The Generation of Fullerenes

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices.Comment: 21 pages; added a not

Cross border Classical Swine Fever control: Improving Dutch and German crisis management systems by an integrated public-private approach

The objective of this research approach is to analyse in which ways crisis management measures against Classical Swine Fever (CSF) can be improved by a public private cross border model. A core activity contains the analysis of information and communication systems: In a case study it has been empirically analysed if a sufficient supply of public and private information enables crisis managers at both sides of the Dutch-German border area to take decisions about CSF control more efficient. At the end of this approach a new crisis management model had been developed. One of the most important aspects thereby is the assessment of data: (1) within private quality management systems in normal times according to the benefit for public management tasks in times of crisis and (2) within public crisis management systems according to the benefit for cross-border CSF-control activities. To this effect two different methodological approaches have been combined within the model: (1) a method to identify and illustrate public actors and their options in crisis management decision making and (2) a system of communication and information exchange between public and private as well as Dutch and German actors (engage& exchange model) which permit to collect and to evaluate data in addition for a predefined time period are activated

Long-term monitoring of Molonglo calibrators

Before and after every 12 hour synthesis observation, the Molonglo Observatory Synthesis Telescope (MOST) measures the flux densities of ~5 compact extragalactic radio sources, chosen from a list of 55 calibrators. From 1984 to 1996, the MOST made some 58 000 such measurements. We have developed an algorithm to process this dataset to produce a light curve for each source spanning this thirteen year period. We find that 18 of the 55 calibrators are variable, on time scales between one and ten years. There is the tendency for sources closer to the Galactic Plane to be more likely to vary, which suggests that the variability is a result of refractive scintillation in the Galactic interstellar medium. The sources with the flattest radio spectra show the highest levels of variability, an effect possibly resulting from differing orientations of the radio axes to the line of sight.Comment: 18 pages, 9 embedded EPS files. To appear in Publications of the Astronomical Society of Australia. Data available electronically at http://www.physics.usyd.edu.au/astrop/scan

Selective Enzymatic Oxidation of Silanes to Silanols

Compared to the biological world's rich chemistry for functionalizing carbon, enzymatic transformations of the heavier homologue silicon are rare. We report that a wild‐type cytochrome P450 monooxygenase (P450_(BM3) from Bacillus megaterium, CYP102A1) has promiscuous activity for oxidation of hydrosilanes to give silanols. Directed evolution was applied to enhance this non‐native activity and create a highly efficient catalyst for selective silane oxidation under mild conditions with oxygen as the terminal oxidant. The evolved enzyme leaves C−H bonds present in the silane substrates untouched, and this biotransformation does not lead to disiloxane formation, a common problem in silanol syntheses. Computational studies reveal that catalysis proceeds through hydrogen atom abstraction followed by radical rebound, as observed in the native C−H hydroxylation mechanism of the P450 enzyme. This enzymatic silane oxidation extends nature's impressive catalytic repertoire

Exhaustive generation of kk-critical H\mathcal H-free graphs

We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$. We also show that there are only finitely many $4$-critical graphs $(P_8,C_4)$-free graphs. For each case of these cases we also give the complete lists of critical graphs and vertex-critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the $3$-colorability problem in the respective classes. Moreover, we prove that for every $t$, the class of 4-critical planar $P_t$-free graphs is finite. We also determine all 27 4-critical planar $(P_7,C_6)$-free graphs. We also prove that every $P_{10}$-free graph of girth at least five is 3-colorable, and determine the smallest 4-chromatic $P_{12}$-free graph of girth five. Moreover, we show that every $P_{13}$-free graph of girth at least six and every $P_{16}$-free graph of girth at least seven is 3-colorable. This strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with arXiv:1504.0697

Superconducting Superstructure for the TESLA Collider

We discuss the new layout of a cavity chain (superstructure) allowing, we hope, significant cost reduction of the RF system of both linacs of the TESLA linear collider. The proposed scheme increases the fill factor and thus makes an effective gradient of an accelerator higher. We present mainly computations we have performed up to now and which encouraged us to order the copper model of the scheme, still keeping in mind that experiments with a beam will be necessary to prove if the proposed solution can be used for the acceleration.Comment: 11 page

Topological Designs

We give an exponential upper and a quadratic lower bound on the number of pairwise non-isotopic simple closed curves can be placed on a closed surface of genus g such that any two of the curves intersects at most once. Although the gap is large, both bounds are the best known for large genus. In genus one and two, we solve the problem exactly. Our methods generalize to variants in which the allowed number of pairwise intersections is odd, even, or bounded, and to surfaces with boundary components.Comment: 14 p., 4 Figures. To appear in Geometriae Dedicat