On near-standardness in Hilbert spaces.
On the averaging method for differential equations with delay.
On the Continuity of Internal Functions
On the existence of factor sets by external equivalences in IST.
On the shift-window phenomenon of super-functions.
On the theory of grossone.
On Tykhonov's theorem for convergence of solutions of slow and fast systems.
-symmetric bi-capacities
Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order , instead of for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of -symmetric bi- capacities, in the same spirit as for -symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature,...
Perturbations singulières des équations différentielles ordinaires et analyse non-standard
Propriétés des classes d’éléments -standard
Quantifier elimination in quasianalytic structures via non-standard analysis
The paper is a continuation of an earlier one where we developed a theory of active and non-active infinitesimals and intended to establish quantifier elimination in quasianalytic structures. That article, however, did not attain full generality, which refers to one of its results, namely the theorem on an active infinitesimal, playing an essential role in our non-standard analysis. The general case was covered in our subsequent preprint, which constitutes a basis for the approach presented here....
Quantum logics and bivariable functions
New approach to characterization of orthomodular lattices by means of special types of bivariable functions is suggested. Under special marginal conditions a bivariable function can operate as, for example, infimum measure, supremum measure or symmetric difference measure for two elements of an orthomodular lattice.
Rückert Nullstellensatz for normed, non-discrete fields using non-standard analysis.
Set-like equivalence and inner and outer cuts
Some connections between measure, indiscernibility and representation of cuts
Spherical completeness with infinitesimals.
In the theory of nonarchimedean normed spaces over valued fields other than R or C, the property of spherical completeness is of utmost importance in several contexts, and it appears to play the role conventional completeness does in some topics of classical functional analysis. In this note we give various characterizations of spherical completeness for general ultrametric spaces, related to but different from the notions of pseudo-convergent sequence and pseudo-limit introduced by Ostrowski in...
Statistical Solutions of PDEs by Nonstandard Densities.
Sull'ordinamento dei numeri reali non-standard
Several order-theoretic properties of the real axis, of the monads and of the infinites in nonstandard models of Analysis are considered. Pseudometrizability and topological completeness of related uniformities are studied.
Sur l'équation aux différences affine du premier ordre unidimensionnelle
On étudie les phénomènes de retard à la bifurcation et de butée pour des systèmes discrets lents-rapides du plan. On donne une explication géométrique de ces phénomènes basée sur l’examen de fonctions reliefs. On démontre ensuite l’existence et la vie brève des longs canards, qui sont des trajectoires ne présentant pas de butée. Trois exemples illustrent ces phénomènes. Le premier expose la problématique, le second permet une expérimentation de l’étude théorique sur les longs canards, le troisième...
Sur une classe d'algèbre de fonctions généralisées application aux systèmes différentiels