Minimizes production of free radicals that lead to aging. In addition to the. Quantitative aspects of fatty acid biohydrogenation, absorption and transfer of milk.
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- I. Antoniou, “Internal Time and Irreversibility of Relativistic Dynamical Systems,” Thesis (Free University of Brussels, 1988).Google Scholar
- I. Antoniou and B. Misra, “Non-unitary transformation of conservative to dissipative evolutions,” J. Phys. A Math. Gen.24, 2723–2729 (1991).Google Scholar
- I. Antoniou and B. Misra “Relativistic internal time operator,” Int. J. Theor. Phys. 31, 119–136 (1992).Google Scholar
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- B. Misra, I. Prigogine, and M. Courbage, “Liapunov variable: entropy and measurements in quantum mechanics,” Proc. Natl. Acad. Sci. USA76, 4768–4772 (1979).Google Scholar
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- I. Antoniou and I. Prigogine, “Intrinsic irreversibility and integrability of dynamics,” Physica A192, 443–464 (1993).Google Scholar
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- I. Antoniou and Z. Suchanecki, “The fuzzy logic of chaos and probabilistic inference,” Found. Phys. 27, 333–362 (1997).Google Scholar
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- A. Khinchin, Mathematical Foundations of Information Theory (Dover, New York, 1957).Google Scholar
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- I. Antoniou and F. Bosco, “spectral decomposition of contracting probabilistic dynamical systems,” Chaos, Solitons and Fractals9, 401–418 (1998).Google Scholar
- I. Antoniou and F. Bosco, “On the spectral properties of a Markov model for learning processes,” J. Mod. Phys. C11, 213–220 (2000).Google Scholar
- I. Antoniou, V. Basios, and F. Bosco, “Probabilistic control of chaos: chaotic maps under control,” Computers Math. Applic.34, 373–389 (1997).Google Scholar
- I. Antoniou, V. Basios, and F. Bosco, “Absolute controllability condition for probabilistic control of chaos,” J. Bifurcation Chaos8, 409–413 (1998).Google Scholar
- I. Antoniou and Z. Suchanecki, “Non-uniform Time operator, chaos and wavelets on the interval,” Chaos, Solitons and Fractals11, 423–435 (2000).Google Scholar
- I. Antoniou, V. Sadovnichii, and S. Shkarin, “Time operators and shift representation of dynamical systems,” Physica A299, 299–313 (1999).Google Scholar
- I. Antoniou, I. Prigogine, V. Sadovnichii, and S. Shkarin “Time operator for diffusion,” Chaos, Solitons and Fractals11, 465–477 (2000).Google Scholar
- E. Wigner, “The unreasonable effectiveness of mathematics in the natural sciences,” Comm. Pure Appl. Math.13, 1–14 (1960).Google Scholar
- E. Spandagos, The Life and Works of Constantine Caratheodory (Aithra, Athens, 2000).Google Scholar
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- Constantine Caratheodory: 125 Years from His Birth, special issue (Aristoteles University of Thessaloniki, 1999).Google Scholar
- Th. Rassias, ed., C. Caratheodory: An International Tribute (World Scientific, Singapore, 1991).Google Scholar
- A. Sommerfeld, Thermodynamics and Statistical Mechanics (Academic, New York, 1955).Google Scholar
- M. Zemansky, Heat and Thermodynamics, 5th edn. (McGraw–Hill, London, 1968).Google Scholar
- A. Pippard, The Elements of Classical Thermodynamics (Cambridge University Press, London, 1997).Google Scholar
- H. Callen, Thermodynamics (John Wiley, New York, 1960).Google Scholar
- C. Caratheodory, “Untersuchungen über die Grundlagen der Thermodynamik,“ Math. Ann. 67, 355 (1909).Google Scholar
