Abstract
In this paper a “classical procedure” is discussed for building mathematical models of physical, technological and real-life phenomena. The method is accompanied by appropriate remarks and applications.
In Chapter 1 the procedure is discussed for the model building, which is characterized by some steps of the investigation.
In Chapter 2 remarks are given related to concepts involved, to applicability of the method, to reasonability of the problem, etc.
By these remarks the investigator faces views for examination and problems for solution.
In Chapter 3 applications are illustrated, by which one can see how the method for model building can be applied.
The applications are distinguished into applications of “complete cycle” and of “incomplete cycle”.
The paper is dedicated to Leon Brillouin, the outstanding scientist and human, whose memory will always be a source for inspiration in my work, and for whom my admiration, respect and gratitude are unlimited.
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Bibliography
Ayala, F.: (a) “Biological evaluation: Natural selection or random walk”? American Scientist, (Nov–Dec. 1974), pp. 672–701, U.S.A. (b) “Competition between species”, American Scientist (1972), pp. 348–357, U.S.A.
Bartholomew, D.: “Stochastic models for social processes”, 2nd Ed., John Wiley and Sons, New York (1973), Chapter I, U.S.A.
Birckoff, Garrett: “Mathematics and computer science”, American Scientist, (Jan–Feb. 1975) pp. 83–91, U.S.A.
Brillouin, L.: (a) “Scientific uncertainty and information”, Academic Press, New York (1946), U.S.A. (b) “Relativity re-examined”, Academic Press, New York (1970), U.S.
Coleman, S.: “Introduction to mathematical sociology”, The Free Press of Glencoe, Collier-Macmillan Lim., London (1964), pp. 526–528, England.
Cortes, F., Przeworski, A. and Sprague, J.: “Systems analysis for social scientists”, John Wiley and Sons, New York (1974), U.S.A.
Courant, R.: (a) “Methods of applied mathematics”, in the book: “Recent advances in science” of Shammos, M. and Murphy, G. Science Editions, Inc., New York (1961), U.S.A. (b) “Boundary value problems in modern dynamics”, Proc, Intern. Congress of Math, Vol. II (1950)
Education in Applied Mathematics: SIAM Review, Vol. 9, No. w (April 1967), U.S.A.
Gandolfo, G.: “Mathematical methods and models in economic dynamics,” North Holland Publ. Co., Amsterdam (1971).
Goel, N., Maitra, S. and Montroll, E.: “On the Volterra and other nonlinear models on interacting populations”, Review of Modern Physics, Vol. 43, No. 2, Part 1 (April 1971) pp. 231–276, U.S.A.
Gomatan, J.: “A new model for interacting populations”? I: “Two species system”, pp. 347, 353 II: Principle of competitive exclusion, pp. 355-364; Bulletin of Mathematical Biology, Vol. 36 (1974), U.S.A.
Goodwin, B.: “Temporal organization in cells”, Academic Press, New York (1963), U.S.A.
Keisler, H.: “Model theory”, Proc, Intern. Congress of Math, Vol. I (1970)
Kostitzin, V.: “Biologie mathematique,” Librarie Armand Colin, Paris (1937), France.
Lavrentiev, M.: “Some improperly-posed problems of mathematical physics”, Springer-Verlag, New York (1967), U.S.A.
Lin, C. and Segel, L.: “Mathematics applied to deterministic problems in the Natural Sciences”, Macmillan Publ. Co., New York (1974), U.S.A.
Lotka, A.: “Elements of physical biology”, Baltimore, Williams (1974), U.S.A.
Magiros, P.: (a) “Physical problems discussed mathematically”, Bulletin Greek Math. Soc., Vol. 6, II, No. 1 (1956), Athens, Greece. (b) “Methods for defining principal modes of nonlinear systems utilizing infinite determinants”, Journal of Math. Physics, Vol. 2, No. 66 (Nov-Dec, 1960), Americal Institute of Physics, U.S.A. (c) “Motion in a Newtonian field modified by a general force”, Journal of Franklin Institute (Sept. 1964), U.S.A. (d) “The role of mathematics in the investigation of physical and social phenomena,” Greek Math. Soc. “The Euclide”, (May–June, 1973), Athens, Greece.
Marčhac, G.: “Methods and problems of computational mathematics”, Proc, Intern. Congress of Math, Vol. I (1970).
Mesaronič, M.: “Systems theory and biology”, Proc, III Systems Symposium Spring-Verlag, New York (1968), U.S.A.
Miranker, N.: “A well-posed problem for a backward heat equation”, Proc. Amer Math. Soc. (April 1961), U.S.A.
Neumann, John Von: “The mathematician”, Collected Works, Vol. I, pp. 1–9, Oxford, New York (1961).
Rapoport, A.: “Mathematics outside the physician sciences”, SIAM Review (Apr. 1973), pp. 481–502, U.S.A.
Papoulis, A.: “Probability random variables and stochastic processes”, McGraw-Hill Book Co., New York (1965), Chapter 1, U.S.A.
Poincare, H.: (a) “Science and hypothesis”, Dover (1952), New York, U.S.A. (b) “The value of science”, Dover, (1958), New York, U.S.A.
Volterra, V.: „Leçons sur la théorie mathematique de la lutte pour la vie,“ Gauthier Villar set Cie, Paris (1931), France
Will, G.: “Gravitation theory”, Scientific American (Nov. 1974), U.S.A.
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© 1985 D. Reidel Publishing Company, Dordrecht, Holland
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Magiros, D.G. (1985). Mathematical Models of Physical and Social Systems. In: Tzafestas, S.G. (eds) Selected Papers of Demetrios G. Magiros. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5368-0_11
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DOI: https://doi.org/10.1007/978-94-009-5368-0_11
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