we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

We document the discovery of two generating functions for ζ(2n + 2), analogous to earlier work for ζ(2n + 1) and ζ(4n + 3), initiated by Koecher and pursued further by Borwein, Bradley and others.

At Rolls-Royce, a study determined that manufacturing part cost can be estimated from dimensional data in the part definition. The method appears to be more accurate than mass-based parametric models or process simulation cost models. Additional advantages are: part definition information is causally related to part manufacturing cost; part definition information is easily available during the ...

‘Scientific community’ is common currency in the study of science, largely due to Kuhn’s use of the term in his highly influential book The Structure of Scientific Revolutions. As this article explains, however, ‘scientific community’ was not of Kuhn’s coining. It was hinted at by Peirce, and expressly designated by Royce. On a few occasions Fleck affirmed a scientific community, while Polanyi ...

The category k-BFAlg of all k-algebras with a bilinear form, whose objects are pairs (R,b) where R is k-algebra and b:R×R→k mapping, equivalent to the unital A for which canonical homomorphism (k,1)→(A,1A) splitting monomorphism in k-Mod. Call left inverses this “weak augmentations” algebra. There isomorphism between weak augmentation (A,bA) form bA compatible multiplication A, i.e., such that ...