- C. Caratheodory, Sitzber Preuss. Acad. Wiss. Physik-Math. Kl.39 (1925).Google Scholar
- P. Rastal, “Classical thermodynamics simplified,” J. Math. Phys.11, 2955–2965 (1970).Google Scholar
- F. Weinhold, “Thermodynamics and geometry,” Physics Today3, 23–30 (1976).Google Scholar
- M. Peterson, “Analogy between thermodynamics and mechanics,” Am. J. Phys.47, 488–490 (1979).Google Scholar
- P. Landsberg, Thermodynamics (Interscience, New York, 1961).Google Scholar
- G. Giannakopoulos, Chemical Thermodynamics (University of Athens, 1974).Google Scholar
- O. Redlich, “Fundamental thermodynamics since Caratheodory,” Rev. Mod. Phys.40, 556–563 (1968).Google Scholar
- C. Caratheodory, Vorlesungen uber reelle Functionen (Teubner, Leipzig, 1918, 1927).Google Scholar
- C. Caratheodory, Algebraic Theory of Measure and Integration, 2nd edn. (Chelsea, New York, 1986).Google Scholar
- H. Royden, Real Analysis, 3rd edn. (McMillan, New York, 1988). Caratheodory's way to define measurable sets is considered (p. 58) to be the best. A clear discussion of Caratheodory's extension theorem is presented in p. 295.Google Scholar
- M. Gurtin and W. Williams, “An axiomatic formulation for continuous thermodynamics,” Arch. Rat. Mech. Anal.26, 83–117 (1967).Google Scholar
- M. Gurtin, W. Williams, and W. Ziemer, “Geometric measure theory and the axioms of continuum thermodynamics,” Arch. Rat. Mech. Anal.92, 1–22 (1986).Google Scholar
- I. Antoniou and Z. Suchanecki, “Densities of singular measures and generalized spectral decomposition,” in Generalized Functions, Operator Theory, and Dynamical Systems, Res. Not. Math. 399, I. Antoniou and G. Lumer, eds. (Chapman &; Hall/CCR, 1999), pp. 56–67.Google Scholar
- C. Truesdell, The Elements of Continuum Mechanics (Springer, Berlin, 1966).Google Scholar
- A. Bressan, Relativistic Theories of Materials (Springer, Berlin, 1978).Google Scholar
- J. Serrin, ed., New Perspectives on Thermodynamics (Springer, Berlin, 1986).Google Scholar
- E. Schroedinger, What is Life? (Cambridge University Press, Cambridge, 1944).Google Scholar
- I. Prigogine, Introduction to Thermodynamics of Irreversible Processes (Wiley, New York, 1967).Google Scholar
- P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations(Wiley, New York, 1971).Google Scholar
- I. Prigogine, From Being to Becoming (Freeman, New York, 1981).Google Scholar
- D. Kondepudi and I. Prigogine, “sensitivity of non-equilibrium systems,” Physica A107, 1–24 (1981).Google Scholar
- D. Kondepudi, “sensitivity of chemical dissipative structures to external fields: Formation of propagating bands,” Physica A115, 552–566 (1982).Google Scholar
- C. Papaseit, N. Pochon, and J. Tabony, “Microtubule self-organization is gravity-dependent,” Proc. Natl. Acad. Sci. USA97, 8364–8368 (2000).Google Scholar
- L. Boltzmann, J. Reine Angew. Math.100, 201 (1887).Google Scholar
- L. Boltzmann, Lectures on Gas Theory (English translation of the original, 1896, 1898; University of California Press, Berkeley, 1964; Dover reprint, New York, 1995).Google Scholar
- I. Farquhar, Ergodic Theory in Statistical Mechanics (Wiley, New York, 1964).Google Scholar
- S. Brush, The Kind of Motion we Call Heat: A History of the Kinetic Theory of Gases (North-Holland, Amsterdam, 1976).Google Scholar
- M. Plancherel, Arch. Sci. Phys.33, 254 (1912); iAnn. Phys.42, 1061–1063 (1913).Google Scholar
- A. Rosenthal, Ann. Phys.42, 796–806; 43, 894–904 (1913).Google Scholar
- L. Boltzmann, Akad. Wiss. Wien66, 275–370 (1872).Google Scholar
