Correlations between two sets of angular relation equations

It is shown here that the angular relation equations between direct and reciprocal vectors are very similar to the angular relation equations in Euler's theorem. These two sets of equations are usually treated separately as unrelated equations in different fields. In this careful study, the connection between the two sets of angular equations is revealed by considering the cosine rule for the spherical triangle. It is found that understanding of the correlation is hindered by the facts that the same variables are defined differently and different symbols are used to represent them in the two fields. Understanding the connection between different concepts is not only stimulating and beneficial, but also a fundamental tool in innovation and research, and has historical significance. The background of the work presented here contains elements of many scientific disciplines. This work illustrates the common ground of two theories usually considered separately and is therefore of benefit not only for its own sake but also to illustrate a general principle that a theory relevant to one discipline can often be used in another. The paper works with chemistry related concepts using mathematical methodologies unfamiliar to the usual audience of mainstream experimental and theoretical chemists.

Sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization

The Canadian Middle Atmosphere Model is used to examine the sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization. Momentum conservation requires that the parameterized gravity wave momentum flux at the top of the model be zero and corresponds to the physical boundary condition of no momentum flux at the top of the atmosphere. Allowing momentum flux to escape the model domain violates momentum conservation. Here the impact of momentum conservation in two sets of model simulations is investigated. In the first set, the simulation of present-day climate for two model-lid height configurations, 0.001 and 10 hPa, which are identical below 10 hPa, is considered. The impact of momentum conservation on the climate with the model lid at 0.001 hPa is minimal, which is expected because of the small amount of gravity wave momentum flux reaching 0.001 hPa. When the lid is lowered to 10 hPa and momentum is conserved, there is only a modest impact on the climate in the Northern Hemisphere; however, the Southern Hemisphere climate is more adversely affected by the deflection of resolved waves near the model lid. When momentum is not conserved in the 10-hPa model the climate is further degraded in both hemispheres, particularly in winter at high latitudes, and the impact of momentum conservation extends all the way to the surface. In the second set of simulations, the impact of momentum conservation and model-lid height on the modeled response to ozone depletion in the Southern Hemisphere is considered, and it is found that the response can display significant sensitivity to both factors. In particular, both the lower-stratospheric polar temperature and surface responses are significantly altered when the lid is lowered, with the effect being most severe when momentum is not conserved. The implications with regard to the current round of Intergovernmental Panel on Climate Change model projections are discussed.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Arnold v. Britton: a ratio and two sets of obiter dicta

Arnold v Britton marks the final stage of the longstanding dispute as to the correct interpretation of a number of 99-year leases of chalets on a leisure park at Oxwich, in the Gower peninsula, near Swansea. The aspect of the case which has attracted most discussion has, understandably, been its main ratio: the proper way to construe a provision of a lease which arguably has an absurd result. This will be considered in this case-note. The judgment of the Supreme Court – particularly the judgment of Lord Neuberger PSC – does, however contain some observations on the possible reform of the law on service charges which are of interest to those engaged in this field. It also contains some obiter comments on ‘letting schemes’ which are – in the view of the present author – highly unorthodox. These three rather disparate issues which are raised by this case will be considered in turn. As they have little in common with each other, they will be considered as separate sections.

