Coupled systems of nonlinear wave equations and finite-dimensional lie algebras I

We study coupled systems of nonlinear wave equations from the point of view of their formal Darboux integrability. By making use of Vessiot's geometric theory of differential equations, it is possible to associate to each system of nonlinear wave equations a module of vector fields on the second-order jet bundle — the Vessiot distribution. By imposing certain conditions of the structure of the Vessiot distributions, we identify the so-called separable Vessiot distributions. By expressing the separable Vessiot distributions in a basis of singular vector fields, we show that there are, at most, 27 equivalence classes of such distributions. Of these, 14 classes are associated with Darboux integrable nonlinear systems. We take one of these Darboux integrable classes and show that it is in correspondence with the class of six-dimensional simply transitive Lie algebras. Finally, this later result is used to reduce the problem of constructing exact general solutions of the nonlinear wave equations understudy to the integration of Lie systems. These systems were first discovered by Sophus Lie as the most general class of ordinary differential equations which admit nonlinear superposition principles.     

On Two Theorems about Symplectic Reflection Algebras

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl Algebra W, and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP (2n)) and, as a consequence, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg (Invent Math 147:243–348, 2002), which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones). Dedicated to my friend J.-C. Cortet.     

Optical coherence tomography based imaging of dental demineralisation and cavity restoration in 840 nm and 1310 nm wavelength regions

In this paper, a study of in-house built optical coherence tomography (OCT) system with a wavelength of 840 nm for imaging of dental caries, progress in demineralisation and cavity restoration is presented. The caries when imaged with the 840 nm OCT system showed minute demineralisation in the order of 5 μm. The OCT system was also proposed to study the growth of lesion and this was demonstrated by artificially inducing caries with a demineralisation solution of pH 4.8. The progress of carious lesion to a depth of about 50–60 μm after 60 hours of demineralisation was clearly observed with the 840 nm OCT system. The tooth samples were subjected to accelerated demineralisation condition at pH of approximately 2.3 to study the adverse effects and the onset of cavity formation was clearly observed. The restoration of cavity was also studied by employing different restorative materials (filled and unfilled). In the case of restoration without filler material (unfilled), the restoration boundaries were clearly observed. Overall, results were comparable with that of the widely used 1310 nm OCT system. In the case of restoration with filler material, the 1310 nm OCT imaging displayed better imaging capacity due to lower scattering than 840 nm imaging.     

Ein Beitrag zur radiometrischen Bestimmung des Ziehsteinverschleißes beim Ziehen von Stahldraht

Es wird ein zuvelässiges und sehr empfindliches radiometrisches Verfahren zur Bestimmung des Ziehsteinverschleiβes beim Ziehen von Stahldraht beschrieben. Im Vergleich zu den in der Literatur angegebenen radiometrischen Meβverfahren ist das behandelte Verfahren weniger zeitaufwending und gestattet es, bei einem vertretbaren Aufwand gröβere Verscuhsreihen durchzuführen. Mit Hilfe dieser Methode ist es möglich, langwierige groβtechnische Versuche zu umgehen und gleichzeitig eine wesentlich exaktere Aussage ūber den Verschleiβ unter verschiedenen Ziehbedingungen zu erhalten.     

Darstellung und Weitergabe der Expositionseinheit Röntgen im DAMW Teil II: Die Hohlraum-Ionisationskammern für 60Co- und 137Cs-γ-Strahlung

Nachdem in ersten Teil der Arbeit eine Beschreibung der Normalmeβeinrichtungen (Freiluft-Ionisationskammern) des DAMW zur Darstellung der Einheit der Exposition für den Energiebereich der Röntgenstrahlung erfolgte, werden hier die entsprechenden Einrichtungen für die Gammastrahlung von ⁶⁶Co und ¹³⁷Cs behandelt. Grundlage für die definitionsgemäβe Bestimmung der Einheit bilden dabei verschidene Hohlraum-Inoisationskammern aus Reinstgraphit, deren Aufbau erläwtert wird. Sie sind vom zylindrischen Typ und haben Meβvolumina von ca. 2 cm³, 8 cm³ cm³ und 100 cm³. Als Ladungsmeβeinrichtung wird ebenfalls ein elektromctrischer Fotozellenkompensator verwendet. Die Bestimmung der in kollimierten Strahlenbündeln notwendigen Korrektionsfaktoren wird im einzelnen behandelt. Der maximale Fehler bei der Darstellung der Einheit der Exposition betrāgt 2%.     

Determining Optimum Conditions for Measuring by Gamma-ray Backscattering

The paper is concerned on the calculation of the optimal thickness of measured material from the point of view of measurement error. The minimum relative error of a measurement is determined as a function of the gamma radiaiton linear attenuation coefficient and the thickness of the material used. Various types of fluctuations are considered and attention is paid to the background detected in the same arrangement without measured material. The results are summarized into simple figures. The conclusion is made that the optimal thickness increases with poorer quality of the measuring instrument.     

Aktivierungsanalytische Untersuchung von Zirkoniumlegierungen

Durch Aktivierungsanalyse mit Reaktorneutronen (zerstörungsfrei und mit chemischer Aufarbeitung) sowie mittels zerstörungsfreier Untersuchungen an einem Neutronengenerator wurden O, Al, Si, P, Mn, Cu, Nb, Mo, Cd, Ti, Cr und Hf in Zirkoniumlegierungen bestimmt.     

Separation of Macroamounts of Metal Pairs – Part 1. Separation of Cadmium and Cobalt

The separation factors of cadmium and cobalt were performed on varying cadmium, zinc and cobalt concentrations in the original aqueous solution. A long chain amine (Amberlite LA-2) and an organophosphorus solvent (TBP) have been investigated. In most cases the values of the separation factor increases with the increase of metal concentration in the aqueous phase. The various possibilities of chemical and radiochemical separations of the metal pair are reported.