DRAFT VERSION The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor representations of the Rotation and Lorentz groups are irreducible. The spinor fields are space-time dependent spinors, solutions of the free Dirac equation. We define the Majorana-Fourier transform and relate it to the linear momentum of a spin one-half Poincare group representation. We sh...

Despite the fact that soccer is one of the most popular sports in the world, little attention has been paid to this game scientifically which could otherwise provide a broad range of interesting outcomes. Sport equipment has a significant effect on how a game is played. Different features of the soccer ball such as its size, structure, weight and potential incoming pressure also affect the natu...

Poincare inequalities are a simple way to obtain lower bounds on the distortion of mappings X into Y. These are shown below to be sharp when we consider the Lp spaces. A Poincare inequality is one of the following type: suppose Ψ : [0, ∞) → [0, ∞) is a nondecreasing function and that au,v, bu,v are finite arrays of real numbers (for u, v ∈ X, and not all of the numbers 0). We say that functions...

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...