L. Kauffman introduced a graphical link invariant which is the normalized Jones polynomial [4][5]. It is well-known that the polynomial is derived from the fundamental representation of the quantum group Uq(sl2). Further, G. Kuperberg constructed a graphical link invariant associated with the fundamental representation of the quantum group Uq(sl3) [10]. H. Murakami, T. Ohtsuki and S. Yamada int...

In this note, we prove a lower bound for the positive kinkiness of a closed braid which we then use to derive an estimate for the positive kinkiness of a link in terms of its Seifert system. As an application, we show that certain pretzel knots cannot be unknotted using only positive crossing changes. We also describe a subgroup of infinite rank in the smooth knot concordance group of which no ...

The following discussion is based on [5, 1] and, with regard to [2], is relevant to the discussions in Chapter 5 and in Section 6.6 on multihop wireless systems. Consider a network with a set of N nodes and L links. Let α(l) be the transmitting node and ω(l) be the receiving node of link l. Each node n maintains a set of J packet queues, Xn, one for each flow. A flow j is determined by a destin...

There exists a natural filtration on the module freely generated by knots (or links). This filtration is called the Vassiliev filtration and has many nice properties. In particular every quotient of this filtration is finite dimensional. A knot invariant which vanishes on some module of this filtration is called a Vassiliev invariant. Almost every knot invariant defined in algebraic term can be...

We consider the operation of Whitehead double on a component of a link and study the behavior of Milnor invariants under this operation. We show that this operation turns a link whose Milnor invariants of length ≤ k are all zero into a link with vanishing Milnor invariants of length ≤ 2k+1, and we provide formulas for the first non-vanishing ones. As a consequence, we obtain statements relating...

BACKGROUND Emergence of drug-resistant strains of Candida and inefficiency of conventional antifungal therapy has necessitated the search for alternative and new antifungal agents. Inhibition of virulence and biofilm are the potential drug targets. In this study, the oils of Carum copticum, Thymus vulgaris and their major active compound thymol as revealed by Gas chromatography and gas chromato...

Let L = 1∪· · ·∪ d+1 be an oriented link in S3, and let L(q) be the d-component link 1 ∪· · ·∪ d regarded in the homology 3-sphere that results from performing 1/q-surgery on d+1. Results about the Alexander polynomial and twisted Alexander polynomials of L(q) corresponding to finite-image representations are obtained. The behavior of the invariants as q increases without bound is described.

For any finite link L in R we prove the existence of a high-energy complex-valued eigenfunction of the hydrogen atom such that its nodal set contains a union of connected components diffeomorphic to L. This problem goes back to Berry, who constructed such eigenfunctions in the case where L is the trefoil knot or the Hopf link and asked the question about the general result.

Consider the link bandwidth allocation for transport of correlated traac on a single link with nite buuer capacity under a maximum allowable delay constraint d max. In our measurement architecture, traac is decomposed into three frequency regions: low-frequency (LF) traac in 0 < j!j ! L , high-frequency (HF) traac in j!j ! H and mid-frequency (MF) traac in ! L < j!j < ! H. The zero-frequency co...