A set of four soil reference materials with certified values of total element contents and their extractable fractions

A set of certified reference materials of four natural soils denoted as CRM 7001-4 was prepared. They consist of light sandy soils with normal and elevated, silty clay loam with normal, and loam with elevated element levels. Certified and/or information values were established for the total contents of the elements As, Ba, Be, Cd, Co, Cr, Cu, Hg, Mn, Ni, Pb, V, Zn, and their fractions, extractable with aqua regia, and boiling and cold 2 mol L^–1 nitric acid, from results of a 28 laboratory intercomparison using various methods of atomic absorption spectrometry, optical emission spectrometry, mass spectrometry, electrochemical methods, spectrophotometry, instrumental neutron activation analysis, and X-ray fluorescence.     

On the minimum order of graphs with given semigroup

Denote by M(n) the smallest positive integer such that for every n-element monoid M there is a graph G with at most M(n) vertices such that End(G) is isomorphic to M. It is proved that $\text{2}\text{(1 + o(1))n}\text{log}{}_2\text{n}\text{≤M(n)≤n ·}\text{2n}\text{+ O(n)}$. Moreover, for almost all n-element monoids M there is a graph G with at most 12 · n · log₂n + n vertices such that End(G) is isomorphic to M.     

Finitely generated relatively universal varieties of Heyting algebras

Given distinct varieties and of the same type, we say that is relatively -universal if there exists an embedding :K from a universal categoryK such that for every pairA, B ofK-objects, a homomorphismf:A B has the formf=_g for someK-morphismg:A B if and only if Im(f) . Finitely generated relatively -universal varieties of Heyting algebras are described for the variety of Boolean algebras, the variety generated by a three element chain, and for the variety generated by the four element Boolean algebra with an added greatest element.Dedicated to the memory of Alan DayPresented by J. Sichler.The support of the NSERC is gratefully acknowledged.     

Equimorphy in varieties of distributive double p-algebras

Any finitely generated regular variety V of distributive double p-algebras is finitely determined, meaning that for some finite cardinal n(V), any subclass S V of algebras with isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result follows from our structural characterization of those finitely generated almost regular varieties which are finitely determined. We conjecture that any finitely generated, finitely determined variety of distributive double p-algebras must be almost regular.     

On Full and Faithful Kan Extensions

The paper introduces some mild requirements under which a Kan extension is a full embedding that preserves factorization systems and colimits of -directed diagrams. The existence of such Kan extensions is then used to establish conditions equivalent to algebraic universality of concrete categories such as varieties of algebras of any given similarity type.     

Isomorphic edge disjoint subgraphs of hypergraphs

We show that any k‐uniform hypergraph with n edges contains two isomorphic edge disjoint subgraphs of size for k = 4, 5 and 6. This is best possible up to a logarithmic factor due to an upper bound construction of Erd?s, Pach, and Pyber who show there exist k‐uniform hypergraphs with n edges and with no two edge disjoint isomorphic subgraphs with size larger than . Furthermore, our result extends results Erd?s, Pach and Pyber who also established the lower bound for k = 2 (eg. for graphs), and of Gould and Rödl who established the result for k = 3. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 767–793, 2016     

On endomorphism monoids in varieties of bands

It will be proved that every non-trivial variety \({\mathbb{V}}\) of bands (idempotent semigroups) contains a proper generating class of non-isomorphic bands B such that B generates \({\mathbb{V}}\) and any band \({B\prime}\) having the same endomorphism monoid as B is isomorphic to B or to the opposite band B^op. Consequently, every sharply greater band variety has a sharply greater class of endomorphism monoids.