title: Override and restricted union for partial functions

authors: Stokes, Tim

abstract: The override operation  is a natural one in computer science, and has connections with other areas of mathematics such as hyperplane arrangements. For arbitrary functions f and g, f  g is the function with
domain dom(f) ∪ dom(g) that agrees with f on dom(f) and with g on dom(g)\ dom(f). Jackson and the author have shown that there is no finite axiomatisation of algebras of functions of signature (). But adding operations (such as update) to this minimal signature can lead to finite axiomatisations. For the functional signature (, \) where \ is set-theoretic difference, Cirulis has given a finite equational axiomatisation as subtraction o-semilattices. Define f  g = (f g)∩(g f) for all functions f and g; this is the largest domain restriction of the binary relation f ∪ g that gives a partial function. Now f ∩g = f\(f\g) and f g = f  (f  g) for all functions f,g, so the signatures () and (, ∩) are both intermediate between () and (, \) in expressive power. We show that each is finitely axiomatised, with the former giving a proper quasivariety and the latter the variety of associative distributive o-semilattices in the sense of Cirulis.

text: Override and restricted union for partial functions The override operation  is a natural one in computer science, and has connections with other areas of mathematics such as hyperplane arrangements. For arbitrary functions f and g, f  g is the function with
domain dom(f) ∪ dom(g) that agrees with f on dom(f) and with g on dom(g)\ dom(f). Jackson and the author have shown that there is no finite axiomatisation of algebras of functions of signature (). But adding operations (such as update) to this minimal signature can lead to finite axiomatisations. For the functional signature (, \) where \ is set-theoretic difference, Cirulis has given a finite equational axiomatisation as subtraction o-semilattices. Define f  g = (f g)∩(g f) for all functions f and g; this is the largest domain restriction of the binary relation f ∪ g that gives a partial function. Now f ∩g = f\(f\g) and f g = f  (f  g) for all functions f,g, so the signatures () and (, ∩) are both intermediate between () and (, \) in expressive power. We show that each is finitely axiomatised, with the former giving a proper quasivariety and the latter the variety of associative distributive o-semilattices in the sense of Cirulis.

year: 2024-08-12

title: A combined optical, thermal and electrical performance model of a Building Integrated Photovoltaic/Thermal Concentrator (BIPVTC)

authors: Anderson, Timothy Nicholas

subjects: component

abstract: The electrical output of concentrating photovoltaic devices is significantly affected by the temperature of the photovoltaic cells. The ability to actively cool photovoltaic cells under concentrated radiation allows their electrical efficiency to be maintained particularly during periods of high solar radiation when concentration offers the maximum benefit. In this study, the design of a novel photovoltaic/thermal solar concentrator for building integration (BIPVTC) is discussed. The optical, thermal and electrical performance of the collector was theoretically modelled and validated with experimental data. The results show that BIPVTC offers improved electrical yields from both concentrating radiation onto the photovoltaic cells and also by actively cooling them.

text: A combined optical, thermal and electrical performance model of a Building Integrated Photovoltaic/Thermal Concentrator (BIPVTC) The electrical output of concentrating photovoltaic devices is significantly affected by the temperature of the photovoltaic cells. The ability to actively cool photovoltaic cells under concentrated radiation allows their electrical efficiency to be maintained particularly during periods of high solar radiation when concentration offers the maximum benefit. In this study, the design of a novel photovoltaic/thermal solar concentrator for building integration (BIPVTC) is discussed. The optical, thermal and electrical performance of the collector was theoretically modelled and validated with experimental data. The results show that BIPVTC offers improved electrical yields from both concentrating radiation onto the photovoltaic cells and also by actively cooling them.

year: 2011

title: Summerhill school is it possible in Aotearoa New Zealand?: Challenging the neo-liberal ideologies in our hegemonic schooling system

authors: Peck, Mikaere Michelle S.

