Perspex machine IX: transreal analysis

We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We then generalise all of the common, real, trigonometric functions to transreal functions and show that transreal (sin x)/x is well defined everywhere. This raises the possibility that transreal analysis is total, in other words, that every function and every limit is everywhere well defined. If so, transreal analysis should be an adequate mathematical basis for analysing the perspex machine - a theoretical, super-Turing machine that operates on a total geometry. We go on to dispel all of the standard counter "proofs" that purport to show that division by zero is impossible. This is done simply by carrying the proof through in transreal arithmetic or transreal analysis. We find that either the supposed counter proof has no content or else that it supports the contention that division by zero is possible. The supposed counter proofs rely on extending the standard systems in arbitrary and inconsistent ways and then showing, tautologously, that the chosen extensions are not consistent. This shows only that the chosen extensions are inconsistent and does not bear on the question of whether division by zero is logically possible. By contrast, transreal arithmetic is total and consistent so it defeats any possible "straw man" argument. Finally, we show how to arrange that a function has finite or else unmeasurable (nullity) values, but no infinite values. This arithmetical arrangement might prove useful in mathematical physics because it outlaws naked singularities in all equations.

Monte Carlo numerical treatment of large linear algebra problems

In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm for evaluating bilinear forms of matrix powers since they form the so-called Krylov subspaces. Results are presented comparing the performance of the Robust and Non-robust Monte Carlo algorithms. The algorithms are tested on large dense matrices as well as on large unstructured sparse matrices.

Free amino acids and sugars in rye grain: implications for acrylamide formation

Acrylamide forms from free asparagine and sugars during cooking, and products derived from the grain of cereals, including rye, contribute a large proportion of total dietary intake. In this study, free amino acid and sugar concentrations were measured in the grain of a range of rye varieties grown at locations in Hungary, France, Poland, and the United Kingdom and harvested in 2005, 2006, and 2007. Genetic and environmental (location and harvest year) effects on the levels of acrylamide precursors were assessed. The data showed free asparagine concentration to be the main determinant of acrylamide formation in heated rye flour, as it is in wheat. However, in contrast to wheat, sugar, particularly sucrose, concentration also correlated both with asparagine concentration and with acrylamide formed. Free asparagine concentration was shown to be under genetic (G), environmental (E), and integrated (G × E) control. The same was true for glucose, whereas maltose and fructose were affected mainly by environmental factors and sucrose was largely under genetic control. The ratio of variation due to varieties (genotype) to the total variation (a measure of heritability) for free asparagine concentration in the grain was 23%. Free asparagine concentration was closely associated with bran yield, whereas sugar concentration was associated with low Hagberg falling number. Rye grain was found to contain much higher concentrations of free proline than wheat grain, and less acrylamide formed per unit of asparagine in rye than in wheat flour.

Ananke

Ananke, Homeric “compulsion,” becomes an important philosophical term among the pre-Socratics. To Thales it is the natural necessity that powers all phenomena and compels divinities to epiphany (71 A12 DK).

Personifications

Artists as early as Homer created personifications – representations of nouns in human form – to explain aspects of the primary characters, particularly Olympian divinities: the Litai (Prayers) as daughters of Zeus, for example, express an aspect of Zeus' broad-ranging powers.

Land administration in a micro-state: the role of land use planning

Land policy in micro-states and the land administration that underpins it is often devised within a legacy framework inherited from a colonial past. Independence has allowed self-determination of the future political direction yet the range, legal framework, institutional structure and administration systems tend to mirror those of ex-colonial powers. Do land policies, administration systems and processes developed to serve large heavily populated countries scale down to serve the requirements of micro-states? The evidence suggests not: many land administration systems in the Caribbean face difficulties due to poor records, unclear title, exploitation of state lands, incomplete or ongoing land reform programmes, irregular or illegal settlement and non-enforced planning regulations. Land matters are typically the responsibility of several government departments and agencies responsible for land titling and registration, cadastral surveying of property interests, physical planning, taxation and financial regulation. Although planning is regarded as a land administration function, organisational responsibility usually rests with local rather than central government in large countries, but in microstates local government may be politically weak, under-resourced or even non-existent. Using a case study approach this paper explores how planning functions are organised in the Caribbean state of St Vincent & the Grenadines in relation to land administration as a whole and compares the arrangement with other independent micro-states in the region.

