The classsification of fuzzy subgroups of some finite Abelian p-groups of rank 3
- Authors: Appiah, Isaac Kwadwo
- Date: 2016
- Subjects: Fuzzy sets Abelian groups Finite groups
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10353/2468 , vital:27845
- Description: An important trend in fuzzy group theory in recent years has been the notion of classification of fuzzy subgroups using a suitable equivalence relation. In this dissertation, we have successfully used the natural equivalence relation defined by Murali and Makamba in [81] and a natural fuzzy isomorphism to classify fuzzy subgroups of some finite abelian p-groups of rank three of the form Zpn + Zp + Zp for any fixed prime integer p and any positive integer n. This was achieved through the usage of a suitable technique of enumerating distinct fuzzy subgroups and non-isomorphic fuzzy subgroups of G. We commence by giving a brief discussion on the theory of fuzzy sets and fuzzy subgroups from the perspective of group theory through to the theory of sets, leading us to establish a linkage among these theories. We have also shown in this dissertation that the converse of theorem 3.1 proposed by Das in [24] is incorrect by giving a counter example and restate the theorem. We have then reviewed and enriched the study conducted by Ngcibi in [94] by characterising the non-isomorphic fuzzy subgroups in that study. We have also developed a formula to compute the crisp subgroups of the under-studied group and provide its proof. Furthermore, we have compared the equivalence relation under which the classification problem is based with various versions of equivalence studied in the literature. We managed to use this counting technique to obtain explicit formulae for the number of maximal chains, distinct fuzzy subgroups, non-isomorphic maximal chains and non-isomorphic fuzzy subgroups of these groups and their proofs are provided.
- Full Text:
- Date Issued: 2016
- Authors: Appiah, Isaac Kwadwo
- Date: 2016
- Subjects: Fuzzy sets Abelian groups Finite groups
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10353/2468 , vital:27845
- Description: An important trend in fuzzy group theory in recent years has been the notion of classification of fuzzy subgroups using a suitable equivalence relation. In this dissertation, we have successfully used the natural equivalence relation defined by Murali and Makamba in [81] and a natural fuzzy isomorphism to classify fuzzy subgroups of some finite abelian p-groups of rank three of the form Zpn + Zp + Zp for any fixed prime integer p and any positive integer n. This was achieved through the usage of a suitable technique of enumerating distinct fuzzy subgroups and non-isomorphic fuzzy subgroups of G. We commence by giving a brief discussion on the theory of fuzzy sets and fuzzy subgroups from the perspective of group theory through to the theory of sets, leading us to establish a linkage among these theories. We have also shown in this dissertation that the converse of theorem 3.1 proposed by Das in [24] is incorrect by giving a counter example and restate the theorem. We have then reviewed and enriched the study conducted by Ngcibi in [94] by characterising the non-isomorphic fuzzy subgroups in that study. We have also developed a formula to compute the crisp subgroups of the under-studied group and provide its proof. Furthermore, we have compared the equivalence relation under which the classification problem is based with various versions of equivalence studied in the literature. We managed to use this counting technique to obtain explicit formulae for the number of maximal chains, distinct fuzzy subgroups, non-isomorphic maximal chains and non-isomorphic fuzzy subgroups of these groups and their proofs are provided.
- Full Text:
- Date Issued: 2016
The classification of fuzzy subgroups of some finite non-cyclic abelian p- groups of rank 3, with emphasis on the number of distinct fuzzy subgroups
- Authors: Appiah, Isaac Kwadwo
- Date: 2021-03
- Subjects: Fuzzy sets , Commutative algebra
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10353/20783 , vital:46563
- Description: In [6] and [7] we classi_ed fuzzy subgroups of some rank-3 abelian groups of the form G = Zpn + Zp + Zp for any _xed prime integer p and any positive integer n, using the natural equivalence relation de_ned in [40]. In this thesis, we extend our classi_cation of fuzzy subgroups in [6] to the group G = Zpn + Zpm + Zp for any _xed prime integer p; m = 2 and any positive integer n using the same natural equivalence relation studied in [40]. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups of G for any n;m _ 2 and (iii) distinct fuzzy subgroups for m = 2 and n _ 2. We have also developed user-friendly polynomial formulae for the number of (iv) subgroups, (v) maximal chains for the group G = Zpn + Zpm for any n;m _ 2; any _xed prime positive integer p and (vi) distinct fuzzy subgroups of Zpn + Zpm for m equal to 2 and 3, and n _ 2 and provided their proofs. , Thesis (PhD) -- Faculty of Science and Agriculture, 2021
- Full Text:
- Date Issued: 2021-03
- Authors: Appiah, Isaac Kwadwo
- Date: 2021-03
- Subjects: Fuzzy sets , Commutative algebra
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10353/20783 , vital:46563
- Description: In [6] and [7] we classi_ed fuzzy subgroups of some rank-3 abelian groups of the form G = Zpn + Zp + Zp for any _xed prime integer p and any positive integer n, using the natural equivalence relation de_ned in [40]. In this thesis, we extend our classi_cation of fuzzy subgroups in [6] to the group G = Zpn + Zpm + Zp for any _xed prime integer p; m = 2 and any positive integer n using the same natural equivalence relation studied in [40]. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups of G for any n;m _ 2 and (iii) distinct fuzzy subgroups for m = 2 and n _ 2. We have also developed user-friendly polynomial formulae for the number of (iv) subgroups, (v) maximal chains for the group G = Zpn + Zpm for any n;m _ 2; any _xed prime positive integer p and (vi) distinct fuzzy subgroups of Zpn + Zpm for m equal to 2 and 3, and n _ 2 and provided their proofs. , Thesis (PhD) -- Faculty of Science and Agriculture, 2021