Overview and response to reviewers of The Singing Neanderthals

Why are humans musical? Why do people in all cultures sing or play instruments? Why do we appear to have specialized neurological apparatus for hearing and interpreting music as distinct from other sounds? And how does our musicality relate to language and to our evolutionary history? Anthropologists and archaeologists have paid little attention to the origin of music and musicality — far less than for either language or ‘art’. While art has been seen as an index of cognitive complexity and language as an essential tool of communication, music has suffered from our perception that it is an epiphenomenal ‘leisure activity’, and archaeologically inaccessible to boot. Nothing could be further from the truth, according to Steven Mithen; music is integral to human social life, he argues, and we can investigate its ancestry with the same rich range of analyses — neurological, physiological, ethnographic, linguistic, ethological and even archaeological — which have been deployed to study language. In The Singing Neanderthals Steven Mithen poses these questions and proposes a bold hypothesis to answer them. Mithen argues that musicality is a fundamental part of being human, that this capacity is of great antiquity, and that a holistic protolanguage of musical emotive expression predates language and was an essential precursor to it. This is an argument with implications which extend far beyond the mere origins of music itself into the very motives of human origins. Any argument of such range is bound to attract discussion and critique; we here present commentaries by archaeologists Clive Gamble and Iain Morley and linguists Alison Wray and Maggie Tallerman, along with Mithen's response to them. Whether right or wrong, Mithen has raised fascinating and important issues. And it adds a great deal of charm to the time-honoured, perhaps shopworn image of the Neanderthals shambling ineffectively through the pages of Pleistocene prehistory to imagine them humming, crooning or belting out a cappella harmonies as they went.

A shift to randomness of brain oscillations in people with autism

BACKGROUND: Resting-state functional magnetic resonance imaging (fMRI) enables investigation of the intrinsic functional organization of the brain. Fractal parameters such as the Hurst exponent, H, describe the complexity of endogenous low-frequency fMRI time series on a continuum from random (H = .5) to ordered (H = 1). Shifts in fractal scaling of physiological time series have been associated with neurological and cardiac conditions. METHODS: Resting-state fMRI time series were recorded in 30 male adults with an autism spectrum condition (ASC) and 33 age- and IQ-matched male volunteers. The Hurst exponent was estimated in the wavelet domain and between-group differences were investigated at global and voxel level and in regions known to be involved in autism. RESULTS: Complex fractal scaling of fMRI time series was found in both groups but globally there was a significant shift to randomness in the ASC (mean H = .758, SD = .045) compared with neurotypical volunteers (mean H = .788, SD = .047). Between-group differences in H, which was always reduced in the ASC group, were seen in most regions previously reported to be involved in autism, including cortical midline structures, medial temporal structures, lateral temporal and parietal structures, insula, amygdala, basal ganglia, thalamus, and inferior frontal gyrus. Severity of autistic symptoms was negatively correlated with H in retrosplenial and right anterior insular cortex. CONCLUSIONS: Autism is associated with a small but significant shift to randomness of endogenous brain oscillations. Complexity measures may provide physiological indicators for autism as they have done for other medical conditions.

Costs to farmers of a tuberculosis breakdown

An on-farm survey of 151 cattle farmers who had experienced a bovine tuberculosis (Mycobacterium bovis) breakdown on their farms was undertaken in 2003 to assess the costs associated with the breakdown. In 90 per cent of cases the cost was estimated to be less than 18,513 pound for dairy herds and less than El 1,462 for beef herds, but with a range from 229 pound to 103,817 pound. The main cost was the slaughter of reactor cattle. For the majority of the farmers, the compensation payments seemed to meet most of the costs of their breakdowns, although a majority was still left with net losses.

Potential contribution of natural enemies to patterns of local adaptation in plants

Genetic differentiation among plant populations and adaptation to local environmental conditions are well documented. However, few studies have examined the potential contribution of plant antagonists, such as insect herbivores and pathogens, to the pattern of local adaptation. Here, a reciprocal transplant experiment was set up at three sites across Europe using two common plant species, Holcus lanatus and Plantago lanceolata. The amount of damage by the main above-ground plant antagonists was measured: a rust fungus infecting Holcus and a specialist beetle feeding on Plantago, both in low-density monoculture plots and in competition with interspecific neighbours. Strong genetic differentiation among provenances in the amount of damage by antagonists in both species was found. Local provenances of Holcus had significantly higher amounts of rust infection than foreign provenances, whereas local provenances of Plantago were significantly less damaged by the specialist beetle than the foreign provenances. The presence of surrounding vegetation affected the amount of damage but had little influence on the ranking of plant provenances. The opposite pattern of population differentiation in resistance to local antagonists in the two species suggests that it will be difficult to predict the consequences of plant translocations for interactions with organisms of higher trophic levels.