title: About Laplace transforms of the distribution of births in the initial population with unchanging net maternity rates.
abstract: "The solutions of the integral equation for the stable population by Laplace transform have been examined by shifting the origin from t=0 to other points in time.  The relationship between the birth functions generated by the initial populations measured from different points of time has been found to be very simple and straight forward."  The author also shows "that for a stable population, the total number of births in the next generation can be expressed as a simple function of the net reproduction rate, the intrinsic rate of growth and number of births at the beginning of the process.  For the stationary population, the same relationship simplifies even further and is given in terms of the product of the number of births at the beginning of the process and the average age of motherhood."
authors.forename: S
authors.initials: S
authors.lastname: Mitra
mesh_terms: D000367:Age Factors; D003710:Demography; D005298:Fertility; D008423:Maternal Age; D008962:Models, Theoretical; D010290:Parents; D011153:Population; D011154:Population Characteristics; D011156:Population Density; D011157:Population Dynamics; D011158:Population Growth; D012106:Research
keywords: Age Factors; Demographic Analysis; Demographic Factors; Fertility; Maternal Age; Mathematical Model; Models, Theoretical; Parental Age; Population; Population Characteristics; Population Dynamics; Population Growth; Population Size; Research Methodology; Stable Population; Theoretical Studies; World