A. M. Mathai Centre for Mathematical and Statistical Sciences: A Brief History of the Centre and Prof. Dr. A. M. Mathai’s Research and Education Programs at the Occasion of His 85th Anniversary — Oak Academic Publishing
Research ArticleOpen AccessGoogle Scholar indexed
A. M. Mathai Centre for Mathematical and Statistical Sciences: A Brief History of the Centre and Prof. Dr. A. M. Mathai’s Research and Education Programs at the Occasion of His 85th Anniversary
Office for Outer Space Affairs, United Nations Vienna International Centre, Vienna, Austria
1 Office for Outer Space Affairs, United Nations Vienna International Centre, Vienna, Austria
A brief history of the Centre for Mathematical and Statistical Sciences, Kerala, India, is given and an overview of Mathai’s research and education programs in the following topics is outlined: Fractional Calculus; Functions of Matrix Argument — M-transforms, M-convolutions; Kr ä tzel integrals; Pathway Models; Geometrical Probabilities; Astrophysics — reaction rate theory, solar neutrinos; Special Functions — G and H-functions; Multivariate Analysis; Algorithms for Non-linear Least Squares; Characterizations — characterizations of densities, information measure, axiomatic definitions, pseudo analytic functions of matrix argument and characterization of the normal probability law; Mathai’s Entropy — entropy optimization; Analysis of Variance; Population Problems and Social Sciences; Quadratic and Bilinear Forms; Linear Algebra; Probability and Statistics .
KeywordsFractional CalculusFunctions of Matrix ArgumentSpecial Functions of Mathematical PhysicsGeometrical ProbabilitiesMultivariate AnalysisCharacterizationAlgorithmsQuadratic and Bilinear FormsEntropyReactionDiffusionSolar Neutrinos
Beck, C. (2004). Superstatistics: Theory and Applications. Continuum Mechanics and Thermodynamics, 16, 293-304. https://doi.org/10.1007/s00161-003-0145-1
Cohen, E. G. D. (2004). Superstatistics. Physica D: Nonlinear Phenomena, 193, 35-52. https://doi.org/10.1016/j.physd.2004.01.007
Constantine, A. G. (1963). Some Noncentral Distribution Problems in Multivariate Analysis. Annals of Mathematical Statistics 34, 1270-1285. https://doi.org/10.1214/aoms/1177703863
Critchfield, C. L. (1972). Analytic Forms of the Thermonuclear Function. In F. Reines (Ed.), Cosmology, Fusion & Other Matters: George Gamow Memorial Volume (pp. 186-191). Colorado: Colorado Associated University Press.
Davis Jr., R. (2003). A Half Century with Solar Neutrinos. Reviews of Modern Physics, 75, 985-994. https://doi.org/10.1103/RevModPhys.75.985
Fowler, A. W. (1984). Experimental and Theoretical Nuclear Astrophysics: The Quest for the Origin of the Elements. Reviews of Modern Physics, 56, 149-179. https://doi.org/10.1103/RevModPhys.56.149
George, A., & Mathai, A. M. (1974). Applications of the Concepts of Affinity and Distance to Population Problems. Journal of Biosocial Sciences (London), 6, 347-356. https://doi.org/10.1017/S0021932000009706
George, A., & Mathai, A. M. (1975). Distribution of Inter-Live-Birth Intervals. Sankhya Series B, 37, 332-342.
Gordon, F. S., & Mathai, A. M. (1972). Characterization of Multivariate Normal Distribution using Regression Properties. Annals of Mathematical Statistics, 43, 53-65. https://doi.org/10.1214/aoms/1177692714
Haubold, H. J., & Mathai, A. M. (1988). Gravitational Instability in a Multicomponent Cosmological Medium. Journal of Mathematical Physics, 29, 2069-2077. https://doi.org/10.1063/1.527864
Haubold, H. J., & Mathai, A. M. (1997). Sun. In J. H. Shirley, & R. W. Fairbridge (Eds.), Encyclopaedia of Planetary Sciences (pp. 786-794). London: Chapman and Hall. https://doi.org/10.1007/1-4020-4520-4_390
Haubold, H. J., & Mathai, A. M. (1998). Structure of the Universe,. In G. L. Trigg (Ed.), Encyclopedia of Applied Physics (pp. 47-51).
