Recognition of plane-to-plane map-germs

We present a complete set of criteria for determining A-types of plane-to-plane map-germs of corank one with A-codimension <7, which provides a new insight into the A-classification theory from the viewpoint of recognition problem. As an application to generic differential geometry, we discuss about projections of smooth surfaces in 3-space.Comment: 22 page

Binary differential equations at parabolic and umbilical points for 22-parameter families of surfaces

We determine local topological types of binary differential equations of asymptotic curves at parabolic and flat umbilical points for generic $2$-parameter families of surfaces in $\mathbb P^3$ by comparing our projective classification of Monge forms and classification of general BDE obtained by Tari and Oliver. In particular, generic bifurcations of the parabolic curve are classified. The flecnodal curve is also examined by direct computations, and we present new bifurcation diagrams in typical examples.Comment: 20 page

Turning fish soup back into fish: The wicked problem of African Community land rights

Africa’s postcolonial disputes over community land rights are a “wicked” problem, not evil, but resistant to resolution. This article investigates three such disputes in Kenya (Endorois, Ogiek and Nubian community) where the African Commission and Court of Human and Peoples’ Rights have determined in the communities’ favour but the implementation is not progressing, both because of opposition by the state and the complex and long-standing nature of the cases. The legal history of colonial trust lands and recent community land legislation is discussed, the three key cases are summarized, and issues of indigenous people’s status, admissibility and respondent government discussed in relation to the UN Declarations on Rights of Indigenous Peoples (1987), Right to Development (1986), and Land Issues (2009). Practical and political aspects of implementing the determinations are examined, and recommendations proposed.Keywords: Indigenous people’s rights; Endorois; Ogiek; Nubian community; Kibera; land law reform; African Union enforcement