Stability of solutions of linear difference equations with periodic coefficients

This paper represents the last technical contribution of Professor Patrick Parks before his untimely death in February 1995. The remaining authors of the paper, which was subsequently completed, wish to dedicate the article to Patrick. A frequency criterion for the stability of solutions of linear difference equations with periodic coefficients is established. The stability criterion is based on a consideration of the behaviour of a frequency hodograph with respect to the origin of coordinates in the complex plane. The formulation of this criterion does not depend on the order of the difference equation.

Some numerical experiments on the effect of the variation of static stability in two-layer quasi-geostrophic models

A method to solve a quasi-geostrophic two-layer model including the variation of static stability is presented. The divergent part of the wind is incorporated by means of an iterative procedure. The procedure is rather fast and the time of computation is only 60–70% longer than for the usual two-layer model. The method of solution is justified by the conservation of the difference between the gross static stability and the kinetic energy. To eliminate the side-boundary conditions the experiments have been performed on a zonal channel model. The investigation falls mainly into three parts: The first part (section 5) contains a discussion of the significance of some physically inconsistent approximations. It is shown that physical inconsistencies are rather serious and for these inconsistent models which were studied the total kinetic energy increased faster than the gross static stability. In the next part (section 6) we are studying the effect of a Jacobian difference operator which conserves the total kinetic energy. The use of this operator in two-layer models will give a slight improvement but probably does not have any practical use in short periodic forecasts. It is also shown that the energy-conservative operator will change the wave-speed in an erroneous way if the wave-number or the grid-length is large in the meridional direction. In the final part (section 7) we investigate the behaviour of baroclinic waves for some different initial states and for two energy-consistent models, one with constant and one with variable static stability. According to the linear theory the waves adjust rather rapidly in such a way that the temperature wave will lag behind the pressure wave independent of the initial configuration. Thus, both models give rise to a baroclinic development even if the initial state is quasi-barotropic. The effect of the variation of static stability is very small, qualitative differences in the development are only observed during the first 12 hours. For an amplifying wave we will get a stabilization over the troughs and an instabilization over the ridges.

The Masters in Teaching and Learning (MTL): a retrospective, intrinsic case study of the process of policy into practice and its impact on teacher participants

The research reported here is a retrospective case study of the recent (2010) introduction of the Masters in Teaching and Learning (MTL) as a post-graduate level programme of professional development for teachers. It contributes to the debate and research over the past two decades about the impact of post-graduate professional development and appropriate ways of delivering it. The study is located within an extensive body of literature dealing with the importance of the teaching profession with regard to the success of schools and pupils and the impact of professional development on teaching quality and of teaching quality on attainment. A further relevant context is the ongoing tension between the teaching profession and academics on the one hand and government and political actors on the other, in respect of the approaches to professional development and to the control of educational processes. The research questions which inform the study deal with the perspectives of various participants – policy makers, programme directors, coaches and teachers studying for the MTL – on the extent to which the MTL is likely to have an ameliorative effect on teaching and pupil attainment, their experiences of the process of policy development and their experiences as course participants. The study adopts a case study approach which involves elite interviews with those responsible for the development and implementation of the MTL, questionnaires completed by MTL course participants and a comparison group taking a conventional MA and in depth interviews with participants and coaches. The results revealed tensions and difficulties associated with the development of the MTL including uneasy relationships between HE institutions and government agencies, ideas about ‘producer capture’, the relevance of the MBA model and concern over the role of coaches. However, while acknowledging various difficulties and some misconceived expectations they viewed its potential to meet its expressed aims positively, given time. Course participants were positive about their experience of the MTL and felt that it had contributed to many aspects of their professional development. Most saw it as a positive experience despite the variable quality of support from their schools, particularly in the form of the school-based coach the concept of which had been heralded as the bellwether of the MTL. It was striking that the responses of the MTL participants were very similar to those of teachers taking a conventional MA. A finding which would repay further investigation is that while the great majority of course participants felt that the MTL (and the MA) had contributed to their becoming more effective teachers they were much less confident that it had contributed to increased pupil attainment.

Seeds of growth? Agricultural productivity and the transitional dynamics of the Ramsey model

A two-sector Ramsey-type model of growth is developed to investigate the relationship between agricultural productivity and economy-wide growth. The framework takes into account the peculiarities of agriculture both in production ( reliance on a fixed natural resource base) and in consumption (life-sustaining role and low income elasticity of food demand). The transitional dynamics of the model establish that when preferences respect Engel's law, the level and growth rate of agricultural productivity influence the speed of capital accumulation. A calibration exercise shows that a small difference in agricultural productivity has drastic implications for the rate and pattern of growth of the economy. Hence, low agricultural productivity can form a bottleneck limiting growth, because high food prices result in a low saving rate.

The failure of meta-analytic asymptotics for the seemingly efficient estimator of the common risk difference

We consider the case of a multicenter trial in which the center specific sample sizes are potentially small. Under homogeneity, the conventional procedure is to pool information using a weighted estimator where the weights used are inverse estimated center-specific variances. Whereas this procedure is efficient for conventional asymptotics (e. g. center-specific sample sizes become large, number of center fixed), it is commonly believed that the efficiency of this estimator holds true also for meta-analytic asymptotics (e.g. center-specific sample size bounded, potentially small, and number of centers large). In this contribution we demonstrate that this estimator fails to be efficient. In fact, it shows a persistent bias with increasing number of centers showing that it isnot meta-consistent. In addition, we show that the Cochran and Mantel-Haenszel weighted estimators are meta-consistent and, in more generality, provide conditions on the weights such that the associated weighted estimator is meta-consistent.