Haubold, H. J., & Mathai, A. M. (Eds.) (2010). Proceedings of the Third UN/ESA/NASA Workshop on the International Heliophysical Year 2007 and Basic Space Science. Berlin and Heidelberg: Springer. https://doi.org/10.1007/978-3-642-03325-4
Haubold, H. J., Mathai, A. M., & Saxena, R. K. (2011). Mittag-Leffler Functions and Their Applications. Journal of Applied Mathematics, 2011, Article ID: 298628. https://doi.org/10.1155/2011/298628
Herz, C. S. (1955). Bessel Functions of Matrix Argument. Annals of Mathematics, 63, 474-523.
James, A. T. (1961). Zonal Polynomials of the Real Positive Definite Symmetric Matrices. Annals of Mathematics, 74, 456-469. https://doi.org/10.2307/1970291
Kounias, S., & Mathai, A. M. (1988). Maximizing the Sum of Integers When Their Sum of Squares Is Fixed. Optimization, 19, 123-131. https://doi.org/10.1080/02331938808843325
Kratzel, E. (1979). Integral Transforms the Bessel Type. In Generalized Functions & Operational Calculus, Proc. Conf. Verna, 1975 (pp. 148-165). Sofia: Bulg. Acad. Sci.
Mathai, A. M. (1965). An Approximate Analysis of a Two-Way Layout. Biometrics, 21, 376-385. https://doi.org/10.2307/2528097
Mathai, A. M. (1982). On a Conjecture in Geometric Probability Regarding Asymptotic Normality of a Random Simplex. Annals of Probability, 10, 247-251. https://doi.org/10.1214/aop/1176993929
Mathai, A. M. (1989). On a System of Differential Equations Connected with the Gravitational Instability in a Multi-Component Medium in Newtonian Cosmology. Studies in Applied Mathematics, 80, 75-93. https://doi.org/10.1002/sapm198980175
Mathai, A. M. (1993a). A Handbook of Generalized Special Function for Statistical and Physical Sciences. Oxford: Oxford University Press.
Mathai, A. M. (1993b). On Generalized Laplacianness of Bilinear Forms in Normal Variables. Journal of Multivariate Analysis, 45, 239-246. https://doi.org/10.1006/jmva.1993.1036
Mathai, A. M. (1993c). The Residual Effect of a Growth-Decay Mechanism and the Distribution of Covariance Structures. Canadian Journal of Statistics, 21, 277-283. https://doi.org/10.2307/3315753
Mathai, A. M. (1997). Jacobians of Matrix Transformations and Functions of Matrix Argument. New York: World Scientific Publishing. https://doi.org/10.1142/3438
Mathai, A. M. (1998). Pollution by Vehicular Travels from the Suburbs to the City Core. Environmetrics, 9, 617-628. https://doi.org/10.1002/(SICI)1099-095X(199811/12)9:6 3.0.CO;2-E
Mathai, A. M. (1999a). An Introduction to Geometrical Probability: Distributional Aspects with Applications. Newark: Gordon and Breach.
Mathai, A. M. (1999b). Random p-Parallelotope in Euclidean n-Space. Advances in Applied Probability, 31, 343-354. https://doi.org/10.1239/aap/1029955138
Mathai, A. M. (1999c). Buffon Type Problem in the Euclidean Space R3. Rendiconti del Circolo Matematico di Palermo, XLVIII, 487-506. https://doi.org/10.1007/BF02844338
Mathai, A. M. (2003). Order Statistics from a Logistic Distribution and Applications to Survival & Reliability Analysis. IEEE Transactions on Reliability, 52, 200-206. https://doi.org/10.1109/TR.2003.813432
Mathai, A. M. (2005). A Pathway to Matrix-Variate Gamma and Normal Densities. Linear Algebra and Its Applications, 396, 317-328. https://doi.org/10.1016/j.laa.2004.09.022
Mathai, A. M. (2007). Random Volumes under a General Matrix-Variate Model. Linear Algebra and its Applications, 425, 162-170. https://doi.org/10.1016/j.laa.2007.03.022
Mathai, A. M. (2009). Fractional Integrals in the Matrix-Variate Cases and Connection to Statistical Distributions. Integral Transforms and Special Functions, 20, 871-882. https://doi.org/10.1080/10652460902867791
Mathai, A. M. (2012). Generalized Kratzel Integral and Associated Statistical Densities. International Journal of Mathematical Analysis, 6, 2501-2510.
