Optimizing MIDAS III over South Africa
- Authors: Giday, Nigussie Mezgebe
- Date: 2014
- Subjects: Multi-Instrument Data Analysis System (MIDAS) , Global Positioning System , Ionosphere -- South Africa , Ionospheric electron density -- South Africa , Ionosondes -- South Africa , Tomography -- Scientific applications -- South Africa
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5517 , http://hdl.handle.net/10962/d1011277 , Multi-Instrument Data Analysis System (MIDAS) , Global Positioning System , Ionosphere -- South Africa , Ionospheric electron density -- South Africa , Ionosondes -- South Africa , Tomography -- Scientific applications -- South Africa
- Description: In this thesis an ionospheric tomographic algorithm called Multi-Instrument Data Anal- ysis System (MIDAS) is used to reconstruct electron density profiles using the Global Positioning System (GPS) data recorded from 53 GPS receivers over the South African region. MIDAS, developed by the Invert group at the University of Bath in the UK, is an inversion algorithm that produces a time dependent 3D image of the electron density of the ionosphere. GPS receivers record the time delay and phase advance of the trans- ionospheric GPS signals that traverse through the ionosphere from which the ionospheric parameter called Total Electron Content (TEC) can be computed. TEC, the line integral of the electron density along the satellite-receiver signal path, is ingested by ionospheric tomographic algorithms such as MIDAS to produce a time dependent 3D electron density profile. In order to validate electron density profiles from MIDAS, MIDAS derived NmF2 values were compared with ionosonde derived NmF2 values extracted from their respective 1D electron density profiles at 15 minute intervals for all four South African ionosonde stations (Grahamstown, Hermanus, Louisvale, and Madimbo). MIDAS 2D images of the electron density showed good diurnal and seasonal patterns; where a comparison of the 2D images at 12h00 UT for all the validation days exhibited maximum electron concentration during the autumn and summer and a minimum during the winter. A root mean square error (rmse) value as small as 0.88x 10¹¹[el=m³] was calculated for the Louisvale ionosonde station during the winter season and a maximum rmse value of 1.92x 10¹¹[el=m³] was ob- tained during the autumn season. The r² values were the least during the autumn and relatively large during summer and winter; similarly the rmse values were found to be a maximum during the autumn and a minimum during the winter indicating that MIDAS performs better during the winter than during the autumn and spring seasons. It is also observed that MIDAS performs better at Louisvale and Madimbo than at Grahamstown and Hermanus. In conclusion, the MIDAS reconstruction has showed good agreement with the ionosonde measurements; therefore, MIDAS can be considered a useful tool to study the ionosphere over the South African region.
- Full Text:
- Date Issued: 2014
- Authors: Giday, Nigussie Mezgebe
- Date: 2014
- Subjects: Multi-Instrument Data Analysis System (MIDAS) , Global Positioning System , Ionosphere -- South Africa , Ionospheric electron density -- South Africa , Ionosondes -- South Africa , Tomography -- Scientific applications -- South Africa
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5517 , http://hdl.handle.net/10962/d1011277 , Multi-Instrument Data Analysis System (MIDAS) , Global Positioning System , Ionosphere -- South Africa , Ionospheric electron density -- South Africa , Ionosondes -- South Africa , Tomography -- Scientific applications -- South Africa
- Description: In this thesis an ionospheric tomographic algorithm called Multi-Instrument Data Anal- ysis System (MIDAS) is used to reconstruct electron density profiles using the Global Positioning System (GPS) data recorded from 53 GPS receivers over the South African region. MIDAS, developed by the Invert group at the University of Bath in the UK, is an inversion algorithm that produces a time dependent 3D image of the electron density of the ionosphere. GPS receivers record the time delay and phase advance of the trans- ionospheric GPS signals that traverse through the ionosphere from which the ionospheric parameter called Total Electron Content (TEC) can be computed. TEC, the line integral of the electron density along the satellite-receiver signal path, is ingested by ionospheric tomographic algorithms such as MIDAS to produce a time dependent 3D electron density profile. In order to validate electron density profiles from MIDAS, MIDAS derived NmF2 values were compared with ionosonde derived NmF2 values extracted from their respective 1D electron density profiles at 15 minute intervals for all four South African ionosonde stations (Grahamstown, Hermanus, Louisvale, and Madimbo). MIDAS 2D images of the electron density showed good diurnal and seasonal patterns; where a comparison of the 2D images at 12h00 UT for all the validation days exhibited maximum electron concentration during the autumn and summer and a minimum during the winter. A root mean square error (rmse) value as small as 0.88x 10¹¹[el=m³] was calculated for the Louisvale ionosonde station during the winter season and a maximum rmse value of 1.92x 10¹¹[el=m³] was ob- tained during the autumn season. The r² values were the least during the autumn and relatively large during summer and winter; similarly the rmse values were found to be a maximum during the autumn and a minimum during the winter indicating that MIDAS performs better during the winter than during the autumn and spring seasons. It is also observed that MIDAS performs better at Louisvale and Madimbo than at Grahamstown and Hermanus. In conclusion, the MIDAS reconstruction has showed good agreement with the ionosonde measurements; therefore, MIDAS can be considered a useful tool to study the ionosphere over the South African region.
