A nine point theorem for 3-connected graphs

We prove that a 3-connected cubic graph contains a cycle through any nine points.     

Eikonal contributions to ultra high energy neutrino–nucleon cross sections in low scale gravity models

We calculate low scale gravity effects on the cross section for neutrino–nucleon scattering at center of mass energies up to the Greisen–Zatsepin–Kuzmin (GZK) scale, in the eikonal approximation. We compare the cases of an infinitely thin brane embedded in n=5$n=5$ compactified extra-dimensions, and of a brane with a physical tension MS=1 TeV$M_S=1\text{TeV}$ and MS=10 TeV$M_S=10\text{TeV}$. The extra dimensional Planck scale MD$M_D$ is set at ¹⁰³ GeV${10}^3\text{GeV}$ and 2×¹⁰³ GeV$2\times {10}^3\text{GeV}$. We also compare our calculations with neutral current standard model calculations in the same energy range, and compare the thin brane eikonal cross section to its saddle point approximation. New physics effects enhance the cross section by orders of magnitude on average. They are quite sensitive to MS$M_S$ and MD$M_D$ choices, though much less sensitive to n.     

Synthesis of Highly Fluorinated Arene Complexes of [Rh(Chelating Phosphine)]+ Cations,and their use in Synthesis and Catalysis

The synthesis of rhodium complexes with weakly binding highly fluorinated benzene ligands is described: 1,2,3-F₃C₆H₃, 1,2,3,4-F₄C₆H₂ and 1,2,3,4,5-F₅C₆H are shown to bind with cationic [Rh(Cy₂P(CH₂)_xPCy₂)]⁺ fragments (x=1, 2). Their structures and reactivity with alkenes, and use in catalysis for promoting the Tishchenko reaction of a simple aldehyde, are demonstrated. Key to the synthesis of these complexes is the highly concentrated reaction conditions and use of the [Al{OC(CF₃)₃}₄]⁻ anion.     

Computation of Galois groups over function fields

Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.

     

Asymptotic enumeration of dense 0-1 matrices with specified line sums

Let s=(s₁,s₂,…,sm) and t=(t₁,t₂,…,tn) be vectors of non-negative integers with . Let B(s,t) be the number of m×n matrices over {0,1} with jth row sum equal to sj for 1?j?m and kth column sum equal to tk for 1?k?n. Equivalently, B(s,t) is the number of bipartite graphs with m vertices in one part with degrees given by s, and n vertices in the other part with degrees given by t. Most research on the asymptotics of B(s,t) has focused on the sparse case, where the best result is that of Greenhill, McKay and Wang (2006). In the case of dense matrices, the only precise result is for the case of equal row sums and equal column sums (Canfield and McKay, 2005). This paper extends the analytic methods used by the latter paper to the case where the row and column sums can vary within certain limits. Interestingly, the result can be expressed by the same formula which holds in the sparse case.     

Ultraviolet radiation-induced limitation to epilithic microbial growth in arid deserts--dosimetric experiments in the hyperarid core of the Atacama Desert

Experiments were conducted during November 2003 in the dry core of the Atacama Desert, Yungay, Chile to test the hypothesis that UV radiation, in environments where liquid water is not available, and thus enzymatic repair of UV-induced damage is inhibited, can prevent epilithic colonization. Novel dosimeters made from the cryptoendolithic, desiccation and radiation-resistant cyanobacterium Chroococcidiopsis sp. isolated from the dry Negev desert, Israel, showed that monolayers of this organism were killed within one day. The diurnal profile of microbial loss of viability was investigated with dosimeters of Bacillus subtilis, which similarly showed cell death within one day. Soil grains obtained from south of Yungay where liquid water is more abundant and transported to the hyperarid core showed killing of indigenous vegetative organisms within one day. Gypsum and mineral grain coverings of 1mm were sufficient to prevent measurable UV-induced damage of Chroococcidiopsis and B. subtilis after 8d exposure. These results show that under extreme desiccation and an ambient UV flux the surface of rocks can potentially be rendered sterile, but that millimetre thick mineral coverings can protect organisms from UV-induced killing, consistent with the observed patterns of lithophytic colonization in the Atacama Desert. These data further show that UV radiation can be an important limiting factor in surface biological rock weathering in arid regions.     

Programmable fluidic production of microparticles with configurable anisotropy

We report a technique for continuous production of microparticles of variable size with new forms of anisotropy including alternating bond angles, configurable patchiness, and uniform roughness. The sequence and shape of the anisotropic particles are configured by exploiting a combination of confinement effects and microfluidics to pack precursor colloids with different properties into a narrow, terminal channel. The width and length of the channel relative to the particle size fully specify the configuration of the anisotropic particle that will be produced. The precursor spheres packed in the production zone are then permanently bonded into particles by thermal fusing. The flow in the production zone is reversed to release the particles for collection and use. Particles produced have linear chain structure with precisely configured, repeatable bond angles. With software programmable microfluidics, sequence and shape anisotropy are combined to yield synthesized homogeneous (type "A"), surfactantlike (type "A-B") or triblock (type "A-B-A") internal sequences in a single device. By controlling the dimensions of the microfluidic production zone, triangular prisms and particles with controlled roughness and patchiness are produced. The fabrication method is performed with precursors spheres with diameter as small as 3.0 microm.     

RESTRICTED LIE ALGEBRAS WITH MAXIMAL 0-PIM

In this paper it is shown that the projective cover of the trivial irreducible module of a finite-dimensional solvable restricted Lie algebra is induced from the one dimensional trivial module of a maximal torus. As a consequence, the number of the isomorphism classes of irreducible modules with a fixed p-character for a finite-dimensional solvable restricted Lie algebra L is bounded above by p ^MT(L), where MT(L) denotes the maximal dimension of a torus in L. Finally, it is proved that in characteristic p > 3 the projective cover of the trivial irreducible L-module is induced from the one-dimensional trivial module of a torus of maximal dimension, only if L is solvable.     

Towards nitrogen transfer catalysis: reactive lattice nitrogen in cobalt molybdenum nitride

Lattice nitrogen within the catalyst Co(3)Mo(3)N is both reactive and likely highly mobile, enabling potential novel nitrogen transfer pathways; evidence suggests that loss and subsequent regain of lattice nitrogen in the system reversibly cycles through the previously unknown nitride, Co(6)Mo(6)N.     

Asymptotic enumeration of tournaments with a given score sequence containing a specified digraph

This paper studies the probability that a random tournament with specified score sequence contains a specified subgraph. The exact asymptotic value is found in the case that the scores are not too far from regular and the subgraph is not too large. An n‐dimensional saddle‐point method is used. As a sample application, we prove that almost all tournaments with a given score sequence (not too far from regular) have a trivial automorphism group. ©2000 John Wiley & Sons, Inc. Random Struct. Alg., 16: 47–57, 2000