Sentence examples for cases we obtain from inspiring English sources

In both cases we obtain the optimal convergent rate.

In many cases we obtain analytic representations, at least to a large extent.

In each of the three cases, we obtain a series of hypergroup algebras which include the commutative convolution algebras of K-biinvariant functions on G as special cases.

As special cases, we obtain the following E-optimal designs: (a) Group divisible (GD) designs with λ2=λ1+1 and (b) Rectangular designs with 2 rows and having λ3=λ2−1=λ1+1.

In both cases we obtain very simple and intuitive position-feedback solutions that do not rely on, rather unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-loop system with a Hamiltonian structure with desired potential and kinetic energy functions.

As special cases we obtain in particular, partitions of unity (a) in the Malliavin test functions on an abstract Wiener space; (b) in the first order Sobolev spaces on pinned and free loop spaces; (c) in the first order Sobolev spaces associated with reversible Fleming Viot processes.

In both these cases, we obtained a detailed public response from the companies.

In several cases we obtained a significant loss of the entrapped dye above the background level.

In both cases, we obtained similar results.

In five cases we obtained grouping clusters evidenced by colours.

Among these cases, we obtained an average acceleration factor of 82.38.