Homotopy Type Theory in Lean

We discuss the homotopy type theory library in the Lean proof assistant. The library is especially geared toward synthetic homotopy theory. Of particular interest is the use of just a few primitive notions of higher inductive types, namely quotients and truncations, and the use of cubical methods.Comment: 17 pages, accepted for ITP 201

Penetration of fusidic acid and rifampicin into cerebrospinal fluid in low-grade inflammatory meningitis caused by Staphylococcus epidermidis

AbstractCerebrospinal fluid (CSF) concentration-time curves of rifampicin and fusidic acid were studied in a patient with post-operative meningitis caused by Staphylococcus epidermidis. The patient was treated with this combination of antimicrobial agents because of a severe hypersensitivity reaction to vancomycin. Peak CSF concentrations of rifampicin exceeded the MIC by > 60-fold, while those of fusidic acid just reached the MIC. CSF concentrations of fusidic acid were relatively stable within the range reported for patients with uninflamed meninges, but serum levels were surprisingly low. An increase in the metabolism of fusidic acid induced by rifampicin cannot be excluded

Logic, logical form and the disunity of truth

Monists say that the nature of truth is invariant, whichever sentence you consider; pluralists say that the nature of truth varies between different sets of sentences. The orthodoxy is that logic and logical form favour monism: there must be a single property that is preserved in any valid inference; and any truth-functional complex must be true in the same way as its components. The orthodoxy, I argue, is mistaken. Logic and logical form impose only structural constraints on a metaphysics of truth. Monistic theories are not guaranteed to satisfy these constraints, and there is a pluralistic theory that does so

Influence of surface oxide characteristics and speciation on corrosion, electrochemical properties and metal release of atomized 316L stainless steel powders

Surface oxide characteristics of powder particles are important to consider for any toxicological risk assessment based on in-vitro or in-vivo tests. This study focuses on a multi-analytical approach (X-ray photoelectron spectroscopy, Auger electron spectroscopy, scanning- and transmission electron microscopy, and different electrochemical techniques) for in-depth characterization of surface oxides of inert-gas-atomized (GA) AISI 316L stainless steel powder, compared with massive sheet and a water-atomized (WA) 316L powder. Implications of differences in surface oxide phases and their surface distribution on corrosion, electrochemical properties and metal release are systematically discussed. Cr was enriched in an inner surface layer for both GA powders, with Mn and S enriched in the outermost surface oxide. The surface oxide was 2-5 nm thick for both GA powder size fractions, amorphous for the GA powder size

Influence of surface oxide characteristics and speciation on corrosion, electrochemical properties and metal release of atomized 316L stainless steel powders

Surface oxide characteristics of powder particles are important to consider for any toxicological risk assessment based on in-vitro or in-vivo tests. This study focuses on a multi-analytical approach (X-ray photoelectron spectroscopy, Auger electron spectroscopy, scanning- and transmission electron microscopy, and different electrochemical techniques) for in-depth characterization of surface oxides of inert-gas-atomized (GA) AISI 316L stainless steel powder, compared with massive sheet and a water-atomized (WA) 316L powder. Implications of differences in surface oxide phases and their surface distribution on corrosion, electrochemical properties and metal release are systematically discussed. Cr was enriched in an inner surface layer for both GA powders, with Mn and S enriched in the outermost surface oxide. The surface oxide was 2-5 nm thick for both GA powder size fractions, amorphous for the GA powder size

Extension and approximation of mm-subharmonic functions

Let $\Omega\subset \mathbb C^n$ be a bounded domain, and let $f$ be a real-valued function defined on the whole topological boundary $\partial \Omega$. The aim of this paper is to find a characterization of the functions $f$ which can be extended to the inside to a $m$-subharmonic function under suitable assumptions on $\Omega$. We shall do so by using a function algebraic approach with focus on $m$-subharmonic functions defined on compact sets. We end this note with some remarks on approximation of $m$-subharmonic functions