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“.      

Local Strain Measurement within Tendon

Abstract:  Tendon is a dense connective tissue, responsible for transmitting the forces generated by muscles to the skeleton. It is composed of a hierarchical arrangement of crimped collagen fibres, interspersed with proteoglycan matrix and cells, known as tenocytes. During physiological loading, tendons are subjected to strains in the region of 5–6%, which result in the straightening and realignment of the collagen fibres, generating variable local strain fields within the tendon. This study demonstrates a technique for analysing local strains within viable tendon explants, during both loading and unloading of the tissue. Samples were strained in a custom-designed rig, allowing real-time visualisation of cell nuclei, used as local discrete markers, on a confocal microscope. Results indicated that local strains within the fascicle are smaller than the applied strains, never exceeding 1.2%, even at 8% gross applied strain. By contrast, the sliding of adjacent collagen units was recorded at each strain increment in this study, reaching a mean maximum of 3.9% of the applied displacement. Loading–unloading studies indicated that sliding behaviour is reversible up to strains of 5%, and provides the major extension mechanism within the rat-tail tendon. This technique can be extended to further analyse shearing behaviour within the matrix.     

Electrosprayed and selenized Cu/In metal particle films

Nano-particulate copper and indium metal layers of 1-2 μm have been deposited by non-vacuum techniques such as doctor blade, screen printing and electrospray using alcoholic suspension pastes. Electrospray showed a high efficiency of material usage and yielded the most uniform morphology. The metal precursor layers were subjected to a thermal treatment (500-600 °C) in selenium vapor to convert the porous metal layers into CuInSe₂ compound layers. The chemical conversion, investigated by X-ray diffraction, showed the presence of the In₂O₃ impurity phase in the precursor as well as in the selenized layers.     

Preparation and properties of heavy-metal halide glasses

We have studied the effect of In³⁺, Pb²⁺, Gd³⁺, and Cl (heavier ions) substitutions for Al³⁺, Ba²⁺, La³⁺, and F^? on the crystallization stability and UV/IR optical properties of HBLAN fluorohafnatc glasses (HfF₄-BaF₂-LaF₃-AlF₃-NaF system). We obtained stable glasses containing InF₃ and BaCl₂ instead of AlF₃ and BaF₂, respectively, and offering increased IR transmission. The presence of CCl₄ in the process atmosphere and the removal of oxygen-containing impurities via directional solidification are shown to have an advantageous effect on the optical quality of the glasses. The fluoride-chloride glasses are capable of accommodating about 1.5 times higher levels of rare-earth activators in comparison with their fluoride analogs.     

Thermal Stressed State of a Hollow Metallic Cylinder under the Action of Electromagnetic Fields in the Mode of Damped Sinusoid

We determine the temperature fields and stresses formed in a long hollow conducting cylinder under the action of pulsed electromagnetic fields specified by the values of the axial component of the vector of intensity of a uniform magnetic field on the inner and outer surfaces. We consider the case where the electromagnetic action obeys the law of damped sinusoid on the inner and outer surfaces of the cylinder.     

Evaluation of image similarity by histogram intersection

Colour is the most widely used attribute in image retrieval and object recognition. A technique known as histogram intersection has been widely studied and is considered to be effective for color‐image indexing. The key issue of this algorithm is the selection of an appropriate color space and optimal quantization of the selected color space. The goal of this article is to measure the model performance in predicting human judgment in similarity measurement for various images, to explore the capability of the model with a wide set of color spaces, and to find the optimal quantization of the selected color spaces. Six color spaces and twelve quantization levels are involved in evaluating the performance of histogram intersection. The categorical judgment and rank order experiments were conducted to measure image similarity. The CIELAB color space was found to perform at least as good as or better than the other color spaces tested, and the ability to predict image similarity increased with the number of bins used in the histograms, for up to 512 bins (8 per channel). With more than 512 bins, further improvement was negligible for the image datasets used in this study. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 265–274, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20122     

A computational analysis of LCP methods for bilinear and concave quadratic programming

The use of a sequential linear complementarity problem (SLCP) algorithm for finding a global minimum of bilinear programming problem (BLP) or a concave quadratic program (CQP) is examined. The algorithm consists of solving a sequence of linear complementarity problems (LCP). A branch-and-bound method is also considered in this study. This algorithm is based on the reformulation of a BLP into an LCP with a linear function to minimize. Computational experience with small and medium scale BLPs and CQPs indicates that the SLCP algorithm is quite efficient in finding a global minimum (or at least a solution that is quite near the optimum), but it is, in general, unable to establish that such a solution has been found. An algorithm to find a lower-bound for the BLP can overcome this drawback in some cases. Furthermore the SLCP algorithm is shown to be robust and compares favorably with the branch-and-bound method and another alternative technique.     

Algorithms for determining planar area properties from peripheral points

The determination of planar properties—cross sectional areas, centroids, moments of inertia, and so forth—plays a central role in the solution of many diverse engineering problems. Despite the increasing availability of computational power to engineers and students alike in recent years with the advent of small desktop computers, however, the traditionally laborious and error-prone methods of making these determinations, involving area decomposition or strip integration, are still being taught to the present generation of engineering students, mostly due to a lack of suitable alternative techniques. These classical methods are found to be particularly difficult to adapt to general computational algorithms. This work presents a novel approach, requiring only the peripheral points of any planar area as inputs, and is ideally suited for numerical methods. It is shown that all planar properties of technical interest can be generated, once and for all, with straightforward algorithms that are readily programmed in any scientific computing language, or adapted to typical spreadsheet formats. These algorithms are fully general and require no decision-making on the part of the user. Various worked examples are presented.