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.

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.

A pseudo-euclidean Jordan algebra is a Jordan algebra 𝔍 with an associative non-degenerate symmetric bilinear form B. We study the structure of the pseudo-euclidean Jordan algebras over a field 𝕂 of characteristic not two, and we obtain an inductive description of these algebras in terms of double extensions and generalized double extensions. Next, we study the symplectic pseudo-euclidean Jordan 𝕂-algebras, and we give some informations on a particular class of these algebras, namely the class of symplectic Jordan–Manin Algebras.

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.