the purpose of this paper is to introduce the concept of pairwise f-closedness in bitopological spaces. this space contains both of pairwise strongcompactness and pairwise s-closedness and contained in pairwise quasi h-closedness. the characteristics and relationships concerning this new class ofspaces with other corresponding types are established. moreover, several ofits basic and important p...

We consider a diffeomorphism f of a compact manifold M which is Almost Axiom A, i.e. f is hyperbolic in a neighborhood of some compact f -invariant set, except in some singular set of neutral points. We prove that if there exists some f -invariant set of hyperbolic points with positive unstable-Lebesgue measure such that for every point in this set the stable and unstable leaves are “long enoug...

The projective hull X̂ of a compact set X ⊂ P is an analogue of the classical polynomial hull of a set in C. In the special case that X ⊂ C ⊂ P, the affine part X̂ ∩C can be defined as the set of points x ∈ C for which there exists a constant Mx so that |p(x)| ≤ M x sup X |p| for all polynomials p of degree ≤ d, and any d ≥ 1. Let X̂(M) be the set of points x where Mx can be chosen ≤ M . Using an ...

The projective hull X̂ of a compact set X ⊂ P is an analogue of the classical polynomial hull of a set in C. In the special case that X ⊂ C ⊂ P, the affine part X̂ ∩C can be defined as the set of points x ∈ C for which there exists a constant Mx so that |p(x)| ≤ M x sup X |p| for all polynomials p of degree ≤ d, and any d ≥ 1. Let X̂(M) be the set of points x where Mx can be chosen ≤ M . Using an ...

In this study, a Multi-Objective Genetic Algorithm (MOGA) is utilized to extract interpretable and compact fuzzy rule bases for modeling nonlinear Multi-input Multi-output (MIMO) systems. In the process of non- linear system identi cation, structure selection, parameter estimation, model performance and model validation are important objectives. Furthermore, se- curing low-level and high-level ...