Charge conjugation from space-time inversion in QED: discrete and continuous groups

We show that the CPT groups of QED emerge naturally from the PT and P (or T) subgroups of the Lorentz group. We also find relationships between these discrete groups and continuous groups, like the connected Lorentz and Poincar\'e groups and their universal coverings.Comment: 7 page

Optimal railway infrastructure maintenance and repair policies to manage risk under uncertainty with adaptive control

The aim of this paper is to apply two adaptive control formulations under uncertainty, say open-loop and closed-loop, to the process of developing maintenance and repair policies for railway infrastructures. To establish the optimal maintenance and repair policies for railway lines, we use a previous design of risk model based on two factors: the criticality and the deterioration ratios of the facilities. Thus, our theory benefits from the Reliability Centered Management methodology application, but it also explicitly models uncertainty in characterizing a facility deterioration rate to decide the optimal policy to maintain the railway infrastructures. This may be the major contribution of this work. To verify the models presented, a computation study has been developed and tested for a real scenario: the railway line Villalba-Cercedilla in Madrid (Spain). Our results demonstrate again that applying any adaptive formulation, the cost of the railway lines maintenance shown is decreased. Moreover applying a Closed Loop Formulation the cost associated to the risk takes smaller values (40% less cost for the same risk than the deterministic approach), but with an Open Loop formulation the generated risk in the railway line is also smaller

From Perturbation Theory to Confinement: How the String Tension is built up

We study the spatial volume dependence of electric flux energies for SU(2) Yang-Mills fields on the torus with twisted boundary conditions. The results approach smoothly the rotational invariant Confinement regime. The would-be string tension is very close to the infinite volume result already for volumes of $(1.2 \ {\rm fm.})^3$. We speculate on the consequences of our result for the Confinement mechanism.Comment: 6p, ps-file (uuencoded). Contribution to Lattice'93 Conference (Dallas, 1993). Preprint INLO-PUB 18/93, FTUAM-93/4

A remark on approximation with polynomials and greedy bases

We investigate properties of the $m$-th error of approximation by polynomials with constant coefficients $\mathcal{D}_{m}(x)$ and with modulus-constant coefficients $\mathcal{D}_{m}^{\ast}(x)$ introduced by Bern\'a and Blasco (2016) to study greedy bases in Banach spaces. We characterize when $\liminf_{m}{\mathcal{D}_{m}(x)}$ and $\liminf_{m}{\mathcal{D}_{m}^*(x)}$ are equivalent to $\| x\|$ in terms of the democracy and superdemocracy functions, and provide sufficient conditions ensuring that $\lim_{m}{\mathcal{D}_{m}^*(x)} = \lim_{m}{\mathcal{D}_{m}(x)} = \| x\|$, extending previous very particular results