Abstract
Over the past two decades, the fact that many games have been formulated as variational inequalities problems has led to relevant developments related with the existence and uniqueness of equilibriums, and with their calculation methodologies. Based on this approach, this study applies sufficient conditions for Cournot equilibriums existence and uniqueness, proving that while existence holds, uniqueness cannot be proved in general. To find one of the existent equilibriums, this study also proposes a novel variational inequalities algorithm which is globally convergent and easy to implement. It iteratively computes searching directions of the equilibrium by generating hyper-planes that separate the equilibrium from the intermediate solutions obtained relaxing the original Cournot game. Unlike other related algorithms, the proposed algorithm does not require Jacobian matrixes evaluation, and the iterative relaxed games can easily be solved using convex and quadratic optimisation models. Numerical results show the operation and convergence of the algorithm.

Abstract
Mayer's energy decomposition method was applied inthe study of the relative stability of cis and trans isomers of 1,2-disubstituted ethylenes, XHC=CHX (X = F, Cl, Br) and 2-butene. The trans to cis isomerization energy for each system was determined at the Hartree-Fock level, with several basis sets, and then divided into monoatomic and diatomic energy contributions. The results point to a different energy distribution for the dihaloethylenes, known for exhibiting a cis isomer that is more stable than the trans one, a behavior that is known as the cis effect, when compared to 2-butene. The main stabilizing effects of the cis isomer in the dihaloethylenes, at this level of theory, are energy terms associated with the interaction of the X substituents with the C atoms.

Abstract

Abstract
This paper describes the methodology developed to build estimates of electricity prices having the horizon of one week. This approach uses artificial neural networks and includes a particular treatment of weekends and national holidays as a way to improve the quality of the results. The developed approach was tested using data obtained from the Spanish market operator for the time period of 2006 to 2008. The obtained value of MAPE - Mean Absolute Percentage Error - was 12,62% for workdays and 10,73% for holidays and weekends. The obtained results show that this study has interest to the market agents in question, since realistic forecasting was achieved.

Abstract
This letter proposes a new concept applied to state estimation based on replacing traditional regression models by a criterion of maximizing error correntropy introducing a novel way to identify and correct large errors.

Abstract
This paper reports new results in adopting entropy concepts to the training of neural networks to perform wind power prediction as a function of wind characteristics (speed and direction) in wind parks connected to a power grid. Renyi's entropy is combined with a Parzen windows estimation of the error pdf to form the basis of two criteria (minimum entropy and maximum correntropy) under which neural networks are trained. The results are favorably compared in online and offline training with the traditional minimum square error (MSE) criterion. Real case examples for two distinct wind parks are presented.