Developing non-destructive techniques to predict 'Hayward' kiwifruit storability : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Technology at Massey University, Palmerston North, New Zealand

A significant portion of New Zealand’s kiwifruit production is held as stock in local coolstores for extended periods of time before being exported. Many pre-harvest factors contribute to variation in fruit quality at harvest and during coolstorage, and results in the difficulty in segregating fruit for their storage outcomes. The objective of this work was to develop non-destructive techniques utilised at harvest to predict storability of individual or batches of ‘Hayward’ kiwifruit based on (near) skin properties. Segregation of fruit with low storage potential at harvest could enable that fruit to be sold earlier in the season reducing total fruit loss and improving profitability later in the season. The potential for optical coherence tomography (OCT) to detect near surface cellular structural differences in kiwifruit as a result of preharvest factors was demonstrated through quantitative image analysis of 3D OCT images of intact fruit from five commercial cultivars. Visualisation and characterisation of large parenchyma cells in the outer pericarp of kiwifruit was achieved by developing an automated image processing technique. This work established the usefulness of OCT to perform rapid analysis and differentiation of the microstructures of sub-surface cells between kiwifruit cultivars. However, the effects of preharvest conditions between batches of fruit within a cultivar were not detectable from image analysis and hence, the ability to provide segregation or prediction for fruit from the same cultivar was assumed to be limited. Total soluble solids concentration (TSS) and flesh firmness (FF) are two important quality attributes indicating the eating quality and storability of stored kiwifruit. Prediction of TSS and FF using non-destructive techniques would allow strategic marketing of fruit. This work demonstrated that visible-near-infrared (Vis-NIR) spectroscopy could be utilised as the sole input at harvest, to provide quantitative prediction of post-storage TSS by generating blackbox regression models. However the level of accuracy achieved was not adequate for online sorting purposes. Quantitative prediction of FF remained unsuccessful. Improved ways of physical measurements for FF may help reduce the undesirable variation observed on the same fruit and increase prediction capability. More promising results were obtained by developing blackbox classification models using Vis-NIR spectroscopy at harvest to segregate storability of individual kiwifruit based on the export FF criterion of 1 kgf (9.8 N). Through appropriate machine learning techniques, the surface properties of fruit at harvest captured in the form of spectral data were correlated to post-storage FF via pattern recognition. The best prediction was obtained for fruit stored at 0°C for 125 days: approximately 50% of the soft fruit and 80% of the good fruit could be identified. The developed model was capable of performing classification both within (at the fruit level) and between grower lines. Model validation suggested that segregation between grower lines at harvest achieved 30% reduction in soft fruit after storage. Should the model be applied in the industry to enable sequential marketing, $11.2 million NZD/annum could be saved because of reduced fruit loss, repacking and condition checking costs

A Dynamical Approach to the Perron-Frobenius Theory and Generalized Krein-Rutman Type Theorems

We present a new dynamical approach to the classical Perron-Frobenius theory by using some elementary knowledge on linear ODEs. It is completely self-contained and significantly different from those in the literature. As a result, we develop a complex version of the Perron-Frobenius theory and prove a variety of generalized Krein-Rutman type theorems for real operators. In particular, we establish some new Krein-Rutman type theorems for sectorial operators in a formalism that can be directly applied to elliptic operators, which allow us to reduce significantly the technical PDE arguments involved in the study of the principal eigenvalue problems of these operators.Comment: 40 page