British public policy and multinationals during the “Dollar Gap” era, 1945–1960

This article examines the role of British exchange and import controls in stimulating the dramatic increase in overseas (particularly American) multinationals in Britain from the end of the Second World War to the late 1950s, together with the ways in which the government used controls to regulate the foreign direct investment (FDI) inflow. Exchange controls were both an important stimulus to inward investment and a powerful and flexible means of regulating its volume and character. Government was relatively successful in using these powers to maximize the dollar balance and industrial benefits of FDI to Britain, given initially severe dollar and capacity constraints, and in liberalizing policy once these constraints receded and competition from other FDI hosts intensified.

Public policy and foreign-based enterprises in Britain prior to the Second World War

This article examines the early evolution of British policy, prior to the Second World War. The British government adopted an ‘open’ policy towards foreign direct investment (FDI), despite periodic fears that some foreign acquisitions of UK firms in key sectors might be detrimental to the national interest, and a few ad hoc attempts to deal with particular instances of this kind. During the 1930s, when the inflow of foreign firms accelerated following Britain's adoption of general tariff protection, the government developed a sophisticated admissions policy, based on an assessment of the likely net benefit of each applicant to the British economy. Its limited regulatory powers were used to maximize the potential of immigrant firms for technology transfer, enhanced competition, industrial diversification, and employment creation (particularly in the depressed regions), while protecting British industries suffering from excess capacity.

Considering heteroglossia in language and development in Sub-Saharan Africa

Countries throughout the sub-Saharan (SSA) region have a complex linguistic heritage having their origins in opportunistic boundary changes effected by Western colonial powers at the Berlin Conference 1884-85. Postcolonial language-in-education policies valorizing ex-colonial languages have contributed at least in part to underachievement in education and thus the underdevelopment of human resources in SSA countries. This situation is not likely to improve whilst unresolved questions concerning the choice of language(s) that would best support social and economic development remain. Whilst policy attempts to develop local languages have been discussed within the framework of the African Union, and some countries have experimented with models of multilingual education during the past decade, the goalposts have already changed as a result of migration and trade. This paper argues that language policy makers need to be cognizant of changing language ecologies and their relationship with emerging linguistic and economic markets. The concept of language, within such a framework, has to be viewed in relation to the multiplicity of language markets within the shifting landscapes of people, culture, economics and the geo-politics of the 21st Century. Whilst, on the one hand, this refers to the hegemony of dominant powerful languages and the social relations of disempowerment, on the other hand, it also refers to existing and evolving social spaces and local language capabilities and choices. Within this framework the article argues that socially constructed dominant macro language markets need to be viewed also in relation to other, self-defined, community meso- and individual micro- language markets and their possibilities for social, economic and political development. It is through pursuing this argument that this article assesses the validity of Omoniyi’s argument in this volume, for the need to focus on the concept of language capital within multilingual contexts in the SSA region as compared to Bourdieu’s concept of linguistic capital.  

High-resolution global climate simulations with the ECMWF model in Project Athena: experimental design, model climate, and seasonal forecast skill

The sensitivity to the horizontal resolution of the climate, anthropogenic climate change, and seasonal predictive skill of the ECMWF model has been studied as part of Project Athena—an international collaboration formed to test the hypothesis that substantial progress in simulating and predicting climate can be achieved if mesoscale and subsynoptic atmospheric phenomena are more realistically represented in climate models. In this study the experiments carried out with the ECMWF model (atmosphere only) are described in detail. Here, the focus is on the tropics and the Northern Hemisphere extratropics during boreal winter. The resolutions considered in Project Athena for the ECMWF model are T159 (126 km), T511 (39 km), T1279 (16 km), and T2047 (10 km). It was found that increasing horizontal resolution improves the tropical precipitation, the tropical atmospheric circulation, the frequency of occurrence of Euro-Atlantic blocking, and the representation of extratropical cyclones in large parts of the Northern Hemisphere extratropics. All of these improvements come from the increase in resolution from T159 to T511 with relatively small changes for further resolution increases to T1279 and T2047, although it should be noted that results from this very highest resolution are from a previously untested model version. Problems in simulating the Madden–Julian oscillation remain unchanged for all resolutions tested. There is some evidence that increasing horizontal resolution to T1279 leads to moderate increases in seasonal forecast skill during boreal winter in the tropics and Northern Hemisphere extratropics. Sensitivity experiments are discussed, which helps to foster a better understanding of some of the resolution dependence found for the ECMWF model in Project Athena

