title: Poisson representation methods for stochastic models of chemical reactions

authors: Chaturvedi, Subhash

abstract: A comprehensive discussion of the stochastic master equation approach to chemical reactions is presented. After a review of the various system size expansion methods that have been developed for an asymptotic solution of stochastic master equations, a new technique, the Poisson representation method is introduced. The technique is based on an expansion of the probability distribution in Poisson distributions and enables chemical master equations to be transformed into exact Fokker-Planck equations. 
The Fokker-Planck equations obtained using the Poisson representation are used to investigate some general features of chemical reaction systems whose steady state is thermodynamic equilibrium. The solutions for such systems are discussed from grand canonical and canonical ensemble points of view. 
Basic formulae for the two time correlation functions are derived using the Poisson representation method. The formulae for the chemical systems in thermodynamic equilibrium are shown to relate directly to the fluctuation-dissipation theorems which may be derived from equilibrium statistical mechanical considerations. For non-equilibrium systems, the formulae are shown to be generalisations of these fluctuation-dissipation theorems, but containing an extra term which arises entirely from the non equilibrium nature of the system.
In a chemical reaction mechanism, if only bimolecular reactions occur, the Fokker-Planck equations derived using the Poisson representation method involve no higher than second order derivatives. The mathematical equivalence between Fokker-Planck equations and stochastic differential equations is used to derive stochastic differential equations for chemical reaction systems. When trimolecular or higher reactions are present, the Fokker-Planck equations involve third or higher order derivatives. It is shown how the concept of a stochastic differential equation may be generalised in such cases. 
The stochastic differential equations lend themselves to a straightforward perturbative expansion in the inverse powers of the system size. These perturbative methods are applied to some interesting examples of non equilibrium reaction systems. Some novel features of the Poisson representation quasi probability which arise in these cases are discussed. 
A chemical reaction model which exhibits a second order phase transition behaviour is investigated in detail (including the process of spatial diffusion) and the first two terms in a perturbative expansion for the spatial and two time correlation functions are calculated.
A stochastic model of a chemical reaction which exhibits spatial and temporal oscillations is analysed below the instability thresholds. The same model is used to show how the Poisson representation method may be applied to calculate the spatial and two time correlation functions in finite systems with boundary conditions.

text: Poisson representation methods for stochastic models of chemical reactions A comprehensive discussion of the stochastic master equation approach to chemical reactions is presented. After a review of the various system size expansion methods that have been developed for an asymptotic solution of stochastic master equations, a new technique, the Poisson representation method is introduced. The technique is based on an expansion of the probability distribution in Poisson distributions and enables chemical master equations to be transformed into exact Fokker-Planck equations. 
The Fokker-Planck equations obtained using the Poisson representation are used to investigate some general features of chemical reaction systems whose steady state is thermodynamic equilibrium. The solutions for such systems are discussed from grand canonical and canonical ensemble points of view. 
Basic formulae for the two time correlation functions are derived using the Poisson representation method. The formulae for the chemical systems in thermodynamic equilibrium are shown to relate directly to the fluctuation-dissipation theorems which may be derived from equilibrium statistical mechanical considerations. For non-equilibrium systems, the formulae are shown to be generalisations of these fluctuation-dissipation theorems, but containing an extra term which arises entirely from the non equilibrium nature of the system.
In a chemical reaction mechanism, if only bimolecular reactions occur, the Fokker-Planck equations derived using the Poisson representation method involve no higher than second order derivatives. The mathematical equivalence between Fokker-Planck equations and stochastic differential equations is used to derive stochastic differential equations for chemical reaction systems. When trimolecular or higher reactions are present, the Fokker-Planck equations involve third or higher order derivatives. It is shown how the concept of a stochastic differential equation may be generalised in such cases. 
The stochastic differential equations lend themselves to a straightforward perturbative expansion in the inverse powers of the system size. These perturbative methods are applied to some interesting examples of non equilibrium reaction systems. Some novel features of the Poisson representation quasi probability which arise in these cases are discussed. 
A chemical reaction model which exhibits a second order phase transition behaviour is investigated in detail (including the process of spatial diffusion) and the first two terms in a perturbative expansion for the spatial and two time correlation functions are calculated.
A stochastic model of a chemical reaction which exhibits spatial and temporal oscillations is analysed below the instability thresholds. The same model is used to show how the Poisson representation method may be applied to calculate the spatial and two time correlation functions in finite systems with boundary conditions.

