Thomas Fincke und die <Emphasis Type="Italic">Geometria rotundi</Emphasis>

Thomas Fincke (January 6^th, 1561–April 24^th, 1656), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be „abreast of the mathematics of his time“.      

Bemerkungen zu “Himmelsbeobachtungen in karolingischer Zeit

Additional remarks are given for the data of auroras during the earlier centuries.     

Review on testers for measuring flow properties of bulk solids

 The author was asked by the International Fine Particle Research Institue (IFPRI) to write a critical review on shear testers for IFPRI-members. The review was delivered to IFPRI in summer 1999. Following the contract with IFPRI it was not allowed to publish the review elsewhere for at least two years. Granular Matter invited the author to submit the review in the original form; during the refereeing process (besides other changes) it turned out that some remarks should be added here for clarification: - Since 1999, the author is not aware of a really new device for testing bulk solid properties, which could lead to a change of the general comments and conclusions provided in the review. It was argued, that the review is referring too much to the work of Jenike, while the works of Johanson and Peschl were not adequately cited. Both are excellent engineers with a lot of experience, but their basic ideas are not available in published form, and if, they are not set in relation to alternative approaches so that an objective comparison in detail would be a future research issue rather than a topic in this report. A discussion on the influence of electrostatic charges was missing. There hardly is an influence, since the particles are in continuous contact. Only with non-conducting plastic particles electrostatic charges could cause problems. But no relevant experiments and results are known. In closed systems, the effect of electric charges is thus mainly neglected, but it is clear that electrostatic forces are eminent in flows with a free surface – an issue not addressed in this review. Received: 1 November 2002     

The stiffness matrix in elastically articulated rigid-body systems

Discussed in this paper is the Cartesian stiffness matrix, which recently has received special attention within the robotics research community. Stiffness is a fundamental concept in mechanics; its representation in mechanical systems whose potential energy is describable by a finite set of generalized coordinates takes the form of a square matrix that is known to be, moreover, symmetric and positive-definite or, at least, semi-definite. We attempt to elucidate in this paper the notion of “asymmetric stiffness matrices”. In doing so, we show that to qualify for a stiffness matrix, the matrix should be symmetric and either positive semi-definite or positive-definite. We derive the conditions under which a matrix mapping small-amplitude displacement screws into elastic wrenches fails to be symmetric. From the discussion, it should be apparent that the asymmetric matrix thus derived cannot be, properly speaking, a stiffness matrix. The concept is illustrated with an example.     

Characterization and optimization of linearly tapered slot antenna pattern

A parametric study of linearly tapered slot antenna (LTSA) in air and a method for optimization of its pattern are presented. A method of moments code is utilized to investigate the behavior of LTSA’s as the length, height and the taper angle varies. It is shown that the antenna pattern can be improved using a top layer of dielectric material with varying permittivity.     

The Continuous Interpolating Self-organizing Map

The self-organizing map (SOM) [5] provides a general data approximation method which is suitable for several application domains. The topology preservation is an important feature in data-analysis and may also be advantageous for the evaluation of the data in a function approximation or regression task. For this reason the interpolated self-organizing map (I-SOM) adds an output layer to the SOM architecture which computes a real valued output vector. This paper presents an extension of I-SOM towards a continuous interpolation. It is compared to RBF and to the parametrized self-organizing map.     

Quasi-optical measurement of complex dielectric constant at 300 GHz

A two beam interferometer in the Martin-Puplett configuration is used to determine the complex dielectric constant at 300 GHz of teflon, TPX-plastics, SPECTRALON and paraffin waxes with melting temperatures of 48° C and 72° C, respectively. The design of the quasi-optical system leads to a constant beam diameter at the power detector independent of path delay and frequency. The power detector signal is recorded not only along one period but over about 50 periods. A spectrum estimation routine allows to determine more exactly amplitude and phase angle of the signal. A basic problem is noticed: imperfect detector and source match cause harmonic distortion of the power detector signal. The effects on processing the loss tangent and the invalidation are shown. Finally loss tangent and dielectric constant are determined indirectly by optimizing an equivalent microwave circuit using a commercial available microwave design system to take multiple reflections and losses in consideration.