Singular covers in free lattices

A covering a>b in a lattice is called a singular cover if a is join irreducible and b is meet irreducible. A classification of the singular covers which occur in free lattices is given.     

Unbounded semidistributive lattices

We consider two properties which are close to being lower bounded in the class of finite join semidistributive lattices. An example is constructed in which a finite join semidistributive lattice has both these two properties, but it is not lower bounded. Translated fromAlgebra i Logika, Vol. 39, No. 1, pp. 87–92, January–February, 2000.     

Interval Dismantlable Lattices

A finite lattice is interval dismantlable if it can be partitioned into an ideal and a filter, each of which can be partitioned into an ideal and a filter, etc., until you reach 1-element lattices. In this note, we find a quasi-equational basis for the pseudoquasivariety of interval dismantlable lattices, and show that there are infinitely many minimal interval non-dismantlable lattices.     

Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.     

Modeling Surface Engineering: Use of Polymetallic Iron Cages and Computer Graphics To Understand the Mode of Action of a Corrosion Inhibitor

Simple organic molecules can have many functions. The active ingredient in the corrosion inhibitor 3-(4-methylbenzoyl)propionate works because it addresses the metal sites of a surface through carboxylate groups, forms hydrogen bonds with surface hydroxide groups (see picture), and provides excellent surface coverage through efficient packing of substituted aromatic groups.