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| Roger Chalkley Professsor, Mathematical Sciences Ph.D., University of Cincinnati, 1958 Ch.E., University of Cincinnati, 1954 Address: 822-A Old Chemistry Building PO Box 45221-0025 Cincinnati, Ohio 45221-0025 phone: 513-556-4074 fax: 513-555-7228 Roger.Chalkley@uc.edu http://math.uc.edu/~chalklr/ |
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Biography: Since 1957, my research interests have been concerned mainly with ordinary differential equations having meromorphic coefficients on a region of the complex plane. |
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Research Areas: My most recent publications are: Basic global relative invariants for homogeneous linear differential equations, Memoirs of the American Mathematical Society 156 (March 2002), Number 744, 1-204. Lazarus Fuchs' transformation for solving rational first-order differential equations, Journal of Mathematical Analysis and Applications, 187 (1994) 961 - 985. A persymmetric determinant, Journal of Mathematical Analysis and Applications, 187 (1994) 107 - 117. Semi-invariants and relative invariants for homogeneous linear differential equations, Journal of Mathematical Analysis and Applications, 176 (1993) 49 - 75. A formula giving the known relative invariants for homogeneous linear differential equations, Journal of Differential Equations, 100 (1992) 379 - 404. The differential equation Q = 0 in which Q is a quadratic form in y", y', y having meromorphic coefficients, Proceedings of the American Mathematical Society , 116 (1992) 427 - 435. Relative invariants for homogeneous linear differential equations, Journal of Differential Equations, 80 (1989) 107 - 153. New contributions to the related work of Paul Appell, Lazarus Fuchs, Georg Hamel, and Paul Painlevé on nonlinear differential equations whose solutions are free of movable branch points, Journal of Differential Equations, 68 (1987) 72 - 117. My principal research during the years 1995-2001 was published in March of 2002 as the Memoir of the American Mathematical Society titled “Basic global relative invariants for homogeneous linear differential equations.” It appears in Volume 156 as Number 744 (the fifth of 5 numbers). This Memoir presents remarkable new results of a rigorous nature for a subject that defied adequate treatment by mathematicians during the years from 1888 to1989. It is completely self-contained and consists of 204 + five pages. < back > |
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