Integrating Hamiltonian systems defined on the Lie groups SO(4) and SO(1,3)

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E³, the spheres S³ and the hyperboloids H³ with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions is illustrated.

Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

Modelling monsoons: understanding and predicting current and future behaviour

The global monsoon system is so varied and complex that understanding and predicting its diverse behaviour remains a challenge that will occupy modellers for many years to come. Despite the difficult task ahead, an improved monsoon modelling capability has been realized through the inclusion of more detailed physics of the climate system and higher resolution in our numerical models. Perhaps the most crucial improvement to date has been the development of coupled ocean-atmosphere models. From subseasonal to interdecadal time scales, only through the inclusion of air-sea interaction can the proper phasing and teleconnections of convection be attained with respect to sea surface temperature variations. Even then, the response to slow variations in remote forcings (e.g., El Niño—Southern Oscillation) does not result in a robust solution, as there are a host of competing modes of variability that must be represented, including those that appear to be chaotic. Understanding the links between monsoons and land surface processes is not as mature as that explored regarding air-sea interactions. A land surface forcing signal appears to dominate the onset of wet season rainfall over the North American monsoon region, though the relative role of ocean versus land forcing remains a topic of investigation in all the monsoon systems. Also, improved forecasts have been made during periods in which additional sounding observations are available for data assimilation. Thus, there is untapped predictability that can only be attained through the development of a more comprehensive observing system for all monsoon regions. Additionally, improved parameterizations - for example, of convection, cloud, radiation, and boundary layer schemes as well as land surface processes - are essential to realize the full potential of monsoon predictability. A more comprehensive assessment is needed of the impact of black carbon aerosols, which may modulate that of other anthropogenic greenhouse gases. Dynamical considerations require ever increased horizontal resolution (probably to 0.5 degree or higher) in order to resolve many monsoon features including, but not limited to, the Mei-Yu/Baiu sudden onset and withdrawal, low-level jet orientation and variability, and orographic forced rainfall. Under anthropogenic climate change many competing factors complicate making robust projections of monsoon changes. Absent aerosol effects, increased land-sea temperature contrast suggests strengthened monsoon circulation due to climate change. However, increased aerosol emissions will reflect more solar radiation back to space, which may temper or even reduce the strength of monsoon circulations compared to the present day. Precipitation may behave independently from the circulation under warming conditions in which an increased atmospheric moisture loading, based purely on thermodynamic considerations, could result in increased monsoon rainfall under climate change. The challenge to improve model parameterizations and include more complex processes and feedbacks pushes computing resources to their limit, thus requiring continuous upgrades of computational infrastructure to ensure progress in understanding and predicting current and future behaviour of monsoons.

Domesticating the calendar: the hours and the almanac in Tudor England

This article examines two genres of text which were extremely popular in the late-medieval and early modern periods, and it pays particular attention to women users. The printed almanacs of sixteenth-century England were enormously influential; yet their contents are so formulaic and repetitive as to appear almost empty of valuable information. Their most striking feature is their astrological guidance for the reader, and this has led to them being considered 'merely' the repository of popular superstition. Only in the last decade have themes of gender and medicine been given serious consideration in relation to almanacs; but this work has focused on the seventeenth century. This chapter centres on a detailed analysis of sixteenth-century English almanacs, and the various kinds of scientific and household guidance they offered to women readers. Both compilers and users needed to chart a safe course through the religious and scientific battles of the time; and the complexities involved are demonstrated by considering the almanacs in relation to competing sources of guidance. These latter are Books of Hours and 'scientific' works such as medical calendars compiled by Oxford scholars in the late middle ages. A key feature of this chapter is that it gives practical interpretations of this complex information, for the guidance of modern readers unfamiliar with astrology.

