In this paper, we consider a pursuit-evasion game of inertial players, where pursuer’s control is subject to integral constraint, and evader’s control is subject to geometric constraint. In the pursuit problem, the main tool is the strategy of parallel pursuit. Sufficient conditions are obtained for the solvability of pursuit-evasion problems. Also, the main lemma describing the monotonicity of an attainability domain of the evader is proved and an explicit analytical formula for this domain is given. As one of the important results of our paper, the Isaacs Life-line game is solved for a special case.

The subject of this paper is to analyse the Math Principia of Economic 3D Black Holes in Roegenian economics. This idea is totally new in the related literature, excepting our papers. In details, we study two special problems: (i) math origin of economic 3D black holes, (ii) entropy and internal political stability depending on national income and the total investment, for economic RN 3D black hole. To solve these problems, it was necessary to jump from macroeconomic side to microeconomic side (a substantial approach so different), to complete the thermodynamics-economics dictionary with new entities, to introduce the flow between two macroeconomic systems, to study the Schwarzschild type metric properties on an economic 4D system, together with Rindler coordinates, Einstein 4D PDEs, and economic RN 3D black hole. In addition, we introduce some economic Ricci type flows or waves, for further research.