Sentence examples for sample problem with from inspiring English sources

Otherwise, if we reject the null hypothesis of homogeneity in (1), the hypothesis to be tested is (2) H 0 : μ 1 = μ 2   subject   to   Σ 1 ≠ Σ 2. This is the usual test for equality of means in a two sample problem with unequal covariance matrices, also called Behrens-Fisher problem (see [ 25]).

Numerical results are shown for sample problems with the Mie Grüneisen equation of state for characterizing the materials of interests in both one and two space dimensions that demonstrate the feasibility of the proposed method for interface-sharpening of compressible two-phase flow.

There were sample problems with a flat gamma prior for the smoothness parameter σ 1 2.

This was identified as a difficult computational problem [ Ghosh et al., 2008], but if we assume that the standard errors of the stage 1 and 2 estimates are fixed and known, this reduces to a sampling problem with weights given by the marginal power of each SNP.

Figure 7 shows a sample problem generated with SES, while Fig. 8 shows an example of the knowledge expressed in Prolog.

Overall, the predicted GX-FBA solution for this sample problem agrees with expected metabolic behavior when oxygen concentration in the medium is reduced.

For small samples (problems with fewer than 400 units and up to three outputs and three inputs), Algorithm #1 fits results better than Algorithm #2, which is more efficient as of samples that exceed 800 units.11 Since the samples analyzed in our research are made up of around a hundred schools, we apply the simple Algorithm #1, which is described below.12.

samples to make decisions and a larger sample size problem (with continuous/discrete decision variables fixed) is solved to re-evaluate the objective values.

This greatly diminishes the sampling problem associated with the conventional strategy.

This provides an efficient and objective way of decomposing parameter space into a finite number of regions representing qualitatively distinct phenotypes, which greatly diminishes the sampling problem encountered with the conventional strategy described in the introduction.

New operations are presented at the top of each sheet, sometimes with sample problems and a cursory explanation.