title: Almost weak Asplund spaces

authors: Somasundaram, Sivajah

abstract: Continuous convex functions have long been known to be generically differentiable on Euclidean spaces. However, in 1968 Asplund decided to investigate and classify those Banach spaces that possess this Euclidean space property. Specifically, Asplund investigated those Banach spaces on which every continuous convex function is Gâteaux (Fréchet) differentiable at the points of a residual subset of their domain. Such spaces are now known as weak Asplund (Asplund) spaces. While the study of Asplund spaces has flourished into a beautifully detailed story admitting several characterisations, the corresponding theory for weak Asplund spaces has been rather thin. In particular, there are no known characterisations for this class of spaces. 
In one attempt to provide such a characterisation, the class of Gâteaux differentiability spaces, that is, those spaces on which every continuous convex function is densely Gâteaux differentiable, was introduced. While it follows from the definition that every weak Asplund space is a Gâteaux differentiability space, it has been a long standing open problem, first asked by Larman and Phelps in 1979, as to whether every Gâteaux differentiability space is a weak Asplund space. 
The main goal of this thesis is to construct a Gâteaux differentiability space that is not weak Asplund, thus answering the question of Larman and Phelps from 1979. We achieve this counter-example by considering Banach spaces of the form (C(K),∥·∥∞), where K is a compact Hausdorff space.

text: Almost weak Asplund spaces Continuous convex functions have long been known to be generically differentiable on Euclidean spaces. However, in 1968 Asplund decided to investigate and classify those Banach spaces that possess this Euclidean space property. Specifically, Asplund investigated those Banach spaces on which every continuous convex function is Gâteaux (Fréchet) differentiable at the points of a residual subset of their domain. Such spaces are now known as weak Asplund (Asplund) spaces. While the study of Asplund spaces has flourished into a beautifully detailed story admitting several characterisations, the corresponding theory for weak Asplund spaces has been rather thin. In particular, there are no known characterisations for this class of spaces. 
In one attempt to provide such a characterisation, the class of Gâteaux differentiability spaces, that is, those spaces on which every continuous convex function is densely Gâteaux differentiable, was introduced. While it follows from the definition that every weak Asplund space is a Gâteaux differentiability space, it has been a long standing open problem, first asked by Larman and Phelps in 1979, as to whether every Gâteaux differentiability space is a weak Asplund space. 
The main goal of this thesis is to construct a Gâteaux differentiability space that is not weak Asplund, thus answering the question of Larman and Phelps from 1979. We achieve this counter-example by considering Banach spaces of the form (C(K),∥·∥∞), where K is a compact Hausdorff space.

year: 2004

title: A review of 3D/4D printing of poly-lactic acid composites with bio-derived reinforcements

authors: Muthe, Lakshmi Priya

abstract: Poly-lactic acid (PLA) has become a commonly used polymer for additive manufacturing because of its bio-derived nature, useful mechanical properties, and excellent processability. Reinforcing PLA with bio-derived materials has been shown to improve the physical, mechanical, and thermal properties of 3D printed composites and, in some cases, to produce active materials for shape-changing hygromorphic structures. PLA also displays shape memory as a response to changes in temperature, making it a popular choice for 4D printing. This review aims to present an overview of the current state of 3D/4D printing PLA composites with bio-derived reinforcements and highlight the recent progress and future opportunities. This comprehensive overview summarises the different forms of bio-derived reinforcements for PLA used in fused deposition modelling (FDM), factors influencing the resulting printed composites’ performance, and research gaps that need addressing. The current methods used before, during, and after printing to enhance the material properties and the impending need for innovative filament production and printing technologies have been brought to attention.

text: A review of 3D/4D printing of poly-lactic acid composites with bio-derived reinforcements Poly-lactic acid (PLA) has become a commonly used polymer for additive manufacturing because of its bio-derived nature, useful mechanical properties, and excellent processability. Reinforcing PLA with bio-derived materials has been shown to improve the physical, mechanical, and thermal properties of 3D printed composites and, in some cases, to produce active materials for shape-changing hygromorphic structures. PLA also displays shape memory as a response to changes in temperature, making it a popular choice for 4D printing. This review aims to present an overview of the current state of 3D/4D printing PLA composites with bio-derived reinforcements and highlight the recent progress and future opportunities. This comprehensive overview summarises the different forms of bio-derived reinforcements for PLA used in fused deposition modelling (FDM), factors influencing the resulting printed composites’ performance, and research gaps that need addressing. The current methods used before, during, and after printing to enhance the material properties and the impending need for innovative filament production and printing technologies have been brought to attention.

year: 2022

title: Operational forest restoration plan for Kukutaaruhe Gully: Part 2

authors: Elliot Noe, Elizabeth

abstract: Kukutaaruhe Gully is a minor branch of Hamilton’s extensive gully system, and runs from the corner of Bankwood and Clarkin Road, behind Fairfield College, connecting with Donny Park in the north and out into the Waikato River. The Kukutaaruhe Education Trust was established to support the implementation of the Fairfield Project, which is a partnership between Ngati Wairere, local community and Fairfield College. The project’s goals include the establishment of an ecological and environmental education centre on the approximately 12 ha of land behind Fairfield College and restoration of the adjacent Kukutaaruhe Gully. In 2019, the University of Waikato’s Environmental Research Institute was contracted by the Kukutaaruhe Education Trust to create an Operational Forest Restoration plan for Kukutaaruhe Gully. This is one in a three-part series created together under one contract:
• Part 1 of 3 is an Overview of the Kukutaaruhe Gully Restoration Initiative
• Part 2 of 3 is this document, the Operational Forest Restoration plan for Kukutaaruhe Gully
• Part 3 of 3 is an Ecological Restoration Plan Template.

text: Operational forest restoration plan for Kukutaaruhe Gully: Part 2 Kukutaaruhe Gully is a minor branch of Hamilton’s extensive gully system, and runs from the corner of Bankwood and Clarkin Road, behind Fairfield College, connecting with Donny Park in the north and out into the Waikato River. The Kukutaaruhe Education Trust was established to support the implementation of the Fairfield Project, which is a partnership between Ngati Wairere, local community and Fairfield College. The project’s goals include the establishment of an ecological and environmental education centre on the approximately 12 ha of land behind Fairfield College and restoration of the adjacent Kukutaaruhe Gully. In 2019, the University of Waikato’s Environmental Research Institute was contracted by the Kukutaaruhe Education Trust to create an Operational Forest Restoration plan for Kukutaaruhe Gully. This is one in a three-part series created together under one contract:
• Part 1 of 3 is an Overview of the Kukutaaruhe Gully Restoration Initiative
• Part 2 of 3 is this document, the Operational Forest Restoration plan for Kukutaaruhe Gully
• Part 3 of 3 is an Ecological Restoration Plan Template.

year: 2020-10