Baizhanov and Baldwin [1] introduce the notions of benign and weakly benign sets to investigate the preservation of stability by naming arbitrary subsets of a stable structure. They connect the notion with work of Baldwin, Benedikt, Bouscaren, Casanovas, Poizat, and Ziegler. Stimulated by [1], we investigate here the existence of benign or weakly benign sets. Definition 0.1 1. The set A is beni...

* Correspondence: abasalt. [email protected] Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran Full list of author information is available at the end of the article Abstract In this paper, we prove the Hyers-Ulam stability and the superstability for cubic functional equation by using the fixed point alternative theorem. As a consequence, we show that the cubic m...

We prove rigorously the occurrence of zero-mode Bose-Einstein condensation for a class of continuous homogeneous systems of boson particles with superstable interactions. This is the first example of a translation invariant continuous Bose-system, where the existence of the Bose-Einstein condensation is proved rigorously for the case of non-trivial two-body particle interactions, provided there...

Metric Abstract Elementary Classes (MAECs) correspond to an amalgam of the notions of Abstract Elementary Classes (AECs) and Elementary Class in the Continuous Logic. In this work, we study a proof of uniqueness (up to isomorphism) of Limit Models in MAECs [ViZa10a, Za1x], under superstability-like assumptions. Assuming this uniqueness of Limit Models, it is possible to do a preliminar study of...

This paper presents basic theoretical results for partial constant return maps (PCRMs) from controlled manifold piecewise linear chaotic circuits. Applying the instantaneous state setting method to the circuit, the chaotic attractor is changed into various superstable periodic orbits corresponding to the PCRM. Using an efficient algorithm, an important example of the PCRM can be analyzed almost...

We study Lascar strong types and Galois types and especially their relation to notions of type which have finite character. We define a notion of a strong type with finite character, so called Lascar type. We show that this notion is stronger than Galois type over countable sets in simple and superstable finitary AECs. Furthermore we give and example where the Galois type itself does not have f...

We study the theory of a Hilbert space H as a module for a unital C∗-algebra A from the point of view of continuous logic. We show this theory, in an appropiate lenguage, has quantifier elimination and it is superstable. We show that for every v ∈ H the type tp(v/∅) is in correspondence with the positive linear functional over A defined by v. Finally, we characterize forking, orthogonality and ...