Foutz (1977) uses the Inverse Function Theorem to prove the existence of a unique and consistent solution to the likelihood equations. This note extends his results in three useful directions. The ...

Let Fn be a free group of rank n with free basis x1, ⋯, xn. Let {y1, ⋯, yk} be a set of k ≤ n elements of Fn, where each yi is represented by a word Yi(x1, ⋯, xn) in the generators xj. Let ∂ yi/∂ xj ...

Inverse problems, central to modern applied mathematics, involve deducing unknown parameters or functions in differential equations from observed spectral data. This field is pivotal in understanding ...