We deene the notion of weak relative pseudo-complement, and we show that, for an arbitrary lattice, the property of weak relative pseudo-complementation is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main interest for this notion is in relation with the theory of closure operators. We prove that if a complete lattice L is completely inf-di...

In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...

We demonstrate a single-site and single-atom-resolved fluorescence imaging of bosonic Mott insulator $^7$Li atoms in an optical lattice. The images are obtained by implementing Raman sideband cooling on deep two-dimensional square lattice, where we collect scattered photons with high numerical aperture objective lens. lattice is created folded retro-reflected beam configuration that can reach 2...

The aim of the present paper is to define the localization BL-algebra of a BL-algebra A with respect to a topology F on A. In the last part of the paper is proved that the maximal BL-algebra of quotients (defined in [5]) and the BLalgebra of fractions relative to a ∧-closed system (defined in [4]) are BL-algebras of localization. A remarkable construction in ring theory is the localization ring...

For a minimal inequality derived from a maximal lattice-free simplicial polytope in R, we investigate the region where minimal liftings are uniquely defined, and we characterize when this region covers R. We then use this characterization to show that a minimal inequality derived from a maximal lattice-free simplex in R with exactly one lattice point in the relative interior of each facet has a...

the present study investigates the performance and relative accuracy of four lattice-hole theory based equations of state in modeling and correlating the liquid density of pure refrigerants. following the gathering of a database of 5740 experimental liquid density datapoints of 36 pure refrigerants belonging to five different categories including cfcs, hcfcs, pfcs, hfcs and hfes, ranging from 6...

This paper proposes a new lattice filter structure that has the following properties. When the filter is Linear Time Invariant (LTI), it is equivalent to the celebrated Gray Markel Lattice. When the lattice parameters vary with time it sustains arbitrary rate of time variations without sacrificing a prescribed degree of stability, provided that the lattice coefficients are magnitude bounded in ...

Epidemiologic studies have suggested that daily fluid intake that achieves at least 2.5 L of urine output per day is protective against kidney stones. However, the precise quantitative nature of the association between fluid intake and kidney stone risk, as well as the effect of specific types of fluids on such risk, are not entirely clear.We conducted a systematic review and dose-response meta...