A lower bound for the optimal crossing-free Hamiltonian cycle problem

Consider a drawing in the plane ofK _n , the complete graph onn vertices. If all edges are restricted to be straight line segments, the drawing is called rectilinear. Consider a Hamiltonian cycle in a drawing ofK _n . If no pair of the edges of the cycle cross, it is called a crossing-free Hamiltonian cycle (cfhc). Let (n) represent the maximum number of cfhc's of any drawing ofK _n , and (n) the maximum number of cfhc's of any rectilinear drawing ofK _n . The problem of determining (n) and (n), and determining which drawings have this many cfhc's, is known as the optimal cfhc problem. We present a brief survey of recent work on this problem, and then, employing a recursive counting argument based on computer enumeration, we establish a substantially improved lower bound for (n) and (n). In particular, it is shown that (n) is at leastk × 3.2684 ⁿ . We conjecture that both (n) and (n) are at mostc × 4.5 ⁿ .This research, part of which was conducted at Queen's University, was supported by an N.S.E.R.C. postgraduate scholarship.     

Characterization of NOx species in dehydrated and hydrated Na- and Ba-Y, FAU zeolites formed in NO2 adsorption

Adsorbed ionic NO_x species formed upon the interaction of NO₂ with dehydrated or hydrated Na- and Ba-Y, FAU zeolites were characterized using FT-IR/TPD, solid state NMR, and XANES techniques. NO₂ disproportionates on both dehydrated catalyst materials forming NO⁺ and NO₃⁻ species. These ionic species are stabilized by their interactions with the negatively charged zeolite framework and the charge compensating cations (Na⁺ and Ba²⁺), respectively. Although the nature of the adsorbed NO_x species formed on the two catalysts is similar, their thermal stabilities are strongly dependent on the charge compensating cations. In the presence of water in the channels of these zeolite materials new paths open for reactions between NO⁺ and H₂O, and NO₂ and H₂O, resulting in significant changes in the adsorbed ionic species observed. These combined spectroscopic investigations afforded the understanding of the interactions between water and NO₂ on these zeolite catalysts.     

Development of a cryopreservation protocol for the microcyclic rust-fungus Puccinia spegazzinii

The rust fungus Puccinia spegazzinii (Basidiomycotina: Uredinales) has been identified as a potential classical biological control agent for the invasive weed Mikania micrantha (Asteraceae). Long-term, live storage of this pathogen is required for reference. As biotrophs, almost all rusts species cannot be preserved by traditional cryopreservation protocols, which rely on in vitro culture techniques. In addition, the embedded teliospores and delicate basidiospores of this microcyclic rust are not amenable to direct plunge freezing. Continuous culture of the rust on living plants is both laborious and expensive, so a variety of approaches for cryopreservation and storage were tested. These methods included traditional approaches to fungal cryopreservation such as variation of cooling rate regime and alginate encapsulation techniques. However, an in situ cryopreservation technique was the only method identified as having any potential for the long-term cryopreservation of the 10 isolates tested. Material from either petiole or stem tissue remained viable after cryopreservation, determined by the ability of the material to produce basidiospores. However, despite great progress being made in developing an optimal cryopreservation method, infection of the host plant by basidiospores produced from previously cryopreserved teliospores, embedded in leaf petioles, was not achieved.     

Mechanistic investigations in α‐hydroxycarbonyls reduction by BH4‐

BH₄^‐, a well‐known and widely used reducing agent for carbonyl compounds, has been reported to have the ability to participate in dihydrogen bonding, an interaction with applications in catalysis, stereoselectivity and crystal engineering. Specifically, α‐hydroxycarbonyls are activated for reduction by dihydrogen bonding that occurs between BH₄^‐ and hydroxyl group. We explored the effect of the interaction on the mechanism of these reactions by examining their activation parameters. We found that dihydrogen bonding activates α‐hydroxycyclopentanone for reduction with NBu₄BH₄ by lowering the activation enthalpy by 6.6 kcal/mol. While the activation entropy is a significant component of the barrier, the changes resulting from the occurrence of dihydrogen bonding are manifested predominantly in the enthalpy term. Computational studies suggest that, while internal hydrogen bonding is allowed by the flexibility of the carbon backbone, that interaction is outweighed by dihydrogen bonding once BH₄^‐ is present in the system. Experimentally, a red shift of the hydroxyl frequency is observed upon addition of BH₄^‐ to the reaction mixture, suggesting a dihydrogen bonding interaction. The flexibility of the substrate's skeleton or the selectivity of the hydride sites in BH₄^‐ does not account for the lack of directing effect of the dihydrogen bonding. When a substrate with a rigid naphthalene backbone moiety, 2‐hydroxyacenaphthylen‐1(2H)‐one, is reduced, the stereochemical outcome is very similar to the one corresponding to the α‐hydroxycyclopentanone. Copyright © 2012 John Wiley & Sons, Ltd.     

Theoretical analysis of spin-resolved photoemission data from ferromagnetic Fe(001)

To interpret recent spin-, energy- and angle-resolved experimental photoemission spectra at photon energies ranging from 20 to 70 eV, one-step calculations on the basis of a non-relativistic Green function formalism have been performed together with a calculation of the corresponding bulk band structure and momentum-resolved layer-by-layer quasi-particle density of states. The theoretical spectra are in good agreement with the data. Individual features are explained in terms of bulk interband transitions and emission from a majority-spin surface resonance. Self-energy corrections are found to be important and in qualitative disagreement with recent microscopic theory.     

Electron transport in modulation-doped GaAs v-groove quantum wires

We report the growth of modulation-doped GaAs/Al_xGa_1−xAs v-groove quantum wires and structural, electrical and optical investigations of their electronic states and transport properties. By using alternative group III precursors on partially SiO₂ masked pre-patterned GaAs substrates, samples have been fabricated which permit electrical measurements of single isolated wire structures without the need for additional electron-beam lithography. Magneto-transport was measured as a function of tilt angle of the incident magnetic field to identify the formation of low-dimensional electron gases in different parts of the structure. Photoluminescence investigations reveal 1D and 2D confined states which show different carrier heating when electric fields are applied along the wire structure.     

Rovibrational and energetic analysis of the hydroxyethynyl anion (CCOH−)

For the first time, high-level structural and rovibrational data are provided for the hyroxyethynyl anion, CCOH^?. CCOH^? is a promising molecule for interstellar detection even though no new anions have been observed in the interstellar medium for the past half-decade. The large dipole moment of the corresponding neutral radical may be key for its creation as has been hypothesised and supported for other anions known to exist in various astronomical environments. Highly accurate quartic force fields are employed where previous benchmarks have produced spectroscopic constants and anharmonic vibrational frequencies within 20 MHz and 1 cm^?1, respectively, of experiment. This same approach is applied here for CCOH^? and its deuterated isotopologue with the goal of assisting laboratory experiments and/or astronomical observers in the potential detection of this anion.