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Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2019, Volume 147, Issue 4, pp. 1699 - 1707
We show that the torsion of any simple closed curve \Gamma in Euclidean 3-space changes sign at least 4 times provided that it is star-shaped and locally... 
MATHEMATICS | osculating plane | MATHEMATICS, APPLIED | vertex | tennis ball theorem | Torsion | 4 VERTICES | inflection
Journal Article
Advances in Computational Mathematics, ISSN 1019-7168, 8/2015, Volume 41, Issue 4, pp. 813 - 832
Journal Article
Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, ISSN 1300-7688, 06/2017, Volume 21, Issue 2, pp. 357 - 366
In this study, a brief summary about quaternions and quaternionic curves are firstly presented. Also, the definition of focal curve is given. The focal curve... 
Quaternionic curves | Semi-Euclidean space | Focal curves | Quaternions | Osculating hypersphere
Journal Article
Journal of Geometry, ISSN 0047-2468, 8/2019, Volume 110, Issue 2, pp. 1 - 20
We consider two types of developable surfaces along a frontal curve on an embedded surface in the Euclidean 3-space. One is called the osculating developable... 
Geometry | contour generators | Primary 57R45 | osculating developable surfaces | Frontal curves on embedded surfaces | Mathematics | Secondary 58Kxx | normal developable surfaces
Journal Article
SYMMETRY-BASEL, ISSN 2073-8994, 03/2019, Volume 11, Issue 3, p. 387
In this paper, new types of associated curves, which are defined as rectifying-direction, osculating-direction, and normal-direction, in a three-dimensional... 
rectifying-direction curve | MULTIDISCIPLINARY SCIENCES | HELICES | Lie group | osculating-direction curve | MANNHEIM PARTNER CURVES | normal-direction curve
Journal Article
Tuijin Jishu/Journal of Propulsion Technology, ISSN 1001-4055, 02/2018, Volume 39, Issue 2, pp. 277 - 285
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 03/2018, Volume 25, Issue 1, pp. 149 - 154
In this work, we define a quaternionic osculating curves and give the conditions for curves to be osculating with the help of curvature functions. 
Real quaternion | osculating curve | Frenet equations | 53A04 | curvature function | 11R52
Journal Article
GEORGIAN MATHEMATICAL JOURNAL, ISSN 1072-947X, 03/2018, Volume 25, Issue 1, pp. 149 - 154
In this work, we define a quaternionic osculating curves and give the conditions for curves to be osculating with the help of curvature functions. 
Real quaternion | MATHEMATICS | curvature function | osculating curve | Frenet equations | MINKOWSKI SPACE-TIME
Journal Article
International Journal of Pure and Applied Mathematics, ISSN 1311-8080, 2015, Volume 100, Issue 4, pp. 497 - 506
Journal Article
International Journal of Pure and Applied Mathematics, ISSN 1311-8080, 2015, Volume 100, Issue 4, pp. 443 - 447
Journal Article
Journal of Dynamical Systems and Geometric Theories, ISSN 1726-037X, 01/2017, Volume 15, Issue 1, pp. 1 - 13
In this paper we give the necessary and sufficient conditions for bi-null curves in ℝ 6 3 to be osculating, normal or rectifying curves in terms of their... 
Bi-null curves | osculating curves | 53B30 | 53A04 | normal curves | rectifying curves | semi-Euclidean space
Journal Article
Designs, Codes and Cryptography, ISSN 0925-1022, 12/2014, Volume 73, Issue 3, pp. 1023 - 1026
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 06/2018, Volume 194, Issue 1, pp. 29 - 36
We consider the moduli space of pointed non-singular curves of genus g whose Weierstrass gap sequence has the largest gap equal to . We stratify the moduli... 
Moduli spaces | Weierstrass gap sequence | Weierstrass semigroup | CANONICAL IDEAL | EXISTENCE | MATHEMATICS | SEMIGROUPS | OSCULATING SPACES | WEIERSTRASS GAP SEQUENCES | TRIGONAL CURVES | GORENSTEIN CURVES
Journal Article
Boletim da Sociedade Paranaense de Matematica, ISSN 0037-8712, 2017, Volume 35, Issue 2, pp. 39 - 48
In this paper, we give the first kind and second kind osculating curves in the lightlike cone. In addition we characterize osculating curves in terms of their... 
Lightlike cone | Osculating curve | lightlike cone
Journal Article
Moscow Mathematical Journal, ISSN 1609-3321, 10/2017, Volume 17, Issue 4, pp. 667 - 689
The evolute of a smooth curve in an m-dimensional Euclidean space is the locus of centers of its osculating spheres, and the evolute of a spacial polygon is... 
Evolute | Discrete differential geometry | Osculating sphere | Hypocycloid | hypocycloid | MATHEMATICS | MATHEMATICS, APPLIED | INVOLUTES | osculating sphere | discrete differential geometry
Journal Article
Algorithms, ISSN 1999-4893, 2016, Volume 9, Issue 1, p. 15
A new orthogonal projection method for computing the minimum distance between a point and a spatial parametric curve is presented. It consists of a geometric... 
Newton's method | Point projection | Global convergence | Osculating circle | Osculating sphere | Convergence analysis | osculating sphere | Newton’s method | convergence analysis | point projection | global convergence | osculating circle
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 2/2017, Volume 45, Issue 1, pp. 191 - 243
We establish a combinatorial connection between the real geometry and the K-theory of complex Schubert curves $$S(\lambda _\bullet )$$ S ( λ ∙ ) , which are... 
Schubert calculus | Young tableaux | Mathematics | K-theory | Jeu de taquin | Monodromy | Osculating flag | Secondary 14N15 | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Primary 05E99 | TABLEAUX | MATHEMATICS | LIMIT LINEAR SERIES | CALCULUS | Algorithms
Journal Article
Novi Sad Journal of Mathematics, ISSN 1450-5444, 2018, Volume 48, Issue 1, pp. 9 - 20
Journal Article
Journal of Dynamical Systems and Geometric Theories, ISSN 1726-037X, 01/2016, Volume 14, Issue 1, pp. 65 - 84
In this study, the osculating curves in Euclidean space E 3 and E 4 , well known in differential geometry, are studied through the instrumentality of... 
Real quaternion | 53C50 | 53A04 | 11R52 | Frenet equations | Osculating curve | Curvature
Journal Article
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