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This chapter is the first investigation of the notion of double extension to triple systems. We appropriate this notion of double extension to quadratic Lie triple systems so that we give an inductive description of all quadratic Lie triple systems. Moreover, we prove that any Jordan triple system is either a \(T^*\)-extension of a Jordan triple system or an ideal of codimension one of a \(T^*\)-extension. Many other results about Lie and Jordan triple systems are offered.
Amir Baklouti; Samiha Hidri. Inductive Description of Quadratic Lie and Pseudo-Euclidean Jordan Triple Systems. Forum for Interdisciplinary Mathematics 2020, 65 -93.
AMA StyleAmir Baklouti, Samiha Hidri. Inductive Description of Quadratic Lie and Pseudo-Euclidean Jordan Triple Systems. Forum for Interdisciplinary Mathematics. 2020; ():65-93.
Chicago/Turabian StyleAmir Baklouti; Samiha Hidri. 2020. "Inductive Description of Quadratic Lie and Pseudo-Euclidean Jordan Triple Systems." Forum for Interdisciplinary Mathematics , no. : 65-93.
In this paper, we develop a preventive maintenance (PM) strategy for a solar photovoltaic system composed of solar panels functioning as a series system. The photovoltaic system is considered in a failed state whenever its efficiency drops below a predefined threshold or any electrical wiring element is damaged. In such a situation of failure, a minimal repair is performed. The proposed PM strategy suggests systematically replacing n panels with their respective wiring system every time units T over a finite operating time span H. The panels to be preventively replaced are selected by the maintenance agent after an on-site overall assessment of all panels, making sure every time not to replace panels previously replaced during a given replacement cycle of all panels of the system. An analytical model is proposed in order to simultaneously determine the optimal PM period, T, and the optimal number of solar panels, n, to be replaced at each PM. This is done by modeling and minimizing the expected total maintenance cost over the finite operating time horizon H. A numerical example is presented to illustrate the use of the proposed modelling approach and to discuss the obtained results. The latter provide the optimal solutions (T*, n*) for different combinations of input parameters. They also show the economic relevance of the proposed PM strategy through estimation of the economic gain when comparing the situations with and without preventive maintenance.
Amir Baklouti; Lahcen Mifdal; Sofiene Dellagi; Anis Chelbi. An Optimal Preventive Maintenance Policy for a Solar Photovoltaic System. Sustainability 2020, 12, 4266 .
AMA StyleAmir Baklouti, Lahcen Mifdal, Sofiene Dellagi, Anis Chelbi. An Optimal Preventive Maintenance Policy for a Solar Photovoltaic System. Sustainability. 2020; 12 (10):4266.
Chicago/Turabian StyleAmir Baklouti; Lahcen Mifdal; Sofiene Dellagi; Anis Chelbi. 2020. "An Optimal Preventive Maintenance Policy for a Solar Photovoltaic System." Sustainability 12, no. 10: 4266.
We study the structure of symplectic Jacobi-Jordan algebras. In particular, we give inductive descriptions of these algebras by introducing some processes of double extensions and their isometries. This paper also contains several interesting examples.
Amir Baklouti; Saïd Benayadi. Symplectic Jacobi-Jordan algebras. Linear and Multilinear Algebra 2019, 69, 1557 -1578.
AMA StyleAmir Baklouti, Saïd Benayadi. Symplectic Jacobi-Jordan algebras. Linear and Multilinear Algebra. 2019; 69 (8):1557-1578.
Chicago/Turabian StyleAmir Baklouti; Saïd Benayadi. 2019. "Symplectic Jacobi-Jordan algebras." Linear and Multilinear Algebra 69, no. 8: 1557-1578.
Amir Baklouti. Quadratic Hom-Lie triple systems. Journal of Geometry and Physics 2017, 121, 166 -175.
AMA StyleAmir Baklouti. Quadratic Hom-Lie triple systems. Journal of Geometry and Physics. 2017; 121 ():166-175.
Chicago/Turabian StyleAmir Baklouti. 2017. "Quadratic Hom-Lie triple systems." Journal of Geometry and Physics 121, no. : 166-175.
This paper is bringing a better knowledge of associative triple systems and their related algebraic structures. We prove that any associative triple system is either a T*-extension of an associative triple system or an ideal of codimension one of a T*-extension of an associative triple system. Morover, we give several information about the structure of symmetric associative triple systems
Almotairi Kh; Baklouti A. Associative Triple Systems with Nondegenerate Bilinear Forms. Journal of Physical Mathematics 2017, 8, 1 -4.
AMA StyleAlmotairi Kh, Baklouti A. Associative Triple Systems with Nondegenerate Bilinear Forms. Journal of Physical Mathematics. 2017; 8 (4):1-4.
Chicago/Turabian StyleAlmotairi Kh; Baklouti A. 2017. "Associative Triple Systems with Nondegenerate Bilinear Forms." Journal of Physical Mathematics 8, no. 4: 1-4.
A pseudo-euclidean Jordan algebra is a Jordan algebra
Amir Baklouti; Saïd Benayadi. Pseudo-Euclidean Jordan Algebras. Communications in Algebra 2015, 43, 2094 -2123.
AMA StyleAmir Baklouti, Saïd Benayadi. Pseudo-Euclidean Jordan Algebras. Communications in Algebra. 2015; 43 (5):2094-2123.
Chicago/Turabian StyleAmir Baklouti; Saïd Benayadi. 2015. "Pseudo-Euclidean Jordan Algebras." Communications in Algebra 43, no. 5: 2094-2123.
Jordan superalgebras which are endowed with an even nondegenerate supersymmetric associative bilinear form are called pseudo-Euclidean Jordan superalgebras. In this work, we introduce the notion of T*-extension of Jordan superalgebras to give some examples of such superalgebras. The main result of this article is to give an inductive description of solvable pseudo-Euclidean Jordan superalgebras. We obtain this description by introducing the notions of double extension and generalized double extension of Jordan superalgebras.
Amir Baklouti; Warda Ben Salah; Saber Mansour. Solvable Pseudo-Euclidean Jordan Superalgebras. Communications in Algebra 2013, 41, 2441 -2466.
AMA StyleAmir Baklouti, Warda Ben Salah, Saber Mansour. Solvable Pseudo-Euclidean Jordan Superalgebras. Communications in Algebra. 2013; 41 (7):2441-2466.
Chicago/Turabian StyleAmir Baklouti; Warda Ben Salah; Saber Mansour. 2013. "Solvable Pseudo-Euclidean Jordan Superalgebras." Communications in Algebra 41, no. 7: 2441-2466.
A commutative associative algebra [Formula: see text] is called symmetric symplectic if it is endowed with both an associative non-degenerate symmetric bilinear form B and an invertible B-antisymmetric derivation D. We give a description of the commutative associative symmetric symplectic
Amir Baklouti; Saïd Benayadi. Symmetric Symplectic Commutative Associative Algebras and Related Lie Algebras. Algebra Colloquium 2011, 18, 973 -986.
AMA StyleAmir Baklouti, Saïd Benayadi. Symmetric Symplectic Commutative Associative Algebras and Related Lie Algebras. Algebra Colloquium. 2011; 18 (spec01):973-986.
Chicago/Turabian StyleAmir Baklouti; Saïd Benayadi. 2011. "Symmetric Symplectic Commutative Associative Algebras and Related Lie Algebras." Algebra Colloquium 18, no. spec01: 973-986.