Trump Makes Bipartisan Pitch In First State Of The Union, But Also Plays To Base

President Trump delivers the State of the Union address in the House chamber of the Capitol on Tuesday.

In his roughly 90-minute speech, Trump declared "the state of our union is strong because our people are strong." And referencing the immigration debate, Trump said "Americans are dreamers too."

(Image credit: Mark Wilson/Getty Images)

News : NPR http://ift.tt/2BFzymj January 31, 2018 at 04:24AM

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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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