Papers and Stuff
Here are some of my papers.
Some of them are regenerated from old source files, which explains
the dates. The paper on restarting search algorithms is a preprint
version which does not include the graphics.
Co-authors who are students appear in bold.
- 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, 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, to appear in Proc. Roy. Soc. Edinburgh Sect. A
- W. Jiang, F. Ghasempour, F. Mendivil, S. Peterson, E.R. Vrscay, An algorithm to construct conformable networks that occupy arbitrary regions in R^3, to appear in Applied Mathematical Modelling
- 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, to appear in Fractals
- 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 to appear in Fractals