- Full Text:
- Date Issued: 2014
A study of the existence of equilibrium in mathematical economics
- Authors: Xotyeni, Zukisa Gqabi
- Date: 2008
- Subjects: Equilibrium (Economics) -- Mathematical models , Macroeconomics -- Mathematical models , Economics -- Mathematical models , Welfare economics -- Mathematical models , Lattice theory , Economics, Mathematical
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5418 , http://hdl.handle.net/10962/d1005232 , Equilibrium (Economics) -- Mathematical models , Macroeconomics -- Mathematical models , Economics -- Mathematical models , Welfare economics -- Mathematical models , Lattice theory , Economics, Mathematical
- Description: In this thesis we define and study the existence of an equilibrium situation in which producers maximize their profits relative to the production vectors in their production sets, consumers satisfy their preferences in their consumption sets under certain budget constraint, and for every commodity total demand equals total supply. This competitive equilibrium situation is referred to as the Walrasian equilibrium. The existence of this equilibrium is investigated from a various mathematical points of view. These include microeconomic theory, simplicial spaces, global analysis and lattice theory.
- Full Text:
- Date Issued: 2008
- Authors: Xotyeni, Zukisa Gqabi
- Date: 2008
- Subjects: Equilibrium (Economics) -- Mathematical models , Macroeconomics -- Mathematical models , Economics -- Mathematical models , Welfare economics -- Mathematical models , Lattice theory , Economics, Mathematical
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5418 , http://hdl.handle.net/10962/d1005232 , Equilibrium (Economics) -- Mathematical models , Macroeconomics -- Mathematical models , Economics -- Mathematical models , Welfare economics -- Mathematical models , Lattice theory , Economics, Mathematical
- Description: In this thesis we define and study the existence of an equilibrium situation in which producers maximize their profits relative to the production vectors in their production sets, consumers satisfy their preferences in their consumption sets under certain budget constraint, and for every commodity total demand equals total supply. This competitive equilibrium situation is referred to as the Walrasian equilibrium. The existence of this equilibrium is investigated from a various mathematical points of view. These include microeconomic theory, simplicial spaces, global analysis and lattice theory.
