A Mathematical Model of the Human External Respiratory System

Dantzig, George B.; DeHaven, James C.; Cooper, Irwin; Johnson, Selmer Martin; DeLand, Edward Charles; Kanter, H. E.; Sams, Crawford F.

doi:10.1353/pbm.1961.0008

Cited by 17 publications

(6 citation statements)

References 6 publications

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“…Then in 1959 two of the present authors (DeHaven and/ DeLand), along with Dantzig and associates [7], showed how nonlinear programming methods for representing/'chemical phenomena can be applied to biological systems. These mathematical methods have recently been used to construct a model of the human external respiratory system [8].…”

mentioning

confidence: 86%

Analysis of Chemical Constituents of Blood by Digital Computer

et al. 1964

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confidence: 86%

Analysis of Chemical Constituents of Blood by Digital Computer

et al. 1964

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“…As an example we obtain a point with all components strictly positive for the dual of a geometric program. The problem is a multiphase chemical equilibrium developed by Dantzig, De Haven and Sams [1]. + 10" 4 x 10 +10-*^+ 10-5 x 2 + 10-6 JC 3 + 10" 10 x 4 + + .0001118x 9 ;c 1 +10- 4 ;t 11 <l.…”

Section: Examplementioning

confidence: 99%

On finding a point in the relative interior of a polyhedral set and degeneracy in geometric programming

Jefferson¹,

Scott²

1978

J. Aust. Math. Soc. Series B, Appl. Math

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Geometric programming is now a well-established branch of optimization theory which has its origin in the analysis of posynomial programs. Geometric programming transforms a mathematical program with nonlinear objective function and nonlinear inequality constraints into a dual problem with nonlinear objective function and linear constraints. Although the dual problem is potentially simpler to solve, there are certain computational difficulties to be overcome. The gradient of the dual objective function is not defined for components whose values are zero. Moreover, certain dual variables may be constrained to be zero (geometric programming degeneracy).To resolve these problems, a means to find a solution in the relative interior of a set of linear equalities and inequalities is developed. It is then applied to the analysis of dual geometric programs.

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“…The antecedents of the mathematical theory for this model are due to Gibbs [7], Dantzig, et al [8], Clasen [9], and Shapiro and Shapley [107, taken chronologically. Work in the literature which develops from a view similar to the present research may be reviewed in McLean [117 who also mentions an earlier work by Borsook and Schott [12].…”

Section: Background Of the Mathematical Modelmentioning

confidence: 99%

“…Dantzig [87 and DeHaven and DeLand [13] contain the detailed development of the earlier "respiratory" model, of which the present plasma and red cell compartments are elaborations; [8][9][10]13] contain the details of the mathematical structure upon which these models are founded.…”

Section: Background Of the Mathematical Modelmentioning

confidence: 99%

“…Although the later elaborations described here are naturally more sophisticated than that of [8,13], it will not be necessary to repeat here all the earlier rigorous arguments and justifications; e.g., the mathematical conditions for a unique solution, the effects of carbamino reactions and buffering L; the dissociation curve for hemoglobin, or the important theorems on multiplicative systems. Instead, we wish to present a convincing argument that the thermo- …”

Section: Background Of the Mathematical Modelmentioning

confidence: 99%

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