Nonassociative cyclic algebras

Nonassociative quaternion algebras were first discovered over the real numbers independently by Dickson and Albert and provided some of the first examples of nonassociative division algebras. They were later classified completely by Waterhouse. Cyclic algebras can be seen as a natural generalisation of the classical quaternion algebras. With this in mind we generalise nonassociative quaternion algebras and introduce nonassociative cyclic algebras. These provide new examples of nonassociative central division algebras with Nucleus a separable field extension of degree n.     

Mixing of X and Y states from QCD sum rules analysis

We study \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} states as mixed states in QCD sum rules. By calculating the two-point correlation functions of pure states of their corresponding currents, we review the mass and coupling constant predictions of \begin{document}$ J^{PC} = 1^{++} $\end{document}, \begin{document}$1^{--}$\end{document}, and \begin{document}$ 1^{-+} $\end{document} states. By calculating the two-point mixed correlation functions of \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} currents, we estimate the mass and coupling constants of the corresponding "physical state" that couples to both \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} currents. Our results suggest that for \begin{document}$ 1^{++} $\end{document} states, the \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} components are more likely to mix, while for \begin{document}$ 1^{--} $\end{document} and \begin{document}$ 1^{-+} $\end{document} states, there is less mixing between \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document}. Our results suggest the Y series of states have more complicated components.     

Reactions of selenourea with benzoyl- and 2-thienoylbromoacetylenes: synthesis of 1,3-diselenetanes and 1,4-diselenafulvenes

A novel reaction of selenourea with benzoylbromoacetylene and 2-thienoylbromoacetylene is described. The reaction proceeds in the presence of triethylamine at −30 to 0 °C to afford new 4- and 5-membered heterocycles.     

Broad sub-continuum resonances and the case for finite-energy sum-rules

There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension condensates containing at least one pair. We extract the direct single-instanton contribution to the sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass-resonance contributions within the pseudoscalar channel. Received: 15 September 1997 / Revised version: 15 November 1997 / Published online: 26 February 1998     

Medium-dependent lithiated side products in the reductive lithiation of allylic phenyl thioethers. Diethyl ether versus tetrahydrofuran

Diethyl ether is a convenient solvent for the reductive lithiation of allylic phenyl thioethers without the serious complications, which occur when the reaction is carried out in tetrahydrofuran.     

Glutathionylated γG and γA subunits of hemoglobin F: a novel post‐translational modification found in extremely premature infants by LC‐MS and nanoLC‐MS/MS

Oxidative stress plays an important role in the development of various disease processes and is a putative mechanism in the development of bronchopulmonary dysplasia, the most common complication of extreme preterm birth. Glutathione, a major endogenous antioxidant and redox buffer, also mediates cellular functions through protein thiolation. We sought to determine if post‐translational thiol modification of hemoglobin F occurs in neonates by examining erythrocyte samples obtained during the first month of life from premature infants, born at 23 0/7 – 28 6/7 weeks gestational age, who were enrolled at our center in the Prematurity and Respiratory Outcomes Program (PROP). Using liquid chromatography‐mass spectrometry (LC‐MS), we report the novel finding of in vivo and in vitro glutathionylation of γG and γA subunits of Hgb F. Through tandem mass spectrometry (nanoLC‐MS/MS), we confirmed the adduction site as the Cys‐γ94 residue and through high‐resolution mass spectrometry determined that the modification occurs in both γ subunits. We also identified glutathionylation of the β subunit of Hgb A in our patient samples; we did not find modified α subunits of Hgb A or F. In conclusion, we are the first to report that glutathionylation of γG and γA of Hgb F occurs in premature infants. Additional studies of this post‐translational modification are needed to determine its physiologic impact on Hgb F function and if sG‐Hgb is a biomarker for clinical morbidities associated with oxidative stress in premature infants. Copyright © 2014 John Wiley & Sons, Ltd.     

Euclidean semi-matchings of random samples

A linear programming relaxation of the minimal matching problem is studied for graphs with edge weights determined by the distances between points in a Euclidean space. The relaxed problem has a simple geometric interpretation that suggests the name minimal semi-matching. The main result is the determination of the asymptotic behavior of the length of the minimal semi-matching. It is analogous to the theorem of Beardwood, Halton and Hammersley (1959) on the asymptotic behavior of the traveling salesman problem. Associated results on the length of non-random Euclidean semi-matchings and large deviation inequalities for random semi-matchings are also given.Research supported in part by NSF Grant #DMS-8812868, ARO contract DAAL03-89-G-0092.P001, AFOSR-89-08301.A and NSA-MDA-904-89-2034.     

The Nielsen identities for the two-point functions of QED and QCD

We consider the Nielsen identities for the twopoint functions of full QCD and QED in the class of Lorentz gauges. For pedagogical reasons the identities are first derived in QED to demonstrate the gauge independence of the photon self-energy, and of the electron mass shell. In QCD we derive the general identity and hence the identities for the quark, gluon and ghost propagators. The explicit contributions to the gluon and ghost identities are calculated to one-loop order, and then we show that the quark identity requires that in on-shell schemes the quark mass renormalisation must be gauge independent. Furthermore, we obtain formal solutions for the gluon selfenergy and ghost propagator in terms of the gauge dependence of other, independent Green functions.