A Quotient of the Set [BG, BU(n)] for a Finite Group G of Small Rank

We construct a natural map from the set [BG,BU(n)] into a set of characters of the Sylow p-subgroups of G and prove that this natural map is a surjection for all finite groups G of rank two. We show, furthermore, that this same natural map is in fact a bijection for two types of finite groups G: those with periodic cohomology and those of rank two with odd order.Comment: 14 page

Fuel character effects on the J79 and F101 engine combustion systems

The effects of select fuel property variations on two major engine classifications are summarized. Thirteen refined and blended fuels were used which exhibited significant variations in hydrogen content, aromatic type, initial boiling point, final boiling point, and viscosity. Trends were very similar but the degree of fuel sensitivity was not constant. For both systems the dominant fuel property during high pressure operation was found to be fuel hydrogen content. For operation at low pressure test points the fuel volatility and viscosity became the dominant fuel properties for both systems. Aromatic type and final boiling point did not significantly affect combustion data. Correlations of other fuel properties with these and other performance parameters are presented

Shari\u27ah, Democracy, and the Modern Nation-State: Some Reflections on Islam, Popular Rule, and Pluralism

In this article, the author examines two considerations that are critical to a full and meaningful assessment of the degree to which Islam, and Islamic law in particular, can find authentic expressions of themselves under what may reasonably be considered a democratic form of government. The first of these has to do with the scope of Islamic law, or more properly, the scope of the interpretive authority of Muslim jurists, and whether a State that is governed by Shari‘ah must necessarily give priority to the views of religious scholars over those of all others in every aspect of life. Does establishing speed limits, formulating economic policy, or setting standards for medical licensing all fall under the legal authority of the jurists? If not, is there any basis other than political fiat upon which the scope of this jurisdiction might be defined? The second consideration is connected to the question of whether in contemplating the relationship between Islam and democracy, we have not conflated the framework within which modern democracy is packaged, namely the Nation-State (and some would insist on adding capitalism), with the spirit and essence of democratic rule. If we could imagine a State structure whose integrity was not equated with the ability to exercise an absolute monopoly over law-making and the concomitant imposition of a uniform standard of conduct on all of its citizens, would the idea of Islamic democracy present as many apparent difficulties as it presently does? The author’s objective is to add a dimension to the discussion on Islam and democracy that will render future assessments and proposals more nuanced and circumspect

Extracting scaling laws from numerical dynamo models

Earth's magnetic field is generated by processes in the electrically conducting, liquid outer core, subsumed under the term `geodynamo'. In the last decades, great effort has been put into the numerical simulation of core dynamics following from the magnetohydrodynamic (MHD) equations. However, the numerical simulations are far from Earth's core in terms of several control parameters. Different scaling analyses found simple scaling laws for quantities like heat transport, flow velocity, magnetic field strength and magnetic dissipation time. We use an extensive dataset of 116 numerical dynamo models compiled by Christensen and co-workers to analyse these scalings from a rigorous model selection point of view. Our method of choice is leave-one-out cross-validation which rates models according to their predictive abilities. In contrast to earlier results, we find that diffusive processes are not negligible for the flow velocity and magnetic field strength in the numerical dynamos. Also the scaling of the magnetic dissipation time turns out to be more complex than previously suggested. Assuming that the processes relevant in the numerical models are the same as in Earth's core, we use this scaling to estimate an Ohmic dissipation of 3-8 TW for the core. This appears to be consistent with recent high CMB heat flux scenarios.Comment: 21 pages, 11 figure

Organic Farm incomes in England and Wales 2004-05(OF 0189)

Results from research work carried out for the Department of Environment, Food and Rural Affairs (DEFRA) by the Organic Research Group at the Institute of Rural Sciences, UWA on the economic performance of organic farms in 2004/05 are presented in this report. This report is the last of a series1 of four on organic farm incomes from 2001/02 through to 2004/05 as part of project OF0189. The main aim of this work is to assess the financial performance of organic farms differentiated by farm type, in order to inform DEFRA policy-making with respect to economics of organic farming, and to provide a basis for assessments by farmers, advisers and other interested parties of the farm-level implications of conversion to and continued organic farming. This research area builds on previous economics work on organic farming carried out by Institute of Rural Sciences, UWA (Project OF0190, covering 1995/96 to 1998/99). In this report, time series financial data are shown for an identical farm sample for the 2003/04 and 2004/05 financial years, covering seven organic farm types including cropping, horticulture, lowland and LFA dairy, lowland and LFA cattle and sheep and mixed farming systems. The identical farm samples comprise farms that are present in both 2003/04 and 2004/05. The total number of organic farms for 2004/05, also referred to as the full farm sample data, is shown alongside the identical datasets. Summarised and detailed financial input, output, income, returns to labour and capital, liabilities and assets and some physical performance measures are presented based on current Farm Business Survey (FBS) data collection and collation guidelines. The full samples of organic farms per robust farm type are sufficiently large to give some reasonable level of confidence in the data; however, it should be noted that the organic farm samples are not statistically representative of their type, although the results can be seen as a reasonable indication of farm income levels for comparable organic and conventional farms. Smaller identical farm samples should be treated more cautiously as there is a possibility for outliers (especially larger farms) to have some influence on the average results. An additional element of this work is the inclusion of comparable conventional farm data for the farm types shown. Each organic farm within this study was matched with an appropriate cluster of conventional farms based on the resource endowment indicators for individual organic farms. Broadly speaking, the indicators included farm type, FBS region, Less Favoured Area (LFA) status, utilisable agricultural area (UAA), milk quota holding (where applicable) and farm business size. The cluster farm data were averaged for each farm type to derive the comparable conventional farm (CCF) data based on the organic farms from the identical and full farm samples. Overall, the identical sample of organic farms showed a similar or higher level of net farm income for all farm types in 2004/05 than in 2003/04 with the exception of lowland dairy farms, which decreased over the period. On comparing the organic data with the comparable conventional data, the greatest differences in performance were seen in the cropping, lowland cattle and sheep and mixed farm types where organic farms performed significantly better in 2004/05. LFA cattle and sheep farm types performed similarly to the comparable conventional farm samples while LFA organic dairy farms achieved lower net farm incomes than the conventional comparison farms. The full sample datasets compared similarly to the identical datasets for both organic and conventional farms in 2004/05. Gross margin data are presented for organic dairy herds on a herd size and top five performing herd basis. Cattle and sheep gross margins are shown for lowland and LFA farm types. Crops shown include winter and spring wheat, spring barley, winter and spring oats, beans, ware potatoes, calabrese, cauliflower and cabbage crops. Where applicable, 2003/04 gross margin data are shown alongside the 2004/05 data. Benchmarking data are shown for organic milk, suckler store, finishing beef and lamb production enterprises. The results for the beef and lamb enterprises show the significance of support payments in making these enterprises viable, raising questions about the possible impact of the single farm payment on producer perceptions of their profitability