Working Welfare Recipients: A Comparison of the Family Support Act and the Personal Responsibility and Work Opportunity Reconciliation Act

This Note compares the work requirements of the Family Support Act ( FSA ) with those promulgated by the Personal Responsibility and Work Opportunity Reconciliation Act ( PRWORA ) This Note concludes that the fairest and most effective welfare program offers a combination of work, education, and training, and proposes suggestions for implementing the existing work requirements to ensure long-term self sufficiency for welfare recipients

Intrinsically dynamic population models

Intrinsically dynamic models (IDMs) depict populations whose cumulative growth rate over a number of intervals equals the product of the long term growth rates (that is the dominant roots or dominant eigenvalues) associated with each of those intervals. Here the focus is on the birth trajectory produced by a sequence of population projection (Leslie) matrices. The elements of a Leslie matrix are represented as straightforward functions of the roots of the matrix, and new relationships are presented linking the roots of a matrix to its Net Reproduction Rate and stable mean age of childbearing. Incorporating mortality changes in the rates of reproduction yields an IDM when the subordinate roots are held constant over time. In IDMs, the birth trajectory generated by any specified sequence of Leslie matrices can be found analytically. In the Leslie model with 15 year age groups, the constant subordinate root assumption leads to reasonable changes in the age pattern of fertility, and equations (27) and (30) provide the population size and structure that result from changing levels of net reproduction. IDMs generalize the fixed rate stable population model. They can characterize any observed population, and can provide new insights into dynamic demographic behavior, including the momentum associated with gradual or irregular paths to zero growth.dynamic models, dynamic population models, eigenvalues, Leslie matrices, population momentum

The metastable birth trajectory

The metastable model generalizes the stable population model by allowing net maternity to change exponentially over age and time. As a result, the metastable model generates an exponentially quadratic birth trajectory, which is characterized by a constant proportion of births by age of mother. The metastable model is well suited to analyzing steady fertility declines and transitions between two regimes of fixed vital rates.dynamic population models, metastable population, quadratic exponential trajectory, stable population

Toward a General Model for Populations with Changing Rates

Formal demography has yet to move beyond assuming that demographic rates are constant over time, an assumption that is both unrealistic and constraining. To generalize the fixed rate stable model to the changing rate dynamic model, this paper explores the mathematical regularities that underlie the behavior of all populations. At any time, the composition of a population can be expressed in terms of current circumstances, using the rates of a "latent" stable model. Closed form solutions for the equations governing dynamic multistate models are not always possible, but are presented for certain special cases. Those solutions provide opportunities for specifying dynamic models of potentially great value, especially for analyses of cyclical and hierarchical populations.dynamic, mathematical demography, multistate, population models, stable population

On the Impact of Spatial Momentum

Momentum, the population growth that occurs after a fall in fertility to replacement level, has long been appreciated as a factor in the future population growth of many countries. This paper argues that another aspect of growing populations - their high proportion rural - is also a source of significant growth, and refers to the additional growth attributable to geographical redistribution as spatial momentum. Using simplifying assumptions, a model for analyzing spatial momentum is developed based on population composition, rates of growth, and levels of interregional migration. Calculations are then done using (i) hypothetical populations exhibiting a range of plausible demographic behavior, and (ii) the population of Mexico, 1970. The results show that spatial momentum can have a substantial impact on ultimate population size under commonly encountered circumstances.population growth, population momentum, spatial momentum, urbanization

2d Model Field Theories at Finite Temperature and Density

In certain 1+1 dimensional field theoretic toy models, one can go all the way from microscopic quarks via the hadron spectrum to the properties of hot and dense baryonic matter in an essentially analytic way. This "miracle" is illustrated through case studies of two popular large N models, the Gross-Neveu and the 't Hooft model - caricatures of the Nambu-Jona-Lasinio model and real QCD, respectively. The main emphasis will be on aspects related to spontaneous symmetry breaking (discrete or continuous chiral symmetry, translational invariance) and confinement.Comment: 90 pages, 27 figures, Contribution to the Festschrift in honor of Boris Ioffe, edited by M. Shifma

Minimal surfaces and eigenvalue problems

We show that metrics that maximize the k-th Steklov eigenvalue on surfaces with boundary arise from free boundary minimal surfaces in the unit ball. We prove several properties of the volumes of these minimal submanifolds. For free boundary minimal submanifolds in the ball we show that the boundary volume is reduced up to second order under conformal transformations of the ball. For two-dimensional stationary integer multiplicity rectifiable varifolds that are stationary for deformations that preserve the ball, we prove that the boundary length is reduced under conformal transformations. We also give an overview of some of the known results on extremal metrics of the Laplacian on closed surfaces, and give a survey of our recent results from [FS2] on extremal metrics for Steklov eigenvalues on compact surfaces with boundary.Comment: 17 pages. To appear in Contemporary Mathematic