Concordance of Bing doubles and boundary genus

Cha and Kim proved that if a knot K is not algebraically slice, then no iterated Bing double of K is concordant to the unlink. We prove that if K has nontrivial signature $\sigma$, then the n-iterated Bing double of K is not concordant to any boundary link with boundary surfaces of genus less than $2^{n-1}\sigma$. The same result holds with $\sigma$ replaced by $2\tau$, twice the Ozsvath-Szabo knot concordance invariant.Comment: 13 pages, 7 figure

Relationships between braid length and the number of braid strands

For a knot K, let b_n(K) be the minimum length of an n-stranded braid representative of K. Examples of knots exist for which b_n(K) is a non-increasing function. We investigate the behavior of b_n(K). We develop bounds on the function in terms of the genus of K, with stronger results for homogeneous knots and braid positive knots. For knots of nine or fewer crossings, we show that b_n(K) is an increasing function and determine it completely.Comment: 9 pages, 2 figures; minor revision

Structural, Electronic, and Vibrational Properties of Amino-adamantane and Rimantadine Isomers

We performed a first principles total energy investigation on the structural, electronic, and vibrational properties of adamantane molecules, functionalized with amine and ethanamine groups. We computed the vibrational signatures of amantadine and rimantadine isomers with the functional groups bonded to different carbon sites. By comparing our results with recent infrared and Raman spectroscopic data, we discuss the possible presence of different isomers in experimental samples

Functionalized adamantane: fundamental building blocks for nanostructure self-assembly

We report first principles calculations on the electronic and structural properties of chemically functionalized adamantane molecules, either in isolated or crystalline forms. Boron and nitrogen functionalized molecules, aza-, tetra-aza-, bora-, and tetra-bora-adamantane, were found to be very stable in terms of energetics, consistent with available experimental data. Additionally, a hypothetical molecular crystal in a zincblende structure, involving the pair tetra-bora-adamantane and tetra-aza-adamantane, was investigated. This molecular crystal presented a direct and large electronic bandgap and a bulk modulus of 20 GPa. The viability of using those functionalized molecules as fundamental building blocks for nanostructure self-assembly is discussed