A major index for matchings and set partitions

We introduce a statistic pmaj(P) for partitions of [n], and show that it is equidistributed with cr₂, the number of 2-crossings, over all partitions of [n] with given sets of minimal block elements and maximal block elements. This generalizes the classical result of equidistribution for the permutation statistics inv and maj.     

Fluorescence Detection of the Ornamental Fish Cardinal Tetra (Paracheirodon axelrodi)

The fluorescence spectra of the tropical fish, Cardinal Tetra ( Paracheirodon axelrodi ), originating in the Amazon region of Brazil, were determined. These spectra were then treated using factor analysis, generating two contributing spectra and separating out the noise. Time-resolved fluorescence results indicated that the fluorescent system in the epidermis undergoes excited state reaction. Excited state proton transfer is suggested as being present. Both intentionally stressed and nonstressed individuals were used and some small differences were noted in the contributions of the two calculated contributing spectra to the experimental spectra, presumably as a function of stress. The results are compared with those obtained by the standard determination of cortisol level using the whole body extraction method and it is suggested that the method could be tested as an improved, nondestructive way to determine stress in this species, which is a necessary step in the development of "best management practices" of methods for storage and transport of the fish.     

Use of dynamically coated capillaries with added cyclodextrins for the analysis of opium using capillary electrophoresis

A rapid, precise, accurate, and robust method using capillary electrophoresis (CE) with dynamically coated capillaries for the analysis of the major opium alkaloids in opium is presented. Dynamic coating of the capillary surface is accomplished using a commercially available reagent kit (polycation coating followed by polyanion coating). The addition of dual cyclodextrins (hydroxypropyl-beta-cyclodextrin and dimethyl-beta-cyclodextrin) to the run buffer imparts excellent selectivity for the opium alkaloids. For the determination of morphine, papaverine, codeine, noscapine and thebaine in opium gum and opium latex samples (using tetracaine as an internal standard) good agreement with values obtained by gradient high-performance liquid chromatography is obtained. Compared to the latter technique, CE affords better resolution with significantly faster analysis time (12 min versus 29 min). Dynamically coated capillaries, which give rise to a relatively high and robust electroosmotic flow (EOF) at the background electrolyte pH of 2.5, allow for rapid analysis and excellent migration time and peak area precision (RSDs < or = 0.12% and < or = 1.2%, respectively). Reproducible separations (relative migration times) for over 500 samples have been obtained on a single capillary. The nature of the injection solvent, the injection time and the contents of the waste vials have a profound effect on the pressure injection precision of the relatively hydrophobic solutes. The CE conditions reported in this study are also applicable to the analysis of lysergic acid diethylamide (LSD) exhibits.     

Electrocatalysis by Polyoxometalate-Protected Gold Nanoparticles

Electrocatalysis by polyoxometalate (POM)-monolayer protected gold nanoparticles is herein demonstrated using a newly discovered phenomenon that makes it possible to observe the electrochemistry of dilute aqueous solutions of these colloidal nanostructures. To preserve the integrity of the gold nanoparticles’ electrostatically-stabilized POM-monolayer structures, deposition and drying of the POM-protected metal(0) NPs on the electrode surface must be avoided. Overcoming this constraint, we here show that POM-monolayer protected gold nanoparticles can be induced to reversibly associate with electrode surfaces, resulting in dramatic current amplification and well behaved, quasi-reversible cyclic voltammetric behavior at remarkably small electrolyte concentrations, thus making it possible to investigate electrocatalysis by dilute aqueous solutions of POM-protected gold NPs.     

When the dual of an ideal is a ring

Let R be a commutative integral domain with identity with quotient field K, and let I be a nonzero ideal of R. We analyze several general and particular instances when I^–1 is a subring of K. We then apply some of our results to show that certain non-maximal prime ideals in Prüfer domains are divisorial.     

Realizing Holonomic Constraints in Classical and Quantum Mechanics

We consider the problem of constraining a particle to a smooth compact submanifold Σ of configuration space using a sequence of increasing potentials. We compare the classical and quantum versions of this procedure. This leads to new results in both cases: an unbounded energy theorem in the classical case, and a quantum averaging theorem. Our two step approach, consisting of an expansion in a dilation parameter, followed by averaging in normal directions, emphasizes the role of the normal bundle of Σ, and shows when the limiting phase space will be larger (or different) than expected. Received: 16 November 2000 / Accepted: 2 February 2001     

Selective catch and release of a synthetically useful phosphine ligand

The selective catch and release of the synthetically useful (o-biphenyl)(t-butyl)₂P from basic and non basic compounds, utilizing solid phase supported sulfonic acid sources is demonstrated.     

Muscle spindles are concentrated in the superior vocalis subcompartment of the human thyroarytenoid muscle

It is hypothesized that different parts of the thyroarytenoid muscle (TA) are functionally specialized. Specifically, the TA is divided into a lateral muscularis compartment and a medial vocalis compartment. This study examined the distribution of muscle spindles throughout the human TA as an indicator of these functional differences. Histological cross-sections from the anterior, middle, and posterior regions of five human membranous vocal folds were examined for the number and location of muscle spindles. There was an average of 6.1 muscle spindles in sections from each region with no significant variation between the different regions (p < .05). However, in sections from all three regions, the muscle spindles were always found to be concentrated in the superior medial quadrant of the TA (mean 85.9%, p < .01). The inferior medial, superior lateral, and inferior lateral quadrants of the TA contained 11.96%, 2.17%, and 0%, respectively, of the total muscle spindles. Within the superior medial quadrant, most of the muscle spindles were localized in the most superficial part of the muscle.The results of this study demonstrate that the majority of TA muscle spindlesare concentrated in its superior medial quadrant, an area we have termed the superior vocalis subcompartment (SC. This finding suggests that the superior vocalis SC is functionally distinct from the remainder of the TA. It is hypothesized that tension in the superior vocalis SC can be controlled independently from the remainder of the TA, and this capability is used to effect the biomechanics of vocal fold vibration during phonation.     

Enumeration of trees by inversions

Mallows and Riordan “The Inversion Enumerator for Labeled Trees,” Bulletin of the American Mathematics Society, vol. 74 [1968] pp. 92-94) first defined the inversion polynomial, J_n(q) for trees with n vertices and found its generating function. In the present work, we define inversion polynomials for ordered, plane, and cyclic trees, and find their values at q = 0, ± 1. Our techniques involve the use of generating functions (including Lagrange inversion), hypergeometric series, and binomial coefficient identities, induction, and bijections. We also derive asymptotic formulae for those results for which we do not have a closed form. © 1995 John Wiley & Sons, Inc.