Sentence examples for a the associated from inspiring English sources

(a) The associated modular function space is the vector space L ρ ( X, Σ ), or briefly L ρ defined by L ρ = { f ∈ M ; ρ ( λ f ) → 0  as  λ → 0 }.

(a) The associated modular function space is the vector space L ρ , or briefly L ρ, defined by L ρ = { f ∈ M ; ρ ( λ f ) → 0  as  λ → 0 }.

In particular, given any two objects, M, N ∈ A, the associated map (3.1) H ∗ ev G : H ∗ (Hom ∗ (M, N ) ) → H ∗ (Hom ∗ (ev G M, ev G N ) ) is an isomorphism.

Since this reduces the required tip current significantly, down to ~10−5 A, the associated space charge degradation on the pulse duration and the emittance are largely suppressed in the typical high acceleration electric field in the order of 108 V/m for the accelerator applications21.

Because of the compactness of the semigroup S ( t ) (and consequently S ˆ α ( t ), S α ( t ) ) generated by A, the associated linear system of (13) is not completely controllable but it is approximately controllable.

We will denote by A and A ∗ the associated and augmented associated seminorms { p α : α ∈ I }, respectively.

The Rev. Paul M. Mayer, a priest associated with the Federation of Christian Ministries, officiated.

I am loosely translating the name of a song associated with the Passover seder.

Not a single person associated the painting with anything Jewish.

To enter a competition associated with the film visit Guardian Extra.

Patience is not a commodity associated with the Old Firm.