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     

Pd (II)‐catalyzed vinyl addition polymerization of novel functionalized norbornene bearing dimethyl carboxylate groups

Three novel functionalized polynorbornenes (PNB) with pendant dimethyl carboxylate group (carboxylates—acetate, propionate, and butyrate) are synthesized as a vinyl‐type with a palladium (II) catalyst in high yield. The effects of size of substitutents, molar ratio of monomer to catalyst, solvent polarity, reaction time, and temperature on the polymerization of exo‐norbornene dimethyl propionate were systematically investigated. The low molar ratio and temperature, as well as high polarity of solvent, and long reaction time, are favorable for the enhancement of the monomer conversion, especially, the solvent have an obvious effect on the catalyst activity. The resulting poly(cis‐norbornene‐exo‐2,3‐dimethyl carboxylates) (PNB‐dimethyl carboxylates) show good solubility in common organic solvent and high thermal stability up to 360 °C. The glass transition temperature was detected by DMA at 331, 324, and 318 °C for acetate, propionate, and butyrate, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3391–3399, 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.     

MODELING HARVEST SCHEDULING IN MULTIFUNCTIONAL PLANNING OF FORESTS FOR LONGTERM WATER YIELD OPTIMIZATION

In this study, wood production and hydrologic functions of forests were accommodated within a planning procedure for separate working circles (areas dedicated to certain forest functions) that were delineated according to an Ecosystem‐Based Functional Planning approach. Mixed integer goal programming was used as the optimization technique. The timing and scheduling of a maintenance cutting (partial harvest) was the decision variable in the modeling effort, and an original formulation was developed as a multiobjective planning procedure. Four sample planning strategies were developed and model outputs were evaluated according to these strategies. Spatial characteristics of stands were considered, and used to prohibit the regeneration of adjacent stands during the same time period. Because of the positive relationship between qualified water production and standing timber volume in the forest, the model attempts to maximize qualified water production levels by increasing standing volume stocks in the forest through the delay of regeneration activities.     

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.     

Effect of chemical modification on oligomerization capacity of alumina support for Pd-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> catalyst

Effect of modification with an alkali metal on the acid properties of alumina supports and on the oligomerization capacity and working stability of Pd-Al₂O₃ catalysts was studied.     

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.     

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%.     

Synthesis and cytotoxicity of 28-carboxymethoxy lupane triterpenoids.Preference of 28-O-acylation over 28-O-alkylation of betulm by ethyl bromoacetate

28-Carboxymethoxy lupane tritepenoids 3 and 4 were synthesized by alkylation of betulin with the THP protected 2- hydroxyethyl iodide followed by oxidation and reduction.Direct reaction of betulin(5) or betulone(10) with ethyl bromoacetate led to 28-O-acylation,instead of 28-O-alkylation.The targeted compounds 3 and 4 were not cytotoxic at the highest concentration tested(75μmol/L),suggesting that elongation of the chain length at the 28-position in both betulinic acid(1) and betulonic acid(2) was detrim...