Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3)

We complete the computation of spectral measures for SU(3) nimrep graphs arising in subfactor theory, namely the SU(3) ADE graphs associated with SU(3) modular invariants and the McKay graphs of finite subgroups of SU(3). For the SU(2) graphs the spectral measures distill onto very special subsets of the semicircle/circle, whilst for the SU(3) graphs the spectral measures distill onto very special subsets of the discoid/torus. The theory of nimreps allows us to compute these measures precisely. We have previously determined spectral measures for some nimrep graphs arising in subfactor theory, particularly those associated with all SU(2) modular invariants, all subgroups of SU(2), the torus, SU(3), and some SU(3) graphs.Comment: 38 pages, 21 figure

The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants

We determine the Nakayama automorphism of the almost Calabi-Yau algebra A associated to the braided subfactors or nimrep graphs associated to each SU(3) modular invariant. We use this to determine a resolution of A as an A-A bimodule, which will yield a projective resolution of A.Comment: 46 pages which constitutes the published version, plus an Appendix detailing some long calculations. arXiv admin note: text overlap with arXiv:1110.454

The effect of undernutrition on brain-rhythm development

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Mineral resource information in support of national, regional and local planning : Greater Manchester (comprising cities of Manchester, Salford and the Metropolitan Boroughs of Bolton, Bury, Oldham, Rochdale, Stockport, Tameside, Trafford and Wigan)

This report is one of a series prepared by the British Geological Survey for various administrative areas in England for the Office of the Deputy Prime Minister’s research project Mineral Resource Information in Support of National, Regional and Local Planning. The accompanying map relates to Greater Manchester, comprising the cities of Manchester and Salford and Metropolitan Boroughs of Bolton, Bury, Oldham, Rochdale, Stockport, Tameside, Trafford and Wigan, and delineates the mineral resources of current, or potential, economic interest in the area and the sites where minerals are or have been worked. It also relates these to national planning designations, which may represent constraints on the extraction of minerals. Three major elements of information are presented: • the geological distribution and importance of mineral resources • the extent of mineral planning permissions and the location of current mineral workings • the extent of selected, nationally-designated planning constraints This wide range of information, much of which is scattered and not always available in a consistent and convenient form, is presented on a digitally-generated summary map on the scale of 1:100 000. This scale is convenient for the overall display of the data and allows for a legible topographic base on which to depict the information. However, all the data are held digitally at larger scales using a Geographical Information System (GIS), which allows easy revision, updating and customisation of the information together with its possible integration with other datasets. The information will form part of a Summary of the Mineral Resources of the North West Region. The purpose of the work is to assist all interested parties involved in the preparation and review of development plans, both in relation to the extraction of minerals and the protection of mineral resources from sterilisation. It provides a knowledge base, in a consistent format, on the nature and extent of mineral resources and the environmental constraints, which may affect their extraction. An important objective is to provide baseline data for the long term. The results may also provide a starting point for discussions on specific planning proposals for mineral extraction or on proposals, which may sterilise resources. It is anticipated that the maps and report will also provide valuable background data for a much wider audience, including the different sectors of the minerals industry, other agencies and authorities (e.g. The Planning Inspectorate Agency, the Environment Agency, the Countryside Agency and English Nature), environmental interests and the general public. Basic mineral resource information is essential to support mineral exploration and development activities, for resource management and land-use planning, and to establish baseline data for environmental impact studies and environmental guidelines. It also enables a more sustainable pattern and standard of development to be achieved by valuing mineral resources as national assets. The mineral resources covered are sand and gravel, crushed rock aggregate, brick clay, building stone, peat, coal, and hydrocarbons

Island Density in Homoepitaxial Growth:Improved Monte Carlo Results

We reexamine the density of two dimensional islands in the submonolayer regime of a homoepitaxially growing surface using the coarse grained Monte Carlo simulation with random sequential updating rather than parallel updating. It turns out that the power law dependence of the density of islands on the deposition rate agrees much better with the theoretical prediction than previous data obtained by other methods if random sequential instead of parallel updating is used.Comment: Latex with 2 PS figure file

