Sentence examples for both the linear case from inspiring English sources

On the other hand, negative integer values of n are excluded for the following reason: In both the linear case (equation (1)) and the Lane-Emden case (equation (8)), when oscillatory solutions occur, their oscillations always develop about a trivial solution ((y=0) in most well-known cases; see [6]) which serves as a baseline for the oscillations.

In section Numerical results we present numerical results for both the linear case and the classical stiff system described by the Schlögl reaction [ 34].

This article is devoted to study the large time behavior of the solution to a conservative aggregation-fragmentation equation, a class of equations that arises in many applications and that has been widely studied both in the linear case [8, 14, 18, 19] and with nonlinearities [6, 9 11, 13, 20].

In the past, both linear and quadratic boundary treatments have been used and error bounds have been derived in both cases, showing that the linear case gives uniform second-order accuracy, whereas the quadratic case gives third-order accuracy at the boundaries and second-order accuracy internally.

This contrasts with the Dirichlet case where both quadratic and linear treatments give O Δ2) error, although the coefficient of error may be much larger for the linear case.

Therefore, the linear case is discussed first.

Uses folding in the linear case, which speeds up linear SVM training by an order of magnitude.

Computationally checkable LMI conditions are provided for the linear case.

While for the linear case these kinetic boundary conditions suffice, we need additional conditions in the non-linear case.

Then, the linear case of SHS is investigated to show the application of the theorem.

As in the linear case, it shrinks coefficients and produces some coefficients that are exactly zero.