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Vita

October **, ****

Eric S. Key Professor Emeritus of Mathematics

Department of Mathematical Sciences Home Address:

University of Wisconsin-Milwaukee 442 Copper Beech Circle Milwaukee, Wisconsin 53201 Elkins Park, PA 19027

ad3yg6@r.postjobfree.com ad3yg6@r.postjobfree.com

414-***-**** 414-***-****

Degrees

BA magna cum laude in mathematics and with distinction in all subjects 1977, MA 1980, PhD 1983, Cornell University.

Employment

University of Wisconsin-Milwaukee. Assistant Professor of Mathematics, 1983-1989. Associate Pro- fessor of Mathematics, 1989-2005. Professor of Mathematics, 2005-2016. Professor Emeritus of Mathematics 2016 - Present. Medical College of Wisconsin, Associate Adjunct Professor in Bio- statistics, 1995- . Current Positions: Medical College of Wisconsin, Associate Adjunct Professor in Biostatistics.

Personal Information

Born 22 December, 1954, Hackensack, New Jersey

Teaching Experience

College Algebra Analytic Geometry

Trigonometry Calculus with Precalculus

Calculus with Physics Calculus I, II, III

Advanced Calculus Real Analysis

Vector Analysis Complex Analysis

Measure Theory Linear Algebra and Di erential Equations Advanced Linear Algebra Introductory Abstract Algebra Probability Theory (calculus prequisite) Probability Theory (measure theory prerequisite) Stochastic Processes (graduate level) Stochastic Processes (undergraduate level) Statistics for High School Teachers Mathematical Statistics (calculus prerequisite) PhD Theses Directed

J. Wood. May 2012. Modeling Processes With Heavy Tails.

G. Vachadze. May 2003. Finite Mixture Models and Their Applications in Finance.

S. Karmakar. August 1992. Compositions of Random Mobius Transformations and Their Applications.

A. Abeyratne. May, 1991. Limiting Distributions for Multitype Branching Processes with Immigration in a Random Environment.

Publications

1. A recipe for bivariate copulas. Communications in Statistics. To appear. 2016. October 11, 2017 2

2. A note on the spectral radius of a product of companion matrices. With H. Volkmer. Electronic Journal of Linear Algebra. Volume 27. pp 879 - 881. 2014. 3. Di erentiating arctangent directly. College Mathematics Journal, Volume 40, Number 4, pp 287-288, 2009.

4. On Parrondo's paradox: How to construct unfair games by composing fair games. With D. Abbott and M. M. Klosek. ANZIAM Journal 47, pp 495-511, 2006. 5. On the number of records in an iid discrete sequence. Journal of Theoretical Probability 18, No. 1, pp 99 - 108, 2005.

6. A painless approach to least squares. The College Mathematics Journal 36, No. 1, pp 65 - 67, 2005.

7. Eigenvalue multiplicities of products of companion matrices. With H. Volkmer. Electronic Journal of Linear Algebra, Volume 11, pp 103 - 114. 2004. 8. Compositions of random mobius transformations. With S. Karmakar. Stochastic Analysis and Applications, Vol. 22, No. 3 pp 525 - 557. 2004

9. Solution to a functional equation and its application to stable and stable-type distributions. With G. G. Hamedani and H. Volkmer. Statistics and Probability Letters 69, pp 1 - 9. 2004 10. A characterization of discrete uniform distributions based on orderings. Journal of Statistical Theory and Applications 3, No. 1, pp 1 - 4, 2004.

11. Perturbation of orthonormal bases in L

2

-Spaces. With X. He and H. Volkmer. Integral Equa- tions and Operator Theory Volume 41, Number 4: 396 - 409 (2001) 12. Some characterizations of the normal distribution. With N. Bansal, J. Behboodian, G. G. Hamedani, H. Volkmer and H. Zhang. Statistics and Probability Letters 42: 393 - 400, 1999 13. Symmetric measure-preserving systems. Real Analysis Exchange, Volume 24, Number 1: 411

- 422, 1998-1999.

14. Divergence rates for the number of rare numbers. Journal of Theoretical Probability, Volume 9, Number 2: 413 - 428, 1996.

15. On entire characteristic functions of order 2. Sankhya, Series A, Volume 56, Part 3: 431 - 437, 1994.

16. Disks, shells and integrating inverses. The College Mathemetics Journal, Volume 25, Number 2: 136 - 138, 1994.

17. Rare numbers. Journal of Theoretical Probability, Volume 5, Number 2: 375 - 389, 1992. 18. Lower bounds for the maximal Lyapunov exponent. Journal of Theoretical Probability, Volume 3, Number 3: 477 - 488, 1990.

19. A probabilistic approach to a conjecture of Ramanujan. The Journal of the Ramanujan Math- ematical Society, Volume 4, Number 2: 109 - 119, 1989. 20. Lyapunov exponents for matrices with invariant subspaces. The Annals of Probability Volume 16, Number 4: 1721-1728, 1988.

21. Computable examples of the maximal Lyapunov exponent. Probability Theory and Related Fields 75: 97-107, 1987.

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22. Limiting distributions and regeneration times for multitype branching processes with immi- gration in a random environment. The Annals of Probability Volume 15, Number 1: 344-353, 1987.

23. Using random matrices to give recurrence and transience criteria for random walk in a random environment. In Richard Durrett, editor, Particle Systems, Random Media and Large Devia- tions, pages 253-258. Contemporary Mathematics Volume 41, American Mathematical Society, 1985. Revised and reprinted in Joel E. Cohen, Harry Kesten and Charles Newman, Editors, Random Matrices and Their Applications, pages 255-261. Contemporary Mathematics Volume 50, American Mathematical Society, 1986.

24. Recurrence and transience criteria for random walk in a random environment. The Annals of Probability Volume 12, Number 2: 529-560, 1984.

25. Recurrence and Transience Criteria and a Limit Law for Generalized Random Walk in a Ran- dom Environment. PhD thesis, Cornell University, 1983.

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