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.     

Mapping rule-based systems onto multicomputers using simulated annealing

In this paper, we present a static load balancing method for mapping production rules in an expert system onto processors of a message-passing multicomputer. The method uses simulated annealing to achieve a nearly optimal allocation of production rules onto processor nodes. The approach balances the initial rule distribution to avoid higher communication demand among processor nodes at run time. A formal mapping model is developed and a new cost function is defined for the annealing process. New heuristic swap functions and cooling policies are provided to ensure the quality of the annealing process. A software load balancing package, SIMAL, was implemented on a SUN workstation to carry out the benchmark experiments. The overhead associated with this mapping method is O(m In m), where m is the number of rules in the production system. Two benchmark production systems, Toru-waltz and Tourney, are mapped onto a hypercube computer with 32 nodes. Experimental benchmark results verify the effectiveness of the rule mapping method. The method can be applied for distributed artificial intelligence processing or for the parallel execution of cooperating expert systems on a message-passing multicomputer.     

Highly ordered microstructures of poly(styrene-b-isoprene) block copolymers induced by solution meniscus

Microstructures of hundreds of micron thick poly(styrene-block-isoprene) copolymer films solution-cast in a cylindrical tube with the solvent evaporation controlled were investigated by transmission electron microscope (TEM), small angle X-ray scattering (SAXS) and optical microscope (OM). In a block copolymer with cylindrical polyisoprene microdomains, the orientation of the cylinders was varied along radial direction of the cylindrical tube. Highly aligned hexagonal arrays of in-plane polyisoprene cylinders were formed with their cylindrical axis parallel to the circumference of the tube in the regimes close to the wall edge. In contrast randomly ordered microdomains were observed at the center of the tube. We have also found that the orientation depends on the solvent evaporation rate and an intermediate rate (∼2.3 nL/s) provides the best orientation. In the case of a block copolymer with a bicontinuous double gyroid structure, we obtained a globally ordered microstructure where [111] crystallographic direction was parallel to the circumference of the tube. For both block copolymers, the area of highly ordered arrays of nanoscopic domains is over 1 mm². Development of the orientation was explained by coupling two orthogonal fields: (1) The flow of a solution induced by strong capillary force at a meniscus between the cylindrical tube wall and the block copolymer solution and (2) the solvent evaporation.     

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.     

Algorithms in the W-Hierarchy

We show new upper bounds for problems in the W-hierarchy of fixed-parameter complexity. A crucial ingredient of our proofs is an extension to the W-RAM model, which permits more-powerful operations but remains equivalent to the original. We use the extended model to give new upper bounds for Subsetsum, Maximum Irredundant Set, and various problems concerning intersection of finite-state machines.     

Polynomial-Space Decidable Membership Problems for Recurrent Systems over Sets of Natural Numbers

A finite recurrent system over sets of natural numbers of dimension n is a pair composed of n n-ary functions over sets of natural numbers and an n-tuple of singleton sets of natural numbers. Every function is applied to the entries of the tuple and computes a set of natural numbers, that may also be empty. The results are composed into another tuple, and the process is started anew. Thus, a finite recurrent system defines an infinite sequence of n-tuples containing sets of natural numbers. The last entry of a generated n-tuple is called the output of a step, and the union of the output sets of all steps is the set defined by the finite recurrent system. Membership problems ask whether a given number is in a specified output set or in some output set. We study membership problems for special finite recurrent systems, whose functions are built from the set operations union, intersection and complementation and the arithmetical operations addition and multiplication. Sum and product of two sets of natural numbers are defined elementwise. We restrict the set of operations from which functions are built and determine the impact on the complexity of the membership problems. We focus on PSPACE-decidable membership problems and show completeness results for the complexity classes NL, NP and PSPACE.