Geometric structure of b 2,2-orbihedra and interpolation of operators

We compute the normals to faces of b _2,2-orbihedra and apply the results to Operator Interpolation Theory.     

Generalized Nash equilibrium problems and Newton methods

The generalized Nash equilibrium problem, where the feasible sets of the players may depend on the other players’ strategies, is emerging as an important modeling tool. However, its use is limited by its great analytical complexity. We consider several Newton methods, analyze their features and compare their range of applicability. We illustrate in detail the results obtained by applying them to a model for internet switching.     

Simultaneous determination of β2‐agonists in human urine by fast‐gas chromatography/mass spectrometry: method validation and clinical application

A fast screening protocol was developed and validated for the simultaneous determination of 15 β₂‐agonists in human urine (bambuterol, cimbuterol, clenbuterol, fenoterol, formoterol, isoproterenol, mapenterol, metaproterenol, procaterol, ractopamine, ritodrine, salbutamol, salmeterol, terbutaline, tulobuterol). The overall sample processing includes deconjugation with enzyme hydrolysis, liquid–liquid extraction, followed by derivatization of the extract and detection of β₂‐agonists trimethylsilyl‐derivatives by fast‐gas chromatography/electron impact–mass spectrometry (fast‐GC/EI‐MS). Sample extraction and derivatization were optimized with the purpose of improving recoveries and reaction yields for a variety of analytes with different structures simultaneously, while keeping the procedure simple and reliable. Validation parameters were determined for each analyte under investigation, including selectivity, linearity, intra‐ and inter‐assay precision, extraction recoveries and signal to noise ratio (S/N) at the lowest calibration level. Fast‐GC/MS sequences, based on the use of short columns, high carrier‐gas velocity and fast temperature ramping, allow considerable reduction of the analysis time (7 min), while maintaining adequate chromatographic resolution. The overall GC cycle time was less than 9 min, allowing a processing rate of 6 samples/h. High MS‐sampling rate, using a benchtop quadrupole mass analyzer, resulted in accurate peak shape definition under both scan and selected ion monitoring modes, and high sensitivity in the latter mode. The method was successfully tested on real samples arising from clinical treatments. Copyright © 2009 John Wiley & Sons, Ltd.     

Ulam stability for a delay differential equation

We study the Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability for a delay differential equation. Some examples are given.     

Greenish‐yellow‐, yellow‐, and orange‐light‐emitting iridium(III) polypyridyl complexes with poly(ε‐caprolactone)–bipyridine macroligands

A set of novel greenish‐yellow‐, yellow‐, and orange‐light‐emitting polymeric iridium(III) complexes were synthesized with the bridge‐splitting method. The respective dimeric precursor complexes, [Ir(ppy)₂‐μ‐Cl]₂ (ppy = 2‐phenylpyridine) and [Ir(ppy? CHO)₂‐μ‐Cl]₂ [ppy? CHO = 4‐(2‐pyridyl)benzaldehyde], were coordinated to 2,2′‐bipyridine carrying poly(ε‐caprolactone) tails. The resulting emissive polymers were characterized with one‐dimensional (¹H) and two‐dimensional (¹H? ¹H correlation spectroscopy) nuclear magnetic resonance and infrared spectroscopy, gel permeation chromatography, and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry, and the successful coordination of the iridium(III) centers to the 2,2′‐bipyridine macroligand was revealed. The thermal behavior was studied with differential scanning calorimetry and correlated with atomic force microscopy. Furthermore, the quantitative coordination was verified by both the photophysical and electrochemical properties of the mononuclear iridium(III) compounds. The photoluminescence spectra showed strong emissions at 535 and 570 nm. The color shifts depended on the substituents of the cyclometallating ligands. Cyclic voltammetry gave oxidation potentials of 1.23 V and 1.46 V. Upon the excitation of the films at 365 nm, yellow light was observed, and this could allow potential applications in light‐emitting devices. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2765–2776, 2005     

Trumpet with near-perfect harmonicity: design and acoustic results

This paper presents a mathematical design methodology for determining the shape of a trumpet air column that has near-perfect harmonicity, whose components are discontinuity-free, and whose input impedance peak heights are balanced over the playing range. The simulation model employed assumes linear wave propagation and uses cylindrical element discretization with a plane wave approximation. Acoustic measurements are made using a test set-up with an estimated relative measurement error of ±3 cents. Comparisons of measured results are given for the presented design (Macaluso trumpet) and the same trumpet air column with the bell replaced by a commercially used generic trumpet bell of unknown shape (Generic trumpet). For acoustic resonance modes 2-13 (233-1515 Hz), the measured root-mean-square (rms) harmonicity deviation is 5 cents for the Macaluso trumpet, whereas it is 18 cents for the Generic trumpet. However, considering the estimated measurement uncertainty, each of those deviations is somewhat over-stated. For that same range of resonances, the rms deviation between measured and calculated resonance frequencies for the Macaluso trumpet is 3 cents, thus validating the presented simulation model and equations.     

Preparation of functional spherical polysilsesquioxane/gold nanoparticle composites and their applications in DNA assay

Functional spherical solid and hollow particles of polysilsesquioxanes (PSQs) containing amine, thiol, and vinyl groups were prepared by polymerizing organotrialkoxysilanes (OTASs) containing corresponding chemical groups. Fluorescent PSQ particles were prepared by physically entrapping Rhodamine 6G, Coumarin 7, and Fluoresceine sodium salts. The intensity of fluorescent light increased initially with increasing amount of entrapped fluorophores and then leveled off or decreased slightly after reaching a maximum value. PSQ particles containing gold nanoparticles (GNPs), both inside and on the surface, were prepared by the in situ reduction of gold ions by the PSQ particles. When the reduction reaction was carried out for extended periods of time, the GNP that had formed inside the poly(3-mercaptopropyl)silsesquioxane (PMPSQ) and polyvinylsilsesequioxane (PVSQ) particles underwent interesting morphological changes. PSQ particles containing amine and thiol groups fixed the GNPs on the surface, which could be utilized further in binding amine-modified oligo-DNA strands. The aggregation of PSQ/GNP particles combined with complementary oligo-DNA strands was examined to demonstrate that these particles could be applied to DNA assays and isolation. The particles were characterized by scanning electron microscopy, transmission electron microscopy, solid state nuclear magnetic resonance spectroscopy, ultraviolet/visible spectroscopy, and fluorescence microscopy.     

An electrochemical study on the substituted spinel LiMn1.95Cr0.05O4

Cyclic voltammetry, galvanostatic charge?Cdischarge technique, potentiostatic intermittent titration technique (PITT), and electrochemical impedance spectroscopy (EIS) were used to study the behavior of a LiMn_1.95Cr_0.05O₄ (substituted lithium?Cmanganese spinel) electrode in nonaqueous electrolytes at 25 °C. Quantitative and qualitative changes of the electrode transport parameters as functions of lithium concentration were analyzed. Several equivalent circuits are discussed; the results obtained by different methods are compared. The PITT and EIS results are in good agreement; the chemical diffusion coefficient D varies within 10^?14?C10^?9 cm² s^?1 depending on the lithium content in the Li_xMn_1.95Cr_0.05O₄ electrode.