- J. Loschmidt, Akad. Wiss. Wien73, 128–142 (1876).Google Scholar
- E. Zermelo, Ann. Phys.57, 485–494 (1896).Google Scholar
- H. Poincaré, C. R. Acad. Sci.108, 550–553 (1889); Acta Math.13, 1 (1890).Google Scholar
- C. Caratheodory, Sitz. Preuss. Akad. Wiss. Phys. Math. 580–584 (1919).Google Scholar
- J. Gibbs, Elementary Principles of Statistical Mechanics (Yale University Press, 1902; Dover reprint, New York, 1960).Google Scholar
- G. Birkhoff, Proc. Natl. Acad. Sci. USA17, 650–660 (1931).Google Scholar
- I. Cornfeld, S. Fomin, and Ya. Sinai, Ergodic Theory (Springer, Berlin, 1982).Google Scholar
- J. von Neumann, Ann. Math.33, 587 (1932).Google Scholar
- E. Hopf, J. Math. and Phys.13, 51–102 (1934).Google Scholar
- G. Birkhoff and B. Koopman, Proc. Natl. Acad. Sci. USA18, 279–282 (1932).Google Scholar
- M. Stone, Linear Transformations in Hilbert Space and their Applications in Analysis (American Mathematical Society, New York, 1932).Google Scholar
- J. von Neumann, Mathematical Foundations of Quantum Mechanics (Springer, 1932; English translation, Princeton University Press, New Jersey, 1955).Google Scholar
- B. Koopman, “Hamiltonian systems and transformations in Hilbert spaces,” Proc. Nat. Acad. Sci. USA17, 315–318 (1931).Google Scholar
- R. Goodrich, K. Gustafson, and B. Misra, “On a converse to Koopman Lemma and irreversibility,” J. Statist. Phys. 43, 317–320 (1986).Google Scholar
- M. Nadkarni, Spectral Theory of Dynamical Systems (Birkhäuser, Basel, Switzerland, 1998).Google Scholar
- B. Koopman and J. von Neumann, “Dynamical systems of continuous spectra,” Proc. Nat. Acad. Sci. USA18, 255–266 (1932).Google Scholar
- I. Antoniou and Z. Suchanecki, in Evolution Equations and their Applications in Physical and Life Sciences, G. Lumer and L. Weiss, eds. (Marcel Dekker, New York, 2001), pp. 301–310.Google Scholar
- I. Antoniou and S. A. Shkarin, “Decay spectrum and decay subspace of normal operators,” Proc. Roy. Edinb. Soc. 131A, 1245–1255 (2001).Google Scholar
- I. Antoniou and S. Shkarin, “Decaying measures,” Russ. Math. Doclady61, 24–27 (2000); Proc. Roy. Edinb. Soc.131A, 1257–1273 (2001).Google Scholar
- A. Lasota and M. Mackey, Chaos, Fractals, and Noise (Springer, New York, 1994).Google Scholar
- N. S. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, 1979).Google Scholar
- B. Misra and I. Prigogine, “Time probability and dynamics,” in Long Time Predictions in Dynamical Systems, C. Horton, L. Reichl, and V. Szebehely, eds. (Wiley, New York, 1983), pp. 21–43.Google Scholar
- B. Misra, “Nonequilibrium entropy, Lyapunov variables, and ergodic properties of classical systems,” Proc. Natl. Acad. USA75, 1627–1631 (1978).Google Scholar
- I. Antoniou, “Internal Time and Irreversibility of Relativistic Dynamical Systems,” Thesis (Free University of Brussels, 1988).Google Scholar
- I. Antoniou and B. Misra, “Non-unitary transformation of conservative to dissipative evolutions,” J. Phys. A Math. Gen.24, 2723–2729 (1991).Google Scholar
- I. Antoniou and B. Misra “Relativistic internal time operator,” Int. J. Theor. Phys. 31, 119–136 (1992).Google Scholar
- O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vol. I, II (Springer, New York, 1979, 1981).Google Scholar
- B. Misra, I. Prigogine, and M. Courbage, “Liapunov variable: entropy and measurements in quantum mechanics,” Proc. Natl. Acad. Sci. USA76, 4768–4772 (1979).Google Scholar
- M. Courbage, “On necessary and sufficient conditions for the existence of time and entropy operators in quantum mechanics,” Lett. Math. Phys.4, 425–432 (1980).Google Scholar
