The topological Tverberg theorem states that for any prime power q and continuous map from a (d+ 1)(q− 1)-simplex to Rd, there are q disjoint faces Fi of the simplex whose images intersect. It is possible to put conditions on which pairs of vertices of the simplex that are allowed to be in the same face Fi. A graph with the same vertex set as the simplex, and with two vertices adjacent if they ...

Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by the gluing equations for SL(3,C)representations. In particular we prove local rigidity of the “geometric” representation in SL(3,C), recovering a recent result of Menal-Ferrer and Porti. More generally we give a crit...

A path-tracking criterion for the so-called LHD (load-haul-dump) truck used in underground mining is proposed in this paper. It exploits the particular configuration of this vehicle, composed of two units connected by an actuated articulation. The task is to follow the path represented by the middle of the tunnel, maintaining the whole vehicle at a reduced distance from the path itself, to decr...

In this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. The stages for prey have been considered. The proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. The model is analyzed by using linear stability analysis to ob...

This paper considers Lur’e type descriptor systems (LDS). The concept of strongly absolute stability is defined for LDS and such a notion is a generalization of absolute stability for Lur’e type standard state-space systems (LSS). A reduced-order LSS is obtained by a standard coordinate transformation and it is shown that the strongly absolute stability of the LDS is equivalent to the absolute ...

Abstract: In this paper, the robust D-stability problem for discrete uncertain multiple time-delay systems is examined on the basis of their such reduced-order models (the slow and fast subsystems), which are obtained by time-scale separation method. Under the condition that the slow and fast subsystems of the nominal system are both D(α, r)-stable, a D-stability criterion for the slow and fast...

We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a ‘small’ deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of discontinuous groups, we introduce the concepts from a group theoretic perspectiv...

We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a ‘small’ deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of discontinuous groups, we introduce the concepts from a group theoretic perspectiv...

It is well known that the time-varying Kalman Filter (KF) is globally exponentially stable and optimal in the sense of minimum variance under some conditions. However, nonlinear approximations such as the extended KF linearizes the system about the estimated state trajectories, leading in general to loss of both global stability and optimality. Nonlinear observers tend to have strong, often glo...