the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

the focus of studies in the field of passive walking has often been on straight walking, while less attention has been paid to the field of turning motions. in this paper, the passive motions of a finite width rimless wheel as the simplest 3d model of passive biped walkers was investigated with a focus on turning motions. for this purpose, the hybrid model of the system consisting of continuous...

Poincaré maps often prove to be invaluable tools in the study of long-term behaviour and qualitative properties of a given dynamical system. While the analytic theory of these maps is fully explored, finding numerical algorithms that allow the computation of Poincaré maps in concrete problems is far from trivial. For the verification it is desirable to approximate the Poincaré map over as large...

The focus of studies in the field of passive walking has often been on straight walking, while less attention has been paid to the field of turning motions. In this paper, the passive motions of a finite width rimless wheel as the simplest 3D model of passive biped walkers was investigated with a focus on turning motions. For this purpose, the hybrid model of the system consisting of continuous...

In this paper, we develop a physiological oscillator model of which the output mimics the shape of the R-R interval Poincaré plot. To validate the model, simulations of various nervous conditions are compared with heart rate variability (HRV) data obtained from subjects under each prescribed condition. For a variety of sympathovagal balances, our model generates Poincaré plots that undergo alte...

Considering the existence of nonconformal stochastic fluctuations in the metric tensor a generalized uncertainty principle and a deformed dispersion relation (associated to the propagation of photons) are deduced. Matching our model with the so called quantum κ–Poincaré group will allow us to deduce that the fluctuation–dissipation theorem could be fulfilled without needing a restoring mechanis...

The artist M.C. Escher was the first artist to create patterns in the hyperbolic plane. He used both the Poincaré disk model and the Poincaré half-plane model of hyperbolic geometry. We discuss some of the theory of hyperbolic patterns and show Escher-inspired designs in both of these models.

Non-anticommutative Grassmann coordinates in four-dimensional twistdeformed N = 1 Euclidean superspace are decomposed into geometrical ones and quantum shift operators. This decomposition leads to the mapping from the commutative to the non-anticommutative supersymmetric field theory. We apply this mapping to the Wess-Zumino model in commutative field theory and derive the corresponding non-ant...