Sentence examples for dual elements from inspiring English sources

The dual elements of The Daughter's source material (acclaimed new Belvoir St production, long-enduring classic) help explain why stage-to-screen adaptations are popular in the first place.

Through this idea, he developed the principle of duality in projective geometry, which states that if a theorem is true, then its dual theorem obtained by switching dual elements (lines and points) and their corresponding statements is also true.

His development of the pole and polar lines associated with conic sections led to the principle of duality (exchanging "dual" elements, such as points and lines, along with their corresponding statements, in a true theorem produces a true "dual statement") and a dispute over priority with the German mathematician Julius Plücker for its discovery.

But, in nonconvex multiobjective optimization problem there exist no guarantee to existence dual elements for determining properly efficient solutions.

Proof We define a map G : A × V ˆ → V ˆ ∗ × Q ∗ by G ( ℓ, ( u ¯, p ) ) = ( a ( ℓ, u ¯ ) + b ( p ) − m, b ( u ¯ ) − c ( p ) ), where V ˆ ∗ and Q ∗ are the duals of V ˆ and Q, and a ( ℓ, u ¯ ), b ( p ), and c ( p ) are the associated dual elements given by the Riesz theorem.

Broad themes one and two from the analysis map respectively to the dual elements of the recently published NICE Guideline [ 25], namely the 'assessment' and 'management' of psoriasis (see Figure  1 for a diagrammatic representation of the analytic themes and how they map to the NICE Guideline elements).

This is a known cone so-called Bishop Phelps cone generated by augmented dual element ((-y^, alpha )) and the norm (Vert cdot Vert).

Furthermore, it precisely captures the dual element isotope trends characteristic of different reaction pathways as well as their range of variation consistent with observed bulk isotope fractionation.

Consider the augmented dual element ((y^,alpha )) and define the following sublevel of zero begin{aligned} S y^,alpha )={yin mathbb {R}^{P}: langle y^,yrangle + alpha Vert yVert le 0 }.

A dual element Passive-Infrared (PIR) sensor is used with a rotating slit aperture to map a narrow scanning beam on the sensing elements through each lens of a Fresnel lens array.

The Theorem 6 shows that if the point (hat{y}in Y) is a properly efficient element, then there exists some augmented dual element ((y^, alpha ) in (mathbb {R}^{p}_)^{a#}) such that the sublevel (S y^,alpha )) separates (-mathbb {R}^{p}_) and ((Ybackslash bd(Y -{hat{y}}.) Assume that (hat{Y -{hat{yroperly efficient element of (1).