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https://hdl.handle.net/10539/26093
On lie and Noether symmetries of differential equations.
Kara, A. H.
The inverse problem in the Calculus of Variations involves determining the Lagrangians,
if any, associated with a given (system of) differential equation(s). One
can classify Lagrangians according to the Lie algebra of symmetries of the Action
integral (the Noether algebra). We give a complete classification of first-order Lagrangians
defined on the line and produce results pertaining to the dimensionality
of the algebra of Noether symmetries and compare and contrast these with similar
results on the algebra of Lie symmetries of the corresponding Euler-Lagrange .equations.
It is proved that the maximum dimension of the Noether point symmetry
algebra of a particle Lagrangian. is five whereas it is known that the maximum dimension
Qf the Lie algebra of the corresponding scalar second-order Euler-Lagrange
equation is eight. Moreover, we show th'a.t a particle Lagrangian does not admit a
maximal four-dimensional Noether point symmeiry algebra and consequently a particle
Lagrangian admits the maximal r E {O, 1,2,3, 5}-dimensional Noether point
symmetry algebra,
It is well .known that an important means of analyzing differential equations lies in
the knowledge of the first integrals of the equation. We deliver an algorithm for
finding first integrals of partial differential equations and show how some of the
symmetry properties of the first integrals help to 'further' reduce the order of the
equations and sometimes completely solve the equations.
Finally, we discuss some open questions. These include the inverse problem and
classification of partial differential equations. ALo, there is the question of the
extension of the results to 'higher' dimensions.
A thesis submitted to the faculty of Science, University of the Witwatersrand, in
fulfilment of the requirements for the degree of Doctor of Philosophy,
1994-01-01T00:00:00ZThe conformational stability of a detoxification enzyme widely used as a fusion-protein affinity tag.
https://hdl.handle.net/10539/26092
The conformational stability of a detoxification enzyme widely used as a fusion-protein affinity tag.
Kaplan, Warren H
A glutathione S-transferase (Sj26GST) from Schistosoma japonicum, which functions in
the parasite's Phase II detoxification pathway, is expressed by the Pharmacia pGEX-2T
plasmid and is widely used as a fusion-protein affinity tag. It contains all 217 residues
of Sj26GST and an ad titional 9-residue peptide linker with a thrombin cleavage site at
its C-terminus. Size-exclusion HPLC (SEC-HPLC) and SDS-PAGE studies indicate that
purification of the homodimeric protein under nonreducing conditions results in the
reversible for-ration of significant amounts of 160 -kDa and larger aggregates without
a loss in catalytic activity. The basis for oxidative aggregation can be ascribed to the high
degree of exposure of the four cysteine residues per subunit. The conformational stability
of the dimeric protein was studied by urea- and temperature-induced unfolding
techniques. Fluorescence-spectroscopy, SEC-HPLC, urea- and temperature-gradient gel
electrophoresis, ultraviolet melting, differential scanning micro calorimetry , and enzyme
activity were employed to monitor structural and functional changes. The unfolding data
indicate the absence of thermodynamically stable intermediates and that the
umolding/refolding transition is a two-state process involving folded native dimer and
unfolded monomer. The stability of the protein was found to be dependent on its
concentration with a ~GO(H20) = 26 ±1.7 kcal/mol. The conformational stability was
unchanged in the presence of the leading antischistosomal drug Praziquantel, which
bound the protein with a Kd = 9 ±1.8 p,M. The strong relationship observed between
the m-v,llue and the size of the protein indicates that the amount of protem. surface
exposed to solvent upon unfolding is the major structural de.erminant for the dependence
of the protein's free energy of unfolding on urea concentration. 'Ihermograms obtained
by differential scanning calorimetry also fitted to a two-state irreversible unfolding
transition, both in the presence and absence of Praziquantel, with values of ~Cp = 1779
cal mol-IK-I
, ~HcaI = 227 kcal/mol, AHVH ::::::233 kcal/mol (r :::::~:HVHIAlIcal = 1.02)
and AS = 354 cal mol''K". The low ~Cp and ~S, when compared with the theoretically
determined values, implied that the thermal denaturation of Sj26GST did not result in
complete unfolding of the protein,
A thesis submitted to the Faculty of Science, University of the Witwatersrand, in
fulfilment of the requirements for the degree of Doctor of Philosophy.
1997-01-01T00:00:00ZThe international monetary fund interventions in Greece post the 2008 global economic crises
https://hdl.handle.net/10539/26091
The international monetary fund interventions in Greece post the 2008 global economic crises
Dakile, Dumisani Andrias
The 2008 global economic crises which originated in the United States of America had a devastating effect to the international community. The International Monetary Fund played a significant role as the Global Development Finance Institutions during the 2008 global economic crises. The purpose of this research is to understand how the IMF intervened in Greece because of the 2008 global economic crises and how such interventions affected the working class and the poor. The researcher adopted a qualitative research methodology, undertook interviews and used questionnaires to experts, academics, trade unionist, embassy representative knowledgeable on the 2008 economic crises and the IMF role in the Greece crises. The researcher also reviewed various documents and reports as a further resource to comprehend, gain more sight and to obtain pertinent and appropriate data on the subject matter. The researcher utilized uniform questions for all the participants across.
The research has established the role that was played by the IMF in the Greece crises which has been very controversial, why Greece it continues to be in economic crises and what should be done differently to resolve the Greece crises. It has established how the working class and the poor had been affected the IMF intervention in Greece and lastly it has proposed measures which need to be undertaken by the Greece to resolve the crises.
A research report submitted to the Faculty of Commerce, Law and
Management of the University of Witwatersrand, Johannesburg in part of the
requirements for the Degree in Management in Public and Development.
April 2018
2018-01-01T00:00:00ZA preformulation study of pyridoxal hydrochloride for solid dosage form desigh and development
https://hdl.handle.net/10539/26090
A preformulation study of pyridoxal hydrochloride for solid dosage form desigh and development
Durig, Thomas.
In this dissertation physicochemical properties of the Bs vitamer, pyridoxal hydrochloride (PL HC1), are investigated with the aim of generating the necessary profile for the rational development of a stable, safe and effective formulation containing this drug. Recent research suggests that administration of PL HC1 may be particularly effective in raising the depleted intracellular pyridoxal phosphate levels found in many asthmatics treated with theophylline. The solubility characteristics of PL HC1 suggest that its absorption and bioavailability should not be problematic
A Dissertation Submitted to the Faculty of Medicine, University of the Witwatersrand, Johannesburg for the Degree of Master of Pharmacy.
Johannesburg, August 1991
1991-08-01T00:00:00Z