Quantum symmetries and the Weyl–Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase space. Each such phase-space representation is a Weyl–Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by 'factorizing' the Weyl–Wigner product. However, not every real, unitary representation on phase space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl–Wigner product and can be factorized. The conditions under which this is possible are examined. Examples are presented.

Acquisition of the English article system in SLA and the Missing Surface Inflection Hypothesis

This paper examines the article system in interlanguage grammar focusing on Japanese learners of English, whose native language lacks articles. It will be demonstrated that for the acquisition of the English article system, count/mass distinctions and definiteness are the crucial factors. Although Japanese does not employ the article system to encode these aspects, it will be argued that they are nevertheless syntactically encoded through its classifier system. Hence, the problem for these learners must be to map these features onto the appropriate surface forms as the Missing Surface Inflection Hypothesis predicts (Prévost & White 2000). This suggestion will further be supported empirically by a fill-in-the article task. It will be concluded that these Japanese learners understand the English article system fairly well, possibly due to their native language, yet have problems with realizing the relevant features (i.e. count/mass distinctions and definiteness) in the target language.

(FAB12_1_002) 'Would you know the new, you must search the old': William Lethaby's 'Architecture, Mysticism and Myth' (1891) and the 'Hypnerotomachia Poliphili' (1499)

Published in the final months of 1891, Architecture, Mysticism and Myth was the first architectural treatise written by the late nineteenth-century English architect and theorist William Richard Lethaby (1857-1931).' Documenting the characteristic attributes of the architectural myth of the "temple idea", and its presence amongst architectures of multiple ancient cultures, the text was endowed with a distinctly historical tone. In examining the motives behind myth, which Lethaby defined as the interaction and reaction between the natural universe and the built environment, Lethaby also injected a series of theoretical considerations into the text. It is clear that Lethaby's interest in the temple idea was not limited to its curious, prolific presence in past architectures, hut also embraced a consideration of what lessons the temple idea may contribute to the struggle of the late nineteenth-century English architect to define an "art of the future".

Using FCD Mapper Software and Landsat Images to Assess Forest Canopy Density in Landscapes in Australia and the Philippines

Using Landsat imagery, forest canopy density (FCD) estimated with the FCD Mapper®, was correlated with predominant height (PDH, measured as the average height of the tallest 50 trees per hectare) for 20 field plots measured in native forest at Noosa Heads, south-east Queensland, Australia. A corresponding image was used to calculate FCD in Leyte Island, the Philippines and was validated on the ground for accuracy. The FCD Mapper was produced for the International Tropical Timber Organisation and estimates FCD as an index of canopy density using reflectance characteristics of Landsat Enhanced Thematic (ETM) Mapper images. The FCD Mapper is a ‘semi-expert’ computer program which uses interactive screens to allow the operator to make decisions concerning the classification of land into bare soil, grass and forest. At Noosa, a positive strong nonlinear relationship (r2 = 0.86) was found between FCD and PDH for 15 field plots with variable PDH but complete canopy closure. An additional five field plots were measured in forest with a broken canopy and the software assessed these plots as having a much lower FCD than forest with canopy closure. FCD estimates for forest and agricultural land in the island of Leyte and subsequent field validation showed that at appropriate settings, the FCD Mapper differentiated between tropical rainforest and banana or coconut plantation. These findings suggest that in forests with a closed canopy this remote sensing technique has promise for forest inventory and productivity assessment. The findings also suggest that the software has promise for discriminating between native forest with a complete canopy and forest which has a broken canopy, such as coconut or banana plantation.

Effect of ionic strength and clay mineralogy on Na-Ca exchange and the SAR-ESP relationship

The relationship between sodium adsorption ratio (SAR) and exchangeable sodium percentage (ESP) for all soils has traditionally been assumed to be similar to that developed by the United States Salinity Laboratory (USSL) in 1954. However, under certain conditions, this relationship has been shown not to be constant, but to vary with both ionic strength and clay mineralogy. We conducted a detailed experiment to determine the effect of ionic strength on the Na+-Ca2+ exchange of four clay minerals (kaolinite, illite, pyrophyllite, and montmorillonite), with results related to the diffuse double-layer (DDL) model. Clays in which external exchange sites dominated (kaolinite and pyrophyllite) tended to show an overall preference for Na+, with the magnitude of this preference increasing with decreasing ESP. For these external surfaces, increases in ionic strength were found to increase preference for Na+. Although illite (2:1 non-expanding mineral) was expected to be dominated by external surfaces, this clay displayed an overall preference for Ca2+, possibly indicating the opening of quasicrystals and the formation of internal exchange surfaces. For the expanding 2:1 clay, montmorillonite, Na+-Ca2+ exchange varied due to the formation of quasicrystals (and internal exchange surfaces) from individual clay platelets. At small ionic strength and large ESP, the clay platelets dispersed and were dominated by external exchange surfaces (displaying preference for Na+). However, as ionic strength increased and ESP decreased, quasicrystals (and internal exchange surfaces) formed, and preference for Ca2+ increased. Therefore, the relationship between SAR and ESP is not constant and should be determined directly for the soil of interest.

A review of the use of the basic cation saturation ratio and the "ideal" soil

The use of 'balanced' Ca, Mg, and K ratios, as prescribed by the basic cation saturation ratio (BCSR) concept, is still used by some private soil-testing laboratories for the interpretation of soil analytical data. This review aims to examine the suitability of the BCSR concept as a method for the interpretation of soil analytical data. According to the BCSR concept, maximum plant growth will be achieved only when the soil’s exchangeable Ca, Mg, and K concentrations are approximately 65 % Ca, 10 % Mg, and 5 % K (termed the ‘ideal soil’). This ‘ideal soil’ was originally proposed by Firman Bear and co-workers in New Jersey (USA) during the 1940s as a method of reducing luxury K uptake by alfalfa (Medicago sativa L.). At about the same time, William Albrecht, working in Missouri (USA), concluded through his own investigations that plants require a soil with a high Ca saturation for optimal growth. Whilst it now appears that several of Albrecht’s experiments were fundamentally flawed, the BCSR (‘balanced soil’) concept has been widely promoted, suggesting that the prescribed cationic ratios provide optimum chemical, physical, and biological soil properties. Our examination of data from numerous studies (particularly those of Albrecht and Bear, themselves) would suggest that, within the ranges commonly found in soils, the chemical, physical, and biological fertility of a soil is generally not influenced by the ratios of Ca, Mg, and K. The data do not support the claims of the BCSR, and continued promotion of the BCSR will result in the inefficient use of resources in agriculture and horticulture.