A Criterion for Property C

A criterion for the half-plane property

We establish a convenient necessary and sufficient condition for a multiaffine real polynomial to be stable, and use it to verify that the half-plane property holds for seven small matroids that resisted the efforts of Choe, Oxley, Sokal, and Wagner [5]. In recent years, matroid theory has found connections with certain analytic properties of real multivariate polynomials. These properties are ...

Property (T) for C*-dynamical systems

In this paper, we introduce a notion of property (T) for a C<span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: norm...

On Baer type criterion for $C$-dense‎, ‎$C$-closed and quasi injectivity

‎For the subclasses $mathcal{M}_1$ and $mathcal{M}_2$ of‎ ‎monomorphisms in a concrete category $mathcal{C}$‎, ‎if $mathcal‎{M}_2subseteq mathcal{M}_1$‎, ‎then $mathcal{M}_1$-injectivity‎ ‎implies $mathcal{M}_2$-injectivity‎. ‎The Baer type criterion is about‎ ‎the converse of this fact‎. ‎In this paper‎, ‎we apply injectivity to the classes of $C$-dense‎, ‎$C$-closed‎ ‎monomorphisms‎. ‎The con...

A Criterion for the Failure of Ruelle's Property

On a new criterion for the H-matrix property

A new criterion for identifying generalized diagonally dominant matrices (GDDM, or H -matrices) was given in [K. Ojiro, H. Niki, M. Usui, A note on a new criterion for the H -matrix property, J. Comput. Appl. Math. 150 (2003) 293–302], where the criterion is effective when the given matrix is irreducible. However, when the matrix is reducible, it may lead to a false answer. In this work, to ove...