Mathai, A. M. (2013). Fractional Integral Operators in the Complex Matrix-Variate Case. Linear Algebra and its Applications, 439, 2901-2913. https://doi.org/10.1016/j.laa.2013.08.023
Mathai, A. M. (2014). Fractional Integral Operators Involving Many Matrix Variables. Linear Algebra and its Applications, 446, 196-215. https://doi.org/10.1016/j.laa.2014.01.003
Mathai, A. M. (2015). Fractional Differential Operators in the Complex Matrix-Variate Case. Linear Algebra and its Applications, 478, 200-217. https://doi.org/10.1016/j.laa.2015.03.038
Mathai, A. M. (2017). A Variant of Type-1 Beta and Dirichlet Integrals. Journal of the Ramanujan Society of Mathematics and Mathematical Sciences, 6, 25-40.
Mathai, A. M. (2018). Mellin Convolutions, Statistical Distributions and Farctional Calculus. Fractional Calculus & Applied Analysis, 21, 376-398. https://doi.org/10.1515/fca-2018-0022
Mathai, A. M. (2019). Extended Fractional Integrals, Products and Ratios of Matrices and Statistical Distributions. 67th Annual Conference of Bharat Ganita Parishad, Lucknow, India, November 2019.
Mathai, A. M., & Davis, T. A. (1973). A Mathematical Explanation of the Emergence of Foliar Spirals in Coconut and Other Palm Trees. Proceedings of the National Science Academy (India), 39, 194-202.
Mathai, A. M., & Davis, T. A. (1974). Constructing a Sunflower Head. Mathematical Biosciences, 20, 117-133. https://doi.org/10.1016/0025-5564(74)90072-8
Mathai, A. M., & Haubold, H. J. (1988). Modern Problems in Nuclear and Neutrino Astrophysics. Berlin: Akademie-Verlag.
Mathai, A. M., & Haubold, H. J. (2008). Special Functions for Applied Scientists. New York: Springer. https://doi.org/10.1007/978-0-387-75894-7
Mathai, A. M., & Haubold, H. J. (2017a). Linear Algebra for Physicists and Engineers. Berlin: De Gruyter. https://doi.org/10.1515/9783110562507
Mathai, A. M., & Haubold, H. J. (2017b). Probability and Statistics for Physicists and Engineers. Berlin: De Gruyter. https://doi.org/10.1515/9783110562545
Mathai, A. M., & Haubold, H. J. (2017c). Fractional and Multivariable Calculus: Model Building and Optimization Problems. Switzerland: Springer. https://doi.org/10.1007/978-3-319-59993-9
Mathai, A. M., & Haubold, H. J. (2018a). United Nations Basic Space Science Initiative (UNBSSI) 1991-2012 and beyond. Creative Education, 9, 192-248. https://doi.org/10.4236/ce.2018.92015
Mathai, A. M., & Haubold, H. J. (2018b). Matrix Methods and Fractional Calculus. London: World Scientific Publishing. https://doi.org/10.1142/10639
Mathai, A. M., & Haubold, H. J. (2018c). An Introduction to Fractional Calculus. New York: Nova Science Publishers. https://doi.org/10.1142/10639
Mathai, A. M., & Haubold, H. J. (2018d). Erdélyi-Kober Fractional Calculus: From a Statistical Perspective, Inspired by Solar Neutrino Physics. In Springer Briefs in Mathematical Physics Volume 31. Singapore: Springer. https://doi.org/10.1007/978-981-13-1159-8
Mathai, A. M., & Katiyar, R. S. (1979). Exact Percentage Points for Testing Independence. Biometrika, 66, 353-356. https://doi.org/10.1093/biomet/66.2.353
Mathai, A. M., & Katiyar, R. S. (1993). A New Algorithm for Nonlinear Least Squares. Researches in Mathematical Statistics (Russian), 207, 143-157. (Translation by the American Mathematical Society)
Mathai, A. M., & Moschopoulos, P. G. (1999). Pollution by Vehicular Travels from Satellite Townships to the City. Environmetrics, 10, 791-802. https://doi.org/10.1002/(SICI)1099-095X(199911/12)10:6 3.0.CO;2-R
Mathai, A. M., & Pederzoli, G. (1977). Characterization of the Normal Probability Law. New Delhi: Wiley Eastern; and New York: Wiley Halsted.
