The Cigler simple derivation of the q-Carlitz-Dobinski formula is recalled and it is noticed that the formula may be interpreted as the average of powers of random variable X q with the q-Poisson distribution. In parallel new q-Cigler-Dobinski and psi-Carlitz-Dobinski formulas are introduced. At first let us anticipate with ψ-remark. ψ denotes an extension of 1 n! n≥0 sequence to quite arbitrar...

Yeast prions are heritable amyloid aggregates of functional yeast proteins; their propagation to subsequent cell generations is dependent upon fragmentation of prion protein aggregates by molecular chaperone proteins. Mounting evidence indicates the J-protein Sis1 may act as an amyloid specificity factor, recognizing prion and other amyloid aggregates and enabling Ssa and Hsp104 to act in prion...

We prove that the family of all invariant sets of iterated systems of contractions R → R is a nowhere dense Fσ type subset in the space of the non-empty compact subsets of R equipped with the Hausdorff metric. An iterated function system (IFS for short) is a finite collection (T1, . . . , Tn) of weak contractions of a metric space X. By a weak contraction we mean a mapping T : X → X such that d...