Franklin Mendivil
Curriculum Vitae


Address


Department of Mathematics and Statistics
Acadia University
Wolfville, NS B4P 2R6

(902) 585-1368
franklin.mendivil@acadiau.ca


Education

Ph.D. in Mathematics, March 1996
Georgia Institute of Technology
Thesis: Compactifications and Function Spaces
Advisor: George Cain

M.S. in Applied Mathematics, June 1991
Georgia Institute of Technology

B.S. in Civil Engineering (with highest honor), September 1989
Georgia Institute of Technology


Employment History

2010 -
Full Professor
Department of Mathematics and Statistics
Acadia University

2003 - 2010

Associate Professor
Department of Mathematics and Statistics
Acadia University

2000 - 2003

Assistant Professor
Department of Mathematics and Statistics
Acadia University

1998 - 2000

NSF University-Industrial Collaborative Postdoctoral Fellow
Georgia Tech School of Mathematics and Iterated Systems, Inc.
Fractal Geometry and Analysis, Stochastic Optimization, Image Processing.

1996 - 1998

Postdoctoral Research Associate
Applied Mathematics , University of Waterloo
Theory of Fractals and Applications to Image Processing

1991 - 1995

TA and Instructor of calculus and linear algebra courses
Georgia Institute of Technology

1989-1990

Research Assistant for Dr. R. Shonkwiler
Worked on Genetic Algorithms to solve Inverse Fractal Problem
Georgia Institute of Technology

1989

Lab Assistant in Hydraulics Lab
Helped with a study for Savannah River Power Station
Georgia Institute of Technology


Books

  1. R. Shonkwiler and F. Mendivil, Explorations in Monte Carlo Methods , Undergraduate Texts in Mathematics, Springer, 2009

  2. Herb Kunze, Davide La Torre, Franklin Mendivil and Edward Vrscay, Fractal-based methods in analysis , Springer, 2011.

Selected Publications

  1. F. Mendivil Countable compactifications and a generalized Hahn-Mazurkeiwicz type theorem Topology Appl. 72 1996.

  2. F. Mendivil and E.R. Vrscay Correspondence between fractal-wavelet transforms and Iterated Function Systems with grey-level maps in Fractals in Engineering, edited by J. Levy Vehel, E. Lutton and C. Tricot, Springer-Verlag, 1997.

  3. F. Mendivil and E.R. Vrscay (1997), Fractal-Based Techniques in Image Compression, Canadian Conference on Electrical and Computer Engineering, St. John's, Newfoundland, May 1997, 486-489.

  4. E.R. Vrscay and F. Mendivil (1997), Generalized Fractal-Wavelet Transforms for Image Representation and Compression, Canadian Conference on Electrical and Computer Engineering, St. John's, Newfoundland, May 1997, 490-495.

  5. F. Mendivil, A generalization of IFS with probabilities to infinitely many maps Rocky Mountain J. Math. 28 no. 3. (1998)

  6. B. Forte and F. Mendivil A classical ergodic property for IFS: A simple proof Ergodic Theory Dynam. Systems 18 no 3. (1998)

  7. B. Forte, F. Mendivil and E.R. Vrscay "Chaos Games" for Iterated Function Systems with grey level maps SIAM J. Math. Anal. 29 no 4. (1998)

  8. F. Mendivil and D. Piche Two algorithms for non-separable wavelet transforms and applications to image compression in Fractals: Theory and Applications in Engineering, edited by M. Dekking, J. Levy VEhel, E. Lutton and C. Tricot, Springer-Verlag, 1999.

  9. B. Forte, F. Mendivil and E.R. Vrscay IFS-type operators on integral transforms in Fractals: Theory and Applications in Engineering, edited by M. Dekking, J. Levy VEhel, E. Lutton and C. Tricot, Springer-Verlag, 1999.

