Quadrature domains and kernel function zipping

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati

Conditions for negative specific heat in systems of attracting classical particles

We identify conditions for the presence of negative specific heat in non-relativistic self-gravitating systems and similar systems of attracting particles. The method used, is to analyse the Virial theorem and two soluble models of systems of attracting particles, and to map the sign of the specific heat for different combinations of the number of spatial dimensions of the system, $D$($\geq 2$), and the exponent, $\nu$($\neq 0$), in the force potential, $\phi=Cr^\nu$. Negative specific heat in such systems is found to be present exactly for $\nu=-1$, at least for $D \geq 3$. For many combinations of $D$ and $\nu$ representing long-range forces, the specific heat is positive or zero, for both models and the Virial theorem. Hence negative specific heat is not caused by long-range forces as such. We also find that negative specific heat appears when $\nu$ is negative, and there is no singular point in a certain density distribution. A possible mechanism behind this is suggested.Comment: 11 pages, 1 figure, Published version (including correlation between positive specific heat and singular points

Exact General Solutions to Extraordinary N-body Problems

We solve the N-body problems in which the total potential energy is any function of the mass-weighted root-mean-square radius of the system of N point masses. The fundamental breathing mode of such systems vibrates non-linearly for ever. If the potential is supplemented by any function that scales as the inverse square of the radius there is still no damping of the fundamental breathing mode. For such systems a remarkable new statistical equilibrium is found for the other coordinates and momenta, which persists even as the radius changes continually.Comment: 15 pages, LaTeX. Accepted for publication in Proc. Roy. Soc.

Temporary nutrient deficiency - a difficult case for diagnosis and prognosis by plant analysis

Plant analysis aims to either detect deficiency at the time of sampling (diagnosis) or predict its occurrence at a later stage of growth (prognosis). Its use is based on the presumption that the plant nutrient status will either be constant with plant age or follow a predictable pattern of change over time after sampling. However, a period of deficiency during plant growth followed by the recovery of nutrient uptake to satisfactory rates may cause an irreversible impairment of growth which plant analysis fails to diagnose or predict. Several cases are considered, each involving a temporary deficiency of, or interruption to nutrient supply. Such cases generally involve but are not restricted to micronutrient deficiency. For example, B deficiency impairs early seedling growth when seeds low in B are planted, even on B fertilised soils. Low B concentration in seeds diagnoses the subsequent impairment of seed germination or seedling establishment: however, leaf analysis after emergence does not. Similarly, Zn deficiency impairs early growth of transplanted oilseed rape (Brassica napus L.) seedlings and eventually depresses seed yield. However, leaf analysis during crop growth fails to diagnose a Zn deficiency. Finally, temporary B deficiency induced by low vapour pressure deficit or low soil water especially during reproductive development may depress yield markedly but remain difficult to diagnose by plant analysis. Strategies for diagnosing and predicting such temporary deficiencies are discussed including the measurement of environmental parameters such as pan evaporation or rainfall and their inclusion in multi‐variate regression models of plant response to nutrients

LSE centre for economic performance: bankers’ bonuses

A new series of Election Analyses is now available from the LSE’s Centre for Economic Performance (CEP). The series will discuss the research evidence on some of the key policy battlegrounds of the 2010 General Election, including macroeconomic policy, immigration, health, education, crime, poverty and inequality, labour market policy, regional policy, energy and the environment, financial regulation and bankers’ bonuses, and foreign aid. The latest CEP Election Analysis, by Brian Bell, gives an overview of bankers’ bonuses and extreme wage inequality, one of the key battlegrounds of the 2010 General Election. The publication is summarised below and can be found in full on the CEP Election Analysis Site

Connectivism: Its place in theory-informed research and innovation in technology-enabled learning

The sociotechnical context for learning and education is dynamic and makes great demands on those trying to seize the opportunities presented by emerging technologies. The goal of this paper is to explore certain theories for our plans and actions in technology-enabled learning. Although presented as a successor to previous learning theories, connectivism alone is insufficient to inform learning and its support by technology in an internetworked world. However, because of its presence in massive open online courses (MOOCs), connectivism is influential in the practice of those who take these courses and who wish to apply it in teaching and learning. Thus connectivism is perceived as relevant by its practitioners but as lacking in rigour by its critics. Five scenarios of change are presented with frameworks of different theories to explore the variety of approaches educators can take in the contexts for change and their associated research/evaluation. I argue that the choice of which theories to use depends on the scope and purposes of the intervention, the funding available to resource the research/evaluation, and the experience and philosophical stances of the researchers/practitioners

Bell's inequalities I: An explanation for their experimental violation

Derivations of two Bell's inequalities are given in a form appropriate to the interpretation of experimental data for explicit determination of all the correlations. They are arithmetic identities independent of statistical reasoning and thus cannot be violated by data that meets the conditions for their validity. Two experimentally performable procedures are described to meet these conditions. Once such data are acquired, it follows that the measured correlations cannot all equal a negative cosine of angular differences. The relation between this finding and the predictions of quantum mechanics is discussed in a companion paper.Comment: 15 pages, 2 figure