This short article is devoted to the dynamics of controlled (and, therefore, open) systems. The internal forces, which appear only in the presence of external free controls and depend explicitely on them, are considered. Such interactive forces may be regarded as feedbacks generated in the system by the external free controls. In particular, one is able to interpret the interactive controls as ...

We prove that whenever a Kac-Moody group over a finite field is a lattice of its buildings, it has a fundamental domain with respect to which the induction cocycle is L for any p∈ [1; +∞). The proof uses elementary counting arguments for root group actions on buildings. The applications are the possibility to apply some lattice superrigidity, and the normal subgroup property for Kac-Moody latti...

In this paper, we consider different ways of generating dynamical systems on 3-manifolds. We first derive explicit differential equations for dynamical systems defined on generic hyperbolic 3-manifolds by using automorphic function theory to uniformize the upper half-space model. It is achieved via the modification of the standard Poincaré theta series to generate systems invariant within each ...

Problems of geometric probability for an arbitrary convex body of resolution in the euclidean space E3 has been investigated in [1]. In [9] Buffon’s problem is solved for a lattice of right-angled parallelepipeds in the 3-dimensional space. In this note we want to use the results in [5] for to solve problems of intersection for a particular lattice that we describe: the fundamental cell C0 of t...

We present a theory of qualitative rigid body mechanics and describe a program that uses this theory to compute qualitative dynamic simulations. The program works directly from a qualitative representation of geometry (qc-space). It employs a new qualitative representation for forces that reduces ambiguity in force sums and hence reduces branching.

The Kaluza-Klein idea of extra spacetime dimensions continues to pervade current attempts to unify the fundamental forces, but in ways somewhat different from that originally envisaged. We present a modern perspective on the role of internal dimensions in physics, focussing in particular on su-perstring theory. A novel result is the interpretation of Kaluza-Klein string states as extreme black ...

The purpose of this paper is to compute of fundamental relations of hypergroups. In this regards first we study some basic properties of fundamental relation of hypergroups, then we show that any given group is isomorphic to the fundamental group of a nontrivial hypergroup. Finally we study the connections between categories of hypergroups and groups via the fundam...

Solving Pell’s equation is of relevance in finding fundamental units in real quadratic fields and for this reason polynomial solutions are of interest in that they can supply the fundamental units in infinite families of such fields. In this paper an algorithm is described which allows one to construct, for each positive integer n, a finite collection, {Fi}, of multi-variable polynomials (with ...