Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].     

In vivo solid-phase microextraction for single rodent pharmacokinetics studies of carbamazepine and carbamazepine-10,11-epoxide in mice

The use of solid-phase microextraction (SPME) for in vivo sampling of drugs and metabolites in the bloodstream of freely moving animals eliminates the need for blood withdrawal in order to generate pharmacokinetics (PK) profiles in support of pharmaceutical drug discovery studies. In this study, SPME was applied for in vivo sampling in mice for the first time and enables the use of a single animal to construct the entire PK profile. In vivo SPME sampling procedure used commercial prototype single-use in vivo SPME probes with a biocompatible extractive coating and a polyurethane sampling interface designed to facilitate repeated sampling from the same animal. Pre-equilibrium in vivo SPME sampling, kinetic on-fibre standardization calibration and liquid chromatography–tandem mass spectrometry analysis (LC–MS/MS) were used to determine unbound and total circulating concentrations of carbamazepine (CBZ) and its active metabolite carbamazepine-10,11-epoxide (CBZEP) in mice (n = 7) after 2 mg/kg intravenous dosing. The method was linear in the range of 1–2000 ng/mL CBZ in whole blood with acceptable accuracy (93–97%) and precision (<17% RSD). The single dose PK results obtained using in vivo SPME sampling compare well to results obtained by serial automated blood sampling as well as by the more conventional method of terminal blood collection from multiple animals/time point. In vivo SPME offers the advantages of serial and repeated sampling from the same animal, speed, improved sample clean-up, decreased animal use and the ability to obtain both free and total drug concentrations from the same experiment.     

Ancillary nitrile substituents as convenient IR spectroscopic reporters for self-assembly of mercapto- and isocyanoazulenes on Au(111)

Synthesis and self-assembly of structurally related mercapto- and isocyanoazulenes, including novel 2-mercapto-1,3-dicyanoazulene (4) and 2-isocyano-1,3-dicyanoazulene (5), are reported. Exposing 5 adsorbed on Au(111) to a solution of 4 displaces the isocyanoazulene monolayer with that of the mercaptoazulene as judged by ν(C≡N) signatures of these films.     

Reactions of π-allyl with atomic oxygen and hydroxyl on Ag(110)

The oxidation of the adsorbed π-allyl (η³-C₃H₅), prepared on atomic oxygen- and hydroxyl-covered Ag(110) by dissociation of allyl chloride (C₃H₅Cl), is investigated with temperature-programmed desorption and high-resolution electron energy loss spectroscopy. Allyl chloride adsorbs molecularly on oxygen-covered Ag(110) at 110 K. Upon heating to 180 K, some allyl chloride dissociates to form π-allyl and atomic chlorine, and the remainder desorbs molecularly. The π-allyl undergoes combustion to form hydroxyl or carbonate until all of the free oxygen is consumed by 200 K. Migratory insertion of hydroxyl into excess π-allyl commences near 220 and finishes by 250 K, forming adsorbed allyl alcohol (C₃H₅OH), which reacts either with excess hydroxyl near 240 K to form allyl alkoxy (η¹(O)-C₃H₅O) and water, or with π-allyl at 250 K to form allyl alkoxy and propylene (C₃H₆). Th allyl alkoxy evolves acrolein (C₃H₄O) by β-hydrogen elimination near 285 K, and propylene is evolved concurrently as the hydrogen released by this reaction rapidly scavenges π-allyl. Finally, the remaining π-allyl dimerizes to form 1,5-hexadiene (C₆H₁₀), which desorbs at 315 K. The gross observations of reaction pathways and temperatures are used to evaluate important aspects of the thermochemistry of these reactions.     

The splitting number of the complete graph

If a given graphG can be obtained bys vertex identifications from a suitable planar graph ands is the minimum number for which this is possible thens is called the splitting number ofG. Here a formula for the splitting number of the complete graph is derived.     

Release from speech-on-speech masking by adding a delayed masker at a different location

The amount of masking exerted by one speech sound on another can be reduced by presenting the masker twice, from two different locations in the horizontal plane, with one of the presentations delayed to simulate an acoustical reflection. Three experiments were conducted on various aspects of this phenomenon. Experiment 1 varied the number of masking talkers from one to three and the signal-to-noise (S/N) ratio from -12 to +4 dB. Evidence of masking release was found for every combination of these variables tested. For the most difficult conditions (multiple maskers and negative S/N) the amount of release was approximately 10 dB. Experiment 2 varied the timing of leading and lagging masker presentations over a broad range, to include shorter delay times where room reflections of speech are rarely noticed by listeners and longer delays where reflections can become disruptive. Substantial masking release was found for all of the shorter delay times tested, and negligible release was found at the longer delays. Finally, Experiment 3 used speech-spectrum noise as a masker and searched for possible energetic masking release as a function of the lead-lag time delay. Release of up to 4 dB was found whenever delays were 2 ms or less. No energetic masking release was found at longer delays.     

Embedding a quantum rank three quadric in a quantum P3

We continue the classification, begun in [11], [14] and [12], of quadratic Artin-Schelter regular algebras of global dimension 4 which map onto a twisted homogeneous coordinate ring of a quadric hypersurfcice in P³. In this paper, we consider those cases where the quadric has rank 3. We also give sufficient conditions for the point scheme of any quadratic regular algebra of global dimension 4 to be the graph of an automorphism.     

Comparison of magnetic resonance imaging-based vocal tract area functions obtained from the same speaker in 1994 and 2002

A new set of area functions for vowels has been obtained with magnetic resonance imaging from the same speaker as that previously reported in 1996 [Story et al., J. Acoust. Soc. Am. 100, 537-554 (1996)]. The new area functions were derived from image data collected in 2002, whereas the previously reported area functions were based on magnetic resonance images obtained in 1994. When compared, the new area function sets indicated a tendency toward a constricted pharyngeal region and expanded oral cavity relative to the previous set. Based on calculated formant frequencies and sensitivity functions, these morphological differences were shown to have the primary acoustic effect of systematically shifting the second formant (F2) downward in frequency. Multiple instances of target vocal tract shapes from a specific speaker provide additional sampling of the possible area functions that may be produced during speech production. This may be of benefit for understanding intraspeaker variability in vowel production and for further development of speech synthesizers and speech models that utilize area function information.