- Full Text:
- Date Issued: 2021-03
Conductivity profiles for a horizontally uniform earth
- Authors: Murrell, Hugh Crozier
- Date: 1983
- Subjects: Coen, Shimon -- Criticism and interpretation Wang-Ho Yu, Michael -- Criticism and interpretation Algorithms
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5395 , http://hdl.handle.net/10962/d1001984
- Description: An investigation is made into the mathematics behind the noniterative inversion algorithm of Shimon Coen and Michael Wang-Ho Yu [1981]. The algorithm determines the conductivity profile of a horizontally uniform earth from surface measurements of apparent resistivity with a Schlumberger array. The algorithm is checked by performing the inversion on both artifical and raw field data
- Full Text:
- Date Issued: 1983
- Authors: Murrell, Hugh Crozier
- Date: 1983
- Subjects: Coen, Shimon -- Criticism and interpretation Wang-Ho Yu, Michael -- Criticism and interpretation Algorithms
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5395 , http://hdl.handle.net/10962/d1001984
- Description: An investigation is made into the mathematics behind the noniterative inversion algorithm of Shimon Coen and Michael Wang-Ho Yu [1981]. The algorithm determines the conductivity profile of a horizontally uniform earth from surface measurements of apparent resistivity with a Schlumberger array. The algorithm is checked by performing the inversion on both artifical and raw field data
- Full Text:
- Date Issued: 1983
On the association of graphs to rings
- Authors: Mzulwini, Sboniso
- Date: 2020
- Subjects: Categories (Mathematics)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10948/47060 , vital:39779
- Description: Let R be a commutative ring with nonzero identity, and let Z (R) be the set of its zerodivisors. There exists an association between a simple graph (R) and the set Z(R) of nonzero zero-divisors of R. In this dissertation we investigate how the properties of R a⁄ect the properties of (R) and vice versa. There are other graphs that are associated with R. Some of these are shown to be special cases of the congruence-based zero-divisor graph.
- Full Text:
- Date Issued: 2020
- Authors: Mzulwini, Sboniso
- Date: 2020
- Subjects: Categories (Mathematics)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10948/47060 , vital:39779
- Description: Let R be a commutative ring with nonzero identity, and let Z (R) be the set of its zerodivisors. There exists an association between a simple graph (R) and the set Z(R) of nonzero zero-divisors of R. In this dissertation we investigate how the properties of R a⁄ect the properties of (R) and vice versa. There are other graphs that are associated with R. Some of these are shown to be special cases of the congruence-based zero-divisor graph.
- Full Text:
- Date Issued: 2020
Uhadi
- Nyoka, Malcolm Everitt Mlungiseleli
- Authors: Nyoka, Malcolm Everitt Mlungiseleli
- Date: 196?
- Subjects: Xhosa poetry Xhosa language -- Texts
- Language: Xhosa
- Type: text
- Identifier: http://hdl.handle.net/10962/45610 , vital:25524 , This image is held at the Cory Library for Humanities Research at Rhodes University. For further information contact cory@ru.ac.za. The digitisation of this image was made possible through a generous grant received from the Andrew W. Mellon Foundation 2014-2017. , MS 16 335(a)
- Description: A collection of poems by M.E.M. Nyoka. This is the handwritten manuscript predating the actual publication of this unique Xhosa poetry in 1962.
- Full Text:
- Date Issued: 196?
- Authors: Nyoka, Malcolm Everitt Mlungiseleli
- Date: 196?
- Subjects: Xhosa poetry Xhosa language -- Texts
- Language: Xhosa
- Type: text
- Identifier: http://hdl.handle.net/10962/45610 , vital:25524 , This image is held at the Cory Library for Humanities Research at Rhodes University. For further information contact cory@ru.ac.za. The digitisation of this image was made possible through a generous grant received from the Andrew W. Mellon Foundation 2014-2017. , MS 16 335(a)
- Description: A collection of poems by M.E.M. Nyoka. This is the handwritten manuscript predating the actual publication of this unique Xhosa poetry in 1962.
- Full Text:
- Date Issued: 196?
Effect of a low density dust shell on the propagation of gravitational waves:
- Bishop, Nigel T, van der Walt, Petrus J, Naidoo, Monos
- Authors: Bishop, Nigel T , van der Walt, Petrus J , Naidoo, Monos
- Date: 2020
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/159935 , vital:40357 , https://0-doi.org.wam.seals.ac.za/10.1007/s10714-020-02740-9
- Description: Using the Bondi-Sachs formalism, the problem of a gravitational wave source surrounded by a spherical dust shell is considered. Using linearized perturbation theory, the geometry is found in the regions: in the shell, exterior to the shell, and interior to the shell. It is found that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust.
- Full Text:
- Date Issued: 2020
- Authors: Bishop, Nigel T , van der Walt, Petrus J , Naidoo, Monos
- Date: 2020
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/159935 , vital:40357 , https://0-doi.org.wam.seals.ac.za/10.1007/s10714-020-02740-9
- Description: Using the Bondi-Sachs formalism, the problem of a gravitational wave source surrounded by a spherical dust shell is considered. Using linearized perturbation theory, the geometry is found in the regions: in the shell, exterior to the shell, and interior to the shell. It is found that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust.
