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MOULAY A. BARKATOU
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2010- Today

2000-2009

Sergei A. Abramov, Moulay A. Barkatou: On D'Alembertian Solutions of Linear Differential and Difference Equations. J. Symbolic Computation 44(2009), no 1, 48--59.
Moulay A. Barkatou, Eckhard Pfl�gel: On the Moser- and super-reduction algorithms of systems of linear differential equations and their complexity. J. Symb. Comput. 44(8): 1017-1036 (2009)
Sergei A. Abramov, Moulay A. Barkatou, D. E. Khmelnov: On m-Interlacing Solutions of Linear Difference Equations . Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing, Kobe Japan 2009, pages 1--17
Moulay A. Barkatou, Thomas Cluzeau, Carole El Bacha: Algorithms for regular solutions of higher-order linear differential systems, Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computations (Seoul, Korea), ACM, New York, pages 7—14, ISSAC 2009
Moulay Barkatou, Thomas Cluzeau, Carole El Bacha: Frobenius Method for Computing Power Series Solutions of Linear Higher-Order Differential System. Proceedings of the 19th International Symposium on Mathematical Theory on Networks and Systems (MTNS), July 5-9, Budapest, Hungary, pages 1059-1066, 2009.
S. Abramov, M. Barkatou. On Entire Solutions of Linear Difference Equations with Polynomial Coefficients, in Computer Algebra Systems in Teaching and Reasearch (Siedlce, Poland, 28-31 January 2009) Vol 1, pp. 7-17.

Moulay A. Barkatou, Gary Broughton, Eckhard Pfl�gel: Regular Systems of Linear Functional Equations and Applications . In the Proceedings of the 2008 International Symposium on Symbolic and Algebraic Computation, RISC, Hagenberg, Austria, ACM, New York, Pages 15--22. ISSAC 2008.
S. Abramov, M. Barkatou. Subanalytic Solutions of Linear Difference Equations and Multidimensional Hypergeometric Sequences. Proc. X Belarussian Mathematical Conference (3-7 November, 2008, Minsk), Part 3, pp. 41-42.

Moulay A. Barkatou, Eckhard Pfl�gel: Computing Super-Irreducible Forms of Systems of Linear Differential Equations via Moser-Reduction: A New Approach. in the Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation (Waterloo, Canada), ACM, New York, pages 1-8. ISSAC 2007.
Moulay A. Barkatou, Hassan El Houari, M'hammed El Kahoui: Triangulable Locally Nilpotent Derivations in Three Variables, J. Pure Appl. Algebra 212 (2008), no. 9, 2129--2139. arXiv:0705.2492 .
Moulay A. Barkatou, Hassan El Houari, M'hammed El Kahoui: Characterization of rank two locally nilpotent derivations in dimension three. arXiv:0705.2489.
S. Abramov, M. Barkatou. D'Alembertian Series Solutions of LODE with Polynomial Coefficients, International Conference � Differential Equations and Related Topics �, Petrovskii Conference, 21- 26 May 2007, Moscow State University.

Sergei A. Abramov, Moulay A. Barkatou, Mark van Hoeij: Apparent singularities of linear difference equations with polynomial coefficients. Appl. Algebra Eng. Commun. Comput. 17(2): 117-133 (2006)
Nicolas LeRoux, Moulay A. Barkatou: Rank Reduction of a Class of Pfaffian Systems in two variables, Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, ACM, New York, Pages 204—211. ISSAC 2006
M. Barkatou: Factoring Systems of Linear Functional Systems Using Eigenrings. Computer algebra 2006, 22--42, World Sci. Publ., Hackensack, NJ, 2007.

Moulay Barkatou, Thomas Cluzeau, Jacques-Arthur Weil: Factoring Partial Differential Systems in Positive Characteristic. D. Wang (Ed.), Differential Equations with Symbolic Computation (DESC Book),pages 213-238, Birkha�ser (2005).

M. Barkatou: On Super-Irreducible Forms of Linear Differential Systems with Rational Function Coefficients, Journal of Computational and Applied Mathematics 162 (2004). 1--15

M. Barkatou, F. Chyzak, M. Loday-Richaud: Remarques algorithmiques li�es au rang d'un op�rateur diff�rentiel lin�aire, From combinatorics to dynamical systems, 87--129, IRMA Lect. Math. Theor. Phys., 3, de Gruyter, Berlin, 2003.

