The ‘time of occurrence’ in quantum mechanics

Apart from serving as a parameter in describing the evolution of a system, time appears also as an observable property of a system in experiments where one measures ‘the time of occurrence’ of an event associated with the system. However, while the observables normally encountered in quantum theory (and characterized by self-adjoint operators or projection-valued measures) correspond to instantaneous measurements, a time of occurrence measurement involves continuous observations being performed on the system to monitor when the event occurs. It is argued that a time of occurrence observable should be represented by a positive-operator-valued measure on the interval over which the experiment is carried out. It is shown that while the requirement of time-translation invariance and the spectral condition rule out the possibility of a self-adjoint time operator (Pauli’s theorem), they do allow for time of occurrence observables to be represented by suitable positive-operator-valued measures. It is also shown that the uncertainty in the time of occurrence of an event satisfies the time-energy uncertainty relation as a consequence of the time-translation invariance, only if the time of occurrence experiment is performed on the entire time axis.     

Intramolecular charge transfer and formation of luminescence centers of 4-nitro-4-dimethylaminobutadiene in binary solvents

Absorption and luminescence spectra of a 4-nitro-4-dimethylaminobutadiene molecule in binary solvents have been experimentally obtained and investigated. Formation of the absorption spectra is associated with a chromophore grouping of the molecule in a bent state, while the bathochromic shift of the band in the absorption spectrum is consistent with the theory of dipole-dipole interaction of a bipolar molecule with solvent molecules. The fluorescence spectrum and its form and bathochromic shift depend not only on the solvent polarity but also on the proportion and kind of binary mixture of solvents. For a certain proportion of the binary solvent, radiation has been generated at λ=610 nm in pumping by a nitrogen laser. Reported at the International Conference on Luminescence, November, 22–24, 1994, Moscow. Belarusian State University, 4, F. Skorina Ave., Minsk, 220080, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 119–121, January–February, 1997.     

Absorption properties of commercial lead chromates

Summary The results obtained for halogen absorption with different preparations of lead chromates are discussed. It has been found that pure lead chromate is a poor external absorbent for microanalytical determinations of halogens. Differences in the absorption properties of lead chromates of various origins can be explained by the presence of PbO · PbCrO₄ and by its different mechanical structures.

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Absorptionseigenschaften handelsüblicher Bleichromate

Zusammenfassung Die Ergebnisse der Halogenabsorption an Bleichromat verschiedener Herkunft werden diskutiert. Dabei wurde festgestellt, daß reines Bleichromat für mikroanalytische Halogenbestimmungen unzureichend ist. Unterschiedliche Absorptionseigenschaften dieser Verbindung können durch das Vorhandensein von PbO · PbCrO₄ sowie durch die verschiedene mechanische Struktur erklärt werden.

     

Part IV. Review and evaluation of spark source mass spectrometry as an analytical method

Summary The analytical features and most important fields of application of spark source mass spectrometry are described with respect to the trace analysis of highpurity materials and the multielement analysis of technical alloys, geochemical and cosmochemical, biological and radioactive materials, as well as in environmental analysis. Comparisons are made to other analytical methods. The distribution of the method as well as opportunities for contract analysis are indicated and developmental tendencies discussed.

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Überblick und Bewertung der Funken-Massenspektrometrie als Analysenmethode

Zusammenfassung Die Analyseneigenschaften und wichtigsten Einsatzgebiete der Funken-Massenspektrometrie zur Spurenanalyse an hochreinen Materialien und zur Multielementanalyse an technischen Legierungen, geo- und kosmochemischen, biologischen und radioaktiven Materialien sowie in der Umweltanalytik werden beschrieben. Vergleiche zu anderen Analysenverfahren werden gegeben. Die Verbreitung der Methode sowie Möglichkeiten der Auftragsanalytik werden angegeben und Entwicklungstendenzen diskutiert.

     

Markov inequalities on partially ordered spaces

Let X(ω) be a random element taking values in a linear space $\text{X}$ endowed with the partial order ≤; let $\text{G}$₀ be the class of nonnegative order-preserving functions on $\text{X}$ such that, for each g∈$\text{G}$₀, E[g(X)] is defined; and let $\text{G}$₁?$\text{G}$₀ be the subclass of concave functions. A version of Markov's inequality for such spaces in P(X ≥ x) ≤ inf_$\text{G}$0E[g(X)]/g(x). Moreover, if E(X) = ξ is defined and if Jensen's inequality applies, we have a further inequality P(X≥x) ≤ inf_$\text{G}$1E[g(X)]/g(x) ≤ inf_$\text{G}$1g(ξ)/g(x). Applications are given using a variety or orderings of interest in statistics and applied probability.     

Trace element enrichment on a quartz glass surface used as a sample support of an X-ray spectrometer for the subnanogram range

Summary A procedure for trace element enrichment on a quartz glass surface by matrix removal is described. It is applied for sample preparation on quartz glass flats which are used as sample supports for an X-ray fluorescence spectrometer yielding minimum detectable limits of about 20 pg. Measurements on the elements Cr, Fe, Co, Ni, Cu, Zn, As, Hg, and Pb gave recovery efficiencies between 97 and 100%.

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Spurenelementanreicherung an der Quarzglasoberfläche von Probenträgern eines Röntgenfluorescenzspektrometers für den Subnanogramnibereich

Zusammenfassung Es wird ein Verfahren zur Spurenelementanreicherung durch Entfernen der Matrix auf einer Quarzglasoberfläche beschrieben. Das Verfahren wird zur Probenherstellung auf hochebenen Quarzglasblöcken angewendet, die als Probenträger für ein Röntgenfluorescenzspektrometer dienen, das im Subnanogramnibereich arbeiten kann. Für die Elemente Cr, Fe, Co, Ni, Cu, Zn, As, Hg und Pb wurden Ausbeuten zwischen 97 und 100% gemessen.