Abstract: This paper is concerned with obtaining the inverse of polynomial functions using semidefinite programming (SDP). Given a polynomial function and a nominal point at which the Jacobian of the ...

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 ...

In this paper we study the relations of four possible generalized inverses of a general distribution functions and their right-continuity properties. We correct a right-continuity result of the ...

Hypergeometric functions are at the heart of many analytical and applied mathematical investigations. These functions, generally defined via power series that extend the geometric series, have been ...

Universality theorems occupy a central role in analytic number theory, demonstrating that families of analytic functions—including the prototypical Riemann zeta-function—can approximate an extensive ...

The counterexamples presented here are the first of this kind for notions of differentiability that satisfy a chain rule. Their context arises naturally from requiring differentiability of crucial ...

Department of Biostatistics & Bioinformatics, Rollins School of Public Health, Winship Cancer Institute, Atlanta, USA. Department of Biostatistics and Computational Biology University of Rochester, ...