On the system of rational difference equations x(n) = A+(1)over-bar y(n-p), y(n) = A+(gamma(n-1))over-bar x(n-r)y(n-5)

In this paper, we study the behavior of the positive solutions of the system of two difference equations [GRAPHICS] where p >= 1, r >= 1, s >= 1, A >= 0, and x(1-r), x(2-r),..., x(0), y(1-max) {p.s},..., y(0) are positive real numbers. (c) 2005 Elsevier Inc. All rights reserved.

Measurement of apolipoprotein B-48 in the Svedberg flotation rate (Sf) > 400, Sf 60 – 400 and Sf 20 – 60 lipoprotein fractions reveals novel findings with respect to the effects of dietary fatty acids on triacylglycerol-rich lipoproteins in postmenopausal women

The present study was designed to examine whether the type of fat ingested in an initial test meal influences the response and density distribution of dietary-derived lipoproteins in the Svedberg flotation rate (Sf)>400, Sf 60 - 400 and Sf 20 - 60 lipoprotein fractions. A single-blind randomized within-subject crossover design was used to study the effects of palm oil, safflower oil, a mixture of fish and safflower oil, and olive oil on postprandial apolipoprotein (apo) B-48, retinyl ester and triacylglycerol responses in each lipoprotein fraction following an initial test meal containing one of the oils and a second standardized test meal. For all dietary oils, late postprandial (300min) concentrations of triacylglycerol and apo B-48 were significantly higher in the Sf 60 - 400 fraction than in the Sf>400 fraction (P<0.02). Significantly greater apo B-48 incremental areas under the curve (IAUCs) were also observed in the Sf 60 - 400 fraction than in the Sf>400 fraction following palm oil, safflower oil and olive oil (P<0.04), with a similar non-significant trend for fish/safflower oil. Olive oil resulted in a significantly greater apo B-48 IAUC in the Sf>400 fraction (P<0.02) than did any of the other dietary oils, as well as a tendency for a higher IAUC in the Sf 60 - 400 fraction compared with the palm, safflower and fish/safflower oils. In conclusion, we have found that the majority of intestinally derived lipoproteins present in the circulation following meals enriched with saturated, polyunsaturated or monounsaturated fatty acids are of the density and size of small chylomicrons and chylomicron remnants. Olive oil resulted in a greater apo B-48 response compared with the other dietary oils following sequential test meals, suggesting the formation of a greater number of small (Sf 60 - 400) and large (Sf>400) apo B-48-containing lipoproteins in response to this dietary oil.

Physicality, difference, and the challenge of representation: Werner Herzog in the Light of the new waves

This chapter looks into the gap between presentational realism and the representation of physical experience in Werner Herzog's work so as to retrieve the indexical trace – or the absolute materiality of death. To that end, it draws links between Herzog and other directors akin to realism in its various forms, including surrealism. In particular, it focuses on François Truffaut and Glauber Rocha, representing respectively the Nouvelle Vague and the Cinema Novo, whose works had a decisive weight on Herzog’s aesthetic choices to the point of originating distinct phases of his outputs. The analyses, though restricted to a small number of films, intends to re-evaluate Herzog’s position within, and contribution to, film history.

Utilizing electronic effects in the modulation of BTPhen ligands with respect to the partitioning of minor actinides from lanthanides

Effects of bromine substitution at the 5 and 5,6-positions of the 1,10-phenanthroline nucleus of BTPhen ligand on their extraction properties for Ln(III) andAn(III) cations have been studied. Compared to C5-BTPhen, electronic modulation in BrC5-BTPhen and Br2C5-BTPhen enabled these ligands to be fine-tuned in order to enhance the separation selectivity of Am(III) from Eu(III)

Beyond difference: female participation in the Brazilian film revival of the 1990s

In this chapter, I will focus on the female participation in what became known as ‘The Retomada do Cinema Brasileiro’, or the Brazilian Film Revival, by thinking beyond differences of gender, class, age and ethnicity. I will first re-consider the Retomada phenomenon against the backdrop of its historical time, so as to evaluate whether the production boom of the period translated into a creative peak, and, if so, how much of this carried onto the present day. I will then look at the female participation in this phenomenon not just in terms of numerical growth of women film directors, admittedly impressive, but only partially reflective of the drastic changes in the modes of production and address effected by the neoliberal policies introduced in the country in the mid 1990s. I will argue that the most decisive contribution brought about by the rise of women in Brazilian filmmaking has been the spread of team work and shared authorship, as opposed to a mere aspiration to the auteur pantheon, as determined by a notoriously male-oriented tradition. Granted, films focusing on female victimisation were rife during the Retomada period and persist to this day, and they have been, and continue to be, invaluable for the understanding of women’s struggles in the country. However, rather than resorting to feminist readings of representational strategies in these films, I will draw attention to other, presentational aesthetic experiments, open to the documentary contingent and the unpredictable real, which, I argue, suspend the pedagogical character of representational narratives. In order to demonstrate that new theoretical tools are needed to understand the gender powers at play in contemporary world cinema, I will, to conclude, analyse an excerpt of the film, Delicate Crime (Crime delicado, Beto Brant, 2006), where team work comes out as a particularly effective female, and feminist, procedure.