In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and investigate special residuated lattices in order to obtain new characterizations for the directly indecomposable subvariety of Stonean residuated lattices. Free algebra in varieties of Stonean residuated lattices is constructed. We introduce in re...

We investigate graphs with the property that all longest paths or all longest cycles have empty intersection. In this paper, we find such graphs as subgraphs of cubic lattices.

We say that a C*-algebra A has the ‘sublattice property’ if the set P(A) of all projections in A is a sublattice of the projection lattice of its enveloping von Neumann algebra A∗∗. It is shown that this property is equivalent to the requirement that all pairs of projections have strictly positive ‘angle’. We discuss this property in relation to some results obtained by C. Akemann and by A. Laz...

Let L be a congruence-uniform lattice. In this note, we investigate the shard order on L that was introduced by N. Reading. When L is a poset of regions of a hyperplane arrangement the shard order always is a lattice. For general L, however, this fails. We provide a necessary condition for the shard order to be a lattice, and we show how to construct a congruence-uniform lattice L′ from L such ...

We answer a question of Vorobets by showing that the lattice property for flat surfaces is equivalent to the existence of a positive lower bound for the areas of affine triangles. We show that the set of affine equivalence classes of lattice surfaces with a fixed positive lower bound for the areas of triangles is finite and we obtain explicit bounds on its cardinality. We deduce several other c...

Important recent discoveries suggest that Ginsparg-Wilson-Lüscher (GWL) symmetry has analogous dynamical consequences for the theory on the lattice as chiral symmetry does in the continuum. While it is well known that inherent property of lattice chiral symmetry is fermion doubling, we show here that inherent property of GWL symmetry is that the symmetry transformation couples fermionic degrees...

In this paper, a novel orthogonal 2-D lattice structure is incorporated into the design of a nonseparable 2-D fourchannel perfect reconstruction filter bank. The proposed filter bank is obtained by using the polyphase decomposition technique which requires the design of an orthogonal 2-D lattice filter. Due to constraint of perfect reconstruction, each stage of this lattice filter bank is simpl...

In a canonical way we establish an AZ{identity (see [9]) and its consequences, the LYM{inequality and the Sperner{property, for the Boolean interval lattice. Further, the Bollobas{inequality for the Boolean interval lattice turns out to be just the LYM{ inequality for the Boolean lattice. We also present an Intersection Theorem for this lattice. Perhaps more surprising is that by our approach t...

Abstruct-A lattice structure and an algorithm are presented for the design of two-channel QMF banks, satisfying a sufficient condition for perfect reconstruction. The structure inherently has the perfect-reconstruction property, Hhile the algorithm ensures a good stophand attenuation for each of the analysis filters. Implementations of such lattice structures are robust in the sense that the pe...