We establish certain ‘homological properties’ of the stable Higson corona used by Emerson and Meyer to study the Dirac-dual-Dirac approach to the Baum-Connes conjecture [5]. These are used to obtain explicit isomorphisms between the K-theory of the stable Higson corona of certain spaces X and the topological K-theory of natural geometric boundaries of X. This is sufficient to give a simple proo...

We present an algorithm to compute a full set of irreducible representations of a supersolvable group G over a finite field K, charK |G|, which is not assumed to be a splitting field of G. The main subroutines of our algorithm are a modification of the algorithm of Baum and Clausen (Math. Comp. 63 (1994), 351–359) to obtain information on algebraically conjugate representations, and an effectiv...

The standard method for training Hidden Markov Models optimizes a point estimate of the model parameters. This estimate, which can be viewed as the maximum of a posterior probability density over the model parameters, may be susceptible to over-tting, and contains no indication of parameter uncertainty. Also, this maximummay be unrepresentative of the posterior probability distribution. In this...

Based on the Cayley, Grothendieck, Knudsen Mumford theory of determinants we extend the CM polarisation to the Hilbert scheme. The Baum Fulton Macpherson GRR Theorem enables us to show that on any flat, proper, local complete intersection family the restriction of the extension and the original CM sheaf are isomorphic (under a mild hypothesis on the base). As a consequence the CM stability impl...

Let {Xni , i≥ 1,n≥ 1} be an array of rowwise ρ̃-mixing random variables. Some sufficient conditions for complete convergence for weighted sums of arrays of rowwise ρ̃-mixing random variables are presented without assumptions of identical distribution. As applications, the Baum and Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of ρ̃-mixing random vari...

The complete convergence for pairwise negative quadrant dependent PNQD random variables is studied. So far there has not been the generalmoment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. ...

Based on the Cayley, Grothendieck, Knudsen Mumford theory of determinants we extend the CM polarisation to the Hilbert scheme. The Baum Fulton Macpherson GRR Theorem enables us to show that on any flat, proper, local complete intersection family the restriction of the extension and the original CM sheaf are isomorphic (under a mild hypothesis on the base). As a consequence the CM stability impl...

We study several duality isomorphisms between equivariant bivariant K-theory groups, generalising Kasparov’s first and second Poincaré duality isomorphisms. We use the first duality to define an equivariant generalisation of Lefschetz invariants of generalised self-maps. The second duality is related to the description of bivariant Kasparov theory for commutative C∗-algebras by families of elli...

This paper previews a new approach being developed for modeling the dynamic behavior of cloth. This work extends the cloth-particle static draping model of Breen and House to include dynamics, and extends constrained dynamics simulation techniques developed by Witkin, Gleicher and Welch to yield performance enhancements. Fundamental to this approach is a new hierarchical approximation algorithm...