A Note on Log-Convexity of q-Catalan Numbers

The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q = 1, to the Catalan numbers: 1, 1, 2, 5, 14,…, a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted. Received January 2, 2007     

Application of electron-attachment reactions to enhance selectivity of electron-capture detector for nitroaromatic explosives

The differences in the extent of electron-attachment reactions between thermal electrons and selected classes of organic molecules with high electron affinities were investigated. The investigations showed that interactions of thermal electrons with nitroaromatic compounds lead to the formation of neutral products with very low electron affinities. By contrast, a number of other analytes with high electron affinities such as polyhalogenated organic compounds, lead to products with high electron affinities. This difference was exploited to differentiate between nitroaromatic and polychlorinated organic compounds with a tandem arrangement consisting of two electron-capture detectors connected in series with an electron-attachment reactor.     

Selective sums of loopy partizan graph games

A loopy partizan graph game is a two-person game of perfect information which is played on a labelled digraph. The disjunctive sum, the continued conjunctive sum, and the selective sum are formulations for playing several l.p.g.g.'s simultaneously, so as to form a single compound game. In this paper, we present an analysis of the selective sum by utilizing certain elements of the theories for the disjunctive sum and the continued conjunctive sum.     

Differential inhibition of postnatal brain,spinal cord and body growth by a growth hormone antagonist

Background  

Growth hormone (GH) plays an incompletely understood role in the development of the central nervous system (CNS). In this study, we use transgenic mice expressing a growth hormone antagonist (GHA) to explore the role of GH in regulating postnatal brain, spinal cord and body growth into adulthood. The GHA transgene encodes a protein that inhibits the binding of GH to its receptor, specifically antagonizing the trophic effects of endogenous GH.     

Tunneling in the proton transfer between two water molecules

SCF CNDO calculations were performed for the species H₅O⁺₂ at several positions of the intervening proton and at interoxygen distances of 2.65, 2.70 and 2.75 Å. The energy profile was fitted to a potential energy function containing a quadratic term plus a gaussian. The eigenvalues and eigenvectors were obtained by using the variational method with the eigenfunctions of the parabolic potential as basis set. The results indicate that at 2.65 Å the top of the barrier is below the first energy level and that at 2.75 Å the first two energy levels are below the top of the barrier with the splitting of the symmetric-antisymmetric pair of 0.00132 au indicating that tunneling occurs at a frequency of 10¹⁴ reciprocal seconds.     

Transfer measurements for the Ti+Ni systems at near barrier energies

Large enhancements have been observed in the sub-barrier fusion cross sections for Ti+Ni systems in our previous studies. Coupled channel calculations incorporating couplings to 2⁺ and 3⁻ states failed to explain these enhancements completely. A possibilty of transfer channels contributing to the residual enhancements had been suggested. In order to investigate the role of relevant transfer channels, measurements of one- and two-nucleon transfer were carried out for ^46,48Ti+⁶¹Ni systems. The present paper gives the results of these studies.     

Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach

Aeromedical and ground ambulance services often team up in responding to trauma crashes, especially when the emergency helicopter is unable to land at the crash scene. We propose location-coverage models and a greedy heuristic for their solution to simultaneously locate ground and air ambulances, and landing zones (transfer points). We provide a coverage definition based on both response time and total service time, and consider three coverage options; only ground emergency medical services (EMS) coverage, only air EMS coverage, or joint coverage of ground and air EMS in which the patient is transferred from an ambulance into an emergency helicopter at a transfer point. To analyze this complex coverage situation we develop two sets of models, which are variations of the Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP). These models address uncertainty in spatial distribution of motor vehicle crash locations by providing coverage to a given set of both crash nodes and paths. The models also consider unavailability of ground ambulances by drawing upon concepts from backup coverage models. We illustrate our results on a case study that uses crash data from the state of New Mexico. The case study shows that crash node and path coverage percentage values decrease when ground ambulances are utilized only within their own jurisdiction.     

Determination of inorganic ions in mineral water by gradient elution moving boundary electrophoresis

A sensitive method was developed for the determination of the major inorganic ions in commercial mineral waters using gradient elution moving boundary electrophoresis with capacitively coupled contactless conductivity detection. This application was the first to demonstrate the separation of cations and anions simultaneously using gradient elution moving boundary electrophoresis. Seven ionic analytes (calcium, chloride, magnesium, nitrate, potassium, sodium, and sulfate) were separated in less than 7 min with detection values in the low μmol/L to sub-μmol/L range. Calculated values of the major ions in three commercial mineral waters were compared to reported values with good correlation. In another application, phosphate and arsenate were separated in less than 2 min with limits of detection of 300 and 140 nmol/L, respectively. For all standard analyses, the RSD for migration times and peak areas were under 3%.     

Using FTIR spectroscopy to detect sericin on historic silk

Silks represent some of the most precious ancient and historic textile artefacts in collections worldwide.Their optimum preservation demands an appreciation of their characteristics.One important concern,especially with regard to ancient Chinese silks,is whether the fabrics have been degummed.Silks with remnant sericin gum coating the fibroin fibres would require different conservation protocol.In previous research on aged silks,the presence of sericin has been inferred from amino acid analysis of hydrolysa...     

Iron-catalyzed Doyle-Kirmse reaction of allyl sulfides with (trimethylsilyl)diazomethane

[formula: see text] Iron salts efficiently catalyze the Doyle-Kirmse reaction of allyl sulfides with (trimethylsilyl)diazomethane and ethyl diazoacetate in dichloroethane at 83 degrees C. Competitive dimerization is less of a problem with (trimethylsilyl)diazomethane than with ethyl diazoacetate. Good results are obtained using only 1.5 equiv of (trimethylsilyl)diazomethane, even without slow addition. Phosphine ligands affect the kinetics, but not the diastereoselectivity. Dppe and BINAP lead to higher yields than dppp, but no enantioselection was detected with R-(+)-BINAP.