In this paper, we present Carnap’s modal logic C, which is one of the first attempts to use the concept of possible world (that of state description in the Carnapian original terminology) in shaping the semantics for modalities. Some older technical results, which concern the logic C, are summarized, namely two different kinds of axiomatization of C, one unusual characterization of C as the only set of formulae having one special property, and semantical and syntactical relations of C to S5. The fact that C is not closed under the universal substitution is shortly discussed. Finally, the predicate version of C, which is not axiomatizable, is defined., V tomto příspěvku prezentujeme Carnapovu modální logiku C, která je jedním z prvních pokusů o využití konceptu možného světa (státního popisu v karnapské původní terminologii) při formování sémantiky modalit. Jsou shrnuty některé starší technické výsledky, které se týkají logiky C, a to dva různé druhy axiomatizace C, jedna neobvyklá charakterizace C jako jediná množina vzorců s jednou speciální vlastností a sémantické a syntaktické vztahy C až S5. Krátce je diskutována skutečnost, že C není uzavřena pod univerzální substitucí. Nakonec je definována predikátová verze C, která není axiomatizovatelná., and Vít Punčochář
In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell. The diffusion on the endoplasmic reticulum, modeled as a Riemannian manifold, is described by the Laplace-Beltrami operator. For the binding process to the surface of the endoplasmic reticulum, different scalings with powers of the homogenization parameter are considered. This leads to three qualitatively different models in the homogenization limit.