Let Γ denote a bipartite distance-regular graph with diameter D ≥ 4, valency k ≥ 3 and intersection numbers ci , bi (0 ≤ i ≤ D). By a pseudo cosine sequence of Γ we mean a sequence of scalars σ0, . . . , σD such that σ0 = 1 and ciσi−1 + biσi+1 = kσ1σi for 1 ≤ i ≤ D − 1. By an associated pseudo primitive idempotent we mean a nonzero scalar multiple of the matrix ∑D i=0 σi Ai , where A0, . . . , ...

$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact triangulated categories. In this paper, we show that the idempotent completion an extriangulated category admits natural structure. As application, prove recollement is still recollement.