Convergent product is an assembly shape concept integrating functions and sub-functions to form a final product. To conceptualize the convergent product problem, a web-based network is considered in which a collection of base functions and sub-functions configure the nodes and each arc in the network is considered to be a link between two nodes. The aim is to find an optimal tree of functionali...

ing from the multiplication of 8\ by S2 . Special example : T* • T.* is absolutely convergent, but 1\ and T* are each divergent when r < § and * < §. In the divergent series 8/ the terms increase without limit in numerical value, as v increases without limit. The same is true of S2 . Herein lies the difference between this pair of divergent series yielding an absolutely convergent product, and ...

Message-passing algorithms have emerged as powerful techniques for approximate inference in graphical models. When these algorithms converge, they can be shown to find local (or sometimes even global) optima of variational formulations to the inference problem. But many of the most popular algorithms are not guaranteed to converge. This has lead to recent interest in convergent message-passing ...

The notion of convergent star product is generally understood as the data of a one parameter family {Et}t∈I ⊂ C∞(M) of function algebras on a Poisson manifold (M, { , }). On each of them one is given an associative algebra structure ⋆t which respect to which the function space Et is closed. The family of products {⋆t} should moreover define in some sense a deformation of the commutative pointwi...

W. L. Bynum introduced the weakly convergent sequence coefficient WCS(A') of the Banach space X as WCS(Jf) = sup{M: for each weakly convergent sequence {xn} in X , there is some y e co({x«}) such that M • lim sup ||x,, y\\ < A({x„})} . We consider the weakly convergent sequence coefficient of the /^-product space Z = (fTjLi Xi)t of tne finite non-Schur space Xx, ... , X„ and show that WCS(Z) = ...