Sentence examples for integral due to from inspiring English sources

Malononitrile substitutions show a large effect in lowering the molecular LUMO energy level but induce a smaller charge transfer integral due to the resulting reduced crystal order caused by the resulting steric hindrance.

Similarly to the experimental results, simulations show that the charge separation in sample #2 turns out to be small (8% reduction in overlap integral) due to the strong exciton's binding energy (Eb = 40.04 meV).

The larger transfer integral due to the improved alignment of donor and acceptor states results in fast electron transfer across the interface, and the larger spatial separation of the bound electron hole pair has been shown to suppress the formation of BCPs, as the electron and hole are pushed out of their respective Coulomb capture radii, creating free charge carriers directly.

Applied to product measures this integration theory may be considered as an abstract version of the double operator integrals due to Birman and Solomyak.

In other words, the traction-free surface of the V-shaped notch does contribute to the J-integral due to the non-zero projected values induced from the J2-integral.

The magnitudes of the magnetic fields in this study are small enough to neglect phase changes in the transfer integrals due to the magnetic field.

I will describe a beautiful construction of the simplest quantum group from such integrals, due to Felder and Wieczerkowski: no prior knowledge or interest in quantum groups required.

The second formulation comprises a sum of boundary and field integrals; due to the field integrals, it has noticeably higher computational cost, obtaining though higher accuracy.

The numerical implementation is achieved using quadratic elements and domain integrals due to the shell curvature are transformed to the boundary.

The object we consider in this paper is a class of oscillatory integrals due to Ricci and Stein [5] T f ( x ) = p. v. ∫ R n e i P ( x, y ) K ( x − y ) f ( y ) d y, (1.5).

Using the same technique, in this paper, we establish certain new Grüss type fractional integral inequalities involving the generalized fractional integral operator due to Curiel and Galué (see [17]).