title: Wittrick-Williams algorithm proof of bracketing and convergence theorems for eigenvalues of constrained structures with positive and negative penalty parameters

authors: Ilanko, Sinniah

subjects: Wittrick-Williams algorithm

abstract: The well-established Wittrick-Williams algorithm is used to derive novel and general proofs that show that the eigenvalues of systems with constraints can be bracketed by replacing the constraints by positive and negative pairs of either ordinary or inertial penalty parameters. It is also shown that convergence occurs from both above and below when the numerical values of these parameters are increased towards infinity. The proofs are applicable in many contexts but are derived in that of structural systems, for which the eigenvalues are either buckling load factors or the squares of natural frequencies of vibration; ordinary penalty parameters are stiffnesses of translational and rotational springs; and inertial penalty parameters are either masses or rotary inertias. The penalty parameters can be used to constrain a system or to impose constraints between systems. It is shown that the use of inertial penalty parameters has several advantages compared with using ordinary ones. Then the pth eigenvalue of a system with n constraints is bounded closely from above by the (p+n)th eigenvalue of the system with very large positive inertial penalty parameters and from below by the pth eigenvalue, when large negative values are used instead. This work is expected to enhance the versatility of numerical eigenproblem methods, e.g. the Rayleigh-Ritz method.

text: Wittrick-Williams algorithm proof of bracketing and convergence theorems for eigenvalues of constrained structures with positive and negative penalty parameters The well-established Wittrick-Williams algorithm is used to derive novel and general proofs that show that the eigenvalues of systems with constraints can be bracketed by replacing the constraints by positive and negative pairs of either ordinary or inertial penalty parameters. It is also shown that convergence occurs from both above and below when the numerical values of these parameters are increased towards infinity. The proofs are applicable in many contexts but are derived in that of structural systems, for which the eigenvalues are either buckling load factors or the squares of natural frequencies of vibration; ordinary penalty parameters are stiffnesses of translational and rotational springs; and inertial penalty parameters are either masses or rotary inertias. The penalty parameters can be used to constrain a system or to impose constraints between systems. It is shown that the use of inertial penalty parameters has several advantages compared with using ordinary ones. Then the pth eigenvalue of a system with n constraints is bounded closely from above by the (p+n)th eigenvalue of the system with very large positive inertial penalty parameters and from below by the pth eigenvalue, when large negative values are used instead. This work is expected to enhance the versatility of numerical eigenproblem methods, e.g. the Rayleigh-Ritz method.

year: 2007

title: Traumatic brain injury in New Zealand: a silent epidemic?

authors: Starkey, Nicola J.

subjects: New Zealand

abstract: In 2008 I was fortunate enough to be invited to be part of a research team on a large population based project focusing on the incidence and outcome of traumatic brain injury (TBI) in New Zealand (led by Professor Valery Feigin National Institute of Stroke and Applied Neurosciences, AUT University). At the time I knew little about TBI or population based research, but the last five years have changed that. My involvement in the project has led to on-going collaborations and friendships, and continues to provide me with on-going challenges as a researcher. More importantly, however, thanks to those who participated in our research, it has given me an enormous appreciation of the daily challenges faced by those affected by TBI and the desire to do research that ultimately will make a difference for them and other TBI survivors.

text: Traumatic brain injury in New Zealand: a silent epidemic? In 2008 I was fortunate enough to be invited to be part of a research team on a large population based project focusing on the incidence and outcome of traumatic brain injury (TBI) in New Zealand (led by Professor Valery Feigin National Institute of Stroke and Applied Neurosciences, AUT University). At the time I knew little about TBI or population based research, but the last five years have changed that. My involvement in the project has led to on-going collaborations and friendships, and continues to provide me with on-going challenges as a researcher. More importantly, however, thanks to those who participated in our research, it has given me an enormous appreciation of the daily challenges faced by those affected by TBI and the desire to do research that ultimately will make a difference for them and other TBI survivors.

year: 2013

title: Tino rangatiratanga in health policies and practises

authors: Wihongi, Helen Annette

subjects: tino rangatiratanga

abstract: The purpose of my doctoral research was to investigate tino rangatiratanga in health policies and practises in Aotearoa. My research involved defining tino rangatiratanga and exploring the expression of tino rangatiratanga in health policy and practises. A kaupapa Māori analysis of the 1996 National Cervical Screening Programme’s Policy document was at the core of the policy investigation. The analysis involved developing a kaupapa Māori analysing framework and then analysing the 1996 National Cervical Screening Policy document for empirical and normative judgements at four discursive levels, health gains, health objectives, health goals and fundamental underlying values. A Kaupapa Māori research design drew on interdisciplinary scholarship on colonisation, Te Tiriti o Waitangi, community psychology, public policy, disability theory, feminist theory and discourse theory.

