Sentence examples for all the distinct elements from inspiring English sources

The cylinder model was filled with cubic array of spheres with a specified radius, and was considered as a whole mixture with uniform contact properties for all the distinct elements.

Horovitz perfectly captures not just his experiences as a caddie, but the distinct elements of the university town itself.

In 1901, in a paper before the French Geologic Society, Lugeon presented his synthesis of all the distinct and seemingly disparate elements of Alpine geology.

Then, M l ( x ) = ∏ ξ ∈ B l ( x − ξ ) Open image in new window, where B l are all distinct elements of the sequence { ( α l ) m : m = ∏ j = 1 s q j s j, q j = p j m j, 0 ≤ s j ≤ h − 1 } Open image in new window.

Thus, M 0 1 ( x ) Open image in new window, M 1 1 ( x ) Open image in new window, and M 2 1 ( x ) Open image in new window have, as roots, all distinct elements in the sets B 0 1 = { α 0 } ⊂ G 1 Open image in new window, B 1 1 = { α 1, α 1 2 } ⊂ G 3 Open image in new window, and B 2 1 = { α 2, α 2 2, α 2 4, α 2 8 } ⊂ G 15 Open image in new window, respectively.

A graph is complete if E contains all pairs of distinct elements of V. G A = (A, E A) is a subgraph of G = (V, E) if A ⊆ V and E A = E ⋂ (A× A).

In all, the work has three distinct elements played simultaneously: the main melody, the continuous thirty-second note broken chord figures, and a descending eighth note motif.

This is because each triangle has exactly two tails, and in a set of conflict-free triangles, all the tails must be distinct elements.

The group then consists of eight distinct elements, all of which can be generated by various combinations of just two operations: a 90° rotation and a flip.

For any six tips u, v, x, y, c, d∈ S, which may not be all of them distinct, we use θ u, v, x, y, c, d) to denote the number of distinct elements among these tips.

where ({sum nolimits }_{c}) denotes the summation over all the ({{n}choose {m}}) combinations of m distinct elements {i 1, …, i m } from {1, 2, …, n}.