- Full Text:
- Date Issued: 2020
Weather neutral models for short-term electricity demand forecasting
- Authors: Nyulu, Thandekile
- Date: 2013
- Subjects: Electric power consumption -- Forecasting -- Mathematical models , Forecasting -- Mathematical models
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:10578 , http://hdl.handle.net/10948/d1018751
- Description: Energy demand forecasting, and specifically electricity demand forecasting, is a fun-damental feature in both industry and research. Forecasting techniques assist all electricity market participants in accurate planning, selling and purchasing decisions and strategies. Generation and distribution of electricity require appropriate, precise and accurate forecasting methods. Also accurate forecasting models assist producers, researchers and economists to make proper and beneficial future decisions. There are several research papers, which investigate this fundamental aspect and attempt var-ious statistical techniques. Although weather and economic effects have significant influences on electricity demand, in this study they are purposely eliminated from investigation. This research considers calendar-related effects such as months of the year, weekdays and holidays (that is, public holidays, the day before a public holiday, the day after a public holiday, school holidays, university holidays, Easter holidays and major religious holidays) and includes university exams, general election days, day after elections, and municipal elections in the analysis. Regression analysis, cate-gorical regression and auto-regression are used to illustrate the relationships between response variable and explanatory variables. The main objective of the investigation was to build forecasting models based on this calendar data only and to observe how accurate the models can be without taking into account weather effects and economic effects, hence weather neutral models. Weather and economic factors have to be forecasted, and these forecasts are not so accurate and calendar events are known for sure (error-free). Collecting data for weather and economic factors is costly and time consuming, while obtaining calendar data is relatively easy.
- Full Text:
- Date Issued: 2013
- Authors: Nyulu, Thandekile
- Date: 2013
- Subjects: Electric power consumption -- Forecasting -- Mathematical models , Forecasting -- Mathematical models
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:10578 , http://hdl.handle.net/10948/d1018751
- Description: Energy demand forecasting, and specifically electricity demand forecasting, is a fun-damental feature in both industry and research. Forecasting techniques assist all electricity market participants in accurate planning, selling and purchasing decisions and strategies. Generation and distribution of electricity require appropriate, precise and accurate forecasting methods. Also accurate forecasting models assist producers, researchers and economists to make proper and beneficial future decisions. There are several research papers, which investigate this fundamental aspect and attempt var-ious statistical techniques. Although weather and economic effects have significant influences on electricity demand, in this study they are purposely eliminated from investigation. This research considers calendar-related effects such as months of the year, weekdays and holidays (that is, public holidays, the day before a public holiday, the day after a public holiday, school holidays, university holidays, Easter holidays and major religious holidays) and includes university exams, general election days, day after elections, and municipal elections in the analysis. Regression analysis, cate-gorical regression and auto-regression are used to illustrate the relationships between response variable and explanatory variables. The main objective of the investigation was to build forecasting models based on this calendar data only and to observe how accurate the models can be without taking into account weather effects and economic effects, hence weather neutral models. Weather and economic factors have to be forecasted, and these forecasts are not so accurate and calendar events are known for sure (error-free). Collecting data for weather and economic factors is costly and time consuming, while obtaining calendar data is relatively easy.
- Full Text:
- Date Issued: 2013
Studying a Tumor Growth Partial Differential Equation via the Black–Scholes Equation
- Winter Sinkala, Tembinkosi F. Nkalashe
- Authors: Winter Sinkala , Tembinkosi F. Nkalashe
- Date: 2020
- Language: English
- Type: Journal Article
- Identifier: http://hdl.handle.net/11260/4551 , vital:44132
- Full Text:
- Authors: Winter Sinkala , Tembinkosi F. Nkalashe
- Date: 2020
- Language: English
- Type: Journal Article
- Identifier: http://hdl.handle.net/11260/4551 , vital:44132
- Full Text:
On a class of pseudo-differential operators in IRⁿ
- Authors: Matjila, D M
- Date: 1988
- Subjects: Pseudodifferential operators Operator theory
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5392 , http://hdl.handle.net/10962/d1001981
- Description: The class of pseudo-differential operators with symbols from Sm (superscript) po̧̧ (subscipt)(Ωx IRⁿ) has been extensively studied.The main assumption which characterises this class of symbols is that a(x,Ȩ) є Sm (superscript)po̧̧ (subscipt)(Ωx IRⁿ) should have a polynomial growth in the Ȩ variable only. The x-variable is controlled on compact subsets of Ω. A polynomial growth in both the x and Ȩ variables on a C°°(lR²ⁿ) function a(x,Ȩ) gives rise to a different class of symbols and a corresponding class of operators. In this work, such symbols and the action of the operators on the functional spaces S(lRⁿ) , S'(lRⁿ) and the Sobolev spaces Qs (superscript) (lRⁿ) (s є lRⁿ) are studied. A study of the calculus (i.e. transposes, adjoints and compositions) and the functional analysis of these operators is done with special attention to L-boundedness and compactness. The class of hypoelliptic pseudo-differential operators in IRⁿ is introduced as a subclass of those considered earlier.These operators possess the property that they allow a pseudo- inverse or parametrix. In conclusion. the spectral theory of these operators is considered. Since a general spectral theory would be beyond the scope of this work, only some special cases of the pseudo-differential operators in IRⁿ are considered. A few applications of this spectral theory are discussed
