title: Approximation of non-linear cost functions in p-graph structures

authors: Ong, Benjamin H.Y.

abstract: P-graph employs combinatorial and optimisation algorithms to solve process network synthesis (PNS) problem. However, the P-graph framework requires linear cost functions when optimising PNS problems. As a result, a high error between the user-input linear cost function and the actual non-linear cost function is likely to occur. This paper presents a new method to incorporate multiple linear cost functions in parallel for raw materials, operating units and products in P-graph problems to accurately approximate the non-linear functional form of most cost estimation functions. This was achieved by dividing the original cost functions into multiple equal segments that then could be individually represented by linear sub-functions. Application of the new method to a simple wood-to-fuel processing example influences the optimal P-graph process structure such that a previously uneconomic side-product route (pyrolysis) becomes economic and increases the overall profit. The results also demonstrate that the linear approximation error decreases with increasing numbers of segments and linear cost sub-functions. The time increase to solve the new problem structure, which has over threefold more operating units, is negligible for this simple case, but may be significant for more complex problems.

text: Approximation of non-linear cost functions in p-graph structures P-graph employs combinatorial and optimisation algorithms to solve process network synthesis (PNS) problem. However, the P-graph framework requires linear cost functions when optimising PNS problems. As a result, a high error between the user-input linear cost function and the actual non-linear cost function is likely to occur. This paper presents a new method to incorporate multiple linear cost functions in parallel for raw materials, operating units and products in P-graph problems to accurately approximate the non-linear functional form of most cost estimation functions. This was achieved by dividing the original cost functions into multiple equal segments that then could be individually represented by linear sub-functions. Application of the new method to a simple wood-to-fuel processing example influences the optimal P-graph process structure such that a previously uneconomic side-product route (pyrolysis) becomes economic and increases the overall profit. The results also demonstrate that the linear approximation error decreases with increasing numbers of segments and linear cost sub-functions. The time increase to solve the new problem structure, which has over threefold more operating units, is negligible for this simple case, but may be significant for more complex problems.

year: 2016

title: The factors responsible for the varying levels of UMF® in mānuka (Leptospermum scoparium) honey

authors: Stephens, Jonathan McDonald Counsell

subjects: Leptospermum scoparium

abstract: The variability in the level of the non-peroxide antibacterial component (UMF®) of mānuka honey produced in New Zealand was studied. A field analysis confirmed considerable variability existed in the honeys, and a number of hypotheses to explain this variability were proposed and examined.

Nectar derived from Leptospermum scoparium (mānuka), was confirmed to be the
source of UMF®.

The dilution of mānuka honey with nectar derived from other floral sources was found to proportionally reduce the UMF® in monofloral mānuka honey. The utilisation of the thixotropic properties of mānuka honey allowed the degree of dilution in the field samples to be established, and an adjustment of the field results to account for the dilution of UMF® by other honey types revealed all monofloral mānuka honey contains UMF®. However, in the monofloral mānuka honey, significantly different levels of UMF® activity were found to come from reasonably well-defined geographic regions.

The cause of the variable levels of UMF® activity in mānuka honey would appear to be the different varieties of L. scoparium being harvested by the honeybees, and the environmental parameters influencing nectar production or another species interacting with L. scoparium do not appear to influence UMF® activity.

Three methods were used to establish genetic variability within regions of the North Island of New Zealand that gave rise to the various levels of UMF® activity. Analyses of morphological characteristics, chemotaxonomic essential oil profiles, and population genetics of L. scoparium populations were conducted, and the conclusions that were drawn from each of these were very similar. Two major divisions were identified, each divided into two varieties. The northern division, which contained the core populations from Northland and Waikato, represented the previously described L. scoparium var. incanum and L. scoparium var. linifolium. This division yielded mānuka honey with high UMF® activity. The southern division, which contained the core populations from the Central North Island and East Coast, represented the previously described L. scoparium var. myrtifolium and an unnamed variety. The latter, growing principally on the East Coast, uniquely contains triketones essential oils. The southern division yielded mānuka honey with low UMF® activity. Hybridisation between these varieties will occur, leading to a continuum of UMF® activity in mānuka honey.

The data indicated multiple dispersions of L. scoparium to New Zealand from the evolutionary centre of the persistent-capsule Leptospermum group in south-east Australia, and later regional dispersal in New Zealand.

