The irreducibility of a representation of a real Lie algebra may depend on whether the representation space is a real or complex Hilbert space. The unitary projective representations of the Poincare group on complex Hilbert spaces were studied by Wigner and many others. Although the Poincare group has a real Lie algebra, we do not know of any study of the orthogonal projective representations o...

Two 4-manifolds are stably diffeomorphic if they become diffeomorphic after connected sum with S × S’s. This paper shows that two closed, orientable, homotopy equivalent, smooth 4-manifolds are stably diffeomorphic provided a certain map from the second homology of the fundamental group with coefficients in Z2 to the L-theory of the group is injective. This injectivity is implied by the Borel/N...

For a smooth fibre bundle F i −→ E p −→ B where F is a compact manifold with or without boundary, a vertical vector field V gives rise to a transfer τ V as an S-map. Our goal is to show these transfers satisfy an equation analogous to one that the index of vector fields satisfy. This equation gives results involving equivariant vector fields as well as a characterization of those transfers defi...

In this paper, the nonlinear oscillations induced by friction in a ball-on-socket system are investigated. The time response was obtained solving differential equations of friction-noise model finite element ball with multiple modes. different patterns motion were analyzed via bifurcation diagram, Poincare map, and recurrence plot. Lyapunov exponents discontinuous distributed contact calculated...

The concept of Diff 4 invariant Poincare transformations is a cornerstone of T(opological) G(eometro)D(ynamics). This concept makes it possible to understand the concept of subjective time and irreversibelity as well as nontriviality of S-matrix at quantum level. In this paper the possibility of identifying Diff 4 invariant Poincare transformations as the recently discovered Lorentz invariant d...

We propose a model-based reinforcement learning algorithm for biped walking in which the robot learns to appropriately place the swing leg. This decision is based on a learned model of the Poincare map of the periodic walking pattern. The model maps from a state at the middle of a step and foot placement to a state at next middle of a step. We also modify the desired walking cycle frequency bas...

A five-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is studied. Its stationary solutions and stability are presented; the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations with the changing of Reynolds number, ...

Three-tori solutions of the Navier-Stokes equations and their dynamics are elucidated by use of a global Poincare map. The flow is contained in a finite annular gap between two concentric cylinders, driven by the steady rotation and axial harmonic oscillations of the inner cylinder. The three-tori solutions undergo global bifurcations, including a new gluing bifurcation, associated with homocli...