On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively model set constraint problems and to encode them automatically into SAT instances. We apply our technique to the Social Golfer Problem and we also use it to break symmetries of the problem. Our technique is simpler, more declarative, and less error-prone than direct and improved hand modeling. The SAT instances that we automatically generate contain less clauses than improved hand-written instances such as in [20], and with unit propagation they also contain less variables. Moreover, they are well-suited for SAT solvers and they are solved faster as shown when solving difficult instances of the Social Golfer Problem.

The non-relativistic interacting electron gas in an external field of positively charged massive cores is dealt with in the scheme of second quantization. Ladder operators that change between stationary states of contiguous energy eigenvalues are derived. The method is particularized to the two-electron Helium atom in order to explain it avoiding too much notation. Applying the lowering operator on the ground state must give zero because no state with lower energy does exist. Equations for the ground state and ground state energy are obtained this way and solved, giving closed--form expressions for the ground state, its energy and electronic density of Helium. The theory in its lowest order gives 0.63% error. The application to more complex systems and higher degrees of approximation seems straightforward. The foundations of the density functional theory and how to go beyond it are seen quite clearly.

Conjugated polymers are experiencing a surge of renewed interest due to their promising applications in various organic electronic devices. These include organic light-emitting diodes (OLEDs), field-effect transistors (FETs), and organic photovoltaic (OPV) devices, among many others. Their appeal stems from distinct advantages they hold over traditional inorganic semiconductors. Unlike inorganic semiconductors, where electrons are often considered to be in delocalized, free, or quasi-free states (as described by Bloch's theory), electrons in conjugated polymers behave differently. They are strongly coupled within highly localized $\sigma$ or $\pi$-orbitals and interact significantly with the ionic cores. This means they are far from the idealized delocalized states presumed by Bloch's theory approaches. Consequently, after nearly a century of applying Bloch's theory to the electronic transport properties of inorganic materials, there is a clear need for a new theoretical framework to explain efficient charge transport in these organic solids. Our presented model addresses this need by incorporating crucial electron-electron interactions. Specifically, it accounts for both intra-site interactions and interactions between the $\pi$-states located at alternating sites along the polymer chain. This framework provides a many-body charge conduction mechanism and explains the semiconducting properties of the undoped material. A significant outcome of our model is the prediction of two novel flat bands of excited bonding states. Intriguingly, these states obey Bose--Einstein statistics and facilitate charge transport. Furthermore, our model accurately reproduces experimental data, providing an excellent fit for measured UV-Vis absorption and electroluminescent spectra.