Approximation of circular arcs by parametric polynomial curves

In this paper the approximation of circular arcs by parametric polynomial curves is studied. If the angular length of the circular arc is h, a parametric polynomial curve of arbitrary degree \(n \in {\mathbb{N}}\) , which interpolates given arc at a particular point, can be constructed with radial distance bounded by h ²ⁿ . This is a generalization of the result obtained by Lyche and Mørken for odd n.     

Interpolation by $G^2$ Quintic Pythagorean-Hodograph Curves

In this paper, the $G^2$ interpolation by Pythagorean-hodograph (PH) quintic curves in $\mathbb{R}^d$, $d ≥2$, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension $d$, they supply a $G^2$ quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the interpolating curve as unknowns. Although several solutions might exist, the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data case. The numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation method. Numerical examples confirm the efficiency of the proposed method.     

μ-Synchrotron radiation excited X-ray fluorescence microprobe trace element studies on spherules of the Cretaceous/Tertiary boundary transitions of NE-Mexico and Haiti samples

Synchrotron radiation, collimated to a μm scale was used for the determination of trace elements in micro-tektites and spherule material for the first time. The experimental set-up of the SXRF microprobe at beamline L at HASYLAB at DESY offers a suitable method for performing non-destructive in situ multi-element analysis focusing on spatial trace element distributions and mineral phases of the melted ejecta material from the Cretaceous/Tertiary boundary. The spatial distribution of trace elements was determined in melt inclusions as well as in phase transitions in selected parts of chlorite–smectite spherules and tektite glass material by using a beam with a diameter of 15 μm collimated with a glass capillary for line- and area scans as well as for single point measurements for elements with Z between 19 and 92. The analyzed spherules show alteration features but also zonation and carbonate inclusions, originating from the Chicxulub impact event. These initial results demonstrate the potential of μ-SXRF analysis for the discrimination of alteration and primary signals of the spherules and re-construction of their genetic evolution. It could be shown that the spherules represent a complex mixture of different materials from the subsurface at the Chicxulub impact site.     

Integrated endoscopy system for simultaneous imaging and spectroscopy for early lung cancer detection

An integrated endoscopy system for simultaneous imaging and spectroscopy was developed to facilitate more accurate and convenient detection of early lung cancers. A specially designed three-CCD camera in combination with a dedicated light source permits capture of both white-light color images and tissue autofluorescence images without the need to switch between two different cameras. A mirror with an optical fiber at its center, placed at an interim imaging plane inside the camera unit, facilitates simultaneous imaging and spectroscopy measurements in either white-light reflectance mode or fluorescence mode. The system has been successfully tested in a clinic, demonstrating a practical approach to improve both diagnostic sensitivity and specificity at the same time.     

Microwave determination of the mechanical strains in glass-reinforced plastic articles 1. Investigation of the anisotropic properties of glass-reinforced plastics in the millimeter range

Certain free-space methods of investigating the anisotropic properties of glass-reinforced plastics in the millimeter range are examined and the apparatus employed is described.     

Magnetooptical absorption of a molecular crystal in the exciton frequency range

Nonlinear absorption of a molecular crystal in an external magnetic field is considered. The exciton absorption shape functions under polarized laser radiation and a weak magnetic field, as well as the mechanisms responsible for the formation of a hysteresis loop in the dependence of the output light intensity on the applied magnetic field, were studied for the particular case of benzene. It was established that, for the magnetooptical response of the molecular crystal under study, the formation of bistable loops is inverse in character, which makes it possible to monitor and control the behavior of bistable elements in optical logics systems with an external magnetic field at a fixed illumination frequency.     

Symbolic dynamics in investigation of quaternionic Julia sets

We focus our attention on the dynamics of the simplest quaternionic quadratic function f_Q(X) = X² + Q. The discussion can be reduced to a complex parameter Q and a three dimensional subspace. The images of quaternionic Julia sets suggest a natural decomposition. We find that it can be derived from a certain symbolic dynamics giving rise to fractal fibrations. The starting point are the equators and their preimages. If the parameter Q is real, fibrations are trivial, obtained by rotation of the complex Julia set. Repeating itineraries, on the other hand, define curves connecting periodic points.     

Ein vereinfachtes Verfahren zur Anreicherung der Pyridinnucleotid-Transhydrogenase

Zusammenfassung Es wird eine Methode zur Isolierung von NADPH₂-NAD-Transhydrogenase (NADPH₂-NAD-Oxydoreduktase, TD-Transhydrogenase, EC 1.6.1.1.) beschrieben. Aus Rinderherzmitochondrien werden durch Homogenisieren in starken Digitoninlösungen^* Lipoproteidkomplexe herausgelöst, die das Ferment enthalten, dessen Aktivität jedoch schnell absinkt. Durch hochtouriges Zentrifugieren und Gelfiltration durch Sephadex G-100 wird ein digitoninfreies, in der Ultrazentrifuge einheitlich sedimentierendes Fermentpräparat hergestellt. Gegenüber dem bisherigen Verfahren¹ weist das beschriebene folgende Vorteile auf: Die Methode ist einfacher und das auf diese Weise gewonnene Protein läßt sich lyophilisieren; auch ist die Beimengung der zweiten Transhydrogenaseaktivität (NADH₂-NAD-Transhydrogenase, DD-Transhydrogenase) geringer als in Präparaten, die mit der Methode nachKaplan ¹ hergestellt werden.

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A method for the isolation of NADPH₂-NAD-transhydrogenase is described. By homogenisation in strong digitonin solutions lipoprotein complexes are dissolved from beef heart mitochondria containing the enzyme, the activity of which is yet diminishing rapidly. By High speed centrifugation and gel filtration on Sephadex G-100 a stable digitonin-free enzyme preparation uniformically sedimenting is produced.

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