We study the behavior of two maps in an effort to better understand the stability of ωlimit sets ω(x, f ) as we perturb either x or f , or both. The first map is the set-valued function Λ taking f in C(I ,I) to its collection of ω-limit points Λ( f ) = ⋃x∈I ω(x, f ), and the second is the map Ω taking f in C(I ,I) to its collection of ω-limit sets Ω( f )= {ω(x, f ) : x ∈ I}.We characterize thos...

Using the theory of Pell equation, we study non-trivial positive integer solutions Diophantine equations $z^2=f(x)^2\pm f(x)f(y)+f(y)^2$ for certain polynomials f(x), which mean to construct integral triangles with two sides given by values f(x) and f(y) intersection angle $120^\circ$ or $60^\circ$.

We calculate the decay constant ratios f c=fJ= and f b=f . In the calculation we take into account the mock meson structures of the mesons, as well as the di erence of the wave functions at origin of the vector and pseudoscalar mesons studied by Ahmady and Mendel. We nd that the di erent spin structures of the mesons much a ect the ratios. We incorporate our results in the prediction of the bra...