Sentence examples for singular expansion from inspiring English sources

The latter stems from the singular expansion of C g (z).

We show that for various energy models the singular expansions of both these functions are essentially equal modulo some constant.

Then the probability of a particular structure σ to be the mfe-structure of a uniformly random input sequence is (1) P = W ∑ σ ′ W. In this section we compute two generating functions and their singular expansions [ 11].

Step (69) uses the singular function expansion of H 12, step (70) substitutes the construction of (X_{2_{mathsf {Int}}}), step (71) rearranges terms and step (72) leverages the orthonormality of the right singular functions.

We know from Lemma 1 that there exists a singular value expansion for H 11, so let (left {sigma _{11}^{ k)}, U_{11}^{ k)}, V_{11}^{ k)}right }_{k=1}^{infty }) be a singular system for the operator (mathsf {H}_{11}: mathcal {T}_{1}rightarrow mathcal {R}_{1}) (see Lemma 5 in Appendix B for the definition of a singular system).

Moreover, the operation of C on any ({x}in mathcal {X}) can be expanded as ( mathsf {C} {x} = sum _{k} sigma _{k} langle {x}, {v}_{k} rangle {u}_{k}, ) which is called the singular value expansion of C x. See Section 16.1 and 16.2 of [32] for a proof.

It is confirmed that faster convergence is obtained using the singular eigen-expansions in approximating stationary Navier-Stokes solutions in general domains.

— When the three-million-pound Great Platte River Road Archway, as long as a football field, was suspended over Interstate 80 here nearly a decade and a half ago, promoters hailed it as a singular monument to westward expansion that would draw at least a million visitors a year.

Pairs of singular vectors and corresponding expansion coefficients constitute pairs of SVD spatial modes.

The integral equation is converted to a pair of the singular integral equations using asymptotic expansion method.

Coefficients of the singular terms of the asymptotic expansion were determined by comparison with the numerical solution in the close vicinity of the singular contour.