330 research outputs found
A note on the Banach space of preregular maps
No full textThe aim of this paper is to give simple proofs for Jeurnink's characterizations of preregular maps in terms of Θ-maps acting between Banach lattices. For Banach lattices E and F, we achieve our goal by considering the space Lβ(E, F) of all those linear maps T: E → F for which there exists a constant K such that {double pipe}Vn i=1 {pipe}Txi{pipe} ≤ K {double pipe}Vn i=1{pipe}xi for all finite sequences x1, ..., xn e{open}E. We show that, if Lβ(E; F), and the spaces L Θ (E; F) of Θ -map and Lpr(E; F) of preregular maps are respectively endowed with their canonical norms, then they are identical Banach space
Rehabilitation for Cas Labuschagne : good enough, timely enough?
No full textDATA BESKIKBAARHEIDSVERKLARING : Datadeling is nie van toepassing nie, aangesien geen nuwe
data in die studie geskep of ontleed is nie.This research is part of the project, ‘Contextualized Reformed Theology in South Africa’, directed by Dr Andre Ungerer of the Reformed Theological College, Faculty of Theology, University of Pretoria.Special Collection: Wim Dreyer Dedication, sub-edited by Jaco Beyers (University of Pretoria, South Africa).During the General
Church Assembly of 2010, the Netherdutch Reformed Church of Africa (NRCA) confessed her
previous justification of apartheid as wrongdoing. It led to serious dissatisfaction in the more
conservative part of the Church, eventually ending in the painful church schism of 2011.
Afterwards, the leadership had to handle several related issues. And then, out of the blue, an
outstanding matter arose from the past’s nebulae – unfinished business between the Church
and prof. Cas Labuschagne. He was a dissident with prof. Albert Geyser who acted against
the church’s justification of apartheid during the sixties. After a fierce struggle and much
desperation, he left South Africa for the Netherlands in 1967. Almost 40 years later, in 2008,
correspondence occurred between the NRCA and Labuschagne to see if reconciliation was possible,
but without any positive results. Labuschagne distrusted the Church’s motives and argued that
only a public excuse would settle matters. Due to the run-up to the decision in 2010 and the
church schism in 2011, the case gathered some cyber dust. Professors A.G. van Aarde, J.
Buitendag and W.A. Dreyer played a prominent role in bringing the outstanding matter of Cas
Labuschagne to the attention of the author of this article. It led to a visit in 2017 and more
correspondence to clarify issues. Eventually, reconciliation had occurred only a few months
before he died in 2019.
CONTRIBUTION : This article contributes to revealing an untold story in which different leaders
of the NRCA played a prominent role. It is about a struggle for reconciliation, events behind
the scenes, and a story with a good end – events the church and the academic community
should know about.http://www.hts.org.zaam2024Reformed Theological CollegeNon
A crossed product approach to Orlicz spaces
No full textWe show how the known theory of non-commutative Orlicz spaces for semifinite von Neumann
algebras equipped with an faithful normal semifinite trace may be recovered using crossed
product techniques. Then using this as a template, we construct analogues of such spaces for type
III algebras. The constructed spaces naturally dovetail with and closely mimic the behaviour of
Haagerup Lp-spaces.We then define a modified K-method of interpolation which seems to better
fit the present context, and give a formal prescription for using this method to define what may
be regarded as type III Riesz–Fischer spacesNational Research Foundatio
Derivations on operator algebras
No full textDissertation (MSc)--University of Pretoria, 2004.This work primarily provides some detail of results on domain properties of closed (unbounded) derivations on C*- algebras. The focus is on Section 4: Domain Properties where a combination of topological and algebraic conditions for certain results are illustrated. Various earlier results are incorporated into the proofs of Section 4. Section 1: Basics lists some basic functional analysis results, operator algebra theory (of particular importance is the continuous functional calculus and certain results on the state and pure state space) and a special section on operator closedness. Some HahnBanach results are also listed. The results of this section were obtained from various sources (Zhu, K. [24), Kadison, R.V. and Ringrose, J.R [8), Goldberg, S. [6), Rudin, W. [20), Sakai, S. [22), Labuschagne, L.E. [10) and others). The development of the representation theory presented in Section 1.1.7 was compiled from