An ordered monoid is a structure with an identity element (1′), a binary composition operator (;) and an antisymmetric partial order (≤), satisfying certain axioms. A representation of an ordered monoid is a 1-1 map which maps elements of an ordered monoid to binary relations in such a way that 1′ is mapped to the identity relation, ; corresponds to composition of binary relations and ≤ corresp...

the complexation reactions between mg2+, ca2+, sr2+ and ba2+ metal cations with 15-crown-5 (15c5) were studied in acetonitrile (an)-methanol (meoh) binary mixtures at different temperatures using conductometric method. 15c54 forms 1:1 complexes with mg2+, ca2+ and sr2+ cations in solutions. the ma2+ cation forms a 2:1 complex (ratio of lighand to cation) in solutions. a linear relation was obse...

The rough set theory usually is used in datamining. At this time, we will suppose the approximation operator to satisfy some wonderful properties. It need us to think about the basis algebra, the binary relation and the approximation operator’s form in the rough set model. Lfuzzy rough approximation operator is a general fuzzy rough approximation operator. Comparing with the others rough approx...

We use our definition of an underlying co-bipartite graph which encodes a given binary relation to propose a new approach to defining a sub-relation or incrementally maintaining a relation which will define only a polynomial number of concepts.

The paper studies the subsequence relation through a notion of an intransitive binary relation on words in traces generated by prefix-rewriting systems. The relation was introduced in 1988 by V.F. Turchin for loop approximation in supercompilation. We study properties of this relation and introduce some refinements of the subsequence relation that inherit the useful features of Turchin’s relation.

We consider several ordinal formulations of submodularity, defined for arbitrary binary relations on lattices. Two of these formulations are essentially due to David Kreps (A Representation Theorem for “Preference for Flexibility”, Econometrica, 1979) and one is a weakening of a notion due to Paul Milgrom and Chris Shannon (Monotone Comparative Statics, Econometrica, 1994). We show that any ref...