First real-time measurement of the evolving 2H/1H ratio during water evaporation from plant leaves

We have studied the temporal behaviour of the deuterium isotope ratio of water vapour emerging from a freshly cut plant leaf placed in a dry nitrogen atmosphere. The leaf material was placed directly inside the sample gas cell of the stable isotope ratio infrared spectrometer. At the reduced pressure ( approximately 40 mbar) inside the cell, the appearance of water evaporating from the leaf is easily probed by the spectrometer, as well as the evolving isotope ratios, with a precision of about 1 per thousand. The demonstration experiment we describe measures the 2H/1H isotope ratio only, but the experiment can be easily extended to include the 18O/16O and 17O/16O isotope ratios. Plant leaf water isotope ratios provide important information towards quantification of the different components in the ecosystem water and carbon dioxide exchange.     

Zur Eigenwerttheorie einer Klasse symmetrischer Operatoren

Ohne ZusammenfassungHerrnErich Kamke zum 70. Geburtstag am 18. August 1960 gewidmet     

Anwendung von Erneuerungstheoremen und Taubersätzen für eine Verallgemeinerung der Erneuerungsprozesse

Ohne ZusammenfassungHerrn Werner Meyer-König zum 60. Geburtstag am 26.5. 1972 gewidmet     

Zur Eigenwerttheorie einer Klasse Rieszscher Operatoren

Ohne Zusammenfassung     

Approximation durch Folgen linearer positiver operatoren

Ohne Zusammenfassung     

Martingales and the Robbins-Monro procedure in D[0, 1]

The Robbins-Monro procedure for recursive estimation of a zero point of a regression function f is investigated for the case f defined on and with values in the space D[0, 1] of real-valued functions on [0, 1] that are right-continuous and have left-hand limits, endowed with Skorohod's J₁-topology. There are proved an a.s. convergence result and an invariance principle where the limit process is a Gaussian Markov process with paths in the space of continuous C[0, 1]-valued functions on [0, 1]. At first the case f(x) ≡ x, i.e., the case of a martingale in D[0, 1], is treated and by this then the general case. An application to an initial value problem with only empirically available function values is sketched.