title: There are no multiply-perfect Fibonacci numbers

authors: Broughan, Kevin A.

subjects: maths

abstract: Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors.

text: There are no multiply-perfect Fibonacci numbers Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors.

year: 2011

title: State-based and process-based value passing

authors: Reeves, Steve

subjects: computer science

abstract: State-based and process-based formalisms each come with their own distinct set of assumptions and properties. To combine them in a useful way it is important to be sure of these assumptions in order that the formalisms are combined in ways which have, or which allow, the intended combined properties. Consequently we cannot necessarily expect to take on state-based formalism and one process-based formalism and combine them and get something sensible, especially since the act of combining can have subtle consequences.
Here we concentrate on value-passing, how it is treated in each formalism, and how the formalisms can be combined so as to preserve certain properties. Specifically, the aim is to take from the many process-based formalisms definitions that will best fit with our chosen stat-based formalism, namely Z, so that the fit is simple, has no unintended consequences and is as elegant as possible.

text: State-based and process-based value passing State-based and process-based formalisms each come with their own distinct set of assumptions and properties. To combine them in a useful way it is important to be sure of these assumptions in order that the formalisms are combined in ways which have, or which allow, the intended combined properties. Consequently we cannot necessarily expect to take on state-based formalism and one process-based formalism and combine them and get something sensible, especially since the act of combining can have subtle consequences.
Here we concentrate on value-passing, how it is treated in each formalism, and how the formalisms can be combined so as to preserve certain properties. Specifically, the aim is to take from the many process-based formalisms definitions that will best fit with our chosen stat-based formalism, namely Z, so that the fit is simple, has no unintended consequences and is as elegant as possible.

year: 2003

title: How is the circular economy emerging in Aotearoa New Zealand? Research Brief

authors: Diprose, G

abstract: The results of the environmental scan show that there is grass-roots activity and that we have some high level conceptualisations of circular economies (CE) however there is little in-between. As such, it is in the middle that activity needs to occur to transition towards a circular economy. We see a need to move beyond business-as-usual with an entity focus to an ‘ecosystem phase.’ This means that for CE, partnerships are needed across business, organisations, Treaty partners, institutions, NGOs and stakeholders to form collaborations around material and people flows in order for ecosystems to form and create circular economies.

text: How is the circular economy emerging in Aotearoa New Zealand? Research Brief The results of the environmental scan show that there is grass-roots activity and that we have some high level conceptualisations of circular economies (CE) however there is little in-between. As such, it is in the middle that activity needs to occur to transition towards a circular economy. We see a need to move beyond business-as-usual with an entity focus to an ‘ecosystem phase.’ This means that for CE, partnerships are needed across business, organisations, Treaty partners, institutions, NGOs and stakeholders to form collaborations around material and people flows in order for ecosystems to form and create circular economies.

year: 2022