We study stochastic partly dissipative lattice systems with random coupled coefficients and multiplicative/additive white noise in a weighted space of infinite sequences. We first show that these stochastic partly dissipative lattice differential equations generate a random dynamical system. We then establish the existence of a tempered random bounded absorbing set and a global compact random a...

We consider quantum gravity model with the squared curvature action. We construct lattice discretization of the model (both on hy-percubic and simplicial lattices) starting from its teleparallel equivalent. The resulting lattice models have the actions that are bounded from below while Einstein equations (without matter) appear in their classical limit.

In this paper we continue to study varieties of K-lattices, focusing on their bounded versions. These (bounded) commutative residuated lattices arise from a specific kind construction: the twist-product lattice. Twist-products were first considered by Kalman in 1958 deal with order involutions plain lattices, but extension concept has attracted some attention lately. We describe lower part latt...

We consider fundamental properties of weak interlaced bilattices and give a characterization theorem of them, that is, for any weak interlaced bilattice W there exists a bounded lattice L such that W can be embedded into a typical weak interlaced bilattice K(L). Hence, any interlaced bilattice can be embedded into the weak interlaced bilattice K(L) for some lattice L.

We consider quantum gravity model with the squared curvature action. We construct lattice discretization of the model (both on hy-percubic and simplicial lattices) starting from its teleparallel equivalent. The resulting lattice models have the actions that are bounded from below while Einstein equations (without matter) appear in their classical limit.

In this paper we introduce the comaximal graph of a finite bounded lattice L, denoted by Γ(L). We also study the interplay of lattice-theoretic properties of L with graphtheoretic properties of Γ(L). 2010 Mathematics Subject Classification: 05C10, 06A07, 06B10

The purpose of this note is to illustrate a construction technique which has proved useful, and apply it to solve an interesting problem. For a more complete discussion of the theory of bounded homomorphisms and lattices, see Chapter II of [3]. 1. Unbounded lattices We begin with a well known criterion for meet semidistributivity. If L is a finite lattice and a ∈ J(L), let κ(a) be the largest e...

It is known that classical logic CL is the single maximal consistent logic over intuitionistic logic Int, which is moreover the single one even over the substructural logic FLew. On the other hand, if we consider maximal consistent logics over a weaker logic, there may be uncountablymany of them. Since the subvariety lattice of a given variety V of residuated lattices is dually isomorphic to th...

In 1998, Burago-Kleiner and McMullen independently proved the existence of separated nets in R which are not bi-Lipschitz equivalent (BL) to a lattice. A finer equivalence relation than BL is bounded displacement after dilation (BDD). Separated nets arise naturally as return times to a section for minimal R-actions. We analyze the separated nets which arise via these constructions, focusing par...