Figure 9. Mean function and eigenfunctions for longitudinal behavioral data. The estimated mean function μ^ and the first three estimated spherical eigenfunctions ϕ^1, ϕ^2, ϕ^3 for the ...

The subject of Prof. Titchmarsh's book is the expansion of an arbitrary function in terms of the eigenfunctions of linear differential equations; to be precise, in terms of functions which satisfy ...

Semyon Dyatlov (MIT): The fractal uncertainty principle Jeffrey Galkowski (University College London): The gauge transform and applications Ilya Kachkovskiy (Michigian State):The Bloch structure at ...

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The Solution of the Inner Neumann Problem 149 §11. The Solution of the Outer Neumann Problem for the Case (𝑬) and for the Ordinary Case 152 §12. The Eigenfunctions Corresponding to the Pole 𝜁 = 1 in ...

4.2, 4.3: Derivation of wave equation; standard boundary conditions. 4.4: String with fixed ends, d'Alembert's solution. 7.7.8: Circular membrane: Eigenfunctions & Initial value problems 7.7.9 + ...

We present the Quantum Section Method as a quantization technique to compute the eigenvalues and the eigenfunctions of quantum systems. As an instructive example we apply this procedure to quantize ...

Once identified, the equilibration of these modes is accelerated by the enhanced sampling method of choice. An attractive way of determining the collective variables is to relate them to the ...

Abstract: This article develops data-driven methods to identify eigenfunctions of the Koopman operator associated with a dynamical system and subspaces that are invariant under the operator. We build ...