- Full Text:
- Date Issued: 2008
Moral reform and the desiderata of responses to wrongdoing: the production of a "morally autonomous person freely attached to the good"
- Authors: Waller, Heath Frederick
- Date: 2004 , 2013-06-14
- Subjects: Victims of crimes -- Attitudes , Criminals -- Rehabilitation , Punishment -- Psychological aspects , Social ethics , Punishment
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:2730 , http://hdl.handle.net/10962/d1003805 , Victims of crimes -- Attitudes , Criminals -- Rehabilitation , Punishment -- Psychological aspects , Social ethics , Punishment
- Description: Moral reform is a neglected response to wrongdoing that has been incorrectly portrayed as a practice involving illegitimate treatment of wrongdoers and as totally unsatisfying to those theorists advocating backward-looking practices such as retributive punishment. A clear explanation of the ethical legitimacy and practical necessity of the reformative techniques moral reform involves has been missed, and this paper details the design of moral reform proper in order to fill this gap in punishment theory. The moral reform of an offender is identified as a desideratum of responses to wrongdoing and it is explained what moral reform ought to entail. The claim that moral reform qualifies as the overriding aim of responses to wrongdoing is argued for on the grounds that this practice is capable of achieving all the established ends of responses to wrongdoing. The legitimate desiderata of our practices are identified as those usually selected as the ends of punishment practices, and moral reform must accomplish these if it is to be accepted. Moral reform is shown to realise the goals of punishments as the fortunate effects of what is done to achieve an offender's moral improvement and of what reformees do in taking responsibility for their actions. The suffering involved in moral reform receives particular emphasis since the practice will never satisfy unless it accommodates the widely-held intuition that the offender must suffer sufficiently as a consequence of his wrongdoing. Moral reform is further portrayed as the most meaningful practice for its ability to satisfy the appropriate needs and desires victims have in response to their victimization. A central claim of the thesis is that moral reform best serves the victim, since it most effectively relieves the victim's emotional responses to wrongdoing and is as adept as punishment at the expression of these same emotions. Reformers advocate a constructive response to wrongdoing that benefits all affected parties. , KMBT_363 , Adobe Acrobat 9.54 Paper Capture Plug-in
- Full Text:
- Date Issued: 2004
- Authors: Waller, Heath Frederick
- Date: 2004 , 2013-06-14
- Subjects: Victims of crimes -- Attitudes , Criminals -- Rehabilitation , Punishment -- Psychological aspects , Social ethics , Punishment
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:2730 , http://hdl.handle.net/10962/d1003805 , Victims of crimes -- Attitudes , Criminals -- Rehabilitation , Punishment -- Psychological aspects , Social ethics , Punishment
- Description: Moral reform is a neglected response to wrongdoing that has been incorrectly portrayed as a practice involving illegitimate treatment of wrongdoers and as totally unsatisfying to those theorists advocating backward-looking practices such as retributive punishment. A clear explanation of the ethical legitimacy and practical necessity of the reformative techniques moral reform involves has been missed, and this paper details the design of moral reform proper in order to fill this gap in punishment theory. The moral reform of an offender is identified as a desideratum of responses to wrongdoing and it is explained what moral reform ought to entail. The claim that moral reform qualifies as the overriding aim of responses to wrongdoing is argued for on the grounds that this practice is capable of achieving all the established ends of responses to wrongdoing. The legitimate desiderata of our practices are identified as those usually selected as the ends of punishment practices, and moral reform must accomplish these if it is to be accepted. Moral reform is shown to realise the goals of punishments as the fortunate effects of what is done to achieve an offender's moral improvement and of what reformees do in taking responsibility for their actions. The suffering involved in moral reform receives particular emphasis since the practice will never satisfy unless it accommodates the widely-held intuition that the offender must suffer sufficiently as a consequence of his wrongdoing. Moral reform is further portrayed as the most meaningful practice for its ability to satisfy the appropriate needs and desires victims have in response to their victimization. A central claim of the thesis is that moral reform best serves the victim, since it most effectively relieves the victim's emotional responses to wrongdoing and is as adept as punishment at the expression of these same emotions. Reformers advocate a constructive response to wrongdoing that benefits all affected parties. , KMBT_363 , Adobe Acrobat 9.54 Paper Capture Plug-in
- Full Text:
- Date Issued: 2004
Chemical studies of necic acid analogues
- Guthrie-Strachan, Jeffry James
- Authors: Guthrie-Strachan, Jeffry James
- Date: 1997
- Subjects: Organic acids , Chemistry, Organic
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4425 , http://hdl.handle.net/10962/d1006909 , Organic acids , Chemistry, Organic
- Description: Various aldehydes have been reacted with methyl acrylate under Baylis-Hillman conditions, using DABCO as a catalyst, to afford a range of α-substituted acrylic esters containing an allylic hydroxy group. Selected Baylis-Hillman products have been brominated, hydrolysed and acetylated to afford substrates for the synthesis of necic acid analogues. The diastereo- and regioselectivity of nucleophilic attack, using sodium methylmercaptan, on the Baylis-Hillman products and selected brominated derivatives was investigated. The allylic hydroxy compounds favour conjugate addition with the generation of a new chiral centre, while the allylic bromo derivatives favour substitution (SN and SN') (S[subscript N] and S[subscript N]') with consequent loss of chirality. (E)-2-Isopropylcrotonic acid, a vital precursor in the synthesis of all stereoisomers of trachelanthic and viridifloric acid, was synthesised in an attempt to obtain the necic acid components required for total alkaloid synthesis of lycopsamine and its derivatives. This precursor and salicylic acid were then used to prepare esters of retronecine, a dihydroxy necine base obtained via extraction and consequent hydrolysis of retrorsine.
