Sentence examples for representations we show from inspiring English sources

For unitary representations we show that a vector v is smooth if the corresponding positive definite function ⟨π(g)v,v⟩ is smooth.

After describing the foundations of the framework and highlighting its advantages with respect to close representations, we show its adaptability to a variety of facial mesh surface processing tasks which includes mesh regularity assessment, facial surface cropping, facial surface compression, and facial surface alignment.

Based on the parity of this representation we show how the mirror neuron system may facilitate the interaction between two robots.

Using this representation we show how to employ model-based diagnosis techniques for debugging faulty configuration knowledge bases, detecting infeasible requirements, and for reconfiguring old configurations.

For a modulus in the adjoint representation, we show that the theory does not have stable vacua with homogeneous anisotropic non-Abelian field strength condensates, although there are metastable vacua.

In a visual representation, we show strong connectivity as bold bonds and weak connectivity as standard bonds.

Then, using this channel representation, we show in Section 3 how the correlation between these time-frequency channels can be used in a selective MIMO BC to reduce the number of feedback bits while conserving the full multiplexing gain.

As a representation, we show the differences in the node degree (i.e., degree centrality) for each enzyme among the chaperonin substrate classes.

"And for me and Alan [Yang, the co-writer] the representation we showed was of the immigrant story, parents a little closed-off, kids a little ungrateful, kids that learn about their parents' story and then aren't sure what to do with that information.

By applying representation theory we show how to decompose a Hilbert space of solutions to certain classes of equations as direct integrals.

In a representation result we show that the class of revision functions captured by Horn compliant total preorders over possible worlds is precisely that given by the (extended) set of Horn revision postulates.