Sentence examples for achieved at a unique from inspiring English sources
It is well known that e f ( x ) is a continuous convex function, and for every x ∈ H, the infimum in (1.1) is achieved at a unique point prox f ( x ).
cAMP regulation of PKA is achieved via a unique three-component signaling system.
Yet by the time of his death at the age of 95, he had achieved a unique position in the country's intellectual life.
It is apparent that fleas achieved a unique expansion of acid phosphatases, at least nine members of which were identified in the salivary glands using MS/MS.
Thus the function h achieves its maximum at a unique point x = x 0. Thus h ( x ) ≤ 1 ϵ x 0 m + e − M x 0. (50..
From (2.7), the strict convexity and the continuity of (J cdot)), (J cdot)) must achieve its minimum at a unique point in ({mathscr{H}}).
(3.1) Furthermore, (J cdot)) achieves its minimum at a unique point ((hat{y}_{T},hat{z}_{T})) in (mathbb{X}) and ({hat{y}_{T}},{hat{z}_{T}})=0 textit{ a.e. in } Omega quadLongleftrightarrowquadbig| (u_{1},v_{1} big| _{mathbb{X}}leq varepsilon.
De Plata achieved prominence as a unique individual who made his own rules.
The home has achieved a unique synthesis, where the environment has been adjusted to follow function.
By the middle of the 14th century, Italian painters had achieved a unique position in Europe.
