Incomplete data problems in X-ray computerized tomography

Summary In the present paper we study truncated projections for the fanbeam geometry in computerized tomography. First we derive consistency conditions for the divergent beam transform. Then we study a singular value decomposition for the case where only the interior rays in the fan are provided, as for example in region-of-interest tomography. We show that the high angular frequency components of the searched-for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition.The work of the authors was supported by the Deutsche Forschungsgemeinschaft under grant Lo 310/2-4     

Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.     

Sliding spark spectroscopy

Summary A new analytical radiation source combined with fiber optics linked to a diode array detection device with modified software is described. The direct-reading spectrometer simultaneously covers the wavelength range 185–510 nm with a spectral resolution of <1.5 nm. Intense optical emission is observed when positionally stable high-current surface sparks supplied by a pulse-generator with definite discharge parameters (max. 800 Ampere/pulse) are sliding over compact non-conductive materials such as plastics, glasses, quartz filters or powder pellets. Substrate vaporization, ionization and excitation processes in the surface discharge plasma channel generate emission corresponding to neutral and ionic states. The spectra are essentially composed of lines emitted by the electrode material (e.g. copper, silver), from the substrate under investigation, radiation continuum as well as structured background from the surrounding air atmosphere. Due to the occurrence of emission lines of reactive fillers, inorganic pigments and stabilizers, a rapid multi-element screening method is demonstrated. A rapid identification system (mix-up test) of PVC or fire-retardant thermoplastics within one second has been realized from the atomic emission line intensity originating from the sputtered copper electrode material according to its increased volatility in the presence of chlorine (modified Beilstein test).Puls-Plasma-Technik GmbH, Dortmund     

Bemerkungen zur Synthese von 3-Aminotoluol-5-sulfonsäure und 2-Aminotoluol-3-sulfonsäure

Some comments on the synthesis of 3-aminotoluene-5-sulfonic acid and 2-aminotoluene-3-sulfonic acid. Sulfonation of 3-nitrotoluene ( 5 ) yields predominantly the unsymetrical isomer 5-nitrotoluene-2-sulfonic acid ( 7 ), and lesser amounts of 5-nitrotoluene-3-sulfonic acid ( 6 ), previously reported as the major product. The desired 5-aminotoluene-3-sulfonic acid ( 3 ) was synthesized in preparative amounts from 6-aminotoluene-3-sulfonic acid (4) via the following sequence of reactions: diazotation and Sandmeyer replacement of 6-chlorotoluene-3-sulfonic acid ( 13 ), nitration of the sulfonyl chloride 14 under suitable conditions to give isomer free 6-chloro-5-nitrotoluene-3-sulfonyl chloride ( 15 ), hydrolysis to the sulfonic acid 16 and finally, simultaneous hydrogenolysis and reduction to 3 . The isomeric 7 was unequivocally prepared from 2-amino-5-nitrotoluene ( 9 ) via two routes: (1) diazotation, Sandmeyer thiocyanatation to 5-nitro-2-thiocyanatotoluene ( 10 ), Na₂S reduction to the di(2-methyl-4-nitro-phenyl)-disulfide ( 11 ), treatment with nitric acid and chlorine to give 5-nitrotoluene-2-sulfonyl chloride ( 12 ) and finally alkaline hydrolysis to 7 ; (2) Meerwein's SO₂ treatment of the diazonium salt derived from 9 leads directly to 12 and thence to 7 . 2-Aminotoluene-3-sulfonic acid ( 1 ) was prepared from the key intermediate 3-amino-2-nitrotoluene ( 18 ) via the same two routes used to prepare 7 from 9 . Both reaction sequences provided 2-nitrotoluene-3-sulfonly chloride, the hydrolysis product of which was reduced to 1 . Intermediate 18 was prepared in the following four steps from m-toluic acid ( 19 ): nitration to the 2-nitroderivative ( 20 ), whose acid chloride ( 21 ) was converted to 2-nitro-m-toluamide ( 22 ), and Hoffmann rearrangement to 18 .