Non-equilibrium states of a photon cavity pumped by an atomic beam

We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we prove that the mean photon number in the cavity stabilizes in time. The limiting state of the cavity in this case exists and it is independent of the initial state. We calculate the characteristic functional of this non-quasi-free non-equilibrium state. We also calculate the energy flux in both the ideal and open cavity and the entropy production for the ideal cavity.Comment: Corrected energy production calculations and made some changes to ease the readin

Mineral resource information in support of national, regional and local planning : Cheshire (comprising Cheshire, Boroughs of Halton and Warrington)

This report is one of a series prepared by the British Geological Survey for various administrative areas in England for the Office of the Deputy Prime Minister’s research project Mineral Resource Information in Support of National, Regional and Local Planning. The accompanying map relates to the county of Cheshire (comprising Cheshire, Boroughs of Halton and Warrington), and delineates the mineral resources of current, or potential, economic interest in the area and the sites where minerals are or have been worked. It also relates these to national planning designations, which may represent constraints on the extraction of minerals. Three major elements of information are presented: • the geological distribution and importance of mineral resources; • the extent of mineral planning permissions and the location of current mineral workings; and • the extent of selected, nationally-designated planning constraints. This wide range of information, much of which is scattered and not always available in a consistent and convenient form, is presented on a digitally-generated summary map on the scale of 1:100 000. This scale is convenient for the overall display of the data and allows for a legible topographic base on which to depict the information. However, all the data are held digitally at larger scales using a Geographical Information System (GIS), which allows easy revision, updating and customisation of the information together with its possible integration with other datasets. The information will form part of a Summary of the Mineral Resources of the North West Region. The purpose of the work is to assist all interested parties involved in the preparation and review of development plans, both in relation to the extraction of minerals and the protection of mineral resources from sterilisation. It provides a knowledge base, in a consistent format, on the nature and extent of mineral resources and the environmental constraints, which may affect their extraction. An important objective is to provide baseline data for the long term. The results may also provide a starting point for discussion on specific planning proposals for minerals extraction or on proposals, which may sterilise resources. It is anticipated that the map and report will also provide valuable background data for a much wider audience, including the different sectors of the minerals industry, other agencies and authorities (e.g. The Planning Inspectorate Agency, the Environment Agency, The Countryside Agency and English Nature), environmental interests and the general public. Basic mineral resource information is essential to support mineral exploration and development activities, for resource management and land-use planning, and to establish baseline data for environmental impact studies and environmental guidelines. It also enables a more sustainable pattern and standard of development to be achieved by valuing mineral resources as national assets. The mineral resources covered are sand and gravel, crushed rock aggregate, silica sand, salt, brick clay, building stones, peat, coal, hydrocarbons and metalliferous mineralisation

Mineral resource information in support of national, regional and local planning : Gloucestershire (comprising Gloucestershire and South Gloucestershire)

This report is one of a series prepared by the British Geological Survey for various administrative areas in England for the Office of the Deputy Prime Minister’s research project Mineral Resource Information in Support of National, Regional and Local Planning. The accompanying map relates to the county of Gloucestershire, comprising Gloucestershire and South Gloucestershire, and delineates the mineral resources of current, or potential, economic interest in the area and the sites where minerals are or have been worked. It also relates these to national planning designations, which may represent constraints on the extraction of minerals. Three major elements of information are presented: • the geological distribution and importance of mineral resources; • the extent of mineral planning permissions and the location of current mineral workings; and • the extent of selected, nationally-designated planning constraints. This wide range of information, much of which is scattered and not always available in a consistent and convenient form, is presented on a digitally-generated summary map on the scale of 1:100 000. This scale is convenient for the overall display of the data and allows for a legible topographic base on which to depict the information. However, all the data are held digitally at larger scales using a Geographical Information System (GIS), which allows easy revision, updating and customisation of the information together with its possible integration with other datasets. The information will form part of a Summary of the Mineral Resources of the South West Region. The purpose of the work is to assist all interested parties involved in the preparation and review of development plans, both in relation to the extraction of minerals and the protection of mineral resources from sterilisation. It provides a knowledge base, in a consistent format, on the nature and extent of mineral resources and the environmental constraints, which may affect their extraction. An important objective is to provide baseline data for the long term. The results may also provide a starting point for discussions on specific planning proposals for mineral extraction or on proposals, which may sterilise resources. It is anticipated that the maps and report will also provide valuable background data for a much wider audience, including the different sectors of the minerals industry, other agencies and authorities (e.g. The Planning Inspectorate Agency, the Environment Agency, the Countryside Agency and English Nature), environmental interests and the general public. Basic mineral resource information is essential to support mineral exploration and development activities, for resource management and land-use planning, and to establish baseline data for environmental impact studies and environmental guidelines. It also enables a more sustainable pattern and standard of development to be achieved by valuing mineral resources as national assets. The mineral resources covered are sand and gravel, bedrock sand, crushed rock aggregate, building stone, hydrocarbons, and coal

