This essay was inspired by the thoughts of Daniela Tinková on the role of the Czech Enlightenment. We begin by acknowledging its importance for a deeper understanding of Czech history, before going on to address four problem areas. The first is the significance of Enlightenment efforts in the field of popular education (Volksaufklärung), which in the Czech context necessarily introduced the need for vernacularization. These efforts thus have an important, hitherto undervalued place among the factors that strengthened the impetus of national agitation (the second phase of the Czech national movement). We also consider the role played in the national movement of a clergy trained under the Josephenist system, and the defining characteristics of that clergy.
A homothetic arithmetic function of ratio K is a function f ∶ ℕ → R such that f(Kn)=f(n) for every n ∈ ℕ Periodic arithmetic funtions are always homothetic, while the converse is not true in general. In this paper we study homothetic and periodic arithmetic functions. In particular we give an upper bound for the number of elements of f(ℕ) in terms of the period and the ratio of f.