Sentence examples for linear differential expressions from inspiring English sources

Later, some authors studied the defect index of L 2, which, in fact, is a class of fourth-order formally self-adjoint linear differential expressions with real coefficient, and they have obtained a few excellent results [5 8].

The problem on the defect index of the second-order formally self-adjoint linear differential expression with real coefficients L y = − ( p y ′ ) ′ + q y, on  [ a, b ), was first studied by Weyl [4].

In this study, the spectrum and resolvent of the maximal differential operator (L_{lambda}) generated by the linear differential expression ell_{lambda} y)=y^{primeprime}+q_{1}(x y^{prime}+ bigl[ lambda ^{2}+lambda q_{2}(x)+q_{3}(x) bigr] y and the boundary condition (y^{prime}(0 -hy(0 -hy have been investigated in the space (L_{2}(mathbb{R} ^)).

Test for differential expression: Differentially expressed genes were identified by fitting the moderated t-test linear model to the data (separately for each gene).

The linear model and differential expression functions were applied to all microarray data sets.

This procedure allows for both increases and decreases in gene expression to be detected using linear models of differential expression.

The third analysis offered by Pathway Processor 2.0 is the application of the recently developed GSVA, coupled with linear models for differential expression analysis.

In conclusion, array quality measures can be used to set quality thresholds, to provide valuable information that can be used to improve the linear model of differential expression, or to correct expression signal prior to assessing differential expression.

To address this issue, we created a linear model measuring differential expression with region and with disease, which also takes into account four major cell types in the brain using linear regression (Materials and methods).

The gene regulatory dynamics follows a system of linear differential equations: where x t) is expression vector at time t and A is the connectivity matrix with a i,j as the regulatory strength of gene j on gene i (a ij = 0 if j does not regulate i).

Linear differential equation.