Whither NSF?--The higher derivatives

Whither the Future of NSF Advanced Computing Infrastructure?

The period functions’ higher order derivatives

We prove a formula for the n-th derivative of the period function T in a period annulus of a planar differential system. For n = 1, we obtain Freire, Gasull and Guillamon formula for the period’s first derivative [17]. We apply such a result to hamiltonian systems with separable variables and other systems. We give some sufficient conditions for the period function of conservative second order ...

Spline Interpolation and the Higher Derivatives.

The Chain Rule for Higher Derivatives

Perhaps the most important theorem of elementary differential calculus is the Chain Rule. It states, roughly, that the composite of two differentiable functions is again differentiable, and it gives a formula for the derivative of this composite. A Chain Rule of Order n should state, roughly, that the composite of two functions that are n times differentiable is again n times differentiable, an...

Instantaneous Higher Order Phase Derivatives

We present methods, based on the short time Fourier transform, which may be used to analyze the structure of multicomponent FM modulated signals instantaneously in time and frequency. The methods build on previously presented cross-spectral methods. In this paper, we introduce the concept of higher order short time Fourier transform phase derivatives, which may be used to estimate signal trajec...