- Full Text:
- Date Issued: 1988
- Authors: Matjila, D M
- Date: 1988
- Subjects: Pseudodifferential operators Operator theory
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5392 , http://hdl.handle.net/10962/d1001981
- Description: The class of pseudo-differential operators with symbols from Sm (superscript) po̧̧ (subscipt)(Ωx IRⁿ) has been extensively studied.The main assumption which characterises this class of symbols is that a(x,Ȩ) є Sm (superscript)po̧̧ (subscipt)(Ωx IRⁿ) should have a polynomial growth in the Ȩ variable only. The x-variable is controlled on compact subsets of Ω. A polynomial growth in both the x and Ȩ variables on a C°°(lR²ⁿ) function a(x,Ȩ) gives rise to a different class of symbols and a corresponding class of operators. In this work, such symbols and the action of the operators on the functional spaces S(lRⁿ) , S'(lRⁿ) and the Sobolev spaces Qs (superscript) (lRⁿ) (s є lRⁿ) are studied. A study of the calculus (i.e. transposes, adjoints and compositions) and the functional analysis of these operators is done with special attention to L-boundedness and compactness. The class of hypoelliptic pseudo-differential operators in IRⁿ is introduced as a subclass of those considered earlier.These operators possess the property that they allow a pseudo- inverse or parametrix. In conclusion. the spectral theory of these operators is considered. Since a general spectral theory would be beyond the scope of this work, only some special cases of the pseudo-differential operators in IRⁿ are considered. A few applications of this spectral theory are discussed
- Full Text:
- Date Issued: 1988
JEOR Fagara Reprints.pdf
- Authors: Oyedeji, Adebola Omowunmi
- Language: English
- Identifier: http://hdl.handle.net/11260/2492 , vital:41892
- Description: Various articles from Prof Adebola Oyedeji
- Full Text:
- Authors: Oyedeji, Adebola Omowunmi
- Language: English
- Identifier: http://hdl.handle.net/11260/2492 , vital:41892
- Description: Various articles from Prof Adebola Oyedeji
- Full Text:
Ndeti nshiti yangali
- Bemba women at Kitwe, Performer not specified, Composer not specified, Tracey, Hugh
- Authors: Bemba women at Kitwe , Performer not specified , Composer not specified , Tracey, Hugh
- Date: 1949
- Subjects: Folk Music , Field recordings , Africa, Sub-Saharan , Africa Zambia city not specified f-za
- Language: Bemba
- Type: sound recordings , field recordings , sound recording-musical
- Identifier: http://hdl.handle.net/10962/376945 , vital:67065 , International Library of African Music, Rhodes University, Makhanda, South Africa , Hugh Tracey Commercial Records, Rhodes University, Makhanda, South Africa , AC0494-C3Z13a
- Description: Indigenous music
- Full Text: false
- Date Issued: 1949
- Authors: Bemba women at Kitwe , Performer not specified , Composer not specified , Tracey, Hugh
- Date: 1949
- Subjects: Folk Music , Field recordings , Africa, Sub-Saharan , Africa Zambia city not specified f-za
- Language: Bemba
- Type: sound recordings , field recordings , sound recording-musical
- Identifier: http://hdl.handle.net/10962/376945 , vital:67065 , International Library of African Music, Rhodes University, Makhanda, South Africa , Hugh Tracey Commercial Records, Rhodes University, Makhanda, South Africa , AC0494-C3Z13a
- Description: Indigenous music
- Full Text: false
- Date Issued: 1949
Graviton multipoint functions at the AdS boundary
- Authors: Brustein, R , Medved, A J M
- Date: 2013
- Language: English
- Type: text , Article
- Identifier: vital:6819 , http://hdl.handle.net/10962/d1004425
- Description: The gauge-gravity duality can be used to relate connected multipoint graviton functions to connected multipoint correlation functions of the stress tensor of a strongly coupled fluid. Here, we show how to construct the connected graviton functions for a particular kinematic regime that is ideal for discriminating between different gravitational theories, in particular between Einstein theory and its leading-order string theory correction. Our analysis begins with the one-particle irreducible graviton amplitudes in an anti-de Sitter black brane background.We show how these can be used to calculate the connected graviton functions and demonstrate that the two types of amplitudes agree in some cases. It is then asserted on physical grounds that this agreement persists in all cases for both Einstein gravity and its leading-order correction. This outcome implies that the corresponding field-theory correlation functions can be read off directly from the bulk Lagrangian, just as can be done for the ratio of the shear viscosity to the entropy density.
- Full Text:
- Date Issued: 2013
- Authors: Brustein, R , Medved, A J M
- Date: 2013
- Language: English
- Type: text , Article
- Identifier: vital:6819 , http://hdl.handle.net/10962/d1004425
- Description: The gauge-gravity duality can be used to relate connected multipoint graviton functions to connected multipoint correlation functions of the stress tensor of a strongly coupled fluid. Here, we show how to construct the connected graviton functions for a particular kinematic regime that is ideal for discriminating between different gravitational theories, in particular between Einstein theory and its leading-order string theory correction. Our analysis begins with the one-particle irreducible graviton amplitudes in an anti-de Sitter black brane background.We show how these can be used to calculate the connected graviton functions and demonstrate that the two types of amplitudes agree in some cases. It is then asserted on physical grounds that this agreement persists in all cases for both Einstein gravity and its leading-order correction. This outcome implies that the corresponding field-theory correlation functions can be read off directly from the bulk Lagrangian, just as can be done for the ratio of the shear viscosity to the entropy density.
