for any value of x in the interval (a, b). Chebyshev motivated his problem by investigation of limit theorems in probability theory, with some related work done even earlier by Heine. It was completely resolved by Markov; for more detailed comments and description of the related developments see Shohat and Tamarkin (1943), Akhiezer (1965) and Gautschi (1981). Here we will not describe the well ...

In the recent new edition of the collected works of T.J. Stieltjes, one of us gave an impression of the impact of Stieltjes' work a century after his death 43]. In this paper we give an update and mention some observations which were missing from 43] and some results which appeared during the last two years and which are directly related to Stieltjes' work. In particular there is a large sectio...

Neural controlled differential equations (NCDEs), which are continuous analogues to recurrent neural networks (RNNs), a specialized model in (irregular) time-series processing. In comparison with similar models, e.g., ordinary (NODEs), the key distinctive characteristics of NCDEs i) adoption path created by an interpolation algorithm from each raw discrete sample and ii) Riemann--Stieltjes inte...