M. Barkatou, G. Chen. Some Formal Invariants of Linear Difference Systems and their computation, J. Reine Angew Math 533(2001). 1--23
M. Barkatou. Gevrey character of formal solutions of difference-differential equations, Journal of Difference Equations and Applications, 2001, Vol. 7, pp. 587-599.
M. Barkatou, L. Gerbaud, A. Bolopion, G. Villard. R�solution symbolique d'�quations diff�rentielles ordinaires en vue de l'�tude de circuits d'�lectronique de puissance, Revue Internationale de g�nie �lectrique, volume 4 - No 1-2/2001, pages 105-120.

1990-1999

Moulay A. Barkatou: On Rational Solutions of Systems of Linear Differential Equations. J. Symb. Comput. 28(4-5): 547-567 (1999)
Moulay A. Barkatou, Eckhard Pfl�gel: An Algorithm Computing the Regular Formal Solutions of a System of Linear Differential Equations. J. Symb. Comput. 28(4-5): 569-587 (1999)
Moulay A. Barkatou: Rational Solutions of Matrix Difference Equations: the problem of equivalence and factorization. Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation (Vancouver, BC), 277--282, ACM, New York, 1999.
M. Barkatou, G. Chen. Computing the Exponential Part of a Formal Fundamental Matrix Solution of a linear difference system, Journal of Difference Equations and Applications, Vol. 5, No 3, (1999), 1--26.

Sergei A. Abramov, Moulay A. Barkatou: Rational solutions of first order linear difference systems. Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation (Rostock), 124--13, ACM, New York, 1998.
Moulay A. Barkatou, Eckhard Pfl�gel: On the equivalence problem of linear differential systems and its application for factoring completely reducible systems. Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation (Rostock), 268--275, ACM, New York, 1998.

M. Barkatou, A. Duval. Sur la somme de certaines s�ries de factorielles, Annales de la Facult� des Sciences de Toulouse, volume 6, no 1 (1997), 7--58.
M. Barkatou, F. Jung. Formal solutions of linear differential and difference equations. (Russian) Translated from English by S. A. Abramov. Programmirovanie 1997, no. 1, 24--42.
M. Barkatou, F. Jung. On Solutions of linear differential and difference equations. Program. Comput. Software 23 (1997), no. 1, 17--30.

Moulay A. Barkatou: An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system. Appl. Algebra Eng. Commun. Comput. 8(1): 1-23 (1996).

Moulay A. Barkatou: A rational version of Moser's Algorithm, Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation (Montreal), 297-303, ACM, New York, 1995.

M. Barkatou, A. Duval. Sur les s�ries formelles solutions d'�quations aux diff�rences polynomiales, Ann. Inst. Fourier fascicule 2 du tome 44 (1994), 495--524.

Moulay A. Barkatou: An Algorithm for Computing a Companion Block Diagonal Form for a System of Linear Differential Equations. Appl. Algebra Eng. Commun. Comput. 4: 185-195 (1993).

Moulay A. Barkatou: Characterization of regular singular linear systems of difference equations. Numerical Algorithms. 1(2):139-154.

1988-1989

Moulay A. Barkatou: On the reduction of linear systems of difference equations, Proceedings of the International Symposium on Symbolic and Algebraic Computation 1989. ACM Press (1989).

Moulay A. Barkatou: Rational Newton algorithm for computing formal solutions of linear differential equations. Symbolic and Algebraic computation (Rome, 1988), 183--195, Lecture Notes in Comput. Sci., 358, Springer, Berlin, 1989.

Other invited talks and presentations:

� On the Asymptotic Solutions of Systems of Differential Equations at Irregular Singularities �. Workshop on Nonlinear Analysis and Applications 2012, Mehdia, Tunisia, December 16-19, 2012.

� Solving Linear Ordinary Differential Systems in Closed Form �. LSMS Third Annual Meeting. (LSMS-2012), The American University of Beirut, Beirut, April 27-28, 2012.

� On the Exponential Parts of Singular Linear Differential Equations �. The second conference ``Symbolic Computation and its Applications" May 17-20, 2012, RWTH Aachen University, Germany.

