A spectral Paley-Wiener theorem

The Fourier inversion formula in polar form is \(f(x) = \int_0^\infty {P_\lambda } f(x)d\lambda \) for suitable functionsf on ? ⁿ , whereP _λ f(x) is given by convolution off with a multiple of the usual spherical function associated with the Euclidean motion group. In this form, Fourier inversion is essentially a statement of the spectral theorem for the Laplacian and the key question is: how are the properties off andP _λ f related? This paper provides a Paley-Wiener theorem within this avenue of thought generalizing a result due to Strichartz and provides a spectral reformulation of a Paley-Wiener theorem for the Fourier transform due to Helgason. As an application we prove support theorems for certain functions of the Laplacian.     

SENSITIZED PHOTOOXYGENATION ACCORDING TO TYPE I MECHANISM (RADICAL MECHANISM) — PART III. EXPERIMENTS WITH CONTINUOUS ILLUMINATION

Abstract— The photochemical reaction in the system thionine (sensitizer), allylthiourea (ATU, acceptor), and oxygen was studied with continuous illumination. In oxygen-free aqueous solution thionine is photoreduced to leucothionine. With oxygen, however, a photooxygenation of the acceptor takes place. At the same time the quantum yield of the bleaching reaction of thionine decreases markedly in comparison with that of the oxygen-free solution. At about 100 sec after the beginning of illumination, the overall quantum yield of the bleaching reaction diminishes further because the leucothionine formed during the reaction now becomes transformed into thionine. The quantum yields do not change significantly over the range of oxygen concentrations studied (initial concentration 1 × 10^-5 to 5 × 10^-5 M ). In addition they are independent of the light intensity. The influence of the pH and the acceptor concentration were also investigated.
The sensitizer is not only bleached reductively, but is also partly destroyed by oxidation. The results are in agreement with the reaction scheme elucidated by flash photolysis measurements.
In accordance with this reaction scheme, the primary reaction (a) of the reductive bleaching of the sensitizer, (b) of the photooxygenation of the acceptor and (c) of the oxidative destruction of the sensitizer, is identical in all cases. This process is the redox reaction between the sensitizer triplet and the acceptor, where a semithionine and an ATU-radical are formed. The reaction represents an example of a Type I photooxygenation according to the notation of Gollnick.     

Determination of the sulfur components of gasoline streams by capillary column gas chromatography with sulfur chemiluminescence detection

A method using a sulfur chemiluminescence detector (SCD) has been developed for the qualitative and quantitative determination of sulfur components in stabilized gasoline-range process streams, including blended gasolines containing between 1 and > 4000 ppm total sulfur. The detection limit per sulfur component was approximately 50 ppb. On-column injection was employed for optimum precision and accuracy. A new probe material was found which did not soften under FID operating conditions. A new method, using a hydrogen sulfide permeation tube, was developed for rapid alignment of the probe in the FID.     

Recherches dans la série des cyclitols XXXVII Etude par spectrométrie de masse

Low resolution mass spectra of cyclohexane-triols, -tetrols, -pentols and -hexols and of some of their deuterium labelled derivatives have been measured. The results indicate that for some geometrical isomers quantitative differences between ion intensities are significant, allowing to deduce the stereochemistry of the molecule from its mass spectrum. In all these compounds the electron impact induced elimination of water occurs mainly by interaction between OH groups. There is a correlation between the relative abundance of (M – H₂O)⁺ and (M ?2 H₂O)⁺ ions and the number of axial hydroxyls in the more stable conformation of the molecule. Difficulties encountered in deducing fragmentation patterns, and determination of number and position of deuterium atoms in the molecule of ms-inositol are discussed.