On Gaps Between Bounded Operators
On Gaussian conditional independence structures
The simultaneous occurrence of conditional independences among subvectors of a regular Gaussian vector is examined. All configurations of the conditional independences within four jointly regular Gaussian variables are found and completely characterized in terms of implications involving conditional independence statements. The statements induced by the separation in any simple graph are shown to correspond to such a configuration within a regular Gaussian vector.
On general linear semigroups.
On general matrices having the Perron-Frobenius property.
On generalized Hermite matrix polynomials.
On generalized inverses of banded matrices.
On generalized inverses of singular matrix pencils
Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate singular matrix pencils. The relations between the Kronecker structure of a singular matrix pencil and the...
On generating regular elements in the semigroup of binary relations.
On Geršgorin-type problems and ovals of cassini.
On graphs with the largest Laplacian index
Let be a connected simple graph on vertices. The Laplacian index of , namely, the greatest Laplacian eigenvalue of , is well known to be bounded above by . In this paper, we give structural characterizations for graphs with the largest Laplacian index . Regular graphs, Hamiltonian graphs and planar graphs with the largest Laplacian index are investigated. We present a necessary and sufficient condition on and for the existence of a -regular graph of order with the largest Laplacian...
On Hallian digraphs, permanents and transversals
On hardly linearly provable systems
A well-known theorem of Rabin yields a dimensional lower bound on the width of complete polynomial proofs of a system of linear algebraic inequalities. In this note we investigate a practically motivated class of systems where the same lower bound can be obtained on the width of almost all (noncomplete) linear proofs. The proof of our result is based on the Helly Theorem.
On Hermite-Hermite matrix polynomials
In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite matrix polynomials is proposed.
On inequalities involving the Hadamard product of matrices.
On infinite bounded-Toeplitz extensions of Toeplitz matrices.
On Invariant Parametric Covariance Families.
On invariants of a set of matrices.
On inverses of triangular matrices with monotone entries.
On Inverses of Vandermonde and Confluent Vandermonde Matrices III.