Applications to Astrophysics Problems


Solar Neutrino Fractional Diffusion Equation Fractional Reaction Astrophysics Problem Nonextensive Statistical Mechanic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. A. Information theory and statistical distribution theoryGoogle Scholar
  2. Mathai, A.M. and Rathie, P.N. (1977): Probability and Statistics, Macmillan, London.Google Scholar
  3. Mathai, A.M. and Rathie, P.N. (1975): Basic Concepts in Information Theory and Statistics: Axiomatic Foundations and Applications, Wiley Halsted, New York and Wiley Eastern, New Delhi.MATHGoogle Scholar
  4. Mathai, A.M. (1999): An Introduction to Geometrical Probability: Distributional Aspects with Applications, Gordon and Breach, Amsterdam. B. Generalized special functions of mathematical physics Google Scholar
  5. Mathai, A.M. and Saxena, R.K. (1973): Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Springer-Verlag, Heidelberg.MATHGoogle Scholar
  6. Mathai, A.M. and Saxena, R.K.(1978): The H-function with Applications in Statistics and Other Disciplines, Wiley Halsted, New York and Wiley Eastern, New Delhi.MATHGoogle Scholar
  7. Mathai, A.M. (1993): A Handbook of Generalized Special Functions for Statistical and Physical Sciences, Clarendon Press, Oxford. C. Matrix transformations and functions of matrix argument MATHGoogle Scholar
  8. Mathai, A.M. and Provost S.B. (1992): Quadratic Forms in Random Variables: Theory and Applications, Marcel Dekker, New York.MATHGoogle Scholar
  9. Mathai, A.M., Provost, S.B., and Hayakawa, T. (1995): Bilinear Forms and Zonal Polynomials, Springer-Verlag, New York.MATHGoogle Scholar
  10. Mathai, A.M. (1997): Jacobians of Matrix Transformations and Functions of Matrix Argument, World Scientific, New York. D. Fractional calculus MATHGoogle Scholar
  11. Srivastava, H.M. and Saxena, R.K. (2001): Operators of fractional integration and their applications. Applied Mathematics and Computation, 118, 1-52. E. Stable distributions MATHCrossRefMathSciNetGoogle Scholar
  12. Jose, K.K. and Seetha Lekshmi, V. (2004): Geometric Stable Distributions: Theory and Applications, A SET Publication, Science Educational Trust, Palai. F. Gamma functions Google Scholar
  13. Chaudry, M.A. and Zubair, S.M. (2002): On a Class of Incomplete Gamma Functions with Applications, Chapman & Hall /CRC, New York. Section 9.1 Google Scholar
  14. Boltzmann, L.: Entropie und Wahrscheinlichkeit (1872-1905). Ostwalds Klassiker der Exakten Wissenschaften, Band 286, Verlag Harri Deutsch, Frankfurt am Main 2002.Google Scholar
  15. Planck, M.: Die Ableitung der Strahlungsgesetze (1895-1900): Sieben Abhandlungen aus dem Gebiet der Elektrischen Strahlungstheorie. Ostwalds Klassiker der Exakten Wissenschaften, Band 206, Verlag Harri Deutsch, Frankfurt am Main 2001.Google Scholar
  16. Einstein, A. und von Smoluchowski, M.: Untersuchungen ueber die Theorie der Brownschen Bewegung; Abhandlung ueber die Brownsche Bewegung und verwandte Erscheinungen. Ostwalds Klassiker der Exakten Wissenschaften, Reprint der Baende 199 und 207, Verlag Harri Deutsch, Frankfurt am Main 2001.Google Scholar
  17. Pais, A. (1982): Subtle is the Lord...: The Science and the Life of Albert Einstein, Oxford University Press, Oxford.Google Scholar
  18. Bach, A. (1990): Boltzmann’s probability distribution of 1877. Archive for History of Exact Sciences, 41(1),1–40.MATHMathSciNetGoogle Scholar
  19. Nicolis, G. and Prigogine, I. (1977): Self-Organization in Nonequilibrium Systems, Wiley, New York.MATHGoogle Scholar
  20. Haken, H. (2000): Information and Self-Organization: A Macroscopic Approach to Complex Systems, Springer-Verlag, Berlin, Heidelberg.MATHGoogle Scholar
  21. Tsallis, C. and Gell-Mann, M. (Eds.) (2004): Nonextensive Entropy: Interdisciplinary Applications, Oxford University Press, New York.MATHGoogle Scholar
  22. Haubold, H.J., Mathai, A.M., and Saxena, R.K. (2004): Boltzmann-Gibbs entropy versus Tsallis entropy: Recent contributions to resolving the argument of Einstein concerning “Neither Herr Boltzmann nor Herr Planck has given a definition of W”? Astrophysics and Space Science, 290, 241–245.MATHCrossRefADSGoogle Scholar
  23. Masi, M.(2005): A step beyond Tsallis and Renyi entropies. Physics Letters, A338, 217–224. Section 9.2 ADSMathSciNetGoogle Scholar
