As an example, the filter-based case presented in Section 3 (centered at zero frequency) yields the same asymptotic limit as the one reported in , which applies to filter-based cases centered at a non-zero frequency.
Comparing expression (18) to expression (8), we can see that the derived upper asymptotic limit for this linear and causal medium, given by its 1st order phase approximation, has the same square root form, and its coefficient is larger (by 29%).
The asymptotic limit for the optimum case is determined as
The asymptotic limit given by (19) does not contradict limits given by (18), (8) and (2).
For each case, we ran the model with a time step of 1 year for 200 years, long enough to ensure that the proportion of women had approached its asymptotic limit. Initial populations for each age cohort of male and female faculty were determined from averages for the 1990-1998 data.
pool and the faculty at Mountain University will match, reaching the asymptotic limit of 50% female in 57 years.
TABLE 7 Comparison of Output Characteristics of the Five Cases of the Differential Equations Model Current Equal Equal Females Summary Conditions Exits Hires Equality Only time to 30% female, years 18 13 10 9 4 time to 40% female, years -- 51* 28 20 7 time to 50% female, years -- -- -- 57* 11 time to 75% female, years -- -- -- -- 22 asymptotic limit 34% 40% 43% 50% 100% (maximum %F) endpoint, years** 40 51 49 57 70 alternative endpoint, 33 43 42 49 62 years*** * Asymptotic limit ** Assuming measurement error of 0.5% or within 5 persons.
Likewise, the effect of differential rates of attrition accounts for the long times to reach the asymptotic limits of each case.