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Journal articles on the topic 'Type-2 bishop frame'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Ahmet, Kazan, and Bayram Karadag H. "Magnetic Curves According to Bishop Frame and Type-2 Bishop Frame in Euclidean 3-Space." British Journal of Mathematics & Computer Science 22, no. 4 (2017): 1–18. https://doi.org/10.9734/BJMCS/2017/33330.

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In this paper, we define the notions of <em>T</em>-magnetic, <em>N<sub>1</sub></em>-magnetic, <em>N<sub>2</sub></em>-magnetic curves according to Bishop frame and ξ<sub>1</sub>-magnetic, ξ<sub>2</sub>-magnetic, <em>B</em>-magnetic curves according to type-2 Bishop frame in Euclidean 3-space. Also, we obtain the magnetic vector field <em>V</em> when the curve is <em>T</em>-magnetic, <em>N<sub>1</sub></em>-magnetic,<em> N<sub>2</sub></em>-magnetic trajectory of <em>V</em> according to Bishop frame and ξ<sub>1</sub>-magnetic, ξ<sub>2</sub>-magnetic, <em>B</em>-magnetic trajectory of <em>V </em>ac

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2

Yilmaz, Amine, and Emin Özyilmaz. "Relation between Darboux and type-2 Bishop frames in Euclidean space." International Journal of Geometric Methods in Modern Physics 13, no. 07 (2016): 1650101. http://dx.doi.org/10.1142/s0219887816501012.

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In this work, we investigate relationships between Darboux and type-2 Bishop frames in Euclidean space. Then, we obtain the geodesic curvature of the spherical image curve of the Darboux vector of the type-2 Bishop frame. Also, we give transition matrix between the Darboux and type-2 Bishop frames of the type-2 Bishop frames of the spherical images of the edges [Formula: see text] and [Formula: see text]. Finally, we express some interesting relations and illustrate of the examples by the aid Maple programe.

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3

Liu, Haiming, and Donghe Pei. "Cusps of Bishop Spherical Indicatrixes and Their Visualizations." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/215614.

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The main result of this paper is using Bishop Frame and “Type-2 Bishop Frame” to study the cusps of Bishop spherical images and type-2 Bishop spherical images which are deeply related to a space curve and to make them visualized by computer. We find that the singular points of the Bishop spherical images and type-2 Bishop spherical images correspond to the point where Bishop curvatures and type-2 Bishop curvatures vanished and their derivatives are not equal to zero. As applications and illustration of the main results, two examples are given.

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4

KORPINAR, TALAT, HATICE OZDEMIR, and ZELIHA KORPINAR. "NEW VERSION OF FERMI-WALKER DERIVATIVES ACCORDING TO THE TYPE-2 BISHOP FRAME WITH ENERGY." Journal of Science and Arts 21, no. 1 (2021): 113–24. http://dx.doi.org/10.46939/j.sci.arts-21.1-a11.

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In this paper, we obtain the Fermi-Walker derivatives of , , magnetic curves according to the type-2 Bishop frame in the space. Moreover, we obtain the energy of the Fermi-Walker derivative of magnetic curves according to the type-2 Bishop frame in space. Finally, we have energy relations of some vector fields associated with type-2 Bishop frame in the space.

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5

Kazan, Ahmet, and H. Karadağ. "Magnetic Curves According to Bishop Frame and Type-2 Bishop Frame in Euclidean 3-Space." British Journal of Mathematics & Computer Science 22, no. 4 (2017): 1–18. http://dx.doi.org/10.9734/bjmcs/2017/33330.

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6

Gurbuz, Nevin. "Bishop 2-type frame for non-null curves." International Mathematical Forum 12 (2017): 879–89. http://dx.doi.org/10.12988/imf.2017.71084.

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7

KORPINAR, ZELIHA, та TALAT KORPINAR. "SMARANDACHE Π1B CURVES OF BIHARMONIC NEW TYPE CONSTANT Π2 - SLOPE CURVES ACCORDING TO TYPE-2 BISHOP FRAME IN THE SOL SPACE". Journal of Science and Arts 21, № 3 (2021): 681–88. http://dx.doi.org/10.46939/j.sci.arts-21.3-a08.

