Sentence examples for derivatives in the second from inspiring English sources

The melting points or boiling points of common heteroaromatic compounds and their substituted derivatives are compared with those of benzene and its derivatives in the second table.

The relative sign change in the normal derivatives in the second part of (1.17) is of course being a side-effect of the opposite orientations of the outward unit normals to (Omega _{pm }) at points in (mathcal {C}= partial Omega _{pm }).

Using the notation E ( u ), from (2.1) we get ∂ t ( u φ N ) + ( u n + 1 φ N ) u x + φ N ( P ∗ E ( u ) ) = 0, and from (2.3), we also obtain ∂ t ( φ N ∂ x u ) + u n + 1 φ N ∂ x 2 u + ( n + 1 ) u n ( φ N ∂ x u ) ∂ x u + φ N ∂ x ( P ∗ E ( u ) ) = 0. We need to eliminate the second derivatives in the second term in the above equality.

First, the di-F-substitution on any site of main ligand dpq) can make the components of the LUMO of the derivative mainly distribute in the main ligand, whereas those of the LUMO in the parent complex I mainly distribute on the co-ligands, and then we can say that the di-F-substitution can activate the main ligand and passivate the co-ligands of the derivatives in the first excited states.

The second derivatives in the third equation have the meaning of the bending moment (when multiplied with EI), which is continuous for all x on the beam.

where is the derivative (in the second variable of the function ) in normal meaning and is the scalar product.

To construct some other new and useful iterative methods for finding the unitary polar factor of a matrix, we could again use the first sub-step of (9) along with different kinds of approximation for the newly appearing first derivative in the second sub-step.

and a similar expression holds for the derivative in the third line of (25).

Spatial derivatives involved in the first-order differential equations system are calculated by Fourier pseudospectral method, while the time derivative of the system is discretized by a predictor corrector method.

According the report, this effective manipulation enabled the CIO to triple the size of the portfolio that eventually produced its headline-grabbing derivatives losses in the first three months of 2012.

The degree of the coefficients is bounded by the order K of the first derivative in the given second-order equation if (K>1), and by 2 if (K=1).