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published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

published_or_final_version / abstract / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Mechanical Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

This thesis is an account of an investigation into the problems associated with the production of patterns to ensure a garment of satisfactory fit. Essentially, the method described in this thesis consists of defining a number of crucial shaping points on the body and measuring their spatial co-ordinates. A method is then developed which translates these three-dimensional co-ordinates into patterns whose shapes are such that when joined together with darts suitably positioned, the two dimensional pieces of cloth cut from them are transformed into a threedimensional garment of accurate fit. A computer program has been developed which will: (i) read the three-dimensional co-ordinates of the human body, (ii) calculate the accurate angle of dart needed to be inserted into the pattern to convert it into a three-dimensional'shell', (iii) plot a full size skin and/or block pattern which when sewn into a garment will fit the measured body perfectly.

Product densities have been widely used in the literature to give a concrete description of the distribution of a point process. A rigorous description of properties of product densities is presented with examples to show that in some sense these results are the best possible. Product densities are then used to discuss positive dependence properties of point processes. There are many ways of describing positive dependence. Two well known notions for Bernoulli random variables are the strong FKG inequalities and association, the strong FKG inequalities being much stronger. It is known, for example, from van den Berg and Burton, that the strong FKG inequalities are equivalent to all conditional distributions being associated, which is equivalent to all conditional distributions being positively correlated. In the case of point processes for which product densities exist, analogs of such positive dependence properties are given. Examples are presented to show that unlike the Bernoulli case none of these conditions are equivalent, although some are shown to be implied by others. / Graduation date: 1988

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