arXiv subjects
Publications and source records attributed to Diego Saa.
The algebra of fourvectors is described. The fourvectors are more appropriate than the Hamilton quaternions for its use in Physics and the sciences in general. The fourvectors embrace the 3D vectors in a natural form. It is shown the excellent ability to perform rotations with the use of fourvectors, as well as their use in relativity for producing Lorentz boosts, which are understood as simple rotations.
The inequality is computed through the so-called Gini index. The population is assumed to have the variable of interest distributed according to the Gamma probability distribution. The results show that the Gini index is reduced when the population is grouped. The number of individuals in the groups is the relevant parameter, but this number does not need to be very large in order to obtain a very substantial reduction of inequality.
The probability distribution function for thermodynamics and econophysics is obtained by solving an equilibrium equation. This approach is different from the common one of optimizing the entropy of the system or obtaining the state of maximum probability, which usually obtains as a result the Boltzmann distribution. The Gamma distribution is proposed as a better equation to describe the blackbody radiation in substitution of Planck's radiation equation. Also, a new form of entropy is proposed, that maintains the correct relation with the Clausius' formula.
Goedel's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by Goedel to prove his undecidability and incompleteness theorems is proved in this paper. This means that those theorems are invalid.