Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

Describing seasonal variability in the distribution of daily effective temperatures for 1985-2009 compared to 1904-1984 for De Bilt, Holland

This paper proposes a method for describing the distribution of observed temperatures on any day of the year such that the distribution and summary statistics of interest derived from the distribution vary smoothly through the year. The method removes the noise inherent in calculating summary statistics directly from the data thus easing comparisons of distributions and summary statistics between different periods. The method is demonstrated using daily effective temperatures (DET) derived from observations of temperature and wind speed at De Bilt, Holland. Distributions and summary statistics are obtained from 1985 to 2009 and compared to the period 1904–1984. A two-stage process first obtains parameters of a theoretical probability distribution, in this case the generalized extreme value (GEV) distribution, which describes the distribution of DET on any day of the year. Second, linear models describe seasonal variation in the parameters. Model predictions provide parameters of the GEV distribution, and therefore summary statistics, that vary smoothly through the year. There is evidence of an increasing mean temperature, a decrease in the variability in temperatures mainly in the winter and more positive skew, more warm days, in the summer. In the winter, the 2% point, the value below which 2% of observations are expected to fall, has risen by 1.2 °C, in the summer the 98% point has risen by 0.8 °C. Medians have risen by 1.1 and 0.9 °C in winter and summer, respectively. The method can be used to describe distributions of future climate projections and other climate variables. Further extensions to the methodology are suggested.

“There’s something very familiar about all this”: generic play and performance in the Back to the Future trilogy (Robert Zemeckis, 1985, 1989, 1990)

The Back to the Future Trilogy incorporates several different generic elements, including aspects of the fifties teen movie, science fiction, comedy and the western. These different modes playfully intertwine with each other creating a complex world of repetitions, echoes and modulations. This essay seeks to interrogate the construction of generic elements and the play between them through a close analysis of a repeated performance. Genre is signalled through various strategies employed within the construction of mise-en-scène, a significant portion of this, as I would like to argue, is transmitted through performance. The material detail of a performance – incorporating gesture, movement, voice, and even surrounding elements such as costume – as well as the way it its presented within a film is key to the establishment, invocation and coherence of genre. Furthermore, attention to the complexity of performance details, particularly in the manner in which they reverberate across texts, demonstrates the intricacy of genre and its inherent mutability. The Back to the Future trilogy represents a specific interest in the flexibility of genre. Within each film, and especially across all three, aspects of various genres are interlaced through both visual and narrative detail, thus constructing a dense layer of references both within and without the texts. To explore this patterning in more detail I will interrogate the contribution of performance to generic play through close analysis of Thomas F. Wilson’s performance of Biff/Griff/Burford Tannen and his central encounter with Marty McFly (Michael J. Fox) in each film. These moments take place in a fifties diner, a 1980s retro diner and a saloon respectively, each space contributing the similarities and differences in each repetition. Close attention to Wilson’s performance of each related character, which contains both modulations and repetitions used specifically to place each film’s central generic theme, demonstrates how embedded the play between genres and their flexibility is within the trilogy.

Changes in global net radiative imbalance 1985-2012

Combining satellite data, atmospheric reanalyses and climate model simulations, variability in the net downward radiative flux imbalance at the top of Earth's atmosphere (N) is reconstructed and linked to recent climate change. Over the 1985-1999 period mean N (0.34 ± 0.67 Wm–2) is lower than for the 2000-2012 period (0.62 ± 0.43 Wm–2, uncertainties at 90% confidence level) despite the slower rate of surface temperature rise since 2000. While the precise magnitude of N remains uncertain, the reconstruction captures interannual variability which is dominated by the eruption of Mt. Pinatubo in 1991 and the El Niño Southern Oscillation. Monthly deseasonalized interannual variability in N generated by an ensemble of 9 climate model simulations using prescribed sea surface temperature and radiative forcings and from the satellite-based reconstruction is significantly correlated (r ∼ 0.6) over the 1985-2012 period.

Assessing the carcinogenic potential of low-dose exposures to chemical mixtures in the environment: the challenge ahead

Lifestyle factors are responsible for a considerable portion of cancer incidence worldwide, but credible estimates from the World Health Organization and the International Agency for Research on Cancer (IARC) suggest that the fraction of cancers attributable to toxic environmental exposures is between 7% and 19%. To explore the hypothesis that low-dose exposures to mixtures of chemicals in the environment may be combining to contribute to environmental carcinogenesis, we reviewed 11 hallmark phenotypes of cancer, multiple priority target sites for disruption in each area and prototypical chemical disruptors for all targets, this included dose-response characterizations, evidence of low-dose effects and cross-hallmark effects for all targets and chemicals. In total, 85 examples of chemicals were reviewed for actions on key pathways/mechanisms related to carcinogenesis. Only 15% (13/85) were found to have evidence of a dose-response threshold, whereas 59% (50/85) exerted low-dose effects. No dose-response information was found for the remaining 26% (22/85). Our analysis suggests that the cumulative effects of individual (non-carcinogenic) chemicals acting on different pathways, and a variety of related systems, organs, tissues and cells could plausibly conspire to produce carcinogenic synergies. Additional basic research on carcinogenesis and research focused on low-dose effects of chemical mixtures needs to be rigorously pursued before the merits of this hypothesis can be further advanced. However, the structure of the World Health Organization International Programme on Chemical Safety 'Mode of Action' framework should be revisited as it has inherent weaknesses that are not fully aligned with our current understanding of cancer biology.

Combining satellite observations and reanalysis energy transports to estimate global net surface energy fluxes 1985-2012

Two methods are developed to estimate net surface energy fluxes based upon satellite-based reconstructions of radiative fluxes at the top of atmosphere and the atmospheric energy tendencies and transports from the ERA-Interim reanalysis. Method 1 applies the mass adjusted energy divergence from ERA-Interim while method 2 estimates energy divergence based upon the net energy difference at the top of atmosphere and the surface from ERA-Interim. To optimise the surface flux and its variability over ocean, the divergences over land are constrained to match the monthly area mean surface net energy flux variability derived from a simple relationship between the surface net energy flux and the surface temperature change. The energy divergences over the oceans are then adjusted to remove an unphysical residual global mean atmospheric energy divergence. The estimated net surface energy fluxes are compared with other data sets from reanalysis and atmospheric model simulations. The spatial correlation coefficients of multi-annual means between the estimations made here and other data sets are all around 0.9. There are good agreements in area mean anomaly variability over the global ocean, but discrepancies in the trend over the eastern Pacific are apparent.

Questioning Kenneth N. Waltz (1924-2013)

Two little-known academics examine the doctoral thesis of a young theorist, Kenneth Waltz. They conclude that his work is important, despite its ambiguities. Some years later, they catch up with Professor Waltz between classes and explore how his ideas have developed.