Amount of substance and the Mole

The International System of Units, the SI, is built upon seven base quantities and seven base units, as summarized in the table below. Although most of these are familiar to all scientists, the quantity “amount of substance” and its unit “mole” are less familiar and are mainly used by chemists.1 In the chemistry community, the unit “mole” is familiar, but the name of the corresponding quantity “amount of substance” is not so familiar, and the concept is still a source of difficulty for many students. This article reviews and clarifies these two concepts2 and discusses the definition of the unit “mole” and its possible revision.

Examination of the persistency of milk fatty acid composition responses to fish oil and sunflower oil in the diet of dairy cows

Based on the potential benefits of cis-9, trans-11 conjugated linoleic acid (CLA) for human health, there is a need to develop effective strategies for enhancing milk fat CLA concentrations. Levels of cis-9, trans-11 CLA in milk can be increased by supplements of fish oil (FO) and sunflower oil (SO), but there is considerable variation in the response. Part of this variance may reflect time-dependent ruminal adaptations to high levels of lipid in the diet, which lead to alterations in the formation of specific biohydrogenation intermediates. To test this hypothesis, 16 late lactation Holstein-British Friesian cows were used in a repeated measures randomized block design to examine milk fatty acid composition responses to FO and SO in the diet over a 28-d period. Cows were allocated at random to corn silage-based rations (8 per treatment) containing 0 (control) or 45 g of oil supplement/ kg of dry matter consisting (1:2; wt/wt) of FO and SO (FSO), and milk composition was determined on alternate days from d 1. Compared with the control, the FSO diet decreased mean dry matter intake (21.1 vs. 17.9 kg/d), milk fat (47.7 vs. 32.6 g/kg), and protein content (36.1 vs. 33.3 g/kg), but had no effect on milk yield (27.1 vs. 26.4 kg/d). Reductions in milk fat content relative to the FSO diet were associated with increases in milk trans-10 18: 1, trans-10, cis-12 CLA, and trans-9, cis-11 CLA concentrations (r(2) = 0.74, 0.57, and 0.80, respectively). Compared with the control, the FSO diet reduced milk 4: 0 to 18: 0 and cis 18:1 content and increased trans 18:1, trans 18:2, cis-9, trans-11 CLA, 20: 5 n-3, and 22: 6 n-3 concentrations. The FSO diet caused a rapid elevation in milk cis-9, trans-11 CLA content, reaching a maximum of 5.37 g/100 g of fatty acids on d 5, but these increases were transient, declining to 2.35 g/100 g of fatty acids by d 15. They remained relatively constant thereafter. Even though concentrations of trans-11 18: 1 followed the same pattern of temporal changes as cis-9, trans-11 CLA, the total trans 18:1 content of FSO milk was unchanged because of the concomitant increases in the concentration of other isomers (Delta(4-10) and Delta(12-15)), predominantely trans-10 18:1. In conclusion, supplementing diets with FSO enhances milk fat cis-9, trans-11 CLA content, but the high level of enrichment declines because of changes in ruminal biohydrogenation that result in trans-10 replacing trans-11 as the major 18:1 biohydrogenation intermediate formed in the rumen.

Amount of substance and the mole

The unit mole is very familiar amongst both chemists and physicists, but the name of the corresponding quantity 'amount of substance' is not so familiar and the concept is still a source of difficulty for many students. This paper reviews and clarifies these concepts and also discusses the definition of the unit mole, and its possible revision.

Learning across business sectors: facets of innovation in aerospace and construction

Innovation is notoriously difficult to define and is invariably intertwined with issues of knowledge creation, continuous improvement and organisational change. An extensive literature classifies numerous types of innovation and militates against any simplistic attempt at definition. It is widely accepted that innovation is at least partly dependent upon the surrounding environment. Industry recipes and institutionally embedded practices shape the environment within which innovation occurs. Recent research directions have addressed the diffusion of innovation and its dependence upon social and institutional structures. In this respect, it is highly pertinent to compare the way that innovation is interpreted and enacted in different industrial sectors. The comparison between UK aerospace and construction is especially revealing because the two sectors are so different and therefore constitute radically different climates for innovation. Empirical research is reported based on semi-structured interviews with practitioners from both sectors. Interpretations of innovation are found to differ dramatically between aerospace and construction. Within the context of an ongoing struggle to define innovation, both industries are striving to become more innovative. The aerospace sector is found to emphasise technical innovation whereas the construction sector emphasises process innovation. An overriding cultural bias in Western economies towards technological innovation results in the common perception that aerospace is much more innovative than construction. The experienced realities of practitioners in the two sectors are much more complex.