subjects: Matriarchal society

abstract: The original purpose of this thesis is to explore the possibility of setting up a school in Aotearoa (New Zealand) that operates according to the principles and philosophies of Summerhill School in Suffolk, England. An examination of Summerhill School is therefore the purpose of this study, particularly because of its commitment to self-regulation and direct democracy for children. My argument within this study is that Summerhill presents precisely the type of model Māori as Tangata Whenua (Indigenous people of Aotearoa) need in our design of an alternative schooling programme, given that self-regulation and direct democracy are traits conducive to achieving Tino Rangitiratanga (Self-government, autonomy and control). In claiming this however, not only would Tangata Whenua benefit from this model of schooling; indeed it has the potential to serve the purpose of all people regardless of age race or gender. At present, no school in Aotearoa has replicated Summerhill's principles and philosophies in their entirety. 
Given the constraints of a Master's thesis, this piece of work is therefore only intended as a theoretical background study for a much larger kaupapa (purpose). It is my intention to produce a further and more comprehensive study in the future using Summerhill as a vehicle to initiate a model school in Aotearoa that is completely antithetical to the dominant neo-liberal philosophy of our age. To this end, my study intends to demonstrate how neo-liberal schooling is universally dictated by global money market trends, and how it is an ideology fueled by the indifferent acceptance of the general population. In other words, neo-liberal theory is a theory of capitalist colonisation. 
In order to address the long term vision, this project will be comprised of two major components. The first will be a study of the principal philosophies that govern Summerhill School. As I will argue, Summerhill creates an environment that is uniquely successful and fulfilling for the children who attend. At the same time, it will also be shown how it is a philosophy that is entirely contrary to a neo-liberal mindset; an antidote, to a certain extent, to the ills of contemporary schooling. The second component will address the historical movement of schooling in Aotearoa since the Labour Party's landslide victory in 1984, and how the New Zealand Curriculum has been affected by these changes. I intend to trace the importation of neo-liberal methodologies into Aotearoa such as the 'Picot Taskforce,' 'Tomorrows Schools' and 'Bulk Funding,' to name but a few. The neo-liberal ideologies that have swept through this country in the last two decades have relentlessly metamorphosised departments into businesses and forced ministries into the marketplace, hence causing the 'ideological reduction of education' and confining it to the parameters of schooling.
The purpose of this research project is to act as a catalyst for the ultimate materialization of an original vision; the implementation of a school like Summerhill in Aotearoa. A study of the neo-liberal ideologies that currently dominate this country is imperative in order to understand the current schooling situation in Aotearoa and create an informed comparison between the 'learning for freedom' style of Summerhill and the 'learning to earn' style of our status quo schools. It is my hope to strengthen the argument in favour of Summerhill philosophy by offering an understanding of the difference between the two completely opposing methods of learning.

text: Summerhill school is it possible in Aotearoa New Zealand?: Challenging the neo-liberal ideologies in our hegemonic schooling system The original purpose of this thesis is to explore the possibility of setting up a school in Aotearoa (New Zealand) that operates according to the principles and philosophies of Summerhill School in Suffolk, England. An examination of Summerhill School is therefore the purpose of this study, particularly because of its commitment to self-regulation and direct democracy for children. My argument within this study is that Summerhill presents precisely the type of model Māori as Tangata Whenua (Indigenous people of Aotearoa) need in our design of an alternative schooling programme, given that self-regulation and direct democracy are traits conducive to achieving Tino Rangitiratanga (Self-government, autonomy and control). In claiming this however, not only would Tangata Whenua benefit from this model of schooling; indeed it has the potential to serve the purpose of all people regardless of age race or gender. At present, no school in Aotearoa has replicated Summerhill's principles and philosophies in their entirety. 
Given the constraints of a Master's thesis, this piece of work is therefore only intended as a theoretical background study for a much larger kaupapa (purpose). It is my intention to produce a further and more comprehensive study in the future using Summerhill as a vehicle to initiate a model school in Aotearoa that is completely antithetical to the dominant neo-liberal philosophy of our age. To this end, my study intends to demonstrate how neo-liberal schooling is universally dictated by global money market trends, and how it is an ideology fueled by the indifferent acceptance of the general population. In other words, neo-liberal theory is a theory of capitalist colonisation. 
In order to address the long term vision, this project will be comprised of two major components. The first will be a study of the principal philosophies that govern Summerhill School. As I will argue, Summerhill creates an environment that is uniquely successful and fulfilling for the children who attend. At the same time, it will also be shown how it is a philosophy that is entirely contrary to a neo-liberal mindset; an antidote, to a certain extent, to the ills of contemporary schooling. The second component will address the historical movement of schooling in Aotearoa since the Labour Party's landslide victory in 1984, and how the New Zealand Curriculum has been affected by these changes. I intend to trace the importation of neo-liberal methodologies into Aotearoa such as the 'Picot Taskforce,' 'Tomorrows Schools' and 'Bulk Funding,' to name but a few. The neo-liberal ideologies that have swept through this country in the last two decades have relentlessly metamorphosised departments into businesses and forced ministries into the marketplace, hence causing the 'ideological reduction of education' and confining it to the parameters of schooling.
The purpose of this research project is to act as a catalyst for the ultimate materialization of an original vision; the implementation of a school like Summerhill in Aotearoa. A study of the neo-liberal ideologies that currently dominate this country is imperative in order to understand the current schooling situation in Aotearoa and create an informed comparison between the 'learning for freedom' style of Summerhill and the 'learning to earn' style of our status quo schools. It is my hope to strengthen the argument in favour of Summerhill philosophy by offering an understanding of the difference between the two completely opposing methods of learning.

year: 2009