� On the Exponential Parts of Linear Differential Equations with Meromorphic Coefficients and Their Computation �. Functional Equations in LIMoges 2012, Analytic and algebraic approaches to integrability, March 5-7, 2012.

� Symbolic Methods for Solving Systems of Linear Ordinary Differential Equations �, June 13-17, 2011, Lehrstuhl B für Mathematik, RWTH Aachen University Germany,

� Removing Apparent Singularities of Systems of Linear Differential Equations with Rational Function Coefficients �. The Second Workshop Differential Equations by Algebraic Methods (DEAM2), February 9–11, 2011, JKU Linz

� On the Problem of Removing Apparent Singularities of Linear Differential Equations with Polynomial Coefficients �, Applications of Computer Algebra (ACA) 2010, University of Vlora, Vlora, Albania, 24-27 June, 2010

� Local Reduced Forms of Systems of Linear Functional Equations and Applications �, Applications of Computer Algebra (ACA) 2009, Montreal, Canada, juin 2009,

� On Subanalytic Solutions of Linear Difference Equations with Polynomial Coefficients �, Seminario Iberoamericano de Matem\'aticas, Singularidades en Tordesillas, Instituto Interunivesitario de Iberoam\'etica, 21 abril de 2009.

� On Entire Solutions of Linear Difference Equations with Polynomial Coefficients � , Premier colloque Franco-Tunisien de Math�matiques, 16-20 mars 2009, Djerba, Tunisie.

� Hypergeometric Solutions of Systems of Linear Difference Equations and Applications �, Seminar ALGO, INRIA Rocquencourt, Paris, Octobre 2008.

� Hypergeometric Solutions of Systems of Linear Difference Equations and Applications � Symbolic Analysis Workshop \@ FoCM, Hong Kong. June 24-26, 2008.

� Factorization and Hypergeometric Solutions of Linear Difference Equations� Seminar at the Key Laboratory of Mathematics Mechanization. Academy of Mathematics and Systems Science. Beijing- China. June 19 , 2008.

� Sur les s�ries d'Alambertiennes solutions d'�quations diff�rentielles lin�aires � coefficients polynomiaux �

Premier colloque franco-maghrebin du calcul formel, du 23 au 26 mai 2008- Sfax - Iles de Kerkennah.

� Reduced Forms of Systems of Linear Functional Equations and Applications � 12-th Workshop On Computer Algebra, The Joint Institute for Nuclear Research, May 14-16, 2008, Dubna, Russia

� Direct Symbolic Methods for Solving Systems of Linear Differential Equations �, Waterloo University, July 2007

� On the Formal Solutions of Linear Systems of Differential Equations near a Singular Point �, 11th Workshop On Computer Algebra, The Joint Institute for Nuclear Research, May 24-25, 2007, Dubna, Russia

� On D'Alembertian Series Solutions of Linear Ordinary Differential Equations with Polynomial Coefficients �, 11-th Workshop On Computer Algebra, The Joint Institute for Nuclear Research, May 24-25, 2007, Dubna, Russia

� Direct algebraic methods for solving systems of linear differential �quations �, Workshop Algebraic Theory of Differential Equations, Heriot-Watt University, Edinburgh, 31 July to 11 August 2006,

� Exponential Parts of Singular Differential Equations �, Waterloo Workshop on Computer Algebra, Waterloo Workshop on Computer Algebra, Waterloo, Ontario, CANADA, 10-12 Avril 2006,

� Rational Solutions of Linear Differential Systems �, Journ�es ``Hamilton", Limoges July, 3-6 2006

� On the exponential parts of the formal solutions of a linear differential system �, Fondations of Computational Mathematics, Workshop on Computational Dynamics, Santander, July 7-9 2005

� Removing Apparent Singularities of Linear Difference Equations with Polynomial Coefficients �, International Conference on Constructive and Computational Mathematics, Marrakech, December 14-17 2005

� Desingularization of Difference Operators �, Seminar CAFE, INRIA Sophia- Antipolis, October2004

� Continuation Of Holomorphic Solutions Of Linear Differential Equations With Polynomial Coefficients. �, International Conference Kolmogorov And Contemporary Mathematics, Moscow, June 16-21, 2003.

� Rank Reduction of Linear Differential Systems with an Irregular Singularity �, Computer Algebra Group Seminar, University of Marralesh, September 2003.

