Sentence examples for arbitrary directions from inspiring English sources

Specifically, the weak form for the penalty method is acquired by requiring that the directional derivative of the penalty functional Π k vanishes for all arbitrary directions δ u h in the homogeneous zero Dirichlet space X 0 h, i.e. (A.1) D Π k (u h ) [ δ u h ] = 0, ∀ δ u h ∈ X 0 h.

The discrete weak form for the weakly penalized formulation can be obtained by requiring that the directional derivative of the total potential energy functional vanishes in all arbitrary directions δ u h ∈ X 0 h at u h, i.e. (29) D Π P (u h ) [ δ u h ] = 0, ∀ δ u h ∈ X 0 h, with X 0 h the homogeneous zero Dirichlet subspace of X h.

His pictures got bigger and stranger, with elements that escaped from the frame to go off in seemingly arbitrary directions on the wall.

"But the more I listened to the writers, I felt they were taking the characters in pretty arbitrary directions, seemingly not based on any kind of knowledge of psychiatry or Mafia life.

Two Australian physicists — brothers and lifelong cricket fans — have now devised equations based on Newton's second law of motion that they say explain the influence of wind on balls that are spinning in arbitrary directions.

Its principal directions are found to point in arbitrary directions, uncorrelated with the Fe–O bonds.

Proof Suppose that d is an arbitrary direction.

The crack is oriented in arbitrary direction.

We analyze the response of these composites to a dynamic load with an arbitrary direction.

This paper presents a general solution to the exponent q for any arbitrary direction of scaling.

An external pulling force is acted on the cylinder in an arbitrary direction.