The role of African Union law in integrating Africa

This article traces how the development of regional law is linked to the state of regional integration in Africa. Given the prominent role European Union law plays in the functioning of the European Union, the question is posed whether there is similar scope for the development of ‘African Union law’, a term not established hitherto. Initially devoid from the necessary supranational elements required to adopt law that would automatically bind member states, the African Union is leaning towards a functionalist approach paving the way for transfer of sovereign powers to African Union institutions. It is argued that law-making capacity, be it through the activities of the Pan-African Parliament, the Peace and Security Council or the African court system are necessary requirements to accelerate the process of regional integration. African Union law will hold member states accountable to comply with international and continentally agreed standards on inter alia democracy, good governance and human rights

Strange pulsation modes in luminous red giants

We show that the spectrum of radial pulsation modes in luminous red giants consists of both normal modes and a second set of modes with periods similar to those of the normal modes. These additional modes are the red giant analogues of the strange modes found in classical Cepheids and RR Lyrae variables. Here, we describe the behaviour of strange and normal modes in luminous red giants and discuss the dependence of both the strange and normal modes on the outer boundary conditions. The strange modes always appear to be damped, much more so than the normal modes. They should never be observed as self-excited modes in real red giants but they may be detected in the spectrum of solar-like oscillations. A strange mode with a period close to that of a normal mode can influence both the period and growth rate of the normal mode.Comment: 6 pages, 5 figures, accepted by MNRA

A cross-country comparison of market structures in European banking

In order to assess the effect of EMU on market conditions for banks based in countries which adopt the Single Currency, we use the H indicator suggested by Panzar and Rosse (1987). Our contribution is to assess results separately for large and small banks, and for interest income and total income as a dependent variable. From a panel of banks over the period 1992-1996, we provide evidence that European banking markets for large banks in the mid-1990s were still characterised by monopolistic competition, as compared to the United States. Regarding small banks, the level of competition appears to be even lower, especially in France and Germany. EMU would therefore imply a notable rise in competition for small banks in France and Germany, as well as an increase in competition for large banks, especially in Italy. JEL Classification: G21, L12banking, competition, contestability, EMU, panel data analysis

Denominators of Bernoulli polynomials

For a positive integer $n$ let $\mathfrak{P}_n=\prod_{s_p(n)\ge p} p,$ where $p$ runs over all primes and $s_p(n)$ is the sum of the base $p$ digits of $n$. For all $n$ we prove that $\mathfrak{P}_n$ is divisible by all "small" primes with at most one exception. We also show that $\mathfrak{P}_n$ is large, has many prime factors exceeding $\sqrt{n}$, with the largest one exceeding $n^{20/37}$. We establish Kellner's conjecture, which says that the number of prime factors exceeding $\sqrt{n}$ grows asymptotically as $\kappa \sqrt{n}/\log n$ for some constant $\kappa$ with $\kappa=2$. Further, we compare the sizes of $\mathfrak{P}_n$ and $\mathfrak{P}_{n+1}$, leading to the somewhat surprising conclusion that although $\mathfrak{P}_n$ tends to infinity with $n$, the inequality $\mathfrak{P}_n>\mathfrak{P}_{n+1}$ is more frequent than its reverse.Comment: 25 page

Visual analysis for drum sequence transcription

A system is presented for analysing drum performance video sequences. A novel ellipse detection algorithm is introduced that automatically locates drum tops. This algorithm fits ellipses to edge clusters, and ranks them according to various fitness criteria. A background/foreground segmentation method is then used to extract the silhouette of the drummer and drum sticks. Coupled with a motion intensity feature, this allows for the detection of ‘hits’ in each of the extracted regions. In order to obtain a transcription of the performance, each of these regions is automatically labeled with the corresponding instrument class. A partial audio transcription and color cues are used to measure the compatibility between a region and its label, the Kuhn-Munkres algorithm is then employed to find the optimal labeling. Experimental results demonstrate the ability of visual analysis to enhance the performance of an audio drum transcription system