Sentence examples for a remainder term from inspiring English sources

We also prove a strengthened form of Gross's logarithmic Sobolev inequality with a "remainder term" added to the left side.

To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term.

We find the optimal constant in a resulting Poincaré–Hardy inequality, which includes a further remainder term which makes it sharp also locally: the resulting operator is in fact critical in the sense of [17].

When the initial data is a sum of such quadratic oscillations, we prove that the associate solution is the superposition of the nonlinear evolution of each of them, up to a small remainder term.

It turns out, however, that we can deal with an incomplete canonical form (with a sufficiently small remainder term).

with a well defined remainder term that is 2 π ν -periodic in time.

Finally, in Theorem 4.3 we prove a sharpened form of (1.10), the complementary Golden Thompsen inequality of Hiai and Petz, incorporating a relative entropy remainder term.

After transforming the problem into a second-order system equation with remainder term, an adaptive second-order Arnoldi method is applied for the reduction of the computational complexity of structures, incorporating classical free- and constrained-layer damping treatments.

We show that the spectrum of the Friedrichs extension A of the operator res○A0○ext C∞c X →L2 X) is discrete, and derive asymptotics for the number Nχ of eigenvalues of A less or equal λ and with eigenfunctions in the χ-isotypic component of L2 X) as λ→∞, giving also an estimate for the remainder term in case that G is a finite group.

where is a positive integer, and is the remainder term.

Also, we state a conjecture on the exact value of the remainder term.