Several verifiable sufficient conditions for regularity and singularity of interval matrices are given. As an application, a verifiable sufficient condition is derived for an interval matrix to have all eigenvalues real.

The description logic (DL) SROIQ [1] provides a logical foundation for the new version of the web ontology language OWL 2. In comparison to the DL SHOIN which underpins the first version of OWL, SROIQ provides several new constructors for classes and axioms. One of the new powerful features of SROIQ are so-called complex role inclusion axioms (RIAs) which allow for expressing implications betwe...

In the literature there are various regularity conditions as well as many different so-called almost parallelogram conditions on the subdivisions of quadrilateral grids. In this paper we investigate and clarify their relations. 2002 Elsevier Science B.V. All rights reserved.

We give some new regularity conditions for Fenchel duality in separated locally convex vector spaces, written in terms of the notion of quasi interior and quasi-relative interior, respectively. We provide also an example of a convex optimization problem for which the classical generalized interior-point conditions given so far in the literature cannot be applied, while the one given by us is ap...

Let v and ω be the velocity and the vorticity of the a suitable weak solution of the 3D Navier-Stokes equations in a space-time domain containing z0 = (x0, t0), and Qz0,r = Bx0,r×(t0−r 2, t0) be a parabolic cylinder in the domain. We show that if v × ω |ω| ∈ L γ,α x,t (Qz0,r) or ω × v |v| ∈ L γ,α x,t (Qz0,r), where L γ,α x,t denotes the Serrin type of class, then z0 is a regular point for v. Th...

Given a Lévy process X with Lévy measure ν, conditions ensuring that limt→0 1t E f(Xt) = ∫ f(x)ν(dx) are given. The moment functions f considered here can be unbounded as well as satisfy simpler regularity conditions than those considered in some previous works. Also, the rate of convergence is determined when f vanishes in a neighborhood of the origin and satisfies other regularity conditions ...

In the Avoider-Enforcer game on the complete graph Kn, the players (Avoider and Enforcer) each take an edge in turn. Enforcer wins the game when he can require Avoider’s graph to have a given property P . The important parameter is τE(P), the most number of rounds required for Enforcer to win if Avoider plays with an optimal strategy (τE(P) = ∞ if Avoider can finish the game without creating a ...

The following sharpening of Turán’s theorem is proved. Let Tn,p denote the complete p– partite graph of order n having the maximum number of edges. If G is an n-vertex Kp+1-free graph with e(Tn,p) − t edges then there exists an (at most) p-chromatic subgraph H0 such that e(H0) ≥ e(G)− t. Using this result we present a concise, contemporary proof (i.e., one using Szemerédi’s regularity lemma) fo...

We give a simple constructive version of Szemerédi’s Regularity Lemma, based on the computation of singular values of matrices. Mathematical Reviews Subject Numbers: 05C85, 68R10.