Around 1987 a German mathematician named Matthias Gunther found a new way of obtaining the existence of isometric embeddings of a Riemannian manifold. His proof appeared in [1, 2]. His approach avoids the so-called Nash-Moser iteration scheme and, therefore, the need to prove smooth tame or Moser-type estimates for the inverse of the linearized operator. This simplifies the proof of Nash’s isom...

Mateja Jamnik, Alan Bundy, Ian Green Department of Arti cial Intelligence, 80 South Bridge Edinburgh, EH1 1HN, UK [email protected], [email protected], [email protected] Abstract Human mathematicians often \prove" theorems by the use of diagrams and manipulations on them. We call these diagrammatic proofs. In (Jamnik, Bundy, & Green 1997) we presented how \informal" reasoning with diagrams can...

Human mathematicians often "prove" theorems by the use of diagrams and manipulations on them. We call these diagrammatic proofs. rn (Jamnik, Bundy, & Green 1997) we presented how "informal" reasoning with diagrams can be automated. Three stages of proof extraction procedure were identified. First, concrete rather than general diagrams are used to prove particular instances of the universally qu...

We show how to integrate implicit inductive theorem proving into free variable sequent and tableau calculi and compare the appropri-ateness of tableau calculi for this integration with that of sequent calculi. When rst-order validity is introduced to students it comes with some complete calculus. If this calculus happens to be an analytic calculus augmented with a Cut rule like a sequent or tab...

background: informal payments in the health sector of many developing countries are considered as a major impediment to health care reforms. informal payments are a form of systemic fraud and have adverse effects on the performance of the health system. in this study, the frequency and extent of informal payments as well as the determinants of these payments were investigated in general hospita...

Previous research on the care-giver burden experienced by adult children has typically focused on the adult child and parent dyad. This study uses information on multiple informal care-givers and examines how characteristics of the informal care-giving network affect the adult child's care-giver burden. In 2007, 602 Dutch care-givers who were assisting their older parents reported on parental a...

Koskenniemi's model of two-level morphology has been very influential in recent years, but definitions of the formalism have generally been phrased in terms of a compilation (sometimes left unspecified) into a form of finite-state transducers, or else have consisted of an informal outline of the intended interpretation of the rule-formalism itself. Analyses of the properties of the formalism ha...

This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines that process informal concepts such as computable (total) functions beyond the limits of any given Turing machine or formal system, that is, these machines ca...

Programs that implement computer communications protocols can exhibit extremely complicated behavior, and neither informal reasoning nor testing is reliable enough to establish their correctness: In this paper we discuss the application of modular program verification techniques to protocols. This approach is more reliable than informal reasoning, but has an advantage over formal reasoning base...