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
Selected Publications
- F. Mendivil
Countable compactifications and a generalized
Hahn-Mazurkeiwicz type theorem Topology Appl. 72
1996.
- 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.
-
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.
-
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.
- 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 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.
- 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.
- 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, 1239-1254
- 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)
- F. Mendivil, J. Silver Chaos Games for Wavelet
Analysis and Wavelet Synthesis,
Comput. Math. Appl. 46 (2003), no. 5-6, 863-873.
- F. Mendivil Fractals, Graphs, and Fields
Amer. Math. Monthly 110 (2003), no. 6, 503-515.
- 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.
- 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.
- 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).
- F. Mendivil, T. Taylor Thin sets with fat shadows: Projections of
Cantor Sets Amer. Math. Monthly 115 (2008), no. 5, 451-456.
- J. Levy-Vehel, F. Mendivil, E. Lutton Overcompressing JPEG Images with Evolution Algorithms
EvoWorkshops2007: 383-390.
- D. La Torre, F. Mendivil Iterated function systems on multifunctions and
inverse problems , J. Math. Anal. Appl. 340 (2008) 1469-1479.
- D. La Torre, F. Mendivil Union-additive multimeasures and self-similarity ,
Commun. Math. Anal. 7 (2009), no. 2, 51-61.
- 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.
- F. Mendivil, R. Shonkwiler Annealing a Genetic Algorithm for constrained optimization
J. Optim. Theory Appl. 147 (2010), no. 2, 395-410.
- 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.
- J. Levy-Vehel, F. Mendivil Multifractal and higher-dimensional zeta functions
Nonlinearity 24 (2011) 259-276.
- F. Mendivil, J. C. Saunders On Minkowski measurability Fractals
19 no. 4 (2011), 455 - 467.
- D. La Torre, F. Mendivil Minkowski-additive multimeasures, monotonicity
and self-similarity, Image Anal. Stereol. 30 no. 3 (2011), 135-142.
- F. Mendivil, D. Patterson Dynamics of finite linear cellular automata over $Z_N$
Rocky Mountain J. Math. 42 no. 2 (2012), 695-709.
- 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.
- 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.
- K. Hare, F. Mendivil, L. Zuberman The sizes of rearrangments of Cantor sets,
Canad. Math. Bull. 56 no. 2 (2013), 354 - 365.
- J. Levy-Vehel, F. Mendivil Christiane's Hair, Amer. Math. Monthly 129 (2013) no. 9, 771-786.
- D. La Torre, F. Mendivil A Chaos Game Algorithm for Generalized Iterated Function Systems, Appl. Math. Comput. 224 (2013), 238-249.
- 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.
- D. La Torre, F. Mendivil The Monge-Kantorovich metric on multimeasures and self-similar multimeasures, Set-Valued Var. Anal. 23 (2015), pp. 319-331.
- D. Day , F. Mendivil Fractal measures with uniform marginals , J. Math. Anal. Appl. 429 (2015), pp. 1096-1112.
- F. Mendivil Time-dependent iteration of random functions , Chaos Solitons Fractals 75 (2015), pp. 178-184.
- F. Mendivil, O. Stenflo V-Variable image compression , Fractals 23 , no. 2 (2015), pp. 1550007
- 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.
- 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,
Real Anal. Exchange 40 , no 2 (2015), pp 421-434.
- J. Hooper, F. Mendivil Transposition as a permutation: a tale of group actions and modular arithmetic
Math. Magazine 89 (2016), pp. 16-35.
- 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 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.
- 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 multimeasure-based approach,
Ann. Oper. Res. (2016) pp 1-13, doi:10.1007/s10479-016-2298-x
- F. Mendivil, Computing the Monge-Kantorovich Distance Comp. Appl. Math. 36 no 3 (2017), pp 1389-1402.
- S. Alwadani , F. Mendivil, R. Shonkwiler, Limiting distribution and mixing time for genetic algorithms, in
Nature Inspired Computing and Optimization: Theory and Applications, edited by Srikanta Patnaik, Xin-She Yang, Kazumi Nakamatsu, Springer-Verlag (2017).
- D. La Torre, F. Mendivil,
Stochastic linear optimization under partial uncertainty and incomplete information using the notion of probability multimeasure,
Journal of the Operational Research Society (2018) pp 1-8, doi:10.1057/s41274-017-0249-9
- D. La torre, S. Marsiglio, F. Mendivil, F. Privileggi,
Fractal Attractors and Singular Invariant Measures in Two-Sector Growth Models with Random
Factor Shares ,
Commun. Nonlinear Sci. Numer. Simul. 58 (2018) pp 185-201.
