title: Rangitoto Island field trip, Auckland

authors: Lowe, David J.

subjects: Rangitoto

abstract: Rangitoto, Māori for ‘blood red sky’ (also ‘lava, scoria’), derives from the phrase Ngā Rangi-i-totongia-a Tama-te-kapua (the full name for the island) meaning “the day the blood of Tamatekapua was shed”, referring to a battle between Tamatekapua and Hoturoa, commanders of the Arawa and Tainui canoes, respectively, at Islington Bay. The Island is arguably Auckland’s most beloved and omnipresent landscape feature. It is a symmetrical, ~6-km wide, basaltic shield volcano that last erupted c. 550‒500 calendar/calibrated (cal.) yr BP (c. 1400‒1450 AD), not long after arrival and settlement of Polynesians in the Auckland region (c. 1280 AD). It is by far the largest, and the youngest, volcano in the Auckland Volcanic Field (AVF). The AVF consists of ~53 individual eruptive centres, all of which lie within the boundaries of the Auckland urban area. Recent research on deposits in a 150-m-long drill core obtained from Rangitoto Island in February, 2014, and on cryptotephras in sediments from Lake Pupuke on North Shore and on tephras in wetlands on adjacent Motutapu Island, has revealed Rangitoto’s complex history, with three main phases (1‒3) suggested. The flora on Rangitoto is unique among the islands situated in the Hauraki Gulf because of the island’s young age, and the fact that technically Rangitoto is an ‘oceanic’ island. Its flora and fauna are derived entirely from long distance dispersal. The island contains some 582 vascular plant taxa of which 228 (39%) are indigenous.

text: Rangitoto Island field trip, Auckland Rangitoto, Māori for ‘blood red sky’ (also ‘lava, scoria’), derives from the phrase Ngā Rangi-i-totongia-a Tama-te-kapua (the full name for the island) meaning “the day the blood of Tamatekapua was shed”, referring to a battle between Tamatekapua and Hoturoa, commanders of the Arawa and Tainui canoes, respectively, at Islington Bay. The Island is arguably Auckland’s most beloved and omnipresent landscape feature. It is a symmetrical, ~6-km wide, basaltic shield volcano that last erupted c. 550‒500 calendar/calibrated (cal.) yr BP (c. 1400‒1450 AD), not long after arrival and settlement of Polynesians in the Auckland region (c. 1280 AD). It is by far the largest, and the youngest, volcano in the Auckland Volcanic Field (AVF). The AVF consists of ~53 individual eruptive centres, all of which lie within the boundaries of the Auckland urban area. Recent research on deposits in a 150-m-long drill core obtained from Rangitoto Island in February, 2014, and on cryptotephras in sediments from Lake Pupuke on North Shore and on tephras in wetlands on adjacent Motutapu Island, has revealed Rangitoto’s complex history, with three main phases (1‒3) suggested. The flora on Rangitoto is unique among the islands situated in the Hauraki Gulf because of the island’s young age, and the fact that technically Rangitoto is an ‘oceanic’ island. Its flora and fauna are derived entirely from long distance dispersal. The island contains some 582 vascular plant taxa of which 228 (39%) are indigenous.

year: 2017-11-28

title: Multiply perfect numbers of low abundancy

authors: Zhou, Qizhi

subjects: multiperfect numbers

abstract: The purpose of this thesis is to investigate the properties of multiperfect numbers with low abundancy, and to include the structure, bounds, and density of certain multiperfect numbers. As a significant result of this thesis, an exploration of the structure of an odd 4-perfect number has been made. An extension of Euler’s theorem on the structure of any odd perfect number to odd 2k-perfect numbers has also been obtained. In order to study multiperfect numbers, it is necessary to discuss the factorization of the sum of divisors, in particular for (qe), for prime q. This concept is applied to investigate multiperfect numbers with a so-called flat shape N = 2ap1 · · ·pm. If some prime divisors of N are fixed then there are finitely many flat even 3-perfect numbers. If N is a flat 4-perfect number and the exponent of 2 is not congruent to 1 (mod 12), then the exponent is even. If all odd prime divisors of N are Mersenne primes, where N is even, flat and multiperfect, then N is a perfect number. In more general cases, some necessary conditions for the divisibility by 3 of an even 4-perfect number N = 2ab are obtained, where b is an odd positive integer. Two new ideas, namely flat primes and thin primes, are introduced since these appear often in multiperfect numbers. The relative density of flat primes to all primes is given by 2 times Artin’s constant. An upper bound of the number of thin primes is T(x) less less x log2 x . The sum of the reciprocals of the thin primes is finite.

