Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 11 June 2020Accepted: 21 April 2021Published online: 07 September 2021Keywordsmonotone inclusions, nonlinear resolvent, forward-backward splitting, forward-backward-forward four-operator splittingAMS Subject Headings90C25, 65K05, 90C30Publication DataISSN (print): 1052-62...

Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under G extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a G-invariant...

We extend RBPP, the state-of-the-art, translation-based planner for conformant probabilistic planning (CPP) with deterministic actions, to handle a wide set of CPPs with stochastic actions. Our planner uses relevance analysis to divide a probabilistic ”failure-allowance” between the initial state and the stochastic actions. Using its ”initial-state allowance,” it uses relevance analysis to sele...

framework for powerset semantics. We now cast the powerset semantics in our general relation-based framework, which enables us to establish when naı̈ve evaluation works for it. For a set D of database objects and a set C of complete objects, we have a pairR “ pRval,Rsemq of relations withRval Ď Dˆ2 C andRsem Ď 2 ˆC. The first relation corresponds to applying multiple valuations (e.g., relating D...

This paper explores the set theoretic assumptions used in the current published proof of Fermat’s Last Theorem, how these assumptions figure in the methods Wiles uses, and the currently known prospects for a proof using weaker assumptions. Does the proof of Fermat’s Last Theorem (FLT) go beyond Zermelo Fraenkel set theory (ZFC)? Or does it merely use Peano Arithmetic (PA) or some weaker fragmen...

We propose a novel variational approach to the depth–from–defocus problem. The quality of such methods strongly depends on the modelling of the image formation (forward operator) that connects depth with out–of–focus blur. Therefore, we discuss different image formation models and design a forward operator that preserves essential physical properties such as a maximum–minimum principle for the ...

This paper develops a new operator called the generalized ordered weighted power utility averaging (GOWPUA) operator, which first introduces the risk attitude of decision makers (DMs) in the aggregation process. We study its properties and families. To determine the GOWPUA operator weights, we put forward an orness measure of the GOWPUA operator and analyze its properties. Considering that diff...

We propose a novel variational approach to the depth–from–defocus problem. The quality of such methods strongly depends on the modelling of the image formation (forward operator) that connects depth with out–of–focus blur. Therefore, we discuss different image formation models and design a forward operator that preserves essential physical properties such as a maximum–minimum principle for the ...

It is shown how Lawvere’s one-to-one translation between Birkhoff’s description of varieties and the categorical one (see [6]) turns Hu’s theorem on varieties generated by a primal algebra (see [4], [5]) into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.