'They Shall Speak the Arabic Language and Take Pride in it': reconsidering the fate of Coptic after the Arab Conquest

The complaints on the adoption of Arabic by the Copts that are voiced by the Apocalypse of Pseudo-Samuel have often been quoted as the expiring words of the dying Coptic language. This article seeks to show that they are not to be taken so literally, and that they should rather be inserted in the context of a rift within the medieval Coptic church over the question of language choice, and beyond this, over that of accommodation with the Muslims. The use of Arabic by the episcopal church of Miṣr and by some prominent figures around it, which was linked to their proximity to the Fatimid court, was resented and denounced by more traditional circles, centred on the Patriarchate and on some important monasteries such as the one at Qalamūn where the Apocalypse was written. The suggestion is also made that the text is contemporary with the beginning of Coptic literary production in Arabic and with the introduction of Egyptian Christians at the caliphal court, namely in the last quarter of the tenth century, at the time of Severus ibn al-Muqqafa‘.

The current status of anticoagulant resistance in rats and mice in the UK

Introduction: Resistance to anticoagulants in Norway rats (Rattus norvegicus) and house mice (Mus domesticus) has been studied in the UK since the early 1960s. In no other country in the world is our understanding of resistance phenomena so extensive and profound. Almost every aspect of resistance in the key rodent target species has been examined in laboratory and field trials and results obtained by independent researchers have been published. It is the principal purpose of this document to present a short synopsis of this information. More recently, however, the development of genetical techniques has provided a definitive means of detection of resistant genotypes among pest rodent populations. Preliminary information from a number of such surveys will also be presented. Resistance in Norway rats: A total of nine different anticoagulant resistance mutations (single nucleotide polymorphisms or SNPs) are found among Norway rats in the UK. In no other country worldwide are present so many different forms of Norway rat resistance. Among these nine SNPs, five are known to confer on rats that carry them a significant degree of resistance to anticoagulant rodenticides. These mutations are: L128Q, Y139S, L120Q, Y139C and Y139F. The latter three mutations confer, to varying degrees, practical resistance to bromadiolone and difenacoum, the two second-generation anticoagulants in predominant use in the UK. It is the recommendation of RRAG that bromadiolone and difenacoum should not be used against rats carrying the L120Q, Y139C and Y139F mutations because this will promote the spread of resistance and jeopardise the long-term efficacy of anticoagulants. Brodifacoum, flocoumafen and difethialone are effective against these three genotypes but cannot presently be used because of the regulatory restriction that they can only be applied against rats that are living and feeding predominantly indoors. Our understanding of the geographical distribution of Norway rat resistance in incomplete but is rapidly increasing. In particular, the mapping of the focus of L120Q Norway rat resistance in central-southern England by DNA sequencing is well advanced. We now know that rats carrying this resistance mutation are present across a large