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 ...

We propose a supersymmetric model that defines M-theory. It possesses SO(1, 10) super Poincare symmetry and is constructed based on the Lorentzian 3-algebra associated with U(N) Lie algebra. This model is a supersymmetric generalization of the model in arXiv:0902.1333. From our model, we derive BFSS matrix theory and IIB matrix model in the naive large N limit by taking appropriate BPS vacua. 1...

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...

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 ...

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differ...

Certain spaces satisfying Poincare duality are shown to have the homotopy type of simple Poincare complexes. The motivation for and applications of this result are the study of free actions of finite groups on manifolds. Let X be a finite CW complex with finite fundamental group ir. Then X is an n-dimensional Poincare complex if there is a class [X] E H, (X) such that the slant product with the...

We introduce the notion of real structure in our spectral geometry. This notion is motivated by Atiyah’s KR-theory and by Tomita’s involution J. It allows us to remove two unpleasant features of the “Connes-Lott” description of the standard model, namely, the use of bivector potentials and the asymmetry in the Poincare duality and in the unimodularity condition.

The N = 1 self-dual supergravity has SL(2,C) symmetry and the lefthanded and right-handed local supersymmetries. These symmetries result in SU(2) charges as the angular-momentum and the supercharges. The model possesses also the invariance under the general translation transforms and this invariance leads to the energy-momentum. All the definitions are generally covariant. As the SU(2) charges ...

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