Abstract We consider the binary supremum function $$\sup :Z\times Z\rightarrow Z$$ sup : Z × → on a sup semilattice Z and its topological properties with respect to Scott topology product topology. It is well known that...

Multiple twinning in crystalline solids forming quintuples of twins is known since 1957 (Segall). It ever has attracted the attention not only of crystal growth and crystallography research, but also of cluster physics, physical chemistry, surface science, thin films and materials research. This review gives a comprehensive record of four decades work on fivefold twinned structures (frequently ...

for some real number X, the symbol V denoting the lattice least upper bound. Any ring R is regular [10] if for each xER there is an xaER such that xx°x = x. It is evident that every regular F-ring R contains a maximal bounded sub-F-ring R, the F-ring of all xER satisfying equation (1.1). The relationship between a regular F-ring and its maximal bounded sub-F-ring is analogous to that between th...

A (distributive) p-algebra is an algebra 〈L;∨,∧, ∗, 0, 1〉 whose reduct 〈L;∨,∧, 0, 1〉 is a bounded (distributive) lattice and whose unary operation ∗ is characterized by x ≤ a if and only if a ∧ x = 0. If L is a p-algebra, B(L) = { x ∈ L : x = x } and D(L) = { x ∈ L : x = 1 } then 〈B(L);∪,∧, 0, 1〉 is a Boolean algebra when a ∪ b is defined to be (a∗ ∧ b∗)∗, for any a, b ∈ B(L), D∗(L) = { x ∨ x∗ ...

In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.

The lattice Boltzmann method (LBM) is employed to simulate stratified plane Couette (SPC) flows in their statistically stationary turbulent state. aim assess the suitability of LBM for direct simulation wall-bounded, sheared turbulence under influence stable stratification. SPC flow generated by two parallel plates moving opposite directions with velocities ± U w, and buoyancy fixed at b w uppe...

The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an binary operations (not necessarily t-norms) defined the fixed subintervals may not be t-norm. Some necessary and sufficient conditions are presented in this article for ensuring that two is, fact, In particular, results here provide answer open problem put forward by Ertuğrul Yeşilyurt, <italic...

In a recent work (Wang et al. 2020), partial order ⪯, join operation ⊔ and meet ⊓ of probabilistic linguistic term sets (PLTSs) were introduced it was proved that L1 L2 ⪯ L2. this paper, we demonstrate its operations are not satisfy the above requirement. To requirement, modify operations. Moreover, define negation PLTSs based on ⪯. The combinations proposed negation, modified yield bounded, di...