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In this paper, we study Smarandache Π1B curves of biharmonic new type constant Π2 -slope curves according to type-2 Bishop frame in the Sol space. Type-2 Bishop equations of Smarandache Π1B curves are obtained in terms of base curve's type-2 Bishop invariants. Subsequently, we express some interesting relations.

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8

Al-Dayel, Ibrahim, and E. M. Solouma. "Characteristic Properties of Type-2 Smarandache Ruled Surfaces According to the Type-2 Bishop Frame in E 3." Advances in Mathematical Physics 2021 (October 22, 2021): 1–7. http://dx.doi.org/10.1155/2021/8575443.

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In this paper, we define and investigate a special kind of ruled surfaces called type-2 Smarandache ruled surfaces related to the type-2 Bishop frame in E 3 . From this point and depending on the type-2 Bishop curvature, we provide the necessary and sufficient conditions that allow these surfaces to be developable in a minimal amount of time. Furthermore, an example is given to clear the results.

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9

Boyacıoğlu Kalkan, Özgür, and Süleyman Şenyurt. "Osculating Type Ruled Surfaces with Type-2 Bishop Frame in E3." Symmetry 16, no. 4 (2024): 498. http://dx.doi.org/10.3390/sym16040498.

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The aim of this work is to investigate osculating type ruled surfaces with a type 2-Bishop frame in E3. We accomplish this by employing the symmetry of osculating curves. We examine osculating type ruled surfaces by taking into account the curvatures of the base curve. We investigate the geometric properties of these surfaces, focusing on their cylindrical and developable characteristics. Moreover, we calculate the Gaussian and mean curvatures and provide the requirements for the surface to be flat and minimal. We determine the requirements for the curves lying on this surface to be geodesic,

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10

Mahmoud, Wageeda Mohamed, Mohamed Abdellatif Soliman, and Samar Abdel Hafez Moukhtar. "Generating and Characterization Loft Surface by Type-2-Bishop Frame in Isotropic Space." International Journal of Membrane Science and Technology 10, no. 3 (2023): 1951–68. http://dx.doi.org/10.15379/ijmst.v10i3.1864.

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This paper aims to design and generate a loft surface using three distinct curves (Hermitee cubic curve, straight line, and quadratic Bezier curve) and analyze its characteristics in isotropic space using type-2-Bishop. Moreover, the loft surface's 1st and 2nd - fundamental forms in the loft surface were investigated. In addition, their Gaussian, mean, and second Gaussian curvatures in I3 were computed using the first and second type-2-Bishop curvatures. Furthermore, the required and adequate conditions for the surface with type 2-Bishop curvatures that are developable, minimal, and Weingarten

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11

Gurbuz, Nevin. "Total anholonomies with Bishop 2-type frame in R_1^3." Nonlinear Analysis and Differential Equations 7, no. 1 (2019): 115–24. http://dx.doi.org/10.12988/nade.2019.9914.

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12

Körpinar, Talat, та Essin Turhan. "Biharmonic constant Π₁-slope curves according to type-2 bishop frame in Heisenberg group Heis³". Boletim da Sociedade Paranaense de Matemática 32, № 2 (2014): 73. http://dx.doi.org/10.5269/bspm.v32i2.19549.

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In this paper, we introduce constant Π₁- slope curves according to type-2 Bishop frame in the Heisenberg group Heis³. We characterize the biharmonic constant Π₁- slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric equations in the Heisenberg group Heis³. Additionally, we illustrate our main theorem.

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13

Körpinar, Talat, та Essin Turhan. "Integral equations of biharmonic constant π₁-slope curves according to type-2 Bishop frame in the SOL space". Boletim da Sociedade Paranaense de Matemática 31, № 2 (2013): 205. http://dx.doi.org/10.5269/bspm.v31i2.17619.

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In this paper, we study biharmonic constant Π₁- slope curves according to type-2 Bishop frame in the SOL³. We characterize the biharmonic constant Π₁- slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric integral equations in the SOL³.

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14

Kiziltug, S., S. Kaya, and O. Tarakci. "Tube surfaces with type-2 Bishop frame of Weingarten types in E^3." International Journal of Mathematical Analysis 7 (2013): 9–18. http://dx.doi.org/10.12988/ijma.2013.13002.

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15

Kofoglu, Nil. "Slant helices according to type-2 Bishop frame in Weyl space." International Mathematical Forum 15, no. 4 (2020): 173–83. http://dx.doi.org/10.12988/imf.2020.91263.

