Effects of zero-filling and apodization on spectral integrals in discrete Fourier-transform spectroscopy of noisy data

The influence of noise on the standard deviation of spectral integrals is examined. Calculations assuming discrete Fourier-transform data are compared with Monte-Carlo simulations. The effects of zero-filling and apodization are examined for free-induction-decay (FID) signals and for symmetric spin-echo signals in one and two dimensions, with particular attention to features not previously presented in the literature. Findings suggest that for mild apodization, the known sensitivity enhancement due to zero-filling in either the real or the imaginary part signal [E. Bartholdi, R.R. Ernst, Fourier spectroscopy and the causality principle, J. Magn. Reson., 11 (1973) 9-19] is maintained; however, for stronger apodization filters, this enhancement can be obliterated completely. It is shown that results obtained by analysis of one-dimensional signals can be readily applied to multi-dimensional data. Furthermore, zero-filling has a negligible effect for symmetric spin-echo signals with implications for signal averaging in magnetic resonance imaging and spectroscopic imaging.     

Spectroscopic and atomic force microscopy investigations of hybrid materials composed of fullerenes and 3-aminopropyltrimethoxysilane

Fullerene based materials may open a new horizon in many fields of science. In this study we fabricated thin films of the hybrid materials formed as a result of interactions between C₆₀ fullerenes and 3-aminopropyltrimethoxysilane (APTMS). The deposition technique was a combination of spin-coating and evaporation methods. Interactions within the films were investigated by means of X-ray photoelectron spectroscopy and near edge X-ray absorption fine structure spectroscopy (NEXAFS). Surface morphology was measured by atomic force microscopy (AFM). We found that there are strong chemical reactions between the nucleophilic nitrogen atoms from APTMS and electrophilic fullerene molecules. Results of NEXAFS investigations suggest that due to direct interactions between APTMS and C₆₀ the electronic structure of the fullerene molecules changes while at the same time AFM proved that the C₆₀ molecule diameter is not altered.     

On bounded time-dependent perturbations of operator cosine functions

In this note it is shown that the Cauchy problem associated with the infinitesimal generatorA of a strongly continuous operator cosine function remains uniformly well-posed under bounded time-dependent perturbations ofA.     

Periodische operatorwertige Cosinusfunktionen

In dieser Note werden stark stetige periodische Cosinusfunktionen mit Werten im Bereich der stetigen linearen Operatoren auf einem Banachraum untersucht. Dabei ergänzen und präzisieren wir die Untersuchungen von E. Giusti. Insbesondere wird ein durchsichtiger und vollständiger Beweis eines Satzes von Giusti über die Charakterisierung periodischer Cosinusfunktionen mit Hilfe von Spektraleigenschaften ihres infinitesimalen Erzeugers angegeben.     

Estimation of lake water—groundwater interactions in meromictic mining lakes by modelling isotope signatures of lake water

Abstract

A method is presented to assess lake water–groundwater interactions by modelling isotope signatures of lake water using meteorological parameters and field data. The modelling of δ¹⁸O and δD variations offers information about the groundwater influx into a meromictic Lusatian mining lake. Therefore, a water balance model is combined with an isotope water balance model to estimate analogies between simulated and measured isotope signatures within the lake water body. The model is operated with different evaporation rates to predict δ¹⁸O and δD values in a lake that is only controlled by weather conditions with neither groundwater inflow nor outflow. Comparisons between modelled and measured isotope values show whether the lake is fed by the groundwater or not. Furthermore, our investigations show that an adaptation of the Craig and Gordon model [H. Craig, L.I. Gordon. Deuterium and oxygen-18 variations in the ocean and the marine atmosphere. In Stable Isotopes in Oceanographic Studies and Paleotemperature, Spoleto, E. Tongiorgi (Ed.), pp. 9–130, Consiglio Nazionale delle Ricerche, Laboratorio di Geologia Nucleare, Pisa (1965).] to specific conditions in temperate regions seems necessary.