Sentence examples for examples we prove from inspiring English sources

As examples, we prove the reduced group C⁎-algebras of the (non-amenable) affine groups of the affine planes have a rigidity property.

[14] In the following examples, we prove that label-free MST is a valuable tool to study the binding of numerous types of ligands to different protein classes.

Additionally, in specific examples, we prove whether the non-informative margins condition is satisfied or not, and in a simulation study we demonstrate the consequences when the conditional models are compatible but do not satisfy the non-informative margins condition.

As an example, we prove a closed high-order form of the classical Jacobiʼs formula.

As an example, we prove that the standard Podleś sphere is equivariantly Poincaré dual to itself.

For example, we prove that enforcing arc consistency on the original formulation is equivalent to enforcing it on the hidden transformation.

As an example, we prove the existence of the multi-polaron in the Pekar Tomasevich approximation, for certain values of the coupling constant.

As a concrete example, we prove a linear rate of convergence for a hidden Markov mixture of two isotropic Gaussians given a suitable mean separation and an initialization within a ball of large radius around (one of) the true parameters.

For example, we prove that the performance of the forward checking algorithm applied to the hidden transformation of a problem is within a polynomial bound of the performance of the same algorithm applied to the dual transformation of the problem.

For example, we prove a result analogous to Sakai's famous characterization of von Neumann algebras as the C*-algebras with predual, namely, that the σ-weakly closed unital (not-necessarily-selfadjoint) subalgebras of B(H) for a Hilbert space H, are exactly the unital operator algebras which possess an operator space predual.

For example, we prove (12).