Sentence examples for a graded vector from inspiring English sources

Let be an endomorphism of degree zero of a graded vector space.

Thus is a graded vector space, with being the -dimensional ech homology group with compact carriers of.

Thus H* X) = {H q (X)} is a graded vector space, H q (X) being the q-dimensional Čech homology group with compact carriers of X.

Thus (H X)={H_{q}(X)} ) (here X is a Hausdorff topological space) is a graded vector space, (H_{q}(X) ) being the q-dimensional C̆ech homology group with compact carriers of X.

Then, as a graded vector space, we define H o m s 0 (P 1, P 2 ) as Hom s 0 - M o d ∞ (i 1 ∗ (P 1 ), i 2 ∗ (P 2 ) ).

Let P be a graded vector space and write (2.6) B (a, b ) P = B A 1 ⊗ ⋯ ⊗ B A r ⊗ P ⊗ B B 1 ⊗ ⋯ ⊗ B B s for the bar construction of P. When (a, b ) is fixed or understood from the context, we simply write B P. We make a note that B P is naturally an object of C h l f where the lattice is Z r + s and the filtration is induced by the length filtrations on the bar constructions.

Two braided vector spaces of diagonal type with the same generalized Dynkin diagram are called twist equivalent; then the corresponding Nichols algebras are isomorphic as graded vector spaces [20, Proposition 3.9].

As graded vector spaces, both are equal to T V = ⨁ n = 0 ∞ V ⊗ n.

To obtain a graded decode of choice, we projected the data onto the vector normal to the hyperplane.

The expression of the toxin EndoA, encoded by the chromosomal ydcE gene, was regulated by an endogenous, xylose-inducible promoter, while the ydcD gene, which encodes the unstable antitoxin EndoB, was inserted into a food-grade vector backbone, where its expression was driven by the native, constitutive promoter PylxM.

Firstly, a clinical grade vector will be required to carry the ST DNA in place of pcDNA3.