We study the homotopy relation between the standard 2-local geometry ∆ and the Bouc complex for the sporadic group Co3. We also give a result concerning the relative projectivity of the reduced Lefschetz module L̃(∆).

Topological properties of the matching complex were first studied by Bouc in connection with Quillen complexes, and topological properties of the chessboard complex were first studied by Garst in connection with Tits coset complexes. Björner, Lovász, Vrécica and Živaljević established bounds on the connectivity of these complexes and conjectured that these bounds are sharp. In this paper we sho...

In this paper feedforward controller is designed to eliminate nonlinear hysteresis behaviors of a piezoelectric stack actuator (PSA) driven system. The control design is based on inverse Prandtl-Ishlinskii (P-I) hysteresis model identified using particle swarm optimization (PSO) technique. Based on the identified P-I model, both the inverse P-I hysteresis model and feedforward controller can be...

In this paper the semi-active control is achieved by a base isolation system. The magnetorheological dampers (MRD) hysteretic force is described by models based on nonlinear differential equation Bouc-Wen. The Bouc-Wen model is able to capture, in an analytical form, a range of shapes of hysteretic cycles which match the behavior of a wide class of nonlinear systems. In order to reduce the seis...

Despite the fact that shape-memory alloy (SMA) has several mechanical advantages as it continues being used as an actuator in engineering applications, using it still remains as a challenge since it shows both non-linear and hysteretic behavior. To improve the efficiency of SMA application, it is required to do research not only on modeling it, but also on control hysteresis behavior of these m...

The Bouc-Wen hysteresis model is widely employed to mathematically represent the dynamical behavior of several physical devices, materials and systems such as magnetorheological dampers, lanthanide zirconium or aluminum oxides, mechanical structures or biomedical systems. However, these mathematical models must account for different properties such as the bounded-input bounded-output stability,...

We establish an algebraic version of the classical result that a G-map f between G-complexes which restricts to a homotopy equivalence fH on H-fixed sets for all subgroups H of G is a G-homotopy equivalence. This is used to give an alternative proof of a theorem of Bouc. We also include a number of illustrations and applications.