University, Diss., 2002--Tübingen.

The classical SIR and SIS epidemiological models are extended by considering the number of adequate contacts per infective in unit time as a function of the total population in such a way that this number grows less rapidly as the total population increases. A diffusion term is added to the SIS model and this leads to a reaction–diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the SIR and SIS models, with the disease–free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, for both models, the endemic equilibrium is locally asymptotically stable and traveling wave solutions are found for the SIS diffusion model. Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous SIR and SIS models are presented. In particular, for the SIS model, a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided. On the other hand the SIS model is extended to a Volterra integral equation, for which the existence of multiple endemic equilibria is proved. This fact is confirmed by numerical simulations. / Dissertation (MSc)--University of Pretoria, 2012. / Mathematics and Applied Mathematics / unrestricted

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L'objet de ce travail est l'étude des points tournants dégénérés. Nous considèrerons des équations différentielles réelles, du premier ordre, singulièrement perturbées à un paramètre réel et admettant une telle singularité. En nous plaçant dans les hypothèses d'apparition de solutions (de type) "vrai canard", nous donnerons alors à cette équation une forme, dite préparée, plus adaptée au travail que nous effectuerons.<br />Nous montrerons ensuite, pour une classe générale d'équations de ce type, l'existence de solutions "canard". À la suite de quoi, nous étudierons asymptotiquement ces solutions à travers la mise en place d'un cadre formel général. La correspondance ainsi mise en place nous permettra d'implémenter le développement asymptotique en puissances du petit paramètre de perturbation de ces solutions.

By considering Krylov subspace methods in nonstandard inner products, we develop in this thesis new methods for solving large sparse linear systems and examine the effectiveness of existing preconditioners. We focus on saddle point systems and systems with a nonsymmetric, diagonalizable coefficient matrix. For symmetric saddle point systems, we present a preconditioner that renders the preconditioned saddle point matrix nonsymmetric but self-adjoint with respect to an inner product and for which scaling is not required to apply a short-term recurrence method. The robustness and effectiveness of this preconditioner, when applied to a number of test problems, is demonstrated. We additionally utilize combination preconditioning (Stoll and Wathen. SIAM J. Matrix Anal. Appl. 2008; 30:582-608) to develop three new combination preconditioners. One of these is formed from two preconditioners for which only a MINRES-type method can be applied, and yet a conjugate-gradient type method can be applied to the combination preconditioned system. Numerical experiments show that application of these preconditioners can result in faster convergence. When the coefficient matrix is diagonalizable, but potentially nonsymmetric, we present conditions under which the pseudospectra of a preconditioner and coefficient matrix are identical and characterize the pseudospectra when this condition is not exactly fulfilled. We show that when the preconditioner and coefficient matrix are self-adjoint with respect to nearby symmetric bilinear forms the convergence of a particular minimum residual method is bounded by a term that depends on the spectrum of the preconditioned coefficient matrix and a constant that is small when the symmetric bilinear forms are close. An iteration-dependent bound for GMRES in the Euclidean inner product is presented that shows precisely why a standard bound can be pessimistic. We observe that for certain problems known, effective preconditioners are either self-adjoint with respect to the same symmetric bilinear form as the coefficient matrix or one that is nearby.

This dissertation examines four disadvantaged groups in the labour market from a variety of perspectives. Specifically, I looked into older workers, younger workers, nonstandard workers and female workers. In the first chapter, I examine the effects of Ontario eliminating mandatory retirement in 2006 on the labour force participation of older workers and the unemployment of younger workers. My second chapter examines the relationship between nonstandard employment and the subsequent workplace profitability. In my final chapter, I examine the interaction effect of employment status and gender on the issue of work hour mismatches. The first chapter examines the impact of recent labour policy change at a national/provincial level. I find positive and significant effects for the labour force participation rate of older workers in Ontario in the five years following the legislation change of banning mandatory retirement in Onatrio. Similar results are found for both men and women; however, the magnitude of this effect is somewhat smaller for men. In addition, the empirical analysis also reveals a short-run rise in the unemployment rate of younger workers. The second chapter examines the financial implication of nonstandard employment at an organizational level. The results suggest that nonstandard employment is positively associated with subsequent workplace profitability, after controlling for factors that might also affect profitability. Moreover, this significant positive relationship between nonstandard employment and subsequent profitability is primarily driven by capital intensive manufacturing, the real estate/rental/leasing, the retail/trade/consumer service, and the education and health services industries as well as smaller workplaces. Larger workplaces and the rest of the private sector do not display significant results. The final chapter looks into how employment status and gender systematically impact work hour preferences at an individual level. The findings indicate that there is a significant interaction effect between nonstandard employment and gender. Female nonstandard workers prefer to work more hours. Male workers, both nonstandard and standard, are more likely to prefer to work fewer or the same hours. These results conform to labour market trend of increasing labour force participation rates of females and a declining trend among males.

