Abstract This paper presents a new algorithm based on interval methods for rigorously constructing inner estimates of feasible parameter regions together with enclosures the solution set parameter-dependent systems nonlinear equations in low (parameter) dimensions. The proposed method allows to explicitly construct sets around regular value, and enclose particular curve (resp. manifold) by unio...

We present two methods for constructing a flat-band (FB) system having flat energy dispersion over the entire Brillouin zone within tight-binding model, where resulting Hamiltonian may not be easily obtained by existing based on bipartite graph and line techniques. In first method, we derive set of conditions equivalent to appearance FBs given structure. This method allows parameters tuned so t...

This paper focuses on the analysis of a free energy functional, that models dilute suspension magnetic nanoparticles in two-dimensional nematic well. The first part article is devoted to asymptotic global minimizers limit vanishing elastic constant, ℓ→0 where re-scaled constant ℓ inversely proportional domain area. results concern strong H1-convergence and ℓ-independent H2-bound for smooth boun...