766 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
Obtuse cones and Gram matrices with nonnegative inverse
AbstractWe study some properties of Gram matrices with nonnegative inverse which lead to the constructions of obtuse cones. These constructions can find applications in optimization problems, e.g., in methods of convex feasibility problems or of convex minimization problems
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