On the Asymptotic Existence of Hadamard Matrices

It is conjectured that Hadamard matrices exist for all orders $4t$ ($t>0$). However, despite a sustained effort over more than five decades, the strongest overall existence results are asymptotic results of the form: for all odd natural numbers $k$, there is a Hadamard matrix of order $k2^{[a+b\log_2k]}$, where $a$ and $b$ are fixed non-negative constants. To prove the Hadamard Conjecture, it is sufficient to show that we may take $a=2$ and $b=0$. Since Seberry's ground-breaking result, which showed that we may take $a=0$ and $b=2$, there have been several improvements where $b$ has been by stages reduced to 3/8. In this paper, we show that for all $\epsilon>0$, the set of odd numbers $k$ for which there is a Hadamard matrix of order $k2^{2+[\epsilon\log_2k]}$ has positive density in the set of natural numbers. The proof adapts a number-theoretic argument of Erdos and Odlyzko to show that there are enough Paley Hadamard matrices to give the result.Comment: Keywords: Hadamard matrices, Asymptotic existence, Cocyclic Hadamard matrices, Relative difference sets, Riesel numbers, Extended Riemann hypothesis. (Received 2 August 2008, Available online 18 March 2009

English Traders and the Spanish Canary Inquisition in the Canaries during the Reign of Queen Elizabeth

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Editorial: water governance in a climate change world: appraising systemic and adaptive effectiveness

and other research outputs Editorial: water governance in a climate change world: appraising systemic and adaptive effectivenes

Access to out-of-hospital emergency care in Africa : consensus conference recommendations

Abstract: Out-of-hospital emergency care (OHEC) should be accessible to all who require it. However available data suggests that there are a number of barriers to such access in Africa, mainly centred around challenges in public knowledge, perception and appropriate utilisation of OHEC. Having reached consensus in 2013 on a two-tier system of African OHEC, the African Federation for Emergency Medicine (AFEM) OHEC Group sought to gain further consensus on the narrower subject of access to OHEC in Africa. The objective of this paper is to report the outputs and statements arising from the AFEM OHEC access consensus meeting, held in Cape Town, South Africa in April 2015. The discussion was structured around six dimensions of access to care (awareness, availability, accessibility, accommodation, affordability and acceptability) and tackled both Tier-1 (community first responder) and Tier-2 (formal prehospital services and Emergency Medical Services) OHEC systems. In Tier-1 systems, the role of community involvement and support was emphasised, along with the importance of a first responder system acceptable to the community in which it is embedded in order to optimise access. In Tier-2 systems, the consensus group highlighted the primacy of a single toll-free emergency number , matching of Emergency Medical Services resource demand and availability through appropriate planning and the cost-free nature of Tier-2 emergency care, among other factors that impact accessibility. Much work is still needed in prioritising the steps and clarifying the tools and metrics that would enable the ideal of optimal access to OHEC in Africa

Hoogveen en klimaatverandering in Nederland

Voor de instandhouding en ontwikkeling van hoogveen zijn het neerslagoverschot, de temperatuur en de positie in het landschap belangrijk. Gunstige ontwikkelingen doen zich voor in gebieden waar het (actieve) hoogveen water uit zijn omgeving ontvangt. De landelijke instandhoudingsdoelen voor Natura 2000-habitattype Actieve hoogvenen kunnen waarschijnlijk ook onder het klimaatscenario W+ worden gerealiseerd: behoud van kwaliteit en oppervlakte zijn kansrijk en verbetering van kwaliteit en uitbreiding van oppervlakte zijn mogelijk. Voorwaarden hierbij zijn een optimale waterhuishouding. Dat wil zeggen voldoende hoge grondwaterstanden in de zandondergrond en de veenbasis in combinatie met een waterondoorlatende (veen)laag en/of de toevoer van lokaal grondwater. Om hoogvenen op de lange termijn in Nederland te behouden onder het W+- scenario zijn waterhuishoudkundige maatregelen nodig, zoals de aanleg en inrichting van bufferzones en compartimenten en/of door het bevorderen van kwel