A. MONOGRAPHS

1. J. Chaskalovic, Mathematical and Numerical Methods for Partial Differential Equations, Springer-Verlag, 2014.

2. J. Chaskalovic, Méthodes Mathématiques et Numériques pour les Equations aux Dérivées Partielles, Ed. Lavoisier, 2013.

3. J. Chaskalovic, Finite element methods applied to engineering sciences, Springer-Verlag,2008, (completed and translated from the French version).

4. J. Chaskalovic, Méthodes des éléments finis pour les sciences de l’ingénieur, Ed. Lavoisier,2004.

B. PAPERS IN PEER-REVIEWED INTERNATIONAL JOURNALS

B.I) Probabilistic approach applied to a priori and error estimates for solution and approximations to determinist Partial Differential Equation

 

1. J. Chaskalovic, F. Assous, A new probabilistic interpretation of Bramble-Hilbert lemma, Published in Computational Methods in Applied Mathematics, (2019). Download PDF

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2. J. Chaskalovic, F. Assous, From a geometrical interpretation of Bramble-Hilbert lemma to a probability distribution for finite element accuracy, Proceeding Conference of Finite Difference Methods, Lozenetz - Bulgaria, Lecture Notes in Computer Science, Springer, (2018). Download PDF 

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3. J. Chaskalovic, F. Assous, On generalized binomial laws to evaluate finite element accuracy: toward applications for adaptive mesh refinement, arXiv:1812.09192 [math.NA], (2018). Download PDF

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4. J. Chaskalovic, F. Assous, A new mixed functional-probabilistic approach for finite element accuracyarXiv:1803.09552 [math.NA], (2019). Download PDF 

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5. J. Chaskalovic, F. Assous, Explicit k−dependency for Pk finite elements in Wm,p error estimates: application to probabilistic laws for accuracy analysisarXiv:1901.06821 [math.NA], (2019).  Download PDF

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B.II) Mathematical modelling and data mining applied to particle physics

 

1. F. Assous and J. Chaskalovic, Data mining for numerical approximations analysis: a test case of asymptotic solutions to Vlasov-Maxwell equations, Comptes Rendus Mécanique, Vol. 338, pp. 305-310. Download PDF

 

2. F. Assous and J. Chaskalovic, 2011, Data mining methods for performance evaluations to asymptotic numerical models, Journal of Functional Differential Equations , Vol. 18, 1-2, pp. 29 - 49. Download PDF

 

3. F. Assous and J. Chaskalovic, 2011, Data mining techniques for scientific computing: application to asymptotic paraxial approximations to model ultra relativistic particles, Journal of Computational Physics, Vol. 230, pp. 4811 –4827. Download PDF

 

4. F. Assous and J. Chaskalovic, 2012, A new paraxial asymptotic model for the ralativistic Vlasov-Maxwell equations, Comptes Rendus MécaniqueVol 340, pp. 706–714. Download PDF

 

5. J. Chaskalovic and F. Assous, 2012, A new method to evaluate asymptotic numerical models by data mining techniques, Neural, Parallel, and Scientific Computations 20, pp. 283-290. Download PDF

 

6. F. Assous and J. Chaskalovic, 2013, Error estimate evaluation in numerical approximations of partial differential equations: a pilot study using data mining methods, Comptes Rendus Mécanique, Vol 341, pp. 304–313. Download PDF

 

7. F. Assous and J. Chaskalovic, 2014, Indeterminate Constants in Numerical Approximations of PDE’s: a Pilot Study Using Data Mining Techniques, Journal of Computational and Applied Mathematics, Vol 270, pp. 462–470. Download PDF

 

8. F. Assous and J. Chaskalovic, 2014, A paraxial asymptotic model for coupled Vlasov-Maxwell problem in electromagnetics, Journal of Computational and Applied Mathematics, Vol 270, pp. 369–385. Download PDF

 

9. F. Assous and J. Chaskalovic, 2014, Mathematical and numerical methods for Vlasov-Maxwell equations: the contribution of data mining, Comptes Rendus Mécanique, Vol 342,  pp. 560–569. Download PDF

 

10. J. Chaskalovic and F. Assous , 2016, Data mining and probabilistic models for error estimate analysis of finite element method Math. Comp. in Sim., Vol. 129, pp. 50-68.  Download PDF

 

11. J. Chaskalovic and F. Assous, 2016, Probabilistic approach to characterize quantitative uncertainty in numerical approximations, Maths. Model. and Anal.,Vol 22, pp. 106-120.  Download PDF

 

B.III) Mathematical modelling and data mining and applied to Mechanics

 

1. J. Chaskalovic1988, uniqueness result for Navier-Stokes solutions which modelled a tornado, C. R. Acad. Sci. Paris, 307, Série l, pp. 923-926. Download PDF

 

2. J. Chaskalovic1990, On a mathematical model applied to singular updraft meteorological flows, C. R. Acad. Sci. Paris, 311, Série II, pp. 1045-1050. Download PDF

 

3. M. Larchevêque and J. Chaskalovic, 1994, A new mathematical model applied to tornado's genesisInt. J. Engng Sci. Vol. 32, No. l, pp. 187-193. Download PDF

 

4. J. Chaskalovic and S. Naïli,1995, Bifurcation theory applied to buckeld states of a cylindrical shell, Z.A.M.P, Vol. 46, pp. 149-155. Download PDF

