Dimension theory plays a crucial technical role in stability theory and its relatives. The abstract dependence relations defined, although combinatorial in nature, often have surprising geometric meaning in particular cases. This article discusses several aspects of dimension theory, such as categoricity, strongly minimal sets, modularity and the Zil’ber principle, forking, simple theories, ort...

The two main stability results for nearly-integrable Hamiltonian systems are revisited: Nekhoroshev theorem, concerning exponential lower bounds for the stability time (effective stability), and KAM theorem, concerning the preservation of a majority of the nonresonant invariant tori (perpetual stability). To stress the relationship between both theorems, a common approach is given to their proo...

In this paper, we have proposed and analyzed a mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equations.

We introduce the idea of representation stability (and several variations) for a sequence of representations Vn of groups Gn. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical theorems of homological stability to a much broader variety of examples. Represent...

Some groups endure longer, are more stable, and are better able than other groups to incorporate new members or ideas without losing their distinctiveness. I present a simple model of individual behavior based on the thesis that interaction leads to shared knowledge and that relative shared knowlege leads to interaction. Using this model I examine the structural and cultural bases of group stab...

) In Logic across the University: Foundations and Application–Proceedings of the Tsinghua Logic Conference, Beijing, ed. J. van Benthem and F. Liu, 47–54. Volume 47: Studies in Logic. London: College Publications. Levi, Isaac. 1967. Gambling with Truth: An Essay on Induction and the Aims of Science. Cambridge, MA: MIT Press.———. 1980. The Enterprise of Knowledge: An Essay on Knowledge, Cred...

This paper proves that in Size Theory the comparison of multidimensional size functions can be reduced to the 1-dimensional case by a suitable change of variables. Indeed, we show that a foliation in half-planes can be given, such that the restriction of a multidimensional size function to each of these half-planes turns out to be a classical size function in two scalar variables. This leads to...

GRIST is an axiomatic framework for nonstandard set theory with many “levels of standardness.” The paper establishes a number of general consequences of GRIST, in particular, a very strong form of Transfer principle. 2010 Mathematics Subject Classification 26E35 (primary); 03E70, 03H05 (secondary)

In this paper, an almost new control approach called terminal synergetic control which works based on user defined manifold is applied to a nonlinear helicopter model. Stability analysis is convestigated using Lyapunov stability theory. Synergetic controller is applied to this nonlinear fifth-order helicopter model to control height and angle. Simulation results showed that it has faster and sm...