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This paper introduces Hermite's polynomials, in the description of quantum games. Hermite's polynomials are associated with gaussian probability density. The gaussian probability density represents minimum dispersion. I introduce the concept of minimum entropy as a paradigm of both Nash's equilibrium (maximum utility MU) and Hayek equilibrium (minimum entropy ME).

Effective planning of a transportation network influences tactical and operational activities and has a great impact on business. Planning typically considers multiple aspects such as variable transportation costs, various levels of customer service offered, security of goods, and traveling time. These aspects often vary with time. Although the minimum cost flow problem is a widely seen approach to configure a transportation network, there is no much work considering variations on arcs; even more, the problem with varying nodes has hardly been addressed. In this work is developed a mathematical model for the multi-objective minimum cost flow problem, applied in networks with varying attributes on arcs. The model finds the set of non-dominated solutions for a multi-objective stochastic network having variations in attributes of its arcs and nodes, such as cost or transportation time. A modified version of the two-stage method was used to address the stochastic nature of the problem combined with the epsilon-constraint method, which is used for building the set of non-dominated solutions. This paper presents the main features of the model, the theoretical bases and a computational implementation. Experiments were applied in a transport network for the exportation market of ornamental flowers as perishable goods from Mexico to the United States, which considered variations in border crossing times.

Abstract:We determine the proton and electron radii by analyzing constructive resonances at minimum entropy for elements with atomic number Z ≥ 11.We note that those radii can be derived from entropy principles and published photoelectric cross sections data from the National Institute of Standards and Technology (NIST). A resonance region with optimal constructive interference is given by a principal wavelength λ of the order of Bohr atom radius. Our study shows that the proton radius deviations can be measured. Moreover, in the case of the electron, its radius converges to electron classical radius with a value of 2.817 fm. Resonance waves afforded us the possibility to measure the proton and electron radii through an interference term. This term, was a necessary condition in order to have an effective cross section maximum at the threshold. The minimum entropy means minimum proton shape deformation and it was found to be (0.830 ± 0.015) fm and the average proton radius was found to be (0.825 − 0.0341; 0.888 + 0.0405) fm.