Sentence examples for a class of solutions from inspiring English sources

We shall present some properties of a class of solutions of problem (1 - 2).

From them, we derive improved reduced-order bases to approximate a class of solutions over a range of parameter values.

We also introduced a class of solutions uν in 1 1 correspondence with a certain class N0 of σ-finite measures ν on ∂E.

Here we are interested in a class of solutions which we regard to be very natural (see in fact the equivalence results obtained in [36]) and for which all the potential estimates described in this paper continue to hold.

For example, it can be used to to determine efficiently the number of solutions to an \(N\ -item search problem, heN\ -itemerform exhausearchsearches on a class of solutions to an Nproblemete problem and substantially reduce thencemputotional resources required for solving it.

We may consider the existence of a class of solutions that u ( t, x ) = u ( t ) for all x ∈ Ω, and B [ u ( t, x ) ] = 0 for all ( t, x ) ∈ [ − τ, + ∞ ) × ∂ Ω. For any given initial condition ϕ , we show that there exists at least the above-mentioned solution for PDEs (1.6), satisfying the initial condition u for all θ ∈ [ − τ, 0 ].

The Lax Friedrichs, Lax Wendroff and MacCormack methods belong to a class of solution methods that use artificial viscosity.

The proposed methodology is applied to address the estimation problem of a class of solution homopolymerization reactors, and is tested with a methyl-methacrylate polymerization run taken from a previous extended Kalman filter implementation study with experimental data.

It is shown that the standard derivation of the method is incomplete, in the sense that the steady state heat conduction equation admits a class of solution which is not encompassed by the assumed form of response, and a revised derivation is presented.

A class of admissible solutions to a hyperbolic system of equations modeling a gas fluidized bed is constructed.

Ivanov and Lyons [7] obtained a class of soliton solutions of the integrable hierarchy, which has been put forward in a series of works by Qiao [5, 6].