A new version of Bishop frame and an application to spherical images

In this work, we introduce a new version of Bishop frame using a common vector field as binormal vector field of a regular curve and call this frame as “Type-2 Bishop Frame”. Thereafter, by translating type-2 Bishop frame vectors to the center of unit sphere of three-dimensional Euclidean space, we introduce new spherical images and call them as type-2 Bishop spherical images. Frenet-Serret apparatus of these new spherical images are obtained in terms of base curve's type-2 Bishop invariants. Additionally, we express some interesting relations and illustrate two examples of our main results.     

Mechanistic studies of reactions catalysed by diamine oxidase using isotope effects

Diamine oxidase (DAO), the enzyme that is responsible for amine biodegradation in animals, plants and humans, catalyses the biotransformation of amines such as histamine (HA), putrescine, 1-phenylethylamine, tyrosine, tryptamine, serotonine and spermine. The kinetic and solvent isotope effects (SIEs) were applied to study the mechanism of the biotransformation using HA and its methylderivatives. The SIE for the biotransformation of HA, N^τ-methylhistamine and N^π-methylhistamine was found to be 3.58, 2.22 and 5.70 on V_max, and 1.58, 1.06 and 1.14 on V_max/K_M, respectively. On the other hand, the kinetic isotope effect for oxidation of stereospecifically deuterium-labelled [(α R)-²H]-N^τ-methylhistamine and [(α R)-²H]-N^π-methylhistamine was 0.69 and 0.62 on V_max, and 15.06 and 7.50 on V_max/K_M, respectively. These results demonstrate that DAO catalyses amine biotransformation by stereospecifically cleaving the αC\bond H bond in the pro-S position. Moreover, the oxidation of amine to aldehyde involves several transition states, including hybridisation change from sp³ (Schiff base) to sp² (imine), then back again to sp³ to give a final product with hybridisation sp² (aldehyde).     

Originalarbeiten Autoradiographische Untersuchungen zum Verschleiß von Stahl

Bei Verschleißuntersuchungen mit einer Stift-Scheibe-Apparalur, in der an Stelle des Stifles eine neutronenaktivierte Stahlkugel eingesetzt wird, wird in unserem Laboratorium außer Radioaktivitätsmessungen mit Zählgeräten auch die Autoradiographie angewandt. Dazu wird der Schmierstoff mit dem losen Verschleiß abgewaschen und der festhaftende (adhäsive) Verschleiß durch Kontaktautoradiographie abgebildet. Die notwendigen Expositionszeiten liegen meist bei 2 bis 3 Wochen, wobei im allgemeinen TF 14-Filmmaterial verwendet wird.

Experimentelle Beispiele werden gezeigt und diskutiert. Mit neutronenaktivierten Stahlkugdn verschiedener Abklingzeit wurde durch Verghieh von Radioaktivitätsmessungen mit Zählgeräten und Autoradiographie gezeigt, daß die Schwärzung vorwiegend von der ß-Strahlung der entstandenen Radionuklide herrührt.     

A New Approach to Pricing Double-Barrier Options with Arbitrary Payoffs and Exponential Boundaries

Abstract

We consider in this article the arbitrage free pricing of double knock-out barrier options with payoffs that are arbitrary functions of the underlying asset, where we allow exponentially time-varying barrier levels in an otherwise standard Black–Scholes model. Our approach, reminiscent of the method of images of electromagnetics, considerably simplifies the derivation of analytical formulae for this class of exotics by reducing the pricing of any double-barrier problem to that of pricing a related European option. We illustrate the method by reproducing the well-known formulae of Kunitomo and Ikeda (1992 Kunitomo, N. and Ikeda, M. 1992. Pricing options with curved boundaries. Mathematical Finance, 2: 276–298.  [Google Scholar]) for the standard knock-out double-barrier call and put options. We give an explanation for the rapid rate of convergence of the doubly infinite sums for affine payoffs in the stock price, as encountered in the pricing of double-barrier call and put options first observed by Kunitomo and Ikeda (1992 Kunitomo, N. and Ikeda, M. 1992. Pricing options with curved boundaries. Mathematical Finance, 2: 276–298.  [Google Scholar]).     

Forest fire modelling using cellular automata: application to the watershed Oued Laou (Morocco)

ABSTRACT

In this work, we consider the problem of modelling the phenomenon of forest fires using the cellular automata approach. The proposed model takes into account the main parameters that affect this phenomenon like nature and density of vegetation, humidity, wind, and altitude. We developed a decision-aided tool with JAVA which allows to analyse and format several hybrid collected data (satellite images, Digital Terrain Model) relatively to each studied area. The generated scenarios of forest fire spread in the study area will be considered as a guide for strategies in control and prevention of forest fires. As an application, we consider the watershed Oued Laou (Morocco).