School of Science
http://hdl.handle.net/10500/2736
Tue, 31 Mar 2015 00:42:23 GMT2015-03-31T00:42:23ZA Lie symmetry analysis of the heat equation through modified one-parameter local point transformation
http://hdl.handle.net/10500/18414
A Lie symmetry analysis of the heat equation through modified one-parameter local point transformation
Adams, Conny Molatlhegi
Using a Lie symmetry group generator and a generalized form of Manale's formula
for solving second order ordinary di erential equations, we determine new symmetries
for the one and two dimensional heat equations, leading to new solutions. As
an application, we test a formula resulting from this approach on thin plate heat
conduction.
Fri, 01 Aug 2014 00:00:00 GMThttp://hdl.handle.net/10500/184142014-08-01T00:00:00ZA Lie symmetry analysis of the Black-Scholes Merton finance model through modified local one-parameter transformations
http://hdl.handle.net/10500/18410
A Lie symmetry analysis of the Black-Scholes Merton finance model through modified local one-parameter transformations
Masebe, Tshidiso Phanuel
The thesis presents a new method of Symmetry Analysis of the Black-Scholes Merton
Finance Model through modi ed Local one-parameter transformations. We determine
the symmetries of both the one-dimensional and two-dimensional Black-Scholes
equations through a method that involves the limit of in nitesimal ! as it approaches
zero. The method is dealt with extensively in [23]. We further determine an invariant
solution using one of the symmetries in each case. We determine the transformation
of the Black-Scholes equation to heat equation through Lie equivalence transformations.
Further applications where the method is successfully applied include working out
symmetries of both a Gaussian type partial di erential equation and that of a di erential
equation model of epidemiology of HIV and AIDS. We use the new method to
determine the symmetries and calculate invariant solutions for operators providing
them.
Mon, 01 Sep 2014 00:00:00 GMThttp://hdl.handle.net/10500/184102014-09-01T00:00:00ZDeep space radiations-like effects on VO2 smart nano-coatings for heat management in small satelittes
http://hdl.handle.net/10500/18408
Deep space radiations-like effects on VO2 smart nano-coatings for heat management in small satelittes
Mathevula, Langutani Eulenda
Thermal control in spacecraft will be increasingly important as the spacecraft grows smaller and more compact. Such spacecraft with low thermal mass will have to be designed to retain or reject heat more efficiently. The passive smart radiation device (SRD) is a new type of thermal control material for spacecraft. Current space thermal control systems require heaters with an additional power penalty to maintain spacecraft temperatures during cold swings. Because its emissivity can be changed without electrical instruments or mechanical part, the use of SRD decreases the request of spacecraft power budget. The (SRD) based on VO2 films is one of the most important structures of the functional thermal control surface, being lighter, more advanced and without a moving devices. A large portion of the heat exchange between an object in space and the environment is performed throughout radiation, which is in turn determined by the object surface properties. The modulation device is coated on the spacecraft surface and thus provides a thermal window that can adapt to the changing conditions in orbit.
VO2 is well known to have a temperature driven metal to insulator transition ≈ 68ᴼC accompanying a transformation of crystallographic structure, from monoclinic (M-phase, semiconductor) at temperature below 68ᴼC to tetragonal (R-phase, metal) at temperature above 68ᴼC. This transition temperature is accompanied by an increase of infrared reflectivity and a decrease of infrared emissivity with increasing temperature. This flexibility makes VO2 potentially interesting for optical, electrical, and electro-optical switches devices, and as window for energy efficiency buildings applications. This study reports on effect of thickness on VO2 as well as the effect of proton irradiation on VO2 for active smart radiation device (SRD) application. VO2 was deposited on mica by Pulsed laser deposition techniques. The thickness of the film was varied by varying the deposition time. To characterize VO2 the following techniques were performed: XRD, AFM, SEM, TEM, XPS, RBS, RAMAN and transport measurements for optical properties. The effect of proton irradiation was observed using the SEM, where the change in structure, from crystal grains to rods, was observed.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10500/184082014-01-01T00:00:00ZThe application and empirical comparison of item parameters of Classical Test Theory and Partial Credit Model of Rasch in performance assessments
http://hdl.handle.net/10500/18362
The application and empirical comparison of item parameters of Classical Test Theory and Partial Credit Model of Rasch in performance assessments
Mokilane, Paul Moloantoa
This study empirically compares the Classical Test Theory (CTT) and the Partial Credit Model
(PCM) of Rasch focusing on the invariance of item parameters. The invariance concept which is
the consequence of the principle of specific objectivity was tested in both CTT and PCM using the
results of learners who wrote the National Senior Certificate (NSC) Mathematics examinations in
2010. The difficulty levels of the test items were estimated from the independent samples of learn-
ers. The same sample of learners used in the calibration of the difficulty levels of the test items in
the PCM model were also used in the calibration of the difficulty levels of the test items in CTT
model. The estimates of the difficulty levels of the test items were done using RUMM2030 in the
case of PCM while SAS was used in the case of CTT. RUMM2030 and SAS are both the statistical
softwares. The analysis of variance (ANOVA) was used to compare the four different design groups
of test takers. In cases where the ANOVA showed a significant difference between the means of the
design groups, the Tukeys groupings was used to establish where the difference came from.
The research findings were that the test items' difficulty parameter estimates based on the CTT theoretical framework were not invariant across the different independent sample groups. The over-
all findings from this study were that the CTT theoretical framework was unable to produce item
difficulty invariant parameter estimates. The PCM estimates were very stable in the sense that for
most of the items, there was no significant difference between the means of at least three design
groups and the one that deviated from the rest did not deviate that much. The item parameters of
the group that was representative of the population (proportional allocation) and the one where the
same number of learners (50 learners) was taken from different performance categories did not differ
significantly for all the items except for item 6.6 in examination question paper 2. It is apparent
that for the test item parameters to be invariant of the group of test takers in PCM, the group of
test takers must be heterogeneous and each performance category needed to be big enough for the proper calibration of item parameters.
The higher values of the estimated item parameters in CTT were consistently found in the sample
that was dominated by the high proficient learners in Mathematics ("bad") and the lowest values
were consistently calculated in the design group that was dominated by the less proficient learners. This phenomenon was not apparent in the Rasch model.
Thu, 01 May 2014 00:00:00 GMThttp://hdl.handle.net/10500/183622014-05-01T00:00:00Z