The classification of fuzzy groups of finite cyclic groups Zpn Zqm Zr and Zp1 Zp2 Zpn for distinct prime numbers p; q; r; p1; p2; ; pn and n;m 2 Z+
- Authors: Munywoki, Michael Mbindyo
- Date: 2018
- Subjects: Fuzzy sets Finite groups
- Language: English
- Type: Thesis , Doctoral , DPhil
- Identifier: http://hdl.handle.net/10353/17817 , vital:41295
- Description: Let G be the cyclic group Zpn _ Zqm _ Zr where p; q; r are distinct primes and n;m 2 Z+. Using the criss-cut method by Murali and Makamba, we determine in general the number of distinct fuzzy subgroups of G. This is achieved by using the maximal chains of subgroups of the respective groups, and the equivalence relation given in their research papers. For cases of m, the number of fuzzy subgroups is _rst given, from which the general pattern for G is achieved. Murali and Makamba discussed the number of fuzzy subgroups of Zpn _ Zqm using the cross-cut method. A brief revisit of the group Zpn _Zqm is done using the criss-cut method. The formulae for _nding the number of distinct fuzzy subgroups in each of the cases is given and proofs provided. Furthermore, we classify the fuzzy subgroups of the group Zp1_Zp2__ _ __Zpn for p1; p2; _ _ _ ; pn distinct primes and n 2 Z+ using the criss-cut method. An algorithm for counting the distinct fuzzy subgroups of this group is developed.
- Full Text:
- Date Issued: 2018
- Authors: Munywoki, Michael Mbindyo
- Date: 2018
- Subjects: Fuzzy sets Finite groups
- Language: English
- Type: Thesis , Doctoral , DPhil
- Identifier: http://hdl.handle.net/10353/17817 , vital:41295
- Description: Let G be the cyclic group Zpn _ Zqm _ Zr where p; q; r are distinct primes and n;m 2 Z+. Using the criss-cut method by Murali and Makamba, we determine in general the number of distinct fuzzy subgroups of G. This is achieved by using the maximal chains of subgroups of the respective groups, and the equivalence relation given in their research papers. For cases of m, the number of fuzzy subgroups is _rst given, from which the general pattern for G is achieved. Murali and Makamba discussed the number of fuzzy subgroups of Zpn _ Zqm using the cross-cut method. A brief revisit of the group Zpn _Zqm is done using the criss-cut method. The formulae for _nding the number of distinct fuzzy subgroups in each of the cases is given and proofs provided. Furthermore, we classify the fuzzy subgroups of the group Zp1_Zp2__ _ __Zpn for p1; p2; _ _ _ ; pn distinct primes and n 2 Z+ using the criss-cut method. An algorithm for counting the distinct fuzzy subgroups of this group is developed.
- Full Text:
- Date Issued: 2018
Rhodeo, Vol. 22, No. 16
- Date: 1968-08-22
- Subjects: Grahamstown -- Newspapers , Journalism, Students -- South Africa , Rhodes University -- Activate , Rhodes University -- Students , Student newspapers and periodicals -- South Africa
- Language: English
- Type: Text
- Identifier: vital:14590 , http://hdl.handle.net/10962/d1019462
- Description: Rhodeo is the Independent Student Newspaper of Rhodes University. Located in Grahamstown, Rhodeo was established in 1947, and renamed in 1994 as Activate. During apartheid Rhodeo became an active part of the struggle for freedom of expression as part of the now defunct South African Student Press Union. Currently Activate is committed to informing Rhodes University students, staff and community members about relevant issues, mainly on campus. These issues range from hard news to more creative journalism. While Activate acts as a news source, one of its main objectives it to be accessible as a training ground for student journalists. The newspaper is run entirely by the students and is published twice a term. Activate is a free newspaper which receives an annual grant from the Rhodes University Student Representative Council, however, majority of its revenue is generated through advertising.
- Full Text:
- Date Issued: 1968-08-22
- Date: 1968-08-22
- Subjects: Grahamstown -- Newspapers , Journalism, Students -- South Africa , Rhodes University -- Activate , Rhodes University -- Students , Student newspapers and periodicals -- South Africa
- Language: English
- Type: Text
- Identifier: vital:14590 , http://hdl.handle.net/10962/d1019462
- Description: Rhodeo is the Independent Student Newspaper of Rhodes University. Located in Grahamstown, Rhodeo was established in 1947, and renamed in 1994 as Activate. During apartheid Rhodeo became an active part of the struggle for freedom of expression as part of the now defunct South African Student Press Union. Currently Activate is committed to informing Rhodes University students, staff and community members about relevant issues, mainly on campus. These issues range from hard news to more creative journalism. While Activate acts as a news source, one of its main objectives it to be accessible as a training ground for student journalists. The newspaper is run entirely by the students and is published twice a term. Activate is a free newspaper which receives an annual grant from the Rhodes University Student Representative Council, however, majority of its revenue is generated through advertising.
- Full Text:
- Date Issued: 1968-08-22
Composition portfolio
- Authors: Webb, Cassidy Frank
- Date: 2006
- Language: English
- Type: Thesis , Masters , MMus
- Identifier: vital:2659 , http://hdl.handle.net/10962/d1003729
- Description: Introduction: This portfolio consists of musical ideas which I have had for some time now. I have attempted to capture these ideas throughout the portfolio, starting with the smaller works (Brumes et Pluies) and building up to the larger works (James Tiberius, The tide). Brumes et Pluies is minimalistic in style. The interlocking of the two pianos plays an important role in the texture of the piece. The rhythms are repetitive throughout, with only slight variations. Kalahari is more idiomatic, rhythmical and has a main theme which recurs throughout the piece. Melodic fragments are used, sometimes with slight variations. This piece was inspired by the Kalahari desert, with its abundance of life. I enjoy the string quartet because of the homogeneity of sound on the one hand, and the diversity possible by using different techniques and effects on the other. James Tiberius is a work for chamber orchestra. Motifs in the music resemble certain animals. The rhythm is unstable, as is the harmony. There are many melodic fragments throughout. The texture is thin in certain areas (at the beginning) and dense in others (the waltz). The harmony is sometimes unconventional. The Tide was written in response to a memory of a drowning incident I experienced when I was a child. This orchestral piece is strong in form. The opening, for example, is tense and slightly atonal in harmony. The pomposo section tends to utilise most of the orchestra, so the texture is a lot denser here and the harmony is more conventional. I try not to use traditional forms in my composition. Rather, I prefer to compose by re-using and re-introducing ideas as I proceed.
