Sentence examples for with smooth data from inspiring English sources

One method, which we designate as KKH, is superior in this problem with smooth data.

With smooth data, D2 peaks at any discontinuity, whether an increase or a decrease, but given the highly non-smooth nature of these data, the precise year of change indicated by the D2 statistic does not always coincide with a significant change relative to the full data series [18].

Analysis was performed with full experimental datasets of the five scans and with smoothed data and reduced TACs, respectively, as described under the 'Methods' section.

The three-dimensional mesh plots of nocturnal leaf stomatal conductance (gn) and nocturnal leaf stomatal conductance (En) with soil moisture and root-zone temperature were created with smoothed data calculated from running averages using SigmaPlot.

Our hybrid difference scheme for problem (1.1 - 1.2 1.1 - 1.2isication of the Numodification used in [11–14] fof singularly perthebed reactioNumerovschemeroblems with susedcinntly smooth data.

Singularly perturbed reaction-diffusion equations with sufficiently smooth data have been studied extensively; see, for instance, [3, 4] for a survey.

This hybrid difference scheme for the singularly perturbed reaction-diffusion problem with a discontinuous source term is a modification of the difference scheme used in [11 14] for the singularly perturbed reaction-diffusion problem with sufficiently smooth data.

Moreover, using new techniques presented in this paper, we would like to extend results from [13, 14] (based on ideas presented in [15]) where problems of the above form but with appropriately smooth data function have been discussed.

This permits the straightforward application of trapezoidal quadrature and the standard FFT, with superalgebraic convergence for smooth data.

As a branch of partial differential equations, singular perturbation problems for differential equations of elliptic type with smooth coefficients and smooth data, arising in many areas, such as fluid mechanics, heat and mass transfer in chemical engineering, theory of plates and shells, have been extensively studied since the 1960s; see [4] for instance and the references therein.

Zhao [2] proved the global existence and uniqueness of smooth solutions to problem (1.1 - 1.7 1.1 - 1.7oth initial data (u_{0},theta_{0}in H^{3}) and (phi_{0}in H^{5}).