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16

Abdel-Baky, Rashad A., and Fatemah Mofarreh. "Sweeping surfaces according to type-2 Bishop frame in Euclidean 3-space." Asian-European Journal of Mathematics 14, no. 10 (2021): 2150184. http://dx.doi.org/10.1142/s1793557121501849.

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This work is concerned with the study of the kinematic-geometry of a special kind of tube surfaces, so-called sweeping surface in Euclidean 3-space [Formula: see text]. It is generated by a plane curve moving through space such that the movement of any point on the surface is always orthogonal to the plane. In particular, the type-2 Bishop frame is considered and some important theorems are obtained. Also, the problem of singularity and convexity of such sweeping surface is discussed. Finally, an application is presented and plotted using computer aided geometric design.

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17

BOZOK, GÜN, Hülya; Hülya;, Sezin; ERGÜT, and Mahmut Mahmut. "Curves of constant breadth according to type-2 bishop frame in E3." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 66, no. 1 (2017): 206–12. http://dx.doi.org/10.1501/commua1_0000000790.

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18

Damar, Esra, Nural Yuksel, and Aysel Turgut Vanli. "The ruled surfaces according to type-2 Bishop frame in E^3." International Mathematical Forum 12 (2017): 133–43. http://dx.doi.org/10.12988/imf.2017.610131.

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19

Gurbuz, Nevin. "Inextensible curve flows according to Bishop 2-type frame in Minkowski 3-space." International Mathematical Forum 11 (2016): 1167–74. http://dx.doi.org/10.12988/imf.2016.69127.

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20

Kızıltuğ, Sezai. "On Characterization of Inextensible Flows of Curves According to Type-2 Bishop Frame E3." Mathematical and Computational Applications 19, no. 1 (2014): 69–77. http://dx.doi.org/10.3390/mca19010069.

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21

BOZOK, Hülya Gün, Sezin Aykurt SEPET, and Mahmut ERGÜT. "Position Vectors of General Helices According to Type-2 Bishop Frame in E^3." Mathematical Sciences and Applications E-Notes 6, no. 1 (2018): 64–69. http://dx.doi.org/10.36753/mathenot.421762.

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22

AL-Dayel, Ibrahim, Emad Solouma, and Meraj Khan. "On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space." AIMS Mathematics 7, no. 7 (2022): 13454–68. http://dx.doi.org/10.3934/math.2022744.

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<abstract><p>In Euclidean 3-space $ {\mathrm{E}}^3 $, a canonical subject is the focal surface of such a cliched space curve, which would be a two-dimensional corrosive with Lagrangian discontinuities. The tubular surfaces with respect to the B-Darboux frame and type-2 Bishop frame in $ {\mathrm{E}}^3 $ are given. These tubular surfaces' focal surfaces are then defined. For such types of surfaces, we acquire some results becoming Weingarten, flat, linear Weingarten conditions and we demonstrate that in $ {\mathrm{E}}^3 $, a tubular surface has no minimal focal surface. We also prov

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23

Abdel-Aziz, Hossam S. "A study of tube-like surfaces according to type 2 Bishop frame in Euclidean space." Studia Universitatis Babes-Bolyai Matematica 62, no. 2 (2017): 249–59. http://dx.doi.org/10.24193/subbmath.2017.2.10.

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24

Körpinar, Talat, and Essin Turhan. "Asymptotic curves on B-surfaces according to type-2 bishop frame in the sol space." Journal of Dynamical Systems and Geometric Theories 13, no. 2 (2015): 125–36. http://dx.doi.org/10.1080/1726037x.2015.1076227.

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25

Solouma, E. M. "Type-2 Spacelike Bishop Frame and an Application to Spherical Image in Minkowski Space–Time." International Journal of Applied and Computational Mathematics 3, no. 4 (2017): 3575–91. http://dx.doi.org/10.1007/s40819-017-0316-6.

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26

MASAL, Melek, and Ayşe Zeynep AZAK. "THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3." Mathematical Sciences and Applications E-Notes 3, no. 2 (2015): 74–83. http://dx.doi.org/10.36753/mathenot.421334.

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27

Mofarreh, Fatemah, and Rashad A. Abdel-Baky. "Singularities of swept surfaces in Euclidean 3-space." AIMS Mathematics 9, no. 9 (2024): 26049–64. http://dx.doi.org/10.3934/math.20241272.

