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Full-Text Articles in Social and Behavioral Sciences

The Local Index Formula In Semifinite Von Neumann Algebras Ii: The Even Case, Alan Carey, John Phillips, Adam Rennie, F Sukochev Oct 2013

The Local Index Formula In Semifinite Von Neumann Algebras Ii: The Even Case, Alan Carey, John Phillips, Adam Rennie, F Sukochev

Associate Professor Adam Rennie

We generalise the even local index formula of Connes and Moscovici to the case of spectral triples for a ∗-subalgebra A of a general semifinite von Neumann algebra. The proof is a variant of that for the odd case which appears in Part I. To allow for algebras with a non-trivial centre we have to establish a theory of unbounded Fredholm operators in a general semifinite von Neumann algebra and in particular prove a generalised McKean-Singer formula.


Statistical Indicators For Local Government Areas: A Case Study Of The Shoalhaven Lga, 1997, Nell Stetner-Houweling, David Steel, Greg Pullen Jun 2013

Statistical Indicators For Local Government Areas: A Case Study Of The Shoalhaven Lga, 1997, Nell Stetner-Houweling, David Steel, Greg Pullen

Professor David Steel

Decision makers and planers need to have relevant and reliable information to give a picture of how different areas are developing economically and socially. However, there is a perceived lack of timely and easily accessible data at the Local Government Area (LGA) level. This study produced a statistical profile of the Shoalhaven (LGA) by developing a conceptual framework, which represents the key economic, social, and population characteristics of the LGA. The statistical data available from the Australian Bureau of Statistics (ABS) at the level of the LGA, was investigated and summarised. Other sources of information available to create a statistical ...