year: 1977

title: The Plight of Kurdish Natinonalism: Critical Analysis of the Kurds in Turkey, Iran, Iran, and Syria around First World War.

authors: Delan, Handren

subjects: Kurdish Nationalism

abstract: During recent years the Kurdish question has reappeared, more intensely than before, on the international agenda. For years, this questino has been of fundamental concern to the countries of region,and it has led to intense internal controversies and economic and social crisis. The number of Kurds in fourt parts of Kurdistan and within the four borders of countries that have divided it up between themselves totals about 35 million.This makes the Kurds, after Arabs, the Turks, and Persians,the fourth largest nation in the middle east. 

Kurds are, together with the Arabs,Persians and Armenians, one of the most ancient peoples of the near east. The country they inhabit is called Kurdistan. The Kurds have thier own language,Kurdish. Kurdish is a member of the Indo-European family of languages. Like Persian,Afghan and Bakuchi, it is one of the Iranian languages. Kurdish is unrelated to Arabic or Turkish languages.

Kurds have played a signoficant role in the history of this region since it's early epoches. A great deal of information can be found in numerous Greek, Arabs, Rokan , and Armenian.According to them, Kurds founded several important states druing early Islamic epoch between teenth and thirteenth centuries such as Salahadin, Merwandidis, and Ayubiat as well as in the distant past. Sultan Salahadin, the founder of the Ayubiad state, which included Egypt, Syria and Kurdistan, played a particularly significant role in history. 

This thesis attempts to examine the main charecteristics of Kurdish natuionalism. In order to do that, the thesis analyses the social structure of Kurdish scoiety. The thesis thorougly explains the agitation of Kurds against the Ottoman Empire durng nineteenth century and beyond. This thesis examines Kurdish reactions in the course of the First World War against the Empires of Ottoman and Persia, which divided the Kurdish land between themselves. The thesis analyses the stunning obtacles in the face of the Kurds in formatinon of their national state in aftermath of the Ottoman Empire. This study can be a cornerstone to understand the inherent weakness of Kurdish nationalism in integrating all social and sectarian groups within the Kurdish society.

text: The Plight of Kurdish Natinonalism: Critical Analysis of the Kurds in Turkey, Iran, Iran, and Syria around First World War. During recent years the Kurdish question has reappeared, more intensely than before, on the international agenda. For years, this questino has been of fundamental concern to the countries of region,and it has led to intense internal controversies and economic and social crisis. The number of Kurds in fourt parts of Kurdistan and within the four borders of countries that have divided it up between themselves totals about 35 million.This makes the Kurds, after Arabs, the Turks, and Persians,the fourth largest nation in the middle east. 

Kurds are, together with the Arabs,Persians and Armenians, one of the most ancient peoples of the near east. The country they inhabit is called Kurdistan. The Kurds have thier own language,Kurdish. Kurdish is a member of the Indo-European family of languages. Like Persian,Afghan and Bakuchi, it is one of the Iranian languages. Kurdish is unrelated to Arabic or Turkish languages.

Kurds have played a signoficant role in the history of this region since it's early epoches. A great deal of information can be found in numerous Greek, Arabs, Rokan , and Armenian.According to them, Kurds founded several important states druing early Islamic epoch between teenth and thirteenth centuries such as Salahadin, Merwandidis, and Ayubiat as well as in the distant past. Sultan Salahadin, the founder of the Ayubiad state, which included Egypt, Syria and Kurdistan, played a particularly significant role in history. 