  10. F. Mendivil Function algebras and the lattice of compactifications Proc. Amer. Math Soc. 127 (6), 1999.

  11. F. Mendivil, R. Shonkwiler and M.C. Spruill Restarting search algorithms with applications to simulated annealing Adv. in Appl. Probab. 33 (2000)

  12. F. Mendivil, R. Shonkwiler and M.C. Spruill Optimization by Stochastic Methods , Handbook of Stochastic Analysis and Applications , edited by D. Kannan and v. Kakashmikantham, Marcel Dekker. (2001)

  13. F. Mendivil, E.R. Vrscay Fractal vector measures and vector calculus on planar fractal domains Chaos Solitons Fractals 14 (2002) Issue 8, 1239-1254

  14. F. Mendivil, E.R. Vrscay Self-affine vector measures and vector calculus on fractals , in Fractals in Multimedia IMA Volumes in Mathematics and its Applications, Vol 132, M. Barnsley, D. Saupe, E.R. Vrscay, editors, pp. 137-156 (2002)

  15. F. Mendivil, J. Silver Chaos Games for Wavelet Analysis and Wavelet Synthesis, Comput. Math. Appl. 46 (2003), no. 5-6, 863-873.

  16. F. Mendivil Fractals, Graphs, and Fields Amer. Math. Monthly 110 (2003), no. 6, 503-515.

  17. C. Cabrelli, F. Mendivil, U. Molter, R. Shonkwiler, On the Hausdorff h-measure of Cantor Sets Pacific J. Math. 217 (2004) no. 1, 45-59.

  18. F. Mendivil, R. Shonkwiler and M.C. Spruill An analysis of Random Restart and Iterated Improvement for Global Optimization with an application to the Traveling Salesman Problem J. Optim. Theory Appl. , 124 (2005), no. 2, 402-433.

  19. D. La Torre, F. Mendivil, E. R. Vrscay, Iterated function systems on multifunctions Proceedings of MATH EVERYWHERE - Deterministic and stochastic modelling in biomedicine, economics and industry Springer-Verlag (2006).

  20. F. Mendivil, T. Taylor Thin sets with fat shadows: Projections of Cantor Sets Amer. Math. Monthly 115 (2008), no. 5, 451-456.

  21. J. Levy-Vehel, F. Mendivil, E. Lutton Overcompressing JPEG Images with Evolution Algorithms EvoWorkshops2007: 383-390.

  22. D. La Torre, F. Mendivil Iterated function systems on multifunctions and inverse problems , J. Math. Anal. Appl. 340 (2008) 1469-1479.

  23. D. La Torre, F. Mendivil Union-additive multimeasures and self-similarity , Commun. Math. Anal. 7 (2009), no. 2, 51-61.

  24. F. Mendivil, R. Shonkwiler, M. C. Spruill Geometric convergence of genetic algorithms under tempered random restart , J. Appl. Probab. 46 no. 4 (2009), 960-974.

  25. F. Mendivil, R. Shonkwiler Annealing a Genetic Algorithm for constrained optimization J. Optim. Theory Appl. 147 (2010), no. 2, 395-410.

  26. U. Freiberg, D. La Torre, F. Mendivil Iterated function systems and stability of variational problems on self-similar objects Nonlinear Anal. Real World Appl. 12 (2011) 1123-1129.

  27. J. Levy-Vehel, F. Mendivil Multifractal and higher-dimensional zeta functions Nonlinearity 24 (2011) 259-276.

  28. F. Mendivil, J. C. Saunders On Minkowski measurability Fractals 19 no. 4 (2011), 455 - 467.

  29. D. La Torre, F. Mendivil Minkowski-additive multimeasures, monotonicity and self-similarity, Image Anal. Stereol. 30 no. 3 (2011), 135-142.

  30. F. Mendivil, D. Patterson Dynamics of finite linear cellular automata over $Z_N$ Rocky Mountain J. Math. 42 no. 2 (2012), 695-709.

  31. J. Levy-Vehel, F. Mendivil Local complex dimensions of a fractal string, Int. J. Mathematical Modelling and Numerical Optimization special issue on "Fractals, Fractal-based Methods and Applications", 3 , no. 4 (2012), 298-312.

  32. H. Kunze, D. La Torre, F. Mendivil, E.R. Vrscay Generalized fractal transforms and self-similar objects in cone metric spaces, Comput. Math. Appl. 64 (2012), 1761 - 1769.

