Rado’s Theorem characterizes the systems of homogenous linear equations having the property that for any finite partition of the positive integers one cell contains a solution to these equations. Furstenberg and Weiss proved that solutions to those systems can in fact be found in every central set. (Since one cell of any finite partition is central, this generalizes Rado’s Theorem.) We show tha...

to start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ode. then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. it is required to state that the infinite series method is a well-organized method for obtaining exact s...

Abstract This paper develops a New Keynesian model featuring financial intermediation, short- and long-term bonds, credit shocks, scope for unconventional monetary policy. The log-linearized reduces to four equations: Phillips IS curves, as well policy rules the short-term interest rate central bank's long-bond portfolio (QE). Credit shocks QE appear in both curves. In equilibrium, optimal enta...

We revisit the symmetry structure of integrable PDEs, looking at specific example KdV equation. identify 4 nonlocal symmetries depending on a parameter, which we call generating symmetries. explain that since these are symmetries, their commutator algebra is not uniquely determined, and present three possibilities for algebra. In first version, 3 commute; this shows it possible to add further (...