Functional equations on abelian groups with involution

Summary We produce complete solution formulas of selected functional equations of the formf(x +y) ±f(x + σ (ν)) = Σ _I ² =₁ g _l (x)h _l (y),x, y∈G, where the functionsf,g ₁,h ₁ to be determined are complex valued functions on an abelian groupG and where σ:G→G is an involution ofG. The special case of σ=−I encompasses classical functional equations like d’Alembert’s, Wilson’s first generalization of it, Jensen’s equation and the quadratic equation. We solve these equations, the equation for symmetric second differences in product form and similar functional equations for a general involution σ.     

Chemical analysis and distribution investigation of trace elements in indium matrix by spark source mass spectrometry

Summary High-purity indium was analysed by spark source mass spectrometry, using electrical and photoplate detection. For the calibration of the differences in elemental sensitivity, a standard sample was prepared in which 10 impurities were determined by graphite furnace atomic absorption spectrometry. In this way accuracies of less than 40% were obtained for relatively homogeneous elements at ppm and sub-ppm level. About 40 elements could be determined with detection limits of 10 to 30 ppb. Two pattern recognition methods, principal component analysis and clustering analysis, were applied to obtain information on trace element distribution, which indicated that a number of elements were strongly spatially correlated in the analysed sample.

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Chemische Analyse und Verteilungsbestimmung von Spurenelementen in Indium-Matrix durch Funkenquellen-Massenspektrometrie

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On leave from: Department of Chemistry, Nanjing Normal University, Nanjing, People's Republic of China     

Acousto-optic mode coupling of partially coherent light in two-mode optical fibers

An acoustic pulse propagating on a two-mode fiber can act as a beam splitter in a scanning interferometer. When this device is employed in white-light interferometry, the effects of distributed coupling and dispersive interferometer arms need to be considered. A theory suitable for treating acousto-optic interaction of partially coherent light in a moving interaction region was developed. It was found that differential optical dispersion should be negligible and the acoustic pulse length short. Also the coherence time should be short but long compared to the intermodal group delay difference over a pulse length. Experiments with long acoustic pulses were performed, and fairly good agreement with theory was obtained.     

Tube-excited energy-dispersive X-ray fluorescence analysis. II. Energy-dispersive X-ray fluorescence analysis of air particulate material.

The use of monoenergetic exciting radiation of molybdenum obtained with a secondary target set-up, a conventional water-cooled tungsten anode x-ray tube and a Si(Li) semiconductor detector permits many trace and minor constituents from chlorine to strontium to be determined in particulate material collected on cellulose filters. The method is rapid and economical compared to other multielement techniques. The use of one or more single-element thin-film standards to calibrate for the analysis of many elements appears to be possible, but some systematic errors must be prevented. Absorption of the fluorescent radiation is remedied by a simple correction method. The precision and the accuracy of the method were critically examined by independent analysis of a number of samples with instrumental neutron activation analysis and by interlaboratory comparisons on the same samples.     

Implementation of an expert system for the qualitative interpretation of X-ray fluorescence spectra

The implementation of an expert system for the automated qualitative interpretation of energy-dispersive x-ray spectra is discussed. The first step in the interpretation process is the extraction of the relevant data from the spectrum, which is done by a preprocessor program, written in FORTRAN. The expert system itself consists of three parts. The knowledge base contains specific information on energy-dispersive x-ray fluorescence spectrometry presented in the form of IF/THEN rules. The data base contains the reduced spectral data and an array of certainty factors associated with each element; the certainty factor for an element represents the probability of its being present in the sample from which the spectrum was taken. Finally, the inference engine performs manipulation of the knowledge. For a particular state of the data base, the certainty factors for all the elements are iteratively modified until convergence is reached by using the rules from the knowledge base. During each cycle, the inference engine selects one rule from the knowledge base and executes it. Rules are selected on the basis of the chemical elements contained in their IF part and according to their previously assigned focus levels. Execution of the THEN part of the selected rule modifies the certainty factors of a number of elements. At the end of the interpretation session, the system lists the elements which have a high probability of being present in the sample. Optionally, the user can be provided with explanations of the reasoning steps taken during the interpretation. Application of the expert system to a particular spectrum shows that it is useful for the reliable interpretation of spectral data obtained from electron microprobe analysis of industrial aerosol particles.     

Feasibility of instrumental neutron activation analysis for trace element studies in natural soils

Fifty natural surface soils with strongly variable organic matter content and elemental composition were investigated to see to what extent INAA would prove useful for multi-element surveys. A conventional scheme of irradiations and decay intervals was used and 35 elements were investigated. Detection limits of the various trace elements were studied with respect to the influence of elements giving rise to major radionuclides in activated samples. For the 18 elements Na, Al, K, Sc, Cr, Mn, Fe, Co, Zn, Br, Sb, Cs, Ba, La, Sm, Hf, Th, the performance of INAA was very good. Useful results were also obtained for V, As, Se, Rb, Sr, I, Ta, and Au, while the technique appeared marginal for Cl, Zr, Mo, Ag, and Hg, and unsatisfactory for Mg, Ti, Ni, and Cd.     

A heuristic method for dispatching repair men

A company has to provide service to its customers. A service consists of a visit to the customer plus the spending of some given time at the scene. The future customer demand is not known but the probability distribution for the demand may be known. When a customer call comes in, the company must immediately specify a time window within which the start of service will be provided. The problem is for a fixed service level to determine an optimal strategy of route design and time window setting so that the total distance travelled is minimized over the time horizon given. A heuristic method BARTOC (Booking Algorithm for Routing and Timing Of Customers) to solve the problem mentioned above is suggested. BARTOC is based on a cluster-first route-second approach. Some computational results are presented. The results indicate that BARTOC produces high quality solutions.Peter Matthiesen, Inc.Dano Chemo, Inc.     

Classificatin of chinese tea samples according to origin and quality by principal component techniques

Three categories of tea, black, green and oolong tea, with those varieties in each category were analyzed for their contents of cellulose, hemicellulose, lignin, polyphenols, caffeine and amino acids. The data were subjected to multivarige analysis. Principal component analysis and principal component classification provide discrimination between the different categories and varieties. The quality index, assigned to these tea standards by experts, could be predicted form the principal component scores.