Sentence examples for adjoint relations from inspiring English sources

The adjoint relations hold globally, and at the element level with the inclusion of a natural discrete element boundary flux term.

The results are applied to the Q-function for S and H and the Q-function for S and H∞, where H is a self-adjoint operator in a Pontryagin space with a cyclic element w, H∞ is the self-adjoint relation obtained from H and w via a rank one perturbation at infinite coupling, and S is the symmetric operator given by S=H∩H∞.

We may find that the sequence a satisfies an adjoint linear recursive relation, as shown in the following theorem.

It is shown that the feedforward action has relation to the adjoint system of the closed nominal system.

More generally, Lawvere showed how syntax and semantics are related by adjoint functors.

Also, they involve the group adjoint representation which establishes an equivalent relation among all conjugate sub-algebra elements.

If for all triplets of input variables { x i, x j, x k } the rank-root relations are known, then the adjoint tree structure of S can be directly reengineered from this set of relations.

The relations derived contain eigenvalue, eigenvector and adjoint eigenvector sensitivities.

If A and B are self-adjoint operators, the order relation (Ageq B) means, as usual, that (A-B) is a positive operator.

Note that the equivalent backward delayed system is described by a time-delayed BSDE, so the adjoint equation of the time-delayed BSDE via duality relation is an anticipated SDE.

The self-adjoint operators m ˜ x satisfy again the Majorana anticommutation relations { m ˜ x, m ˜ y } = 2 δ x, y 1.