Positive Rational Number of the Form (Equation)

STUDYING THE BEHAVIOR OF SOLUTIONS OF A SECOND-ORDER RATIONAL DIFFERENCE EQUATION AND A RATIONAL SYSTEM

In this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. Also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.  

A fuzzy difference equation of a rational form

N‎umerical ‎q‎uasilinearization scheme ‎for the integral equation form of the Blasius equation

‎The ‎method ‎of ‎quasilinearization ‎is ‎an ‎effective ‎tool ‎to ‎solve nonlinear ‎equations ‎when ‎some ‎conditions‎ on ‎the ‎nonlinear term ‎of ‎the ‎problem ‎are ‎satisfi‎‎ed. ‎W‎hen ‎the ‎conditions ‎hold, ‎applying ‎this ‎techniqu‎e ‎gives ‎two ‎sequences of ‎coupled ‎linear ‎equations‎ and ‎the ‎solutions ‎of ‎th‎ese ‎linear ‎equations ‎are quadratically ‎convergent ‎to ‎the ‎solution ‎o...

Positive Rational Solutions to xy = ymx: A Number-Theoretic Excursion

1. PROLOGUE. Late in the last millennium, the second author ran a seminar course for undergraduates that was intended to introduce them to problem-solving and question-asking in the context of mathematical research. He led them through the classic " difficult " equation x y = y x (x, y > 0), (1) whose solution is much easier than one would think at first glance. Solutions were sought, first ove...

Positive Rational Solutions to X : a Number-theoretic Excursion

Late in the last millennium, the second author ran a seminar course for undergraduates which was intended to introduce them to problem-solving and questionasking in the context of mathematical research. He led them through the classic “difficult” equation x = y, x, y > 0, (1) whose solution is much easier than one would think at first glance. Solutions were sought, first over R, then over Z and...