An upper bound on the independence number of benzenoid systems

Recently, the graph theoretic independence number has been linked to fullerene stability [S. Fajtlowicz, C. Larson, Graph-theoretic independence as a predictor of fullerene stability, Chem. Phys. Lett. 377 (2003) 485-490; S. Fajtlowicz, Fullerene Expanders, A list of Conjectures of Minuteman, Available from S. Fajtlowicz: math0@bayou.uh.edu]. In particular, stable fullerenes seem to minimize their independence numbers. A large piece of evidence for this hypothesis comes from the fact that stable benzenoids—close relatives of fullerenes—do minimize their independence numbers [S. Fajtlowicz, “Pony Express”—Graffiti's conjectures about carcinogenic and stable benzenoids, 〈http://www.math.uh.edu/∼siemion/pony.html〉]. In this paper, an upper bound on the independence number of benzenoids is introduced and proven—giving a limit on how large the independence ratio for benzenoids can be. In conclusion, this bound on independence is correlated to an upper bound on the number of unpaired sites a benzenoid system has with respect to a maximum matching, which is precisely the number of zero eigenvalues in the spectrum of the adjacency matrix (due to a conjecture of Graffiti and its proof by Sachs [S. Fajtlowicz, “Pony Express”—Graffiti's conjectures about carcinogenic and stable benzenoids, 〈http://www.math.uh.edu/∼siemion/pony.html〉; H. Sachs, P. John, S. Fajtlowicz, On Maximum Matchings and Eigenvalues of Benzenoid Graphs, preprint—MATCH]). Thus, since zero eigenvalues and unpaired sites are indicative of instability (reactivity), we get a simple but intuitive bound on how reactive a benzenoid molecule can be.     

On the characteristic map of finite unitary groups

In his classic book on symmetric functions, Macdonald describes a remarkable result by Green relating the character theory of the finite general linear group to transition matrices between bases of symmetric functions. This connection allows one to analyze the character theory of the general linear group via symmetric group combinatorics. Using works of Ennola, Kawanaka, Lusztig and Srinivasan, this paper describes the analogous setting for the finite unitary group. In particular, we explain the connection between Deligne–Lusztig theory and Ennola's efforts to generalize Green's work, and from this we deduce various character theoretic results. Applications include calculating certain sums of character degrees, and giving a model of Deligne–Lusztig type for the finite unitary group, which parallels results of Klyachko and Inglis and Saxl for the finite general linear group.     

Practical syntheses of the C12-C21 epothilone subunit via catalytic asymmetric reductions: Itsuno-Corey oxazaborolidine reduction and asymmetric Noyori hydrogenation

Two practical catalytic asymmetric reductions to introduce the epothilone C15 stereocenter are described (Itsuno-Corey reduction and Noyori hydrogenation).     

Vocal Fold Wound Healing: A Review for Clinicians

SUMMARY: The basic science of wound healing is largely omitted from the curriculum of many voice clinicians. This fact is relatively disheartening as most therapeutic manipulation in the realm of laryngology and voice disorders deals with injured tissue. Therefore, the selection of therapeutic tasks for persons with vocal injury should ideally be informed by basic science in wound healing. Recently, several investigators have initiated lines of research to determine the course of vocal fold wound healing and the potential role of therapeutic agents, including behavioral agents. The current review seeks to provide a foundation of basic wound healing science and present the most current data regarding the wound healing process in the vocal folds.     

Stabilizing Heegaard splittings of toroidal 3-manifolds

Let T be a separating incompressible torus in a 3-manifold M. Assuming that a genus g Heegaard splitting VS_∪W can be positioned nicely with respect to T (e.g., VS_∪W is strongly irreducible), we obtain an upper bound on the number of stabi-lizations required for VS_∪W to become isotopic to a Heegaard splitting which is an amalgamation along T. In particular, if T is a canonical torus in the JSJ decomposition of M, then the number of necessary stabilizations is at most 4g−4. As a corollary, this establishes an upper bound on the number of stabilizations required for VS_∪W and any Heegaard splitting obtained by a Dehn twist of VS_∪W along T to become isotopic.     

Studying surfaces and thin films using Mössbauer spectroscopy

Using a series of bi-layer samples, we show how Conversion Electron Mössbauer Spectroscopy (CEMS) and X-ray Backscatter Mössbauer Spectroscopy (XBS) can be done with the same experimental set up. The penetration depths of the K and L conversion electrons are measured as 51(6) and 330(240) nm, respectively, with relative contributions of 88(9) and 12(9)%. The penetration depth of the Fe-K _α X-ray signal is determined to be 3.6(2) μm. As a demonstration we show data on surface damage effects in electropolished TRIP steels, and by comparing CEMS and XBS Mössbauer patterns we estimate the thickness of a damaged layer (created by sanding) to be 550(50) nm.     

Solution Chemistry of Europium(III) Aqua Ion at Micromolar Concentrations as Probed by Direct Excitation Luminescence Spectroscopy

Direct excitation europium(III) luminescence spectroscopy is used to study the speciation of aqueous europium(III) ions at micromolar concentrations and near neutral pH. The pH and concentration dependence of the europium(III) ⁷F₀→⁵D₀ excitation peak is consistent with the formation of both mononuclear and dinuclear europium(III) hydroxide complexes at pH 6.5. Luminescence intensity and lifetime quenching studies in the presence of Nd^III at pH 5.0 and 6.5 support the formation of a dinuclear complex at pH 6.5. Steady state excitation and time‐resolved luminescence spectroscopy are consistent with the formation of innersphere nitrate and fluoride complexes, but outersphere perchlorate and chloride complexes at pH 6.5 and 5.0.