  24. Emden, R. (1907): Gaskugeln: Anwendungen der Mechanischen Waermetheorie auf Kosmologische und Meteorologische Probleme, Verlag B.G. Teubner, Leipzig und Berlin.MATHGoogle Scholar
  25. Chandrasekhar, S. (1967): An Introduction to the Study of Stellar Structure, Dover, New York.Google Scholar
  26. Stein, R.F. and Cameron, A.G.W. (Eds.) (1966): Stellar Evolution, Plenum Press, New York.Google Scholar
  27. Kourganoff, V. (1973): Introduction to the Physics of Stellar Interiors, D. Reidel Publishing Company, Dordrecht.Google Scholar
  28. Bethe, H.A. (1973): Energy production in stars. Science, 161, 541–547.CrossRefADSGoogle Scholar
  29. Chandrasekhar, S. (1984): On stars, their evolution and their stability. Reviews of Modern Physics, 56, 137–147.CrossRefADSGoogle Scholar
  30. Haubold, H.J. and Mathai, A.M. (1994): Solar nuclear energy generation and the chlorine solar neutrino experiment. in Conference Proceedings No. 320: Basic Space Science, American Institute of Physics, New York, pp. 102–116.Google Scholar
  31. Haubold, H.J. and Mathai, A.M. (1995): Solar structure in terms of Gauss’ hypergeometric function. Astrophysics and Space Science, 228, 77–86.MATHCrossRefADSGoogle Scholar
  32. Clayton, D.D. (1986): Solar structure without computers. American Journal of Physics, 54(4), 354–362. Section 9.3 CrossRefADSMathSciNetGoogle Scholar
  33. Davis Jr., R. (2003): A half-century with solar neutrinos. Reviews of Modern Physics, 75, 985–994.CrossRefADSGoogle Scholar
  34. Davis Jr., R. 1996): A review of measurements of the solar neutrino flux and their variation. Nuclear Physics, B48, 284–298.Google Scholar
  35. Smirnov, A.Yu. (2003): The MSW effect and solar neutrinos. In Tenth International Workshop on Neutrino Telescopes, Proceedings, ed. Milla Baldo Ceolin, Venezia, March 11-14, 2003, Instituto Veneto di Scienze, Lettere ed Arti, Campo Santo Stefano, edizionni papergraf, pp. 23–43.Google Scholar
  36. Haubold, H.J. and Gerth, E. (1990): On the Fourier spectrum analysis of the solar neutrino capture rate. Solar Physics, 127, 347–356.CrossRefADSGoogle Scholar
  37. Haubold, H.J. (1998): Wavelet analysis of the new solar neutrino capture rate data for the Homestake experiment. Astrophysics and Space Science, 258, 201–218.CrossRefADSGoogle Scholar
  38. Dicke, R.H. (1978): Is there as chronometer hidden deep in the Sun? Nature, 276, 676–680.CrossRefADSGoogle Scholar
  39. Kononovich, E.V. (2004): Mean variations of the solar activity cycles: analytical representations. In Proceedings XXVII Seminar on Physics of Auroral Phenomena, Apatity, Kola Science Center, Russian Academy of Science 2004, pp. 83–86.Google Scholar
  40. Burlaga, L.F. and Vinas, A.F. (2005): Triangle for the entropic index q of non-extensive statistical mechanics observed by Voyager 1 in the distant heliosphere. Physica, A356, 375–384.ADSGoogle Scholar
  41. Siegert, S., Friedrich, R., and Peinke, J. (1998): Analysis of data sets of stochastic systems. Physics Letters, A243, 275–280.ADSMathSciNetGoogle Scholar
  42. Risken, H. (1996): The Fokker-Planck Equation, Springer-Verlag, Berlin Heidelberg.MATHGoogle Scholar
  43. Frank, T.D. (2005): Nonlinear Fokker-Planck Equations, Springer-Verlag, Berlin Heidelberg. Section 9.4 MATHGoogle Scholar
  44. Balescu, R. (2000): Statistical Dynamics: Matter out of Equilibrium, Imperial College Press, London.Google Scholar
  45. Van Kampen, N.G. (2003): Stochastic Processes in Physics and Chemistry, Elsevier, Amsterdam.Google Scholar
  46. Balescu, R. (2005): Aspects of Anomalous Transport in Plasmas, Institute of Physics Publishing, Bristol and Philadelphia. Section 9.5 CrossRefGoogle Scholar
  47. West, B.J., Bologna, M., and Grigolini, P.(2005): Physics of Fractal Operators, Springer-Verlag, New York.Google Scholar
  48. Stanislavsky, A.A. (2004): Probability interpretation of the integral of fractional order. Theoretical and Mathematical Physics, 138, 418–431. Section 9.6 CrossRefADSMathSciNetMATHGoogle Scholar
  49. Cohen, E.G.D. (2005): Boltzmann and Einstein: statistics and dynamics - an unsolved problem. Pramana Journal of Physics, 64, 635–643.CrossRefADSGoogle Scholar