part of the counties of Hampshire, Berkshire and Wiltshire, and the resistance spreads into Avon, Oxfordshire and Surrey. It is also found, perhaps as outlier foci, in south-west Scotland and East Sussex. L120Q is currently the most severe form of anticoagulant resistance found in Norway rats and is prevalent over a considerable part of central-southern England. A second form of advanced Norway rat resistance is conferred by the Y139C mutation. This is noteworthy because it occurs in at least four different foci that are widely geographically dispersed, namely in Dumfries and Galloway, Gloucestershire, Yorkshire and Norfolk. Once again, bromadiolone and difenacoum are not recommended for use against rats carrying this genotype and a concern of RRAG is that continued applications of resisted active substances may result in Y139C becoming more or less ubiquitous across much of the UK. Another type of advanced resistance, the Y139F mutation, is present in Kent and Sussex. This means that Norway rats, carrying some degree of resistance to bromadiolone and difenacoum, are now found from the south coast of Kent, west into the city of Bristol, to Yorkshire in the north-east and to the south-west of Scotland. This difficult situation can only deteriorate further where these three genotypes exist and resisted anticoagulants are predominantly used against them. Resistance in house mice: House mouse is not so well understood but the presence in the UK of two resistant genotypes, L128S and Y139C, is confirmed. House mice are naturally tolerant to anticoagulants and such is the nature of this tolerance, and the presence of genetical resistance, that house mice resistant to the first-generation anticoagulants are considered to be widespread in the UK. Consequently, baits containing warfarin, sodium warfarin, chlorophacinone and coumatetralyl are not approved for use against mice. This regulatory position is endorsed by RRAG. Baits containing brodifacoum, flocoumafen and difethialone are effective against house mice and may be applied in practice because house mouse infestations are predominantly indoors. There are some reports of resistance among mice in some areas to the second-generation anticoagulant bromadiolone, while difenacoum remains largely efficacious. Alternatives to anticoagulants: The use of habitat manipulation, that is the removal of harbourage, denial of the availability of food and the prevention of ingress to structures, is an essential component of sustainable rodent pest management. All are of importance in the management of resistant rodents and have the advantage of not selecting for resistant genotypes. The use of these techniques may be particularly valuable in preventing the build-up of rat infestations. However, none can be used to remove any sizeable extant rat infestation and for practical reasons their use against house mice is problematic. Few alternative chemical interventions are available in the European Union because of the removal from the market of zinc phosphide, calciferol and bromethalin. Our virtual complete reliance on the use of anticoagulants for the chemical control of rodents in the UK, and more widely in the EU, calls for improved schemes for resistance management. Of course, these might involve the use of alternatives to anticoagulant rodenticides. Also important is an increasing knowledge of the distribution of resistance mutations in rats and mice and the use of only fully effective anticoagulants against them.

