Sentence examples for unitary case from inspiring English sources

We prove that de Branges spaces of entire functions describe universality limits in the bulk for random matrices, in the unitary case.

In the unitary case, the superconvergence to free Brownian motion and that to the Haar measure are shown to be uniform over the entire unit circle, implying further a free entropic limit theorem and a universality result for unitary free Lévy processes.

The third element does not yet occur in the unitary case described in [22]: it is the projector P S onto the totally anti-symmetric state.

We treat the selfadjoint case, the positive case, the J-unitary case, the positive real case, the dissipative case and the contractive case.

The schemes are also not constrained to the unitary B case and can be extended to any general deterministic B matrix.

To use the well-known case of the melody, moments of quality and of intensity form in that case a unitary whole which is perceptible as a "quality of form," and it is precisely the unitary character of this perception, the fact that it is perceptible in one stroke and immediately as unitary form, that Stumpf tries to account for with the aid of the notion of relation of fusion.

For N = 2 layers, the algorithm is optimal and reduces to that in [45] since the Ws are unitary in this case.

The normal unitary effort, in case of materials that behave structurally, can be expressed by introducing a complex elasticity module: E ′ = E · u + i · v, (16 where, E represents the elasticity module for steel.

In some cases unitary pseudogenes are the direct remains of a gene that has become dysfunctional due to mutations.

A similar formula in the case of unitary operators was obtained by Neidhardt (Math. Nachr. 138 (1988) 7).

For the important special case of unitary analysis polyphase matrices we obtain an explicit expression for the minimum achievable disturbance attenuation.