Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.

Primary proteolysis of caseins in cheddar cheese

Studies were undertaken to investigate proteolysis of the caseins during the initial stages of maturation of Cheddar cheese. Isolated caseins were hydrolyzed by enzymes thought to be of importance during cheese ripening and the resulting peptides isolated and identified. Large peptides were also isolated from Cheddar cheese and identified, thus enabling the extent to which casein degradation studies could be extrapolated to cheese to be established. The proteolytic specificity of chymosin on bovine αs1- and αs2-caseins and of plasmin on bovine αs1-casein were determined. The action of cathepsin D, the principal indigenous acid milk proteinase, on caseins was studied and its pH optimum and sensitivity to NaCI determined. The action of cathepsin D on αs1-, αs2-, β- and κ-caseins was compared with that of chymosin and was found to be generally similar for the hydrolysis of αs1- and κ-caseins but to differ for αs2-and β- caseins. β-Casein in solution was hydrolyzed by cell wall-associated proteinases from three strains of Lactococcus lactis; comparison of electrophoretograms of the hydrolyzates with those of Cheddar cheese indicated that no peptides produced by cell wall-associated proteinases were detectable in the cheeses. All the major peptides in the water-insoluble fraction of Cheddar cheese were isolated and identified. It was found that β-casein was degraded primarily by plasmin and αs1 -casein by chymosin. Initial chymosin and plasmin cleavage sites in αs1-, and β-casein, respectively, identified in these and other studies corresponded to the peptides isolated from cheese. The importance of non-starter lactic acid bacteria (NSLAB) to the maturation of Cheddar was studied in cheeses manufactured from raw, pasteurized or microfiltered milks. NSLAB were found to strongly influence the quality and patterns of proteolysis. Results presented in this thesis are consistent with the hypothesis that primary proteolysis in Cheddar is catalysed primarily by the action of chymosin and plasmin on intact αs1- and β-caseins, respectively. The resulting large peptides so produced are subsequently degraded by these enzymes and by proteinases and peptidases from the starter and NSLAB.

Chemistry of B1- and B10- boranes containing halogen or pseudohalogen groups

The research described in this thesis involved the chemistry of borane-species which contain one or more halide or pseudohalide groups. Both monoboron species e.g. [BH3X]- and "cluster" borane species e.g. [B10H9X]2- and I-Se B11H10 were studied. The first chapter is a review of the syntheses, properties and reactions of halide and pseudohalide species containing from one to ten boron atoms. Chapter Two is a theoretical investigation of' the electronic and molecular structures of two series of boranes i. e. [BH3X]- and [B10H9X]2- where X = H, CI, CN, NCS, SCN and N3. The calculational method used was the Modified Neglect of Differential Overlap (MNDO) method of Dewar et al. The results were compared where possible with experimental results such as the X-ray crystallographically determined structures of [BH3CI]- and [B10H10]2-. Chapter Three concerns halogenated selenaborane clusters and reports an improved synthesis of 12-Br-SeB11H10 and the first structural data for a simple non-metal containing selenaborane cage with the X-ray crystallographically determined structure of 12-1-SeB11H10. Finally, an indepth n.m.r. study of Se2B9H9 is also reported together with attempts to halogenate this compound. The last two chapters are based on single boron systems. Chapter Four concerns the synthetic routes to amine-boranes and -cyanoboranes from [BH4]- and [BH3CN]- substrates. This chapter discusses some difficulties encountered when polyamines were used in these reactions. The characterisation of an unusual ketone isolated from some of these reactions, the X-ray crystallographically determined structure of 4-dimethylamino-pyridine-cyanoborane and a new route to pyrazabole dimeric species are also discussed. The final chapter reports on work carried out at producing BH2X (X = H, CN) adducts of aminophosphines. Three routes were attempted to generate P-B and N-B bonded species with varying degrees of success. Some unusual products of these reactions are discussed including [Ph2(O) PPPh2 ] [Ph2NH]2, the structure of which was determined by X-ray crystallography.

The development of a computer model to optimize the performance of a 50kWp photovoltaic system

A computer model has been developed to optimize the performance of a 50kWp photovoltaic system which supplies electrical energy to a dairy farm at Fota Island in Cork Harbour. Optimization of the system involves maximising the efficiency and increasing the performance and reliability of each hardware unit. The model accepts horizontal insolation, ambient temperature, wind speed, wind direction and load demand as inputs. An optimization program uses the computer model to simulate the optimum operating conditions. From this analysis, criteria are established which are used to improve the photovoltaic system operation. This thesis describes the model concepts, the model implementation and the model verification procedures used during development. It also describes the techniques which are used during system optimization. The software, which is written in FORTRAN, is structured in modular units to provide logical and efficient programming. These modular units may also be used in the modelling and optimization of other photovoltaic systems.

