Some mathematical problems in biology
Author:
S. I. Rubinow
Journal:
Bull. Amer. Math. Soc. 81 (1975), 782794
MSC (1970):
Primary 92A05
MathSciNet review:
0403713
Fulltext PDF
References 
Similar Articles 
Additional Information
 1.
Sol
I. Rubinow, Mathematical problems in the biological sciences,
Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973.
Ten lectures delivered at the Regional Conference on Mathematical Problems
in the Biological Sciences of 5–9 June 1972 at Michigan State
University; Conference Board of the Mathematical Sciences Regional
Conference Series in Applied Mathematics, No. 10. MR 0462660
(57 #2633)
 2.
G. A. Brecher, Mechanism of venous flow under different degrees of aspiration, Amer. J. Physiol. 169 (1952), 423433.
 3.
G. A. Brecher, Venous return, Grune & Stratton, New York, 1956.
 4.
A. C. Guyton, Determination of cardiac output by equating venous return curves with cardiac response curves, Physiol. Rev. 35 (1955), 123129.
 5.
A. C. Guyton, Venous return, Handbook of Physiology, Section 2: Circulation. Vol. II (W. F. Hamilton & P. Dow, eds.), American Physiological Society, Washington, D.C., 1963, pp. 10991133.
 6.
S. I. Rubinow and J. B. Keller, Flow of a viscous fluid through an elastic tube with applications to blood flow, J. Theoret. Biol. 35 (1972), 299313.
 7.
M. R. Roach and A. C. Burton, The reason for the shape of the distensibility curves of arteries, Canad. J. Biochem. & Physiol. 35 (1957), 681690.
 8.
D. L. Fry, A preliminary lung model for simulating the aerodynamics of the bronchial tree, Computers & Biomed. Res. 2 (1968), 111134.
 9.
J. P. Holt, Flow of liquids through "collapsible" tubes, Circ. Res. 7 (1959), 342353.
 10.
J. E. Flaherty, J. B. Keller and S. I. Rubinow, Post buckling behavior of elastic tubes and rings with opposite sides in contact, SIAM J. Appl. Math. 23 (1972), 446455.
 11.
S.
I. Rubinow and Alice
Winzer, Compartment analysis: An inverse problem, Math.
Biosci. 11 (1971), 203–247. MR 0298097
(45 #7149)
 12.
John
Z. Hearon, The kinetics of linear systems with special reference to
periodic reactions, Bull. Math. Biophys. 15 (1953),
121–141. MR 0054807
(14,982d)
 13.
S. I. Rubinow, On closed or almost closed compartment systems, Math. Biosciences 18 (1973), 245253.
 14.
O. Scherbaum and G. Rasch, Cell size distribution and single cell growth in tetrahymena pyriformis GL, Acta Pathol. Microbiol. Scand. 41 (1957), 161182.
 15.
H. Von Foerster, Some remarks on changing populations, The Kinetics of Cellular Proliferation (Frederick Stohlman, ed.), Grune & Stratton, New York and London, 1959, pp. 382407.
 16.
S. I. Rubinow, A maturitytime representation for cell populations, Biophys. J. 8 (1968), 10551073.
 17.
D. M. Prescott, Variations in the individual generation times of tetrahymena geleii HS, Exptl. Cell Res. 16 (1959), 279284.
 18.
J.
L. Lebowitz and S.
I. Rubinow, A theory for the age and generation time distribution
of a microbial population, J. Math. Biol. 1
(1974/75), no. 1, 17–36. MR 0496810
(58 #15282)
 1.
 S. I. Rubinow, Mathematical problems in the biological sciences, Society for Industrial and Applied Mathematics, Philadelphia, 1973. MR 462660
 2.
 G. A. Brecher, Mechanism of venous flow under different degrees of aspiration, Amer. J. Physiol. 169 (1952), 423433.
 3.
 G. A. Brecher, Venous return, Grune & Stratton, New York, 1956.
 4.
 A. C. Guyton, Determination of cardiac output by equating venous return curves with cardiac response curves, Physiol. Rev. 35 (1955), 123129.
 5.
 A. C. Guyton, Venous return, Handbook of Physiology, Section 2: Circulation. Vol. II (W. F. Hamilton & P. Dow, eds.), American Physiological Society, Washington, D.C., 1963, pp. 10991133.
 6.
 S. I. Rubinow and J. B. Keller, Flow of a viscous fluid through an elastic tube with applications to blood flow, J. Theoret. Biol. 35 (1972), 299313.
 7.
 M. R. Roach and A. C. Burton, The reason for the shape of the distensibility curves of arteries, Canad. J. Biochem. & Physiol. 35 (1957), 681690.
 8.
 D. L. Fry, A preliminary lung model for simulating the aerodynamics of the bronchial tree, Computers & Biomed. Res. 2 (1968), 111134.
 9.
 J. P. Holt, Flow of liquids through "collapsible" tubes, Circ. Res. 7 (1959), 342353.
 10.
 J. E. Flaherty, J. B. Keller and S. I. Rubinow, Post buckling behavior of elastic tubes and rings with opposite sides in contact, SIAM J. Appl. Math. 23 (1972), 446455.
 11.
 S. I. Rubinow and A. Winzer, Compartment analysis: An inverse problem, Math. Biosciences 11 (1971), 203247. MR 298097
 12.
 J. Z. Hearon, The kinetics of linear systems with special reference to periodic reactions, Bull. Math. Biophys. 15 (1953), 121141. MR 14, 982. MR 54807
 13.
 S. I. Rubinow, On closed or almost closed compartment systems, Math. Biosciences 18 (1973), 245253.
 14.
 O. Scherbaum and G. Rasch, Cell size distribution and single cell growth in tetrahymena pyriformis GL, Acta Pathol. Microbiol. Scand. 41 (1957), 161182.
 15.
 H. Von Foerster, Some remarks on changing populations, The Kinetics of Cellular Proliferation (Frederick Stohlman, ed.), Grune & Stratton, New York and London, 1959, pp. 382407.
 16.
 S. I. Rubinow, A maturitytime representation for cell populations, Biophys. J. 8 (1968), 10551073.
 17.
 D. M. Prescott, Variations in the individual generation times of tetrahymena geleii HS, Exptl. Cell Res. 16 (1959), 279284.
 18.
 J. L. Lebowitz and S. I. Rubinow, A theory for the age and generation time distribution of a microbial population, J. Math. Biol. 1 (1974), 1736. MR 496810
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Additional Information
DOI:
http://dx.doi.org/10.1090/S000299041975138298
PII:
S 00029904(1975)138298
