Coupling integral

Two states /a and /b that are eigenfunctions of a Hamiltonian Hq in the absence of some external perturbation (e.g., electromagnetic field or static electric field or potential due to surrounding ligands) can be "coupled" by the perturbation V only if the symmetries of V and of the two wavefunctions obey a so-called selection rule. In particular, only if the coupling integral (see Appendix D which deals with time independent perturbation theory)... 

Selected applications of coupled SEE-SEC consider the analysis of tocopherols in plants and oil by-products (65) or the analysis of lipid-soluble vitamins (66) by using a dynamic on-line SEE-SEC coupling, integrated in the SE chromatograph, based on the use of micropacked columns. 

Close-Coupled Integrated Two-Stage Liquefaction (CC-ITSL), 6 843 Close-coupled single-stage horizontal end suction pump, 22 63-64 Close-coupled vertical centrifugal pump designs, 22 64... 

We have assumed here that J can be treated as a constant. In some types of calculation, the explicit distance-dependence of the electron coupling integral must be taken into account. Little is yet known of the appropriate form of such a dependence. ... 

Equation (4.2) can be transformed into two coupled integral equations for the amplitudes on the ground- and excited-state potential-energy surfaces, namely,... 

As noted above, inherent in the expressions derived for et in the previous section is the assumption that the intemuclear separation between reactants, r, is fixed. In fact, kti has a dependence on r, ket = ket(r), arising from solvent trapping (equation 23), and a much stronger dependence on r through the electronic coupling integral V. 

The relevance of a recorded impedance spectrum is not clear, as is the case for experiments done with instrumental methods. A number of potentially occurring errors can give rise to a distortion (small or large) of the impedance spectrum, with a certain impact on the interpretation of the data and the curves. A method to analyse the obtained impedance spectra makes use of so-called Kramers-Kronig transformations50,51, which are a set of coupled integral equations that describe the relationship between the real and imaginary part of the impedance. For impedance Z ... 

The formulation outlined above is in configuration space, but several authors, notably Ghosh and his collaborators (Chaudhury, Ghosh and Sil, 1974) and Mitroy (1993), also Mitroy, Berge and Stelbovics (1994) and Mitroy and Ratnavelu (1995), have preferred to work in momentum space with a set of coupled integral equations rather than the coupled integro-differential equations (3.31) and (3.32). 

This approach, based on a complex-valued realization of the PCM algorithm, reduces to a pair of coupled integral equations for real and imaginary parts of apparent charge density for tr(f,to) [13]. An alternative technique avoiding explicit treatment of the complex permittivity has been also derived [14,15]. The kernel K(f,f, t) of operator K does not appear explicitly. However, its matrix elements can be computed for any pair of basis charge densities p1(r) and p2(r) px k p = Jp2(j) (r, f)d3r, where tp(r, t), given by Equation (1.137), corresponds to p(r) = p2(r). 

To the lowest order, the electronic matrix elements in Eq. (8) are determined by the vibronic coupling integral [37, 38]... 

Interpretation of H NMR spectra is based on consideration of three interrelated types of information integration of signal peaks, chemical shift, and spin-spin coupling. Integration of the signal peaks provides the ratio of hydrogen atoms in the compound. The concept... 

Gollakota, S. V, Lee, J. M., and Davies, O. L., Process Optimization of Close-Coupled Integrated Two-stage Liquefaction by the Use of Cleaned Coals, Fuel Proc. Technol., 22, 205-216 (1989). 

A riser-type of FBR was presenfed by Mafsuda and Hatano (2005) for the photocatalytic removal of NOx. Here, fhe FBR was coupled integrally to a cyclone-separating system that returned the carried-away titanium dioxide-loaded silica-gel particles. 

In this context, several levels of MetM and ACTM coupling/integration can be considered ... 

On-line integration of ACTM into MetM, where feedbacks may be considered. We will use this definition for on-line coupled/integrated modelling... 

Full chain of two-way interactions, feedbacks included on each time step (online coupling/integration)... 

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