This paper examines thirty-five commodities, grouped into three market sectors (energy, metals, agriculture & livestock) in terms of the occurrence of price bubbles. The study was based on monthly data for each commodity separately and, in a panel approach, for selected sectors and for all commodities combined. The GSADF test and its version for panel data – panel GSADF – were used to identify bubbles. The beginning and end of...

Non-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general, is as simple as the calculus we know from undergraduate courses of mathematics. Its theoretical potential is huge, and yet it remains unknown or unappreciated.

The problem of identification of quasi-periodically varying dynamic systems is considered. This problem can be solved using generalized adaptive notch filtering (GANF) algorithms. It is shown that the accuracy of parameter estimates can be significantly increased if the results obtained from GANF are further processed using a cascade of appropriately designed filters. The resulting generalized adaptive notch smoothing (GANS) algorithm...

Dold sequences constitute an important class of integer sequences that play an important role in combinatorics, number theory, topology and dynamical systems. We generalize the notion of Dold sequence for the case of partially ordered sets and describe their properties. In particular we give two alternative descriptions of generalized Dold sequences: by some class of elementary sequences as well as by different...

Consider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...