We show the convergence of 1+λ-ES with standard step-size update-rules on a large family of fitness functions without any convexity assumption or quasi-convexity assumptions ([3, 6]). The result provides a rule for choosing λ and shows the consistency of halting criteria based on thresholds on the step-size. The family of functions under work is defined through a conditionnumber that generalize...

1 Ample Sheaves Let X be a scheme and L an invertible sheaf. Given a global section f ∈ Γ(X,L ) the set Xf = {x ∈ X | germxf / ∈ mxLx} is open (MOS,Lemma 29). The inclusion Xf −→ X is affine (RAS,Lemma 6) and in particular if X is an affine scheme then Xf is itself affine. Given a sequence of global sections f1, . . . , fn the open sets Xfi cover X if and only if the fi generate L (MOS,Lemma 32...

We show the convergence of 1+λ-ES with standard step-size update-rules on a large family of fitness functions without any convexity assumption or quasi-convexity assumptions ([5, 6]). The result provides a rule for choosing λ and shows the consistency of halting criteria based on thresholds on the step-size. The family of functions under work is defined through a conditionnumber that generalize...

Efficient multiplication in finite fields Fqn requires Fq-bases of low density,i.e., such that the products of the basis elements have a sparse expression in the basis. In this paper we introduce a new family of bases: the quasi-normal bases. These bases generalize the notion of normal bases and provide simple exponentiation to the power q in Fqn . For some extension fields Fqn over Fq, we cons...

In this paper, we are concerned with the study of a multi-step iterative scheme with errors insolving a finite family of asymptotically quasinonexpansive self-mappings. We approximate the common fixed points of a finite family of asymptotically quasi-nonexpansive self-mappings by convergence of the scheme in a uniformly convex Banach space. Our results extend and improve some recent results, Q....