Wachstumsverhalten zufÄlliger Potenzreihen

Summary Using the theorems collected in Chapter 2 the paper discusses growth and divergence properties of random power series (rps's) with — generally — independent coefficients a _n. In Chapter 3 assertions about rps's with a _n symmetric relative to 0 are transferred to rps's for which the medians a _n of a _n are 0. Chapter 4 treats analogies between rps's with symmetrized coefficients a _s ⁿ and rps's with centered coefficients a _n -a _n ; they concern growth of random entire functions defined by rps's with arbitrarily dependent coefficients, and local behaviour near the circle of convergence. For some kinds of singular behaviour, e.g. unboundedness of characteristic in every sector of the circle of convergence, Chapter 5 gives necessary and sufficient conditions in connection with the notion of essential divergence. The theorems hold also for -quantiles a _n ( fixed, 0<<1) instead of medians a _n .Herrn Professor Dr. F. Lösch zum 65. Geburtstag gewidmet.     

Über den Einfluß der Anharmonizität auf die thermische Röntgenstreuung an Kristallen

Work already published under the above topic by W.Ludwig and the author was limited to crystal temperatures above the Debye temperature, as it treated the lattice vibrations by classical statistics. In this paper, a complete quantum-statistical treatment is presented. The essential features of the high temperature results remain unchanged: New, temperature dependent dispersion curves may be introduced which, for long waves, are determined by theisothermal elastic constants.     

Stable isotope quality assurance using the ‘Calibrated IRMS’ strategy†

Procedures in our laboratory have always been directed towards complete understanding of all processes involved and corrections needed etc., instead of relying fully on laboratory reference materials. This rather principal strategy (or attitude) is probably not optimal in the economic sense, and is not necessarily more accurate either. Still, it has proven to be very rewarding in its capability to detect caveats that go undiscovered in the standard way of measurement, but that do influence the accuracy or reliability of the measurement procedure. An additional benefit of our laboratory procedures is that it makes us capable of assisting the International Atomic Energy Agency (IAEA) with primary questions like mutual scale assignments and comparison of isotope ratios of the same isotope in different matrices (like δ¹⁸O in water, carbonates and atmospheric CO₂), establishment of the ¹⁷O–¹⁸O relation, and the replenishment of the calibration standards. Finally, for manual preparation systems with a low sample throughput (and thus only few reference materials analysed) it may well be the only way to produce reliable results.     

Eine Bemerkung zur Integrierbarkeit eines Produktes von zwei Funktionen in Sobolewschen Räumen

Ohne Zusammenfassung     

Konvergenz und Summierbarkeit von Reihen zufälliger Variablen

Ohne Zusammenfassung     

Reaktionen mit Phosphonyl- und Thiophosphonyl-dichloriden

Äthan- und Cyclohexanphosphonsäure- bzw. -thiophosphon-säuredichlorid tauschen die Chloratome in Gegenwart säurebindender Mittel gegen Alkoxy- und Alkylmercapto-Gruppen aus. Thiophosphonsäureester-chloride reagieren mit Natriumsulfid zu Dithiophosphonsäuremonoestern, deren Nickelsalze herge-stellt wurden.

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Herrn Prof. Dr.F. Asinger zum 60. Geburtstag herzlichst gewidmet.     

Strong universal consistency of smooth kernel regression estimates

The paper deals with kernel estimates of Nadaraya-Watson type for a regression function with square integrable response variable. For usual bandwidth sequences and smooth nonnegative kernels, e.g., Gaussian and quartic kernels, strongL ₂-consistency is shown without any further condition on the underlying distribution. The proof uses a Tauberian theorem for Cesàro summability.     

Strong Laws of Large Numbers by Elementary Tauberian Arguments

For Kolmogorovs strong law of large numbers an alternative short proof is given which weakens Etemadis condition of pairwise independence. The argument uses the known – and elementary – equivalence of (Cesàro) C₁- and C₂-summability for one-sided bounded sequences. Also other strong laws of large numbers are established, in part via Borel summability.     

ARXPS-studies ofĉ-axis textured — superconducting YBa2Cu3O x -films

YBa₂Cu₃O _x sputter deposited cold on Al₂O₃ and on MgO grows in O₂ annealing epitaxially to a transparent, superconducting film withT _c=80 K. The unscraped surfaces of these films are smooth showing XPS lines changing with photoelectron take-off angle. This enhanced data base allows to separate the different chemical shifts and to obtain their spatial distribution. This yields the identification of the chemical compounds (hydroxide, peroxide, carbonate, carboxyle, cuprate, graphite ...), their amount and their distribution making up the cinder and the cuprate. The cinder grows with O₂-anneal at internal and external surfaces. Because of the large unit cell and of the anisotropy of the cuprate the chemical composition of the surface depends on orientation and changes over distances of the order of 1 nm.The cinder stoichiometry gives insights in the chemistry going on in O₂ annealing. Below the cinder the signature of-axis textured YBa₂Cu₃O _x surfaces are identified, showing that a Ba-oxide layer forms the stable surface. This Ba-oxide-surface coats Cu-oxide and Y-oxide layers yielding so an intrinsically insulating surface layer of about 1 nm thickness. In superconducting cuprates a metallic Ba-level shift occurs as compared to the Ba in oxides or cuprate surfaces or insulating cuprates, whereas Y does not show such a metallic chemical shift in the transition to superconducting cuprates. This asks new questions about charge transfer and superconducting interaction in the grains and the coupling between them.