School of Science
http://hdl.handle.net/10500/2736
Sun, 18 Mar 2018 11:49:33 GMT2018-03-18T11:49:33ZTopics on z-ideals of commutative rings
http://hdl.handle.net/10500/23619
Topics on z-ideals of commutative rings
Tlharesakgosi, Batsile
The first few chapters of the dissertation will catalogue what is known regarding z-ideals in
commutative rings with identity. Some special attention will be paid to z-ideals in function
rings to show how the presence of the topological description simplifies z-covers of arbitrary
ideals. Conditions in an f-ring that ensure that the sum of z-ideals is a z-ideal will be given.
In the latter part of the dissertation I will generalise a result in higher order z-ideals and
introduce a notion of higher order d-ideals
Tue, 01 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10500/236192017-08-01T00:00:00ZGene expression programming for logic circuit design
http://hdl.handle.net/10500/23617
Gene expression programming for logic circuit design
Masimula, Steven Mandla
Finding an optimal solution for the logic circuit design problem is challenging and time-consuming especially
for complex logic circuits. As the number of logic gates increases the task of designing optimal logic circuits
extends beyond human capability. A number of evolutionary algorithms have been invented to tackle a range
of optimisation problems, including logic circuit design. This dissertation explores two of these evolutionary
algorithms i.e. Gene Expression Programming (GEP) and Multi Expression Programming (MEP) with the
aim of integrating their strengths into a new Genetic Programming (GP) algorithm. GEP was invented by
Candida Ferreira in 1999 and published in 2001 [8]. The GEP algorithm inherits the advantages of the Genetic
Algorithm (GA) and GP, and it uses a simple encoding method to solve complex problems [6, 32]. While
GEP emerged as powerful due to its simplicity in implementation and
exibility in genetic operations, it is
not without weaknesses. Some of these inherent weaknesses are discussed in [1, 6, 21]. Like GEP, MEP is a
GP-variant that uses linear chromosomes of xed length [23]. A unique feature of MEP is its ability to store
multiple solutions of a problem in a single chromosome. MEP also has an ability to implement code-reuse which
is achieved through its representation which allow multiple references to a single sub-structure.
This dissertation proposes a new GP algorithm, Improved Gene Expression Programming (IGEP) which im-
proves the performance of the traditional GEP by combining the code-reuse capability and simplicity of gene encoding method from MEP and GEP, respectively. The results obtained using the IGEP and the traditional
GEP show that the two algorithms are comparable in terms of the success rate when applied on simple problems
such as basic logic functions. However, for complex problems such as one-bit Full Adder (FA) and AND-OR
Arithmetic Logic Unit (ALU) the IGEP performs better than the traditional GEP due to the code-reuse in IGEP
Sun, 01 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10500/236172017-10-01T00:00:00ZDevelopment and application of dispersive liquid-liquid microextraction for the determination of tetracyclines in meat by liquid chromatography tandem mass spectrometry
http://hdl.handle.net/10500/23201
Development and application of dispersive liquid-liquid microextraction for the determination of tetracyclines in meat by liquid chromatography tandem mass spectrometry
Mookantsa, Sandy Oshi Squizer
An environmentally friendly, rapid and cost effective analytical procedure based on dispersive liquid-liquid microextraction was developed for the determination of six tetracyclines (TCs) in meat destined for human consumption. Meat extracts were analyzed for TCs using a sensitive and selective analytical technique, liquid chromatography tandem mass spectrometry. Various influencing factors on the extraction, separation and determination of TCs such as pH of mobile phases, type and volume of disperser solvent, type and volume of extraction solvent and sample pH were optimized. Validation parameters such as calibration function, limit of detection (LOD), limit of quantification (LOQ), detection capability (CCα), decision limit (CCβ), accuracy and precision were established according to EU commission decision 2002/657/EC. Linearity in the range of 25-200 μg kg-1 was obtained with regression coefficients ranging from 0.9991 to 0.9998. Recoveries of spiked blank muscle samples at three levels (i.e. 50, 100 and 150 μg kg-1) ranged from 80 to 101% and reproducibility was between 2 and 7%. The LODs and LOQs ranged from 2.22 to 3.59 μg kg-1 and from 7.38 to 11.49 μg kg-1 respectively. The CCα ranged from 105 to 111 μg kg-1 while CCβ ranged from 107 to 122 μg kg-1. The proposed method compared well with the dispersive solid phase extraction method and was successfully applied to the determination of TCs in meat samples. Some of the thirty bovine muscle samples obtained from local abattoirs and butcheries were found to contain two tetracycline antibiotics residues (chlortetracycline and oxytetracycline) with oxytetracycline being the most commonly detected. The concentration levels of the TC residues detected in the eleven bovine muscle samples were between 12.4 and 68.9 μg kg-1, levels that are lower than the European Union set maximum residue level (MRL) of 100 μg kg-1 hence the meat was fit for human consumption.
Mon, 01 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10500/232012016-02-01T00:00:00ZMathematical symbolisation: challenges and instructional strategies for Limpopo Province secondary school learners
http://hdl.handle.net/10500/23154
Mathematical symbolisation: challenges and instructional strategies for Limpopo Province secondary school learners
Mutodi, Paul
This study reports on an investigation into the manner in which mathematical symbols influence learners’ understanding of mathematical concepts. The study was conducted in Greater Sekhukhune and Capricorn districts of Limpopo Province, South Africa. Multistage sampling (for the district), simple random sampling (for the schools), purposive sampling (for the teachers) and stratified random sampling with proportional allocation (for the learners) were used. The study was conducted in six schools randomly selected from rural, semi-urban and urban settings. A sample of 565 FET learners and 15 FET band mathematics teachers participated in the study. This study is guided by four interrelated constructivist theories: symbol sense, algebraic insight, APOS and procept theories. The research instruments for the study consist of questionnaires and interviews. A mixed method approach that was predominantly qualitative was employed. An analysis of learners’ difficulties with mathematical symbols produced three (3) clusters. The main cluster consists of 236 (41.6%) learners who indicate that they experience severe challenges with mathematical symbols compared to 108 (19.1%) learners who indicated that they could confidently handle and manipulate mathematical symbols with understanding. Six (6) categories of challenges with mathematical symbols emerged from learners’ encounters with mathematical symbols: reading mathematical text and symbols, prior knowledge, time allocated for mathematical classes and activities, lack of symbol sense and problem contexts and pedagogical approaches to mathematical symbolisation. Two sets of theme classes related to learners’ difficulties with mathematical symbols and instructional strategies emerged. Learners lack symbol sense for mathematical concepts and algebraic insight for problem solving. Learners stick to procedurally driven symbols at the expense of conceptual and contextual understanding. From a pedagogical perspective teachers indicated that they face the following difficulties when teaching: the challenge of introducing unfamiliar notation in a new topic; reading, writing and verbalising symbols; signifier and signified connections; and teaching both symbolisation and conceptual understanding simultaneously. The study recommends teachers to use strategies such as informed choice of subject matter and a pedagogical approach in which concepts are understood before they are symbolised.
Thu, 01 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10500/231542016-09-01T00:00:00Z