Schur Orthogonality Relations for the Finitary Infinite Symmetric Group

Let S f be the finitary infinite symmetric group. For a certain class of irreducible unitary representations of S f , a version of Schur orthogonality relations is proved. That is, we construct an invariant inner product on the matrix coefficient space of each representation and show that matrix coefficients for distinct representations are orthogonal with respect to these norms.     

The Hurricane Katrina Effect on Mathematics Achievement in Mississippi

Hurricane Katrina caused severe physical damage to the Gulf Coast states of Louisiana, Mississippi, and Alabama. Homes and businesses were destroyed. Natural habitats were annihilated, and many Americans were displaced for days, weeks, and even years. This study investigated the within‐subject effects and contrasts of poverty, rurality, and location within a Katrina distance impact zone on mathematics achievement in fifth‐grade, eighth‐grade, and Algebra I schools in Mississippi during the 2004–2007 school years. Through an analysis of publicly available school data, all school groups were found to have been impacted by Katrina, but the nonpoor/nonrural Algebra I schools within a 90‐mile radius of Katrina's point of landfall were affected the greatest. Interesting patterns in eighth‐grade mathematics achievement results were additionally found. Rural schools were impacted to a greater extent than their nonrural counterparts. Several findings in this study were startling and counterintuitive, but this initial analysis into the impact of Katrina on mathematics achievement in Mississippi illustrated that catastrophic natural disasters like Hurricane Katrina can cause more than just physical damage.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction,which limits their capability for increased predictive accuracy relative to experimental data.This is partly because of the nature of slug flow pneumatic conveying system,which,as a dynamic system,never becomes stable.By utilising conservation of mass (airflow),a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour.The rate of air permeation through slug,one of the important factors in the conservation model,is expressed as a function of a slug permeability factor.Other factors such as slug velocity,slug length and the fraction of stationary layer were also considered.Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model,showing good agreement between the model and experimental results.     

Bipower-type estimation in a noisy diffusion setting

We consider a new class of estimators for volatility functionals in the setting of frequently observed Itō diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of microstructure noise and are closely related to the original concept of bipower variation in the no-noise case. We show that this approach provides efficient estimators for a large class of integrated powers of volatility and prove the associated (stable) central limit theorems. In a more general Itō semimartingale framework this method can be used to define both estimators for the entire quadratic variation of the underlying process and jump-robust estimators which are consistent for various functionals of volatility. As a by-product we obtain a simple test for the presence of jumps in the underlying semimartingale.     

A note on the central limit theorem for bipower variation of general functions

In this paper we present a central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in [O.E. Barndorff-Nielsen, S.E. Graversen, J. Jacod, M. Podolskij, N. Shephard, A central limit theorem for realised power and bipower variations of continuous semimartingales, in: From Stochastic Analysis to Mathematical Finance, Festschrift for Albert Shiryaev, Springer, 2006], where the central limit theorem was shown for even functions. We prove an infeasible central limit theorem for general functions and state some assumptions under which a feasible version of our results can be obtained. Finally, we present some examples from the literature to which our theory can be applied.     

Synthesis of multifunctional hydroxyethyl tetrazoles

A series of di-, tri-, and tetra-tetrazoloalkanes were synthesized from the corresponding nitrile and sodium azide. These were alkylated to give hydroxy terminated chains for possible use as high energy oligomers.     

Novel light-fluorous TEMPO reagents and their application in oxidation reactions

The synthesis of two light-fluorous TEMPO derivatives is reported, along with their application in oxidation reactions.