Exploring the World with Mathematics

• Autorzy: Michael C. Mackey
• Języki publikacji: EN

Abstrakty

EN

This is an account of my scientific and personal friendship with Prof. Andrzej (Andy) Aleksander Lasota from 1977 until his death 28 December, 2006. It is a tale that fascinates me because of the intertwined links between many people both East and West of several generations, and it illustrates what I feel is the strength and beauty of the personal side of the scientific endeavor. This contribution is almost identical to the paper "Adventures in Poland: Having fun and doing research with Andrzej Lasota", Matematyka Stosowana 8 (2007), 5-32. It is in no way to be considered a new contribution, but is rather a record of the second Annual Lecture Commemorating Professor Andrzej Lasota given in Katowice at Uniwersytet Śląski on 16 January, 2009.(original abstract)

Słowa kluczowe

EN

Academic teachers; Higher education; Mathematics

PL

Nauczyciele akademiccy; Szkolnictwo wyższe; Matematyka

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2009
• Tom: 23
• Strony: 11--42

Twórcy

autor

Michael C. Mackey

• McGill University, Montréal, QC Canada

Bibliografia

• Bohm D., A suggested interpretation of quantum mechanics in terms of "hidden" vari- ables: I, Phys. Rev. 85 (1952), 166-179.
• Chow S.N., Existence of periodic solutions of autonomous functional differential equa- tions, J. Differential Equations 15 (1974), 350-378.
• Colijn C., Mackey M.C., A mathematical model of hematopoiesis. I. Periodic chronic myelogenous leukemia, J. Theoret. Biol. 237 (2005), 117-132.
• Komornik J., Lasota A., Asymptotic decomposition of Markov operators, Bull. Polish Acad. Sci. Math. 35 (1987), 321-327.
• Lasota A., Ergodic problems in biology, in: Dynamical systems, Vol. 2-Warsaw, Asterisque, No. 50, Soc. Math. France, Paris, 1977, pp. 239-250.
• Lasota A., Determinism, indeterminism, and mathematics, Found. Sci. 2 (1997), 7375.
• Lasota A., Li T.Y., Yorke J.A., Asymptotic periodicity of the iterates of Markov operators, Trans. Amer. Math. Soc. 286 (1984), 751-764.
• Lasota A., Łoskot K., Mackey M.C., The dynamics of proliferatively coupled cell pop- ulations, Acta Biotheor. 39 (1991), 1-14.
• Lasota A., Mackey M.C., The extinction of slowly evolving dynamical systems, J. Math. Biol. 10 (1980), 333-345.
• Lasota A., Mackey M.C., Globally asymptotic properties of proliferating cell popula- tions, J. Math. Biol. 19 (1984), 43-62.
• Lasota A., Mackey M.C., Probabilistic Properties of Deterministic Systems, Cambridge University Press, New York-Cambridge, 1985.
• Lasota A., Mackey M.C., Noise and statistical periodicity, Phys. D 28 (1987), 143-154.
• Lasota A., Mackey M.C., Stochastic perturbation of dynamical systems: the weak con- vergence of measures, J. Math. Anal. Appl. 138 (1989), 232-248.
• Lasota A., Mackey M.C., Chaos, fractals, and noise, Applied Mathematical Sciences, vol. 97, Springer-Verlag, New York, 1994.
• Lasota A., Mackey M.C., Cell division and the stability of cellular populations, J. Math. Biol. 38 (1999), 241-261.
• Lasota A., Mackey M.C., Statistical stability of strongly perturbed dynamical systems, in: Differential equations with applications to biology (Halifax, NS, 1997), Fields Inst. Commun., Vol. 21, Amer. Math. Soc., Providence, RI, 1999, pp. 363-376.
• Lasota A., Mackey M.C., Tyrcha J., The statistical dynamics of recurrent biological events, J. Math. Biol. 30 (1992), 775-800.
• Lasota A., Mackey M.C., Ważewska-Czyżewska M., Minimizing therapeutically induced anemia, J. Math. Biol. 13 (1981/82), 149-158.
• Lasota A., Traple J., Differential equations with dynamical perturbations, J. Differen- tial Equations 63 (1986), 406-417.
• Losson J., Mackey M.C., Coupled map lattices as models of deterministic and stochastic differential delay equations, Phys. Rev. E 52 (1995), 115-128.
• Mackey M.C., Time's Arrow: The Origins of Thermodynamic Behaviour, Springer- Verlag, Berlin-New York-Heidelberg, 1992.
• Mackey M.C., Glass L., Oscillation and chaos in physiological control systems, Science 197 (1977), 287-289.
• Mackey M.C., Longtin A., Lasota A., Noise-induced global asymptotic stability, J. Stat. Phys. 60 (1990), 735-751.
• Mackey M.C., Milton J.G., A deterministic approach to survival statistics, J. Math. Biol. 28 (1990), 33-48.
• Mackey M.C., Rudnicki R., Global stability in a delayed partial differential equation describing cellular replication, J. Math. Biol. 33 (1994), 89-109.
• Mackey M.C., Rudnicki R., A new criterion for the global stability of simultaneous cell replication and maturation processes, J. Math. Biol. 38 (1999), 195-219.
• Mackey M.C., Santavy M., Selepova P., A mitotic oscillator with a strange attractor and distributions of cell cycle times, in: Nonlinear oscillations in biology and chemistry (Salt Lake City, Utah, 1985), Lecture Notes in Biomath., Vol. 66, Springer, Berlin, 1986, pp. 34-45.
• Mackey M.C., Tyran-Kamińska M., Deterministic Brownian motion: The effects of perturbing a dynamical system by a chaotic semi-dynamical system, Phys. Rep. 422 (2006), 167-222.
• Mackey M.C., Tyran-Kamińska M., Noise and conditional entropy evolution, Phys. A 365 (2006), 360-382.
• Mackey M.C., Tyran-Kamińska M., Temporal behavior of the conditional and Gibbs' entropies, J. Stat. Phys. 124 (2006), 1443-1470.
• Mackey M.C., Tyran-Kamińska M., Central limit theorem behavior in the skew tent map, Chaos Solitons Fractals 38 (2008), 789-805.
• Mackey M.C., Tyran-Kamińska M., Central limit theorems for non-invertible measure preserving maps, Colloq. Math. 110 (2008), 167-191.
• Mackey M.C., Tyran-Kamińska M., Dynamics and density evolution in piecewise de- terministic growth processes, Ann. Polon. Math. 94 (2008), 111-129.
• Murray J.D., Wprowadzenie do biomatematyki (translated by Urszula Foryś and Marek Bodnar), Wydawnictwo Naukowe PWN, Warszawa, 2007.
• Provatas N., Mackey M.C., Asymptotic periodicity and banded chaos, Phys. D 53 (1991), 295-318.
• Provatas N., Mackey M.C., Noise-induced asymptotic periodicity in a piecewise linear map, J. Statist. Phys. 63 (1991), 585-612.
• Rudnicki R., Mackey M.C., Asymptotic similarity and Malthusian growth in au- tonomous and nonautonomous populations, J. Math. Anal. Appl. 187 (1994), 548-566.
• Szarski J., Differential Inequalities, Monografie Matematyczne, T. 43, Państwowe Wydawnictwo Naukowe, Warsaw, 1965.
• Urbaniec J., An interview with Andrzej Lasota: Without the physical world, there would be no mathematics either, Found. Sci. 2 (2002), 183-189.
• Ważewska-Czyżewska M., Lasota A., Mathematical problems of the dynamics of a system of red blood cells, Mat. Stos. 6 (1976), 23-40.