While the show was eventually one of CBS' most popular sitcoms, it struggled in the ratings for the first three seasons (leading to "back-up" mothers if the show was canceled earlier than expected, as detailed in this earlier TV Legends Revealed).
We utilized mathematical induction, proof by contradiction, and direct computations to show that every solution of system (3) is eventually either one of the two prime period 3 solutions or the equilibrium solution.
A classification of nonoscillatory solutions in case is eventually of one sign, will be recalled in Section 4. Nonoscillation of (1.1) can be characterized in terms of solvability of a Riccati difference equation; the methods based on this relation are referred to as the Riccati technique: equation (1.1) is nonoscillatory if and only if there is and a sequence satisfying (2.2). with for.
Concerning (1.1), a nontrivial solution of (1.1) is called nonoscillatory if it is eventually of one sign, otherwise it is said to be oscillatory.
Throughout this section we assume that is eventually of one sign.
Assume that f ( n ) is eventually of one sign for all large t, and there exists a t 1 ≥ t 0 such that f ( n ) ( t ) f ( n − 1 ) ( t ) ≤ 0 for all t ≥ t 1.
Let If is eventually of one sign for all large say then there exist a and an integer with even for or odd for such that implies that for and implies that for.
We call ((x,y)) a proper solution if it is defined on ([t_{0},infty)_{mathbb{T}}) and (sup{ vert x(s) vert, vert y(s) vert : sin [t,infty)_{mathbb{T}}} > 0) for (t geq t_{0}). A solution ((x,y)) is called nonoscillatory if x and y are both nonoscillatory, that is, eventually of one sign. Otherwise, it is said to be oscillatory.
When the history of fourth-wave feminism is eventually written up, one of the defining images will be of Beyoncé standing in front of a glowing sign proclaiming "FEMINIST" at the MTV Video Music Awards.
