A quantitative Lovász criterion for Property B

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 ...

Mono-Size Distribution Index (MSDI): A new criterion for the quantitative description of size distribution

Graphical size distribution is widely used in different fields of science and studies related to powders, droplets, bubbles, and pores. However, in some condition it may also be necessary to express the size distribution quantitatively. In spite of there being several suggested ways to quantify size distribution in the literature, some of these approaches are not applicable for many methods and...

A Quantitative Criterion for Defining Planets

A simple metric can be used to determine whether a planet or exoplanet can clear its orbital zone during a characteristic time scale, such as the lifetime of the host star on the main sequence. This criterion requires only estimates of star mass, planet mass, and orbital period, making it possible to immediately classify 99% of all known exoplanets. All 8 planets and all classifiable exoplanets...

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...