687 research outputs found
On the additive theory of prime numbers II
The undecidability of the additive theory of primes (with identity) as well
as the theory Th(N,+, n -> p\_n), where p\_n denotes the (n+1)-th prime, are
open questions. As a possible approach, we extend the latter theory by adding
some extra function. In this direction we show the undecidability of the
existential part of the theory Th(N, +, n -> p\_n, n -> r\_n), where r\_n is
the remainder of p\_n divided by n in the euclidian division
Strict pseudocontractions and demicontractions, their properties and applications
We give properties of strict pseudocontractions and demicontractions defined
on a Hilbert space, which constitute wide classes of operators that arise in
iterative methods for solving fixed point problems. In particular, we give
necessary and sufficient conditions under which a convex combination and
composition of strict pseudocontractions as well as demicontractions that share
a common fixed point is again a strict pseudocontraction or a demicontraction,
respectively. Moreover, we introduce a generalized relaxation of composition of
demicontraction and give its properties. We apply these properties to prove the
weak convergence of a class of algorithms that is wider than the
Douglas-Rachford algorithm and projected Landweber algorithms. We have also
presented two numerical examples, where we compare the behavior of the
presented methods with the Douglas-Rachford method.Comment: 27 pages, 3 figure
Tree inclusions in windows and slices
is an embedded subtree of if can be obtained by deleting some nodes from : if a node is deleted, all edges adjacent to are also deleted, and outgoing edges are replaced by edges going from the parent of (if it exists) to the children of . Deciding whether is an embedded subtree of is known to be NP-complete. Given two trees (a target and a pattern ) and a natural number , we address two problems: 1. counting the number of windows of having height exactly and containing pattern as an embedded subtree, and 2. counting the number of slices of having height exactly and containing pattern as an embedded subtree
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