Parametrized spaces model locally constant homotopy sheaves

We prove that the homotopy theory of parametrized spaces embeds fully and faithfully in the homotopy theory of simplicial presheaves, and that its essential image consists of the locally homotopically constant objects. This gives a homotopy-theoretic version of the classical identification of covering spaces with locally constant sheaves. We also prove a new version of the classical result that spaces parametrized over X are equivalent to spaces with an action of ΩX. This gives a homotopy-theoretic version of the correspondence between covering spaces and π₁-sets. We then use these two equivalences to study base change functors for parametrized spaces.     

The IR emitting centers in Bi-doped Mg-Al-Si oxide glasses

The properties of IR emission centers are investigated in Bi-doped Mg-Al-silicate glasses having moderate melting temperatures to be fabricated by routine melting in alumina crucibles. The quadratic concentration dependence of absorption in the visible range indicates that the considered optical centers can be Bi₂ dimers forming in a balanced chemical reaction in the glass melt. Their formation enthalpy is evaluated from their concentration variations with the synthesis temperature. The high (up to 85% at low concentrations) luminescence quantum yield and wide emission spectrum makes this glass a promising material for tunable lasers.     

On rational addition theorems

We investigate the functions which admit an addition theorem of the form

     

Catalysis of the kemp elimination by natural coals

Commercially available coals were found to be efficient heterogeneous catalysts of the Kemp elimination reaction in aqueous solutions. A pH-rate profile study suggests that catalysis originates from specific catalytic groups and not simply from the large graphitic surface area. The low-quality lignite coals, which exhibit similar catalytic efficiency per weight to that of molecularly imprinted polymers, are better catalysts for this reaction in comparison with the bituminous coals.     

Comparing material and structural set theories

We study elementary theories of well-pointed toposes and pretoposes, regarded as category-theoretic or “structural” set theories in the spirit of Lawvere's “Elementary Theory of the Category of Sets”. We consider weak intuitionistic and predicative theories of pretoposes, and we also propose category-theoretic versions of stronger axioms such as unbounded separation, replacement, and collection. Finally, we compare all of these theories formally to traditional membership-based or “material” set theories, using a version of the classical construction based on internal well-founded relations.