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<p>This study examines the local singularities of tube surfaces, especially those of swept surfaces $ (SS) $ in Euclidean 3-space $ \mathcal{E}^{3} $. $ SS $ is created by moving a planar curve through space such that the trajectory of any point on the surface remains perpendicular to the plane. The Type-2 Bishop frame is considered, and the singularities of these $ SS $ are analyzed. Examples are offered and illustrated.</p>

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28

BOZOK, Hülya Gün, Sezin AYKURT SEPET, and Mahmut ERGÜT. "Some Characterizations of Constant Ratio Curves According to Type-2 Bishop Frame in Euclidean 3-space E^3." International Electronic Journal of Geometry 10, no. 2 (2017): 67–72. http://dx.doi.org/10.36890/iejg.545054.

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29

Körpinar, Talat. "Parallel Surfaces to B-Surfaces of Biharmonic Constant П1-Slope Curves According to Type-2 Bishop Frame in the Sol Space". Journal of Advanced Physics 7, № 3 (2018): 382–86. http://dx.doi.org/10.1166/jap.2018.1451.

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30

Yılmaz, Süha, and Ümit Ziya Savcı. "A New Version Darboux Vector and Characterization Some Special Curves According to Type-2 Bishop Frame in $$\mathbb {R}^{3}$$ R 3." Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 87, no. 3 (2017): 355–62. http://dx.doi.org/10.1007/s40010-017-0373-6.

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31

Gurbuz, Nevin, and Ersin Isik. "Intrinsic geometry of the nonlinear heat equation for spacelike curves with timelike normal according to Bishop 2-type frame in Minkowski 3-space." International Mathematical Forum 11 (2016): 1109–15. http://dx.doi.org/10.12988/imf.2016.69122.

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32

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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33

GÜR MAZLUM, Sümeyye. "Bishop Frames of Salkowski Curves in E3." Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 13, no. 1 (2023): 79–91. http://dx.doi.org/10.17798/bitlisfen.1345438.

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In this study, alternative, type-1 Bishop, type-2 Bishop and N-Bishop frames of Salkowski curves in E3 are calculated. Moreover, curvatures, Darboux and pol vectors of these frames are found. Also, relationships between the Bishop frames, Darboux vectors and pole vectors are given.

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34

Plamen, Sabev. "ЙЕРУСАЛИМИЯ ОТ ЦЪРКВАТА "СВ. ГЕОРГИ" В АРБАНАСИ/ A JERUSALEM ICON FROM THE CHURCH OF ST. GEORGE IN ARBANASY". EPOHI [EPOCHS] Edition of the Department of History of "St. Cyril and St. Methodius" University of Veliko Tarnovo Issue 2, XXIII, 2015 (2022): 419–27. https://doi.org/10.5281/zenodo.6590928.

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In 2011, I came across a Jerusalem type of icon in the chapel of the “St.  Demetrius” church in Arbanasy.  Due to the long-term exposure to humidity and dust, it needed an urgent restoration and conservation. However, in the museum data it was signed that the place of origin of the icon was the church of St. George in Arbanasy. After a research over older photographic documents, I’ve found that the icon was hang on the wall of the nave of this church, and eventually, due to the church’s closure for restoration, it was moved in the chapel of St. Demetrius churc

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35

Castel, Myra Elise, Neil T. Conlon, Georg F. Bischof, et al. "Abstract 6846: Using CRISPR/Cas9 to edit KRAS in a small cell lung cancer cell line." Cancer Research 85, no. 8_Supplement_1 (2025): 6846. https://doi.org/10.1158/1538-7445.am2025-6846.

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Abstract Introduction: Small cell lung cancer (SCLC) accounts for 10-15% of lung cancers and is the most aggressive subtype. Approximately 16% of SCLCs contain mutations in the KRAS oncogene. The KRASG12C activating mutation is now clinically targetable. There are limited SCLC models containing the KRASG12C mutation available to generate pre-clinical rationale for clinical studies. This study aimed to develop a protocol for the insertion of the KRASG12C mutation in the KRAS wild-type SCLC cell line NCI-H1048 using CRISPR/Cas9 technology. Methods: A protospacer adjacent motif (PAM) was identifi

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36

Dersim, Kaya. "Smarandache curves according to 2 type Bishop frame in Euclidean 3-space." June 15, 2015. https://doi.org/10.5281/zenodo.32331.

