Sentence examples for assumption leads us from inspiring English sources

In a proof by contradiction, we assume the negation of a statement and proceed to prove that the assumption leads us to a contradiction.

The utilization of the assumption leads us to the inequality (411).

This assumption leads us to estimate covariance matrix, given by: begin{aligned} Sigma = Lambda Lambda ' + Phi, end{aligned} and, (Cov(mathbf F,mathbf Y )=mathbf L) or (Cov( Y_i, F_j ) = l_{ij}), The comparison of estimate of covariance to the original covariance tells us how the factor model fits the covariance matrix of original variable by the considered factors.

This assumption leads us to estimate covariance matrix, given by: begin{aligned} Sigma = Lambda Lambda ' + Phi, end{aligned} and, (Cov(mathbf F,mathbf Y )=mathbf L) or (Cov( Y_i, F_j ) = l_{ij}),  where (h_i^2 = sum _{j=1}^{k}l_{ij}^2) (Communality) and (phi _i=Var(Y_i) - h_i^2) (Uniqueness), for (i=1, 2, 3, ldots p).

This assumption leads us to conclude that the segmentation error can be considered zero or equal to the pixel resolution.

This assumption led us to investigate the possibility of introducing different functional group into the benzylic position just by varying the solvent in the rearrangement step (Fig. 5).

This assumption led us to investigate the putative association of HERG1 gene with SCH.

Unfortunately, all these assumptions led us to the same spot in the lane at the same time".

Why would making Normal assumptions lead us to such extremely misleading decisions in the case of online auction insurance underwriting?

As a result, outdated assumptions lead us to miss opportunities and chances worth taking that may be sitting right in front of us.

These assumptions led us to a required sample size of ∼210 children per group, for a total N=420.