Franklin Mendivil
Curriculum Vitae
Address
Department of Mathematics and Statistics
Acadia University
Wolfville, NS B4P 2R6
(902) 5851368
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 UniversityIndustrial 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
19891990
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
 R. Shonkwiler and F. Mendivil,
Explorations in Monte Carlo Methods , Undergraduate Texts in Mathematics, Springer, 2009
 Herb Kunze, Davide La Torre, Franklin Mendivil and Edward Vrscay,
Fractalbased methods in analysis , Springer, 2011.
Selected Publications
 F. Mendivil
Countable compactifications and a generalized
HahnMazurkeiwicz type theorem Topology Appl. 72
1996.
 F. Mendivil and E.R. Vrscay
Correspondence between
fractalwavelet transforms and Iterated Function Systems with
greylevel maps in Fractals in Engineering, edited
by J. Levy Vehel, E. Lutton and C. Tricot, SpringerVerlag, 1997.

F. Mendivil and E.R. Vrscay (1997), FractalBased Techniques in Image Compression,
Canadian Conference on Electrical and Computer Engineering,
St. John's, Newfoundland, May 1997, 486489.

E.R. Vrscay and F. Mendivil (1997), Generalized FractalWavelet Transforms
for Image Representation and Compression,
Canadian Conference on Electrical and Computer Engineering,
St. John's, Newfoundland, May 1997, 490495.
 F. Mendivil, A generalization of IFS with probabilities to infinitely
many maps Rocky Mountain J. Math. 28 no. 3. (1998)
 B. Forte and F. Mendivil
A classical ergodic property for
IFS: A simple proof Ergodic Theory Dynam. Systems
18 no 3. (1998)
 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)
 F. Mendivil and D. Piche
Two algorithms for nonseparable
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,
SpringerVerlag, 1999.
 B. Forte, F. Mendivil and E.R. Vrscay
IFStype operators on integral
transforms in Fractals: Theory and Applications in Engineering, edited
by M. Dekking, J. Levy VEhel, E. Lutton and C. Tricot,
SpringerVerlag, 1999.
 F. Mendivil
Function algebras and the lattice of
compactifications Proc. Amer. Math Soc. 127
(6), 1999.
 F. Mendivil, R. Shonkwiler and M.C. Spruill
Restarting search algorithms with
applications to simulated annealing
Adv. in Appl. Probab. 33 (2000)
 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)
 F. Mendivil, E.R. Vrscay Fractal vector measures and vector
calculus on planar fractal
domains Chaos Solitons Fractals 14 (2002) Issue 8, 12391254
 F. Mendivil, E.R. Vrscay Selfaffine 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. 137156 (2002)
 F. Mendivil, J. Silver Chaos Games for Wavelet
Analysis and Wavelet Synthesis,
Comput. Math. Appl. 46 (2003), no. 56, 863873.
 F. Mendivil Fractals, Graphs, and Fields
Amer. Math. Monthly 110 (2003), no. 6, 503515.
 C. Cabrelli, F. Mendivil, U. Molter, R. Shonkwiler, On the
Hausdorff hmeasure of Cantor Sets Pacific J. Math. 217 (2004) no. 1, 4559.
 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, 402433.
 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
SpringerVerlag (2006).
 F. Mendivil, T. Taylor Thin sets with fat shadows: Projections of
Cantor Sets Amer. Math. Monthly 115 (2008), no. 5, 451456.
 J. LevyVehel, F. Mendivil, E. Lutton Overcompressing JPEG Images with Evolution Algorithms
EvoWorkshops2007: 383390.
 D. La Torre, F. Mendivil Iterated function systems on multifunctions and
inverse problems , J. Math. Anal. Appl. 340 (2008) 14691479.
 D. La Torre, F. Mendivil Unionadditive multimeasures and selfsimilarity ,
Commun. Math. Anal. 7 (2009), no. 2, 5161.
 F. Mendivil, R. Shonkwiler, M. C. Spruill Geometric convergence of genetic algorithms under
tempered random restart , J. Appl. Probab. 46 no. 4 (2009), 960974.
 F. Mendivil, R. Shonkwiler Annealing a Genetic Algorithm for constrained optimization
J. Optim. Theory Appl. 147 (2010), no. 2, 395410.
 U. Freiberg, D. La Torre, F. Mendivil Iterated function systems and stability of
variational problems on selfsimilar objects Nonlinear Anal. Real World Appl. 12 (2011) 11231129.
