Analysis of Flatness Measurement and Form Stability of a Granite Surface Plate

It is rather difficult to compare quantitatively flatness measuring results of one and the same object (e.g. in case of a long-term stability investigation) or the results of a series of products (e.g. from the same machinetool in order to indicate machinetool-influences). An extension of a computerprogram applied to the evaluation of flatness measurement (as described in the CIRP-Annals, vol. 26 (1977), no.1), separates the form deviations of a surface into a geometrical part and a random part.\ud The geometric part consists of a best-fitting non-flat, reference plane, composed of the single curvature of a sphere and the double curvature of a real twisted plane. Three parameters (the dimensionless curvature parameters of sphericity and torsion, together with the direction of the torsionvector) are able to characterize the geometrical part of the surface; a fourth one is a measure for the random part.\ud Advantages of the method are demonstrated with the aid of a long-term investigation into the form stability of a granite surface plate.\ud Another extension of the program makes it now possible to measure surfaces with non-rectangular contours in the same way as it is being done in case of a rectangular surface plate.\u

Complex maps without invariant densities

We consider complex polynomials $f(z) = z^\ell+c_1$ for $\ell \in 2\N$ and $c_1 \in \R$, and find some combinatorial types and values of $\ell$ such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when $\ell$ sufficiently large and also for a class of `long-branched' maps of any critical order.Comment: Typos corrected, minor changes, principally to Section

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Annual Survey of Virginia Law: Workers\u27 Compensation

The Annual Survey last addressed Virginia Workers\u27 Compensation law in 1992. The Virginia Workers\u27 Compensation Commission [the Commission] decides almost 1500 decisions a year and, on average, 300 of these are appealed to the Court of Appeals of Virginia. Consequently, this article discusses only the most significant developments in workers\u27 compensation between January 1993 and June 1995. In doing so, the article attempts to highlight areas of controversy and inconsistency

Public priorities and expectation of climate change impacts in the United Kingdom

Irrespective of the success of climate mitigation efforts, societies worldwide face the challenge of adapting to a changing climate. In this paper, we examine UK residents’ expectations of future threats and opportunities associated with climate change impacts, along with willingness to prioritise different climate change impacts for investment. Using a national survey (n = 2007), we report on three main findings. First, UK residents tend to expect threats related to flooding and wet weather to be more likely and concerning than heat extremes or opportunities. Second, UK residents’ expectations of climate change impacts do not align with expert assessments, especially showing lower estimates of heat-related threats as compared to experts. Third, willingness to allocate resources to potential climate change impacts tends to be more strongly associated with anticipated concern should they occur than climate change belief or the expected likelihood of them occurring. We discuss the implications of our findings for policies and communications about climate change adaptation in the UK and elsewhere

How is cervical cancer screening information communicated in UK websites? A cross-sectional analysis of content and quantitative presentation formats

Objectives: To investigate whether UK websites about cervical cancer screening targeted to the public include (1) information about benefits and risks of screening, possible screening results and cervical cancer statistics, (2) quantitative presentation formats recommended in the risk communication literature and (3) appeals for participation and/or informed decision-making. Design: Cross-sectional analysis of websites using a comprehensive checklist of information items on screening benefits, risks, possible results and cervical cancer statistics. Outcome measures: We recorded the number of websites that contained each of the information items, and the presentation format used for probabilistic information (no quantification provided, verbal quantifiers only, different types of numerical formats and/or graphs). We also recorded the number of websites containing appeals for participation and/or informed decision-making. Setting: Websites were identified through the most common Google search terms used in the UK to find information on cervical screening, according to GoogleTrends and a commercial internet-monitoring programme. Two additional websites were identified by the authors as relevant. Results: After applying exclusion criteria, 14 websites were evaluated, including websites of public and private health service providers, charities, a medical society and a pharmacy. The websites mentioned different benefits, risks of screening and possible results. However, specific content varied between websites. Probabilistic information was often presented using non-recommended formats, including relative risk reductions to express screening benefits, and verbal quantifiers without numbers to express risks. Appeals for participation were present in most websites, with almost half also mentioning informed decision-making. Conclusions: UK websites about cervical cancer screening were generally balanced. However, benefits and risks were presented using different formats, potentially hindering comparisons. Additionally, recommendations from the literature to facilitate understanding of quantitative information and facilitate informed decisions were often not followed. Designing websites that adhere to existing recommendations may support informed screening uptake

The multipliers of periodic points in one-dimensional dynamics

It will be shown that the smooth conjugacy class of an $S-$unimodal map which does not have a periodic attractor neither a Cantor attractor is determined by the multipliers of the periodic orbits. This generalizes a result by M.Shub and D.Sullivan for smooth expanding maps of the circle