text: Multiply perfect numbers of low abundancy The purpose of this thesis is to investigate the properties of multiperfect numbers with low abundancy, and to include the structure, bounds, and density of certain multiperfect numbers. As a significant result of this thesis, an exploration of the structure of an odd 4-perfect number has been made. An extension of Euler’s theorem on the structure of any odd perfect number to odd 2k-perfect numbers has also been obtained. In order to study multiperfect numbers, it is necessary to discuss the factorization of the sum of divisors, in particular for (qe), for prime q. This concept is applied to investigate multiperfect numbers with a so-called flat shape N = 2ap1 · · ·pm. If some prime divisors of N are fixed then there are finitely many flat even 3-perfect numbers. If N is a flat 4-perfect number and the exponent of 2 is not congruent to 1 (mod 12), then the exponent is even. If all odd prime divisors of N are Mersenne primes, where N is even, flat and multiperfect, then N is a perfect number. In more general cases, some necessary conditions for the divisibility by 3 of an even 4-perfect number N = 2ab are obtained, where b is an odd positive integer. Two new ideas, namely flat primes and thin primes, are introduced since these appear often in multiperfect numbers. The relative density of flat primes to all primes is given by 2 times Artin’s constant. An upper bound of the number of thin primes is T(x) less less x log2 x . The sum of the reciprocals of the thin primes is finite.

year: 2010

title: Claiming space and restoring harmony within hui whakatika

authors: Berryman, Mere

subjects: Maori

abstract: The time has come for indigenous, specifically Māori psychologies, to move from the margins, and claim legitimate space within the discipline of psychology (MPRU, 2007). Phinney and Rotheram (1987) argue that there are ethnicallylinked ways of thinking, feeling and acting that are acquired through socialisation. The message implicit in this statement has profound implications for a discipline that seeks to understand and respond to the intricacies of human behaviour. Although the epistemological paradigms emerging from the experiences of indigenous minorities such as Māori may offer a challenge to mainstream knowledge and perspectives (Gordon, 1997), it is clear that disregarding such alternatives may well leave the discipline of psychology impoverished. On the other hand, paying attention to alternative paradigms may well serve to enrich this discipline. This paper presents two successful Hui Whakatika that were led by Māori in mainstream settings. Particular dimensions of, and congruencies between both are explored. The first highlights the vital role of a kaumatua in facilitating and guiding the entire process; the second focuses on the role and experiences of a kaitakawaenga as he works collaboratively with whānau members to find resolution and restore harmony.

text: Claiming space and restoring harmony within hui whakatika The time has come for indigenous, specifically Māori psychologies, to move from the margins, and claim legitimate space within the discipline of psychology (MPRU, 2007). Phinney and Rotheram (1987) argue that there are ethnicallylinked ways of thinking, feeling and acting that are acquired through socialisation. The message implicit in this statement has profound implications for a discipline that seeks to understand and respond to the intricacies of human behaviour. Although the epistemological paradigms emerging from the experiences of indigenous minorities such as Māori may offer a challenge to mainstream knowledge and perspectives (Gordon, 1997), it is clear that disregarding such alternatives may well leave the discipline of psychology impoverished. On the other hand, paying attention to alternative paradigms may well serve to enrich this discipline. This paper presents two successful Hui Whakatika that were led by Māori in mainstream settings. Particular dimensions of, and congruencies between both are explored. The first highlights the vital role of a kaumatua in facilitating and guiding the entire process; the second focuses on the role and experiences of a kaitakawaenga as he works collaboratively with whānau members to find resolution and restore harmony.

year: 2008