- Full Text:
- Date Issued: 2013
Finite element analysis of a composite sandwich beam subjected to a four point bend
- Authors: Hove, Darlington
- Date: 2011
- Subjects: Sandwich construction -- Mathematical models , Composite materials -- Research
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:10503 , http://hdl.handle.net/10948/1465 , Sandwich construction -- Mathematical models , Composite materials -- Research
- Description: The work in this dissertation deals with the global structural response and local damage effects of a simply supported natural fibre composite sandwich beam subjected to a four-point bend. For the global structural response, we are investigating the flexural behaviour of the composite sandwich beam. We begin by using the principle of virtual work to derive the linear and nonlinear Timoshenko beam theory. Based on these theories, we then proceed to develop the respective finite element models and then implement the numerical algorithm in MATLAB. Comparing the numerical results with experimental results from the CSIR, the numerical model correctly and qualitatively recovers the underlying mechanics with some noted deviances which are explained at the end. The local damage effect of interest is delamination and we begin by reviewing delamination theory with more emphasis on the cohesive zone model. The cohesive zone model relates the traction at the interface to the relative displacement of the interface thereby creating a material model of the interface. We then carry out a cohesive zone model delamination case study in MSC.Marc and MSC.Mentat software packages. The delamination modelling is carried out purely as a numerical study as there are no experimental results to validate the numerical results.
- Full Text:
- Date Issued: 2011
- Authors: Hove, Darlington
- Date: 2011
- Subjects: Sandwich construction -- Mathematical models , Composite materials -- Research
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:10503 , http://hdl.handle.net/10948/1465 , Sandwich construction -- Mathematical models , Composite materials -- Research
- Description: The work in this dissertation deals with the global structural response and local damage effects of a simply supported natural fibre composite sandwich beam subjected to a four-point bend. For the global structural response, we are investigating the flexural behaviour of the composite sandwich beam. We begin by using the principle of virtual work to derive the linear and nonlinear Timoshenko beam theory. Based on these theories, we then proceed to develop the respective finite element models and then implement the numerical algorithm in MATLAB. Comparing the numerical results with experimental results from the CSIR, the numerical model correctly and qualitatively recovers the underlying mechanics with some noted deviances which are explained at the end. The local damage effect of interest is delamination and we begin by reviewing delamination theory with more emphasis on the cohesive zone model. The cohesive zone model relates the traction at the interface to the relative displacement of the interface thereby creating a material model of the interface. We then carry out a cohesive zone model delamination case study in MSC.Marc and MSC.Mentat software packages. The delamination modelling is carried out purely as a numerical study as there are no experimental results to validate the numerical results.
- Full Text:
- Date Issued: 2011
Methods for designing and optimizing fuzzy controllers
- Authors: Swartz, Andre Michael
- Date: 2000
- Subjects: Fuzzy sets , Fuzzy systems , Automatic control
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5412 , http://hdl.handle.net/10962/d1005226 , Fuzzy sets , Fuzzy systems , Automatic control
- Description: We start by discussing fuzzy sets and the algebra of fuzzy sets. We consider some properties of fuzzy modeling tools. This is followed by considering the Mamdani and Sugeno models for designing fuzzy controllers. Various methods for using sets of data for desining controllers are discussed. This is followed by a chapter illustrating the use of genetic algorithms in designing and optimizing fuzzy controllers.Finally we look at some previous applications of fuzzy control in telecommunication networks, and illustrate a simple application that was developed as part of the present work.
- Full Text:
- Date Issued: 2000
- Authors: Swartz, Andre Michael
- Date: 2000
- Subjects: Fuzzy sets , Fuzzy systems , Automatic control
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5412 , http://hdl.handle.net/10962/d1005226 , Fuzzy sets , Fuzzy systems , Automatic control
- Description: We start by discussing fuzzy sets and the algebra of fuzzy sets. We consider some properties of fuzzy modeling tools. This is followed by considering the Mamdani and Sugeno models for designing fuzzy controllers. Various methods for using sets of data for desining controllers are discussed. This is followed by a chapter illustrating the use of genetic algorithms in designing and optimizing fuzzy controllers.Finally we look at some previous applications of fuzzy control in telecommunication networks, and illustrate a simple application that was developed as part of the present work.
- Full Text:
- Date Issued: 2000
Factors influencing organisational commitment amongst generation Z in South Africa
- Authors: Masia, Thapelo
- Date: 2020
- Subjects: Staff Retention -- South Africa , Young adults -- Employment -- South Africa
- Language: English
- Type: Thesis , Masters , MCom
- Identifier: http://hdl.handle.net/10948/50294 , vital:42093
- Description: In a world of constant change, organisations face demanding pressures and challenges. Now, more than ever, organisations need to optimise resources in maximising outcomes in order to maintain a competitive advantage. In doing so, it must be acknowledged that people remain the most valuable resource in achieving organisational success. This has led to a war for talent across and between organisations. In South Africa this situation is complicated for many reasons, including the fact that there is a skills shortage crisis faced in South Africa and because many experienced Baby Boomers are now reaching retirement age. This time is also marked by the entry of the newest member of the workforce, this being Generation Z. These considerations make it important for organisations to create relevant strategies to build and retain the organisational commitment of top talent, more specifically that of Generation Z. Organisational commitment is a key organisational consideration in driving employee behaviour and attitude through influencing performance, satisfaction, organisational citizenship and motivation. The aim of this study was to explore the factors influencing organisational commitment amongst Generation Z employees in the South African workplace. This is important in assisting organisations in developing and enhancing attraction and retention strategies for current and future talent.
