M. Mohammed Bachir

Maître de conférences

Mathématiques appliquées et applications des mathématiques

Affectation(s)

SAMM : Statistique, analyse, modélisation multidisciplinaire (UR 4543)

UFR 27 : Mathématiques et informatique

Domaines d'expertise

Mathématiques, probabilités

Recherche

Direction(s) de recherche

Analyse Fonctionnelle et Optimisation.

Direction(s) de thèse

  • Direction de la thèse de LYU  Rongzhen depuis septembre 2022, intitulée : "Optimisation sous contrainte et multiplicateurs de Lagrange en dimension infinie".

  • Co-direction (avec A. Daniilidis) de la Thèse de Gonzalo Flores soutenue le 26 avril 2021, intitulée :

"Applications of the integration of essentially bounded functions and classification of Asymmetric Spaces"

Thèmes de recherche

Mathématiques pures et appliquées

--- Géométrie des espaces de Banach et Topologie.

--- Contrôle Optimal et Optimisation. 

---- Principe de Pontryagin.

Réflexions philosophiques

--- Les erreurs de Spinoza dans ses démonstrations de la Proposition XI de l'Ethique I : Erreurs_Spinoza.pdf

--- Une réflexion à partir de la Nature de Spinoza : Reflexion_Ethique.pdf

--- Exposé : expose-spinoza-samm-2.pd

--- Une herméneutique coranique de l'histoire d'Adam : Heméneutique-Adam-XXI_10.pdf

 

Responsabilités scientifiques

   

  • Membre des comités consultatifs scientifiques (CCS) depuis 2022.

  • Membre du conseil d’UFR depuis 2022.

  • Membre de la commission d’admission en Master 1 MMAEF 2019.

Enseignements

--- Cours M1 Analyse Fonctionnelle.

--- Cours L1 Techniques du calcul.

--- TD Analyse M1.

--- TD Optimisation M1 et L3.

--- TD Algèbre linéaire L2.

--- TD Techniques de calcul L1.

Publications

  • Publications 2023
  • [30] M. Bachir, A. Daniilidis, Extending the Choquet theory: Trace convexity, Houston Math. Journal, 247-282 (2023).
  • [29] M. Bachir,  Vector-valued numerical radius and σ-porosity, Journal of Mathematical Analysis & Applications, (2023).
  • [28] M. Bachir, S. Tapia-Garcia, Non-Linear Operators and Differentiability of Lipschitz Functions, Set-Valued and Variational Analysis  (2023).
  • [27] Bachir M., H. Ben Fredj, Nonlinear differential equations in a Banach subspace of continuous functions, Pure and Applied Functional Analysis, (2023).
  • Publications 2022
  • [26] Bachir M., Norm Attaining operators and variational principle, Studia Mathematica (2022) DOI: 10.4064/sm210628-6-9. 
  • [25] Bachir M., Porosity in the space of Holder-functions, Journal of Mathematical Analysis & Applications, (2022) .
  • Publications 2021
  • [24] Bachir M., Flores G., Tapia-García S. Compact and limited operators, Mathematische Nachrichten, (2021) 294 (6) pp. 1085-1098.
  • [23]  Bachir M., Asymmetric Normed Baire Space, Results in Mathematics, (2021) 76 (176).
  • [22] Bachir M., Nazaret B., Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem, Topology and its Applications, Elsevier, (2021), 289.
  • [21]  Bachir M., Fabre A., Tapia-Garcia S., Finitely determined functions, Advances in Operator Theory, (2021), 6 (28).
  • Publications 2020
  • [20] Bachir M., Flores G., Index of symmetry and topological classification of asymmetric normed spaces, Rocky Mountain J. Math., (2020), 50 (6), pp.1951-1964.
  • [19] Bachir M., Convex Extension of Lower Semicontinuous Functions Defined on Normal Hausdorff Space, Journal of Convex Analysis, Heldermann, (2020), 27 (3) pp. 1033-1049.
  • Publications 2019
  • [18] Bachir M, Blot J., Discrete time Pontryagin principles in Banach spaces, Pure and Applied Functional Analysis, (2019), 4, (1), pp. 21-33.
  • [17] Bachir M, The space of probabilistic 1-Lipschitz maps, Aequationes Mathematicae, Springer Verlag, (2019), 93 (5), pp. 955-983.
  • Publications 2018
  • [16] Bachir M, Well-posedness and inf-convolution, Journal of Optimization Theory and Applications (2018) 177 (2), pp.271-290.
  • [15] Bachir M, An extension of the Banach-Stone theorem, Journal of Australian Mathematical Society (2018) 105 (1), pp.1-23.
  • [14] Bachir M, On the Krein-Milman-Ky Fan theorem for convex compact metrizable sets, Illinois Journal of Mathematics (2018), 62, no 1-4, pp. 1-24.
  • Publications 2017
  • [13] Bachir M, Blot J., Infinite dimensional multipliers and Pontryagin principle for discrete-time problems, Pure and Applied Functional Analysis, (2017), 2, no 3, pp. 411-426.
  • [12] Bachir M, Representation of isometric isomorphisms between monoids of Lipschitz functions, Methods of Functional Analysis and Topology, (2017), 23, no. 4.
  • [11] Bachir M, Limited operators and differentiability, North-Western European Journal of Mathematics (2017), 3, pp. 63-73.
  • Publications 2016
  • [10] Bachir M., A Banach-Stone type Theorem for invariant metric groups, Topology and its Applications, Elsevier, (2016), 209, pp. 189-197.
  • Publications 2015
  • [9] Bachir M., Remarks on Isometries of Products of Linear Spaces, Extracta Mathematicae, (2015), 30, pp. 1-13
  • [8] Bachir M., Blot J., Infinite dimensional infinite-horizon Pontryagin principles for discrete-time problems, Set-Valued and Variational Analysis, Springer, (2015), 23, pp. 43-54.
  • Publications 2014
  • [7] Bachir M., The inf-convolution as a law of monoid. An analogue to the Banach-Stone theorem, Journal of Mathematical Analysis & Applications, (2014), 420, pp. 145-166.
  • Publications 2000-2006
  • [6] Bachir M., The multidirectional mean value inequalities with second order information,Journal of Australian Mathematical Society, (2006), 80, pp.159-172.
  • [5] Bachir M., Lancien G., On the Composition of Differentiable Functions, Canadian Mathematical Bulletin, (2003), 46, pp. 481-494.
  • [4] Bachir M., Daniilidis A., A dual characterisation of the Radon-Nikodym property, Bulletin of the Australian Mathematical Society, (2000), 62, pp. 379-387.
  • [3] Bachir M., Daniilidis A., Penot J.-P., Lower Subdierentiability and Integration, Set-Valued Analysis, Springer Verlag, (2002), 10 , pp.89-108.
  • [2] Bachir M., A Non-Convex Analogue to Fenchel Duality, Journal of Functional Analysis, Elsevier, (2001), 181, pp.300312.
  • [1] Bachir M., Sur la differentiabilité générique et le théorème de Banach-Stone, Comptes Rendus de l'Académie des Sciences, Paris, 330 (2000), 687-690.