Abstract. Let f(X) = (XC + D )M(XC + D) − G be a given nonlinear Hermitian matrix-valued function with M = M∗ and G = G∗, and assume that the variable matrix X satisfies the consistent linear matrix equation XA = B. This paper shows how to characterize the semi-definiteness of f(X) subject to all solutions of XA = B. As applications, a standard method is obtained for finding analytical solution...

Many explanations have been offered for the widely attested problems L2 learners experience with the English article system. One influential proposal from formal linguistics is the Article Choice Parameter and associated Fluctuation Hypothesis (Ionin, Ko & Wexler, 2004) which states that learners of English fluctuate between correct and incorrect usage by sometimes selecting articles on the bas...

Diffusion tensor magnetic resonance imaging (DT-MRI) is a relatively new imaging modality in the field of medical imaging. This modality of imaging allows one to capture the structural connectivity if any between functionally meaningful regions for example, in the brain. The data however can be noisy and requires restoration. In this paper, we present a novel unified model for simultaneous smoo...