From this study two hypotheses were accepted: the variability in the UMF® activity of mānuka honey is due to both the dilution of mānuka honey by other honey types and the variety of L. scoparium harvested.

text: The factors responsible for the varying levels of UMF® in mānuka (Leptospermum scoparium) honey The variability in the level of the non-peroxide antibacterial component (UMF®) of mānuka honey produced in New Zealand was studied. A field analysis confirmed considerable variability existed in the honeys, and a number of hypotheses to explain this variability were proposed and examined.

Nectar derived from Leptospermum scoparium (mānuka), was confirmed to be the
source of UMF®.

The dilution of mānuka honey with nectar derived from other floral sources was found to proportionally reduce the UMF® in monofloral mānuka honey. The utilisation of the thixotropic properties of mānuka honey allowed the degree of dilution in the field samples to be established, and an adjustment of the field results to account for the dilution of UMF® by other honey types revealed all monofloral mānuka honey contains UMF®. However, in the monofloral mānuka honey, significantly different levels of UMF® activity were found to come from reasonably well-defined geographic regions.

The cause of the variable levels of UMF® activity in mānuka honey would appear to be the different varieties of L. scoparium being harvested by the honeybees, and the environmental parameters influencing nectar production or another species interacting with L. scoparium do not appear to influence UMF® activity.

Three methods were used to establish genetic variability within regions of the North Island of New Zealand that gave rise to the various levels of UMF® activity. Analyses of morphological characteristics, chemotaxonomic essential oil profiles, and population genetics of L. scoparium populations were conducted, and the conclusions that were drawn from each of these were very similar. Two major divisions were identified, each divided into two varieties. The northern division, which contained the core populations from Northland and Waikato, represented the previously described L. scoparium var. incanum and L. scoparium var. linifolium. This division yielded mānuka honey with high UMF® activity. The southern division, which contained the core populations from the Central North Island and East Coast, represented the previously described L. scoparium var. myrtifolium and an unnamed variety. The latter, growing principally on the East Coast, uniquely contains triketones essential oils. The southern division yielded mānuka honey with low UMF® activity. Hybridisation between these varieties will occur, leading to a continuum of UMF® activity in mānuka honey.

The data indicated multiple dispersions of L. scoparium to New Zealand from the evolutionary centre of the persistent-capsule Leptospermum group in south-east Australia, and later regional dispersal in New Zealand.

From this study two hypotheses were accepted: the variability in the UMF® activity of mānuka honey is due to both the dilution of mānuka honey by other honey types and the variety of L. scoparium harvested.

year: 2006

title: Kua Tupu Te Pā Harakeke: Developing Healthy Whānau Relationships

authors: Pihama, Leonie

abstract: We have opened this chapter with our ‘pēpeha’. Pēpeha are ways through which our people introduce ourselves. These vary from tribe to tribe. The essence of pēpeha is that they link us to our tribes and all associated with that. Our mountains, our rivers, our canoes, our ancestral lines. It links us to each other. It places us, as Māori, within a wider collective consciousness and relationships. It is important to highlight that the term ‘Māori’ is a term that brings us as tribal peoples together. It is a term that our people have chosen to use as a means of unifying ourselves in the wake of the arrival of our colonizers. Prior to colonization all identification was done through our whānau (extended family structure), hapū (subtribes) or iwi (tribes). The term Māori means to be ‘normal’ or ‘pure’, as such it is a fitting term for an Indigenous People. We have, however, also been active in maintaining our hapū and iwi identities and it is through pēpeha that we can culturally share that identity with each other. Our people have been doing this for generations. And in spite of colonization seeking to undermine our cultural identity, many of us continue to do this.

text: Kua Tupu Te Pā Harakeke: Developing Healthy Whānau Relationships We have opened this chapter with our ‘pēpeha’. Pēpeha are ways through which our people introduce ourselves. These vary from tribe to tribe. The essence of pēpeha is that they link us to our tribes and all associated with that. Our mountains, our rivers, our canoes, our ancestral lines. It links us to each other. It places us, as Māori, within a wider collective consciousness and relationships. It is important to highlight that the term ‘Māori’ is a term that brings us as tribal peoples together. It is a term that our people have chosen to use as a means of unifying ourselves in the wake of the arrival of our colonizers. Prior to colonization all identification was done through our whānau (extended family structure), hapū (subtribes) or iwi (tribes). The term Māori means to be ‘normal’ or ‘pure’, as such it is a fitting term for an Indigenous People. We have, however, also been active in maintaining our hapū and iwi identities and it is through pēpeha that we can culturally share that identity with each other. Our people have been doing this for generations. And in spite of colonization seeking to undermine our cultural identity, many of us continue to do this.

year: 2012