Micropropagation of Begonia and a study of genome stability in Begonia rex

The development of procedures and media for the micropropagation of B. rex are described. Media for the production of plantlets from a number of other Begonia hybrids are also provided. Growth analysis data is given for plants produced in vivo from leaf cuttings and in vitro from mature leaf petioles and immature leaves derived from singly and multiply recycled axenic plantlets. No significant difference was found in phenotype or quantitative vegetative characters for any of the populations assessed. The results presented from studies on the development of broad spectrum media for the propagation of a number of B. rex cultivars using axenic leaf explants on factorial combinations of hormones illustrate the major influence played by the genotype on explant response in vitro and suggest media on which a range of B. rex cultivars may be propagated. Procedures for in vitro irradiation and colchicine treatments to destabilize the B. rex genome have also been described. Variants produced from these treatments indicate the utility of in vitro procedures for the expression of induced somatic variation. Colour variants produced from irradiation treatment have been cultured and prove stable. Polyploids produced as variants from irradiation treatment have been subcultured but prove unstable. Media for the induction and proliferation of callus are outlined. The influence of callus subculture and aging on the stability of the B. rex genome is assessed by chromosomal analysis of cells, in vitro and in regenerants. The B. rex genome is destabilized in callus culture but attenuation of variation occurs on regeneration. Diploid cell lines are maintained in callus subcultures and supplementation of regenerative media with high cytokinin concentrations, casein hydrolysate or adenine failed to produce variants. Callus aging however resulted in the production of polyploids. The presence and expression of pre-existing somatic variation in B. rex pith and root tissue is assessed and polyploids have been produced from pith tissues cultured in vitro. The stability of the B. rex genome and the application of tissue culture to micropropagation and breeding of B. rex are discussed.

Untangling unstructured programs

A method is presented for converting unstructured program schemas to strictly equivalent structured form. The predicates of the original schema are left intact with structuring being achieved by the duplication of he original decision vertices without the introduction of compound predicate expressions, or where possible by function duplication alone. It is shown that structured schemas must have at least as many decision vertices as the original unstructured schema, and must have more when the original schema contains branches out of decision constructs. The structuring method allows the complete avoidance of function duplication, but only at the expense of decision vertex duplication. It is shown that structured schemas have greater space-time requirements in general than their equivalent optimal unstructured counterparts and at best have the same requirements.

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

Fractionation and compositional studies of rabbit skeletal muscle membranes

The observations of Hooke (1665), Schleiden & Schwann (1839) and Virchow (1855) led to the identification of the cell as the basic structural unit of living material. In the intervening years, it has been firmly established that the chemical processes which underlie the proper functioning, development and reproduction of the organism are cellular activities. The development of the electron microscope has enabled cell structure to be studied in detail. A picture of the cell as an entity with a complex and highly organised internal structure has emerged from the work of Palade, Porter, Fernandez-Moran and many others. Although cells from different tissues and organisms differ in aspects of their structure and consequently in function, they have several features in common. A retentive membrane encloses a number of cell constituents, which include membrane-enclosed subcellular structures known as organelles. The cells of most tissues also contain a reticulum or system of branching tubules. The interplay of the biochemical activities of these structures enables the cell to function. Almost thirty years ago, Claude, Palade, Schneider, Hogeboom, de Duve and others set out to analytically fractionate the subcellular components obtained after the fragmentation of liver cells. This approach has become known as subcellular fractionation, and signalled a major conceptual breakthrough in biochemistry (reviewed by de Duve, 1964, 1967, 1971). The significance of this breakthrough has been underlined by the award of the 1974 Nobel Prize in Medicine to de Duve, Palade and Claude. This thesis is concerned with the application of subcellular fractionation techniques to the separation and characterisation of the membrane systems of the rabbit skeletal muscle cell.

