Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

Phase equilibrium studies in the "MnO"-Al2O3-SiO2 system

Phase relations and the liquidus surface in the system "MnO"-Al2O3-SiO2 at manganese-rich alloy saturation have been investigated in the temperature range from 1373 to 1773 K. This system contains the primary-phase fields of tridymite and cristobalite (SiO2); mullite (3Al(2)O(3).2SiO(2)); corundum (Al2O3); galaxite (MnO.Al2O3); manganosite (MnO); tephroite (2MnO.SiO2); rhodonite (MnO.SiO2); spessartine (3MnO.Al2O3.SiO2); and the compound MnO.Al2O3.2SiO(2).

Polarised infrared and differential scanning calorimetry studies on oriented vinyl pipe materials

The molecular orientation in a conventionally extruded PVC pipe, a uniaxially oriented PVC pipe and a biaxially oriented PVC pipe has been studied via Infrared dichroism. The degree of order or crystallinity has also been studied by Differential Scanning Calorimetry and also via Infrared Spectroscopy. The fundamental structural difference between the conventional and oriented pipes was that polymer chains were preferentially aligning in the hoop direction for oriented pipes whereas they were fairly isotropic in the conventional pipe with a slight preferential alignment in the axial direction. Analysis of the C-Cl stretching mode indicated that the uniaxially oriented pipe had much higher alignment of the C-Cl bond in the axial direction than the biaxial pipe, which correlates with higher fracture toughness for circumferential cracking in the biaxial pipe. Both DSC and Infrared spectroscopy detected little change in the crystallinity or order in the oriented pipes compared to the conventionally extruded pipes. (C) 2002 Kluwer Academic Publishers.

'Why does cultural studies want history?'

Cultural studies has often been accused of maintaining too strong a focus on the contemporary and the immediate as a result of its primary interest in popular culture and the media. The role of history, such criticisms suggest, has been displaced by this contemporary emphasis. Nonetheless, much cultural studies work takes a principled stand on the necessity of historicising the products of its research. Consequently, it is worth asking, with British historian Carolyn Steedman--'why does cultural studies want history?' This article begins to answer that question through the discussion of some aspects of a specific research project within Australian cultural studies.

Impact numbers: measures of risk factor impact on the whole population from case-control and cohort studies

Objective: To describe new measures of risk from case-control and cohort studies, which are simple to understand and relate to numbers of the population at risk. Design: Theoretical development of new measures of risk. Setting: Review of literature and previously described measures. Main results: The new measures are: (1) the population impact number (PIN), the number of those in the whole population among whom one case is attributable to the exposure or risk factor (this is equivalent to the reciprocal of the population attributable risk),- (2) the case impact number (CIN) the number of people with the disease or outcome for whom one case will be attributable to the exposure or risk factor (this is equivalent to the reciprocal of the population attributable fraction); (3) the exposure impact number (EIN) the number of people with the exposure among whom one excess case is attributable to the exposure (this is equivalent to the reciprocal of the attributable risk); (4) the exposed cases impact number (ECIN) the number of exposed cases among whom one case is attributable to the exposure (this is equivalent to the reciprocal of the aetiological fraction). The impact number reflects the number of people in each population (the whole population, the cases, all those exposed, and the exposed cases) among whom one case is attributable to the particular risk factor. Conclusions: These new measures should help communicate the impact on a population, of estimates of risk derived from cohort or case-control studies.

Alcohol, tobacco and breast cancer - collaborative reanalysis of individual data from 53 epidemiological studies, including 58 515 women with breast cancer and 95 067 women without the disease

Alcohol and tobacco consumption are closely correlated and published results on their association with breast cancer have not always allowed adequately for confounding between these exposures. Over 80% of the relevant information worldwide on alcohol and tobacco consumption and breast cancer were collated, checked and analysed centrally. Analyses included 58515 women with invasive breast cancer and 95067 controls from 53 studies. Relative risks of breast cancer were estimated, after stratifying by study, age, parity and, where appropriate, women's age when their first child was born and consumption of alcohol and tobacco. The average consumption of alcohol reported by controls from developed countries was 6.0 g per day, i.e. about half a unit/drink of alcohol per day, and was greater in ever-smokers than never-smokers, (8.4 g per day and 5.0 g per day, respectively). Compared with women who reported drinking no alcohol, the relative risk of breast cancer was 1.32 (1.19 - 1.45, P < 0.00001) for an intake of 35 - 44 g per day alcohol, and 1.46 (1.33 - 1.61, P < 0.00001) for greater than or equal to 45 g per day alcohol. The relative risk of breast cancer increased by 7.1% (95% CI 5.5-8.7%; P

'Vigilant Hospitality': The Online Imperative and Teaching Cultural Studies

Information technology (IT) sees information as a fluid, to be stored, regulated and exchanged. This is a profoundly economic model, whose dreams are those of the marketplace – and now, university managers. But no teacher, of course, holds that teaching can be reduced to the movement of information from one point to another. Teaching is never quite absorbed into the models of IT. Where they meet, we do not have the utopia of the virtual classroom, at last freed from the strictures of timetables and the face-to-face; we have, rather, the grinding of two radically irreducible models. This has nothing to do with Luddism; on the contrary, it is the value and necessity of IT for us at present, as teachers. At a time when the tertiary sector’s massive investment in IT is motivated in part by its own dream of the teacherless classroom, one of the pressing tasks for us may be simply to argue as rigorously as we can the structural necessity of our own position as teachers, without nostalgia or humanist sentimentality.