Mathai, A. M., & Princy, T. (2017a). Maxwell-Boltzmann and Rayleigh Distributions for the Rectangular Matrix-Variate Case. Physica A, 532, 287-311.
Mathai, A. M., & Princy, T. (2017b). Analogues of Reliability Analysis for the Matrix-Variate Case. Linear Algebra and Its Applications, 532, 287-311. https://doi.org/10.1016/j.laa.2017.06.022
Mathai, A. M., & Provost, S. B. (1992). Quadratic Forms in Random Variables: Theory and Applications. New York: Marcel Dekker.
Mathai, A. M., & Provost, S. B. (2005). Some Complex Matrix-Variate Statistical Distributions on Rectangular Matrices. Linear Algebra and its Applications, 410, 198-216. https://doi.org/10.1016/j.laa.2005.07.016
Mathai, A. M., & Provost, S. B. (2006). On q-Logistic and Related Distributions. IEEE Transactions on Reliability, 55, 237-244. https://doi.org/10.1109/TR.2006.874927
Mathai, A. M., & Rathie, P. N. (1971). Exact Distribution of Wilks’ Criterion. Annals of Mathematical Statistics, 42, 1010-1019. https://doi.org/10.1214/aoms/1177693329
Mathai, A. M., & Rathie, P. N. (1972). Enumeration of Almost Cubic Maps. Journal of Combinatorial Theory, 13, 83-90. https://doi.org/10.1016/0095-8956(72)90012-3
Mathai, A. M., & Rathie, P. N. (1975). Basic Concepts in Information Theory and Statistics: Axiomatic Foundations and Application. New York: Wiley Halsted; and New Delhi: Wiley Eastern.
Mathai, A. M., & Saxena, R. K. (1969). Distribution of a Product and Structural Setup of Densities. Annals of Mathematical Statistics, 40, 1439-1448. https://doi.org/10.1214/aoms/1177697515
Mathai, A. M., & Saxena, R. K. (1973). Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences. Heidelberg: Springer. https://doi.org/10.1007/BFb0060468
Mathai, A. M., & Saxena, R. K. (1978). The H-Function with Applications in Statistics and Other Disciplines. New York: Wiley Halsted; and New Delhi: Wiley Eastern.
Mathai, A. M., Provost, S. B., & Hayakawa, T. (1995). Bilinear Forms and Zonal Polynomials. In Lecture Notes in Statistics 102. New York: Springer. https://doi.org/10.1007/978-1-4612-4242-0
Mathai, A. M., Saxena, R. K., & Haubold, H. J. (2010). The H-Function: Theory and Applications. New York: Springer. https://doi.org/10.1007/978-1-4419-0916-9
Pyenson, L., Mathai, A. M., & Haubold, H. J. (2019). United Nations Education Program in Space Science and Technology 1988-2018. Creative Education, 10, 2219-2231. https://doi.org/10.4236/ce.2019.1010160
Sakurai, K. (2014). Solar Neutrino Problems—How They Were Solved. Tokyo: Terrapub.
Schulz-Fieguth, M. (2018). Hans-Jürgen Treder—Ein Portrat. Potsdam, Germany: Christian and Cornelius Rüss.
Thomas, S., & Mathai, A. M. (2009). P-Content of p-Parallelotope and Its Connection to Likelihood Ratio Statistics. Sankhya Series A, 71, 49-63.
Treder, H.-J. (1974). Gravitation und weitreichende schwache Wechselwirkungen bei Neutrino-Feldern (Gedanken zu einer Theorie der solaren Neutrinos). Astronomische Nachrichten, 295, 169-184. https://doi.org/10.1002/asna.19742950403
Treder, H.-J. (1989). Fraktale und gebrochene Ableitungen. Annalen der Physik, 46, 74-75. https://doi.org/10.1002/andp.19895010110