This dissertation examines four disadvantaged groups in the labour market from a variety of perspectives. Specifically, I looked into older workers, younger workers, nonstandard workers and female workers. In the first chapter, I examine the effects of Ontario eliminating mandatory retirement in 2006 on the labour force participation of older workers and the unemployment of younger workers. My second chapter examines the relationship between nonstandard employment and the subsequent workplace profitability. In my final chapter, I examine the interaction effect of employment status and gender on the issue of work hour mismatches. The first chapter examines the impact of recent labour policy change at a national/provincial level. I find positive and significant effects for the labour force participation rate of older workers in Ontario in the five years following the legislation change of banning mandatory retirement in Onatrio. Similar results are found for both men and women; however, the magnitude of this effect is somewhat smaller for men. In addition, the empirical analysis also reveals a short-run rise in the unemployment rate of younger workers. The second chapter examines the financial implication of nonstandard employment at an organizational level. The results suggest that nonstandard employment is positively associated with subsequent workplace profitability, after controlling for factors that might also affect profitability. Moreover, this significant positive relationship between nonstandard employment and subsequent profitability is primarily driven by capital intensive manufacturing, the real estate/rental/leasing, the retail/trade/consumer service, and the education and health services industries as well as smaller workplaces. Larger workplaces and the rest of the private sector do not display significant results. The final chapter looks into how employment status and gender systematically impact work hour preferences at an individual level. The findings indicate that there is a significant interaction effect between nonstandard employment and gender. Female nonstandard workers prefer to work more hours. Male workers, both nonstandard and standard, are more likely to prefer to work fewer or the same hours. These results conform to labour market trend of increasing labour force participation rates of females and a declining trend among males.

This thesis is a survey of the studies of Ames,Payne and Schaefer about the partial differential equations with nonstandard auxiliary conditions / this is where the values of the solution are prescribed as a combination of initial time t=0 and at a later time t=T. The first chaper is introductory and contains some historical background of the problem,basic definitions and theorems.In Chapter 2 energy bounds and pointwise bounds for the solutions of the nonstandard hyperbolic problems have been investigated and by means of energy bound the uniqueness of solutions is examined. Similar discussions for the nonstandard parabolic problems have been presented in Chapter 3. Lastly in Chapter 4 a new continuous dependence result has been derived for the nonstandard problem.

abstract: Over the last three decades there has been a rise in the number of workers employed during nonstandard (evening and overnight) hours; accompanying this trend has been a renewed interest in documenting workers, their families, and outcomes associated with nonstandard-hour employment. However, there are important gaps in the current literature. Few have considered how parents who work nonstandard hours care for their children when parental care is unavailable; little is known about who participates in nonparental child care during nonstandard hours, or the characteristics of those who participate. Most pressingly from a policy perspective, it is unclear how participation in nonparental child care during nonstandard hours influences child well-being. This study aims to fill these gaps. This dissertation paints a descriptive portrait of children and parents who use nonstandard child care, explores the relationship between nonstandard hours of nonparental child care participation and various measures of child well-being, and identifies longitudinal patterns of participation in nonstandard-hour child care. I find that children who participate in nonstandard-hours of nonparental child care look significantly different from those who do not participate. In particular, children are more likely to be older, identify as black or Hispanic, and reside with younger, unmarried parents who have lower levels of education. Estimates also suggest a negative relationship between participation in nonstandard-hour child care and child well-being. Specifically, children who participate in nonstandard-hour care show decreased school engagement and school readiness, increased behavioral problems, decreased social competency, and lower levels of physical health. These findings have serious implications for social and education policy. / Dissertation/Thesis / Doctoral Dissertation Public Policy 2015

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22978号 / 理博第4655号 / 新制||理||1669(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 照井 一成, 教授 長谷川 真人, 准教授 河村 彰星 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM