Probability distributions of number of children and maternal age at various order births using age-specific fertility rates by birth order

In this study, a simple analytical framework to find the probability distributions of number of children and maternal age at various order births by making use of data on age-specific fertility rates by birth order was proposed. The proposed framework is applicable to both the period and cohort fertility schedules. The most appealing point of the proposed framework is that it does not require stringent assumptions. The proposed framework has been applied to the cohort birth order-specific fertility schedules of India and its different regions and period birth order-specific fertility schedules, including the United States of America, Russia, and the Netherlands, to demonstrate its usefulness.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.