This paper studies global asymptotic stability for positive solutions to the equation yn = yn−kyn−lyn−m + yn−k + yn−l + yn−m 1 + yn−kyn−l + yn−kyn−m + yn−lyn−m , n = 0, 1, . . . , with y−m, y−m+1, . . . , y−1 ∈ (0,∞) and 1 ≤ k < l < m. The paper also includes a listing of possible semi-cycle structures for various (k, l, m). The results generalize several others in the recent literature.

Many problems encountered when applying machine learning in practice involve predicting a \class" that takes on a continuous numeric value, yet few machine learning schemes are able to do this. This paper describes a \rational reconstruction" of M5, a method developed by Quinlan (1992) for inducing trees of regression models. In order to accommodate data typically encountered in practice it is ...

economists have heralded the formulation of the expected utility theorem as a universal method of choice under uncertainty. in their seminal paper, stigler and becker (stigler & becker, 1977) declared that “human behavior can be explained by a generalized calculus of utility-maximizing behavior” (p.76). the universality of the rational choice theory has been widely criticized by psychologists, ...

We study the qualitative behavior of the positive solutions of a second-order rational fuzzy difference equationwith initial conditions being positive fuzzy numbers, and parameters are positive fuzzy numbers. More precisely, we investigate existence of positive solutions, boundedness and persistence, and stability analysis of a second-order fuzzy rational difference equation. Some numerical exa...

In this note, we consider the following rational difference equation: xn+1 = f (xn−r1 , . . . , xn−rk )g(xn−m1 , . . . , xn−ml )+ 1 f (xn−r1 , . . . , xn−rk )+ g(xn−m1 , . . . , xn−ml ) , n= 0,1, . . . , where f ∈ C((0,+∞)k, (0,+∞)) and g ∈ C((0,+∞)l, (0,+∞)) with k, l ∈ {1,2, . . .}, 0 r1 < · · ·< rk and 0 m1 < · · ·<ml , and the initial values are positive real numbers. We give sufficient con...

By numerically applying the recursive Darboux transformation technique, we study high-order rational solutions of the nonlinear Schrödinger equation that appear spatiotemporally as triangular arrays of Peregrine solitons. These can be considered as rogue wave cascades and complement previously discovered circular cluster forms. In this analysis, we reveal a general parametric restriction for th...