BACKGROUND Little attention is given to the role of migration in global population projection models. Most demographers set future levels of net migration on trajectories towards zero in all countries, nullifying the impact of migration on long-run projected populations. Yet as fertility and mortality rates fall, the role of migration on future population change is becoming more pronounced. OBJECTIVES In this paper we develop future long-run migration scenarios to provide a range of possible outcomes. METHODS Our alternative migration scenarios are linked to the Shared Socioeconomic Pathways (SSP), widely used in research on global environmental change. These are utilized as inputs for a global cohort component projection model to obtain population totals up until 2100 for all countries. CONTRIBUTION The results illustrate the important role of migration assumptions in long-run projections, especially in post-demographic-transition countries. Further, they provide plausible alternatives to projections based on the commonly used, but poorly justified, convergence towards a zero net migration assumption.

This study deals with Utah household projections by age and sex for five-year intervals from 1970-2000. Projections are based on the method used by the bureau of the Census with certain modifications. Two sets of the population projects prepared by the Utah Agricultural Experiment Station, high and low medium, are chosen as the population base. By assuming the household formation pattern in two alternate ways, constant rates and exponential growth rates, two sets of household projections are prepared for each of the two sets of population projections. This study also makes some examinations on the social and economic implications of these projections. The 1960 and 1970 census data are used to project the furniture household headship rates. The households are projected in five categories: Husband-wife household, other male family head, female family head, male primary individual, and female primary individual. Being the prerequisite for household projection, the future population distribution by marital status, namely, single (never married), married with spouse present, and other married, is also prepared.

Let X be a compact Hausdorff topological space. The Banach space C(X) consists of all continuous complex value functions with the supnorm. An operator P on C(X) is called a generalized bicircular projection if P + £f(I − P) is an isometry for all |£f| = 1, £f in C and P2 = P. In this thesis, we study some projections which are the averages of two composition operators or two weighted composition operators on C(X). If a projection is the average of the identity and a composition operator, it is a generalized bicircular projection. And give an example of a projection which is the average of the identity and a weighted composition operator, but not a generalized bicircular projection. We also discuss some projections which are the average of two bounded linear operators on a Banach space. And the main result is that, let T1 and T2 are two bounded linear operators on a Banach space, and Q = T1+T2 2 . If T1 ¡CT2 = T2 ¡CT1 and T2 1 = T2 2 = Id then Q is a tripotent, i.e. Q3 = Q.

Depending on whether the global level of fertility is assumed to converge to the current European TFR (~1.5) or that of Southeast Asia or Central America (~2.5), global population will either decline to 2.3-2.9 billion by 2200 or increase to 33-37 billion, if mortality continues to decline. Furthermore, sizeable human populations exist when the 'voluntary chosen' ideal family size is heavily concentrated around one child per woman with TFRs as low as 0.6-0.8. However, the UN population projections to 2300 use a much narrower band of possible future TFRs. If the two-child norm is not necessarily the end-point transition, what would be the consequences of the currently reported low fertility rates being sustained and becoming widespread? We present new projections for 13 IPCC world regions with scenarios calculated on the basis of regular cohort-component projections by age and sex in single-year time steps up to 2300, each based upon a much broader set of fertility assumptions than currently employed. We create three mortality scenarios based upon maximum life expectancies of 90, 100, 110, as well as a series of "Special" scenarios. Even under conditions of further substantial increases in life expectancy, world population size would decline significantly if the world in the longer run followed the examples of Europe and East Asia. In contrast to Malthusian disaster scenarios, our exercise illustrates the distinct possibility of significant population shrinking associated with increasing life expectancy and human well-being.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Within the next decade India is expected to surpass China as the world's most populous country due to still higher fertility and a younger population. Around 2025 each country will be home to around 1.5 billion people. India is demographically very heterogeneous with some rural illiterate populations still having more than four children on average while educated urban women have fewer than 1.5 children and with great differences between states. We show that the population outlook greatly depends on the degree to which this heterogeneity is explicitly incorporated into the population projection model used. The conventional projection model, considering only the age and sex structures of the population at the national level, results in a lower projected population than the same model applied at the level of states because over time the high-fertility states gain more weight, thus applying the higher rates to more people. The opposite outcome results from an explicit consideration of education differentials because over time the proportion of more educated women with lower fertility increases, thus leading to lower predicted growth than in the conventional model. To comprehensively address this issue, we develop a five-dimensional model of India's population by state, rural/urban place of residence, age, sex, and level of education and show the impacts of different degrees of aggregation. We also provide human capital scenarios for all Indian states that suggest that India will rapidly catch up with other more developed countries in Asia if the recent pace of education expansion is maintained.

The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant under automorphisms of a binary tree. We present a technique by which a slightly relaxed form of the generalized Fourier transform in this case can eventually be computed using only simple tools from linear algebra, which has possible advantages in computational efficiency.

Enrollment projections are used by school administrators to predict the number of students expected to attend a school district within a defined period of time. This dissertation examines methods used for making enrollment projections and seeks to improve these methods through the application of geographic principles. The presented thesis challenges the existing aspatial framework used to calculate grade progression rates, arguing that a spatial framework improves projection accuracy. Grade progression rates are the critical element in enrollment projections and this dissertation's major contribution is the analysis of four different grade progression rate calculations at the school district level. This dissertation also argues that grade progression rates represent spatial relationships of migration that exist between adjacent school districts and uses these spatial relationships to create a new spatial Bayesian approach. This dissertation demonstrates that geographic methods can be successfully integrated to improve enrollment project accuracy through the reduction of the small number problem. In addition, this research identifies the importance of smoothing effects of the modified cohort progression method when compared to Bayesian approaches.

No description available.

This thesis is concerned with the approximation of Cartesian coordinate data by parametric curves and surfaces, with an emphasis upon a technique known as parametric orthogonal distance regression (parametric ODR). The technique has become increasingly popular in the literature over the past decade and has applications in a wide range of fields, including metrology-the science of measurement, and computer aided design (CAD) modelling. Typically, the data are obtained by recording points measured in the surface of some physical artefact, such as a manufactured part. Parametric ODR involves minimizing the shortest distances from the data to the curve or surface in some norm. Under moderate assumptions, these shortest distances are orthogonal projections from the data onto the approximant, hence the nomenclature ODR. The motivation behind this type of approximation is that, by using a distance-based measure, the resulting best fit curve or surface is independent of the position or orientation of the physical artefact from which the data is obtained. The thesis predominately concerns itself with parametric ODR in a least squares setting, although it is indicated how the techniques described can be extended to other error measures in a fairly straightforward manner. The parametric ODR problem is formulated mathematically, and a detailed survey of the existing algorithms for solving it is given. These algorithms are then used as the basis for developing new techniques, with an emphasis placed upon their efficiency and reliability. The algorithms (old and new) detailed in this thesis are illustrated by problems involving well-known geometric elements such as lines, circles, ellipse and ellipsoids, as well as spline curves and surfaces. Numerical considerations specific to these individual elements, including ones not previously reported in the literature, are addressed. We also consider a sub-problem of parametric ODR known as template matching, which involves mapping in an optimal way a set of data into the same frame of reference as a fixed curve or surface.