- Full Text:
- Date Issued: 2006
- Authors: Webb, Cassidy Frank
- Date: 2006
- Language: English
- Type: Thesis , Masters , MMus
- Identifier: vital:2659 , http://hdl.handle.net/10962/d1003729
- Description: Introduction: This portfolio consists of musical ideas which I have had for some time now. I have attempted to capture these ideas throughout the portfolio, starting with the smaller works (Brumes et Pluies) and building up to the larger works (James Tiberius, The tide). Brumes et Pluies is minimalistic in style. The interlocking of the two pianos plays an important role in the texture of the piece. The rhythms are repetitive throughout, with only slight variations. Kalahari is more idiomatic, rhythmical and has a main theme which recurs throughout the piece. Melodic fragments are used, sometimes with slight variations. This piece was inspired by the Kalahari desert, with its abundance of life. I enjoy the string quartet because of the homogeneity of sound on the one hand, and the diversity possible by using different techniques and effects on the other. James Tiberius is a work for chamber orchestra. Motifs in the music resemble certain animals. The rhythm is unstable, as is the harmony. There are many melodic fragments throughout. The texture is thin in certain areas (at the beginning) and dense in others (the waltz). The harmony is sometimes unconventional. The Tide was written in response to a memory of a drowning incident I experienced when I was a child. This orchestral piece is strong in form. The opening, for example, is tense and slightly atonal in harmony. The pomposo section tends to utilise most of the orchestra, so the texture is a lot denser here and the harmony is more conventional. I try not to use traditional forms in my composition. Rather, I prefer to compose by re-using and re-introducing ideas as I proceed.
- Full Text:
- Date Issued: 2006
An investigation into strategies which enable South African women to break through the glass ceiling
- Authors: Peens, Maritha
- Date: 2003
- Subjects: Women executives -- South Africa , Women employees -- Promotions -- South Africa , Sex discrimination in employement -- South Africa , Sex discrimination against women -- South Africa
- Language: English
- Type: Thesis , Masters , MBA
- Identifier: vital:10898 , http://hdl.handle.net/10948/135 , Women executives -- South Africa , Women employees -- Promotions -- South Africa , Sex discrimination in employement -- South Africa , Sex discrimination against women -- South Africa
- Description: The objective of this study was to identify the strategies (personal and organisational) that would enable South African women to break through the glass ceiling. A questionaire was designed based on the strategies found in a literature study on the topic and used to gather inputs from executive women in South Africa. A combination of snowball and self-selection sampling was used. The questionaire was sent to 138 potential respondents, mostly by means of electronic mail. Of the 47 completed questionairs returned, 44 could be used. These were processed and anaylsed using Microsoft Excel spreadsheets and the STATISTICA Version 6 software. In generaL, support was found for personal strategies pertaining to career management, networking (especially the relationship building activities), the reconciliation of home and work responsibilities with the emphasis on building a support system, education, business and organisational insught, skills development and increased input, but not for the assimilation of masculine attributes. Networking opportunities and education, training and development activities were regarded as the organisational strategies with the strongest impact on career progress. The literature was confirmed regarding top management support, an organisational culture conducive to women's advancement, mentorship programmes and a few career development initiatives. Although more than half of the respondents had been exposed to employment equity and affirmative action programmes, they were perceived to have only little to moderate impact on career progress. This was also the case with diversity management programmes. Flexible work arrangements, career adaptation schemes and childcare facilities and programmes were seen as having had little impact on the respondents' career advancement. Only a few of the organisational practices to support women balancing family and work responsibilities were utilised by the respondents' employers. Respondents perceived personal strategies as having greater value than organisational strategies in their progress to executive levels.
- Full Text:
- Date Issued: 2003
An investigation into strategies which enable South African women to break through the glass ceiling
- Authors: Peens, Maritha
- Date: 2003
- Subjects: Women executives -- South Africa , Women employees -- Promotions -- South Africa , Sex discrimination in employement -- South Africa , Sex discrimination against women -- South Africa
- Language: English
- Type: Thesis , Masters , MBA
- Identifier: vital:10898 , http://hdl.handle.net/10948/135 , Women executives -- South Africa , Women employees -- Promotions -- South Africa , Sex discrimination in employement -- South Africa , Sex discrimination against women -- South Africa
- Description: The objective of this study was to identify the strategies (personal and organisational) that would enable South African women to break through the glass ceiling. A questionaire was designed based on the strategies found in a literature study on the topic and used to gather inputs from executive women in South Africa. A combination of snowball and self-selection sampling was used. The questionaire was sent to 138 potential respondents, mostly by means of electronic mail. Of the 47 completed questionairs returned, 44 could be used. These were processed and anaylsed using Microsoft Excel spreadsheets and the STATISTICA Version 6 software. In generaL, support was found for personal strategies pertaining to career management, networking (especially the relationship building activities), the reconciliation of home and work responsibilities with the emphasis on building a support system, education, business and organisational insught, skills development and increased input, but not for the assimilation of masculine attributes. Networking opportunities and education, training and development activities were regarded as the organisational strategies with the strongest impact on career progress. The literature was confirmed regarding top management support, an organisational culture conducive to women's advancement, mentorship programmes and a few career development initiatives. Although more than half of the respondents had been exposed to employment equity and affirmative action programmes, they were perceived to have only little to moderate impact on career progress. This was also the case with diversity management programmes. Flexible work arrangements, career adaptation schemes and childcare facilities and programmes were seen as having had little impact on the respondents' career advancement. Only a few of the organisational practices to support women balancing family and work responsibilities were utilised by the respondents' employers. Respondents perceived personal strategies as having greater value than organisational strategies in their progress to executive levels.
- Full Text:
- Date Issued: 2003
Invariant optimal control on the three-dimensional semi-Euclidean group: control affine and quadratic Hamilton-Poisson systems
- Authors: Barrett, Dennis Ian
- Date: 2014
- Subjects: Automorphisms , Symmetry (Mathematics) , Lyapunov stability , Geometry, Riemannian , Geometry, Affine , Elliptic functions
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/64805 , vital:28605
- Description: In this thesis we consider invariant control systems and Hamilton-Poisson systems on the three dimensional semi-Euclidean group SE(1,1). We first classify the left-invariant control affine systems (under detached feedback equivalence). We provide a complete list of normal forms, as well as classifying conditions. As a corollary to this classification, we derive controllability criteria for control affine systems on SE(1,1). Secondly, we consider quadratic Hamilton-Poisson systems on the (minus) Lie-Poisson space se(1,1)*. These systems are classified up to an affine isomorphism. Six normal forms are identified for the homogeneous case, whereas sixteen representatives (including several infinite families) are obtained for the inhomogeneous systems. Thereafter we consider the stability and integration of the normal forms obtained. For all homogeneous systems, and a subclass of inhomogeneous systems, we perform a complete stability analysis and derive explicit expressions for all integral curves. (The extremal controls of a large class of optimal control problems on SE(1,1) are linearly related to these integral curves.) Lastly, we discuss the Riemannian and sub-Riemannian problems. The (left-invariant) Riemannian and sub-Riemannian structures on SE(1,1) are classified, up to isometric group automorphisms and scaling. Explicit expressions for the geodesics of the normalised structures are found.
- Full Text:
- Date Issued: 2014
- Authors: Barrett, Dennis Ian
- Date: 2014
- Subjects: Automorphisms , Symmetry (Mathematics) , Lyapunov stability , Geometry, Riemannian , Geometry, Affine , Elliptic functions
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/64805 , vital:28605
- Description: In this thesis we consider invariant control systems and Hamilton-Poisson systems on the three dimensional semi-Euclidean group SE(1,1). We first classify the left-invariant control affine systems (under detached feedback equivalence). We provide a complete list of normal forms, as well as classifying conditions. As a corollary to this classification, we derive controllability criteria for control affine systems on SE(1,1). Secondly, we consider quadratic Hamilton-Poisson systems on the (minus) Lie-Poisson space se(1,1)*. These systems are classified up to an affine isomorphism. Six normal forms are identified for the homogeneous case, whereas sixteen representatives (including several infinite families) are obtained for the inhomogeneous systems. Thereafter we consider the stability and integration of the normal forms obtained. For all homogeneous systems, and a subclass of inhomogeneous systems, we perform a complete stability analysis and derive explicit expressions for all integral curves. (The extremal controls of a large class of optimal control problems on SE(1,1) are linearly related to these integral curves.) Lastly, we discuss the Riemannian and sub-Riemannian problems. The (left-invariant) Riemannian and sub-Riemannian structures on SE(1,1) are classified, up to isometric group automorphisms and scaling. Explicit expressions for the geodesics of the normalised structures are found.
- Full Text:
- Date Issued: 2014
HOP expression is regulated by p53 and RAS and characteristic of a cancer gene signature
- Mattison, Stacey A, Blatch, Gregory L, Edkins, Adrienne L
- Authors: Mattison, Stacey A , Blatch, Gregory L , Edkins, Adrienne L
- Date: 2018
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/66278 , vital:28928 , https://doi.org/10.1007/s12192-016-0755-8
- Description: publisher version , The Hsp70/Hsp90 organising protein (HOP) is a co-chaperone essential for client protein transfer from Hsp70 to Hsp90 within the Hsp90 chaperone machine. Although HOP is upregulated in various cancers, there is limited information from in vitro studies on how HOP expression is regulated in cancer. The main objective of this study was to identify the HOP promoter and investigate its activity in cancerous cells. Bioinformatic analysis of the -2500 to +16 bp region of the HOP gene identified a large CpG island and a range of putative cis-elements. Many of the cis-elements were potentially bound by transcription factors which are activated by oncogenic pathways. Luciferase reporter assays demonstrated that the upstream region of the HOP gene contains an active promoter in vitro. Truncation of this region suggested that the core HOP promoter region was -855 to +16 bp. HOP promoter activity was highest in Hs578T, HEK293T and SV40- transformed MEF1 cell lines which expressed mutant or inactive p53. In a mutant p53 background, expression of wild-type p53 led to a reduction in promoter activity, while inhibition of wild-type p53 in HeLa cells increased HOP promoter activity. Additionally, in Hs578T and HEK293T cell lines containing inactive p53, expression of HRAS increased HOP promoter activity. However, HRAS activation of the HOP promoter was inhibited by p53 overexpression. These findings suggest for the first time that HOP expression in cancer may be regulated by both RAS activation and p53 inhibition. Taken together, these data suggest that HOP may be part of the cancer gene signature induced by a combination of mutant p53 and mutated RAS that is associated with cellular transformation.
- Full Text: false
- Date Issued: 2018
- Authors: Mattison, Stacey A , Blatch, Gregory L , Edkins, Adrienne L
- Date: 2018
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/66278 , vital:28928 , https://doi.org/10.1007/s12192-016-0755-8
- Description: publisher version , The Hsp70/Hsp90 organising protein (HOP) is a co-chaperone essential for client protein transfer from Hsp70 to Hsp90 within the Hsp90 chaperone machine. Although HOP is upregulated in various cancers, there is limited information from in vitro studies on how HOP expression is regulated in cancer. The main objective of this study was to identify the HOP promoter and investigate its activity in cancerous cells. Bioinformatic analysis of the -2500 to +16 bp region of the HOP gene identified a large CpG island and a range of putative cis-elements. Many of the cis-elements were potentially bound by transcription factors which are activated by oncogenic pathways. Luciferase reporter assays demonstrated that the upstream region of the HOP gene contains an active promoter in vitro. Truncation of this region suggested that the core HOP promoter region was -855 to +16 bp. HOP promoter activity was highest in Hs578T, HEK293T and SV40- transformed MEF1 cell lines which expressed mutant or inactive p53. In a mutant p53 background, expression of wild-type p53 led to a reduction in promoter activity, while inhibition of wild-type p53 in HeLa cells increased HOP promoter activity. Additionally, in Hs578T and HEK293T cell lines containing inactive p53, expression of HRAS increased HOP promoter activity. However, HRAS activation of the HOP promoter was inhibited by p53 overexpression. These findings suggest for the first time that HOP expression in cancer may be regulated by both RAS activation and p53 inhibition. Taken together, these data suggest that HOP may be part of the cancer gene signature induced by a combination of mutant p53 and mutated RAS that is associated with cellular transformation.
- Full Text: false
- Date Issued: 2018
Leonotis leonurus - Lion's ear
- Authors: Skead, C J (Cuthbert John)
- Date: 1960-05-22
- Subjects: Leonotis leonurus -- South Africa -- Photographs , Trees -- South Africa -- Photographs
- Language: English
- Type: mixed material , photographs , landscape photographs
- Identifier: http://hdl.handle.net/10962/122510 , vital:35298
- Description: Caption "Leonotis leonurus beside railway-line east of Berlin, C. P. 22-05-1960."
- Full Text: false
- Date Issued: 1960-05-22
- Authors: Skead, C J (Cuthbert John)
- Date: 1960-05-22
- Subjects: Leonotis leonurus -- South Africa -- Photographs , Trees -- South Africa -- Photographs
- Language: English
- Type: mixed material , photographs , landscape photographs
- Identifier: http://hdl.handle.net/10962/122510 , vital:35298
- Description: Caption "Leonotis leonurus beside railway-line east of Berlin, C. P. 22-05-1960."
