In this survey, a recent computational methodology paying a special attention to the
separation of mathematical objects from numeral systems involved in their representation is …

Numerous problems arising in engineering applications can have several objectives to be
satisfied. An important class of problems of this kind is lexicographic multi-objective …

Unconventional computing is about breaking boundaries in thinking, acting and computing.
Typical topics of this non-typical field include, but are not limited to physics of computation …

A well-known drawback of algorithms based on Taylor series formulae is that the explicit
calculation of higher order derivatives formally is an over-elaborate task. To avoid the …

The necessity to find the global optimum of multiextremal functions arises in many applied
problems where finding local solutions is insufficient. One of the desirable properties of …

A novel and interesting approach to infinite and infinitesimal numbers was recently
proposed in a series of papers and a book by Sergeyev. This novel numeral system is based …

New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with
initial condition are proposed. They are designed for work on a new kind of a supercomputer …

Abstract The Peano and the Hilbert curves, denoted by P and H respectively, are historically
the first and some of the best known space-filling curves. They have a fractal structure, many …

A recently developed computational methodology for executing numerical calculations with
infinities and infinitesimals is described in this paper. The approach developed has a …

We propose an axiomatization of Sergeyev's theory of Grossone, trying to comply with his
methodological principles. We find that a simplified form of his Divisibility axiom is sufficient …