  33. K. Hare, F. Mendivil, L. Zuberman The sizes of rearrangments of Cantor sets, Canad. Math. Bull. 56 no. 2 (2013), 354 - 365.

  34. J. Levy-Vehel, F. Mendivil Christiane's Hair, Amer. Math. Monthly 129 (2013) no. 9, 771-786.

  35. D. La Torre, F. Mendivil A Chaos Game Algorithm for Generalized Iterated Function Systems, Appl. Math. Comput. 224 (2013), 238-249.

  36. H. Kunze, D. La Torre, F. Mendivil, E.R. Vrscay Continuous evolution of equations and inclusions involving set-valued contraction mappings with applications to generalized fractal transform, Electron. J. Diff. Equ., Vol 2014 (2014), No. 142, pp.1-17.

  37. D. La Torre, F. Mendivil The Monge-Kantorovich metric on multimeasures and self-similar multimeasures, Set-Valued Var. Anal. 23 (2015), pp. 319-331.

  38. D. Day , F. Mendivil Fractal measures with uniform marginals , J. Math. Anal. Appl. 429 (2015), pp. 1096-1112.

  39. F. Mendivil Time-dependent iteration of random functions , Chaos Solitons Fractals 75 (2015), pp. 178-184.

  40. F. Mendivil, O. Stenflo V-Variable image compression , Fractals 23 , no. 2 (2015), pp. 1550007

  41. D. La torre, S. Marsiglio, F. Mendivil, F. Privileggi Self-similar measures in multi-sector endogenous growth models , Chaos Solitons Fractals 79 (2015) pp 40-56.

  42. D. La Torre, F. Mendivil Arclength as the invariant measure for an IFS with probabilities , Fractals 23 no 4 (2015) pp. 1550046.

  43. K. Hare, F. Mendivil, L. Zuberman Packing and Hausdorff measures of Cantor sets associated with series, to appear in Real Anal. Exchange

  44. F. Mendivil Computing the Monge-Kantorovich Distance to appear in Comp. Appl. Math.

  45. J. Hooper, F. Mendivil Transposition as a permutation: a tale of group actions and modular arithmetic Math. Magazine 89 (2016), pp. 16-35.

  46. D. La Torre, F. Mendivil, E.R. Vrscay Iterated function systems on functions of bounded variation Fractals 24 , no 2 (2016), pp. 1650019.

  47. D. La Torre, F. Mendivil, O. Michailovich, E.R. Vrscay (2016) Total Variation Minimization for Measure-Valued Images with Diffusion Spectrum Imaging as Motivation, in Campilho A., Karray F. (eds) Image Analysis and Recognition. ICIAR 2016 Lecture Notes in Computer Science, vol 9730, Springer.

  48. D. La Torre, F. Mendivil, E.R. Vrscay Total variation denoising of probability measures using iterated function systems with probabilities, Proceedings of the International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, AIP Conference Proceedings, 1798 020091 (2017) doi:10.1063/1.4972683

  49. D. La Torre, F. Mendivil, Portfo optimization under partial uncertainty and incomplete information: A probability multimeasure-based approach, to appear in Ann. Oper. Res.

  50. I. Garcia, K. Hare, F. Mendivil, Assouad dimensions of complementary sets, to appear in Proc. Roy. Soc. Edinburgh Sect. A

  51. S. Alwadani , F. Mendivil, R. Shonkwiler, Limiting distribution and mixing time for genetic algorithms, book chapter to appear in Nature Inspired Computing and Optimization: Theory and Applications , Springer-Verlag.

  52. D. La Torre, F. Mendivil, Stochastic linear optimization under partial uncertainty and incomplete information using the notion of probability multimeasure, to appear in Journal of the Operational Research Society

  53. D. La torre, S. Marsiglio, F. Mendivil, F. Privileggi Fractal Attractors and Singular Invariant Measures in Two-Sector Growth Models with Random Factor Shares , to appear in Commun. Nonlinear Sci. Numer. Simul.


Co-authors who are students appear in bold.