- Full Text: false
- Date Issued: 1960-05-22
Contributions to the study of a class of optimal control problems on the matrix lie group SO(3)
- Authors: Rodgerson, Joanne Kelly
- Date: 2009 , 2013-07-12
- Subjects: Matrix groups , Lie groups , Maximum principles (Mathematics) , Elliptic functions , Extremal problems (Mathematics)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5421 , http://hdl.handle.net/10962/d1007199 , Matrix groups , Lie groups , Maximum principles (Mathematics) , Elliptic functions , Extremal problems (Mathematics)
- Description: The purpose of this thesis is to investigate a class of four left-invariant optimal control problems on the special orthogonal group SO(3). The set of all control-affine left-invariant control systems on SO(3) can, without loss, be reduced to a class of four typical controllable left-invariant control systems on SO(3) . The left-invariant optimal control problem on SO(3) involves finding a trajectory-control pair on SO (3), which minimizes a cost functional, and satisfies the given dynamical constraints and boundary conditions in a fixed time. The problem is lifted to the cotangent bundle T*SO(3) = SO(3) x so (3)* using the optimal Hamiltonian on so(3)*, where the maximum principle yields the optimal control. In a contribution to the study of this class of optimal control problems on SO(3), the extremal equations on so(3)* (ident ified with JR3) are integrated via elliptic functions to obtain explicit expressions for the solution curves in each typical case. The energy-Casimir method is used to give sufficient conditions for non-linear stability of the equilibrium states. , KMBT_363 , Adobe Acrobat 9.54 Paper Capture Plug-in
- Full Text:
- Date Issued: 2009
- Authors: Rodgerson, Joanne Kelly
- Date: 2009 , 2013-07-12
- Subjects: Matrix groups , Lie groups , Maximum principles (Mathematics) , Elliptic functions , Extremal problems (Mathematics)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5421 , http://hdl.handle.net/10962/d1007199 , Matrix groups , Lie groups , Maximum principles (Mathematics) , Elliptic functions , Extremal problems (Mathematics)
- Description: The purpose of this thesis is to investigate a class of four left-invariant optimal control problems on the special orthogonal group SO(3). The set of all control-affine left-invariant control systems on SO(3) can, without loss, be reduced to a class of four typical controllable left-invariant control systems on SO(3) . The left-invariant optimal control problem on SO(3) involves finding a trajectory-control pair on SO (3), which minimizes a cost functional, and satisfies the given dynamical constraints and boundary conditions in a fixed time. The problem is lifted to the cotangent bundle T*SO(3) = SO(3) x so (3)* using the optimal Hamiltonian on so(3)*, where the maximum principle yields the optimal control. In a contribution to the study of this class of optimal control problems on SO(3), the extremal equations on so(3)* (ident ified with JR3) are integrated via elliptic functions to obtain explicit expressions for the solution curves in each typical case. The energy-Casimir method is used to give sufficient conditions for non-linear stability of the equilibrium states. , KMBT_363 , Adobe Acrobat 9.54 Paper Capture Plug-in
- Full Text:
- Date Issued: 2009
Contributions to the study of a class of optimal control problems on the orthogonal groups SO(3) and SO(4)
- Authors: Adams, Ross Montague
- Date: 2015
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/64826 , vital:28608
- Description: In this thesis we investigate a class of invariant optimal control problems, and their associated quadratic Hamilton-Poisson systems, on the orthogonal groups SO(3) and SO(4). Specifically, we are concerned with the class of left-invariant control affine systems. We begin by classifying all cost-extended systems on SO(3) under cost equivalence. (Cost-extended systems are closely related to optimal control problems.) A classification of all quadratic Hamilton-Poisson systems on the (minus) Lie-Poisson space so(3)*, under affine equivalence, is also obtained. For the normal forms obtained in our classification (of Hamilton-Poisson systems) we investigate the (Lyapunov) stability nature of the equilibria using spectral and energy-Casimir methods. For a subclass of these systems, we obtain analytic expressions for the integral curves of the associated Hamiltonian vector fields in terms of (basic) Jacobi elliptic functions. The explicit relationship between the classification of cost-extended systems on SO(3) and the classification of quadratic Hamilton- Poisson systems on so(3)* is provided. On SO(4), a classification of all left-invariant control affine systems under L-equivalence is obtained. We then determine which of these representatives are controllable, thus obtaining a classification under detached feedback equivalence. We also obtain a partial classification of quadratic Hamilton-Poisson systems on the Lie-Poisson space so(4)*. An investigation of the stability nature of the equilibria for a subclass of these systems is also done. Several illustrative examples of optimal control problems on the orthogonal group SO(3) are provided. More specifically, we consider an optimal control problem corresponding to a representative of our classification (of cost-extended system) for each possible number of control inputs. For each of these problems, we obtain explicit expressions for the extremal trajectories on the homogeneous space S2 by projecting the extremal trajectories on the group SO(3). The examples provided show how our classifications of cost-extended systems and Hamilton-Poisson systems can be used to obtain the optimal controls and the extremal trajectories corresponding to a large class of optimal control problems on SO(3). An example of a four-input optimal control problem on SO(4) is also provided. This example is provided to show how the solutions of certain problems on SO(4) can be related to the solutions of certain optimal control problems on SO(3).
- Full Text:
- Date Issued: 2015
- Authors: Adams, Ross Montague
- Date: 2015
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/64826 , vital:28608
- Description: In this thesis we investigate a class of invariant optimal control problems, and their associated quadratic Hamilton-Poisson systems, on the orthogonal groups SO(3) and SO(4). Specifically, we are concerned with the class of left-invariant control affine systems. We begin by classifying all cost-extended systems on SO(3) under cost equivalence. (Cost-extended systems are closely related to optimal control problems.) A classification of all quadratic Hamilton-Poisson systems on the (minus) Lie-Poisson space so(3)*, under affine equivalence, is also obtained. For the normal forms obtained in our classification (of Hamilton-Poisson systems) we investigate the (Lyapunov) stability nature of the equilibria using spectral and energy-Casimir methods. For a subclass of these systems, we obtain analytic expressions for the integral curves of the associated Hamiltonian vector fields in terms of (basic) Jacobi elliptic functions. The explicit relationship between the classification of cost-extended systems on SO(3) and the classification of quadratic Hamilton- Poisson systems on so(3)* is provided. On SO(4), a classification of all left-invariant control affine systems under L-equivalence is obtained. We then determine which of these representatives are controllable, thus obtaining a classification under detached feedback equivalence. We also obtain a partial classification of quadratic Hamilton-Poisson systems on the Lie-Poisson space so(4)*. An investigation of the stability nature of the equilibria for a subclass of these systems is also done. Several illustrative examples of optimal control problems on the orthogonal group SO(3) are provided. More specifically, we consider an optimal control problem corresponding to a representative of our classification (of cost-extended system) for each possible number of control inputs. For each of these problems, we obtain explicit expressions for the extremal trajectories on the homogeneous space S2 by projecting the extremal trajectories on the group SO(3). The examples provided show how our classifications of cost-extended systems and Hamilton-Poisson systems can be used to obtain the optimal controls and the extremal trajectories corresponding to a large class of optimal control problems on SO(3). An example of a four-input optimal control problem on SO(4) is also provided. This example is provided to show how the solutions of certain problems on SO(4) can be related to the solutions of certain optimal control problems on SO(3).
