The general properties of a class of two-dimensional dilaton gravity (DG) theories with multiexponential potentials are studied and a subclass of these theories, in which the equations of motion reduce to Toda and Liouville equations, is treated in detail. A combination of parameters of the equations should satisfy a certain constraint that is identified and solved for the general multi-exponen...

The representation of biological systems by means of organismic supercategories, developed in previous papers, is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Baianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete results concern...

This article is concerned with the analysis of one-dimensional compressible Euler equations a singular pressure law, so-called hard sphere equation state. The result twofold. First, we establish existence bounded weak solutions by means viscous regularization and refined compensated compactness arguments. Second, investigate smooth setting providing detailed description impact on breakdown solu...