[1] | Goldhaber, G., and Perlmutter, S. 1998, A study of 42 type Ia supernovae and a resulting measurement of Omega(M) and Omega(Lambda). Physics Reports-Review Section of Physics Letters 307, 325–331. |
[2] | Riess, A. G., Filippenko, A. V., Challis, P., and et al. 1998, Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J., 116, 1009–1038. |
[3] | Garnavich, P. M., Kirshner, R. P., Challis, P., and et al. 1998, Constraints on cosmological models from Hubble Space Telescope observations of high-z supernovae. Astrophys. J. 493, L53+ Part 2. |
[4] | Garnavich, P. M., Kirshner, R. P., Challis, P., and et al. 1998, Constraints on cosmological models from Hubble Space Telescope observations of high-z supernovae. Astrophys. J. 493, L53+ Part 2. |
[5] | Volders, L. 1959, Neutral hydrogen in M 33 and M 101. Bulletin of the Astronomical Institutes of the Netherlands 14, 323–334. |
[6] | De Blok, W. J. G., and McGaugh, S. 1997, The dark and visible matter content of low surface brightness disc galaxies. MNRAS 290, 533–552. |
[7] | Clowe, D., Bradač, M., Gonzalez, A. H., Markevitch, M., Randall, S. W., Jones, C., and Zaritsky, D. 2006, A direct empirical proof of the existence of dark matter. Astrophys. J. 648, L109–L113. |
[8] | Webb, J. K., Flambaum, V. V., Churchill, C. W., Drinkwater, M. J., and Barrow, J. D. 1999, Search for time variation of the fine structure constant. Phys. Rev. Lett. 82, 884–887. (arXiv:astro-ph/9803165) |
[9] | Webb, J. K., Murphy, M. T., Flambaum, V. V., Dzuba, V. A., Barrow, J. D., Churchill, C. W., Prochaska, J. X., and Wolfe, A. M. 2001, Further evidence for cosmological evolution of the fine structure constant. Phys. Rev. Lett. 87, 091301. |
[10] | Khatri, R., and Wandelt, B. D. 2007, 21-cm radiation: A new probe of variation in the fine-structure constant. Phys. Rev. Lett. 98, 111301. |
[11] | Paal, G. 1970, The global structure of the universe and the distribution of quasi-stellar objects. Acta Phys. Acad. Sci. Hung. 30, 51–54. |
[12] | Tifft, W. G. 1973, Properties of the redshift-magnitude bands in the Coma cluster. Astrophys. J. 179, 29–44. |
[13] | Tifft, W. G. 2003, Redshift periodicities, the galaxy-quasar connection. Astrophys. Space Sci. 285, 429–449. |
[14] | Carnot, S. 1824, Reflexions sur la puissance motrice du feu et sur les machines propres a developper cette puissance. Bachelier, Paris. |
[15] | Jaynes, E. T. 2003, Probability theory. The logic of science. Cambridge University Press, Cambridge, UK. |
[16] | Sharma, V., and Annila, A. 2007, Natural process – Natural selection. Biophys. Chem. 127, 123–128. |
[17] | Du Châtelet, E. 1740, Institutions de physique. Paris, France: Prault. Facsimile of 1759 edition Principies mathématiques de la philosophie naturelle I-II. Éditions Jacques Gabay, Paris. |
[18] | ‘s Gravesande, W. 1720, Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam. Leiden, The Netherlands. |
[19] | Jaakkola, S., Sharma, V., and Annila, A. 2008, Cause of chirality consensus. Curr. Chem. Biol. 2, 53–58. (arXiv:0906.0254) |
[20] | Jaakkola, S., El-Showk, S., and Annila, A. 2008, The driving force behind genomic diversity. (arXiv:0807.0892) |
[21] | Grönholm, T., and Annila, A. 2007, Natural distribution. Math. Biosci. 210, 659–667. |
