Convexity of Some Spectral Functions on Hermitian Matrices.

We prove in this note the convexity of the functions $u\circ \lambda$ and more generally $u\circ \lambda_B$ on the space of Hermitian matrices, for $B$ a fixed positive definite hermitian matrix, when $u:\mathbb{R}^m\rightarrow \mathbb{R}\cup \{+\infty \}$ is a symmetric convex function which is lower semi-continuous on $\mathbb{R}^m$, and finite in at least one point of $\mathbb{R}^m$. This is performed by using some optimisation techniques and a generalized Ky Fan inequality

Insecticidal activity of four medicinal plant extracts against Tribolium castaneum (Herbst) (Coleoptera: Tenebrionidae)

Methanol extracts from four medicinal plants, Peganum harmala (Zygophyllaceae), Ajuga iva (Labiateae), Aristolochia baetica (Aristolochiaceae) and Raphanus raphanistrum (Brassicaceae) werestudied for their insecticidal effects on the stored grain pest Tribolium castaneum (Herbst). Response varied with plant species. Larvae growth was significantly inhibited when they were fed with extracts incorporated into the diet. Good insecticidal activity against T. castaneum larvae and adults wasachieved with extract of P. harmala seeds, followed by extract of A. iva, Ari. baetica and R. raphanistrum aerial parts. The extracts of the four plants disrupted the developmental cycle of the insect. Extracts of P. harmala, A. iva and Ari. baetica inhibited F1 progeny production. These naturally occurring plant extracts could be useful for managing populations of T. castaneu

Einstien-Multidimensional Extrapolation methods

In this paper, we present a new framework for the recent multidimensional extrapolation methods: Tensor Global Minimal Polynomial (TG-MPE) and Tensor Global Reduced Rank Extrapolation (TG-RRE) methods. We develop a new approach to the one presented in \cite{17}. The proposed framework highlights, in addition their polynomial feature, the connection of TG-MPE and TG-RRE with nonlinear Krylov subspace methods. A unified algorithm is proposed for their implemention. Theoretical results are given and some numerical experiments on linear and nonlinear problems are considered to confirm the performance of the proposed algorithms