In this Letter we show the existence of bidifferential structures on finite Hopf algebras, which arise from quantum groups at roots of unity.

We prove some general results on the existence of partitions of unity in Sobolev type spaces on various innnite dimensional manifolds. As special cases we obtain in particular, (continuous) partitions of unity a) in the Malliavin test functions on an abstract Wiener space; b) in the rst order Sobolev space on pinned and free loop spaces; c) in the rst order Sobolev spaces associated with revers...

various studies on the national policy on education (npe) have concentrated on the cognitive value of pedagogy and learning of the language aspect but few have viewed its importance on the togetherness of the nation - nigeria. this paper deals with how the language policy can influence and ensure the co-existence of nigeria in achieving self-actualisation, national unity, social, cultural, econ...

It is a crucial aspect of everyday mental functioning that we are in some way aware of ourselves. But it is far from clear at first sight just what this self-awareness consists in, and indeed just what the self is that we are aware of. It is possible to give an answer to the second question that is mundane and unproblematic. The self one is aware of in everyday life is simply the individual tha...

Psychologists and philosophers have recently argued that our concepts of ‘person’ or ‘self’ are plural. Some we should also adopt a corresponding pluralism about the metaphysics self. The aim this paper is twofold. First, I sketch motivate an approach to personal identity supports inference from facts how think self nature On proposed view, self-concept partly determines This provides new justi...

This paper examined the problem of kidnapping and its consequences in Nigeria. Kidnapping has potential creating social tension, psychological trauma (mental emotional problems), insecurity, untimely death others society. It been observed identified that is not a new crime Nigeria other countries world. But apparent current growth rate all parts country benefits perpetrators are deriving from t...

Simon Clarke played an unrivalled role in the intellectual trajectory of his former students and significantly shaped research field sociology post-Soviet Russia. While work appears comprised two distinct lines inquiry, essential unity Simon’s project may be appreciated by zooming on factors that motivated entirety work, such as ethical orientation a desire to understand mediations social relat...

We construct an index theorem for smooth infinite economies that shows that generically the number of equilibria is odd. As a corollary, this gives a new proof of existence and gives conditions that guarantee global uniqueness of equilibria.