A study of the oxygen electrochemistry of ruthenium and iridium

This thesis is concerned with an investigation of the anodic behaviour of ruthenium and iridium in aqueous solution and particularly of oxygen evolution on these metals. The latter process is of major interest in the large-scale production of hydrogen gas by the electrolysis of water. The presence of low levels of ruthenium trichloride ca. 10-4 mol dm-3 in acid solution give a considerable increase in the rate of oxygen evolution from platinum and gold, but not graphite, anodes. The mechanism of this catalytic effect was investigated using potential step and a.c. impedance technique. Earlier suggestions that the effect is due to catalysis by metal ions in solution were proved to be incorrect and it was shown that ruthenium species were incorporated into the surface oxide film. Changes in the oxidation state of these ruthenium species is probably responsible for the lowering of the oxygen overvoltage. Both the theoretical and practical aspects of the reaction were complicated by the fact that at constant potential the rates of both the catalysed and the uncatalysed oxygen evolution processes exhibit an appreciable, continuous decrease with either time or degree of oxidation of the substrate. The anodic behaviour of iridium in the oxide layer region has been investigated using conventional electrochemical techniques such as cyclic voltammetry. Applying a triangular voltage sweep at 10 Hz, 0.01 to 1.50V increases the amount of electric charge which the surface can store in the oxide region. This activation effect and the mechanism of charge storage is discussed in terms of both an expanded lattice theory for oxide growth on noble metals and a more recent theory of irreversible oxide formation with subsequent stoichiometry changes. The lack of hysteresis between the anodic and cathodic peaks at ca. 0.9 V suggests that the process involved here is proton migration in a relatively thick surface layer, i.e. that the reaction involved is some type of oxide-hydroxide transition. Lack of chloride ion inhibition in the anodic region also supports the irreversible oxide formation theory; however, to account for the hydrogen region of the potential sweep a compromise theory involving partial reduction of the outer regions of iridium oxide film is proposed. The loss of charge storage capacity when the activated iridium surface is anodized for a short time above ca. 1.60 V is attributed to loss by corrosion of the outer active layer from the metal surface. The behaviour of iridium at higher anodic potentials in acid solution was investigated. Current-time curves at constant potential and Tafel plots suggested that a change in the mechanism of the oxygen evolution reaction occurs at ca. 1.8 V. Above this potential, corrosion of the metal occurred, giving rise to an absorbance in the visible spectrum of the electrolyte (λ max = 455 nm). It is suggested that the species involved was Ir(O2)2+. A similar investigation in the case of alkaline electrolyte gave no evidence for a change in mechanism at 1.8 V and corrosion of the iridium was not observed. Oxygen evolution overpotentials were much lower for iridium than for platinum in both acidic and alkaline solutions.

The Queen's College, Cork: its origins and early history, 1803-1858

This work examines the origins and early history of the Queen's College, Cork. Designedly there is as much stress on the origins as on the early history, for it is the contention of the work that the College was something more than a legislative mushroom. It was very much in the tradition of the civic universities which added an exciting new dimension to academic life in these islands in the nineteenth century. The first chapter surveys university practice and thinking at the opening of the century, relying exclusively on published sources. The second chapter is devoted specifically to the state of learning in Cork during the period, and makes extensive use of hitherto unpublished manuscript material in relation to the Royal Cork Institution. The third chapter deals with the highly significant evidence on education embodied in the Report of the Select Committee on Irish Education of 1838. This material has not previously been published. In chapter four an extended study is made of relevant letters in the manuscript correspondence of Sir Robert Peel - even the most recent authoritative biography has ignored this material. The remaining three chapters are devoted more specifically to the College, both in the formulation or policy and in its practical working. In chapter six there is an extended survey of early College life based exclusively on hitherto unpublished manuscript material in the College Archives. All of these sources, together with incidental published material, are set out at the end of each chapter.

The purification and characterization of the high and low molecular weight forms of rabbit intestinal adenosine deaminase

Accepted Version

Women's contribution to the development of the English novel: 1621-1818

Women's contribution to literature is no arbitrary or artificial distinction. However much the reformer may welcome, or the conservative lament, the growth of a harmonious sharing of ideals between men and women, that growth has been a hard-fought struggle. It has been an escape from a prison, which, when it did not entirely shut out the greater world, at least enclosed a little world of education meant for women, literature adapted to the supposed limitations of their intellect, and a course of action prescribed by the other sex. To show how the literary efforts of women developed and justified their claims to free activity is the purpose of this thesis.

Variations in total and differential milk somatic cell counts and plasmin levels and their role in proteolysis and quality of milk and cheese