- Full Text:
- Date Issued: 2020
- Authors: Masia, Thapelo
- Date: 2020
- Subjects: Staff Retention -- South Africa , Young adults -- Employment -- South Africa
- Language: English
- Type: Thesis , Masters , MCom
- Identifier: http://hdl.handle.net/10948/50294 , vital:42093
- Description: In a world of constant change, organisations face demanding pressures and challenges. Now, more than ever, organisations need to optimise resources in maximising outcomes in order to maintain a competitive advantage. In doing so, it must be acknowledged that people remain the most valuable resource in achieving organisational success. This has led to a war for talent across and between organisations. In South Africa this situation is complicated for many reasons, including the fact that there is a skills shortage crisis faced in South Africa and because many experienced Baby Boomers are now reaching retirement age. This time is also marked by the entry of the newest member of the workforce, this being Generation Z. These considerations make it important for organisations to create relevant strategies to build and retain the organisational commitment of top talent, more specifically that of Generation Z. Organisational commitment is a key organisational consideration in driving employee behaviour and attitude through influencing performance, satisfaction, organisational citizenship and motivation. The aim of this study was to explore the factors influencing organisational commitment amongst Generation Z employees in the South African workplace. This is important in assisting organisations in developing and enhancing attraction and retention strategies for current and future talent.
- Full Text:
- Date Issued: 2020
Fixed points of single-valued and multi-valued mappings with applications
- Authors: Stofile, Simfumene
- Date: 2013
- Subjects: Fixed point theory Mappings (Mathematics) Coincidence theory (Mathematics) Metric spaces Uniform spaces Set-valued maps
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5397 , http://hdl.handle.net/10962/d1002960
- Description: The relationship between the convergence of a sequence of self mappings of a metric space and their fixed points, known as the stability (or continuity) of fixed points has been of continuing interest and widely studied in fixed point theory. In this thesis we study the stability of common fixed points in a Hausdorff uniform space whose uniformity is generated by a family of pseudometrics, by using some general notations of convergence. These results are then extended to 2-metric spaces due to S. Gähler. In addition, a well-known theorem of T. Suzuki that generalized the Banach Contraction Principle is also extended to 2-metric spaces and applied to obtain a coincidence theorem for a pair of mappings on an arbitrary set with values in a 2-metric space. Further, we prove the existence of coincidence and fixed points of Ćirić type weakly generalized contractions in metric spaces. Subsequently, the above result is utilized to discuss applications to the convergence of modified Mann and Ishikawa iterations in a convex metric space. Finally, we obtain coincidence, fixed and stationary point results for multi-valued and hybrid pairs of mappings on a metric space.
- Full Text:
- Date Issued: 2013
- Authors: Stofile, Simfumene
- Date: 2013
- Subjects: Fixed point theory Mappings (Mathematics) Coincidence theory (Mathematics) Metric spaces Uniform spaces Set-valued maps
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5397 , http://hdl.handle.net/10962/d1002960
- Description: The relationship between the convergence of a sequence of self mappings of a metric space and their fixed points, known as the stability (or continuity) of fixed points has been of continuing interest and widely studied in fixed point theory. In this thesis we study the stability of common fixed points in a Hausdorff uniform space whose uniformity is generated by a family of pseudometrics, by using some general notations of convergence. These results are then extended to 2-metric spaces due to S. Gähler. In addition, a well-known theorem of T. Suzuki that generalized the Banach Contraction Principle is also extended to 2-metric spaces and applied to obtain a coincidence theorem for a pair of mappings on an arbitrary set with values in a 2-metric space. Further, we prove the existence of coincidence and fixed points of Ćirić type weakly generalized contractions in metric spaces. Subsequently, the above result is utilized to discuss applications to the convergence of modified Mann and Ishikawa iterations in a convex metric space. Finally, we obtain coincidence, fixed and stationary point results for multi-valued and hybrid pairs of mappings on a metric space.
- Full Text:
- Date Issued: 2013
Some Remarks on the Solution of Linearisable Second-Order Ordinary Differential Equations via Point Transformations
- Authors: Winter Sinkala
- Date: 2020
- Type: Journal Article
- Identifier: http://hdl.handle.net/11260/4314 , vital:44091
- Full Text:
- Authors: Winter Sinkala
- Date: 2020
- Type: Journal Article
- Identifier: http://hdl.handle.net/11260/4314 , vital:44091
- Full Text:
Investigating cannabinoids and endocannabinoid receptors as drug targets for pain and inflammation
- Authors: Marwarwa, Sinobomi Zamachi
- Date: 2020
- Subjects: Cannabinoids , Cannabinoids Receptors , Inflammation Alternative treatment , Pain Alternative treatment , Drug targeting
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/164468 , vital:41121
