In this paper we extend the well known Kalman-Yacubovic-Popov (KYP) lemma to the case of matrices with general regular inertia. We show that the version of the lemma that was derived for the case of pairs of stable matrices whose rank difference is one, extends to the more general case of matrices with regular inertia and in companion form. We then use this result to derive an easily verifiable...

Select four perfect matchings of 2n vertices, independently at random. We find the asymptotic probability that each of the first and second matchings forms a Hamilton cycle with each of the third and fourth. This is generalised to embrace any fixed number of perfect matchings, where a prescribed set of pairs of matchings must each produce Hamilton cycles (with suitable restrictions on the presc...

We present a direct method for reordering eigenvalues in the generalized periodic real Schur form of a regular K-cyclic matrix pair sequence (Ak, Ek). Following and generalizing existing approaches, reordering consists of consecutively computing the solution to an associated Sylvester-like equation and constructingK pairs of orthogonal matrices. These pairs define an orthogonal K-cyclic equival...

The collection of the rough set pairs of an approximation (U, R) can be made into a Stone algebra by defining two binary operators and one unary operator on the pairs. By introducing a more unary operator, one can get a regular double Stone algebra to describe the rough set pairs of an approximation space. Sequent calculi corresponding to the rough alg...

The invariant eigendistributions on a reductive Lie algebra are solutions of a holonomic D-module which has been proved to be regular by Kashiwara-Hotta. We solve here a conjecture of Sekiguchi saying that in the more general case of symmetric pairs, the corresponding module are still regular.

Several mathematical distances between probabilistic languages have been investigated in the literature, motivated by applications in language modeling, computational biology, syntactic pattern matching and machine learning. In most cases, only pairs of probabilistic regular languages were considered. In this paper we extend previous results to pairs of languages generated by a probabilistic co...

In this article we will build a universal imbedding of a regular HomLie triple system into a Lie algebra and show that the category of regular Hom-Lie triple systems is equivalent to a full subcategory of pairs of Z2graded Lie algebras and Lie algebra automorphism, then finally give some characterizations of this subcategory.