The Computational Complexity of Knot and Link Problems

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, {\sc unknotting problem} is in {\bf NP}. We also consider the problem, {\sc unknotting problem} of determining whether two or more such polygons can be split, or continuously deformed without self-intersection so that they occupy both sides of a plane without intersecting it. We show that it also is in NP. Finally, we show that the problem of determining the genus of a polygonal knot (a generalization of the problem of determining whether it is unknotted) is in {\bf PSPACE}. We also give exponential worst-case running time bounds for deterministic algorithms to solve each of these problems. These algorithms are based on the use of normal surfaces and decision procedures due to W. Haken, with recent extensions by W. Jaco and J. L. Tollefson.Comment: 32 pages, 1 figur

Deep far infrared ISOPHOT survey in "Selected Area 57", I. Observations and source counts

We present here the results of a deep survey in a 0.4 sq.deg. blank field in Selected Area 57 conducted with the ISOPHOT instrument aboard ESAs Infrared Space Observatory (ISO) at both 60 um and 90 um. The resulting sky maps have a spatial resolution of 15 x 23 sq.arcsec. per pixel which is much higher than the 90 x 90 sq.arcsec. pixels of the IRAS All Sky Survey. We describe the main instrumental effects encountered in our data, outline our data reduction and analysis scheme and present astrometry and photometry of the detected point sources. With a formal signal to noise ratio of 6.75 we have source detection limits of 90 mJy at 60 um and 50 mJy at 90 um. To these limits we find cumulated number densities of 5+-3.5 per sq.deg. at 60 um and 14.8+-5.0 per sq.deg.at 90 um. These number densities of sources are found to be lower than previously reported results from ISO but the data do not allow us to discriminate between no-evolution scenarios and various evolutionary models.Comment: 15 pages, 11 figures, accepted by Astronomy & Astrophysic

Noncyclic covers of knot complements

Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, $\Phi (c)$, such that if $K$ is a nontrivial knot in the three-sphere with a diagram with $c$ crossings and a particularly simple JSJ decomposition then the complement of $K$ has a finite-sheeted, noncyclic cover with at most $\Phi (c)$ sheets.Comment: 29 pages, 8 figures, from Ph.D. thesis at Columbia University; Acknowledgments added; Content correcte

Highly-ordered graphene for two dimensional electronics

With expanding interest in graphene-based electronics, it is crucial that high quality graphene films be grown. Sublimation of Si from the 4H-SiC(0001) Si-terminated) surface in ultrahigh vacuum is a demonstrated method to produce epitaxial graphene sheets on a semiconductor. In this paper we show that graphene grown from the SiC$(000\bar{1})$ (C-terminated) surface are of higher quality than those previously grown on SiC(0001). Graphene grown on the C-face can have structural domain sizes more than three times larger than those grown on the Si-face while at the same time reducing SiC substrate disorder from sublimation by an order of magnitude.Comment: Submitted to Appl. Phys. Let

The formation of homogentisate in the biosynthesis of tocopherol and plastoquinone in spinach chloroplasts

Homogentisate is the precursor in the biosynthesis of -tocopherol and plastoquinone-9 in chloroplasts. It is formed of 4-hydroxyphenylpyruvate of the shikimate pathway by the 4-hydroxyphenylpyruvate dioxygenase. In experiments with spinach the dioxygenase was shown to be localized predominatedly in the chloroplasts. Envelope membranes exhibit the highest specific activity, however, because of the high stromal portion of chloroplasts, 60–80% of the total activity is housed in the stroma. The incorporation of 4-hydroxyphenylpyruvate into 2-methyl-6-phytylquinol as the first intermediate in the tocopherol synthesis by the two-step-reaction: 4-Hydroxyphenylpyruvate Homogentisate 2-Methyl-6-phytylquinol was demonstrated by using envelope membranes. Homogentisate originates directly from 4-hydroxyphenylpyruvate of the shikimate pathway. Additionally, a bypass exists in chloroplasts which forms 4-hydroxyphenylpyruvate from tyrosine by an L-amino-acid oxidase of the thylakoids and in peroxisomes by a transaminase reaction. Former results about the dioxygenase in peroxisomes were verified

The structural properties of the multi-layer graphene/4H-SiC(000-1) system as determined by Surface X-ray Diffraction

We present a structural analysis of the multi-layer graphene-4HSiC(000-1}) system using Surface X-Ray Reflectivity. We show for the first time that graphene films grown on the C-terminated (000-1}) surface have a graphene-substrate bond length that is very short (0.162nm). The measured distance rules out a weak Van der Waals interaction to the substrate and instead indicates a strong bond between the first graphene layer and the bulk as predicted by ab-initio calculations. The measurements also indicate that multi-layer graphene grows in a near turbostratic mode on this surface. This result may explain the lack of a broken graphene symmetry inferred from conduction measurements on this system [C. Berger et al., Science 312, 1191 (2006)].Comment: 9 pages with 6 figure

First-Principles Calculations of Hyperfine Interactions in La_2CuO_4

We present the results of first-principles cluster calculations of the electronic structure of La_2CuO_4. Several clusters containing up to nine copper atoms embedded in a background potential were investigated. Spin-polarized calculations were performed both at the Hartree-Fock level and with density functional methods with generalized gradient corrections to the local density approximation. The distinct results for the electronic structure obtained with these two methods are discussed. The dependence of the electric-field gradients at the Cu and the O sites on the cluster size is studied and the results are compared to experiments. The magnetic hyperfine coupling parameters are carefully examined. Special attention is given to a quantitative determination of on-site and transferred hyperfine fields. We provide a detailed analysis that compares the hyperfine fields obtained for various cluster sizes with results from additional calculations of spin states with different multiplicities. From this we conclude that hyperfine couplings are mainly transferred from nearest neighbor Cu^{2+} ions and that contributions from further distant neighbors are marginal. The mechanisms giving rise to transfer of spin density are worked out. Assuming conventional values for the spin-orbit coupling, the total calculated hyperfine interaction parameters are compared to informations from experiments.Comment: 23 pages, 9 figure