On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type

We provide a comprehensive analysis of sharp bilinear estimates of Ozawa-Tsutsumi type for solutions u of the free Schr\"odinger equation, which give sharp control on $|u|^2$ in classical Sobolev spaces. In particular, we provide a generalization of their estimates in such a way that provides a unification with some sharp bilinear estimates proved by Carneiro and Planchon-Vega, via entirely different methods, by seeing them all as special cases of a one parameter family of sharp estimates. We show that the extremal functions are solutions of the Maxwell-Boltzmann functional equation and provide a new proof that this equation admits only Gaussian solutions. We also make a connection to certain sharp estimates on $u^2$ involving certain dispersive Sobolev norms.Comment: 17 pages, references update

Challenges for qualitative electrical reasoning in automotive circuit simulation

Qualitative reasoning about electrical systems has reached a level of achievement which allows it to be used for applications on realistic automotive circuits. The type of circuits for which it is most effective can be characterised as circuits with a single steady state for each combination of inputs. Many automotive circuits with more complex overall behaviour can be approximated using this type of modelling by representing the behaviour of more complex components only at a functional level, or by judicious use of simplifying assumptions. This paper will consider examples of circuitry in modern cars where such approximations of behaviour are unsatisfactory, and will examine the modelling issues that are thrown up by these cases, in order to identify challenges for qualitative electrical reasoning against which future advances in the field can be assessed

The Potential Cost to New Zealand Dairy Farmers from the Introduction of Nitrate-Based Stocking Rate Restrictions

Introducing a stocking rate restriction is one possible course of action for regulators to improve water quality where it is affected by nitrate pollution. To determine the impact of a stocking rate restriction on a range of New Zealand dairy farms, a whole-farm model was optimised with and without a maximum stocking rate of 2.5 cows per hectare. Three farm systems, which differ by their level of feed-related capital, were examined for the changes to the optimal stocking rate and optimal level of animal milk production genetics when utility was maximised. The whole-farm model was optimised through the use of an evolutionary algorithm called differential evolution. The introduction of a stocking rate restriction would have a very large impact on the optimally organised high feed-related capital farm systems, reducing their certainty equivalent by almost half. However, there was no impact on the certainty equivalent of low feed-related capital systems.environmental regulation, dairy farms, whole-farm model, evolutionary algorithm, Environmental Economics and Policy, Livestock Production/Industries, Q12, Q52, C61,

A language for functional interpretation of model based simulation

Functional modeling is in use for the interpretation of the results of model based simulation of engineered systems for design analysis, enabling the automatic generation of a textual design analysis report that expresses the results of the simulation in terms of the system’s purpose. We present a novel functional description language that increases the expressiveness of this approach, allowing a system function to be decomposed in terms of subsidiary functions as well as required effects, increasing the range both of systems and design analysis tasks for which the approach can be used.

The Value of Grid-Scale Variable Renewable Energy Generation in Sub-Saharan Africa

This report was produced for the Green Growth Diagnostics for Africa project, funded by the Engineering and Physical Sciences Research Council.Securing a sufficient supply of reliable and affordable electricity is a huge challenge for countries in sub-Saharan Africa. Many countries in the region are experiencing rapid increases in the size of their populations, and even more rapid growth in their economies. As a result, the region experienced a 45 per cent increase in annual energy consumption between the years 2000-2014, with the growth in some countries much higher. This article surveys the most relevant research, policies and sources of data relevant to generation adequacy assessment in two example SSA countries: Kenya and Ghana. It also includes an exploratory analysis of the temporal relationships between the hydro resource, wind resource and power demand in Kenya, with an emphasis on assessing the impact of limited data availability