title: Constructive Analysis of Partial Differential Equations

authors: Wang, Michael Yuchuan

subjects: Partial Differential Equations

abstract: This thesis presents the results produced in the study of weak solutions of the Dirichlet Problem within Errett Bishop's constructive mathematics. It roughly falls into three major parts: a critical analysis of the classical approaches from a constructive point of view (Chapter 2); constructive results on the existence, stability, and maximality of weak solutions (Chapter 5); and related results on the domains discovered during the course of study on the Dirichlet Problem (Chapters 3 and 6). Chapter 1 introduces constructive mathematics, and Chapter 4 is an auxiliary one in which I give two different constructions of a cut-off function.

text: Constructive Analysis of Partial Differential Equations This thesis presents the results produced in the study of weak solutions of the Dirichlet Problem within Errett Bishop's constructive mathematics. It roughly falls into three major parts: a critical analysis of the classical approaches from a constructive point of view (Chapter 2); constructive results on the existence, stability, and maximality of weak solutions (Chapter 5); and related results on the domains discovered during the course of study on the Dirichlet Problem (Chapters 3 and 6). Chapter 1 introduces constructive mathematics, and Chapter 4 is an auxiliary one in which I give two different constructions of a cut-off function.

year: 1996

title: New evidence for a mid to late-Holocene change in the marine reservoir effect across the South Pacific Gyre

authors: Petchey, Fiona

subjects: archaeology

abstract: Holocene climate change in the South Pacific is of major interest to archaeologists and Quaternary researchers. Regional surface ocean radiocarbon (¹⁴C) values are an established proxy for studying changing oceanographic and climatic conditions. Unfortunately, radiocarbon variability in the marine environment over the period of specific importance to human colonization of the remote Pacific islands—the last 3500 years—has been poorly studied. In order to build robust and accurate archaeological chronologies using shell, it is important to rectify this. In this paper, radiocarbon marine reservoir offsets (ΔR) are presented from eight archaeological sites, ranging in age from 350 cal BP to 3000 cal BP, and compared to coral datasets from the east Australian coastline. The results indicate that a significant decrease in the South Pacific Gyre ΔR occurred between 2600 and 2250 cal BP, most likely caused by changes in ocean circulation and climate. Accurately recording the timing of variability in reservoir offset is critical to untangling changes in society that took place in the Pacific, in particular, the development of Ancestral Polynesian Society.

text: New evidence for a mid to late-Holocene change in the marine reservoir effect across the South Pacific Gyre Holocene climate change in the South Pacific is of major interest to archaeologists and Quaternary researchers. Regional surface ocean radiocarbon (¹⁴C) values are an established proxy for studying changing oceanographic and climatic conditions. Unfortunately, radiocarbon variability in the marine environment over the period of specific importance to human colonization of the remote Pacific islands—the last 3500 years—has been poorly studied. In order to build robust and accurate archaeological chronologies using shell, it is important to rectify this. In this paper, radiocarbon marine reservoir offsets (ΔR) are presented from eight archaeological sites, ranging in age from 350 cal BP to 3000 cal BP, and compared to coral datasets from the east Australian coastline. The results indicate that a significant decrease in the South Pacific Gyre ΔR occurred between 2600 and 2250 cal BP, most likely caused by changes in ocean circulation and climate. Accurately recording the timing of variability in reservoir offset is critical to untangling changes in society that took place in the Pacific, in particular, the development of Ancestral Polynesian Society.

year: 2019

title: Lessons from children in Māori medium for teachers: Encouraging greater efficiency when learning to multiply.

authors: Hāwera, Ngārewa

subjects: children

abstract: This research explores the responses of 44 Year 7-8 students from four Māori medium schools who were asked to solve a multiplication word problem. The findings show that there was a range of mental strategies displayed by the children, 29 of whom were able to solve the problem. However, data also indicates that 15 children were not able to either access the problem or utilise an appropriate strategy to solve it. This paper discusses the strategies shared by all of these children and suggests avenues to further support learners to become multiplicative thinkers.

text: Lessons from children in Māori medium for teachers: Encouraging greater efficiency when learning to multiply. This research explores the responses of 44 Year 7-8 students from four Māori medium schools who were asked to solve a multiplication word problem. The findings show that there was a range of mental strategies displayed by the children, 29 of whom were able to solve the problem. However, data also indicates that 15 children were not able to either access the problem or utilise an appropriate strategy to solve it. This paper discusses the strategies shared by all of these children and suggests avenues to further support learners to become multiplicative thinkers.

year: 2012