- Description: Cannabinoids and the endocannabinoid system have been studied in the past decades but have yet to be fully understood. An insight into interactions that occur between cannabinoid compounds and their receptors is important for understanding the cannabinoids and the endocannabinoid system. Cannabinoids are natural products found in some cannabis plants, and they have similar effects to endocannabinoids, which are chemicals in the body that are involved many aspects of health from appetite, memory, and movement to pain, inflammation and response to cancer. Cannabinoids have a high impact on the treatment of pain and inflammation, they show different antinociceptive mechanisms to existing drugs like opioids, also, they have antimigraine properties better than those achieved by aspirin. The CB1 and CB2 human receptors have been the most studied cannabinoid receptors. In this project, we used a combination of mass-spectrometry to generate plausible chemical fragments and computational techniques to assess the binding of these fragments to these two main CB receptors. CB1 was adapted from the protein data bank (PBD), file 5U09 and the CB2 model was predicted using the hierarchical protocol I-TASSER, starting from the amino acid sequence in UniProt (P34972 CNR2_HUMAN). The proposed active site for CB1 was reported in a publication accompanying the 5U09 PDB model, which was originally generated with a pre-existing ligand in the active site. However, CB2 had to be built from a homology model and the active site determined using a combination of I-TASSER, Maestro, and CASTp the more favourable binding energies were determined by CASTp, leading to the use of the CASTp coordinates as default for docking in the CB2 human receptor. The molecular docking of cannabinoids THC, CBD, CBDV, CBG and CBN on both the CB1 and CB2 proteins was performed to identify the amino acids that interact with these compounds at their active sites. This would provide a guide to a future fragment-based drug discovery (FBDD) synthesis project. The docking in this work showed adequate accuracy with binding energies between -8.23 kcal/mol and -9.97 kcal/mol for CB1 and between -6.78 kcal/mol and -7.74 kcal/mol for CB2. An observation made was that binding energies of the CB1 human receptor docking were higher than those of the CB2 human receptor, which could support the widely held belief that CB1 is more important in cannabinoid interactions. The cannabinoids were then subjected to collision-induced dissociation to produce fragment structures predicted in chapter 2. These hypothetical fragments were docked in the CB1 and CB2 human receptor, the general trend again being the binding energies for the CB1 receptor was again around 10% higher than those of the CB2 receptor. As expected, larger fragments tended to have better binding, with the fragment proposed from m/z 259 with binding energies -9.62 kcal/mol in CB1 and -6.26 kcal/mol. Those fragments with significant lipophilic side chains or some aromatic moiety also showed good binding or around -6.00 kcal/mol, similar to the intact cannabinoids. In our case, this fragment was proposed from m/z 223 with binding energies -7.71 kcal/mol in CB1 and -6.5 kcal/mol in CB2. The results from the fragment dockings were favourable in that they have binding affinities lower than -6.0 kcal/mol which is good enough for the structures to be leads in the creation of fragment libraries. The docking was performed with Autodock 1.5.6 and data visualization with a discovery studio. , Thesis (MSc) -- Faculty of Science, Chemistry, 2020
- Full Text:
- Date Issued: 2020
- Authors: Marwarwa, Sinobomi Zamachi
- Date: 2020
- Subjects: Cannabinoids , Cannabinoids Receptors , Inflammation Alternative treatment , Pain Alternative treatment , Drug targeting
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/164468 , vital:41121
- Description: Cannabinoids and the endocannabinoid system have been studied in the past decades but have yet to be fully understood. An insight into interactions that occur between cannabinoid compounds and their receptors is important for understanding the cannabinoids and the endocannabinoid system. Cannabinoids are natural products found in some cannabis plants, and they have similar effects to endocannabinoids, which are chemicals in the body that are involved many aspects of health from appetite, memory, and movement to pain, inflammation and response to cancer. Cannabinoids have a high impact on the treatment of pain and inflammation, they show different antinociceptive mechanisms to existing drugs like opioids, also, they have antimigraine properties better than those achieved by aspirin. The CB1 and CB2 human receptors have been the most studied cannabinoid receptors. In this project, we used a combination of mass-spectrometry to generate plausible chemical fragments and computational techniques to assess the binding of these fragments to these two main CB receptors. CB1 was adapted from the protein data bank (PBD), file 5U09 and the CB2 model was predicted using the hierarchical protocol I-TASSER, starting from the amino acid sequence in UniProt (P34972 CNR2_HUMAN). The proposed active site for CB1 was reported in a publication accompanying the 5U09 PDB model, which was originally generated with a pre-existing ligand in the active site. However, CB2 had to be built from a homology model and the active site determined using a combination of I-TASSER, Maestro, and CASTp the more favourable binding energies were determined by CASTp, leading to the use of the CASTp coordinates as default for docking in the CB2 human receptor. The molecular docking of cannabinoids THC, CBD, CBDV, CBG and CBN on both the CB1 and CB2 proteins was performed to identify the amino acids that interact with these compounds at their active sites. This would provide a guide to a future fragment-based drug discovery (FBDD) synthesis project. The docking in this work showed adequate accuracy with binding energies between -8.23 kcal/mol and -9.97 kcal/mol for CB1 and between -6.78 kcal/mol and -7.74 kcal/mol for CB2. An observation made was that binding energies of the CB1 human receptor docking were higher than those of the CB2 human receptor, which could support the widely held belief that CB1 is more important in cannabinoid interactions. The cannabinoids were then subjected to collision-induced dissociation to produce fragment structures predicted in chapter 2. These hypothetical fragments were docked in the CB1 and CB2 human receptor, the general trend again being the binding energies for the CB1 receptor was again around 10% higher than those of the CB2 receptor. As expected, larger fragments tended to have better binding, with the fragment proposed from m/z 259 with binding energies -9.62 kcal/mol in CB1 and -6.26 kcal/mol. Those fragments with significant lipophilic side chains or some aromatic moiety also showed good binding or around -6.00 kcal/mol, similar to the intact cannabinoids. In our case, this fragment was proposed from m/z 223 with binding energies -7.71 kcal/mol in CB1 and -6.5 kcal/mol in CB2. The results from the fragment dockings were favourable in that they have binding affinities lower than -6.0 kcal/mol which is good enough for the structures to be leads in the creation of fragment libraries. The docking was performed with Autodock 1.5.6 and data visualization with a discovery studio. , Thesis (MSc) -- Faculty of Science, Chemistry, 2020
