Sentence examples for denotes the essential from inspiring English sources

where essinf (esssup) denotes the essential infimum (essential supremum) of a function.

Here ({text {ess,inf}}^{{mathbb {P}}}) denotes the essential supremum with respect to the probability measure ({mathbb {P}}).

The term "quid" denotes the essential mode of the being of a thing, that is, the mode of being by which it exists as a being of a certain kind.

Specifically, (s(D) = sup{ operatorname{Re}(lambda) : lambdain sigma (D)} ); ({ omega _{0}(G) = lim_{t toinfty} frac{ln{|G t)|}}{t}} ) and ({ omega _{mathrm{ess}}(G) = lim_{t toinfty}frac{ln{|G t)|_{mathrm{ess}}}}{t}}), where the symbol (|cdot|_{mathrm{ess}}) denotes the essential norm of an operator.

It is shown that if is an upper-triangular operator matrix acting on the Hilbert space and if denotes the essential spectrum, then the passage from to is accomplished by removing certain open subsets of from the former.

For a given function essentially bounded, we denote the essential supremum and infimum of by and, respectively.

Findings denote the essential role life chances have on individuals accessing alternative forms of care.

Another example, from the current collections, is Olivier Theyskens's intensely focused use of sensual fabrics, like velvet, to denote the essential difference between masculine and feminine clothes.

Use of the terms associated with feudum to denote the essential characteristics of the early Middle Ages has invested the fief with exaggerated prominence and placed undue emphasis on the importance of a special mode of land tenure to the detriment of other, more significant aspects of social, economic, and political life.

Let T ∈ B ( H ), and let ∥ T ∥ e denote the essential norm of T, that is, the distance from T to the space of compact operators.

From now on, for a given function ξ ∈ L ∞ [ 0, ∞ ], we denote the essential supremum and infimum of ξ by ξ ∗ and ξ ∗, respectively.