Massenspektrometrische Untersuchungen an Azoverbindungen. II—Ermittlung thermodynamischer Größen

The Appearance potentials of azo compounds and their characteristic fragments have been measured. Using these values and the calculated values for the heat of formation of the molecules the heats of formation of molecular ions and fragment ions and the ionization potentials of the latter have been determined. From the dissociation energies it has been concluded that the azo compounds decompose via a two-step pathway.     

Zum Randverhalten der Lösungen gewisser zweidimensionaler Variationsprobleme mit freien Randbedingungen

Ohne Zusammenfassung     

Glättung differenzierbarer Räume

Ohne Zusammenfassung     

Energie-Relaxation warmer Ladungsträger in Germanium und Silizium

Experimental data on warm carrier energy relaxation times in germanium and silicon are reported. Measurements were done by the method of harmonic mixing of microwaves 1 in the temperature range between 77 and 200 °K. Relaxation times obtained forn-type germanium are in agreement with data reported byMorgan 2 as well as that ofSeeger 3 andGibson et al. 4. Measured energy relaxation times forp-type germanium as well as forn- andp-type silicon are reported here for the first time. A qualitative interpretation is given in terms of scattering by acoustic and optical phonons.     

Necessary conditions for Schatten class localization operators

We study time-frequency localization operators of the form , where is the symbol of the operator and are the analysis and synthesis windows, respectively. It is shown in an earlier paper by the authors that a sufficient condition for , the Schatten class of order , is that belongs to the modulation space and the window functions to the modulation space . Here we prove a partial converse: if for every pair of window functions with a uniform norm estimate, then the corresponding symbol must belong to the modulation space . In this sense, modulation spaces are optimal for the study of localization operators. The main ingredients in our proofs are frame theory and Gabor frames. For and , we recapture earlier results, which were obtained by different methods.

     

Formation and decomposition of chemically activated cyclopentoxy radicals from the c-C5H9 + O reaction

The formation and the decomposition of chemically activated cyclopentoxy radicals from the c-C5H9 + O reaction have been studied in the gas phase at room temperature. Two different experimental arrangements have been used. Arrangement A consisted of a laser-flash photolysis set up combined with quantitative Fourier transform infrared spectroscopy and allowed the determination of the stable products at 4 mbar. The c-C5H9 radicals were produced via the reaction c-C5H10 + Cl with chlorine atoms from the photolysis of CFCl3; the O atoms were generated by photolysis of SO2. Arrangement B, a conventional discharge flow-reactor with molecular beam sampling, was used to determine the rate coefficient. Here, the hydrocarbon radicals (c-C5H9, C2H5, CH2OCH3) were produced via the reaction of atomic fluorine with c-C5H10, C2H6, and CH3OCH3, respectively, and detected by mass spectrometry after laser photoionization. For the c-C5H9 + O reaction, the relative contributions of intermediate formation (c-C5H9O) and direct abstraction (c-C5H8 + OH) were found to be 68 +/- 5 and 32 +/- 4%, respectively. The decomposition products of the chemically activated intermediate could be identified, and the following relative branching fractions were obtained: c-C5H8O + H (31 +/- 2%), CH2CH(CH2)2CHO + H (40 +/- 5%), 2 C2H4 + H + CO (17 +/- 5%), and C3H4O + C2H4 + H (12 +/- 5%). Additionally, the product formation of the c-C5H8 + O reaction was studied, and the following relative yields were obtained (mol %): C2H4, 24%; C3H4O, 18%; c-C5H8O, 30%; c-C5H8O, 23%; 4-pentenal, 5%. The rate coefficient of the c-C5H9 + O reaction was determined relative to the reactions C2H5 + O and CH3OCH2 + O leading to k = (1.73 +/- 0.05) x 10(14) cm3 mol(-1) s(-1). The experimental branching fractions are analyzed in terms of statistical rate theory with molecular and transition-state data from quantum chemical calculations, and high-pressure limiting Arrhenius parameters for the unimolecular decomposition reactions of C5H9O species are derived.     

Deformation of Gabor systems

We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames “without inequalities” from lattices to non-uniform sets.