Results 71 to 80 of about 4,855 (191)

Duality properties of indicatrices of knots

, 2012
The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot ...
A.S. McRae, Bena Tshishiku, C.B. Jeon, Charmaine Sia, Colin Adams, Dan Collins, G.T. Jin, H. Schubert, I. Fáry, J.W. Milnor, J.W. Milnor, Katherine Hawkins, N.H. Kuiper, R. Uribe-Vargas, Rob Silversmith, T.F. Banchoff, V.I. Arnold, W. Blaschke, W. Fenchel, Y.-Q. Wu   +19 more
core   +1 more source

Lagrangian approximation of totally real concordances

Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.
Abstract We show that a two‐dimensional totally real concordance can be approximated by a Lagrangian concordance whose Legendrian boundary has been stabilised both positively and negatively sufficiently many times. The main applications that we provide are constructions of knotted Lagrangian concordances in arbitrary four‐dimensional symplectisations ...
Georgios Dimitroglou Rizell
wiley   +1 more source

Nonlinear Optics Through the Field Tensor Formalism

Laser &Photonics Reviews, Volume 19, Issue 2, January 22, 2025.
This review delves into the symmetry properties of electric fields and susceptibility tensors. It explores scenarios where propagation effects are negligible and situations where propagation is significant, elucidating the role of the field tensor in phase‐matching considerations.
Julien Duboisset, Benoît Boulanger, Sophie Brasselet, Patricia Segonds, Joseph Zyss   +4 more
wiley   +1 more source

Transversal Intersection Curves of Two Surfaces in Minkowski 3-Space

Selecciones Matemáticas, 2018
In this paper, we study the differential geometry of the transversal intersection curve of two surfaces in Minkowski 3-space, where each pair satisfies the following types spacelike-lightlike, timelike-lightlike and lightlike-lightlike.
Osmar Alêssio, Sayed A.-N. Badr, Soad A. Hassan, Luciana A. Rodrigues, Fábio N. Silva, M. A. Soliman   +5 more
doaj   +1 more source

Stationary‐Angle Conditions and Bertrand Offsets in Timelike‐Ruled Surfaces

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
In this study, we introduce the concept of stationary‐angle timelike‐ruled surfaces and examine their geometric properties, particularly in relation to their Bertrand offsets. A timelike‐ruled surface is generated by the motion of a straight ruling along a striction curve, and its structure is analyzed using the Blaschke and Darboux frames.
Areej A. Almoneef, Rashad A. Abdel-Baky, Leopoldo Greco   +2 more
wiley   +1 more source

OSCULATING CURVES ACCORDING TO THE EXTENDED DARBOUX FRAME IN E4

Journal of Science and Arts, 2023
In this paper, we define osculating curves according to the extended Darboux frame (ED-frame), in Euclidean 4-space. Then, according to Case 1 and Case 2 ED-frame fields, the necessary and sufficient condition for a unit speed curve lying on the hypersurface to be congruent to an osculating curve is obtained.
openaire   +1 more source

REFLEX—A novel method for the rapid estimation of flood extent

Journal of Flood Risk Management, Volume 17, Issue 4, December 2024.
Abstract Reliable flood hazard mapping is crucial for enhancing flood preparedness, especially in poorly gauged and vulnerable areas. Yet, current flood models are either highly detailed and computationally intensive or oversimplified, failing to capture important flow dynamics.
Mauro Arcorace, Andrea Libertino, Lorenzo Alfieri, Simone Gabellani, Alessia Matanò, Alessandro Masoero, Valerio Basso, Giorgio Boni   +7 more
wiley   +1 more source

Bertrand partner trajectories related to PAFORS [PDF]

Mathematica Bohemica
In this study, we consider the concept of Bertrand partner trajectories related to Positional Adapted Frame on Regular Surfaces (shortly PAFORS) for the particles moving on the different regular surfaces in Euclidean 3-space.
Zehra İşbilir, Kahraman Esen Özen, Murat Tosun   +2 more
doaj   +1 more source

Self-dual Einstein Spaces, Heavenly Metrics and Twistors

, 2010
Four-dimensional quaternion-Kahler metrics, or equivalently self-dual Einstein spaces M, are known to be encoded locally into one real function h subject to Przanowski's Heavenly equation.
Boris Pioline, Calderbank D. M. J., MacCallum M. A. H., Przanowski M., Salamon S. M., Sergei Alexandrov, Stefan Vandoren, Ueno K.   +7 more
core   +3 more sources

Zero‐curvature subconformal structures and dispersionless integrability in dimension five

Journal of the London Mathematical Society, Volume 110, Issue 6, December 2024.
Abstract We extend the recent paradigm “Integrability via Geometry” from dimensions 3 and 4 to higher dimensions, relating dispersionless integrability of partial differential equations to curvature constraints of the background geometry. We observe that in higher dimensions on any solution manifold, the symbol defines a vector distribution equipped ...
Boris Kruglikov, Omid Makhmali
wiley   +1 more source