2024): 85–98. https://doi.org/10.2478/auom-2024-0020.

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Abstract In this study, we examine osculating-type curves with Frenet-type frame in Myller configuration for Euclidean 3-space E 3. We present the necessary characterizations for a curve to be an osculating-type curve. Characterizations originating from the natural structure of Myller configuration are a generalization of osculating curves according to the Frenet frame. Also, we introduce some new results that are not valid for osculating curves. Then, we give an illustrative numerical example supported by a figure.

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ÇİÇEK ÇETİN, Esra, Mehmet BEKTAŞ, and Münevver Yıldırım YILMAZ. "On the Assocıated Curves of a Frenet Curve in R_1^4." Cumhuriyet Science Journal 43, no. 2 (2022): 273–76. http://dx.doi.org/10.17776/csj.885772.

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In the present work, we have dealt with the properties of associated curves of a Frenet curve in R14. In addition to this, we define principal direction curve, B_1 -direction curve, B_2- direction curve of a given Frenet curve by using integral curves of 4-dimensional Minkowski space. Then we introduce some characterizations for general helix and slant helix. Finally, some new associated curves and theorems obtained for space-like curves and time- like curves in R14. Also, an example is given.

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