We show that, for every pseudovariety of groups H, the pseudovariety H̄, consisting of all finite semigroups all of whose subgroups lie in H, is irreducible for join and the Mal’cev and semidirect products. The proof involves a Rees matrix construction which motivates the study of iterated Mal’cev products with the pseudovariety of bands. We further provide a strict infinite filtration for H̄ usi...

Using a probabilistic interpretation of the Burau representation of the braid group offered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string links. This representation is determined by a linear system, and is dominated by finite type string link invariants. For positive string links, the representation matrix can be interpreted as the trans...

Most computational problems for matrix semigroups and groups are inherently difficult to solve and even undecidable starting from dimension three. The questions about the decidability and complexity of problems for two-dimensional matrix semigroups remain open and are directly linked with other challenging problems in the field. In this paper we study the computational complexity of the problem...

In order to investigate the behavior of rare earth elements (REEs) and uranium (U) in marine organism, the concentrations of REEs and U in some brown algae samples taken on the coast of Niigata Prefecture were determined. In addition, laboratory model experiment to uptake these elements using living and dried algae (Undaria pinnatifida and Sargassum hemiphyllum) was also carried out to survey t...

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

It was shown by van Rees [18] that a latin square of order n cannot have more than n(n− 1)/18 latin subsquares of order 3. He conjectured that this bound is only achieved if n is a power of 3. We show that it can only be achieved if n ≡ 3 mod 6. We also state several conditions that are equivalent to achieving the van Rees bound. One of these is that the Cayley table of a loop achieves the van ...

Rare earth elements (REEs) enriched fertilizers have been commonly used in China since the 1980s, thus inducing a growing concern about their environmental impact in agriculture. In this work, the effect of some light REEs nitrate mixture and La(3+) nitrate on seed germination, seedling growth and antioxidant metabolism in Triticum durum was investigated with the aim of clarifying the potential...

Inspired by recent work in the theory of central projections onto hyper-surfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert– Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symme...