In order to understand the number of degrees of freedom we need to include in a Lorentz-invariant theory, we need to develop the representation theory of the Poincaré symmetry. The Poincaré symmetry consists of two sets of symmetries of the Minkowski spacetime. Space-time translations generated by the energy-momentum four vector P , and the Lorentz transformations (rotation and boost) generated...

We consider a free boundary problem modeling tumor growth where the model equations include a diffusion equation for the nutrient concentration and the Stokes equation for the proliferation of tumor cells. For any positive radius R, it is known that there exists a unique radially symmetric stationary solution. The proliferation rate μ and the cell-to-cell adhesiveness γ are two parameters for c...

The title compound, [HgCl(2)(C(4)H(5)N(3))](n), features a two-dimensional network parallel to (001) that is based on an Hg(II) atom octahedrally coordinated by four μ(2)-Cl atoms and two μ(2)-2-amino-pyrimidine (apym) ligands in trans positions, yielding a distorted HgCl(4)N(2) octa-hedron. The coordination network can be described as an uninodal 4-connected net with the sql topology. The Hg(I...

We discuss results of numerical analyses of the 3+1 dimensional Nambu–Jona-Lasinio model at non-zero baryon density. By studying relevant order parameters, it is shown that the model goes through a transition between a vacuum with broken chiral symmetry, and a chirally restored phase at high baryon chemical potential μ with a diquark condensate roughly proportional to the area of the Fermi surf...

We show that more than two generations of quarks and leptons are required to have an anomaly free discrete R symmetry larger than R parity, provided that the supersymmetric standard model can be minimally embedded into a grand unified theory. This connects an explanation for the number of generations with seemingly unrelated problems such as supersymmetry breaking, proton decay, the μ problem, ...