Sentence examples for a proper extended from inspiring English sources

Let be a proper extended real-valued function.

Let φ : C → ℝ ∪ be a proper extended real-valued function.

Let be a proper extended real-valued function and let be a bifunction of into, where is the set of real numbers.

Let f : C × C → R be a bifunction and Φ : C → R ∪ be a proper extended real-valued function, where ℝ denotes the set of real numbers.

Let be a proper extended real-valued function and let be a bifunction of into such that, where is the set of real numbers and.

Let be a proper extended real-valued function and be a bifunction of into, where is the set of real numbers.

Strictly speaking, a proper phase transition from extended to localized states only exists for (D=3), at some critical disorder intensity or, interchangeably, some critical energy known as the mobility edge.

Kemp's book is less a proper biography — he offers no extended account of Leonardo's illegitimate birth to a peasant's daughter, his apprenticeship in Florence to the sculptor Verrocchio, or his subsequent lifelong wanderings in the courts of Milan and France — than a series of intense, learned meditations on Leonardesque themes.

"We don't even intend to stay here long term, but we've scraped every penny together from the extended family to give this boy a proper British education.

Conversely, converting the CUG or GUG codons into a proper AUG codon (Aopt) results in predominant expression of the extended isoform.

This paper demonstrates that a proper design of environmental-regulation pricing strategies is able to promote Extended Product Responsibility for green supply chain firms in a competitive market.