Increased plasmin and plasminogen levels and elevated somatic cell counts (SCC) and polymorphonuclear leucocyte levels (PMN) were evident in late lactation milk. Compositional changes in these milks were associated with increased SCC. The quality of late lactation milks was related to nutritional status of herds, with milks from herds on a high plane of nutrition having composition and clotting properties similar to, or superior to, early-mid lactation milks. Nutritionally-deficient cows had elevated numbers of polymorphonuclear leucocytes (PMNs) in their milk, elevated plasmin levels and increased overall proteolytic activity. The dominant effect of plasmin on proteolysis in milks of low SCC was established. When present in elevated numbers, somatic cells and PMNs in particular had a more significant influence on the proteolysis of both raw and pasteurised milks than plasmin. PMN protease action on the caseins showed proteolysis products of two specific enzymes, cathepsin B and elastase, which were also shown in high SCC milk. Crude extracts of somatic cells had a high specificity on αs1-casein. Cheeses made from late lactation milks had increased breakdown of αs1-casein, suggestive of the action of somatic cell proteinases, which may be linked to textural defects in cheese. Late lactation cheeses also showed decreased production of small peptides and amino acids, the reason for which is unknown. Plasmin, which is elevated in activity in late lactation milk, accelerated the ripening of Gouda-type cheese, but was not associated with defects of texture or flavour. The retention of somatic cell enzymes in cheese curd was confirmed, and a potential role in production of bitter peptides identified. Cheeses made from milks containing high levels of PMNs had accelerated αs1-casein breakdown relative to cheeses made from low PMN milk of the same total SCC, consistent with the demonstrated action of PMN proteinases. The two types of cheese were determined significantly different by blind triangle testing.

Effects of synbiotics on cancer risk biomarkers

Colorectal cancer (CRC) is the fourth most common cause of death from cancer in the world and second most common (behind lung cancer) in developed countries. In recent years there has been much interest in the potential use of prebiotics, probiotics and synbiotics in the prevention and treatment of CRC. We have previously shown that synbiotic consumption in Azoxymethane treated rats modulates the immune system, influences the genotoxic potential of caecal contents and reduces the number of colonic tumours compared to control rats who did not receive the synbiotic. The aim of the current study was to identify biomarkers suitable for use as cancer risk markers and as intervention markers. A second aim was to determine the influence of synbiotic consumption on cancer risk biomarkers such as in vivo colonic mucosal proliferation and genotoxic damage along with examining the genotoxic, cytotoxic and tumour promoting potential of faecal water (FW). Synbiotic consumption altered the composition of the gastrointestinal flora and reduced in vivo genotoxic damage and the genotoxic potential of FW in cancer and polyp subjects. Synbiotic consumption also reduced the proliferative activity in the colonic mucosa in polyp subjects. In both cancer and polyp subjects gene expression in the colonic mucosa was modulated in synbiotic consuming subjects. In this and other studies the activity of natural killer cells, the level of PGE2 in FW, IL-12 production by PBMCs, genotoxic damage in the colonic mucosa and the tumour promoting activities of FW have been identified as possible biomarkers of cancer risk. Future large scale studies investigating these parameters in healthy and diseased individuals are needed to confirm the suitability of these markers in assessing cancer risk and the role of synbiotics in modulating them.

Synthetic and stereochemical aspects of intramolecular reactions of α-diazoketones catalysed by rhodium(II) carboxylates

Chapter 1 of this thesis is a brief introduction to the preparation and reactions of α-diazocarbonyl compounds, with particular emphasis on the areas relating to the research undertaken: C-H insertion, addition to aromatics, and oxonium ylide generation and rearrangement. A short summary of catalyst development illustrates the importance of rhodium(II)carboxylates for α-diazocarbonyl decomposition. Chapter 2 describes intramolecular C-H insertion reactions of α-diazo-β-keto sulphones to form substituted cyclopentanones. Rhodium(II) carboxylates derived from homochiral carboxylic acids were used as catalysts in these reactions and enantioselection achieved through their use is discussed. Chapter 3 describes intramolecular Buchner cyclisation of aryl diazoketones with emphasis on the stereochemical aspects of the cyclisation and subsequent reaction of the bicyclo[5.3.0]decatrienones produced. The partial asymmetric synthesis achieved through use of chiral rhodium(II) carboxylates as catalysts is discussed. The application of the intramolecular Buchner reaction to the synthesis of hydroazulene lactones is illustrated. Chapter 4 demonstrates oxonium ylide formation and rearrangement in the decomposition of an α-diazoketone. The consequences of the use of chiral rhodium(II) carboxylates as catalysts are described. Particularly significant was the discovery that rhodium(II) (S)-mandelate acts as a very efficient catalyst for α-diazoketone decompositions, in general. Moderate asymmetric induction was possible in the decomposition of α-diazoketones with chiral rhodium(II) carboxylates, with rhodium(II) (S)-mandelate being one of the more enantioselective catalysts investigated. However, the asymmetric induction obtained was very dependent on the exact structure of the α-diazoketone, the catalyst, and the nature of the reaction. Chapter 5 contains the experimental details, and the spectral and analytical data for all new compounds reported.