Bratteli, 0. and Robinson, D.W. [3), Section 2.3. Section 2: Derivations provides some background to the roots of derivations in quantum mechanics. The results of Section 2.2 (Commutators) are due to various authors, mainly obtained from Sakai, S. [22). A detailed proof of Theorem 45 is given. Section 2.3 (Differentiability) contains some Singer-Wermer results mainly obtained from Mathieu, M. and Murphy, G.J. [13) and Theorem 50 is proved in detail. Section 2.4 deals with conditions for bounded derivations (Sakai, S. [22)) and (Johnson-Sinclair, cf. (Sakai, S. [22))), and Theorem 51 is proved in detail. Section 2.5 deals with the well published derivation theorem (Sakai, S. [22), Section 2.5 and Bratteli, 0. and Robinson, D.W. [3), Corollary 3.2.47) and a slightly weaker version of the W*- algebra derivation theorem as published in Bratteli, 0. and Robinson, D.W. [3), Corollary 3.2.47, is proved here. Section 3: Derivations as generators first introduces some basic semi-group theory (obtained from Pazy, A. [16), Section 1.1 and 1.2) after which the well-behavedness property is introduced in Section 3.2. Some general results mainly obtained from Sakai, S. [22), Section 3.2, is detailed. The proofs of Theorems 61 and 62 makes use of various previous results and were conducted in detail. Section 3.3 (\Vell-behavedness and generators) draws a link between the well-behavedness property and conditions for a derivation to be a semi-group generator. The results are obtained from Pazy, A. [16), Section 1.4, and Bratteli, 0. and Robinson, D.W. [3), Section 3.2.4. Special care was taken in the outlined proof of Theorem 68. A proof of a domain characterization theorem (due to Bratteli, 0. and Robinson, D.W. [3), Proposition 3.2.55) is provided (Theorem 69) and used in the construction of the counter example of Section 4.G.Mathematics and Applied MathematicsMScUnrestricte
Derivations on operator algebras
No full textDissertation (MSc (Mathematics and Applied Mathematics))--University of Pretoria, 2004.This work primarily provides some detail of results on domain properties of closed (unbounded) derivations on C*-algebras. The focus is on Section 4: Domain Properties where a combination of topological and algebraic conditions for certain results are illustrated. Various earlier results are incorporated into the proofs of Section 4. Section 1: Basics lists some basic functional analysis results, operator algebra theory (of particular importance is the continuous functional calculus and certain results on the state and pure state space) and a special section on operator closedness. Some Hahn-Banach results are also listed. The results of this section were obtained from various sources (Zhu, K. [24], Kadison, R.V. and Ringrose, J.R. [8], Goldberg, S. [6], Rudin, W. [20], Sakai, S. [22], Labuschagne, L.E. [10] and others). The development of the representation theory presented in Section 1.1.7 was compiled from Bratteli, O. and Robinson, D.W. [3], Section 2.3. Section 2: Derivations provides some background to the roots of derivations in quantum mechanics. The results of Section 2.2 (Commutators) are due to various authors, mainly obtained from Sakai, S. [22]. A detailed proof of Theorem 45 is given. Section 2.3 (Differentiability) contains some Singer-Wermer results mainly obtained from Mathieu, M. and Murphy, G.J. [13] and Theorem 50 is proved in detail. Section 2.4 deals with conditions for bounded derivations (Sakai, S. [22] and (Johnson-Sinclair, cf. (Sakai, S. [22])), and Theorem 51 is proved in detail. Section 2.5 deals with the well published derivation theorem (Sakai, S.[22], Section 2.5 and Bratteli, O. and Robinson, D.W. [3], Corollary 3.2.47) and a slightly weaker version of the W *-algebra derivation theorem as published in Bratteli, O. and Robinson, D.W. [3], Corollary 3.2.47, is proved here. Section 3: Derivations as generators first introduces some basic semi-group theory (obtained from Pazy, A. [16], Section 1.1 and 1.2) after which the well-behavedness property is introduced in Section 3.2. Some general results mainly obtained from Sakai, S. [22], Section 3.2, is detailed. The ;proofs of Theorems 61 and 62 makes use of various previous results and were conducted in detail. Section 3.3 (Well-behavedness and generators) draws a link between the well-behavedness property and conditions for a derivation to be a semi-group generator. The results are obtained from Pazy, A. [16], Section 1.4, and Bratteli, O. and Robinson, D.W. [3], Section 3.2.4 Special care was taken in the outlined proof of Theorem 68. A proof of a domain characterization theorem (due to Bratteli, O. and Robinson, D.W. [3], Proposition 3.2.55) is provided (Theorem 69) and used in the construction of the counter example of Section 4.6. Section 4: Domain properties is occupied with un-bounded derivations on C*-algebras and their domain properties. Some initial complex function theory is developed after which four important domain preserving theorems are proved in full detail: the inverse function (Section 4.2), the exponential function (Section 4.3), Fourier analysis on the domain (Section 4.4) and C2-functions on the domain (Section 4.5). The non domain preserving C1 function counter example is presented in Section 4.6. The results of Section 4 appear in Bratteli, O. and Robinson, D.W. [3], Section 3.2.2, and Sakai, S. [22], Section 3.3, and the counter example is due to McIntosh, A. [11]. All the results in Section 4 are presented in full detail not available in this format from any of the sources used. Some Topelitz operator theory is used with reference to Brown, A. and Halmos, P.R. [4], 94, and the Fourier coefficients of a required function is calculated. Some results on direct sum spaces and the core of a linear operator were used from Kadison, R.V. and Ringrose, J.R. [8], Section 2.6 and page 160, as well as Zhu, K. [24], Section 14.2.Mathematics and Applied Mathematicsunrestricte
Peanut Genetic Resources: Status, Challenges, and Use in Peanut Genetic Improvement
No full textPeanut (Arachis hypogaea L.) is an annual food legume grown in over 100 countries for many uses, primarily as vegetable oil or snacks in local or regional diets, and the dried vines are used as fodder for livestock. Around the world, it is popularly known as groundnut because of its unique feature of producing flowers above ground with below-ground development of pods. Genus Arachis originated in South America, with several primary centers of diversity located in Argentina, Bolivia, Brazil, Paraguay, and Uruguay. Spread across these five countries, the genus contains about 83 described species grouped into nine different taxonomic sections with unique genomes and cross-compatibilities. The cultivated species, Arachis hypogaea, originated from a natural hybridization event between two wild Arachis species about 10,000 years ago. Following domestication, it spread to other parts of the world, displaying several secondary centers of diversity. Arachis hypogaea is a tetraploid, while many of the wild species are diploids, with a few other tetraploid and aneuploid species also present in the genus. Large germplasm collections of cultivated as well as wild species are preserved in several gene banks around the world. These germplasm collections provide the primary source of genetic diversity for peanut improvement to meet present and future demands. Several accessions have been used in developing improved cultivars, especially involving interspecific hybridization with the wild species. The derived genetic resources provided populations for molecular and genomic investigations, leading to the development of valuable resources for peanut breeders worldwide. These genetic resources act as a reservoir for many economically important traits, including yield, drought tolerance, resistance to diseases, nutritional quality, and long-term resilience of the crop against evolving pests and pathogens and a changing climate
Ghostreading : retro-spectral interpretations in the novels of David Mitchell
No full textAbstract : In the course of the past nineteen years or so, the novels of British author David Mitchell have been steadily garnering critical scrutiny, with the focus of scholarly interest ranging from postmodernist narrative forms, the Bildungsroman, and discursive identity, to the Utopian, science fiction, and postcolonialism, among many others. Such diverse approaches hinge on the eclectic use of genre in these works, not only from one novel to the next, but more often than not also within a single text. By thus disrupting genre-compliant writing, these novels can be said to work deconstructively to destabilize conventional modes of reading and interpretation. As a result, the formation of the subject – be this the writer, the protagonist-narrator, and/or the reader – is fitfully traced in the interstices between ever-changing syntagmatic and paradigmatic levels of signification. Hence the figure of this composite subject is always in the process of becoming, never fully formed or fully present. One could speak here of the subject as a spectral shape that haunts the pages of the text, much as the plotlines of Mitchell’s novels are haunted by uncanny encounters, virtual personalities, return appearances, and supernatural. Within this framework, I aim to show in this study how Mitchell’s writing rehearses the