- Full Text:
- Date Issued: 2015
Enhancing phosphorus availability in some phosphate fixing soils of the Transkei region, South Africa using goat manure
- Authors: Gichangi, Elias Maina
- Date: 2007
- Subjects: Phosphorus in agriculture , Soils -- Phosphorus content , Phosphatic fertilizers , Soils -- Phosphorus content -- South Africa -- Transkei
- Language: English
- Type: Thesis , Doctoral , PhD (Soil Science)
- Identifier: vital:11960 , http://hdl.handle.net/10353/80 , Phosphorus in agriculture , Soils -- Phosphorus content , Phosphatic fertilizers , Soils -- Phosphorus content -- South Africa -- Transkei
- Description: Low availability of soil phosphorus (P) caused by strong sorption of P is a major constraint to agricultural production in most South African soils, particularly those from the high rainfall areas. The aim of this study was therefore to investigate whether combined addition of goat manure with inorganic P fertilizers could enhance P availability in some P fixing soils of the Transkei region, South Africa. The study addressed the following specific objectives (i) to assess P sorption capacities and requirements of selected soils and their relationship with selected soil properties and single point sorption test, (ii) to assess the effects of goat manure and lime addition on P sorption properties of selected P fixing soils (iii) to assess the temporal changes in concentration of inorganic and microbial biomass P fractions following application of inorganic fertilizer P with goat manure in a laboratory incubation experiment, and, (iv) to assess the effects of goat manure application with inorganic phosphate on inorganic and microbial biomass P fractions, P uptake and dry matter yield of maize. Sorption maxima (Smax) of seven soils examined ranged from 192.3 to 909.1 (mg P kg-1) and were highly and positively correlated with sorption affinity constant (r = 0.93, p = 0.01) and organic C (r = 0.71, p = 0.01). The amount of P required for maintaining a soil solution concentration of 0.2 mg P l-1 ranged from 2.1 to 123.5 mg P kg-1 soil. Soils collected from Qweqwe (a Cambisol), Qunu (an Acrisol), Ncihane (a Luvisol) and Bethania (a Ferralsol) had lower external P requirement values and were classified as lower sorbers, whereas soils from Ntlonyana (a Planosol), Chevy Chase (a Ferralsol) and Flagstaff (a Ferralsol) were classified as moderate sorbers. The results suggested that P availability could be compromised in 43 percent iii of the soils studied and that measures to mitigate the adverse effects of P sorption were needed to ensure that P is not a limiting factor to crop production, where such soils are found. Goat manure addition at varying rates (5, 10 and 20 tha-1 dry weight basis) to two of the moderately P fixing soils from Chevy Chase and Flagstaff, reduced P sorption maxima (Smax) compared to the control treatment. Phosphate sorption decreased with increasing amounts of goat manure in both soils but the extent of reduction was greater on Chevy Chase soil than on Flagstaff soil. The relative liming effects of the different rates of goat manure followed the order 20 t GM ha-1 > 10 t GM ha-1 > 5 t GM ha-1. In a separate experiment, addition of inorganic P at varying rates (0, 90, 180, and 360 kg P ha-1) to Flagstaff soil increased labile P fractions (resin P, biomass P and NaHCO3-Pi) and the increases were greater when goat manure was co-applied. The control treatments contained only 17.2 and 27.5 mg P kg-1 of resin extractable P in the un-amended and manure amended treatments, respectively which increased to 118.2 and 122.7 mg P kg-1 on day 28 of incubation. Biomass P concentration was increased from 16.8 to 43.9 mg P kg-1 in P alone treatments but the fraction was greatly enhanced with manure addition, increasing it from 32.6 to 97.7 mg P kg-1. NaOH-Pi was the largest extractable Pi fraction and ranged from 144.3 to 250.6 mg P kg-1 and 107.5 to 213.2 mg P kg-1 in the unamended and manure amended treatments, respectively. Dry matter yield and P uptake by maize grown in the glasshouse were highly and significantly (p = 0.05) correlated with the different P fractions in the soil. The correlations followed the order resin P (r = 0.85) > NaOH-Pi (r = 0.85) > NaHCO3-Pi (r = 0.84) >> biomass P (r = 0.56) for dry matter yield at 6 weeks after planting. At 12 weeks after planting, goat manure had iv highly significant effects on resin P and biomass P but had no effect on NaHCO3-Pi and NaOH–Pi. The combination of biomass P, resin P and NaHCO3-Pi explained 75.8 percent of the variation in dry matter yield of which 63.0 percent of the variation was explained by biomass P alone. The greatest increase in biomass P occurred when added P was co-applied with 5 or 10 tha-1 goat manure. The predictive equation for maize dry matter yield (DM) was: DM (g) = 1.897 biomass P + 0.645 resin P (r = 0.73). Resin P was the fraction that was most depleted due to plant uptake and decreased by 56 to 68 percent between the 6th week and the 12th week of sampling indicating that it played a greater role in supplying plant available P. The results therefore suggested that the use of goat manure may allow resource poor farmers to use lower levels of commercial phosphate fertilizers because of its effect to reduce soil P sorption. In addition, higher increases in biomass P due to manure addition observed at lower rates of added P indicated that goat manure has potential for enhancing bioavailability and fertilizer use efficiency of small inorganic P applications.
- Full Text:
- Date Issued: 2007
- Authors: Gichangi, Elias Maina
- Date: 2007
- Subjects: Phosphorus in agriculture , Soils -- Phosphorus content , Phosphatic fertilizers , Soils -- Phosphorus content -- South Africa -- Transkei
- Language: English
- Type: Thesis , Doctoral , PhD (Soil Science)
- Identifier: vital:11960 , http://hdl.handle.net/10353/80 , Phosphorus in agriculture , Soils -- Phosphorus content , Phosphatic fertilizers , Soils -- Phosphorus content -- South Africa -- Transkei
- Description: Low availability of soil phosphorus (P) caused by strong sorption of P is a major constraint to agricultural production in most South African soils, particularly those from the high rainfall areas. The aim of this study was therefore to investigate whether combined addition of goat manure with inorganic P fertilizers could enhance P availability in some P fixing soils of the Transkei region, South Africa. The study addressed the following specific objectives (i) to assess P sorption capacities and requirements of selected soils and their relationship with selected soil properties and single point sorption test, (ii) to assess the effects of goat manure and lime addition on P sorption properties of selected P fixing soils (iii) to assess the temporal changes in concentration of inorganic and microbial biomass P fractions following application of inorganic fertilizer P with goat manure in a laboratory incubation experiment, and, (iv) to assess the effects of goat manure application with inorganic phosphate on inorganic and microbial biomass P fractions, P uptake and dry matter yield of maize. Sorption maxima (Smax) of seven soils examined ranged from 192.3 to 909.1 (mg P kg-1) and were highly and positively correlated with sorption affinity constant (r = 0.93, p = 0.01) and organic C (r = 0.71, p = 0.01). The amount of P required for maintaining a soil solution concentration of 0.2 mg P l-1 ranged from 2.1 to 123.5 mg P kg-1 soil. Soils collected from Qweqwe (a Cambisol), Qunu (an Acrisol), Ncihane (a Luvisol) and Bethania (a Ferralsol) had lower external P requirement values and were classified as lower sorbers, whereas soils from Ntlonyana (a Planosol), Chevy Chase (a Ferralsol) and Flagstaff (a Ferralsol) were classified as moderate sorbers. The results suggested that P availability could be compromised in 43 percent iii of the soils studied and that measures to mitigate the adverse effects of P sorption were needed to ensure that P is not a limiting