Several studies have shown an increase in urinary calcium excretion in response to a calcium load. However, because of the inverse changes in PTH levels with a calcium load, the effect of changes in serum calcium per se on its own excretion is unclear in humans. In this study we used a PTH clamp protocol to further characterize calcium-regulated renal calcium and magnesium handling and the rela...

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...

A polynomial is determined by its roots and its leading coefficient. If you set the roots in motion, the critical points will move too. Using only tools from the undergraduate curriculum, we find an inverse square law that determines the velocities of the critical points in terms of the positions and velocities of the roots. As corollaries we get the Polynomial Root Dragging Theorem and the Pol...

Abstract Models in which the covariance matrix has structure of a sparse plus low rank perturbation are ubiquitous data science applications. It is often desirable for algorithms to take advantage such structures, avoiding costly computations that require cubic time and quadratic storage. This accomplished by performing operations maintain example, inversion via Sherman–Morrison–Woodbury formul...

We define positive integer roots of finite matrices in the 2×2 case. Where possible, we try to generalise results n×n matrices.

The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W . Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W , skew-Ham...