- Full Text:
- Date Issued: 2020
Pre-release studies on Zophodia Tapiacola (Dyar) (Pyralidae : Lepidoptera) : a biological control agent against jointed cactus, Optuntia Aurantiaca Lindley
- Authors: Hoffmann, John Hugh
- Date: 1976
- Subjects: Pyralidae , Lepidoptera , Cactus , Weeds -- Biological control , Opuntia
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5857 , http://hdl.handle.net/10962/d1012320 , Pyralidae , Lepidoptera , Cactus , Weeds -- Biological control , Opuntia
- Description: Jointed Cactus, Opuntia aurantiaca Lindley (see frontispiece), is the most important weed plant in South Africa, infesting approximately, 1,2 X 10¹° M² and costing approximately R240 000 per annum. Tordon herbicide effectively kills jointed cactus bushes to which it is applied. However, apart from being expensive and damaging to beneficial vegetation, spray programmes have not successfully controlled the weed because most small O. aurantiaca plants are impossible to detect in the field. Biological control may provide a solution to the problem. Two insects, the cochineal bug, Dactylopius austrinus De Lotto and the pyralid moth, Cactoblastis cactorum Berg., already exercise a degree of control over the weed. The introduction into South Africa of other natural enemies such as Zophodia tapiacola (Dyar) from Argentina, South America, may reduce the density of jointed cactus to below an acceptable economic threshold. Any insect considered for release should not colonise and destroy beneficial plants of which the culivated spineless cacti are the most vulnerable. Pre-release studies on Z. tapiacola have shown that it can only colonise a few species of low growing cacti and that it will not damage the large spineless cacti or other desirable plants. Further, the moths are relatively fecund and each larva destroys significant amounts of O. aurantiaca during its development. Consequently, Z. tapiacola is not only considered safe for release but it has the potential to act as a successful biological control agent of O. aurantiaca in South Africa.
- Full Text:
- Date Issued: 1976
- Authors: Hoffmann, John Hugh
- Date: 1976
- Subjects: Pyralidae , Lepidoptera , Cactus , Weeds -- Biological control , Opuntia
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5857 , http://hdl.handle.net/10962/d1012320 , Pyralidae , Lepidoptera , Cactus , Weeds -- Biological control , Opuntia
- Description: Jointed Cactus, Opuntia aurantiaca Lindley (see frontispiece), is the most important weed plant in South Africa, infesting approximately, 1,2 X 10¹° M² and costing approximately R240 000 per annum. Tordon herbicide effectively kills jointed cactus bushes to which it is applied. However, apart from being expensive and damaging to beneficial vegetation, spray programmes have not successfully controlled the weed because most small O. aurantiaca plants are impossible to detect in the field. Biological control may provide a solution to the problem. Two insects, the cochineal bug, Dactylopius austrinus De Lotto and the pyralid moth, Cactoblastis cactorum Berg., already exercise a degree of control over the weed. The introduction into South Africa of other natural enemies such as Zophodia tapiacola (Dyar) from Argentina, South America, may reduce the density of jointed cactus to below an acceptable economic threshold. Any insect considered for release should not colonise and destroy beneficial plants of which the culivated spineless cacti are the most vulnerable. Pre-release studies on Z. tapiacola have shown that it can only colonise a few species of low growing cacti and that it will not damage the large spineless cacti or other desirable plants. Further, the moths are relatively fecund and each larva destroys significant amounts of O. aurantiaca during its development. Consequently, Z. tapiacola is not only considered safe for release but it has the potential to act as a successful biological control agent of O. aurantiaca in South Africa.
- Full Text:
- Date Issued: 1976
Lag length selection for vector error correction models
- Authors: Sharp, Gary David
- Date: 2010
- Subjects: Akaike Information Criterion Mathematical models -- Evaluation Autoregression (Statistics) Error analysis (Mathematics)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5568 , http://hdl.handle.net/10962/d1002808
- Description: This thesis investigates the problem of model identification in a Vector Autoregressive framework. The study reviews the existing research, conducts an extensive simulation based analysis of thirteen information theoretic criterion (IC), one of which is a novel derivation. The simulation exercise considers the evaluation of seven alternative error restricted vector autoregressive models with four different lag lengths. Alternative sample sizes and parameterisations are also evaluated and compared to results in the existing literature. The results of the comparative analysis provide strong support for the efficiency based criterion of Akaike and in particular the selection capability of the novel criterion, referred to as a modified corrected Akaike information criterion, demonstrates useful finite sample properties.
- Full Text:
- Date Issued: 2010
- Authors: Sharp, Gary David
- Date: 2010
- Subjects: Akaike Information Criterion Mathematical models -- Evaluation Autoregression (Statistics) Error analysis (Mathematics)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5568 , http://hdl.handle.net/10962/d1002808
- Description: This thesis investigates the problem of model identification in a Vector Autoregressive framework. The study reviews the existing research, conducts an extensive simulation based analysis of thirteen information theoretic criterion (IC), one of which is a novel derivation. The simulation exercise considers the evaluation of seven alternative error restricted vector autoregressive models with four different lag lengths. Alternative sample sizes and parameterisations are also evaluated and compared to results in the existing literature. The results of the comparative analysis provide strong support for the efficiency based criterion of Akaike and in particular the selection capability of the novel criterion, referred to as a modified corrected Akaike information criterion, demonstrates useful finite sample properties.
- Full Text:
- Date Issued: 2010