title: Small Column Experiments for Continuous Radial Flow Chromatography

authors: Lee, Sook-Han Yvonne

subjects: continuous radial flow chromatography

abstract: Continuous radial flow chromatography (CRFC) combines radial flow and rotating annular bed chromatography. Solution flows radially from eight fixed ports around the periphery through a rotating annular packed bed towards the axis. Loading, equilibration, elution and reequilibration solutions can be applied simultaneously at different feed ports. Protein is captured on resin in the loading zone and carried around by the annulus to the elution zone to be eluted, making the CRFC a continuous process. 
Small axial flow columns experiments were carried out to represent continuous BSA purification in the CRFC for a range of rotation speeds, flow rates, feed concentration, elution buffer concentration, loading sections and elution secions. Quality of the separation was measured based on productivity and height to width ratio. 
Best operating conditions for BSA purification in the CRFC include 720 deg/hr rotation speed, 1 mL/min flow rate, 1M elution buffer (NaCl) solution, and either 5 or 1.5 mg/mL feed solution. A wide range of loading sections and elution sections can be allocated. Combinations of these best conditions are restricted by total protein load per chromatography cycle. 
Mathematical models solved by finite difference method in Matlab were used to predict CRFC operation under the best conditions. Model accounts for change in solute concentration by convection, film diffusion and uptake into resin. Protein and salt parameters were adjusted to achieve best mached protein peaks. Model simulations agreed well with experimental results. Loading peak width was similar but experimental data showed broader elution peaks. Elution peak height for all simulations was greater while loading peak height were more variable than in the experiments. Peak tailing was observed in both experimental and model data.

text: Small Column Experiments for Continuous Radial Flow Chromatography Continuous radial flow chromatography (CRFC) combines radial flow and rotating annular bed chromatography. Solution flows radially from eight fixed ports around the periphery through a rotating annular packed bed towards the axis. Loading, equilibration, elution and reequilibration solutions can be applied simultaneously at different feed ports. Protein is captured on resin in the loading zone and carried around by the annulus to the elution zone to be eluted, making the CRFC a continuous process. 
Small axial flow columns experiments were carried out to represent continuous BSA purification in the CRFC for a range of rotation speeds, flow rates, feed concentration, elution buffer concentration, loading sections and elution secions. Quality of the separation was measured based on productivity and height to width ratio. 
Best operating conditions for BSA purification in the CRFC include 720 deg/hr rotation speed, 1 mL/min flow rate, 1M elution buffer (NaCl) solution, and either 5 or 1.5 mg/mL feed solution. A wide range of loading sections and elution sections can be allocated. Combinations of these best conditions are restricted by total protein load per chromatography cycle. 
Mathematical models solved by finite difference method in Matlab were used to predict CRFC operation under the best conditions. Model accounts for change in solute concentration by convection, film diffusion and uptake into resin. Protein and salt parameters were adjusted to achieve best mached protein peaks. Model simulations agreed well with experimental results. Loading peak width was similar but experimental data showed broader elution peaks. Elution peak height for all simulations was greater while loading peak height were more variable than in the experiments. Peak tailing was observed in both experimental and model data.

year: 2010

title: Biembeddings of cycle systems using integer Heffter arrays

authors: Cavenagh, Nicholas J.

subjects: mathematics

abstract: In this paper, we use constructions of Heffter arrays to verify the existence of face 2‐colorable embeddings of cycle decompositions of the complete graph. Specifically, for n ≡ 1 (mod 4) and k ≡3(mod 4), n k ≫ ⩾ 7 and when n ≡ 0(mod 3) then k ≡ 7(mod 12), there exist face 2-colorable embeddings of the complete graph K₂ₙₖ₊₁ onto an orientable surface where each face is a cycle of a fixed length k. In these embeddings the vertices of K₂ₙₖ₊₁ will be labeled with the elements of Z₂ₙₖ₊₁ in such a way that the group, (Z₂ₙₖ₊₁, +) acts sharply transitively on the vertices of the embedding. This result is achieved by verifying the existence of nonequivalent Heffter arrays, H (n ; k), which satisfy the conditions: (1) for each row and each column the sequential partial sums determined by the natural ordering must be distinct modulo 2nk + 1; (2) the composition of the natural orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. The existence of Heffter arrays H (n ; k) that satisfy condition (1) was established earlier in Burrage et al. and in this current paper, we vary this construction and show, for k ⩾ 11, that there are at least (n − 2)[((k − 11)/4)!/ ]² such nonequivalent H (n ; k) that satisfy both conditions (1) and (2).

