It is shown that the numbers ci of chains of length i in the proper part L \ {0, 1} of a distributive lattice L of length l + 2 satisfy the inequalities c0 < . . . < c⌊l/2⌋ and c⌊3l/4⌋ > . . . > cl. This proves 75 % of the inequalities implied by the Neggers unimodality conjecture.

Two measures of distributive mixing are examined: the standard deviation σ and the maximum error E, among average concentrations of finite-sized samples. Curves of E versus sample size L are easily interpreted in terms of the size and intensity of the worst flaw in the mixture. E(L) is sensitive to the size of this flaw, regardless of the overall size of the mixture. The measures are used to st...

Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations ⊖ and ⊕ of L are uniquely determined by their system of neighbourhoods of 0 and form a distributive lattice. Moreover we prove that every such uniformity is generated by a family of weakly subadditive [0,+∞]-valued functions on L.

For a completely distributive quantale L, L-fuzzy strongest postcondition predicate transformers are introduced, and it is shown that, under reasonable assumptions, they are linear or affine continuous mappings between continuous L-idempotent semimodules of L-fuzzy monotonic predicates. © 2012 Elsevier B.V. All rights reserved.

We discuss the possible structures for and mutual relationships between a finite distributive lattice L, a maximal sublattice M of L and the corresponding ‘remainder’ R = L\M with the aid of Birkhoff duality, and contrast the results with the analogous situations for a general finite lattice L. @ 1999 Elsevier Science B.V. All rights reserved

It is shown that the numbers ci of chains of length i in the proper part L \ {0, 1} of a distributive lattice L of length l + 2 satisfy the inequalities c0 < . . . < c⌊l/2⌋ and c⌊3l/4⌋ > . . . > cl. This proves 75 % of the inequalities implied by the Neggers unimodality conjecture.

The main goal of this paper is to study the lattice of T L-submodules of a module. It is well-known that the lattice of submodules of a module is modular. In this study, we prove an analogous result for L-sets that is the lattice of L-submodules of a module is modular for an infinitely ∨-distributive lattice.

The concepts of semicompactness, countable semicompactness, and the semi-Lindelöf property are introduced in L-topological spaces, where L is a complete de Morgan algebra. They are defined by means of semiopen L-sets and their inequalities. They do not rely on the structure of basis lattice L and no distributivity in L is required. They can also be characterized by semiclosed L-sets and their i...

A new notion of SP-compactness is introduced in L-topological spaces by means of semi-preopen L-sets and their inequality, where L is a complete De Morgan algebra. This new notion does not depend on the structure of basis lattice L and L does not require any distributivity. This new notion implies semicompactness, hence it also implies compactness. This new notion is a good extension and it has...