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Vol 13 - À paraître

Avancées en Mathématiques Pures et Appliquées

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[FORTHCOMING] Existence globale de solutions du système sphérique-symétrique de Einstein-Vlasov-Maxwell

We prove that the initial value problem with small data for the asymptotically flat spherically symmetric Einstein-Vlasov-Maxwell system admits the global in time solution in the case of the non zero shift vector. This result extends the one already known for chargeless case.

[FORTHCOMING] Dérivations supérieures multiplicatives de type Jordan des anneaux unitaires avec idempotants non-triviaux

Suppose R is a non-zero unital associative ring with a nontrivial idempotent "e". In this paper, we prove that under some mild conditions every multiplicative jordan n-higher derivations on R is additive. Moreover, at the end of the paper, we have presented some applications of multiplicative Jordan n-higher derivations on triangular rings, nest algebra, upper triangular block matrix algebra, prime rings, von Neumann algebras.

[FORTHCOMING] Ensemble de Hitting avec contraintes et arbres de Steiner dans les graphes libres de type SCk et 2K2

Strictly Chordality-k graphs (SCk) are graphs which are either cycle-free or every induced cycle is of length exactly $$${k, k \geq 3}$$$. Strictly chordality-3 and strictly chordality-4 graphs are well known chordal and chordal bipartite graphs, respectively. For $$${k \geq 5}$$$, the study has been recently initiated in [1] and various structural and algorithmic results are reported. In this paper, we study SCk graphs in the algorithmic front and the study concerns the class of graphs where $$${k \geq 5}$$$. We show that recognizing vertex cycle ordering (VCO) for SCk, $$${k \geq 5}$$$ graphs, maximum independent set (MIS), minimum vertex cover, minimum dominating set, feedback vertex set (FVS), odd cycle transversal (OCT), even cycle transversal (ECT) and Steiner tree problem are linear time solvable on SCk graphs, $$${k \geq 5}$$$. We next consider 2K2-free graphs and discussed the algorithmic problems such as FVS, OCT, ECT and Steiner tree problem on the subclasses of 2K2-free graphs.