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#### Algebraic Solution

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Journal Article
Demography (1975) 12 (2): 313–324.
Published: 01 May 1975
... of increment-decrement tables. 8 1 2011 © Population Association of America 1975 1975 Life Table Linear Method Vital Rate Algebraic Solution Life Table Model An erratum to this article is available at http://dx.doi.org/10.2307/2060838 . References Depoid Pierre...
Journal Article
Demography (1976) 13 (2): 287–290.
Published: 01 May 1976
... but presents explicit solutions only for two-table and three-table models. These are derived by solving, in each instance, a set of simultaneous linear equations whose algebraic solution, though straight- forward, is as Schoen rightly observes "a bit complicated." Inasmuch as this com- plexity increases...
Journal Article
Demography (1976) 13 (4): 513–519.
Published: 01 November 1976
... with others, appear to be quite sat-l'" Ix m,* dx = 1. isfactory. This can easily be verified by following steps similar to those described earlier in developing equations (813). Expanding the exponential in (30) and then sim- plifying, the algebraic solution of (30) is obtained as 1* = bOeo[l - 2~* (J.l2...
Journal Article
Demography (1966) 3 (1): 259–275.
Published: 01 March 1966
.... Latent Root Real Root Quadratic Formula Matrix Algebra Characteristic Matrix References 1. Leslie P. H. ( 1945 ). On the Use of Matrices in Certain Population Mathematics . Biometriks , XXXIII , 183 – 212 . 10.1093/biomet/33.3.183 2 For example, see N. Keyfitz, “Mathematical...
Journal Article
Demography (2020) 57 (2): 779–797.
Published: 24 March 2020
... is assumed to be stationary. The initial and ending populations then have the same composition. In the simultaneous equation approach for N states, 2 N – 1 equations need to be solved. Even for N = 3, an explicit algebraic solution is usually not feasible. Maple program XPR3, available in online...
Includes: Supplementary data
Journal Article
Demography (2013) 50 (6): 1969–1971.
Published: 17 October 2013
... to be a useful approach to the identification and estimation of the three-factor APC accounting model. The IE, however, is not a “final” or “universal” solution to the identification problem of linear or APC accounting models. There will never be such a solution within the confines of conventional linear models...
Journal Article
Demography (1967) 4 (2): 423–441.
Published: 01 June 1967
... of matrix algebra. In this article, we shall deal with both the continuous model and the dis- crete model of population growth, but the reader will not see any differential equa- tions or matrix algebra used. Indeed, with this more elementary approach to the subject, we shall study the eventual age- sex...
Journal Article
Demography (1989) 26 (4): 717–726.
Published: 01 November 1989
... that integrates into a linear algebraic solution the rate standardization method based on the log-linear type of analysis. Specifically, with the help of the purging method-first advanced by Clogg (1978) and further discussed by Clogg and Eliason (1988) and Clogg, Shockey, and Eliason (1987)-a system...
Journal Article
Demography (1971) 8 (3): 389–400.
Published: 01 August 1971
... populations are easily obtained in this model by simple algebraic manipulations. A rough but useful further simplification is to divide the population into three groups—pre-reproductive, reproductive, and post-reproductive. For this three-group model simple algebraic expressions connect fertility, mortality...
Journal Article
Demography (1981) 18 (2): 251–256.
Published: 01 May 1981
... index (Sf), which were alluded to in general terms in the previous paper, are now algebraically specified. It is demon- strated that RDf is a natural extension of D; when c > 2, it is possible to stipulate RDf in terms of Sf, but it is not possible to stipulate RDf in a straightforward manner in terms...
Journal Article
Demography (1984) 21 (3): 373–381.
Published: 01 August 1984
...- relation is found among individual states, many of which use it to generate popula- tion estimates for state-funded revenue sharing programs. I This report addresses a logical incon- sistency found in both the ratio-correla- tion and difference-correlation forms and, further, suggests a solution...
Journal Article
Demography (2013) 50 (6): 1981–1984.
Published: 17 October 2013
... on. I classified the proposed solutions into three categories: constrained estimation based on restricting the model, making the model nonlinear, and sleight of hand. Of course, some solutions have elements of two or more categories. The literature is now filled with algebra, matrix manipulations...
Journal Article
Demography (2006) 43 (3): 553–568.
Published: 01 August 2006
... matrix algebra (e.g., Gantmacher 1959) that for any function f, f = Uf (R)U 1. As a result, the population projection matrix in Eq. (4) can be written A(x,n) = exp[nz(x,n = exp[nz(x,n)URU 1] = U{exp[nz(x,n)R]}U 1 = U z(x,n)U 1. (14) Applying the PTR solution of Eq. (7), we nd y(x) = exp[nZ(xy(0) = U Z...
Journal Article
Demography (1973) 10 (3): 421–426.
Published: 01 August 1973
... is presented in this paper, which is based on the transformation of age-specific mortality rates to probabili- ties of dying by means of Reed-Merrell's (1939) approximation. These results, judging from their algebraic expressions, appear to be simpler and operationally more convenient, when compared with those...
Journal Article
Demography (2017) 54 (2): 745–773.
Published: 16 February 2017
... composition as well as peer achievement effects on (1) student math achievement at the high school level using a randomized experiment; (2) different levels of math courses (i.e., general high school math, geometry, and algebra II) using a randomized experiment; and (3) student absenteeism at the high school...
Includes: Supplementary data
Journal Article
Demography (1964) 1 (1): 56–73.
Published: 01 March 1964
... States 1940–2000 (pp. 59 – 60 ). Washington : U.S. Government Printing Office . 5. Birkhoff Garrett , &amp; Maclane Saunders ( 1963 ). A Survey of Modern Algebra . Revised edition New York : The Macmillan Co. . 6. Frazer R. A. , Duncan W. J. , &amp; Collar A. R...
Journal Article
Demography (2009) 46 (3): 429–449.
Published: 01 August 2009
... to the interaction component and devel- oped an algebraic solution that distributed interactions equally among the cross-classi ed variables. Cho and Retherford (1973) and Kim and Strobino (1984) provided alternative decompositions. Both decompositions are based on hierarchical strategies in which the results...
Journal Article
Demography (1999) 36 (1): 111–120.
Published: 01 February 1999
... nativity composition. We present algebraic derivations of these relationships and use data from the 1990 and 1991 panels of the Survey of Income and Program Participation to examine empirically the extent to which levels of welfare receipt for immigrants and natives are sensitive to the use of household...
Journal Article
Demography (1969) 6 (3): 301–322.
Published: 01 August 1969
... of childbearing to change from cohort to cohort, which is important for populations practicing contraception. Second, none of the advanced mathematics used in previous formulations is needed; only the manipulation of sums and inequalities from high school algebra and the concept of “limit” from freshman calculus...
Journal Article
Demography (1968) 5 (1): 382–409.
Published: 01 March 1968
... lector precisa iener solamenie nociones elemeniales de algunos de los terminosusados en algebra de matrics. Esta aproximación elemental va a llevarnos a la introducción de algunas nuevas fórmulas las cuoles simplijican a la vez la comprensión y el cálculo de varias cantidades que son relevantes a la...