Let $\mathscr{C}$ be an extriangulated category with a proper class $\xi$ of $\mathbb{E}$-triangles. We introduce the notions left Frobenius pairs, ($n$-)cotorsion pairs and (weak) Auslander-Buchweitz contexts respect to in $\mathscr{C}$. show how construct cotorsion pais from $n$-cotorsion establish one-to-one correspondence between contexts. also study relation certain that pairs. These work ...

Applying geometric methods of 2-dimensional cell complex theory, we construct a Galois covering bimodule problem satisfying some structure, triangularity and finiteness conditions in order to describe the objects finite representation type. Each admitted A is endowed with quasi multiplicative basis. The main result shows that for from considered class having restrictions schurian universal A', ...

Abstract In this paper we give an example of a closed, strongly one-sided dense set which is not uniform density type. We also show that there type strong

this paper addresses the problem of testing simple hypotheses about the mean of a bivariate normal distribution with identity covariance matrix against restricted alternatives. the lrts and their power functions for such types of hypotheses are derived. furthermore, through some elementary calculus, it is shown that the power function of the lrt satisfies certain monotonicity and symmetry prope...