[22] | Würtz, P., and Annila, A. 2008, Roots of diversity relations. J. Biophys. (doi:10.1155/2008/654672) (arXiv:0906.0251) |
[23] | Annila, A., and Annila, E. 2008, Why did life emerge? Int. J. Astrobiol. 7, 293–300. |
[24] | Annila, A., and Kuismanen, E. 2008, Natural hierarchy emerges from energy dispersal. BioSystems 95, 227–233. |
[25] | Karnani, M., and Annila, A. 2009, Gaia again. BioSystems 95, 82–87. |
[26] | Sharma, V., Kaila, V. R. I., and Annila, A. 2009, Protein folding as an evolutionary process. Physica A 388, 851–862. |
[27] | Würtz, P., and Annila, A. 2010, Ecological succession as an energy dispersal process. BioSystems 100, 70–78. |
[28] | Annila, A., and Salthe, S. 2009, Economies evolve by energy dispersal. Entropy 11, 606–633. |
[29] | Annila, A. 2011, Least-time paths of light. MNRAS 416, 2944–2948. |
[30] | Koskela, M., and Annila, A. 2011, Least-time perihelion precession. MNRAS 417, 1742–1746. |
[31] | Tuisku, P., Pernu, T. K., and Annila, A. 2009, In the light of time. Proc. R. Soc. A. 465, 1173–1198. |
[32] | Annila, A. 2010, The 2nd law of thermodynamics delineates dispersal of energy. Int. Rev. Phys. 4, 29–34. |
[33] | Kaila, V. R. I., and Annila, A. 2008, Natural selection for least action. Proc. R. Soc. A. 464, 3055–3070. |
[34] | Annila, A. 2010, All in action. Entropy 12, 2333–2358. |
[35] | Eddington, A. S. 1928, The nature of physical world. MacMillan, New York, NY. |
[36] | Gibbs, J. W. 1993–1994, The scientific papers of J. Willard Gibbs. Ox Bow Press, Woodbridge, CT. |
[37] | Wyld, H. W. 1961, Formulation of the theory of turbulence in an incompressible fluid. Ann. Phys. 14, 143–165. |
[38] | Keldysh, L. V. 1964, Zh. Eksp. Teor. Fiz. 47, 1515–1527; 1965 Diagram technique for nonequilibrium processes. Sov. Phys. JETP 20, 1018–1026. |
[39] | Boltzmann, L. 1905, Populäre Schriften. Barth, Leipzig, Germany. [Partially transl. Theoretical physics and philosophical problems by B. McGuinness, Reidel, Dordrecht 1974.] |
[40] | De Donder, Th. 1936, Thermodynamic theory of affinity: A book of principles. Oxford University Press, Oxford, UK. |
[41] | Kullback, S. 1959, Information theory and statistics. Wiley, New York, NY. |
[42] | Salthe, S. N. 2002, Summary of the principles of hierarchy theory. General Systems Bulletin 31, 13–17. |
[43] | Salthe, S. N. 2007, The natural philosophy of work. Entropy 9, 83–99. |
[44] | Noether, E. 1918, Invariante Variationprobleme. Nach. v.d. Ges. d. Wiss zu Goettingen, Mathphys. Klasse 235–257; English translation Tavel, M. A. 1971 Invariant variation problem. Transp. Theory Stat. Phys. 1, 183–207. |
[45] | Jaynes, E. T. 1957, Information theory and statistical mechanics. Phys. Rev. 106, 620–630. |
[46] | Roshdi, R. 1992, Optique et Mathematiques: Recherches sur L’Histoire de la Pensee Scientifique en Arabe. Variorum, Aldershot, UK. |
[47] | Lotka, A. J. 1922, Natural selection as a physical principle. Proc. Natl. Acad. Sci. 8, 151–154. |
[48] | Zinn-Justin, J. 2002, Quantum field theory and critical phenomena. Oxford University Press, New York, NY. |
[49] | Peskin, M., and Schroeder, D. 1995, An introduction to quantum field theory. Philadelphia, PA: Westview Press. |