factor to crop production, where such soils are found. Goat manure addition at varying rates (5, 10 and 20 tha-1 dry weight basis) to two of the moderately P fixing soils from Chevy Chase and Flagstaff, reduced P sorption maxima (Smax) compared to the control treatment. Phosphate sorption decreased with increasing amounts of goat manure in both soils but the extent of reduction was greater on Chevy Chase soil than on Flagstaff soil. The relative liming effects of the different rates of goat manure followed the order 20 t GM ha-1 > 10 t GM ha-1 > 5 t GM ha-1. In a separate experiment, addition of inorganic P at varying rates (0, 90, 180, and 360 kg P ha-1) to Flagstaff soil increased labile P fractions (resin P, biomass P and NaHCO3-Pi) and the increases were greater when goat manure was co-applied. The control treatments contained only 17.2 and 27.5 mg P kg-1 of resin extractable P in the un-amended and manure amended treatments, respectively which increased to 118.2 and 122.7 mg P kg-1 on day 28 of incubation. Biomass P concentration was increased from 16.8 to 43.9 mg P kg-1 in P alone treatments but the fraction was greatly enhanced with manure addition, increasing it from 32.6 to 97.7 mg P kg-1. NaOH-Pi was the largest extractable Pi fraction and ranged from 144.3 to 250.6 mg P kg-1 and 107.5 to 213.2 mg P kg-1 in the unamended and manure amended treatments, respectively. Dry matter yield and P uptake by maize grown in the glasshouse were highly and significantly (p = 0.05) correlated with the different P fractions in the soil. The correlations followed the order resin P (r = 0.85) > NaOH-Pi (r = 0.85) > NaHCO3-Pi (r = 0.84) >> biomass P (r = 0.56) for dry matter yield at 6 weeks after planting. At 12 weeks after planting, goat manure had iv highly significant effects on resin P and biomass P but had no effect on NaHCO3-Pi and NaOH–Pi. The combination of biomass P, resin P and NaHCO3-Pi explained 75.8 percent of the variation in dry matter yield of which 63.0 percent of the variation was explained by biomass P alone. The greatest increase in biomass P occurred when added P was co-applied with 5 or 10 tha-1 goat manure. The predictive equation for maize dry matter yield (DM) was: DM (g) = 1.897 biomass P + 0.645 resin P (r = 0.73). Resin P was the fraction that was most depleted due to plant uptake and decreased by 56 to 68 percent between the 6th week and the 12th week of sampling indicating that it played a greater role in supplying plant available P. The results therefore suggested that the use of goat manure may allow resource poor farmers to use lower levels of commercial phosphate fertilizers because of its effect to reduce soil P sorption. In addition, higher increases in biomass P due to manure addition observed at lower rates of added P indicated that goat manure has potential for enhancing bioavailability and fertilizer use efficiency of small inorganic P applications.
- Full Text:
- Date Issued: 2007
Rhodeo, Vol. 22, No. 17
- Date: 1968-08-29
- Subjects: Grahamstown -- Newspapers , Journalism, Students -- South Africa , Rhodes University -- Activate , Rhodes University -- Students , Student newspapers and periodicals -- South Africa
- Language: English
- Type: Text
- Identifier: vital:14591 , http://hdl.handle.net/10962/d1019463
- Description: Rhodeo is the Independent Student Newspaper of Rhodes University. Located in Grahamstown, Rhodeo was established in 1947, and renamed in 1994 as Activate. During apartheid Rhodeo became an active part of the struggle for freedom of expression as part of the now defunct South African Student Press Union. Currently Activate is committed to informing Rhodes University students, staff and community members about relevant issues, mainly on campus. These issues range from hard news to more creative journalism. While Activate acts as a news source, one of its main objectives it to be accessible as a training ground for student journalists. The newspaper is run entirely by the students and is published twice a term. Activate is a free newspaper which receives an annual grant from the Rhodes University Student Representative Council, however, majority of its revenue is generated through advertising.
- Full Text:
- Date Issued: 1968-08-29
- Date: 1968-08-29
- Subjects: Grahamstown -- Newspapers , Journalism, Students -- South Africa , Rhodes University -- Activate , Rhodes University -- Students , Student newspapers and periodicals -- South Africa
- Language: English
- Type: Text
- Identifier: vital:14591 , http://hdl.handle.net/10962/d1019463
- Description: Rhodeo is the Independent Student Newspaper of Rhodes University. Located in Grahamstown, Rhodeo was established in 1947, and renamed in 1994 as Activate. During apartheid Rhodeo became an active part of the struggle for freedom of expression as part of the now defunct South African Student Press Union. Currently Activate is committed to informing Rhodes University students, staff and community members about relevant issues, mainly on campus. These issues range from hard news to more creative journalism. While Activate acts as a news source, one of its main objectives it to be accessible as a training ground for student journalists. The newspaper is run entirely by the students and is published twice a term. Activate is a free newspaper which receives an annual grant from the Rhodes University Student Representative Council, however, majority of its revenue is generated through advertising.
- Full Text:
- Date Issued: 1968-08-29
Rhodeo, Vol. 22, No. 13
- Date: 1968-06-13
- Subjects: Grahamstown -- Newspapers , Journalism, Students -- South Africa , Rhodes University -- Activate , Rhodes University -- Students , Student newspapers and periodicals -- South Africa
- Language: English
- Type: Text
- Identifier: vital:14587 , http://hdl.handle.net/10962/d1019459
- Description: Rhodeo is the Independent Student Newspaper of Rhodes University. Located in Grahamstown, Rhodeo was established in 1947, and renamed in 1994 as Activate. During apartheid Rhodeo became an active part of the struggle for freedom of expression as part of the now defunct South African Student Press Union. Currently Activate is committed to informing Rhodes University students, staff and community members about relevant issues, mainly on campus. These issues range from hard news to more creative journalism. While Activate acts as a news source, one of its main objectives it to be accessible as a training ground for student journalists. The newspaper is run entirely by the students and is published twice a term. Activate is a free newspaper which receives an annual grant from the Rhodes University Student Representative Council, however, majority of its revenue is generated through advertising.
- Full Text:
- Date Issued: 1968-06-13
- Date: 1968-06-13
- Subjects: Grahamstown -- Newspapers , Journalism, Students -- South Africa , Rhodes University -- Activate , Rhodes University -- Students , Student newspapers and periodicals -- South Africa
- Language: English
- Type: Text
- Identifier: vital:14587 , http://hdl.handle.net/10962/d1019459
- Description: Rhodeo is the Independent Student Newspaper of Rhodes University. Located in Grahamstown, Rhodeo was established in 1947, and renamed in 1994 as Activate. During apartheid Rhodeo became an active part of the struggle for freedom of expression as part of the now defunct South African Student Press Union. Currently Activate is committed to informing Rhodes University students, staff and community members about relevant issues, mainly on campus. These issues range from hard news to more creative journalism. While Activate acts as a news source, one of its main objectives it to be accessible as a training ground for student journalists. The newspaper is run entirely by the students and is published twice a term. Activate is a free newspaper which receives an annual grant from the Rhodes University Student Representative Council, however, majority of its revenue is generated through advertising.
