36 resultados para Three-Dimension, Fractional Advection-Diffusion Equation, Fourier Analysis, Convergence, Stability


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* Supported by INTAS 2000-626, INTAS YSF 03-55-1969, INTAS INNO 182, and TIC 2003-09319-c03-03.

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Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.

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The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social con-science applied to international scientific activity.

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2002 Mathematics Subject Classification: 65C05.

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* The author was supported by NSF Grant No. DMS 9706883.

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2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.

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MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45

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2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

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Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.

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Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.

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Mathematics Subject Classification: 26A33, 31B10

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Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.

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A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.

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Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

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Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90