Given a family of graphs $\mathcal{F}$, we define the $\mathcal{F}$-saturation game as follows. Two players alternate adding edges to an initially empty graph on $n$ vertices, with only constraint being that neither player can add edge creates subgraph in $\mathcal{F}$. The ends when no more be added graph. One wishes end quickly possible, while other prolong game. We let $\textrm{sat}_g(n,\mat...

Free vibrations of a harmonic oscillator in the form mathematical pendulum linear and nonlinear formulations are considered. Their comparative analysis is carried out as conservative system with one degree freedom. To solve differential equation, finite difference method Euler’s scheme used. Specific examples given, limits deviations angles, at which solutions problems practically coincide, det...

It is shown that the dual to the linear programming problem that arises in constraint-based models of metabolism can be given a thermodynamic interpretation in which the shadow prices are chemical potential analogues, and the objective is to minimize free energy consumption given a free energy drain corresponding to growth. The interpretation is distinct from conventional nonequilibrium thermod...

In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...