School of Science
http://hdl.handle.net/10500/2736
Mon, 20 Feb 2017 15:35:40 GMT2017-02-20T15:35:40ZQuasi-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.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10500/219492015-01-01T00:00:00ZVariants 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.
Tue, 01 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10500/217952015-12-01T00:00:00Z2-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.
Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10500/212062015-09-01T00:00:00ZStatistical modeling of unemployment duration in South Africa
http://hdl.handle.net/10500/20982
Statistical modeling of unemployment duration in South Africa
Nonyana, Jeanette Zandile
Unemployment in South Africa has continued to be consistently high as indicated by the various reports published by Statistics South Africa. Unemployment is a global problem where in Organisation for Economic Co-operation and Development (OECD) countries it is related to economic condition. The economic conditions are not solely responsible for the problem of unemployment in South Africa. Consistently high unemployment rates are observed irrespective of the level of economic growth, where unemployment responds marginally to changes Gross Domestic Product (GDP). To understand factors that influence unemployment in South Africa, we need to understand the dynamics of the unemployed population. This study aims at providing a statistical tool useful in improving the understanding of the labour market and enhancing of the labour market policy relevancy. Survival techniques are applied to determine duration dependence, probabilities of exiting unemployment, and the association between socio-demographic factors and unemployment duration. A labour force panel data from Statistic South Africa is used to analyse the time it takes an unemployed person to find employment. The dataset has 4.9 million people who were unemployed during the third quarter of 2013. The data is analysed by computing non-parametric and semi-parametric estimates to avoid making assumption about the functional form of the hazard. The results indicate that the hazard of finding employment is reduced as people spend more time in unemployment (negative duration dependence). People who are unemployed for less than six months have higher hazard functions. The hazards of leaving unemployment at any given duration are significantly lower for people in the following categories - females, adults, education level of lower than tertiary, single or divorced, attending school or doing other activities prior to job search and no work experience. The findings suggest an existence of association between demographics and the length of stay in unemployment; which reflect the nature of the labour market. Due to lower exit probabilities young people spent more time unemployed thus growing out of the age group which is more likely to be employed. Seasonal jobs are not convenient for pregnant women and for those with young kids at their care thus decreasing their employment probabilities. Analysis of factors that affect employment probabilities should be based on datasets which have no seasonal components. The findings suggest that the seasonal components on the labour force panel impacted on the results. According to the findings analysis of unemployment durations can be improved by analysing men and women separately. Men and women have different challenges in the labour market, which influence the association between other demographic factors and unemployment duration
Tue, 01 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10500/209822015-12-01T00:00:00Z