The Russia Investigations: Rosenstein Reprieved

The Russia Investigations: Rosenstein Reprieved — For Now

Deputy Attorney General Rod Rosenstein departs the U.S. Capitol through a basement corridor after House and Senate lawmakers from both parties met in a secure room for a classified briefing about the federal investigation into President Trump

The Justice Department's embattled second in command — who is in primary command of the Russia investigation — went to the White House on Monday expecting to be terminated. But that didn't happen.

(Image credit: J. Scott Applewhite/AP)

News : NPR https://ift.tt/2xYGFpP September 29, 2018 at 02:00PM

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Solving Van der Pol equation with ivp_solve

Van der Pol’s differential equation is The equation describes a system with nonlinear damping, the degree of damping given by μ. If μ = 0 the system is linear and undamped, but for positive μ the system is nonlinear and damped. We will plot the phase portrait for the solution to Van der Pol’s equation in Python using SciPy’s new ODE solver ivp_solve . The function ivp_solve does not solve second-order systems of equations directly. It solves systems of first-order equations, but a second-order differential equation can be recast as a pair of first-order equations by introducing the first derivative as a new variable. Since y is the derivative of x , the phase portrait is just the plot of ( x , y ). If μ = 0, we have a simple harmonic oscillator and the phase portrait is simply a circle. For larger values of μ the solutions enter limiting cycles, but the cycles are more complicated than just circles. Here’s the Python code that made the plot. from scipy import linspace from ...

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