This decomposition ( d= partial + bar{partial } ) extends to higher degree differential forms.
The biharmonic equation, the fourth degree differential equation in Eq. 4, can thus be solved with these four boundary conditions and a relevant loading expression, to obtain the expression for transverse deformation w x,y).
Moreover, by combining continuity equations for a cylindrical reservoir with the Darcy equation, we derive the diffusivity equation which is a second degree differential equation that correlates pressure as a function of time and radius of investigation.
Following an approach by Exner et al. (Commun Math Phys 26:531–541, 2014), we establish Lieb Thirring inequalities for general self-adjoint and second-degree differential operators with matrix valued potentials acting in one space-dimension.
As shown in Figure 3, at least 90 small-degree differential nodes must be selected to render the p-value of the pathway less than 0.01.
The three degree differential temperature between the groups was due to the solenoid was turned off when the sham-group was exposed.
As illustrated in Figure 3, when selecting high-degree differential nodes, provided that the number of differential nodes is 5 or greater, the pathway is highly significant (p-value < 0.01).
In this article we focus on elucidating key challenges that must be addressed to determine whether and to what degree differential exposure to environmental mixtures contributes to increased vulnerability of exposed populations.
MicroRNAs differentially expressed in every comparison and the degrees of differential expression are given in Supplementary Table 1.
By observing the residual plot, we can easily find genes that show significant variation in two groups of samples and learn the degrees of differential expression of genes.
