For any cocycle solutions, the invariants are, by definition, invariant under the gauge transformation (32) and (33), and their values must be equal to roots of 1. Therefore, the values of the invariants are fixed for a given class of factor systems ω2(g1, g2). On the other hand...
Definition 2.22 [12] A familyτof soft sets overXunder a fixed parameters setEwhich containsX͠andΦ͠and is closed under finite soft intersection and arbitrary soft union is said to be a soft topology onX. The triple (X, τ, E) is said to be a soft topological space (briefly, ST...
While barlowite itself is an intriguing quantum magnet, it is also the parent of a QSL candidate, Zn-substituted barlowite, whose stability was first predicted by first-principles calculations36,37. Substituting barlowite’s interlayer site with Zn2+isolates the Cu2+kagome layers, leading to Cu...
Definition 3.1 Let be a collection of single valued trapezoidal neutrosophic num- bers. Then, SVTNWHA operator is a function SVTNWHA : is defined as (2) By using arithmetic operations on single valued trapezoi- dal neutrosophic numbers, we get the following theorem. Theorem 3.4 Let...
Definition 2. [6] For any monotonic sequence (a, b, c, d) ⊂ R the trapezoidal ordered fuzzy number (TrOFN) ↔ Tr(a, b, c, d) is defined as the pair of FN T ∇(a, b, c, d) ∈ F and the orientation a d . The fuzzy number T ∇(a, b, c, d) ∈ F is ...