Results 21 to 30 of about 38,049 (200)

Tile Number and Space-Efficient Knot Mosaics [PDF]

, 2017
In this paper we introduce the concept of a space-efficient knot mosaic. That is, we seek to determine how to create knot mosaics using the least number of non-blank tiles necessary to depict the knot.
Adams, Barton, Bazzaz, Bradstock, Bradstock, Bradstock, Brosofske, Burnham, Camac, Clarke, Clarke, Dubayah, Fornwalt, Fu, Gessler, Getis, Gill, Glenn, Gonzalez-Olabarria, Gordon, Hammill, Harpold, Jakubowksi, Kane, Kane, Keeley, Keeley, Knox, Levick, Liyanage, McCarthy, Miller, Mitchard, Moore, Murphy, Nakagawa, Ooi, Ord, Price, Price, Purdie, Purdon, R Development Core Team, Rich, Tozer, Turner, Wasser, Watson, Zuur   +48 more
core   +4 more sources

Space-Efficient Knot Mosaics of Size 7 [PDF]

, 2020
Mosaic knot theory is a young and exciting area of mathematics. Since it is still in its mathematical infancy, there are many basic questions still unanswered. The main goal of the field is to represent knots on a square grid using a certain set of tiles.
Vinal, Gregory
core   +1 more source

Modulation of Lanthanide Luminescence with the Mechanical Bond: Antenna‐Emitter Confinement in a Compact [2]Rotaxane

Angewandte Chemie, EarlyView.
Luminescent lanthanide emitters typically need sensitization from an attached chromophore – an “antenna” – to have useful emission intensities. Here we show that the mechanical bond can be used to connect the antenna to the emitter, providing unique stimuli‐responsiveness to the resulting assemblies.
Anja Ramström, Daisy R. S. Pooler, Huseynagha Abasov, Monika Tomar, Stefano Crespi, Fredrik Schaufelberger   +5 more
wiley   +2 more sources

Legendrian and transverse twist knots

, 2011
In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the $m(5_2)$ knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least $n$ different Legendrian representatives with maximal Thurston--Bennequin ...
Etnyre, John B., Ng, Lenhard L., Vertesi, Vera   +2 more
core   +1 more source

The Non-Orientable 4-Genus of 11 Crossing Non-Alternating Knots [PDF]

Journal of knot theory and its ramifications
The non-orientable 4-genus of a knot K in the three sphere is defined to be the minimum first Betti number of a non-orientable surface F in the four-ball so that K bounds F.
Megan Fairchild
semanticscholar   +1 more source

Tait’s conjectures and odd crossing number amphicheiral knots [PDF]

, 2007
We give a brief historical overview of the Tait conjectures, made 120 years ago in the course of his pioneering work in tabulating the simplest knots, and solved a century later using the Jones polynomial.
A. Stoimenow
semanticscholar   +1 more source

Introduction to disoriented knot theory

, 2018
This paper is an introduction to disoriented knot theory, which is a generalization of the oriented knot and link diagrams and an exposition of new ideas and constructions, including the basic definitions and concepts such as disoriented knot ...
Ismet Altintas
semanticscholar   +1 more source

Region crossing change on origami and link [PDF]

Journal of knot theory and its ramifications
Region Select is a game originally defined on a knot projection. In this paper, Region Select on an origami crease pattern is introduced and investigated.
Tokio Oshikiri, Ayaka Shimizu, Junya Tamura   +2 more
semanticscholar   +1 more source

Untying the Knot: A Fully Recyclable, Solvent‐Free, Wide‐Spectral Photocurable Thermoset Adhesive

Advanced Materials, EarlyView.
This study introduces a solvent‐free, recyclable adhesive that cures rapidly under visible light (400–650 nm) while maintaining robust adhesion across diverse substrates. Recyclable via simple microwave irradiation, it combines high performance with optical and bioadaptive potential, representing a significant advancement toward sustainable, circular ...
Natanel Jarach, Michal Cohen, Rivka Gitt, Hanna Dodiuk, Samuel Kenig, Shlomo Magdassi   +5 more
wiley   +1 more source

The Theory of Pseudoknots

, 2012
Classical knots in $\mathbb{R}^3$ can be represented by diagrams in the plane. These diagrams are formed by curves with a finite number of transverse crossings, where each crossing is decorated to indicate which strand of the knot passes over at that ...
Henrich, Allison, Hoberg, Rebecca, Jablan, Slavik, Johnson, Lee, Minten, Elizabeth, Radovic, Ljiljana   +5 more
core   +1 more source