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“.      

Multivariate Analysis of Finnish Dialect Data An Overview of Lexical Variation

During the process of writing a comprehensive dictionary ofFinnish dialects, a large set of maps describing the regionaldistribution of the dialect words have been compiled in electronicform. In this article, we set out to analyse this corpus ofdata in order to gain new insight on the variation of Finnishdialects. We use a wide range of multivariate data analysismethods, including principal components analysis, independentcomponents analysis, clustering, and multidimensional scaling.We explain how to preprocess the data to overcome the problemof uneven sampling caused by the way the data has been collected.We discuss the results obtained by these methods and comparethem to the traditional view of Finnish dialect groups.     

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.     

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.     

Betriebsmittelbezogene Lastmodellierung in Verteilungsnetzen

Übersicht Der Betriebszustand eines Verteilungsnetzes wird durch die Strombelastung aller Betriebsmittel beschrieben. Mit Hilfe einer statischen Estimationsmethode werden aus einzelnen Messungen und der Kenntnis der Verbrauchsdaten typische Verbraucherkurven (TVK) berechnet, die das elektrische Verhalten verschiedener Verbrauchergruppen widerspiegeln. Auf dieser Basis ist eine betriebsmittelbezogene Lastmodellierung an beliebigen Betriebsmitteln in Abhängigkeit der Verbraucherzusammensetzung unter Berücksichtigung externer Einflüsse wie der Temperatur möglich. Die so gewonnenen Belastungsverläufe erlauben eine Beschreibung des Netzzustands in den Verteilungsnetzen.

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Bus load modelling in distribution systems

Contents The operating state of a distribution system is determined by the bus load current. Based on individual substation measurements and the load composition typical load curves are calculated using statistical estimation theory. These typical load curves describe the electrical behaviour of the different load types (e.g. household, storage heating, commerce etc.). As soon as the typical load curves are determined it is possible to calculate the bus load current in any substation taking external influences such as temperature into consideration. The bus load current serve as load models which completely describe the operating state of the distribution system.

     

Finite element modelling of calendering — some aspects of the effects of temperature gradients and structure inhomogeneities

The compression of a paper web in a calender nip has been simulated using the finite element method. The mechanical properties of the paper were allowed to vary in the thickness and machine directions of the web. This was done in order to model the influence of temperature gradients as well as density variations (due to the presence of fibre floes) on the deformation behaviour in the nip. Paper was assumed to be an elastic-plastic material exhibiting strain hardening. The yielding behaviour was governed by the Drucker-Prager yield condition. Simulations of the deformation behaviour when paper was subjected to a temperature gradient, clearly revealed that the deformation gradually became more concentrated towards the surface layers as the temperature of the surface increased. This is in accordance with experimental results which indicate that temperature-gradient calendering promotes the surface properties, whereas the bulk of the structure is preserved. Modelling the deformation behaviour of a structure containing density variations reveals that the paper may contain an inhomogeneous strain distribution after unloading, i.e. after passage through the nip.