Increases in the use of automated theorem-provers have renewed focus on the relationship between the informal proofs normally found in mathematical research and fully formalised derivations. Whereas some claim that any correct proof will be underwritten by a fully formal proof, sceptics demur. In this paper I look at the relevance of these issues for formalism, construed as an anti-platonistic ...

we present a case of caustic ingestion by a 1.5-year-old boy. the caustic agent was drain opener which is a strong alkaline substance. children in iran and many other countries are still exposed to not “child proof” (child resistant packaging) toxic substance containers. ingestion of caustic agents may lead to necrosis, perforation, and strictures. substances that are ingested more frequently a...

the proof of the local nilpotence theorem for 4-engel groups was completed by g. havas and m. vaughan-lee in 2005. the complete proof on the other hand is spread over several articles and the aim of this paper is to give a complete coherent linear version. in the process we are also able to make few simplifications and in particular we are able to merge two of the key steps into one.

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

Background: Once COVID-19 is transmitted, the corresponding civil responsibility should be clarified by the identification of the transmitter, compensation of the damage and detection of the causal relationship between the damage or harm and the harmful act.    Methods: This research has been prepared by descriptive analytical method and its data has been collected by documentary library tools...