� Sur la r�duction de syst�mes d'�quations pseudo-lin�aires � S�minaire du Laboratoire de Math�matiques Calcul Asymptotique, Universit� de La Rochelle, Avril 2001.

� Sur la factorisation de syst�mes d'�quations pseudo-lin�aires �, S�minaire d'Analyse num�rique, Universit� de Rabat Maroc, D�cembre 2000.

� Sur les probl�mes d'�quivalence et de factorisation de syst�mes aux diff�rences lin�aires. �, Journ�es Equations diff�rentielles et calcul formel, Lille du 16 au 18 mars 2000

� Solving matrix difference equations with rational coefficients � SCG Seminar, University of Waterloo, Canada, July 1999.

� Equivalence de deux syst�mes diff�rentiels lin�aires et applications", Colloque � Panorama de calcul formel � Marrakech, Maroc Mai 10-14 1999.
� Direct Methods for Computing Rational Solutions of Linear Differential Systems �, Mathematics Colloquium, San Diego State University, September 1998

� Rational Solutions of linear differential and difference systems �, Seminar "Symbolic Computations" MSRI, Berkeley, USA, September 1998.

� An Algorithm for Computing the Formal Invariants of Linear Difference System �, (with Guoting CHEN) ASCM'98 August 6-8, 1998, Lanzhou, China, Proceedings of ASCM'98 Zhibin Li (Ed.), Lanzhou University Press.

� Gevrey character of formal solutions of a differential-difference equation with polynomial coefficients �, Workshop � Asymptotic Theory and Multisummability of Power Series in Several Variables �, June 24-27, 1998, Fabri-Institute, Blaubeuren, Germany.

� Recent developments in ISOLDE � , Cathode-2 Castillo de La Mota Workshop, May 11-16, 1998, Medina del Campo, Spain.

� An algorithm for the Computation of the Exponential Part of Formal Solutions of Difference Systems � (with G. Chen), The Sixth Rhine Workshop on Computer Algebra, March 31.- April 3, 1998, Sankt Augustin, Germany.

� ISOLDE: a package for Integrating Systems of Linear Differential Equations �, Cathode 2 Workshop, Han sur less, Belgique , 1-5 september 1997

� A fast algorithm to compute the rational solutions of systems of linear differential �quations � Workshop � Symbolic-Numeric Analysis of Differential Equations � (SNADE'97) Prague, June 16- 18 1997.

� Formes super-irr �ductibles et leurs applications � la recherche de solutions rationnelles d'�quations diff�rentielles �,

dans le cadre du s�minaire Equations fonctionnelles � universit� de Strasbourg I, F�vrier 1997

� Un algorithme rapide pour le calcul des solutions rationnelles d'un syst�me diff�rentiel lin�aire �, S�minaire ALGO, INRIA Rocquencourt, Paris, January 1997.

� On Rational Solutions Of Linear Differential Systems �, Journ�es sur la th�orie de Galois alg�brique et diff�rentielle , Rennes, november 1996.

� On the formal solutions of difference-differential �quations �, The 2nd Marrakesh International Conference on Differential Equations", Marrakech june 1995.

� Formal solutions of an irregular linear differential system �, The 3rd CATHODE workshop, London, Queen Mary and Westfield College, London March 1994.

� On formal solution of linear difference �quations �, The 2nd Cathode Conference, Dagstuhl, RFA, september 1993.

� Solutions formelles d'�quations aux diff�rences polynomiales � aux � Journ�es sur les �quations aux diff�rences �, Strasbourg, f�vrier 1993.

� An Algorithm for Computing Rational Forms Systems of Linear Differential Equations �, Computer Algebra and Differential Equations (CADE), Luminy, june 1992.

� Sur les syst\`emes diff\'erentiels lin\'eaires singuliers �, Journ�es � Calcul formel, int�gration, �quations diff�rentielles �, Limoges 1991

� Caract�risation des syst�mes aux diff�rences � singularit� r�guli�re �, Workshop � Calcul formel en th�orie des syst�mes", Gif sur Yvette, mars 1989.

�Optimisation de DESIR pour les �quations diff�rentielles du second ordre �, Computer Algebra and Differential Equations (CADE) Grenoble 1988, Proceedings CADE 1988, ACM Press (1989).