This thesis attempts to examine the main charecteristics of Kurdish natuionalism. In order to do that, the thesis analyses the social structure of Kurdish scoiety. The thesis thorougly explains the agitation of Kurds against the Ottoman Empire durng nineteenth century and beyond. This thesis examines Kurdish reactions in the course of the First World War against the Empires of Ottoman and Persia, which divided the Kurdish land between themselves. The thesis analyses the stunning obtacles in the face of the Kurds in formatinon of their national state in aftermath of the Ottoman Empire. This study can be a cornerstone to understand the inherent weakness of Kurdish nationalism in integrating all social and sectarian groups within the Kurdish society.

year: 2006

title: Ko wai tō ingoa? The transformative potential of Māori names

authors: Seed-Pihama, Joeliee Elizabeth

subjects: Māori names

abstract: Ingoa tangata (personal names) are an expression of te reo Māori, Māori identity, and tino rangatiratanga (self-determination). Nevertheless, our names are still mispronounced, marginalised and demeaned by individuals and institutions, such as schools, the health system, politics and media. This thesis argues that the gift of a Māori name and the assertion of that name over one’s lifetime is simultaneously a political act of resistance and an act of normalisation – an act of just being Māori. In particular, the thesis reveals how whānau naming practices endure and are important for whānau identity and belonging.

A Kaupapa Māori theoretical approach is used to highlight the mana of our ingoa tangata within te ao Māori (the Māori world). I analyse the experiences of six generations of one whānau and the ways in which they have resisted, reclaimed and regenerated our ingoa tangata and associated practices. Kaupapa Māori theory provides a much-needed theoretical framework that privileges te reo Māori and mātauranga Māori throughout this research. This theory also supports Māori researchers to critique and disrupt Western power dynamics within research as well as maintaining the political imperative of decolonisation and resurgence agendas within the research of Indigenous communities.

This thesis foregrounds Pūrākau as a research method to tell the kōrero ingoa (naming stories) of six generations of one whānau, totalling twenty-six different stories. I explore the possibilities of pūrākau as a method and ako (to teach/ learn) as a powerful component in the building and sharing of stories, as writing tools for the (re)presentation of that material and in expressing the researcher’s positionality. Pūrākau as method also enables the utilisation of our cosmogonies as important sources of mātauranga Māori and therefore as crucial to an analysis of our naming motivations and notions of belonging. Furthermore, I critically analyse the disruptions and interruptions to ingoa tangata caused by institutions of colonialism such as religion, law and education. This research argues for the transformative potential of our ingoa tangata and their associated kōrero ingoa in terms of enhancing identity, embedding whakapapa kōrero and keeping Māori values alive within whānau, and beyond.

text: Ko wai tō ingoa? The transformative potential of Māori names Ingoa tangata (personal names) are an expression of te reo Māori, Māori identity, and tino rangatiratanga (self-determination). Nevertheless, our names are still mispronounced, marginalised and demeaned by individuals and institutions, such as schools, the health system, politics and media. This thesis argues that the gift of a Māori name and the assertion of that name over one’s lifetime is simultaneously a political act of resistance and an act of normalisation – an act of just being Māori. In particular, the thesis reveals how whānau naming practices endure and are important for whānau identity and belonging.

A Kaupapa Māori theoretical approach is used to highlight the mana of our ingoa tangata within te ao Māori (the Māori world). I analyse the experiences of six generations of one whānau and the ways in which they have resisted, reclaimed and regenerated our ingoa tangata and associated practices. Kaupapa Māori theory provides a much-needed theoretical framework that privileges te reo Māori and mātauranga Māori throughout this research. This theory also supports Māori researchers to critique and disrupt Western power dynamics within research as well as maintaining the political imperative of decolonisation and resurgence agendas within the research of Indigenous communities.

This thesis foregrounds Pūrākau as a research method to tell the kōrero ingoa (naming stories) of six generations of one whānau, totalling twenty-six different stories. I explore the possibilities of pūrākau as a method and ako (to teach/ learn) as a powerful component in the building and sharing of stories, as writing tools for the (re)presentation of that material and in expressing the researcher’s positionality. Pūrākau as method also enables the utilisation of our cosmogonies as important sources of mātauranga Māori and therefore as crucial to an analysis of our naming motivations and notions of belonging. Furthermore, I critically analyse the disruptions and interruptions to ingoa tangata caused by institutions of colonialism such as religion, law and education. This research argues for the transformative potential of our ingoa tangata and their associated kōrero ingoa in terms of enhancing identity, embedding whakapapa kōrero and keeping Māori values alive within whānau, and beyond.

year: 2017