Sentence examples for up to a unique from inspiring English sources

Strictly speaking, transition functors (f^*) of a prefibration are well-defined only up to a unique isomorphism, not uniquely.

They all add up to a unique sound landscape which is distinctly Dubai.

Such a factorization is unique up to a unique isomorphism.

Second, objects are always characterized up to isomorphism (in the best cases, up to a unique isomorphism).

Moreover, any two such 2-limit diagrams are equivalent over (I^<), and the equivalence is unique up to a unique isomorphism.

An Extraordinary Scientific Apprenticeship The intensive--and extensive--nature of the job, coupled to the rigorous approach and Pollard's active mentorship, added up to a unique educational experience.

In fact, according to the people at the London Hop Shoot festival, since the weekend, they've been inundated with request for hop shoots from chefs "who have just woken up to a really unique ingredient they could start using".

If all the eigenvalues are distinct, then L has, up to a constant, a unique polynomial for each degree as an eigenfunction.

In particular, if the eigenvalues λ 0, λ 1,..., λ n (for some n) are distinct, then ℙ n has a basis of eigenfunctions and, for reasons of degree, L has (up to a constant) a unique polynomial of degree r (for each r, 0 ≤ r ≤ n) corresponding to λ r as an eigenfunction.

Therefore, if we define ( u, v ) = lim ε → 0 ∫ - 1 + ε 1 - ε p ( x ) u ( x ) v ( x ) d x then L would be a self-adjoint operator on all polynomials of degree n and so, there must be, up to a scalar, a unique polynomial which is an eigenfunction of L for eigenvalue −n(n − 1) + nα.

BBC.co.uk isn't ABCE audited, so these are internal hitbox figures, but February traffic was up to a record 16.1m unique users in the UK.