In this paper we extend the classical Lefschetz version of the KalmanYacubovich-Popov (KYP) lemma to the case of matrices with general regular inertia. We then use this result to derive an easily verifiable spectral condition for a pair of matrices with the same regular inertia to have a common Lyapunov solution (CLS), extending a recent result on CLS existence for pairs of Hurwitz matrices.

In this article we apply the Stenberg criteria to show that the Taylor-Hood P2 − P1 and the Scott-Vogelius P2 − discP1 element pairs satisfy the LBB condition in IR. The Taylor-Hood P2 − P1 pair is shown to be stable on a regular triangulation of the domain. For the ScottVogelius P2−discP1 element pair the mesh is assumed to be a barycenter refinement of a regular triangulation.

We revisit the regular-expression matching problem with respect to prefix-freeness of the pattern. It is known that a prefix-free pattern gives only a linear number of matching substrings in the size of an input text. We improve the previous algorithm and suggest an efficient algorithm that finds all pairs (start, end) of start and end positions of all matching substrings with a single scan of ...

This paper explores the task of translating natural language queries into regular expressions which embody their meaning. In contrast to prior work, the proposed neural model does not utilize domain-specific crafting, learning to translate directly from a parallel corpus. To fully explore the potential of neural models, we propose a methodology for collecting a large corpus1 of regular expressi...

A family of cliques in a graph G is said to be p-regular if any two cliques in the family intersect in exactly p vertices. A graph G is said to have a p-regular k-clique cover if there is a p-regular family H of k-cliques of G such that each edge of G belongs to a clique in H. Such a p-regular kclique cover is separable if the complete subgraphs of order p that arise as intersections of pairs o...

We study germs of pairs of codimension one regular foliations in R. We show that the discriminant of the pair determines the topological type of the pair. We also consider various classifications of the singularities of the discriminant.

Symmetrical subdivisions in the space of Jager Pairs for continued fractions-like expansions will provide us with bounds on their difference. Results will also apply to the classical regular and backwards continued fractions expansions, which are realized as special cases.

For regular sets in Euclidean space, previous work has identified twelve ‘basic’ computability notions to (pairs of) which many previous notions considered in literature were shown to be equivalent. With respect to those basic notions we now investigate on the computability of natural operations on regular sets: union, intersection, complement, convex hull, image, and pre-image under suitable c...

In this paper we develop a simulator modeling a kidney exchange program, in which donor-recipient pairs with characteristics drawn from a distribution based on real data join the system over time, and a centralized authority organizes a suitably chosen set of exchanges among the pairs in the pool at regular intervals of time, as it happens in the Netherlands or in the US. We compare and discuss...

Two sib pairs and a fifth child are described with autosomal recessive ectopia lentis et pupillae. Patients with this disorder need regular ophthalmic review, but do not have the skeletal and metabolic complications associated with other syndromes with ectopia lentis.