We study cobordisms and cobordisms rel boundary of PL locally-flat disk knots Dn−2 ↪→ Dn. Any two disk knots are cobordant if the cobordisms are not required to fix the boundary sphere knots , and any two even-dimensional disk knots with isotopic boundary knots are cobordant rel boundary. However, the cobordism rel boundary theory of odd-dimensional disk knots is more subtle. Generalizing resul...

OBJECTIVE In the past, knot-tying techniques have been evaluated and compared, but there has been a scarcity of objective scoring systems in these comparison studies. Using an objective scoring system, we aimed to compare 3 types of knots: intracorporeal flat-square knots, intracorporeal slip-square knots, and extracorporeal square-knots for their Knot Quality Scores (KQS) and their rates of sl...

We explore algebraic characterizations of 2-knots whose associated knot manifolds fibre over lower-dimensional orbifolds, and consider also some issues related to the groups of higherdimensional fibred knots. Nontrivial classical knot groups have cohomological dimension 2, and the knot is fibred if and only if the commutator subgroup is finitely generated, in which case the commutator subgroup ...

The enamel knot, a transient epithelial structure, appears at the onset of mammalian tooth shape development. Until now, the morphological, cellular and molecular events leading to the formation and disappearance of the enamel knot have not been described. Here we report that the cessation of cell proliferation in the enamel knot in mouse molar teeth is linked with the expression of the cyclin-...

Knots occur in many areas of science and art. The mathematical field of Knot Theory studies an idealised form of knots by viewing them as closed loops in 3-space. They can be formally studied via knot drawings which are well-behaved projections of the knot onto the 2-D plane. Equivalence of knots in 3-space (ambient isotopy) can be encapsulated via sequences of diagram rewriting rules, called R...

Litherland has shown that if a knot is (+)-amphicheiral then its m-twist-spin is reversible. We show that, for classical knots, in many cases the converse holds. The irreversibility (sometimes called noninvertibility) of certain twist-spun knots has been established by Ruberman [10], using the Farber-Levine linking pairing and the Casson-Gordon invariants. More recently, alternative proofs of t...

Focus Research dealing with the manipulation of flexible objects has been on for a while. Most of the existing motion-planning algorithms that determine a trajectory from a start to the goal state revolve around traditional sampling-based and feedback control methods. What has not been done so far is the realisation of desired goal states from different initial states through reactive, global p...

sugar beet (beta vulgaris) is one of the hosts for different root-knot nematode species. in this study, firstly the effect of different inoculum levels including 250+250, 500, 500+250, 750, 500+500 and 1000 second stage juveniles of meloidogyne javanica were evaluated on a susceptible variety named jolgeh. the results showed that all inoculum levels were suitable for infection on sugar beet pla...