- Full Text:
- Date Issued: 1968-06-13
Rhodeo, Vol. 22, No. 8
- Subjects: Grahamstown -- Newspapers , Journalism, Students -- South Africa , Rhodes University -- Activate , Rhodes University -- Students , Student newspapers and periodicals -- South Africa
- Language: English
- Type: Text
- Identifier: vital:14583 , http://hdl.handle.net/10962/d1019455
- Description: Rhodeo is the Independent Student Newspaper of Rhodes University. Located in Grahamstown, Rhodeo was established in 1947, and renamed in 1994 as Activate. During apartheid Rhodeo became an active part of the struggle for freedom of expression as part of the now defunct South African Student Press Union. Currently Activate is committed to informing Rhodes University students, staff and community members about relevant issues, mainly on campus. These issues range from hard news to more creative journalism. While Activate acts as a news source, one of its main objectives it to be accessible as a training ground for student journalists. The newspaper is run entirely by the students and is published twice a term. Activate is a free newspaper which receives an annual grant from the Rhodes University Student Representative Council, however, majority of its revenue is generated through advertising.
- Full Text:
- Subjects: Grahamstown -- Newspapers , Journalism, Students -- South Africa , Rhodes University -- Activate , Rhodes University -- Students , Student newspapers and periodicals -- South Africa
- Language: English
- Type: Text
- Identifier: vital:14583 , http://hdl.handle.net/10962/d1019455
- Description: Rhodeo is the Independent Student Newspaper of Rhodes University. Located in Grahamstown, Rhodeo was established in 1947, and renamed in 1994 as Activate. During apartheid Rhodeo became an active part of the struggle for freedom of expression as part of the now defunct South African Student Press Union. Currently Activate is committed to informing Rhodes University students, staff and community members about relevant issues, mainly on campus. These issues range from hard news to more creative journalism. While Activate acts as a news source, one of its main objectives it to be accessible as a training ground for student journalists. The newspaper is run entirely by the students and is published twice a term. Activate is a free newspaper which receives an annual grant from the Rhodes University Student Representative Council, however, majority of its revenue is generated through advertising.
- Full Text:
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
Cikandya cikailimeni mucalo
- Bemba men at the Mufulira Mine, performer not specified, composer not specified, Tracey, Hugh
- Authors: Bemba men at the Mufulira Mine , 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/10962/375027 , vital:66853 , International Library of African Music, Rhodes University, Makhanda, South Africa , Hugh Tracey Commercial Records, Rhodes University, Makhanda, South Africa , AC0461-C3P22
- Description: Indigenous music
- Full Text: false
- Date Issued: 1949
- Authors: Bemba men at the Mufulira Mine , 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/10962/375027 , vital:66853 , International Library of African Music, Rhodes University, Makhanda, South Africa , Hugh Tracey Commercial Records, Rhodes University, Makhanda, South Africa , AC0461-C3P22
- Description: Indigenous music
- Full Text: false
- Date Issued: 1949
Evaluation of product x pre and post cpv implementation
- Authors: Killian, Christopher Grant
- Date: 2020
- Subjects: Pharmaceutical industry
- Language: English
- Type: Thesis , Masters , MPharm
- Identifier: http://hdl.handle.net/10948/46447 , vital:39577
- Description: Purpose: Stage 3 of the pharmaceutical process validation lifecycle, is called continued process verification (CPV). CPV is the final stage of lifecycle management and is intended to provide ongoing assurance that during routine production that a process remains in a state of control. Since CPV is a relatively new focus area for regulators, many legacy products will not have undergone Stage 3 process validation. Therefore, an opportunity existed to review the impact and challenges of implementing CPV on a legacy product. Methodology: This study employed quantitative analysis to evaluate the impact of CPV on process stability and end product quality for Product X, a legacy product manufactured at a generics manufacturing facility. Initial Stage 3a CPV was used to review historical process data and identify special cause variation. Corrective and preventative actions were taken to address these statistical outliers and the impact of these process changes were evaluated in Stage 3b. Results: CPV implementation appeared to have an effect on process control, stability and capability for Product X. In Stage 3b, an increase in statistical outliers along with significant changes to process mean and standard deviation were seen for the critical process parameters, average mass and hardness. An improvement in process capability for the critical quality attributes, assay and dissolution, was also seen. Conclusion: The largest benefit of CPV implementation, especially for a legacy product, is the process knowledge gained. This provided opportunities for process improvement and ultimately benefited patient safety.
- Full Text:
- Date Issued: 2020
- Authors: Killian, Christopher Grant
- Date: 2020
- Subjects: Pharmaceutical industry
- Language: English
- Type: Thesis , Masters , MPharm
- Identifier: http://hdl.handle.net/10948/46447 , vital:39577
- Description: Purpose: Stage 3 of the pharmaceutical process validation lifecycle, is called continued process verification (CPV). CPV is the final stage of lifecycle management and is intended to provide ongoing assurance that during routine production that a process remains in a state of control. Since CPV is a relatively new focus area for regulators, many legacy products will not have undergone Stage 3 process validation. Therefore, an opportunity existed to review the impact and challenges of implementing CPV on a legacy product. Methodology: This study employed quantitative analysis to evaluate the impact of CPV on process stability and end product quality for Product X, a legacy product manufactured at a generics manufacturing facility. Initial Stage 3a CPV was used to review historical process data and identify special cause variation. Corrective and preventative actions were taken to address these statistical outliers and the impact of these process changes were evaluated in Stage 3b. Results: CPV implementation appeared to have an effect on process control, stability and capability for Product X. In Stage 3b, an increase in statistical outliers along with significant changes to process mean and standard deviation were seen for the critical process parameters, average mass and hardness. An improvement in process capability for the critical quality attributes, assay and dissolution, was also seen. Conclusion: The largest benefit of CPV implementation, especially for a legacy product, is the process knowledge gained. This provided opportunities for process improvement and ultimately benefited patient safety.
- Full Text:
- Date Issued: 2020
Letter from Edmond Robert Wodehouse, to Walter Jardine, 22 May 1864
- Wodehouse, Edmond Robert, Jardine, Walter
- Authors: Wodehouse, Edmond Robert , Jardine, Walter
- Date: 1864-05-22 , 2021-09-29
- Subjects: Jardine, Walter , Botanical Gardens -- South Africa -- Grahamstown
- Type: text , letter
- Identifier: http://hdl.handle.net/10962/197654 , vital:45893 , Cory Library for Humanities Research, Rhodes University
- Description: Jardine Correspondence transcribed by Jean Kelly August 2021. Transcription: Graham’s Town. May 22 1864. I am much obliged to you, Walter, for the Disa Bulbs which arrived yesterday all safe, and with which Mr Tuck of the Botanical Gardens is much pleased. I remain Yours faithfully, Edmund R Wodehouse. ************************************************************************ Noted on scrap paper: Left Cape Town 22nd May 1867 Got to Grahamstown 1st June Bot Gardens 4th June. Walter Jardine.
- Full Text: false
- Authors: Wodehouse, Edmond Robert , Jardine, Walter
- Date: 1864-05-22 , 2021-09-29
- Subjects: Jardine, Walter , Botanical Gardens -- South Africa -- Grahamstown
- Type: text , letter
- Identifier: http://hdl.handle.net/10962/197654 , vital:45893 , Cory Library for Humanities Research, Rhodes University
- Description: Jardine Correspondence transcribed by Jean Kelly August 2021. Transcription: Graham’s Town. May 22 1864. I am much obliged to you, Walter, for the Disa Bulbs which arrived yesterday all safe, and with which Mr Tuck of the Botanical Gardens is much pleased. I remain Yours faithfully, Edmund R Wodehouse. ************************************************************************ Noted on scrap paper: Left Cape Town 22nd May 1867 Got to Grahamstown 1st June Bot Gardens 4th June. Walter Jardine.