text: Biembeddings of cycle systems using integer Heffter arrays In this paper, we use constructions of Heffter arrays to verify the existence of face 2‐colorable embeddings of cycle decompositions of the complete graph. Specifically, for n ≡ 1 (mod 4) and k ≡3(mod 4), n k ≫ ⩾ 7 and when n ≡ 0(mod 3) then k ≡ 7(mod 12), there exist face 2-colorable embeddings of the complete graph K₂ₙₖ₊₁ onto an orientable surface where each face is a cycle of a fixed length k. In these embeddings the vertices of K₂ₙₖ₊₁ will be labeled with the elements of Z₂ₙₖ₊₁ in such a way that the group, (Z₂ₙₖ₊₁, +) acts sharply transitively on the vertices of the embedding. This result is achieved by verifying the existence of nonequivalent Heffter arrays, H (n ; k), which satisfy the conditions: (1) for each row and each column the sequential partial sums determined by the natural ordering must be distinct modulo 2nk + 1; (2) the composition of the natural orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. The existence of Heffter arrays H (n ; k) that satisfy condition (1) was established earlier in Burrage et al. and in this current paper, we vary this construction and show, for k ⩾ 11, that there are at least (n − 2)[((k − 11)/4)!/ ]² such nonequivalent H (n ; k) that satisfy both conditions (1) and (2).

year: 2020

title: Repositioning within indigenous discourses of transformation and self-determination

authors: Berryman, Mere

subjects: research-whanau

abstract: This thesis reflectively and critically examines a series of research case studies initiated by a research-whānau. It explores the thinking, experiences and reflections of this research-whānau, as they worked to enhance the educational achievement of Māori students. Authorship of the thesis was undertaken by me (Mere Berryman). However, the methodology involved a collaborative, retrospective and critical reflection of research-whānau experiences and thinking, in the light of the research findings and experiences since the inception of this research-whānau in 1991. In the course of this work, the research-whānau have been able to explore what it has meant to put the principles of kaupapa Māori research into practice while working within a mainstream organisation (Specialist Education Services then the Ministry of Education). Our research work has involved repositioning ourselves from dependence on Western research methodologies to a better understanding and application of kaupapa Māori conceptualisations of research. 
The thesis begins by identifying mainstream and kaupapa Māori events that have historically and still continue to impact upon Māori students' educational experiences. These events provide the wider context for the work of this research-whānau at the interface of Te Ao Māori and Te Ao Pākehā, and for the 11 case studies that exemplify changes in our thinking and research practice over a period of 15 years. The thesis employs an indigenous (and specifically Māori) worldview as the framework for description, critical reflection, and theorising around these case studies. Common themes are collaboratively co-constructed then each theme is explained in relation to relevant Māori theory.
The thesis concludes with the shifts in theorising and practice made by the research-whānau during the course of our work as we sought to contribute in ways that were more transformative and self-determining. We argue that these shifts in theorising and practice are also required of others if we are to change the status quo and contribute constructively to improving Māori students' potential.

text: Repositioning within indigenous discourses of transformation and self-determination This thesis reflectively and critically examines a series of research case studies initiated by a research-whānau. It explores the thinking, experiences and reflections of this research-whānau, as they worked to enhance the educational achievement of Māori students. Authorship of the thesis was undertaken by me (Mere Berryman). However, the methodology involved a collaborative, retrospective and critical reflection of research-whānau experiences and thinking, in the light of the research findings and experiences since the inception of this research-whānau in 1991. In the course of this work, the research-whānau have been able to explore what it has meant to put the principles of kaupapa Māori research into practice while working within a mainstream organisation (Specialist Education Services then the Ministry of Education). Our research work has involved repositioning ourselves from dependence on Western research methodologies to a better understanding and application of kaupapa Māori conceptualisations of research. 
The thesis begins by identifying mainstream and kaupapa Māori events that have historically and still continue to impact upon Māori students' educational experiences. These events provide the wider context for the work of this research-whānau at the interface of Te Ao Māori and Te Ao Pākehā, and for the 11 case studies that exemplify changes in our thinking and research practice over a period of 15 years. The thesis employs an indigenous (and specifically Māori) worldview as the framework for description, critical reflection, and theorising around these case studies. Common themes are collaboratively co-constructed then each theme is explained in relation to relevant Māori theory.
The thesis concludes with the shifts in theorising and practice made by the research-whānau during the course of our work as we sought to contribute in ways that were more transformative and self-determining. We argue that these shifts in theorising and practice are also required of others if we are to change the status quo and contribute constructively to improving Māori students' potential.

year: 2008