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37

Yoon, Dae Won, та Nevin Ertuğ Gürbüz. "Geometric phases for three cases of the electric field with new type Bishop frame in ℝ13". International Journal of Geometric Methods in Modern Physics, 27 квітня 2022. http://dx.doi.org/10.1142/s0219887822501158.

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In this paper, we study geometric phases for an electric field in Minkowski 3-space. In particular, we consider Bishop 2-type frames of a spacelike and a timelike curve in Minkowski 3-space and investigate three geometric phases for three cases of electric fields with respect to the Bishop 2-type frames along a spacelike and a timelike curve. Also, we compute spatial and time evolutions of the complex frame connected with electric fields for Bishop 2-type in terms of modified Hasimoto transformations. As a result, we give a modified Fermi–Walker parallel derivative and a Rytov parallel transpo

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38

Suha, Yılmaz, and Ziya Savcı Umit. "Smarandache Curves and Applications According to Type-2 Bishop Frame in Euclidean 3-Space." May 10, 2016. https://doi.org/10.5281/zenodo.822231.

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In this paper, we investigate Smarandache curves according to type-2 Bishop frame in Euclidean 3- space and we give some differential geometric properties of Smarandache curves. Also, some characterizations of Smarandache breadth curves in Euclidean 3-space are presented. Besides, we illustrate examples of our results.

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39

"Timelike Sweeping Surfaces According to Type-2 Bishop Frame in Minkowski 3–space." WSEAS TRANSACTIONS ON MATHEMATICS 19 (November 5, 2020). http://dx.doi.org/10.37394/23206.2020.19.60.

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In this paper, we express timelike sweeping surfaces using rotation minimizing frames in Minkowski 3–Space E3 1 . Necessary and sufficient conditions for timelike sweeping surfaces to be developable ruled surfaces are derived. Using these, we analyze the conditions when the resulting timelike developable surface is a cylinder, cone or tangential surface.

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40

Kiziltug, S., S. Kaya, and O. Tarakci. "THE SLANT HELICES ACCORDING TO TYPE-2 BISHOP FRAME IN EUCLIDEAN 3-SPACE." International Journal of Pure and Apllied Mathematics 85, no. 2 (2013). http://dx.doi.org/10.12732/ijpam.v85i2.3.

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41

Yilmaz, S., and Y. Unluturk. "A NOTE ON SPACELIKE CURVES ACCORDING TO TYPE-2 BISHOP FRAME IN MINKOWSKI 3-SPACE $E_{1}^{3}$." International Journal of Pure and Apllied Mathematics 103, no. 2 (2015). http://dx.doi.org/10.12732/ijpam.v103i2.16.

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42

Wen, Yalun, and Prabhakar R. Pagilla. "Motion Control Along Spatial Curves for Robot Manipulators: A Non-Inertial Frame Approach." Journal of Dynamic Systems, Measurement, and Control, March 17, 2025, 1–15. https://doi.org/10.1115/1.4068205.

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Abstract This paper presents an innovative approach to robot motion control that utilizes a non-inertial tool frame with a specific parametrization to maintain constant tool speed. The approach employs an efficient numerical technique that generates the constant speed trajectory, correlating time with the curve's arc length. The robot motion equations are derived along the curve using two types of non-inertial frames: (1) a rotation-minimizing frame (Bishop frame) which leverages its minimal twist property to simplify the motion equations and facilitates stable kinematics at trajectory inflect

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43

Rodriguez, Aleesha, and Amanda Levido. "“My Little Influencer”." M/C Journal 26, no. 2 (2023). http://dx.doi.org/10.5204/mcj.2948.

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Introduction Wooden toys have been a staple in many family homes. Even LEGO's iconic plastic building blocks had humble beginnings as wooden toys (Lauwaert). Arguably, the materiality of wooden toys evokes normative feelings of nostalgia for a simpler past, where the uncomplicated nature of the wooden product provided the space for all sorts of imaginative play. It is through this lens that we find the adaptation of wooden toys into playsets that emulate particular vocations, like a doctor's kit and a carpenter's toolbox, an interesting entry point to consider the boundary of what is an accept

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