- Full Text: false
A study of a class of invariant optimal control problems on the Euclidean group SE(2)
- Authors: Adams, Ross Montague
- Date: 2011
- Subjects: Matrix groups Lie groups Extremal problems (Mathematics) Maximum principles (Mathematics) Hamilton-Jacobi equations Lyapunov stability
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5420 , http://hdl.handle.net/10962/d1006060
- Description: The aim of this thesis is to study a class of left-invariant optimal control problems on the matrix Lie group SE(2). We classify, under detached feedback equivalence, all controllable (left-invariant) control affine systems on SE(2). This result produces six types of control affine systems on SE(2). Hence, we study six associated left-invariant optimal control problems on SE(2). A left-invariant optimal control problem consists of minimizing a cost functional over the trajectory-control pairs of a left-invariant control system subject to appropriate boundary conditions. Each control problem is lifted from SE(2) to T*SE(2) ≅ SE(2) x se (2)*and then reduced to a problem on se (2)*. The maximum principle is used to obtain the optimal control and Hamiltonian corresponding to the normal extremals. Then we derive the (reduced) extremal equations on se (2)*. These equations are explicitly integrated by trigonometric and Jacobi elliptic functions. Finally, we fully classify, under Lyapunov stability, the equilibrium states of the normal extremal equations for each of the six types under consideration.
- Full Text:
- Date Issued: 2011
- Authors: Adams, Ross Montague
- Date: 2011
- Subjects: Matrix groups Lie groups Extremal problems (Mathematics) Maximum principles (Mathematics) Hamilton-Jacobi equations Lyapunov stability
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5420 , http://hdl.handle.net/10962/d1006060
- Description: The aim of this thesis is to study a class of left-invariant optimal control problems on the matrix Lie group SE(2). We classify, under detached feedback equivalence, all controllable (left-invariant) control affine systems on SE(2). This result produces six types of control affine systems on SE(2). Hence, we study six associated left-invariant optimal control problems on SE(2). A left-invariant optimal control problem consists of minimizing a cost functional over the trajectory-control pairs of a left-invariant control system subject to appropriate boundary conditions. Each control problem is lifted from SE(2) to T*SE(2) ≅ SE(2) x se (2)*and then reduced to a problem on se (2)*. The maximum principle is used to obtain the optimal control and Hamiltonian corresponding to the normal extremals. Then we derive the (reduced) extremal equations on se (2)*. These equations are explicitly integrated by trigonometric and Jacobi elliptic functions. Finally, we fully classify, under Lyapunov stability, the equilibrium states of the normal extremal equations for each of the six types under consideration.
- Full Text:
- Date Issued: 2011
Maclear
- Casgrain, P H du P, Great Britain. War Office. Intelligence Division
- Authors: Casgrain, P H du P , Great Britain. War Office. Intelligence Division
- Date: 1900
- Subjects: 3.94 miles = 1 inch 30.5595° S, 22.9375° E , 3.94 miles = 1 inch ; 6945 yards = 1 inch. 30.5595° S, 22.9375° E , Maclear (South Africa) History Maps , Eastern Cape (South Africa) Maps , South Africa History 1836-1909 Maps
- Language: English
- Type: maps , digital maps , cartographic
- Identifier: http://hdl.handle.net/10962/113253 , vital:33736 , Cory Library for Humanities Research, Rhodes University Library, Grahamstown, South Africa , MP570
- Description: [Imperial map of South Africa] : Maclear compiled and lithographed by Mapping Section F.I.D. Cape Town under the superintendance of Capt. P.H. Du P. Casgrain ... from farm surveys and all other available information, [Wood and Ortlepp] [1900].
- Full Text: false
- Date Issued: 1900
- Authors: Casgrain, P H du P , Great Britain. War Office. Intelligence Division
- Date: 1900
- Subjects: 3.94 miles = 1 inch 30.5595° S, 22.9375° E , 3.94 miles = 1 inch ; 6945 yards = 1 inch. 30.5595° S, 22.9375° E , Maclear (South Africa) History Maps , Eastern Cape (South Africa) Maps , South Africa History 1836-1909 Maps
- Language: English
- Type: maps , digital maps , cartographic
- Identifier: http://hdl.handle.net/10962/113253 , vital:33736 , Cory Library for Humanities Research, Rhodes University Library, Grahamstown, South Africa , MP570
- Description: [Imperial map of South Africa] : Maclear compiled and lithographed by Mapping Section F.I.D. Cape Town under the superintendance of Capt. P.H. Du P. Casgrain ... from farm surveys and all other available information, [Wood and Ortlepp] [1900].
- Full Text: false
- Date Issued: 1900
Salt pan
- Casgrain, P H du P, Great Britain. War Office. Intelligence Division
- Authors: Casgrain, P H du P , Great Britain. War Office. Intelligence Division
- Date: 1900
- Subjects: 3.94 miles = 1 inch 30.5595° S, 22.9375° E , 3.94 miles = 1 inch ; 6945 yards = 1 inch. 30.5595° S, 22.9375° E , Salt Pan (South Africa) History Maps , Eastern Cape (South Africa) Maps , South Africa History 1836-1909 Maps South African War 1899-1902 Maps
- Language: English
- Type: maps , digital maps , cartographic
- Identifier: http://hdl.handle.net/10962/113271 , vital:33739 , Cory Library for Humanities Research, Rhodes University Library, Grahamstown, South Africa , MP571
- Description: [Imperial map of South Africa] : Salt Pan compiled and lithographed by Mapping Section F.I.D. Cape Town under the superintendance of Capt. P.H. Du P. Casgrain ... from farm surveys and all other available information, [Wood and Ortlepp] [1900] 3rd edition.
- Full Text: false
- Date Issued: 1900
- Authors: Casgrain, P H du P , Great Britain. War Office. Intelligence Division
- Date: 1900
- Subjects: 3.94 miles = 1 inch 30.5595° S, 22.9375° E , 3.94 miles = 1 inch ; 6945 yards = 1 inch. 30.5595° S, 22.9375° E , Salt Pan (South Africa) History Maps , Eastern Cape (South Africa) Maps , South Africa History 1836-1909 Maps South African War 1899-1902 Maps
- Language: English
- Type: maps , digital maps , cartographic
- Identifier: http://hdl.handle.net/10962/113271 , vital:33739 , Cory Library for Humanities Research, Rhodes University Library, Grahamstown, South Africa , MP571
- Description: [Imperial map of South Africa] : Salt Pan compiled and lithographed by Mapping Section F.I.D. Cape Town under the superintendance of Capt. P.H. Du P. Casgrain ... from farm surveys and all other available information, [Wood and Ortlepp] [1900] 3rd edition.
- Full Text: false
- Date Issued: 1900