[50] | Thirring, W. 1970, Systems with negative specific heat. Z. Physik 235, 339– 352. |
[51] | Pokorski, S. 1987, Gauge field theories. Cambridge University Press. Cambridge, UK. |
[52] | Darwin, C. 1859, On the origin of species. John Murray, London, UK. |
[53] | Penzias, A. A., and Wilson R. W. 1965, A measurement of excess antenna temperature at 4080 Mc/s. Astrophys. J. 142, 419–421. |
[54] | Karnani, M., Pääkkönen, K., and Annila, A. 2009, The physical character of information. Proc. R. Soc. A. 465, 2155–2175. |
[55] | Poynting, J. H. 1920, Collected scientific papers. Cambridge University Press, London. |
[56] | Lavenda, B. H. 1985, Nonequilibrium statistical thermodynamics. John Wiley and Sons, New York, NY. |
[57] | Gouy, L. G. 1889, Sur l'energie utilizable. J. de Physique 8, 501–518. |
[58] | Stodola, A. 1910, Steam and gas turbines. McGraw-Hill, New York, NY. |
[59] | Weinberg, S. 1972, Gravitation and cosmology, principles and applications of the general theory of relativity. Wiley, New York, NY. |
[60] | Berry, M. 2001, Principles of cosmology and gravitation. Cambridge University Press, Cambridge, UK. |
[61] | Taylor, E. F., and Wheeler, J. A. 1992, Spacetime physics. Freeman, New York, NY. |
[62] | Lorenz, L. 1867, On the identity of the vibrations of light with electrical currents. Philos. Mag. 34, 287–301. |
[63] | Einstein, A. 1905, On the electrodynamics of moving bodies. Annalen der Physik 17, 891–921. |
[64] | Connes, A. 1994, Noncommutative geometry (Géométrie non commutative). Academic Press, San Diego, CA. |
[65] | Lemaître, G. 1927, Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques. Annales de la Société Scientifique de Bruxelles 47, 49–56. |
[66] | Hubble, E. 1929, A relation between distance and radial velocity among extra-galactic nebulae. Proc. Natl. Acad. Sci. USA 15, 168–173. |
[67] | Hawking, S. W. 1974, Black hole explosions. Nature 248, 30–31. |
[68] | Sciama, D. W. 1953, On the origin of inertia. MNRAS 113, 34–42. |
[69] | Dicke, R. H. 1961, Dirac's cosmology and Mach's principle. Nature 192, 440–441. |
[70] | Haas, A. 1936, An attempt to a purely theoretical derivation of the mass of the universe. Phys. Rev. 49, 411–412. |
[71] | Tryon, E. P. 1973, Is the universe a vacuum fluctuation? Nature 246, 396–397. |
[72] | Planck, M. 1899, Über irreversible Strahlungsvorgänge. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin 5, 440–480. |
[73] | Bennett, C.L. et al., 2003, First-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary maps and basic results. Astrophys. J. Suppl. Series, 148, 1–27. |
[74] | Salthe, S. N. 1985, Evolving hierarchical systems: Their structure and representation. Columbia University Press, New York, NY. |
[75] | Tully, R. B., and Fisher, J. R. 1977, A new method of determining distances to galaxies. Astronomy and Astrophysics 54, 661–673. |
[76] | Milgrom, M. 1983, A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J. 270, 365–370. |
[77] | Anderson, J. D., Laing, P. A., Lau, E. L., Liu, A. S., Nieto, M. M., and Turyshev, S. G. 1998, Indication, from Pioneer 10/11, Galileo, and Ulysses data, of an apparent anomalous, weak, long-range acceleration. Phys. Rev. Lett. 81, 2858–2861. |
[78] | Bertolami, O., and Páramos, J. 2004, Pioneer's Final Riddle. arXiv:gr-qc/0411020. |