Canonical Coordinates and Meson Spectra for Scalar Deformed N=4 SYM from the AdS/CFT Correspondence

Five supersymmetric scalar deformations of the AdS_5xS^5 geometry are investigated. By switching on condensates for the scalars in the N=4 multiplet with a form which preserves a subgroup of the original R-symmetry, disk and sphere configurations of D3-branes are formed in the dual supergravity background. The analytic, canonical metric for each geometry is formulated and the singularity structure is studied. Quarks are introduced into two of the corresponding field theories using D7-brane probes and the pseudoscalar meson spectrum is calculated. For one of the condensate configurations, a mass gap is found and shown analytically to be present in the massless limit. It is also found that there is a stepped spectrum with eigenstate degeneracy in the limit of small quark masses. In the case of a second, similar deformation, it is necessary to understand the full D3-D7 brane interaction to study the limit of small quark masses. It is seen that simple solutions to the equations of motion for the other three geometries are unlikely to exist.Comment: 16 pages, 7 figures, references added, typos correcte

Mineral resource information in support of national, regional and local planning : Devon (comprising Devon, Plymouth, Torbay, Dartmoor National Park and part of Exmoor National Park)

This report is one of a series prepared by the British Geological Survey for various administrative areas in England for the Office of the Deputy Prime Minister’s research project Mineral Resource Information in Support of National, Regional and Local Planning. The accompanying maps relate to the county of Devon and delineates the mineral resources of current, or potential, economic interest in the area and the sites where minerals are or have been worked. It also relates these to national planning designations, which may represent constraints on the extraction of minerals. Three major elements of information are presented: • the geological distribution and importance of mineral resources; • the extent of mineral planning permissions and the location of current mineral workings; and • the extent of selected, nationally-designated planning constraints. This wide range of information, much of which is scattered and not always available in a consistent and convenient form, is presented on two digitally-generated summary map on the scale of 1:100 000. This scale is convenient for the overall display of the data and allows for a legible topographic base on which to depict the information. However, all the data are held digitally at larger scales using a Geographical Information System (GIS), which allows easy revision, updating and customisation of the information together with its possible integration with other datasets. The information will form part of a Summary of the Mineral Resources of the South West Region. The purpose of the work is to assist all interested parties involved in the preparation and review of development plans, both in relation to the extraction of minerals and the protection of mineral resources from sterilisation. It provides a knowledge base, in a consistent format, on the nature and extent of mineral resources and the environmental constraints, which may affect their extraction. An important objective is to provide baseline data for the long term. The results may also provide a starting point for discussion on specific planning proposals for minerals extraction or on proposals, which may sterilise resources. It is anticipated that the map and report will also provide valuable background data for a much wider audience, including the different sectors of the minerals industry, other agencies and authorities (e.g. The Planning Inspectorate Agency, the Environment Agency, The Countryside Agency and English Nature), environmental interests and the general public. Basic mineral resource information is essential to support mineral exploration and development activities, for resource management and land-use planning, and to establish baseline data for environmental impact studies and environmental guidelines. It also enables a more sustainable pattern and standard of development to be achieved by valuing mineral resources as national assets. The mineral resources covered are sand and gravel, crushed rock aggregate, brick clay, kaolin, ball clay, building stones, hydrocarbons and metalliferous mineralisation