- Full Text:
- Date Issued: 1997
- Authors: Guthrie-Strachan, Jeffry James
- Date: 1997
- Subjects: Organic acids , Chemistry, Organic
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4425 , http://hdl.handle.net/10962/d1006909 , Organic acids , Chemistry, Organic
- Description: Various aldehydes have been reacted with methyl acrylate under Baylis-Hillman conditions, using DABCO as a catalyst, to afford a range of α-substituted acrylic esters containing an allylic hydroxy group. Selected Baylis-Hillman products have been brominated, hydrolysed and acetylated to afford substrates for the synthesis of necic acid analogues. The diastereo- and regioselectivity of nucleophilic attack, using sodium methylmercaptan, on the Baylis-Hillman products and selected brominated derivatives was investigated. The allylic hydroxy compounds favour conjugate addition with the generation of a new chiral centre, while the allylic bromo derivatives favour substitution (SN and SN') (S[subscript N] and S[subscript N]') with consequent loss of chirality. (E)-2-Isopropylcrotonic acid, a vital precursor in the synthesis of all stereoisomers of trachelanthic and viridifloric acid, was synthesised in an attempt to obtain the necic acid components required for total alkaloid synthesis of lycopsamine and its derivatives. This precursor and salicylic acid were then used to prepare esters of retronecine, a dihydroxy necine base obtained via extraction and consequent hydrolysis of retrorsine.
- Full Text:
- Date Issued: 1997
Fuzzy ideals in commutative rings
- Authors: Sekaran, Rajakrishnar
- Date: 1995
- Subjects: Commutative rings , Fuzzy algebra
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5407 , http://hdl.handle.net/10962/d1005221 , Commutative rings , Fuzzy algebra
- Description: In this thesis, we are concerned with various aspects of fuzzy ideals of commutative rings. The central theorem is that of primary decomposition of a fuzzy ideal as an intersection of fuzzy primary ideals in a commutative Noetherian ring. We establish the existence and the two uniqueness theorems of primary decomposition of any fuzzy ideal with membership value 1 at the zero element. In proving this central result, we build up the necessary tools such as fuzzy primary ideals and the related concept of fuzzy maximal ideals, fuzzy prime ideals and fuzzy radicals. Another approach explores various characterizations of fuzzy ideals, namely, generation and level cuts of fuzzy ideals, relation between fuzzy ideals, congruences and quotient fuzzy rings. We also tie up several authors' seemingly different definitions of fuzzy prime, primary, semiprimary and fuzzy radicals available in the literature and show some of their equivalences and implications, providing counter-examples where certain implications fail.
- Full Text:
- Date Issued: 1995
- Authors: Sekaran, Rajakrishnar
- Date: 1995
- Subjects: Commutative rings , Fuzzy algebra
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5407 , http://hdl.handle.net/10962/d1005221 , Commutative rings , Fuzzy algebra
- Description: In this thesis, we are concerned with various aspects of fuzzy ideals of commutative rings. The central theorem is that of primary decomposition of a fuzzy ideal as an intersection of fuzzy primary ideals in a commutative Noetherian ring. We establish the existence and the two uniqueness theorems of primary decomposition of any fuzzy ideal with membership value 1 at the zero element. In proving this central result, we build up the necessary tools such as fuzzy primary ideals and the related concept of fuzzy maximal ideals, fuzzy prime ideals and fuzzy radicals. Another approach explores various characterizations of fuzzy ideals, namely, generation and level cuts of fuzzy ideals, relation between fuzzy ideals, congruences and quotient fuzzy rings. We also tie up several authors' seemingly different definitions of fuzzy prime, primary, semiprimary and fuzzy radicals available in the literature and show some of their equivalences and implications, providing counter-examples where certain implications fail.
