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.     

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.     

The effects of widowhood on physical and mental health, health behaviors, and health outcomes: The Women's Health Initiative.

This study examined whether widowhood was associated with physical and mental health, health behaviors, and health outcomes using a cross-sectional (N=72,247) and prospective (N=55,724) design in women aged 50-79 years participating in the Women's Health Initiative observational study (85.4% White). At baseline, married women reported better physical and mental health and generally better health behaviors than widowed women. Whereas women who remained married over the 3-year period showed stability in mental health, recent widows experienced marked impairments and longer term widows showed stability or slight improvements. Both groups of widows reported more unintentional weight loss over the 3-year period. Changes in physical health and health behaviors were inconsistent, with generally small effect sizes. Findings underscore the resilience of older women and their capacity to reestablish connections, but point to the need for services that strengthen social support among women who have difficulty during this transition. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Moderators of nonverbal indicators of deception: A meta-analytic synthesis.

In many legal proceedings, fact finders scrutinize the demeanor of a defendant or witness, particularly his or her nonverbal behavior, for indicators of deception. This meta-analysis investigated directly observable nonverbal correlates of deception as a function of different moderator variables. Although lay people and professionals alike assume that many nonverbal behaviors are displayed more frequently while lying, of 11 different behaviors observable in the head and body area, only 3 were reliably associated with deception. Nodding, foot and leg movements, and hand movements were negatively related to deception in the overall analyses weighted by sample size. Most people assume that nonverbal behaviors increase while lying; however, these behaviors decreased, whereas others showed no change. There was no evidence that people avoid eye contact while lying, although around the world, gaze aversion is deemed the most important signal of deception. Most effect sizes were found to be heterogeneous. Analyses of moderator variables revealed that many of the observed relationships varied as a function of content, motivation, preparation, sanctioning of the lie, experimental design, and operationalization. Existing theories cannot readily account for the heterogeneity in findings. Thus, practitioners are cautioned against using these indicators in assessing the truthfulness of oral reports. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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.