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Equation 4 · Part 8 · Demography, Migration, and Urban Futures in Practice: An Advanced Technical Guide

subscript

Pa+1,s,t+1=Pa,s,t⋅Sa,s,t+Ma,s,tP_{a+1,s,t+1} = P_{a,s,t} \cdot S_{a,s,t} + M_{a,s,t}
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

Aging the cohort forward. For each one-year (or five-year) step, every age-sex cohort is advanced by applying an age-specific survival ratio — the probability of surviving from one age to the next, derived from a life table built out of registered deaths and mortality schedules — and then subtracting deaths and adding net migrants assigned to that same age and sex [ 1 ] . Symbolically, for a cohort of age a and sex s in year t : Pa+1,s,t+1=Pa,s,t⋅Sa,s,t+Ma,s,tP_{a+1,s,t+1} = P_{a,s,t} \cdot S_{a,s,t} + M_{a,s,t}. where P is the population count, S is the age-and-sex-specific survival ratio for that interval, and M is net migration assigned to that cohort during the interval. The youngest cohort in each step is not aged forward from an existing cohort; it…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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