We introduce the notion of hereditary G-compactness (with respect to interpretation). provide a sufficient condition for poset not be hereditarily G-compact, which we use show that any linear order is G-compact. Assuming long-standing conjecture about unstable NIP theories holds, this implies an theory G-compact if and only it stable (and by result Simon, holds unconditionally $$\aleph _0$$ -ca...

In this paper, we present the existence and uniqueness of strong probabilistic solutions for nonlinear parabolic Stochastic Partial Differential Equations (SPDEs) with Robin boundary conditions in a domain holes. On holes, condition is imposed, while homogeneous Dirichlet prescribed on exterior boundary. The coefficient matrix assumed to be symmetric, random forces are satisfy some types regula...

In this paper we study a class of singular systems with double-phase energy. The main feature is that the associated Euler equation driven by Baouendi-Grushin operator variable coefficient. In such way, continue analysis introduced in [6] to case lack compactness corresponding whole Euclidean space. After establishing related pr...

In this paper we generalize the notion of Semi-continuity and MS-continuity and go on to study Semi-compactness, Semi-cocompactness, Semi-stability and Semi-costability in a ditopological texture space. We also extends the notion of Semi-compactness and Semi-cocompactness to a ditopological texture space modulo an ideal [13].