Quantum Mechanics on Finite Groups

Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert ^*-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum measurements in this framework.     

High resolution applications of laser-induced breakdown spectroscopy for environmental and forensic applications

Laser-induced breakdown spectroscopy (LIBS) has been used in the elemental analysis for a variety of environmental samples and as a proof of concept for a host of forensic applications. In the first application, LIBS was used for the rapid detection of carbon from a number of different soil types. In this application, a major breakthrough was achieved by using a multivariate analytical approach that has brought us closer towards a “universal calibration curve”. In a second application, it has been demonstrated that LIBS in combination with multivariate analysis can be employed to analyze the chemical composition of annual tree growth rings and correlate them to external parameters such as changes in climate, forest fires, and disturbances involving human activity. The objectives of using this technology in fire scar determinations are: 1) To determine the characteristic spectra of wood exposed to forest fires and 2) To examine the viability of this technique for detecting fire occurrences in stems that did not develop fire scars. These examples demonstrate that LIBS-based techniques are inherently well suited for diverse environmental applications. LIBS was also applied to a variety of proof of concept forensic applications such as the analysis of cremains (human cremation remains) and elemental composition analysis of prosthetic implants.     

The calculation of excitation energies based on the relativistic two-component zeroth-order regular approximation and time-dependent density-functional with full use of symmetry

In the present work, we propose a relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. This two-component TDDFT formalism has the correct nonrelativistic limit and affords the correct threefold degeneracy of triplet excitations. The relativistic TDDFT formalism is implemented into the AMSTERDAM DENSITY FUNCTIONAL program package for closed-shell systems with full use of double-group symmetry to reduce the computational effort and facilitate the assignments. The performance of the formalism is tested on some closed-shell atoms, ions, and a few diatomic molecules containing heavy elements. The results show that the fine structure of the excited states for most atoms and ions studied here can be accurately accounted for with a proper XC potential. For the excitation energies of the molecules studied here, the present formalism shows promise and the error encountered is comparable to that of nonrelativistic TDDFT calculations on light elements.     

Automated capillary gas chromatographic analysis of pesticide residues in food

A method for multiresidue pesticide analysis in food is described. After a conventional clean-up, gas chromatographic analysis is performed in a gas chromatograph equipped with two fused-silica capillary columns coated with methylsilicone SP 2100 and methylphenylsilicone OV-17. The effluent from each column is split to electron-capture and nitrogen-phosphorus detectors, which are connected to a dual channel integrator. Therefore, from each gas chromatographic run parallel records of signals from the two detectors are obtained. Calibration of the system is carried out for the SP 2100 column with three test mixtures covering all pesticides. Additionally, four internal standards are included, two responding to the electron-capture detector and the other two to the nitrogen-phosphorus detector. Automated analysis is performed with test mixtures and food samples on the SP 2100 column overnight as a screening procedure. After selection of positive samples a confirmatory test and quantitation are carried out manually applying appropriate test mixtures according to the results of the screening runs.     

The ECHO technique--the more effective way of data evaluation in liquid chromatography-tandem mass spectrometry analysis

The aim of this study was to evaluate the applicability of ECHO technique in pesticide residue analysis using LC/MS/MS instruments with atmospheric pressure chemical (APCI) and electrospray (ESI) ionization. The technique is based on simultaneous injections of reference standards and samples in one run. First and second injections are made ahead and behind a precolumn, respectively, thus resulting in a short difference of retention times between standard and sample peak. The obtained couple of peaks were applied to the easy detection of pesticides and simultaneous estimation of the residue content in real samples in a single run. If residues were not observed, the second sample peak did not occur and the ECHO peaks were used to demonstrate instrument performance in each run and for each analyte. Another advantage of ECHO technique is its potential to compensate matrix effects. The occurrence and compensation of matrix effects using APCI was tested with four matrix types (water containing, acidic, dry and sugar containing) and 22 pesticides. The same matrix types but 58 pesticides were used tests with electrospray ionization. Most often matrix effects had been observed with lemon. The percentage of pesticides showing significant matrix effects did not differ between APCI and ESI. But these effects caused signal enhancement in APCI measurements and signal suppression, when ESI was used. The ECHO technique was able to compensate many matrix effects in measurements with both types of ion sources.     

Bayesian multiple-source localization in an uncertain ocean environment

This paper considers simultaneous localization of multiple acoustic sources when properties of the ocean environment (water column and seabed) are poorly known. A Bayesian formulation is developed in which the environmental parameters, noise statistics, and locations and complex strengths (amplitudes and phases) of multiple sources are considered to be unknown random variables constrained by acoustic data and prior information. Two approaches are considered for estimating source parameters. Focalization maximizes the posterior probability density (PPD) over all parameters using adaptive hybrid optimization. Marginalization integrates the PPD using efficient Markov-chain Monte Carlo methods to produce joint marginal probability distributions for source ranges and depths, from which source locations are obtained. This approach also provides quantitative uncertainty analysis for all parameters, which can aid in understanding of the inverse problem and may be of practical interest (e.g., source-strength probability distributions). In both approaches, closed-form maximum-likelihood expressions for source strengths and noise variance at each frequency allow these parameters to be sampled implicitly, substantially reducing the dimensionality and difficulty of the inversion. Examples are presented of both approaches applied to single- and multi-frequency localization of multiple sources in an uncertain shallow-water environment, and a Monte Carlo performance evaluation study is carried out.     

Sequential Product of Quantum Effects: An Overview

This article presents an overview for the theory of sequential products of quantum effects. We first summarize some of the highlights of this relatively recent field of investigation and then provide some new results. We begin by discussing sequential effect algebras which are effect algebras endowed with a sequential product satisfying certain basic conditions. We then consider sequential products of (discrete) quantum measurements. We next treat transition effect matrices (TEMs) and their associated sequential product. A TEM is a matrix whose entries are effects and whose rows form quantum measurements. We show that TEMs can be employed for the study of quantum Markov chains. Finally, we prove some new results concerning TEMs and vector densities.     

Reductive amination of aldehydes with sodium borohydride and lithium aluminum hydride in the presence of lithium perchlorate

A one-pot high yielding reductive amination of aldehydes with primary and secondary amines using LiClO₄/NaBH₄ and LiClO₄/LiAlH₄ as reducing agents in diethyl ether is described.