CDM: Notes on Divisibility and State Complexity

The complexity of divisibility

We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive tra...

ON MODALITY AND DIVISIBILITY OF POISSON AND BINOMIAL MIXTURES

Some structural aspects of mixtures, in general, have been previously investigated by the author in [I] and [2]. The aim of this article is to investigate some important structural properties of the special cases of Poisson and binomial mixtures in detail. Some necessary and sufficient conditions are arrived at for different modality and divisibility properties of a Poisson mixture based o...

Additions and Corrections "M.H.Alamatsaz- On Modality and Divisibility of Poisson and Binomial Mixtures. J.Sci. I.R. Iran, Vol.l,No.3, Spring 1990

Notes on the genus Pileolaria (Pucciniales)

The results showed that Pileolaria terebinthi, type species of the genus Pileolaria is not a hemi–form or brachy–form rust species as mentioned among literature by several authors. Study on miscellaneous specimens collected from Iran and locus classicus of the species, France, revealed that P. terebinthi is an automacrocyclic rust and its aecial state is not uredinioi...

Some finite groups with divisibility graph containing no triangles

Let $G$ be a finite group. The graph $D(G)$ is a divisibility graph of $G$. Its vertex set is the non-central conjugacy class sizes of $G$ and there is an edge between vertices $a$ and $b$ if and only if $a|b$ or $b|a$. In this paper, we investigate the structure of the divisibility graph $D(G)$ for a non-solvable group with $sigma^{ast}(G)=2$, a finite simple group $G$ that satisfies the one-p...