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“.      

Fault-aware Communication Mapping for NoCs with Guaranteed Latency

As feature sizes shrink, transient failures of on-chip network links become a critical problem. At the same time, many applications require guarantees on both message arrival probability and response time. We address the problem of transient link failures by means of temporally and spatially redundant transmission of messages, such that designer-imposed message arrival probabilities are guaranteed. Response time minimisation is achieved by a heuristic that statically assigns multiple copies of each message to network links, intelligently combining temporal and spatial redundancy. Concerns regarding energy consumption are addressed in two ways. First, we reduce the total amount of transmitted messages, and, second, we minimise the application response time such that the resulted time slack can be exploited for energy savings through voltage reduction. The advantages of the proposed approach are guaranteed message arrival probability and guaranteed worst case application response time.     

Similarity retrieval of iconic image database

The perception of spatial relationships among objects in a picture is one of the important selection criteria to discriminate and retrieve the images in an iconic image database system. The data structure called 2D string, proposed by Chang et al., is adopted to represent symbolic pictures. The 2D string preserves the objects' spatial knowledge embedded in images. Since spatial relationship is a fuzzy concept, the capability of similarity retrieval for the retrieval by subpicture is essential. In this paper, similarity measure based on 2D string longest common subsequence is defined. The algorithm for similarity retrieval is also proposed. Similarity retrieval provides the iconic image database with the distinguishing function different from a conventional database.     

Copper-zirconium tungstate composites exhibiting low and negative thermal expansion influenced by reinforcement phase transformations

A fully-dense Cu-75 vol pct ZrW₂O₈ metal matrix composite was fabricated by hot isostatic pressing of Cu-coated ZrW₂O₈ particles. A small amount of the high-pressure γ-ZrW₂O₈ phase was created during the cooldown and depressurization following densification; near complete transformation to γ-ZrW₂O₈ was achieved by subsequent cold isostatic pressing. The thermal expansion behavior of the composite between 25°C and 325°C was altered by the cold isostatic pressing treatment, and also depended on the length of time that had passed between thermal cycles. The measured thermal expansion coefficients within specific temperature ranges varied from −6·10⁻⁶ K⁻¹ to far above the thermal expansion coefficient of the copper matrix. The complex temperature-dependent expansion/contraction behavior could be justified by considering the evolution of phase transformations taking place in the ZrW₂O₈ phase, which were observed by in-situ synchrotron X-ray diffraction measurements.     

Analytical results for the plectonemic response of supercoiled DNA

The DNA molecule is modeled as an elastic rod with bending and twisting rigidities, subjected to external tension and twist applied at one end, the other end being clamped. We study the plectonemic equilibrium of such a rod, taking into account the impenetrability constraint. Numerical solutions of this boundary value problem have previously shown that purely elastic models can reproduce the supercoiling response of the DNA molecule. Using a variational approach, we derive analytical formulae for the elastic response of the filament, and extend former numerical results.     

Off-Site Exposure to Respirable Aerosols Produced during the Disk-Incorporation of Class B Biosolids

Field experiments were conducted at a Class B biosolids land application site in central Arizona to measure, model, and source-track the off-site transport of aerosols emitted when biosolids were disk-incorporated into soils. Real-time PM10 monitoring provided time-resolved aerosol information sufficient for verifying both off-site concentration and off-site exposure time model results. Under the conditions considered and at a distance of 165?m from the aerosol source, biosolids disk-incorporation resulted in an intermittent exposure to biosolids-derived aerosol concentration between 15 and 40?μg/m3 and an inhalable biosolids dose between 2 and 8?μg. Transport modeling predicted that these doses will decrease with increasing wind speed. In addition, three DNA sequence-based biosolids source tracking methods were applied to aerosol samples and confirmed the presence of biosolids in aerosols at 5, 65, and 165?m from the aerosol source. Field measurements and modeling indicate that the nature of biosolids-derived aerosol exposure is a series of intermittent high concentration puffs, rather than a continuous low concentration.