School of Science
http://hdl.handle.net/10500/2736
2017-03-26T19:05:19ZUnderstanding patterns of aggregation in count data
http://hdl.handle.net/10500/22067
Understanding patterns of aggregation in count data
Sebatjane, Phuti
The term aggregation refers to overdispersion and both are used interchangeably in this thesis. In addressing the problem of prevalence of infectious parasite species faced by most rural livestock farmers, we model the distribution of faecal egg counts of 15 parasite species (13 internal parasites and 2 ticks) common in sheep and goats. Aggregation and excess zeroes is addressed through the use of generalised linear models. The abundance of each species was modelled using six different distributions: the Poisson, negative binomial (NB), zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), zero-altered Poisson (ZAP) and zero-altered negative binomial (ZANB) and their fit was later compared. Excess zero models (ZIP, ZINB, ZAP and ZANB) were found to be a better fit compared to standard count models (Poisson and negative binomial) in all 15 cases. We further investigated how distributional assumption a↵ects aggregation and zero inflation. Aggregation and zero inflation (measured by the dispersion parameter k and the zero inflation probability) were found to vary greatly with distributional assumption; this in turn changed the fixed-effects structure. Serial autocorrelation between adjacent observations was later taken into account by fitting observation driven time series models to the data. Simultaneously taking into account autocorrelation, overdispersion and zero inflation
proved to be successful as zero inflated autoregressive models performed better than zero inflated models in most cases. Apart from contribution to the knowledge of science, predictability of parasite burden will help farmers with effective disease management interventions. Researchers confronted with the task of analysing count data with excess zeroes can use the findings of this illustrative study as a guideline irrespective of their research discipline. Statistical methods from model selection, quantifying of zero inflation through to accounting for serial autocorrelation are described and illustrated.
2016-06-01T00:00:00ZQuasi-orthogonality and real zeros of some 2F2 and 3F2 polynomials
http://hdl.handle.net/10500/21949
Quasi-orthogonality and real zeros of some 2F2 and 3F2 polynomials
Johnston, Sarah Jane; Jordaan, Kerstin
In this paper, we prove the quasi-orthogonality of a family of 2F2 polynomials and several classes of 3F2 polynomials that do not appear in the Askey scheme for hypergeometric orthogonal polynomials. Our results include, as a special case, two 3F2 polynomials considered by Dickinson in 1961. We also discuss the location and interlacing of the real zeros of our polynomials.
2015-01-01T00:00:00ZVariants of P-frames and associated rings
http://hdl.handle.net/10500/21795
Variants of P-frames and associated rings
Nsayi, Jissy Nsonde
We study variants of P-frames and associated rings, which can be viewed as natural
generalizations of the classical variants of P-spaces and associated rings. To be more
precise, we de ne quasi m-rings to be those rings in which every prime d-ideal is either
maximal or minimal. For a completely regular frame L, if the ring RL of real-valued
continuous functions of L is a quasi m-ring, we say L is a quasi cozero complemented
frame. These frames are less restricted than the cozero complemented frames. Using
these frames we study some properties of what are called quasi m-spaces, and observe
that the property of being a quasi m-space is inherited by cozero subspaces, dense z-
embedded subspaces, and regular-closed subspaces among normal quasi m-space.
M. Henriksen, J. Mart nez and R. G. Woods have de ned a Tychono space X to be a
quasi P-space in case every prime z-ideal of C(X) is either minimal or maximal. We call a
point I of L a quasi P-point if every prime z-ideal of RL contained in the maximal ideal
associated with I is either maximal or minimal. If all points of L are quasi P-points, we
say L is a quasi P-frame. This is a conservative de nition in the sense that X is a quasi
P-space if and only if the frame OX is a quasi P-frame. We characterize these frames
in terms of cozero elements, and, among cozero complemented frames, give a su cient
condition for a frame to be a quasi P-frame.
A Tychono space X is called a weak almost P-space if for every two zero-sets E and
F of X with IntE IntF, there is a nowhere dense zero-set H of X such that E F [H.