Interacting effects of change in climate, human population, land use, and water use on biodiversity and ecosystem services

Human population growth and resource use, mediated by changes in climate, land use, and water use, increasingly impact biodiversity and ecosystem services provision. However, impacts of these drivers on biodiversity and ecosystem services are rarely analyzed simultaneously and remain largely unknown. An emerging question is how science can improve the understanding of change in biodiversity and ecosystem service delivery and of potential feedback mechanisms of adaptive governance. We analyzed past and future change in drivers in south-central Sweden. We used the analysis to identify main research challenges and outline important research tasks. Since the 19th century, our study area has experienced substantial and interlinked changes; a 1.6°C temperature increase, rapid population growth, urbanization, and massive changes in land use and water use. Considerable future changes are also projected until the mid-21st century. However, little is known about the impacts on biodiversity and ecosystem services so far, and this in turn hampers future projections of such effects. Therefore, we urge scientists to explore interdisciplinary approaches designed to investigate change in multiple drivers, underlying mechanisms, and interactions over time, including assessment and analysis of matching-scale data from several disciplines. Such a perspective is needed for science to contribute to adaptive governance by constantly improving the understanding of linked change complexities and their impacts.

Construction management research: a field of application

Research in construction management is diverse in content and in quality. There is much to be learned from more fundamental disciplines. Construction is a sub-set of human experience rather than a completely separate phenomenon. Therefore, it is likely that there are few problems in construction requiring the invention of a completely new theory. If construction researchers base their work only on that of other construction researchers, our academic community will become less relevant to the world at large. The theories that we develop or test must be of wider applicability to be of any real interest. In undertaking research, researchers learn a lot about themselves. Perhaps the only difference between research and education is that if we are learning about something which no-one else knows, then it is research, otherwise it is education. Self-awareness of this will help to reduce the chances of publishing work which only reveals a researcher’s own learning curve. Scientific method is not as simplistic as non-scientists claim and is the only real way of overcoming methodological weaknesses in our work. The reporting of research may convey the false impression that it is undertaken in the sequence in which it is written. Construction is not so unique and special as to require a completely different set of methods from other fields of enquiry. Until our research is reported in mainstream journals and conferences, there is little chance that we will influence the wider academic community and a concomitant danger that it will become irrelevant. The most useful insights will come from research which challenges the current orthodoxy rather than research which merely reports it.

Construction research: a field of application

Research in construction management is diverse in content and in quality. There is much to be learned from more fundamental disciplines. Construction is a sub-set of human experience rather than a completely separate phenomenon. Therefore, it is likely that there are few problems in construction requiring the invention of a completely new theory. If construction researchers base their work only on that of other construction researchers, our academic community will become less relevant to the world at large. The theories that we develop or test must be of wider applicability to be of any real interest. In undertaking research, researchers learn a lot about themselves. Perhaps the only difference between research and education is that if we are learning about something which no-one else knows, then it is research, otherwise it is education. Self-awareness of this will help to reduce the chances of publishing work which only reveals a researcher’s own learning curve. Scientific method is not as simplistic as non-scientists claim and is the only real way of overcoming methodological weaknesses in our work. The reporting of research may convey the false impression that it is undertaken in the sequence in which it is written. Construction is not so unique and special as to require a completely different set of methods from other fields of enquiry. Until our research is reported in mainstream journals and conferences, there is little chance that we will influence the wider academic community and a concomitant danger that it will become irrelevant. The most useful insights will come from research which challenges the current orthodoxy rather than research which merely reports it.

Bioorganometallic fulvene-derived titanocene anti-cancer drugs

A review. 6-Substituted fulvenes are interesting and easily accessible starting materials for the synthesis of novel substituted titanocenes via reductive dimerization, carbolithiation or hydridolithiation reactions, which are followed by a transmetallation reaction with titanium tetrachloride in the latter two cases. Depending on the substitution pattern, these titanocenes prove to be bioorganometallic anticancer drugs, which have significant potential against advanced or metastatic renal-cell cancer. Patients bearing these stages of kidney cancer have a poor prognosis so far and therefore real progress in the area of metal-based anticancer drugs may come from this simple and effective synthetic approach. This tutorial review provides an insight into the synthesis of fulvene-derived titanocenes and their activity in preclin. expts.

The sociology of childhood as scientific communication - Observations from a social systems perspective

This article begins by identifying a close relationship between the image of children generated by several sociologists working within the new sociology of childhood perspective and the claims and ambitions of the proponents of children's autonomy rights. The image of the child as a competent, self-controlled human agent are then subjected to observation from the perspective of Niklas Luhmann's social systems theory. The new sociology of childhood's constructivist approach is compared and contrasted with Niklas Luhmann's theory of 'operational constructivism'. The article applies tenets of Luhmann's theory, to the emergence of the new childhood sociologist's image of the child as a competent, self-controlled social agent, to the epistemological status of this image and, in particular, to claims that it derives from scientific endeavour. The article proceeds to identify two theoretical developments within sociology - sociology of identity and social agency - which have brought about fundamental changes in what may be considered 'sociological' and so 'scientific' and paved the way for sociological communications about what children,really are'. In conclusion, it argues that the merging of sociology with polemics, ideology, opinion and personal beliefs and, at the level of social systems, between science and politics represents in Luhmann's terms 'dedifferentiation'- a tendency he claims may have serious adverse consequences for modern society. This warning is applied to the scientific status of sociology - its claim to be able to produce 'facts' for society, upon which social systems, such as politics and law, may rely. Like the mass media, sociology may now be capable of producing only information, and not facts, about children.