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.

---

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%.

---

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.

     

Dithiophosphors?ure-O,O-diethylester zur Spurenanreicherung an Aktivkohle

Zusammenfassung Aus den Reinstmetallen Eisen, Chrom und Mangan können die Elementspuren Bi, Cd, Cu, In, Pb und Tl durch Sorption ihrer DithiophosphorsÄure-O,O-diethylester-Komplexe an Aktivkohle als SpurenfÄnger abgetrennt werden. Die Trennfaktoren betragen in AbhÄngigkeit vom Matrixelement und von der Probeeinwaage 4×10³ bis 5×10⁴. Bei der Bestimmung der Spuren mit der Flammen-AAS werden für alle abgetrennten Elemente Nachweisgrenzen unterhalb 1 g/g erreicht.Teil I: siehe [1]     

New results on (b,c)–inverses

In this paper, we present some necessary and sufficient conditions for the existence of the (b, c)-inverse and several representations for the (b, c)-inverse related to the group inverse. Since Mary inverse, core inverse, dual core inverse and Bott–Duffin (e, f)-inverse are all the special cases of the (b, c)-inverse, related results for these inverses are obtained.     

An Algorithm that Localizes and Counts the Zeros of a $C^2$-Function

We describe an algorithm that localizes the zeros of a given real $C^2$-function $f$ on an interval $[a,b]$. The algorithm generates a sequence of subintervals which contain a single zero of $f$. In particular, the exact number of zeros of $f$ on $[a,b]$ can be determined in this way. Apart from $f$, the only additional input of the algorithm is an upper and a lower bound for $f''$. We also show how the intervals determined by the algorithm can be further refined until they are contained in the basin of attraction of the Newton method for the corresponding zero.     

The (b; c)-inverse in semigroups and rings with involution

We first prove that if a is both left (b; c)-invertible and left (c; b)- invertible, then a is both (b; c)-invertible and (c; b)-invertible in a *-monoid, which generalizes the recent result about the inverse along an element by L. Wang and D. Mosić [Linear Multilinear Algebra, Doi.org/10.1080/03081087. 2019.1679073], under the conditions (ab)* = ab and (ac)* = ac: In addition, we consider that ba is (c; b)-invertible, and at the same time ca is (b; c)-invertible under the same conditions, which extend the related results about Moore- Penrose inverses studied by J. Chen, H. Zou, H. Zhu, and P. Patrício [Mediterr J. Math., 2017, 14: 208] to (b; c)-inverses. As applications, we obtain that under condition (a²)* = a²; a is an EP element if and only if a is one-sided core invertible, if and only if a is group invertible.     

A formula for gap between two closed operators

Aim of this short note is to obtain a formula for the gap between two densely defined unbounded closed operators. It is interesting to note that the formula is very similar to the corresponding formula for the gap between two bounded operators.