 J. LevyVehel, F. Mendivil Multifractal and higherdimensional zeta functions
Nonlinearity 24 (2011) 259276.
 F. Mendivil, J. C. Saunders On Minkowski measurability Fractals
19 no. 4 (2011), 455  467.
 D. La Torre, F. Mendivil Minkowskiadditive multimeasures, monotonicity
and selfsimilarity, Image Anal. Stereol. 30 no. 3 (2011), 135142.
 F. Mendivil, D. Patterson Dynamics of finite linear cellular automata over $Z_N$
Rocky Mountain J. Math. 42 no. 2 (2012), 695709.
 J. LevyVehel, F. Mendivil Local complex dimensions of a fractal string,
Int. J. Mathematical Modelling and Numerical Optimization special issue on "Fractals, Fractalbased Methods and Applications", 3 , no. 4 (2012), 298312.
 H. Kunze, D. La Torre, F. Mendivil, E.R. Vrscay Generalized fractal transforms and selfsimilar objects in cone metric
spaces, Comput. Math. Appl. 64 (2012), 1761  1769.
 K. Hare, F. Mendivil, L. Zuberman The sizes of rearrangments of Cantor sets,
Canad. Math. Bull. 56 no. 2 (2013), 354  365.
 J. LevyVehel, F. Mendivil Christiane's Hair, Amer. Math. Monthly 129 (2013) no. 9, 771786.
 D. La Torre, F. Mendivil A Chaos Game Algorithm for Generalized Iterated Function Systems, Appl. Math. Comput. 224 (2013), 238249.
 H. Kunze, D. La Torre, F. Mendivil, E.R. Vrscay Continuous evolution of equations and inclusions involving setvalued contraction
mappings with applications to generalized fractal transform, Electron. J. Diff. Equ., Vol 2014 (2014), No. 142, pp.117.
 D. La Torre, F. Mendivil The MongeKantorovich metric on multimeasures and selfsimilar multimeasures, SetValued Var. Anal. 23 (2015), pp. 319331.
 D. Day , F. Mendivil Fractal measures with uniform marginals , J. Math. Anal. Appl. 429 (2015), pp. 10961112.
 F. Mendivil Timedependent iteration of random functions , Chaos Solitons Fractals 75 (2015), pp. 178184.
 F. Mendivil, O. Stenflo VVariable image compression , Fractals 23 , no. 2 (2015), pp. 1550007
 D. La torre, S. Marsiglio, F. Mendivil, F. Privileggi Selfsimilar measures in multisector endogenous growth models ,
Chaos Solitons Fractals 79 (2015) pp 4056.
 D. La Torre, F. Mendivil Arclength as the invariant measure for an IFS with probabilities , Fractals
23 no 4 (2015) pp. 1550046.
 K. Hare, F. Mendivil, L. Zuberman Packing and Hausdorff measures of Cantor sets associated with series,
to appear in Real Anal. Exchange
 F. Mendivil Computing the MongeKantorovich Distance to appear in Comp. Appl. Math.
 J. Hooper, F. Mendivil Transposition as a permutation: a tale of group actions and modular arithmetic
Math. Magazine 89 (2016), pp. 1635.
 D. La Torre, F. Mendivil, E.R. Vrscay Iterated function systems on functions of bounded variation
Fractals 24 , no 2 (2016), pp. 1650019.
 D. La Torre, F. Mendivil, O. Michailovich, E.R. Vrscay (2016)
Total Variation Minimization for MeasureValued 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.
 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
 D. La Torre, F. Mendivil, Portfo optimization under partial uncertainty and incomplete information: A probability multimeasurebased approach,
to appear in Ann. Oper. Res.
 I. Garcia, K. Hare, F. Mendivil, Assouad dimensions of complementary sets, to appear in Proc. Roy. Soc. Edinburgh Sect. A
 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 , SpringerVerlag.
 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
 D. La torre, S. Marsiglio, F. Mendivil, F. Privileggi
Fractal Attractors and Singular Invariant Measures in TwoSector Growth Models with Random
Factor Shares ,
to appear in Commun. Nonlinear Sci. Numer. Simul.
Coauthors who are students appear in bold.