title: Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4

authors: Broughan, Kevin A.

subjects: maths

abstract: We say a number is flat if it can be written as a non-trivial power of 2 times an odd squarefree number. The power is the “exponent” and the number of odd primes the “length”. Let N be flat and 4-perfect with exponent a and length m. If a ≢ 1 mod 12, then a is even. If a is even and 3 ∤ N then m is also even. If a ≡ 1 mod 12 then 3 | N and m is even. If N is flat and 3-perfect and 3 ∤ N, then if a a ≡ 1 mod 12, a is even. If
a ≡ 1 mod 12 then m is odd. If N is flat and 3 or 4-perfect then it is divisible by at least one Mersenne prime, but not all odd prime divisors are Mersenne. We also give some conditions for the divisibility by 3 of an arbitrary even 4-perfect number.

text: Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4 We say a number is flat if it can be written as a non-trivial power of 2 times an odd squarefree number. The power is the “exponent” and the number of odd primes the “length”. Let N be flat and 4-perfect with exponent a and length m. If a ≢ 1 mod 12, then a is even. If a is even and 3 ∤ N then m is also even. If a ≡ 1 mod 12 then 3 | N and m is even. If N is flat and 3-perfect and 3 ∤ N, then if a a ≡ 1 mod 12, a is even. If
a ≡ 1 mod 12 then m is odd. If N is flat and 3 or 4-perfect then it is divisible by at least one Mersenne prime, but not all odd prime divisors are Mersenne. We also give some conditions for the divisibility by 3 of an arbitrary even 4-perfect number.

year: 2010

title: Kava and ethno-cultural identity in Oceania

authors: Aporosa, S. 'Apo'

subjects: Identity

abstract: Garibaldi and Turner (Ecol Soc 9:1, 5, 2004) explain the role that particular plants play in facilitating the shared ancestry, practices, and social experience of an ethnicity. This can include spiritual connections, cultural expression and practice, ceremony, exchange, linguistic reflection, socialization, and medicinal and/or dietary systems. They term these plants “cultural keystone species” and icons of identity, plants that if removed would cause some disruptions to the cultural practices and identity of an ethnic group. Undoubtedly, kava (Piper methysticum) is the cultural keystone species for many Oceanic and Pacific peoples, a “differentiating element of common culture” (Zagefka, Ethnicity, concepts of. In: Smith AD, Hou X, Stone J, Dennis R, Rizova P (eds) The Wiley Blackwell encyclopedia of race, ethnicity, and nationalism. West Wiley, Sussex, pp 761–763, 2016) informing their ethno-cultural identity. That influence is also extending to new non-Pacific Island user groups who have embraced elements of kava ethno-cultural identity in what has been termed diasporic identity formation in reverse. This chapter will discuss kava with specific reference to ethnic positionality in Fiji while recognizing the tensions from inside and outside the region that support and threaten the continuance of the kava drinking tradition.

text: Kava and ethno-cultural identity in Oceania Garibaldi and Turner (Ecol Soc 9:1, 5, 2004) explain the role that particular plants play in facilitating the shared ancestry, practices, and social experience of an ethnicity. This can include spiritual connections, cultural expression and practice, ceremony, exchange, linguistic reflection, socialization, and medicinal and/or dietary systems. They term these plants “cultural keystone species” and icons of identity, plants that if removed would cause some disruptions to the cultural practices and identity of an ethnic group. Undoubtedly, kava (Piper methysticum) is the cultural keystone species for many Oceanic and Pacific peoples, a “differentiating element of common culture” (Zagefka, Ethnicity, concepts of. In: Smith AD, Hou X, Stone J, Dennis R, Rizova P (eds) The Wiley Blackwell encyclopedia of race, ethnicity, and nationalism. West Wiley, Sussex, pp 761–763, 2016) informing their ethno-cultural identity. That influence is also extending to new non-Pacific Island user groups who have embraced elements of kava ethno-cultural identity in what has been termed diasporic identity formation in reverse. This chapter will discuss kava with specific reference to ethnic positionality in Fiji while recognizing the tensions from inside and outside the region that support and threaten the continuance of the kava drinking tradition.

year: 2019

title: Inter-propositional relations: An investigation of authentic Māori texts signalled in te reo Māori

authors: Whaanga, Hēmi

subjects: Māori manuscripts

abstract: I report here on a part of a research project involving the investigation of a range of authentic Māori texts in terms of two types of meaning relation - those that operate within propositions (referred to here as 'intra-propositional relations'), and those that link propositions or groups of propositions (referred to here as 'inter-propositional relations'). In focus here is the second of these types, that is, inter-propositional relations, and in particular, the ways in which they are signalled in te reo Māori. The implications of the findings for the teaching and learning of te reo Māori are also discussed.

text: Inter-propositional relations: An investigation of authentic Māori texts signalled in te reo Māori I report here on a part of a research project involving the investigation of a range of authentic Māori texts in terms of two types of meaning relation - those that operate within propositions (referred to here as 'intra-propositional relations'), and those that link propositions or groups of propositions (referred to here as 'inter-propositional relations'). In focus here is the second of these types, that is, inter-propositional relations, and in particular, the ways in which they are signalled in te reo Māori. The implications of the findings for the teaching and learning of te reo Māori are also discussed.

year: 2007-09