Changes in the kurtosis parameter of super-Gaussian beams passing through a spherically aberrated lens

Based on the Collins formula and irradiance moments definition, the propagation of the kurtosis parameter of super-Gaussian beams through a spherically aberrated lens is studied. Detailed numerical results are given. It is shown that, as compared with aberration-free super-Gaussian beams, the profile of spherically aberrated super-Gaussian beams can be leptokurtic, mesokurtic or platykurtic, depending on the aberration and propagation distance. The results for the spherically aberrated Gaussian beams can be dealt with as a special case treated in this paper. Finally, the advantage of our method is pointed out.     

Anomale änderungen physikalischer Eigenschaften beim heterogenen Zerfall übersättigter Fe-Ni-Cu-Legierungen

Zusammenfassung Einige charakteristische ?nderungen physikalischer Werkstoffeigenschaften beim heterogenen Zerfall übers?ttigter Mischkristalle werden am Beispiel der fl?chenzentrierten Eisen-Nickel-Kupfer-Legierungen beschrieben. Bei der Behandlung des Einflusses der Ausscheidungsvorg?nge auf die Rekristallisationserscheinungen tritt die Bedeutung des übers?ttigungsgrades der zerfallenden festen L?sung für den Ablauf dieser Zustands?nderungen besonders klar zutage. Kritische Stadien der Ausscheidung und der Koagulation der heterogenen Phasen sind bei diesen Legierungen für die Erzeugung besonders hochwertiger magnetischer Eigenschaften verantwortlich. Der vorliegende Bericht wurde von Herrn Prof., Dr. Wo. Ostwald angeregt. Für das diesem Arbeitsgebiet entgegengebrachte Interesse m?chte ich Herrn Prof. Ostwald meinen besten Dank aussprechen.     

Mathematical Modeling, Control, Computer Simulation and Laboratory Experiments of a Spatial Servopneumatic Parallel Robot

In this paper, the special construction of a parallel robot, called spatial servopneumatic multi-axis test facility, will be discussed. The investigations include the following aspects: (i) the laboratory set-up of the robot, (ii) various results obtained in laboratory experiments, taking into account quite different control algorithms and command-input signals, (iii) a comparison of the laboratory experiments with the computer simulations of Part I of this paper, and ({vi}) a quality check of the results compared with the cost of the different controller realizations. The results of both the computer simulations and the laboratory experiments show: (i) The dynamic behavior of the parallel structure can be tremendously improved by using sophisticated nonlinear control algorithms. (ii) This improvement has to be paid by a drastically increased amount of work for deriving the model equations and control algorithms, and by augmented hardware cost of the sensing elements and controller electronics. (iii) Carefully developed model equations and identified model parameters provide theoretical models of the complex parallel structure that are very close to reality. This enables the design engineer to systematically investigate constructive alternatives of the design parameters, sensor and actuator concepts, and control strategies of the MAP prior to their hardware realization.This work has been supported by the German Science Foundation (DFG) under Contract No. Ha 1666/6-3.     

A finiteness result for Heegaard splittings

In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of 3g−3 disjoint essential disks. These are characterized by a combinatorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to fact that in general there can exist infinitely many such systems of disks which satisfy just the Casson-Gordon rectangle condition.     

A Triangle Inequality for Measurement

We introduce the triangle inequality for measurement. This is a property that when satisfied by a measurement enables one to construct a metric on the set of elements with measure zero that yields the relative Scott topology. The naturality of this construction permits a categorical solution to the model problem in domain theory for locally compact metric spaces. The first time such a solution has been achieved.     

Beweis eines Satzes über rationale Curven

Ohne Zusammenfassung