title: On the ratio of the sum of divisors and Euler’s totient function II

authors: Broughan, Kevin A.

subjects: Euler’s totient function

abstract: We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the quotient is 4 and n is even.

text: On the ratio of the sum of divisors and Euler’s totient function II We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the quotient is 4 and n is even.

year: 2014

title: Morphodynamics of the Whitianga Tidal Inlet and Buffalo Bay, New Zealand

authors: Steeghs, Lauren

subjects: Eddy formation

abstract: The primary aim of this study was to investigate the sedimentation processes within Buffalo Bay, particularly within and adjacent to the Whitianga tidal inlet, in order to ascertain reasons for the shoaling at both the inlet, and the identified shallow zone around Pandora Rock. 

Comparison of historic bathymetries suggests the ebb delta and ebb discharge channel of the Whitianga tidal inlet are rapidly accreting and the ebb tidal discharge channel is gradually migrating northeast towards Whakapenui Point.  Accretion rates of up to 25 cm y-1 were calculated in the ebb delta and inlet discharge channel area between 1979 and 1995 and aerial photo comparisons suggest the ebb delta area had increased by 400 % between 1990 and 2002.  Results of the hydrodynamic and sediment transport modelling suggest the rapid accretion in the ebb delta vicinity is likely to be caused by a combination of catchment estuary inputs, which are deposited on the ebb tide as the ebb flow decelerates over the ebb delta, and inputs that have been moved south along Buffalo Beach by flood currents and an eddy that forms landward of the ebb tidal discharge.  Residual tidal velocities further suggest a deposition zone in the ebb delta vicinity resulting from opposing currents and the deceleration of currents.  

Hydrodynamic modelling results indicate the isolated shallow zone around Pandora rock appears to be caused by a transient eddy in the southern section of Buffalo Bay.  The eddy is formed by the ebb tidal discharge from the inlet.  Accretion probably occurs in the centre of the eddy which moves north as the ebb tide progresses.  

Results obtained from a current meter and sediment trap deployed in northern Buffalo Bay suggest suspended sediment transport is minimal in northern Buffalo Bay, only occurring with large wave activity.   Results of the hydrodynamic and sediment transport modelling further demonstrate that this area experiences low flow velocities, and has little interaction with the rest of Buffalo Bay.  The minimal sediment input to this area, combined with the occasional erosion of the seafloor, primarily by wave activity, is thought to have resulted in long term erosion of northwestern Buffalo Bay between 1938 and 1979.  Although the beach and nearshore is eroding, it is likely the addition of sediment would act to stabilise this section of eroding beach.  Renourishment material could be provided by the ebb delta, the southern tip of Buffalo Bay or the isolated sandbar northeast of the inlet entrance.

text: Morphodynamics of the Whitianga Tidal Inlet and Buffalo Bay, New Zealand The primary aim of this study was to investigate the sedimentation processes within Buffalo Bay, particularly within and adjacent to the Whitianga tidal inlet, in order to ascertain reasons for the shoaling at both the inlet, and the identified shallow zone around Pandora Rock. 

Comparison of historic bathymetries suggests the ebb delta and ebb discharge channel of the Whitianga tidal inlet are rapidly accreting and the ebb tidal discharge channel is gradually migrating northeast towards Whakapenui Point.  Accretion rates of up to 25 cm y-1 were calculated in the ebb delta and inlet discharge channel area between 1979 and 1995 and aerial photo comparisons suggest the ebb delta area had increased by 400 % between 1990 and 2002.  Results of the hydrodynamic and sediment transport modelling suggest the rapid accretion in the ebb delta vicinity is likely to be caused by a combination of catchment estuary inputs, which are deposited on the ebb tide as the ebb flow decelerates over the ebb delta, and inputs that have been moved south along Buffalo Beach by flood currents and an eddy that forms landward of the ebb tidal discharge.  Residual tidal velocities further suggest a deposition zone in the ebb delta vicinity resulting from opposing currents and the deceleration of currents.  

Hydrodynamic modelling results indicate the isolated shallow zone around Pandora rock appears to be caused by a transient eddy in the southern section of Buffalo Bay.  The eddy is formed by the ebb tidal discharge from the inlet.  Accretion probably occurs in the centre of the eddy which moves north as the ebb tide progresses.  

Results obtained from a current meter and sediment trap deployed in northern Buffalo Bay suggest suspended sediment transport is minimal in northern Buffalo Bay, only occurring with large wave activity.   Results of the hydrodynamic and sediment transport modelling further demonstrate that this area experiences low flow velocities, and has little interaction with the rest of Buffalo Bay.  The minimal sediment input to this area, combined with the occasional erosion of the seafloor, primarily by wave activity, is thought to have resulted in long term erosion of northwestern Buffalo Bay between 1938 and 1979.  Although the beach and nearshore is eroding, it is likely the addition of sediment would act to stabilise this section of eroding beach.  Renourishment material could be provided by the ebb delta, the southern tip of Buffalo Bay or the isolated sandbar northeast of the inlet entrance.

year: 2007

title: Problematic reasoning under the guise of anti-Māori talk: A case study of the Three Waters tweets

authors: Tan, Kyle K. H.

abstract: Drawing from a subset of Twitter/X quotes (or tweets) on the politically controversial Three Waters Reform, this study identified forms of anti-Māori discourse through a deductive analysis. A complementary analysis was conducted to unpack how problematic reasoning fueled racism against Māori. Our results revealed distinct and interconnected themes—“resources,” “culture,” “stirrer,” “privilege,” and “one people”—that portrayed Māori as undeserving, lacking expertise, threatening, and unworthy of equitable treatment, as New Zealand citizens are entitled to enjoy liberal democratic values. Anti-Māori speakers employed problematic reasoning tactics to obstruct the public from understanding the truth or to encourage others to form ill-informed opinions through emotions, supposed authority, and conspiracy. Exemplar tweets were provided to illustrate the myriad instances of false information related to patterns of anti-Māori discourse. Evidence from this study makes the case for addressing racism on social media and creating interventions to expand media literacy amongst the public to discern problematic reasonings.

text: Problematic reasoning under the guise of anti-Māori talk: A case study of the Three Waters tweets Drawing from a subset of Twitter/X quotes (or tweets) on the politically controversial Three Waters Reform, this study identified forms of anti-Māori discourse through a deductive analysis. A complementary analysis was conducted to unpack how problematic reasoning fueled racism against Māori. Our results revealed distinct and interconnected themes—“resources,” “culture,” “stirrer,” “privilege,” and “one people”—that portrayed Māori as undeserving, lacking expertise, threatening, and unworthy of equitable treatment, as New Zealand citizens are entitled to enjoy liberal democratic values. Anti-Māori speakers employed problematic reasoning tactics to obstruct the public from understanding the truth or to encourage others to form ill-informed opinions through emotions, supposed authority, and conspiracy. Exemplar tweets were provided to illustrate the myriad instances of false information related to patterns of anti-Māori discourse. Evidence from this study makes the case for addressing racism on social media and creating interventions to expand media literacy amongst the public to discern problematic reasonings.

year: 2025