I argue that the dominance of Western cultural norms and state-directed policies were made possible by the signing of Te Tiriti o Waitangi. The signing of Te Tiriti saw Crown sovereignty being implemented and tino rangatiratanga ignored. The consequences for Māori have been disastrous with loss of land and economic base which has resulted in poor health status. I also argue that tino rangatiratanga has the potential to transform the social and political context that frame Aotearoa society. Such an approach raises a critical dilemma for the state as meaningful recognition of tino rangatiratanga requires waiving full and absolute sovereignty which currently resides in the state. Hence some scholars argue that tino rangatiratanga is a site for constructive engagement where state and Māori relationships can be renegotiated. The extent to which this potential for constructive engagement is being realised in however is inadequately explored in the scholarly literature. Exploring the relationships between tino rangatiratanga and health policies and practises as undertaken in my thesis will therefore contribute to scholarly knowledge on the subject.

The findings from the research show that tino rangatiratanga is indeed a complex, fluid, multi-faceted and context related concept. Within the context of my research, tino rangatiratanga is defined as Māori sovereignty, self determination, and positive Māori development. As a Māori value it is about mana and tapu of rangatira or leadership personified. Within policies, tino rangatiratanga has emerged through resistance and demonstration and is actualised through Tiriti legislation and policies.

The legitimation of tino rangatiratanga in cervical screening services sees Māori leadership at national, regional and local levels and Māori involvement through wide ranging consultation but the Crown still controls the policy process and therefore the outcomes. Most cervical screening services are still owned and operated by the Crown or Crown agencies.

One of the consequences of Crown control is that Māori women are still twice as likely to get cervical cancer and four times more likely to die from it. To some degree this may be the result of resource allocation and the result of discriminatory service practices but also the result of resistance to the procedure itself.

Tino rangatiratanga within cervical screening services could be strengthened through iwi ownership of some cervical screening register sites. At the time of my field work (2000) there were 14 sites, all owned and operated by Crown agents. Tino rangatiratanga could also be strengthened through funding criteria that ensure practitioners are safe to practise, through the adoption of less invasive procedures and through the legitimation of Māori healing practises such as rongoā and karakia.

Overall if tino rangatiratanga is to be given full effect within the policy domain Māori must have a well established asset base, they must be in control of the decision making making process including resource allocation, service delivery must address the diversities of Māori realities and Māori must be the recipients of policy decisions made.

text: Tino rangatiratanga in health policies and practises The purpose of my doctoral research was to investigate tino rangatiratanga in health policies and practises in Aotearoa. My research involved defining tino rangatiratanga and exploring the expression of tino rangatiratanga in health policy and practises. A kaupapa Māori analysis of the 1996 National Cervical Screening Programme’s Policy document was at the core of the policy investigation. The analysis involved developing a kaupapa Māori analysing framework and then analysing the 1996 National Cervical Screening Policy document for empirical and normative judgements at four discursive levels, health gains, health objectives, health goals and fundamental underlying values. A Kaupapa Māori research design drew on interdisciplinary scholarship on colonisation, Te Tiriti o Waitangi, community psychology, public policy, disability theory, feminist theory and discourse theory.

I argue that the dominance of Western cultural norms and state-directed policies were made possible by the signing of Te Tiriti o Waitangi. The signing of Te Tiriti saw Crown sovereignty being implemented and tino rangatiratanga ignored. The consequences for Māori have been disastrous with loss of land and economic base which has resulted in poor health status. I also argue that tino rangatiratanga has the potential to transform the social and political context that frame Aotearoa society. Such an approach raises a critical dilemma for the state as meaningful recognition of tino rangatiratanga requires waiving full and absolute sovereignty which currently resides in the state. Hence some scholars argue that tino rangatiratanga is a site for constructive engagement where state and Māori relationships can be renegotiated. The extent to which this potential for constructive engagement is being realised in however is inadequately explored in the scholarly literature. Exploring the relationships between tino rangatiratanga and health policies and practises as undertaken in my thesis will therefore contribute to scholarly knowledge on the subject.

The findings from the research show that tino rangatiratanga is indeed a complex, fluid, multi-faceted and context related concept. Within the context of my research, tino rangatiratanga is defined as Māori sovereignty, self determination, and positive Māori development. As a Māori value it is about mana and tapu of rangatira or leadership personified. Within policies, tino rangatiratanga has emerged through resistance and demonstration and is actualised through Tiriti legislation and policies.

The legitimation of tino rangatiratanga in cervical screening services sees Māori leadership at national, regional and local levels and Māori involvement through wide ranging consultation but the Crown still controls the policy process and therefore the outcomes. Most cervical screening services are still owned and operated by the Crown or Crown agencies.

One of the consequences of Crown control is that Māori women are still twice as likely to get cervical cancer and four times more likely to die from it. To some degree this may be the result of resource allocation and the result of discriminatory service practices but also the result of resistance to the procedure itself.

Tino rangatiratanga within cervical screening services could be strengthened through iwi ownership of some cervical screening register sites. At the time of my field work (2000) there were 14 sites, all owned and operated by Crown agents. Tino rangatiratanga could also be strengthened through funding criteria that ensure practitioners are safe to practise, through the adoption of less invasive procedures and through the legitimation of Māori healing practises such as rongoā and karakia.

Overall if tino rangatiratanga is to be given full effect within the policy domain Māori must have a well established asset base, they must be in control of the decision making making process including resource allocation, service delivery must address the diversities of Māori realities and Māori must be the recipients of policy decisions made.

year: 2010