Критерии $L^2$-устойчивости линеаризованных явных разностных схем с регуляризацией для 1D уравнений газовой динамики
The object of study of this paper is a regional economic system which is complex, dynamic and developable by nature. The reproduction of material wealth necessary for the region is provided in the process of functioning of the above system through the interaction between the combinations of subjective (personal) and objective (material) elements, thereby meeting regional environmental and economic needs.
A scalable method for mining graph patterns stable under subsampling is proposed. The existing subsample stability and robustness measures are not antimonotonic according to definitions known so far. We study a broader notion of antimonotonicity for graph patterns, so that measures of subsample stability become antimonotonic. Then we propose gSOFIA for mining the most subsample-stable graph patterns. The experiments on numerous graph datasets show that gSOFIA is very efficient for discovering subsample-stable graph patterns.
An initial–boundary value problem for the generalized Schrödinger equation in a semi-infinite strip is solved.
A new family of two level finite-difference schemes with averaging over spatial variables on a finite mesh is constructed, which covers a set of finite-difference schemes built using various methods. For the family, an abstract approximate transparent boundary condition (TBC) is formulated and the solutions are proved to be absolutely stable in two norms with respect to both initial data and free terms. A discrete TBC is derived, and the stability of the family of schemes with this TBC is proved. The implementation of schemes with the discrete TBC is discussed.