- C.M. Lockhart and B. Misra, “Irreversibility and measurement in quantum mechanics,” Physica A136, 47–76 (1986).Google Scholar
- G. Ordó ñez, T. Petrosky, E. Karpov, and I. Prigogine, “Explicit construction of a time superoperator for quantum unstable systems,” Chaos Solitons and Fractals12, 2591–2601 (2001).Google Scholar
- I. Prigogine, The End of Certainty (Free Press, New York, 1997).Google Scholar
- I. Antoniou and S. Tasaki, “Generalized spectral decomposition of mixing dynamical systems,” Int. J. Quantum Chemistry46, 425–474 (1993).Google Scholar
- I. Antoniou and S. Shkarin, “Extended spectral decomposition of evolution operators,” in Generalized Functions, Operator Theory and Dynamical Systems, Research Notes in Mathematics 399 (Chapman and Hall/CRC, London, 1999).Google Scholar
- I. Antoniou and I. Prigogine, “Intrinsic irreversibility and integrability of dynamics,” Physica A192, 443–464 (1993).Google Scholar
- A. Bohm, Quantum Mechanics, Foundations and Applications, 3rd edn. (Springer, Berlin, 1993).Google Scholar
- A. Bohm and M. Gadella, Dirac Kets, Gamow Vectors and Gelfand Triplets, Lecture Notes on Physics 348 (Springer, Berlin, 1989).Google Scholar
- I. Antoniou and Z. Suchanecki, “The fuzzy logic of chaos and probabilistic inference,” Found. Phys. 27, 333–362 (1997).Google Scholar
- I. Antoniou and Z. Suchanecki, “Logics associated with complex systems,” in Proceedings of the First Panhellenic Symposium on Logic, A. Kakas and A. Synachopoulou, eds. (University of Cyprus editions, ISBN 9963-607-11-X, Nicosia, 1997), pp. 261–274.Google Scholar
- J. Lighthill, “The recently recognized failure of predictability in Newtonian dynamics,” Proc. Roy. Soc. LondonA407, 35–50 (1986).Google Scholar
- T. Bedford, N. Keane, and C. Series, Ergodic Theory Symbolic Dynamics and Hyperbolic Spaces (Oxford University Press, New York, 1991).Google Scholar
- A. Khinchin, Mathematical Foundations of Information Theory (Dover, New York, 1957).Google Scholar
- Y. Kakihara, Abstract Methods in Information Theory (World Scientific, Singapore, 1999).Google Scholar
- I. Antoniou, F. Bosco, and Z. Suchanecki, “spectral decomposition of expanding probabilistic dynamical systems,” Phys. Lett. A239, 153–158 (1998).Google Scholar
- I. Antoniou and F. Bosco, “spectral decomposition of contracting probabilistic dynamical systems,” Chaos, Solitons and Fractals9, 401–418 (1998).Google Scholar
- I. Antoniou and F. Bosco, “On the spectral properties of a Markov model for learning processes,” J. Mod. Phys. C11, 213–220 (2000).Google Scholar
- I. Antoniou, V. Basios, and F. Bosco, “Probabilistic control of chaos: chaotic maps under control,” Computers Math. Applic.34, 373–389 (1997).Google Scholar
- I. Antoniou, V. Basios, and F. Bosco, “Absolute controllability condition for probabilistic control of chaos,” J. Bifurcation Chaos8, 409–413 (1998).Google Scholar
- I. Antoniou and Z. Suchanecki, “Non-uniform Time operator, chaos and wavelets on the interval,” Chaos, Solitons and Fractals11, 423–435 (2000).Google Scholar
- I. Antoniou, V. Sadovnichii, and S. Shkarin, “Time operators and shift representation of dynamical systems,” Physica A299, 299–313 (1999).Google Scholar
- I. Antoniou, I. Prigogine, V. Sadovnichii, and S. Shkarin “Time operator for diffusion,” Chaos, Solitons and Fractals11, 465–477 (2000).Google Scholar
- E. Wigner, “The unreasonable effectiveness of mathematics in the natural sciences,” Comm. Pure Appl. Math.13, 1–14 (1960).Google Scholar