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“.      

The Simulation of Impact Loads on Beam-type Structures using a Pseudo-dynamic Procedure

Abstract:  This study proposes an alternate method for the analysis of beams with solid cross-section or built as a framed structure and subjected to transverse impact loads from an external striker. The procedure used in the analysis is a combination of two essential tools using pseudo-dynamic techniques. The method reported here involves only one degree of freedom for the structure modelling and assumes an elastic contact between an external striker and the beam structure, which in reality does not happen. As only one degree of freedom is considered in the analysis, some important limitations are inherent to the method proposed here. Essentially, there is the difficulty of modelling the displacement field associated with the transient structure behaviour accurately, as a consequence of fast-rate impact loads. Another difficulty faced by the method refers to a local structure behaviour associated with contact loads. The present method can deal with large displacements in transversely loaded beams associated to a collapse mechanism having a simple geometry and defined with precision from a single parameter. This ensures reasonable accuracy in the evaluation of the strain energy absorbing capacity of transversely impacted beam structures using a single degree of freedom model in a pseudo-dynamic procedure.     

Dynamics of Vibroprotective Systems with Roller Dampers of Low-Frequency Vibrations

We study low-frequency vibrations of a vibroprotective system of solid bodies formed by a roller damper and a moving load-carrying body under the action of external harmonic excitations. The dynamic equations of combined motion of the working body of the damper over the hinged roller without sliding and the load-carrying body are deduced and numerically analyzed. A new procedure is proposed for the evaluation of the optimal parameters of adjustment of roller dampers in nonlinear systems.     

Fracture Resistance of Ceramics upon Edge Chipping

Modern methods of determining fracture resistance are analyzed. The necessity of developing a crucially new method based on edge chipping of a brittle material is shown. The results of experimental studies are presented. The applicability of the method to the comparative fracture resistance evaluation of ceramics is substantiated.     

Influence of ion bombardment on the properties and microstructure of unbalanced magnetron deposited niobium coatings

The effect of the ion bombardment to unbalanced magnetron deposited, approximately 1.5 and 4.5 μm thick, Nb coatings have been investigated as the bias voltage was varied from U_B=−75 to −150 V. Increasing bias voltage increased the hardness of the coating from 4.5 to 8.0 GPa. This was associated with residual stress and Ar incorporation into the Nb lattice. Strong {110} texture developed in the samples deposited at low bias voltages, while beyond U_B=−100 V a {111} texture became dominant. However, strong {111} texture was observed only with the thicker 3Nb coatings. Secondary electron microscopy investigation of the coating topography showed fewer defects in the thicker coatings. All coatings exhibited good corrosion resistance, with the thicker coatings clearly outperforming the thinner ones. Excessive bias voltages (U_B=−150 V) was found to lead to poor adhesion and loss of corrosion resistance.     

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.     

Computer Aided Tolerance assignment

Tolerances are basic to the production of every part. This is because perfect parts cannot be produced with existing processes and machines. The determination of tolerances for the individual parts of a functional assembly is critical, but not trivial. Numerous approaches are suggested in past literature for (analytical) tolerance allocation. With the advent of total automation, more attempts are being made to computerize manual design tasks. Tolerance design, assignment and allocation can also be fully automated if the assembly function can be estimated by the computer.

In the present paper, an attempt is made to computerize tolerance assignment. A simple example of a two piece assembly, viz., a fit, is used to demonstrate the developed methodology. A feature extraction is first performed from both detail and assembly drawings. Then, probable assembly interfaces are determined using a rule based procedure. Consequently, tolerances are assigned to the basic dimensions of each feature and to the assembly interfaces using a tolerance database and user interaction. More complex analysis for tolerance allocation is also under study.     

Formaldehyde content of milk in goats fed formaldehyde-treated soybean oil-meal

Formaldehyde is used in ruminant feeding for different purposes including the protection of dietary proteins from ruminal degradation. The formaldehyde content of milk of goats fed various levels of formaldehyde-treated soybean oil-meal has been determined by using a sensitive HPLC method. Results showed a significant linear correlation between ingested formaldehyde and formaldehyde concentration in milk. About 0.02% of ingested formaldehyde was excreted in milk, as free formaldehyde.     

Analytical pyrolysis as a tool for the study of plastic coals

The technique of analytical pyrolysis has been used to characterize 40 similar mid-rank western Kentucky coals of widely differing ASTM Gieseler plasticity. Certain pyrolysis/g.c. variables were shown to correlate well with both ASTM Gieseler and isothermal plasticity. Highly plastic coals were shown to exhibit certain characteristic peaks in the 450 °C pyrogram which were absent in the pyrogram of the non-plastic coals. Two coals, representing the two extremes in plasticity, were selected for further study. After extraction with solvents such as DMF the characteristic peaks were absent in the 450 °C pyrogram of the extraction residue of the highly plastic coal. These peaks were also shown to decrease with increasing severity of air oxidation of the plastic coal. This technique appears to be a useful tool for the analysis of mid-rank plastic coals and supports the view that the substances contained in the bitumen fraction of these coals are involved in the development of the plastic state.     

Acrylonitrile-based copolymers: Synthesis,characterization, and formation of ultrafiltration membranes utilized for the immobilization of proteins

Various high molecular weight copolymers of acrylonitrile and a vinyl comonomer containing an aryl amine, a pyridine, or an aliphatic hydroxyl group were synthesized via slurry polymerization techniques so as to contain from 1 to 15 mol % functional comonomer. The comonomer content was quantitated by ultraviolet absorbance, base titration of acid polymer salts, and/or relative chemical reactivity with trichloro-s-triazine. Thin films were cast from copolymer solutions, coagulated into unsupported ultrafiltration membrances, and characterized with respect to both water permeability and pore size distribution. Analysis by size exclusion chromatography of the membrane permeate of a pool of dextran fractions yielded a continuous distribution curve for membrane pore size over the range 1.5 to 70 nm. The ultrafiltration membranes were used for protein immobilization after appropriate chemical activation. The three distinct types of functional copolymers gave comparable results for α-chymotrypsin, with protein weight loadings of 6–12% and 40–65% retention of enzymatic specific activity.