[79] | Anderson, J. D., and Nieto, M. M. 2009, Astrometric solar-system anomalies. In Relativity in Fundamental Astronomy. Proceedings IAU Symposium No. 261, Klioner, S. A., Seidelman, P. K., and Soffel, M. H. eds. arXiv:0907.2469v2. |
[80] | Francisco, F., Bertolami, O., Gil, P. J. S., and Páramos J. 2011, Modelling the reflective thermal contribution to the acceleration of the Pioneer spacecraft. arXiv:1103.5222. |
[81] | Koschmieder, E. L. 1993, Bénard cells and Taylor vortices. Cambridge University Press, New York, NY. |
[82] | Taylor, G. I. 1923, Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. A 223, 289–343. |
[83] | Feynman, R. P. 1955, Application of quantum mechanics to liquid helium. Prog. Low Temp. Phys. 1, 17–53. |
[84] | De Maupertuis, P.-L. M. 1744, Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles. Mém. Ac. Sc. Paris 417–426. |
[85] | Clemence, G. M. 1947, The relativity effect in planetary motions. Rev. Mod. Phys. 19, 361–364. |
[86] | Zwicky, F. 1933, Die Rotverschiebung von extragalaktischen Nebeln. Helvetica Physica Acta 6, 110–127. |
[87] | Zwicky, F. 1937, On the masses of nebulae and of clusters of nebulae. Astrophys. J. 86, 217–246. |
[88] | Charlton, J. C., and Schramm, D. N. 1986, Percolation of explosive galaxy formation. Astrophys. J. Part 1 310, 26. |
[89] | Bok, B. J., and Reilly, E. F. 1947, Small dark nebulae. Astrophys. J. 105, 255–257. |
[90] | Annila, A. 2011, Physical portrayal of computational complexity. ISRN Computational Mathematics (in press) (www.isrn.com/journals/cm/aip/321372/) (arXiv:0906.1084) |
[91] | Poincaré, J. H. 1890, Sur le problème des trois corps et les équations de la dynamique. Divergence des séries de M. Lindstedt. Acta Mathematica 13, 1–270. |
[92] | Strogatz, S. H. 2000, Nonlinear dynamics and chaos with applications to physics, biology, chemistry and engineering. Westview, Cambridge, MA. |
[93] | Newman, J. R. 1956, The world of mathematics. Simon and Schuster, New York, NY. |
[94] | www.claymath.org/millennium/Navier-Stokes_Equations/ |
[95] | Van Moerbeke, P. 1989, Introduction to algebraic integrable systems and their Panlevé analysis. Proceeding of Symposia in Pure Mathematics 49. |
[96] | Pernu, T. K., and Annila, A. 2012, Natural emergence. Complexity. (in press) |
[97] | Mackay, A. L. 1977, The harvest of a quiet eye - a selection of scientific quotations. Bristol, UK: The Institute of Physics. |
[98] | Kondepudi, D., and Prigogine, I. 1998, Modern thermodynamics. Wiley, New York, NY. |
[99] | Verhulst, P. F. 1845, Recherches mathématiques sur la loi d’accroissement de la population. Nouv. Mém. Acad. Roy. Sci. Belleslett. Bruxelles 18, 1–38. |
[100] | May, R. M. 1976, Simple mathematical models with very complicated dynamics. Nature 261, 459–467. |
[101] | Waage, P., and Guldberg, C. M. 1864, Forhandlinger 35 Videnskabs-Selskabet i Christiana. |
[102] | Cooley, J. W., and Tukey, J. W. 1965, An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301. |
[103] | Lehto, A. 2009, On the Planck scale and properties of matter. Nonlinear Dyn. 55, 279–298. |
[104] | Alonso, M., and Finn, E. J. 1983, Fundamental university physics. 3. Addison-Wesley, Reading, MA:. |