vagaries of the reading process. In the process, I focus on the narrative structure of three specific novels – what I would call the inaugural trio consisting of ghostwritten, number9dream, and Cloud Atlas, insofar as they could be seen to lay the groundwork for the ever-expanding, endlessly shifting fictional world of what Mitchell himself thinks of as his “über-novel” (Huff Post Books, 9 June 2015). I pay close attention to certain, possibly less familiar aspects of narrativity, namely the uncanny, intertextuality, and singularity. Using these three schemes, respectively, in my reading of the three inaugural novels, I seek to demonstrate that Mitchell’s narrative innovations revoke our persistent compulsion to identify ‘the’ reader, but without doing away with the person doing the reading. In short, I aim to show how Mitchell’s writing invites what Valentine Cunningham calls “tactful” readings that would secure “the presence, the rights, the needs of the human subject” (2002: 143).Ph.D. (English
Revisiting the Status Quo of Road Safety Audits in South Africa 2019
No full textPapers presented at the 38th International Southern African Transport Conference on "Disruptive transport technologies - is South and Southern Africa ready?" held at CSIR International Convention Centre, Pretoria, South Africa on 8th to 11th July 2019.A Draft South African Road Safety Audit Manual (SARSAM) was published in 1999 under the guidance of the Committee for Land Transport Officials (COLTO). Early researchers lamented the lack of urgency in implementing road safety audits (Labuschagne, van As & Roodt, 2002). One of the constraints was the lack of training opportunities (van As, Steynberg, van Biljon & Scheepers, 2003). Sporadic training was provided by inter alia the CSIR (1999), Stellenbosch University (2010) and consulting engineering firms. The Education and Training Committee of the South African Road Federation (SARF) became involved in course presentation in 2014. Following the publishing of the second edition of the SARSAM (RTMC, 2012), the SARF course was revised in 2015/16.
To determine the status quo of road audits in South Africa, a survey was conducted of road safety auditors in the country. The current situation with respect to training and the execution of such audits was assessed. The paper did not investigate the quality of road safety audits reports or findings which will require in-depth research. The findings indicate the time auditors spend in the industry, their backgrounds, their level of satisfaction with courses as a whole, the presentations and the training material. There is general consensus that the prices tendered for audits is too low to ensure good quality service, but, notwithstanding, the low prices, clients receive good value for money. There is a concern that all processes, especially formal feedback, are not followed and completed
Crisis Periods, Contagion and Integration Effects in the Major African Equity Markets During the 2007-2009 Global Financial Crisis
No full textThe contribution of the first named author is based on research supported by the National Research Foundation, Grant Number 87502. We thank Antonie Kotzé for providing us with some of the data that we required in this paper.A number of studies assert that during critical events cross-market correlations change substantially. The main focus of this paper is to explicitly test two research hypotheses concerning the effect of increasing cross-market correlations in the 2007-2009 Global Financial Crisis (GFC) compared to the pre-crisis period. These hypotheses state that there was no contagion and no integration effects among the U.S., the U.K., and selected African stock markets (South Africa, Namibia, Egypt, Nigeria, Morocco and Kenya) during the GFC. The crisis periods are formally detected using a statistical method of dividing market states into bullish and bearish markets. The sample period begins in January 2003 and ends in December 2013, and it includes the 2007 U.S. subprime crisis. Obtained results indicate that there is no reason to reject both research hypotheses. Moreover, the results confirm a heterogeneity of the African equity markets in the context of the influence of the recent global crisis.Coenraad Labuschagne: [email protected]żbieta Majewska: [email protected] Olbryś: [email protected] Labuschagne - Department of Finance and Investment Management, University of JohannesburgElżbieta Majewska - Faculty of Mathematics and Informatics, University of BiałystokJoanna Olbryś - Faculty of Computer Science, Bialystok University of TechnologyAduda J., Masila J. M., Onsongo E. 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