It will be convenient to call a space X a ParoviZenko space if (cy) X is a zero-dimensional compact space without isolated points, (p) every two disjoint open F,-sets have disjoint closures, and (y) every nonempty GG-set in X has non-empty interior. Compact spaces satisfying (p) are usually called F-spaces, while spaces satisfying (y) are called almost-P spaces. Examples of F-spaces are the ext...

in the present paper, we introduce some new sequence spaces derived by riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. some topological properties of these spaces are investigated. further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and statistical convergence...

Hamiltonian dynamical systems tend to have infinitely many periodic orbits. For example, for a broad class of symplectic manifolds almost all levels of a proper smooth Hamiltonian carry periodic orbits. The Hamiltonian Seifert conjecture is the existence problem for regular compact energy levels without periodic orbits. Very little is known about how large the set of regular energy values witho...