We present the pointfree version of weakly almost P-spaces. We de ne weakly regular
rings by a condition characterizing the rings C(X) for weak almost P-spaces X. We
show that a reduced f-ring is weakly regular if and only if every prime z-ideal in it which contains only zero-divisors is a d-ideal. We characterize the frames L for which the ring
RL of real-valued continuous functions on L is weakly regular.
We introduce the notions of boundary frames and boundary rings, and use them to
give another ring-theoretic characterization of boundary spaces. We show that X is a
boundary space if and only if C(X) is a boundary ring.
A Tychono space whose Stone- Cech compacti cation is a nite union of closed subspaces
each of which is an F-space is said to be nitely an F-space. Among normal spaces,
S. Larson gave a characterization of these spaces in terms of properties of function rings
C(X). By extending this notion to frames, we show that the normality restriction can
actually be dropped, even in spaces, and thus we sharpen Larson's result.
2015-12-01T00:00:00Z2-ARYL-6,8-Dibromoquinolinones as synthons for the synthesis of Polysubstituted 4-ARYL-6-Oxopyrrolo [3,2,1-ij] Quinolines
http://hdl.handle.net/10500/21206
2-ARYL-6,8-Dibromoquinolinones as synthons for the synthesis of Polysubstituted 4-ARYL-6-Oxopyrrolo [3,2,1-ij] Quinolines
Oyeyiola, Felix Adetunji
The known 2-aryl-6,8-dibromo-2,3-dihydroquinolin-4(1H)-ones 122 were dehydrogenated
using thallium(III) p-tolylsulfonate in dimethoxyethane under reflux to afford the 2-aryl-6,8-dibromoquinolin-4(1H)-ones 136. Palladium-catalyzed Sonogashira cross-coupling of the 2-aryl-6,8-dibromo-2,3-dihydroquinolin-4(1H)-ones with terminal alkynes in the presence of PdCl2(PPh3)2-CuI (as homogeneous catalyst source) and 10% Pd/C-PPh3-CuI (as heterogeneous catalyst source) catalyst mixture and NEt3 as a base and co-solvent in ethanol under reflux afforded the corresponding 6,8-dialkynyl-2-aryl-2,3-dihydroquinolin-4(1H)-ones 138 and 8-alkynyl-2-aryl-6-bromo-2,3-dihydroquinolin-4(1H)-ones 137, respectively. PdCl2-catalyzed
electrophilic cyclization of the 8-alkynyl-2-aryl-6-bromo-2,3-dihydroquinolin-4(1H)-ones in acetonitrile under reflux afforded the 4-aryl-8-bromo-2-phenyl-6H-pyrrolo[3,2,1-ij]quinolin-6-ones 139 or the 2-aryl-6-bromo-8-(4-hydroxybutanoyl)-2,3-dihydroquinolin-4(1H)-ones 140 from the 4-phenylethynyl-substituted or 4-alkylethynyl-substituted precursors, respectively. The 2-aryl-6,8-dibromoquinolin-4(1H)-ones 136 wturn, subjected to similar homogeneous and heterogeneous palladium catalyst sources using NEt3 as a base in DMF-water mixture under reflux and K2CO3 as a base in dioxane under reflux afforded 2,8-disubstituted 4-aryl-6-oxopyrrolo[3,2,1-ij]quinolines 143 and 2-substituted 4-aryl-8-bromo-6-oxopyrrolo[3,2,1-ij]quinolines 142, respectively. The monoalkynylated 4-aryl-8-bromo-2-phenyl-6H-pyrrolo[3,2,1-ij]quinolin-6-ones 139 and 2-substituted 4-aryl-8-bromo-6-oxopyrrolo[3,2,1-ij]quinolines 142 were subsequently transformed using palladium-catalyzed Suzuki-Miyaura cross-coupling with arylboronic acids in the presence of PdCl2(PPh3)2-PCy3 catalyst mixture and K2CO3 as a base in dioxane-water mixture to afford the corresponding novel 8-substituted 2-phenyl-6H-pyrrolo[3,2,1-ij]quinolin-6-ones 141 and 2,8-disubstituted 4-aryl-6-oxopyrrolo[3,2,1-ij]quinolines 144, respectively. All the new compounds were characterized using a combination of 1H NMR, 13C NMR, IR, mass spectroscopic techniques and X-ray crystallography.
2015-09-01T00:00:00Z