Stochastic orderings, folded beta distributions and fairness in coin flips

This paper studies stochastic orderings for folded beta distributions. A necessary and sufficient condition for one folded beta random variable to be larger than another in likelihood ratio order is obtained. The work is motivated by the recent results of Porzio and Ragozini on stochastic orderings for folded binomial distributions. Beta distributions are commonly used to model proportions or probabilities, particularly as conjugate distributions for binomial random variables. Stochastic orderings may arise, for instance, in considerations of fairness in coin flips.     

Analytical characteristics of a continuum-source tungsten coil atomic absorption spectrometer.

A continuum-source tungsten coil electrothermal atomic absorption spectrometer has been assembled, evaluated, and employed in four different applications. The instrument consists of a xenon arc lamp light source, a tungsten coil atomizer, a Czerny-Turner high resolution monochromator, and a linear photodiode array detector. This instrument provides simultaneous multi-element analyses across a 4 nm spectral window with a resolution of 0.024 nm. Such a device might be useful in many different types of analyses. To demonstrate this broad appeal, four very different applications have been evaluated. First of all, the temperature of the gas phase was measured during the atomization cycle of the tungsten coil, using tin as a thermometric element. Secondly, a summation approach for two absorption lines for aluminum falling within the same spectral window (305.5-309.5 nm) was evaluated. This approach improves the sensitivity without requiring any additional preconcentration steps. The third application describes a background subtraction technique, as it is applied to the analysis of an oil emulsion sample. Finally, interference effects caused by Na on the atomization of Pb were studied. The simultaneous measurements of Pb and Na suggests that negative interference arises at least partially from competition between Pb and Na atoms for H2 in the gas phase.     

Explicit bounds for multidimensional linear recurrences with restricted coefficients

This note employs path counting techniques to extend recent results on bounds for odd order linear recurrences to higher dimensions. The results imply optimal zero-free polydisks for multivariable power series with 0, 1 coefficients. Among the applications is a result that states that the optimal zero-free polydisk has radius approximately 1/(v+1), for large dimensions v.     

Spreadsheet Approach to the Linear Least Squares Fit

This paper describes the design, use, and evaluation of World Wide Web-based prelab exercises in senior-level Instrumental Analysis. On-time completion of the prelab assignments was 75%, but use of other on-line resources such as a question-and-answer page was minimal. A midsemester assessment of the prelabs found that the multiple-choice questions were better for increasing conceptual understanding, rather than preparing the students for the actual lab work.     

A general formula for the rate of resonant transfer of energy between two electric multipole moments of arbitrary order using molecular quantum electrodynamics

A general expression is derived for the matrix element for the resonant transfer of energy between an initially excited donor species and an acceptor moiety in the ground state, with each entity possessing an electric multipole moment of arbitrary order. In the quantum electrodynamical framework employed, the coupling between the pair is mediated by the exchange of a single virtual photon. The probability amplitude found from second-order perturbation theory is a product of the electric moments located at each center and the resonant multipole-multipole interaction tensor. Using the Fermi golden rule, a general formula for the rate of energy transfer is obtained. As an illustration of the efficacy of the theory developed, rates of excitation energy exchange are calculated for systems interacting through dipole-quadrupole, dipole-octupole, quadrupole-quadrupole, and the familiar dipole-dipole coupling. For each of the cases examined, the near- and far-zone limits of the migration rate are calculated from the result valid for all donor-acceptor separations beyond wave function overlap. Expression of the octupole contribution to the transfer rate in terms of its irreducible components of weights 1 and 3 leads to new features. The octupole weight-1 term is found to contribute only when the interaction is retarded, while the dipole-octupole weight-1 contribution appears as a higher-order correction term to the dipole-dipole rate. Order of magnitude estimates are given for the contributions of dipole-quadrupole and dipole-octupole terms relative to the leading dipole-dipole rate for near-, intermediate-, and far-zone separations to further understand the role played by higher multipole moments in the transfer of excitation and the mechanism dominating the process.     

Tandem reaction of heterocyclic ketene aminals with diazoesters: Synthesis of pyrimidopyrrolidone derivatives

A tandem reaction of heterocyclic ketene aminals (HKAs) with diazoesters in the presence of a Cu catalyst is demonstrated for the efficient synthesis of pyrimidopyrrolidone derivatives. The reaction shows a broad substrate scope and excellent functional group tolerance. Our method provides rapid access to diverse pyrimidopyrrolidones in moderate to excellent yields under mild reaction conditions.     

A flexible interface for the coupling of capillary gas chromatography with inductively coupled plasma mass spectrometry

The coupling of a capillary gas chromatograph with an ICP-MS is described. The coupling consists of a laboratory-made, easily removable and flexible transfer line and is used for the determination of organotin compounds.     

Host structure dependence of light yield and proportionality in scintillators in terms of hot and thermalized carrier transport

Several outstanding questions, including why complex halide scintillator host structures allow higher light yield and flatter electron energy response than simple monovalent metal halides, have remained unanswered by current models of luminescence in dense ionization tracks. Our measurements of nonlinear quenching kinetic order, recent literature on hot‐electron transport in scintillators, and calculations presented here of hot‐electron velocity from band structure of SrI₂ and NaI, lead us to expand our previously described diffusion and nonlinear quenching model to include hot‐electron transport. Trends in multivalent versus monovalent metal halides, heavier versus lighter halides, and halides versus oxides versus semiconductors can be predicted based on optical phonon frequency, thermalized band edge mobilities, velocity in the upper conduction bands, and hole self‐trapping. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)