A matrix A ∈ Rn×n is eventually nonnegative (respectively, eventually positive) if there exists a positive integer k0 such that for all k ≥ k0, A ≥ 0 (respectively, A > 0). Here inequalities are entrywise and all matrices are real and square. An eigenvalue of A is dominant if its magnitude is equal to the spectral radius of A. A matrix A has the strong Perron-Frobenius property if A has a uniqu...

In this paper, we consider a weakening of the definitions of uniform and perfect one-factorizations of the complete graph. Basically, we want to order the 2n − 1 one-factors of a one-factorization of the complete graph K2n in such a way that the union of any two (cyclically) consecutive one-factors is always isomorphic to the same two-regular graph. This property is termed sequentially uniform;...

A topological property is properly hereditary property if whenever every proper subspace has the property, the whole space has the property. In this note, we will study some topological properties that are preserved by proper subspaces; in fact, we will study the following topological properties: Baire spaces, second category, sequentially compact, hemicompact, δ-normal, and spaces having dispe...

in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).

We introduce sequentially Sr modules over a commutative graded ring and sequentially Sr simplicial complexes. This generalizes two properties for modules and simplicial complexes: being sequentially Cohen-Macaulay, and satisfying Serre’s condition Sr . In analogy with the sequentially CohenMacaulay property, we show that a simplicial complex is sequentially Sr if and only if its pure i-skeleton...

Standard-setting organizations (SSOs) are of growing importance as an institution for coordinating and facilitating the economic activities of intellectual property rights holders. SSOs thus foster economic benefits of standardization and of commercializing innovation. Market adoption of standards that call for standard-compliant products to use intellectual property rights (IPRs), however, rai...

Let P : E → K be an N−homogeneous polynomial, where E is a Banach space over K = R or C . We study properties of the set CP = {x ∈ E : P is weakly sequentially continuous at x}. Introduction Our interest in set of points of weak sequential continuity of a polynomial arises from the following simple observations. If P is any 2−homogeneous scalar valued polynomial on E which is weakly sequentiall...