New time dependent wave solutions to the classical homogeneous Maxwell equations in the vacuum have been found. These waves are not transverse; they exhibit both torsion and spin; they have ̄nite magnetic helicity, A ± B 6= 0, a non-zero Poynting vector, E £H 6= 0;and a non zero second Poincare invariant, E ± B 6= 0: Two four component rank 3 tensors, constructed on topological grounds in terms ...

It is shown how, by carrying out a sequence of three coordinate axis rotations in Poincare space, one can calculate the principal basis and the real, nonnegative eigenvalues of any symmetric polarization scattering matrix. Then the two eigenvalues and the three Eulerian angles of the principal axes in Poincare space constitute a complete set of pure scatterer parameters. A scatterer classificat...

Following the construction of the κ-Minkowski space from the bicrossproduct structure of the κ-Poincare group, we investigate possible differential calculi on this noncommutative space. We discuss then the action of the Lorentz quantum algebra and prove that there are no 4D bicovariant differential calculi, which are Lorentz covariant. We show, however, that there exist a fivedimensional differ...

The following paper introduces a group of novel speech-signal descriptors that reflect phoneme-pronunciation variability and that can be considered as potentially useful features for emotion sensing. The proposed group includes a set of statistical parameters of Poincare maps, derived for formant-frequency evolution and energy evolution of voiced-speech segments. Two groups of Poincare-map char...

Bearings are integral components of rotating machinery and their failure tends to be a catastrophic the machine. Poincare Maps used detect bearing failures using concept non-linear dynamics. Each time-domain vibration signature array has its own Map over period time. Fast Fourier Transform (FFT) is method analysing frequency plots signature. Convolutional Neural Networks (CNN) process Continuou...

A family of critical curves t h a t lie in the r ange of a class of Po inca re h a l f m a p s induced by a saddle focus in three-space is inves t iga ted analyt ical ly . It compr i s e s all " f a r f inal po in t s " of the images of invar iant curves tha t a re subjec t to a s e p a r a t i n g m e c h a n i s m . T h e n u m b e r of b ranches occurr ing on a speci f ic critical cu rve is ...

A method to recognize polarization constellations is proposed. Described method is based on analysis of torsion and curvature of three-dimensional curve. The three-dimensional curve is defined by states of polarization on the Poincare sphere. Key-Words: Fiber optics; Polarization light; Birefringence; Poincare sphere; Space curve; Frenet frame