By a new partial ordering relation “ ≤ ” the set of convex sublattices CS(L) of a lattice L is again a lattice. In this paper we establish some results on the pseudocomplementation of (CS(L); ≤). We show that a lattice L with 0 is dense if and only if CS(L) is dense. Then we prove that a finite distributive lattice is a Stone lattice if and only if CS(L) is Stone. We also prove that an upper co...

The notion of pseudo-annulets is introduced in Stone lattices and characterized in terms of prime filters. Two operator α and β are introduced and obtained that their composition β ◦α is a closure operator on the class of all filters of a Stone lattice. A congruence θ is introduced on a Stone lattice L and proved that the quotient lattice L/θ is a Boolean algebra.

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...

Stone algebras have been characterized by Chen and Grätzer in terms of triples (B;D;'), whereD is a distributive lattice with 1; B is a Boolean algebra, and ' is a bounded lattice homomorphism from B into the lattice of …lters of D: If D is bounded, the construction of these characterizing triples is much simpler, since the homomorphism ' can be replaced by one from B into D itself. The triple ...

This paper concerns residuated lattice-ordered idempotent commutative monoids that are subdirect products of chains. An algebra of this kind is a generalized Sugihara monoid (GSM) if it is generated by the lower bounds of the monoid identity; it is a Sugihara monoid if it has a compatible involution ¬. Our main theorem establishes a category equivalence between GSMs and relative Stone algebras ...

The goal of this paper is to study finite groups admitting a pseudocomplemented subgroup lattice (PK-groups) or a pseudocomplemented normal subgroup lattice (PKN-groups). In particular, we obtain a complete classification of finite PK-groups and of finite nilpotent PKN-groups. We also study groups with a Stone normal subgroup lattice, and we classify finite groups for which every subgroup has a...

In this work we discuss the notion of observable both quantum and classical from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann’s approach to) quantum physics, an observable is represented as a bonded selfadjoint operator on Hilbert space. We will show in part II of this work that there is a com...

this work is a primary achievement in studying the co2 and n2–oil systems. to predict gas-liquid relative permeability curves, a shan-chen type multicomponent multiphase lattice boltzmann model for two-phase flow through 2d porous media is developed. periodic and bounce back boundary conditions are applied to the model with the guo scheme for the external body force (i.e., the pressure gradient...