Sentence examples for a directed triangle from inspiring English sources

Proof Suppose that H u, N contains a directed triangle.

Theorem 3.2 implies that there is a directed triangle ∞ → u N → ε u − 1 ε N → ∞ in H u, N. □.

Links of the type u → v and u ↔ v can be further described as 'Simple closure' and 'Double closure' ties respectively if they close at least a directed triangle (i.e., there existed a node w such that the arcs u → w and w ↔ v already existed).

Because of the transitive action, the form of the directed triangle can be taken as ∞ → u N → r N → ∞.

Theorem 3.7 H u, N contains directed triangles iff there exists a unit ε ∈ Z [ i ] such that ε 2 u 2 ∓ ε u ± 1 ≡ 0 ( mod N ).

Thus, the subgraphs H 1, 2 + i and H 1 + i, 2 + i have directed triangles.

So, the subgraphs H 1, 2 i and H 2 i − 1, 2 i have no directed triangles.

At Shaw's urging, Salter adapted a Shaw short story into a film, "Three" (1969), which Salter directed: a love triangle and French travelogue starring Sam Waterston and Charlotte Rampling.

A film having its festival premiere is "The Private Public," the story of a love triangle, directed by Dana Altman, grandson of the director Robert Altman.

where the above inequality follows as a direct consequence of the triangle inequality.

p-Polarized light from the LED was collimated and directed to an SF11 equilateral triangle prism (Edmund Optics) at an incident angle near SPR resonance angle.