Thessaly and Macedon at Delphi

The Daochos Monument at Delphi has received some scholarly attention from an art-historical and archaeological perspective; this article, however, examines it rather as a reflection of contemporary Thessalian history and discourse, an aspect which has been almost entirely neglected. Through its visual imagery and its inscriptions, the monument adopts and adapts long-standing Thessalian themes of governance and identity, and achieves a delicate balance with Macedonian concerns to forge a symbolic rapprochement between powers and cultures in the Greek north. Its dedicator, Daochos, emerges as far more than just the puppet of Philip II of Macedon. This hostile and largely Demosthenic characterisation, which remains influential even in modern historiography, is far from adequate in allowing for an understanding of the relationship between Thessalian and Macedonian motivations at this time, or of the importance of Delphi as the pan-Hellenic setting of their interaction. Looking closely at the Daochos Monument instead allows for a rare glimpse into the Thessalian perspective in all its complexity.

Combined use of two genetic fingerprinting methods, pulsed-field gel electrophoresis and ribotyping, for characterization of Escherichia coli O157 isolates from food animals, retail meats, and cases of human disease

Two genetic fingerprinting techniques, pulsed-field gel electrophoresis (PFGE) and ribotyping, were used to characterize 207 Escherichia coli O157 isolates from food animals, foods of animal origin, and cases of human disease (206 of the isolates were from the United Kingdom). In addition, 164 of these isolates were also phage typed. The isolates were divided into two general groups: (i) unrelated isolates not known to be epidemiologically linked (n = 154) and originating from food animals, foods and the environment, or humans and (ii) epidemiologically related isolates (n = 53) comprised of four related groups (RGs) originating either from one farm plus the abattoir where cattle from that farm were slaughtered or from one of three different English abattoirs. PFGE was conducted with the restriction endonuclease XbaI. while for ribotyping, two restriction endonucleases (PstI and SphI) were combined to digest genomic DNAs simultaneously. The 207 E. coli O157 isolates produced 97 PFGE profiles and 51 ribotypes. The two genetic fingerprinting methods had similar powers to discriminate the 154 epidemiologically unrelated E. coli O157 isolates in the study (Simpson's index of diversity [D] = 0.98 and 0.94 for PFGE typing and ribotyping, respectively). There was no correlation between the source of an isolate (healthy meat or milk animals, retail meats, or cases of human infection) and either particular PFGE or ribotype profiles or clusters. Combination of the results of both genetic fingerprinting methods produced 146 types, significantly more than when either of the two methods was used individually. Consequently, the superior discriminatory performance of the PFGE-ribotyping combination was proven in two ways: (i) by demonstrating that the majority of the E. coli O157 isolates with unrelated histories were indeed distinguishable types and (ii) by identifying some clonal groups among two of the four RGs of E. coli O157 isolates (comprising PFGE types different by just one or two bands), the relatedness of which would have remained unconfirmed otherwise.

Contested institutions? Traditional leaders and land access and control in communal areas of Eastern Cape Province, South Africa

The South African government has endeavoured to strengthen property rights in communal areas and develop civil society institutions for community-led development and natural resource management. However, the effectiveness of this remains unclear as the emergence and operation of civil society institutions in these areas is potentially constrained by the persistence of traditional authorities. Focusing on the former Transkei region of Eastern Cape Province, three case study communities are used examine the extent to which local institutions overlap in issues of land access and control. Within these communities, traditional leaders (chiefs and headmen) continue to exercise complete and sole authority over land allocation and use this to entrench their own positions. However, in the absence of effective state support, traditional authorities have only limited power over how land is used and in enforcing land rights, particularly over communal resources such as rangeland. This diminishes their local legitimacy and encourages some groups to contest their authority by cutting fences, ignoring collective grazing decisions and refusing to pay ‘fees’ levied on them. They are encouraged in such activities by the presence of democratically elected local civil society institutions such as ward councillors and farmers’ organisations, which have broad appeal and are increasingly responsible for much of the agrarian development that takes place, despite having no direct mandate over land. Where it occurs at all, interaction between these different institutions is generally restricted to approval being required from traditional leaders for land allocated to development projects. On this basis it is argued that a more radical approach to land reform in communal areas is required, which transfers all powers over land to elected and accountable local institutions and integrates land allocation, land management and agrarian development more effectively.