From a chill grey day in London to be transported overnight to tropical heat and brilliant colours in Nigeria is enough to take one's breath away. During the three weeks of our stay we never lost that sense of wonder and strange beauty. At the invitation of Dr. Lambo, who made a memorable contribution to the N.A.M.H. Annual Conference in 1960, Lady Norman and I flew out to attend the first Pan ...

I give an introduction to algorithmic uses of the principle of inclusion–exclusion. The presentation is intended to be be concrete and accessible, at the expense of generality and comprehensiveness. R T 1 The principle of inclusion–exclusion. There are as many odd-sized as even-sized subsets sandwiched between two different sets: For R ⊆ T ,

We describe quantum tomography as an inverse statistical problem. We show results of consistency in different norms, for Pattern Function Projection Estimators as well as for Sieve Maximum Likelihood Estimators for the density matrix of the quantum state and its Wigner function. The density matrix and the Wigner function are two different ways of representing quantum state. Results are derived ...

This report is Chapter 1 in the author’s book Qualitative Computing: A computational journey into non linearity published by World Scientific, Singapore (2011). It presents an historical survey of the evolution of mathematical computation since Sumer four millennia ago. It shows how the laws of logic have evolved in the mind of mathematicians. This evolution has been driven by three major ideas...

Semigroups with an additional unary operation called a (right) closure are investigated. These “closure semigroups” may be viewed as (not necessarily regular) generalisations of inverse semigroups, and several powerful structural aspects of inverse semigroup theory are shown to extend naturally to some important classes of closure semigroups. These include representations as partial transformat...

The crystal of hydroxyapatite, Ca10 (PO4) 6 (OH) 2 has a characteristic that it varies easily depending on the acidic base environment around the enamel. The etymology of apatite is said to come from the Greek word meaning “to deceive” since it contains various elements in the Ca, PO4, and OH areas and changes appearance. In other words, the true character behind the demineralization and remine...

A selection of aspects of the theory of bounded cohomology is presented. The emphasis is on questions motivating the use of that theory as well as on some concrete issues suggested by its study. Specific topics include rigidity, bounds on characteristic classes, quasification, orbit equivalence, amenability. Mathematics Subject Classification (2000). Primary 55N; Secondary 20F.