 

5. J. Chaskalovic,1995, Genesis of singularities inside an updraft atmospherical flow, C.R. Acad. Sci. Paris, 321, Série I, pp. 1647-1652. Download PDF

 

6. J. Chaskalovic and S. Naïli,1996, Existence of solutions for a cylindrical shell with general cross-section in finite displacements, C. R. Acas. Sci. Paris, 322, Série I, pp. 411-418. Download PDF

 

7. J. Chaskalovic1998, Genesis of a singularity line into a regular updraft, Math. Models and Meth. in Appl. Sci., VOl 8, N°3, pp. 431-444.Download PDF

 

8. J. Chaskalovic and A. Chauvière, 1998, Genesis of a swirling source/sink line into an updraft, C. R. Acad. Sci. Paris, 326, Série I, pp. 645-650. Download PDF

 

9. J. Chaskalovic and A. Chauvière, 1999, Thermal convection into swirling source/sink line vortex, C. R. Acad. Sci. Paris, 329, Série I, pp. 237-242.Download PDF

 

10. J. Chaskalovic and A. Chauvière, 1999, Convection thermique dans une ligne de puits ou de sources tourbillonaire, Actes 14ème Congrès Français de MécaniqueDownload PDF

 

11. J. Chaskalovic and A. Chauvière, 2003, Appearance of a source/sink line into a swirling vortex, Math. Models and Meth. in Appl. Sci., Vol 13, N°1, pp. 121-142.Download PDF

 

12. J. Chaskalovic and A. Chauvière, 2005, Dusty debris in tornadoes modelled by high Reynolds number two cells vortices, Int. J. Engng Sci., 43, pp. 1486-1497. Download PDF

 

13. J. Ratsaby and J. Chaskalovic, 2010, On the algorithmic complexity of static structures, J. of Syst. Sci. and Compl., 23, pp. 1037-1053. Download PDF

 

14. J. Ratsaby and J. Chaskalovic, 2010, Interaction of a self vibrating beam with chaotic external forces, Cr. Rendus Méca., 338, N°1, pp. 33-39. Download PDF

 

15. M. Hamdaoui, J. Chaskalovic et al., 2010, Using evolutionary algorithm and data mining methods to optimize bird-like UAV's kinematics, Journal of Aircraft, 47, N°5, pp. 1504-1516. Download PDF

 

B.IV) Data Mining and mathematical modelling applied to Medicine

 

1. Descazeaud A., Chaskalovic J., Zerbib M., Peyromaure M., 2004, The sexual function following radical prostatectomy does not affect patient satisfaction: evaluation by UCLA questionnaire, Prog. Urol., 14 (6), p. 1177-1180. Link to PUBMED

 

2. M. Peyromaure, A. Descazeaud, J. Chaskalovic, Marc Zerbib, 2005, Qualité de vie, fonction sexuelle, et satisfaction globale après prostatectomie radicale, Janvier 2005,Livret des Séminaires d'Uro-Néphrologie de la Pitié - Salpêtrière

 

3. Descazeaud A., Zerbib M., Hofer M.D., Chaskalovic J., Debré B. et al.2005, Evolution of health-related quality of life two to seven years after retropubic radical prostatectomy: evaluation by UCLA prostate cancer index, World J Urol., 23 (4), p. 257-262. Download PDF

 

4. X. L. Nguyen, J. Chaskalovic et al., 2008, Residual subjective daytime sleepiness under CPAP treatment in initially somnolent apnea patients: A pilot study using data mining methods, Sleep Medicine, 9 (5), pp. 511-516. Download PDF

 

5. X. L. Nguyen, J. Chaskalovic et al, 2010, Insomnia symptoms and CPAP compliance in OAS patients: A descriptive study using data mining methods, Sleep Medicine, Vol. 11, pp. 777–784Download PDF

 

6. S. Bunimovich, J. Chaskalovic et al., 2011, A mathematical model of combined Bacillus (BCG) and interleukin (IL-2) immunotherapy os superficial bladder cancer, Journal of Theoretical Biology, Vol. 277, pp. 27 –40. Download PDF

 

7. Xuân-Lan Nguyên, Dominique Rakotonanahary, Joel Chaskalovic et al., 2012, Insomnia related to sleep apnea: effect of long-term auto-adjusting positive airway pressure treatment, European Respiratory Journal, Vol. 41, pp. 593-600. Download PDF

 

8. Marie-Cécile Nierat, Anna L. Hudson, Joël Chaskalovic, Thomas Similowski and Louis Laviolette2015, Repetitive transcranial magnetic stimulation over the supplementary motor area modifies breathing pattern in response to inspiratory loading in normal humans, Frontiers in Physiology, 6 : 273. Download PDF

 

B.IV) Probabilistic and mathematical modelling ap plied to Media research

1. J. Chaskalovic, 2009, Markov chains and Volterra integral equation applied to media researchJ. Func. Diff. Eq., 16, 2, p. 213–235Download PDF

 

2. J. Chaskalovic, 2009, New mathematical models for media exposuresJ. Inter. Maths., Vol. 12, 3, pp. 395-408Download PDF

 

3. J. Chaskalovic, 2009, Gravitation theory for mathematical modeling in geomarketingJ. Inter. Maths., Vol. 12, 3 , pp. 409-420Download PDF