[105] | Ryden, B. 2003, Introduction to cosmology. Addison-Wesley, New York, NY. |
[106] | Crawford, F. S. 1968, Waves in Berkeley physics course. 3. McGraw-Hill, New York, NY. |
[107] | Tifft, W. G. 1996, Global redshift periodicities and periodicity structure. Astrophys. J. 468, 491–518. |
[108] | Napier, W. M. 2003, A statistical evaluation of anomalous redshift claims. Astrophys. Space Sci. 285, 419–427. |
[109] | Chwolson, O. 1924, Über eine mögliche Form fiktiver Doppelsterne. Astronomische Nachrichten 221, 329–330. |
[110] | Einstein, A. 1936, Lens-like action of a star by the deviation of light in the gravitational field. Science 84, 506–507. |
[111] | Rosen, K. H. 1993, Elementary number theory and its applications. Reading, MA: Addison-Wesley. |
[112] | Schramm, W. 2008, The Fourier transform of functions of the greatest common divisor. Integers 8, A50. |
[113] | Richman, F. 1971, Number theory: An introduction to algebra. Wadsworth, Belmont, CA. |
[114] | Feynman, R., Leighton, R. B., and Sands, M. 1963, The Feynman lectures on physics. Addison-Wesley, Reading, MA. |
[115] | Erickson, C. 2005, A geometric perspective on the Riemann zeta function’s partial sums. SURJ Mathematics 22–31. |
[116] | Bernoulli, J. 1967, Opera, Tomus Secundus. Brussels, Belgium: Culture et Civilisation. |
[117] | Mäkelä, T., and Annila, A. 2010, Natural patterns of energy dispersal. Phys. Life. Rev. 7, 477–498. |
[118] | Hardy, G. H., and Littlewood, J. E. 1921, The zeros of Riemann’s zeta function on the critical line. Math. Z. 10, 283–317. |
[119] | Titchmarsh, E. C. 1986, The theory of the Riemann zeta function. Oxford Science Publications, Oxford, UK. |
[120] | www.claymath.org/millennium/Riemann_Hypothesis/ |
[121] | Golub, G. H., and Van Loan, C. F. 1996, Matrix computations. The Johns Hopkins University Press, Baltimore, MD. |
[122] | Franel, J., and Landau, E. 1924, Les suites de Farey et le problème des nombres premiers. Göttinger Nachr. 198–206. |
[123] | Montgomery, H. L. 1973, The pair correlation of zeros of the zeta function. Analytic number theory, Proc. Sympos. Pure Math., XXIV, 181–193. Providence, RI: Am. Math. Soc. |
[124] | Berry, M. V., and Keating, J. P. 1999, H = xp and the Riemann zeros. Supersymmetry and trace formulae: Chaos and disorder. 355–367 eds. Keating, J. P., Khmelnitski, D. E., and Lerner, I. V. Plenum, New York, NY. |
[125] | Spector, D. 1990, Supersymmetry and the Möbius inversion function. Commun. Math. Phys. 127, 239–252. |
[126] | Silverman, J. H. 1992, The arithmetic of elliptic curves. Springer-Verlag, New York, NY. |
[127] | Lang, S. 1992, Algebra. Addison-Wesley, Reading, MA. |
[128] | www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/ |
[129] | Tate, J. 1974, The arithmetic of elliptic curves. Invent. Math. 23, 179–206. |
[130] | Eddington, A. S. 1931, Preliminary note on the masses of the electron, the proton and the Universe. Proc. Camb. Phil. Soc. 27, 15–19. |
[131] | Dirac, P. A. M. 1938, A new basis for cosmology. Proc. R. Soc. A 165, 199–208. |
[132] | Barrow, J. D., and Tipler, F. J. 1986, The anthropic cosmological principle. Oxford University Press, New York, NY. |
[133] | Klein, M. J. 1967, Thermodynamics in Einstein’s thought. Science 157, 509–516. |