We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine plane monomial curve. We also describe the irregularity complex of such a system with respect to its singular support and in particular we prove, using elementary methods, that this irregularity complex is a perverse sheaf as assured by a theorem of Z. Mebkhout.

This article examines small-signal stability of electrical networks composed dominantly three-phase grid-following inverters. We show that the mere existence a high-voltage power flow solution does not necessarily imply stability; this motivates us to develop framework for analysis systematically acknowledges inverter dynamics. identify suitable time-scale decomposition dynamics, and using sing...

where q = e. Let d ≡ 0, 3 (mod 4) be a positive integer, so that −d is a negative discriminant. Denote by Qd the set of positive definite integral binary quadratic forms Q(x, y) = ax + bxy + cy = [a, b, c] with discriminant −d = b − 4ac, including imprimitive forms (if such exist). We let αQ be the unique complex number in the upper half plane H which is a root of Q(x, 1) = 0. Values of j at th...

Abstract We know that to estimate matrix singular values ( especially the largest and the smallest ones ) is an attractive topic in matrix theory and numerical analysis. In this note, we first provide a simple estimate for the smallest singular value σn(A) of n × n positive definite matrix A. Secondly, we obtain some simple estimates for the smallest singular value σn(A) and the largest singula...