title: Decomposing complete tripartite graphs into 5-cycles when the partite sets have similar size

authors: Billington, Elizabeth J.

subjects: graph decomposition

abstract: The problem of finding necessary and sufficient conditions to decompose a complete tripartite graph into 5-cycles was first posed at a conference in 1994 (Mahmoodian and Mirzakhani in Combinatorics Advances, 1995). Since then, many cases of the problem have been solved by various authors; however the case when the partite sets have odd and distinct sizes remains open. In this note, we introduce a new approach to the problem by embedding previously known decompositions into larger ones. Via this approach, we show that when the partite sets have asymptotically similar sizes, the conjectured necessary conditions for a decomposition are also sufficient.

text: Decomposing complete tripartite graphs into 5-cycles when the partite sets have similar size The problem of finding necessary and sufficient conditions to decompose a complete tripartite graph into 5-cycles was first posed at a conference in 1994 (Mahmoodian and Mirzakhani in Combinatorics Advances, 1995). Since then, many cases of the problem have been solved by various authors; however the case when the partite sets have odd and distinct sizes remains open. In this note, we introduce a new approach to the problem by embedding previously known decompositions into larger ones. Via this approach, we show that when the partite sets have asymptotically similar sizes, the conjectured necessary conditions for a decomposition are also sufficient.

year: 2011

title: An analytical model for the break-even credit default swap spread with o counterparty default risk in Hall(2009): A pedagogical approach.

authors: Choi, Daniel F.S.

subjects: Credit Default Swap Spread

abstract: Professor Hull in his textbook [Hull, J. C. Options, Futures, & Other Derivatives, Edition 7, Pearson, 2009] illustrates the determination of the credit default swap (CDS) spread by a numerical example. This paper follows the assumptions used by Professor Hull and provides a reduced form formula for the CDS spread. The CDS spread can be simplified by the Taylor series into a function of two variables, the default probability and the recovery rate. Rearranging this simplified formula, the default probability, expressed as the ratio of the CDS spread and the loss given default, is equivalent to the average default intensity, or, the hazard rate defined in Hull [2009, p.500].

text: An analytical model for the break-even credit default swap spread with o counterparty default risk in Hall(2009): A pedagogical approach. Professor Hull in his textbook [Hull, J. C. Options, Futures, & Other Derivatives, Edition 7, Pearson, 2009] illustrates the determination of the credit default swap (CDS) spread by a numerical example. This paper follows the assumptions used by Professor Hull and provides a reduced form formula for the CDS spread. The CDS spread can be simplified by the Taylor series into a function of two variables, the default probability and the recovery rate. Rearranging this simplified formula, the default probability, expressed as the ratio of the CDS spread and the loss given default, is equivalent to the average default intensity, or, the hazard rate defined in Hull [2009, p.500].

year: 2010

title: The life story model of identity: A bridge between two spaces

authors: Houkamau, Carla Anne

subjects: Maori

abstract: Two questions which continue to absorb Western social psychological researchers are: What is the ‘self’? And ‘What is identity in relation to self?’ At the NMPPS this year this Dr. Love’s keynote threw these matters into relief prompting us as indigenous psychologists to reflect deeply on the nature of ‘selves’. Many questions arise from her address. Do we have ensembled selves? Are we self contained? Are we a bit of both depending on the situation? How do we work within psychology while honouring Māori perspectives?

text: The life story model of identity: A bridge between two spaces Two questions which continue to absorb Western social psychological researchers are: What is the ‘self’? And ‘What is identity in relation to self?’ At the NMPPS this year this Dr. Love’s keynote threw these matters into relief prompting us as indigenous psychologists to reflect deeply on the nature of ‘selves’. Many questions arise from her address. Do we have ensembled selves? Are we self contained? Are we a bit of both depending on the situation? How do we work within psychology while honouring Māori perspectives?

year: 2008