The cyclicity of a hypergraph is an efficiently computable integer that extends the notion of the cyclomatic number of a graph. Generalizing the notion of the degree of a node in a graph, we define the star articulation degree of a subedge in a hypergraph, and then use it to set up the expression for the cyclicity. The basic properties of cyclicity are that it is zero on acyclic hypergraphs and...

We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed.

We prove Kleene theorems for two subclasses of labelled product systems which are inspired from well-studied subclasses of 1bounded Petri nets. For product T-systems we define a corresponding class of expressions. The algorithms from systems to expressions and in the reverse direction are both polynomial time. For product free choice systems with a restriction of structural cyclicity, that is, ...

Abstract The problem of the distribution extreme and very strong magnetic storms with intensities (G5, G4) in first cycles (12 24) epochs lowered solar activity was considered based on homogeneous series geomagnetic index Aa allowance for modern scale intensity disturbances near-Earth space scenario cyclicity. significant decrease number such events active phenomena last cycle may indicate that...

We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces 0<α< 1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.

The objective of this study was to quantify the genetic variation in normal and atypical progesterone profiles and investigate if this information could be useful in an improved genetic evaluation for fertility for dairy cows. The phenotypes derived from normal profiles included cycle length traits, including commencement of luteal activity (C-LA), interluteal interval, luteal phase length. and...