The main purpose of this paper is to use a new way to extend fuzzy implications $I$ from a generalized sublattice $M$ to a bounded lattice $L$, such that the extended implications preserve many of the considered properties of fuzzy implications on $M$.Furthermore, as a special case, we investigate the extension of $(S,N)-$implications. Results indicate that the extended implications preserve ma...

In this note, we consider K3 surfaces X with an action by the alternating group A 5. We show that if a cyclic extension A 5 .C n acts on X then n = 1, 2, or 4. We also determine the A 5-invariant sublattice of the K3 lattice and its discriminant form.

This paper characterizes those finite lattices which are a maximal sublattice of an infinite lattice. There are 145 minimal lattices with this property, and a finite lattice has an infinite minimal extension if and only if it contains one of these 145 as a sublattice. In [12], I. Rival showed that if L is a maximal sublattice of a distributive lattice K with |K| > 2, then |K| ≤ (3/2)|L|. In [1]...

For closure operators Γ and ∆ on the same set X, we say that ∆ is a weak (resp. strong) extension of Γ if Cl(X, Γ) is a complete meet-subsemilattice (resp. complete sublattice) of Cl(X, ∆). This context is used to describe describe the extensions of a finite lattice that preserve various properties.

An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm developed by Martinez et al [J. Comp. Phys. 227 (2008) 3804] to discrete lattices is presented. The method solves the master equation synchronously by recourse to null events that keep all processors time clocks current in a global sense. Boundary conflicts are rigorously solved by adopting a chessboard decomposition ...

It is proposed in [Extension of Fuzzy Logic Operators Defined on Bounded Lattices via Retractions, Computer & Mathematics with Applications, 63: 1026–1038, 2012] a method for extending t-norms, t-conorms and fuzzy negations from a sublattice M of bounded lattice L considering a relaxed notion of sublattices. In this work we apply this method to extend a class of fuzzy negations constructed from...

In this paper, a characterization of the language varieties and congruence varieties corresponding toM -solid pseudovarieties is presented. Taking into account the isomorphisms of the Eilenberg-type correspondences, each complete sublattice of pseudovarieties corresponds to a complete sublattice of language varieties, as well as another one of congruence varieties. For the varieties of tree lan...

In this paper, a characterization of the language varieties and congruence varieties corresponding to M -solid pseudovarieties is presented. Taking into account the isomorphisms of the Eilenberg-type correspondences, each complete sublattice of pseudovarieties corresponds to a complete sublattice of language varieties, as well as another one of congruence varieties. For the varieties of tree la...

The spinel MnV(2)O(4) is a two-sublattice ferrimagnet, with site A occupied by the Mn(2+) ion and site B by the V(3+) ion. The magnon of the system, the transversal fluctuation of the total magnetization, is a complicated mixture of the sublattice A and B transversal magnetic fluctuations. As a result, the magnons' fluctuations suppress in a different way the manganese and vanadium sublattice m...

In this paper, the notion of $L$-convex fuzzy sublattices is introduced and their characterizations are given. Furthermore,  the notion of the degree to which an $L$-subset is an $L$-convex fuzzy sublattice is proposed and its some  characterizations are given. Besides, the $L$-convex fuzzy sublattice degrees of the homomorphic image and pre-image of an $L$-subset are studied. Finally, we obtai...