- Full Text:
- Date Issued: 1995
A computer analysis of some of the Harrison metrics
- Authors: Sadler, Christopher John
- Date: 1975
- Subjects: Computer science -- Mathematics , Software measurement
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5427 , http://hdl.handle.net/10962/d1013151
- Description: In his paper B.K.Harrison concludes with the observation that his "solutions ... are presented as raw material for further research in General Relativity". In the same spirit, the present work started out as an attempt to process that raw material in a production-line powered by a computer. Harrison's solutions uould be fed in at one end, and the finished product, as yet undecided, would appear at the other. In the event, however, the project became more like an exercise in quality control, to continue the analogy. A search was made for algebraic criteria which would distinguish between those solutions which were acceptable for further analysis with particular regard to Gravitational radiation, and those which were not. Regrettably, no criteria could be found which characterised radiative solutions unequivocally, and, at the same time, lent themselves to a computer approach. The result is that the discussion of radiative solutions has had to be relegated to an appendix (Appendix 1), while the main body of the work is concerned with the determination of those quantities (the Newman-Penrose scalars) which would seem to be the foundation of any future computer-based analysis of gravitational radiation. Chapter 1 is an account of the underlying mathematical formulation, defining the terms, concepts and processes involved. In Chapter 2 the transformation of some of the ideas of Chapter 1 into computer software is presented. Chapter 3 is concerned with the specific metrics (the Harrison metrics) and the extent to which they have heen processed. The project has leaned heavily on papers by Harrison for the "raw material", by D' Inverno and Russell Clark, who pioneered the techniques and classified the Harrison metrics, and by Sachs for the treatment of gravitational radiation. However, the analysis of diagonal metrics, the special tetrad of Chapter 2 and the results in Appendix 2 are new.
- Full Text:
- Date Issued: 1975
- Authors: Sadler, Christopher John
- Date: 1975
- Subjects: Computer science -- Mathematics , Software measurement
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5427 , http://hdl.handle.net/10962/d1013151
- Description: In his paper B.K.Harrison concludes with the observation that his "solutions ... are presented as raw material for further research in General Relativity". In the same spirit, the present work started out as an attempt to process that raw material in a production-line powered by a computer. Harrison's solutions uould be fed in at one end, and the finished product, as yet undecided, would appear at the other. In the event, however, the project became more like an exercise in quality control, to continue the analogy. A search was made for algebraic criteria which would distinguish between those solutions which were acceptable for further analysis with particular regard to Gravitational radiation, and those which were not. Regrettably, no criteria could be found which characterised radiative solutions unequivocally, and, at the same time, lent themselves to a computer approach. The result is that the discussion of radiative solutions has had to be relegated to an appendix (Appendix 1), while the main body of the work is concerned with the determination of those quantities (the Newman-Penrose scalars) which would seem to be the foundation of any future computer-based analysis of gravitational radiation. Chapter 1 is an account of the underlying mathematical formulation, defining the terms, concepts and processes involved. In Chapter 2 the transformation of some of the ideas of Chapter 1 into computer software is presented. Chapter 3 is concerned with the specific metrics (the Harrison metrics) and the extent to which they have heen processed. The project has leaned heavily on papers by Harrison for the "raw material", by D' Inverno and Russell Clark, who pioneered the techniques and classified the Harrison metrics, and by Sachs for the treatment of gravitational radiation. However, the analysis of diagonal metrics, the special tetrad of Chapter 2 and the results in Appendix 2 are new.
- Full Text:
- Date Issued: 1975
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