- I. Garcia, K. Hare, F. Mendivil, Assouad dimensions of complementary sets, Proc. Roy. Soc. Edinburgh Sect. A 148 , no. 3 (2018), pp 517-540.
- W. Jiang, F. Ghasempour, F. Mendivil, S. Peterson, E.R. Vrscay, An algorithm to construct conformable tubular networks that occupy arbitrary regions in R^3, Applied Mathematical Modelling 26 (2018), pp. 194-206.
- D. La Torre, E. Maki, F. Mendivil, E.R. Vrscay, Iterated function systems with place-dependent probabilities and the inverse problem of measure approximation using moments, Fractals 26 , no 5 (2018), 1850076.
- H. Kunze, D. La Torre, F. Mendivil, E.R. Vrscay Self-similarity of solutions to integral and differential equations with respect to a fractal measure Fractals 27 , no 2 (2019), 1950014.
- D. La torre, S. Marsiglio, F. Mendivil, F. Privileggi A stochastic economic growth model with health capital and state-dependent probabilities ,
Chaos Solitons Fractals 129 (2019) pp 81-93.
- Neil A. Spencer, Pritam Ranjan, Franklin Mendivil Isomorphism Check for 2^n Factorial Designs with Randomization Restrictions , J. Stat. Theory Pract. 13 no. 4 (2019) Paper no. 60.
- K. Hare, F. Mendivil, L. Zuberman Measures with specified support and arbitrary Assouad dimensions, Proc. Amer. Math Soc. 148 (2020), no. 9, 3881-3895.
- D. La torre, J. Marcoux , F. Mendivil, E.R. Vrscay Denoising of diffusion magnetic resonance images using a modified and differentiable Monge-Kantorovich distance for measure-valued functions
,
Commun. Nonlinear Sci. Numer. Simul. 91 (2020), 105456.
- I. Garcia, K. Hare, F. Mendivil, Almost sure Assouad-like Dimensions of Complementary sets, Math. Z. (2020) https://doi.org/10.1007/s00209-020-02643-0
- D. La Torre, F. Mendivil,
Stochastic efficiency and inefficiency in portfolio optimization with incomplete information: a set-valued probability approach,
Ann. Oper. Res. (2020) https://doi.org/10.1007/s10479-020-03886-0
- F. Mendivil, O. Stenflo Extreme compression of grayscale images ,
Commun. Nonlinear Sci. Numer. Simul. 94 (2021), 105546, 11 pages.
- D. La torre, S. Marsiglio, F. Mendivil, F. Privileggi Public debt dynamics under ambiguity by means of Iterated Function Systems on density functions ,
Discrete Contin. Dyn. Syst. Ser. B 26 , no. 11, (2021), pp 5873-5903.
- I. Garcia, K. Hare, F. Mendivil, Intermediate Assouad-like dimensions, J. Fractal Geom. 8 , no. 3, (2021), pp. 201 - 245.
- D. La torre, S. Marsiglio, F. Mendivil, F. Privileggi Generalized fractal transforms with condensation: a Macroeconomic-Epidemiological application , Pure Appl. Funct. Anal. , 7 (2022) no. 6, 2101 - 2128.
- H. Kunze, D. La Torre, F. Mendivil, E.R. Vrscay, Differential equations using generalized derivatives on fractals , In: KIlgour D. M., et al. (eds),
Recent Developments in Mathematical, Statistical and Computational Sciences AMMCS 2019.
Springer Proceedings in Mathematics & Statistics, vol 343. Springer, Cham. (2021)
- D. La Torre, F. Mendivil, M. Rocca, Modeling Portfolio Efficiency using Stochastic Optimization with Incomplete Information and Partial Uncertainty , Ann. Oper. Res. (2021) https://doi.org/10.1007/s10479-021-04372-x
- K. Hare, F. Mendivil, Assouad-like dimensions of random Moran measures, J. Math. Anal. Appl. 508 issue 2, (2022) 125912.
- K. Gingell, F. Mendivil, Random walks, directed cycles and Markov chains, Amer. Math. Monthly 130 (2023), no. 2, 127-144.
- D. La torre, S. Marsiglio, F. Mendivil, F. Privileggi, Stochastic disease spreading and containment policies under state-dependent probabilities , Econom. Theory (2023)
- K. Hare, F. Mendivil, Assouad-like dimensions of a class of random Moran measures II -- non-homogeneous Moran sets, to appear in J. Fractal Geom.
Co-authors who are students appear in bold .