A vase of catenoids

In this note we construct a vase of catenoids - a symmetric immersed minimal surface with planar and catenoid ends

A note on balance equations for doubly periodic minimal surfaces

Most known examples of doubly periodic minimal surfaces in $\mathbb{R}^3$ with parallel ends limit as a foliation of $\mathbb{R}^3$ by horizontal noded planes, with the location of the nodes satisfying a set of balance equations. Conversely, for each set of points providing a balanced configuration, there is a corresponding three-parameter family of doubly periodic minimal surfaces. In this note we derive a differential equation that is equivalent to the balance equations for doubly periodic minimal surfaces. This allows for the generation of many more solutions to the balance equations, enabling the construction of increasingly complicated surfaces

Regional distribution of photovoltaic deployment in the UK and its determinants: A spatial econometric approach

Photovoltaic (PV) panels offer significant potential for contributing to the UK's energy policy goals relating to decarbonisation of the energy system, security of supply and affordability. The substantive drop in the cost of panels since 2007, coupled with the introduction of the Feed-in Tariff (FiT) Scheme in 2010, has resulted in a rapid increase in installation of PV panels in the UK, from 26.5MWp in 2009 to over 5GW by the end of 2014. Yet there has been no comprehensive analysis of the determinants of PV deployment in the UK. This paper addresses this gap by employing spatial econometrics methods to a recently available data set at a fine geographical detail. Following a traditional regression analysis, a general to specific approach has been adopted where spatial variations in the relationships have been examined utilising the spatial Durbin model using the cross-sectional data relating to the UK NUTS level 3 data. Empirical results indicate that demand for electricity, population density, pollution levels, education level of households and housing types are among the factors that affect PV uptake in a region. Moreover Lagrange Multiplier test results indicate that the spatial Durbin model may be properly applied to describe the PV uptake relationship in the UK as there are significant regional spillover effects

The ability of the European Parliament to enhance the functioning of democracy within the European Union

The European Union consists of a complex institutionalised decision-making system. As the only directly-elected institution, the European Parliament has been empowered through successive treaties to improve the legitimacy and thus reduce the democratic deficit. The latest treaty, namely the Lisbon Treaty, sought to continue this trend by empowering the European Parliament further to a point it now constitutes a major institutional player in the decision-making process. This thesis will therefore attempt to answer the ability of the European Parliament to enhance the functioning of democracy within the European Union. It will do so by examining a number of key policy areas such as appointment of the Commission College, enlargement of the European Union and legislative decision-making. These will be examined in regards to how the European Parliament participates in these fields and cooperates with the European Union’s institutions. It will also be considered how interinstitutional conflict is dealt with and how the European Parliament has internally structured itself in order to accomplish its goals. In order to interpret the findings of this research liberal intergovernmentalism has been identified as a possible explanatory theory with its usefulness in explaining the central position of Member State control in European Union affairs. It will be found the European Parliament is able influence the decision-making process and those actors involved in a manner it was previously unable to do prior to the Lisbon Treaty which as a result has significant impacts on the democratic functioning of the European Union