  50. Boon, J.P. and Tsallis, C. (Eds.) (2005): Nonextensive Statistical Mechanics: New Trends, New Perspectives. Europhysics News, 36, 183–231.Google Scholar
  51. Tsallis, C. (2004): Dynamical scenario for nonextensive statistical mechanics. Physica, A340, 1–10.ADSMathSciNetGoogle Scholar
  52. Saxena, R.K., Mathai, A.M., and Haubold, H.J. (2004): Astrophysical thermonuclear functions for Boltzmann-Gibbs and Tsallis statistics. Physica, A344, 649–656.ADSMathSciNetGoogle Scholar
  53. Tsallis, C., Gell-Mann, M., and Sato, Y. (2005): Asymptotically scale-invariant occupancy of phase space makes the entropy S q extensive. Proceedings of The National Academy of Sciences of the USA, 102, 15377–15382. Section 9.7 Google Scholar
  54. Ben-Avraham, D. and Havlin S. (2000): Diffusion and Reactions in Fractals and Disordered Systems, Cambridge University Press, Cambridge.MATHCrossRefGoogle Scholar
  55. Fowler, W.A. (1984): Experimental and theoretical nuclear astrophysics: The quest for the origin of the elements. Reviews of Modern Physics, 56, 149–179.CrossRefADSGoogle Scholar
  56. Haubold, H.J. and Mathai, A.M. (1995): A heuristic remark on the periodic variation in the number of solar neutrinos detected on Earth. Astrophysics and Space Science, 228, 113–134.CrossRefADSGoogle Scholar
  57. Haubold, H.J. and Mathai, A.M. (1985): The Maxwell-Boltzmannian approach to the nuclear reaction rate theory. Progress of Physics, 33, 623–644.Google Scholar
  58. Anderson, W.J., Haubold, H.J., and Mathai, A.M. (1994): Astrophysical thermonuclear functions. Astrophysics and Space Science, 214, 49–70.MATHCrossRefADSGoogle Scholar
  59. Haubold, H.J. and Mathai, A.M. (2004): The fractional kinetic equation and thermonuclear functions. Astrophysics and Space Science, 273, 53–63.CrossRefADSGoogle Scholar
  60. Tsallis, C. (2004): What should a statistical mechanics satisfy to reflect nature? Physica, D193, 3–34. Section 9.8 ADSMathSciNetGoogle Scholar
  61. Metzler, R. and Klafter, J. (2000): The Random Walk’s Guide to Anomalous Diffusion: A Fractional Dynamics Approach. Physics Reports, 339, 1–77.MATHCrossRefADSMathSciNetGoogle Scholar
  62. Metzler, R. and Klafter, J. (2004): The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics. Journal of Physics A: Math. Gen., 37, R161-R208.MATHCrossRefADSMathSciNetGoogle Scholar
  63. Saxena, R.K., Mathai, A.M., and Haubold, H.J. (2004): On generalized fractional kinetic equations. Physica A, 344, 657–664.CrossRefADSMathSciNetGoogle Scholar
  64. Saxena, R.K., Mathai, A.M., and Haubold, H.J. (2004): Unified fractional kinetic equation and a fractional diffusion equation. Astrophysics and Space Science, 290, 299–310. Section 9.9 CrossRefADSGoogle Scholar
  65. Haken, H. (2004): Synergetics: Introduction and Advanced Topics, Springer-Verlag, Berlin Heidelberg.Google Scholar
  66. Wilhelmsson, H. and Lazzaro, E. (2001): Reaction-Diffusion Problems in the Physics of Hot Plasmas, Institute of Physics Publishing, Bristol and Philadelphia.CrossRefGoogle Scholar
  67. Murray, J.D. (2003): Mathematical Biology. Volume I: An Introduction. Volume II: Spatial Models and Biomedical Applications, Springer-Verlag, Berlin Heidelberg.Google Scholar
  68. Adamatzky, A., De Lacy Costello, B., and Asai, T. (2005): Reaction-Diffusion Computers, Elsevier, Amsterdam.Google Scholar
  69. Vlad, M.O. and Ross, J. (2002): Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: Applications to the theory of Neolithic transition. Physical Review, E66, 061908-1 – 061908-11.ADSMathSciNetGoogle Scholar
  70. Seki, K., Wojcik, M., and Tachiya, M. (2003): Fractional reaction-diffusion equations. Journal of Chemical Physics, 119, 2165–2170.CrossRefADSGoogle Scholar
  71. Henry, B.I. and Wearne, S.L. (2000): Fractional reaction-diffusion. Physica A, 276, 448–455.CrossRefADSMathSciNetGoogle Scholar
  72. Del-Castillo-Negrete, D., Carreras, B.A., and Lynch, V. (2003): Front dynamics in reaction-diffusion systems with Levy flights: A fractional diffusion approach. Physical Review Letters, 91, 018302-1 – 018302-4.CrossRefADSGoogle Scholar
  73. Henry, B.I., Langlands, T.A.M., and Wearne, S.L. (2005): Turing pattern formation in fractional activator-inhibitor systems. Physical Review, E72, 026101-1 – 026101-14.ADSMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Personalised recommendations