The notion of crossed product with a coquasi-Hopf algebra H is introduced and studied. The result of such a crossed product is an algebra in the monoidal category of right H-comodules. We give necessary and sufficient conditions for two crossed products to be equivalent. Then, two structure theorems for coquasi Hopf modules are given. First, these are relative Hopf modules over the crossed prod...

The crossed cube is one of the most notable variations of hypercube, but some properties of the former are superior to those of the latter. For example, the diameter of the crossed cube is almost the half of that of the hypercube. In this paper, we focus on the problem embedding a Hamiltonian cycle through an arbitrary given edge in the crossed cube. We give necessary and sufficient condition f...

Let G be a locally compact group. We show that the category A(G) of actions of G on C∗-algebras (with equivariant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C∗(G), δG); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma catego...

we give the concept of ‘braiding’ for 2-groupoids, and we show that this structure is equivalent tobraided regular, crossed modules.

BACKGROUND Currently, food supplements to improve age-related dementia are required. Therefore, we aimed to determine the effect of the combined extract of Cyperus rotundus and Zingiber officinale (CP1) on the improvement of age-related dementia in rats with AF64A-induced memory deficits. METHODS Male Wistar rats weighing 180-200 g were orally given CP1 at doses of 100, 200 and 300 mg.kg-1 BW...

The relationship of mandibular condyle dimensions and its association with unilateral posterior crossbite (UPXB) has been suggested in the literature. The purpose of this prospective study was to evaluate mandibular condyles on the left and right sides and between crossed and non-crossed sides in the sagittal and coronal planes, using cone-beam computed tomography (CBCT). Twenty CBCT images of ...

A crossed product is the functional analysts’ version of a skew group ring. Thus, if α : G→ Aut(A) is an action of a locally compact group G on a Banach algebra A, then a crossed product Banach algebra encodes the action of G on A, and its representation theory is related to pairs (u, π) consisting of a representation u of G and a representation π of A on the same Banach space such that ugπ(a)u...