INDEX label

Only the so called first quantisation in particular Schrodinger s formulation, starts off heavily on the wrong foot, by assuming an index, label or name to each particle. But this individualisation is immediately wiped out by systematically permuting the labels of all like particles Any one labelled particle occurs simultaneously in all positions occupied by like particles (Post [1963]). 

NB In the inverse we have interchanged the index labels of the irreducihle representation matrix. 

The surface structures observed for gas adsorption on stepped surfaces are listed in Table 5.6. In this table the stepped surfaces are denoted by either their Miller index label or stepped surface designation, depending on which system was used by the original author. By using Table 5.5 one may convert back and forth between these two systems. It is interesting to compare the surface structures formed on stepped surfaces to those... 

This Hamiltonian is similar to the usual electron-phonon Hamiltonian, but the vibrations are like localized phonons and q is an index labeling them, not the wave-vector. We include both diagonal coupling, which describes a change of the electrostatic energy with the distance between atoms, and the off-diagonal coupling, which describes the dependence of the matrix elements tap over the distance between atoms. 

Similar conclusions have been arrived at in an SPR model designed as a DNA probe (24). The DNA probe sequence was immobilised to a thiol modified silver film deposited on a waveguide in a SPR format. The probe showed a characteristic change in the SPR excitation on binding complementary DNA. In this instance the use of an antibody to double stranded DNA could be used in a subsequent step to check the specifity of the result and allow an independent estimation of the level of detection. Without the addition of high molecular weight or refractive index labels however, this technique could not achieve a desirable level of detection, nor eliminate non specific interactions. 

An overview of the energetics and possible depletion mechanisms of excited electronic states is named a Jablonski diagram. Herein, singlet states are symbolized by So, Si, S2, and so on, and triplets by T0, Ti, T2, and so on, where the index labels their energetic order and should not be confused with tensor components. A typical Jablonski diagram for an organic molecule is shown in Figure 19. 

Often in science, one associates transformation properties under coordinate transformations with the sub-index labels of a matrix M = R. And, one can associate such behaviour separately for each member of the index pair. Thus, the human in charge has the freedom to construct relationships between two different coordinate systems, each linked to one of the indices. Generally, R is real orthogonal but not symmetric. 

Collisional contributions in the above set of equations due to the elastic Coulomb interactions are the terms Rap and Qap. We now proceed to express more explicitly the source terms Sn[fa] due to atomic and molecular interactions with neutral particles. These result from the collision integrals Can in (2.1). These integrals may be considered separately for each individual collision process, and then summed up. We omit the index labelling a particular type of process in the following discussion. 

Condition (26b) is, for CASSCF wavefunctions, automatically fulfilled if both p and q belong to the same orbital space (inactive, active or external). From now on the following index labelling will be used ... 

The index is the root you are taking, and the radicand is the number under the radical. If there is no index labeled, then it is just the square root. 

We first assume that the functions have the symmetry of a local site a and thus the wavefunctions xLa realize the irreducible representation of the ath site group, where the index / labels this representation. Let xl.g(R) be the character of a matrix which corresponds to an element R in the /th irreducible representation of the site group, and x g (R) be the character of a matrix corresponding to an element R of a factor group in its th irreducible representation. The character of an reducible representation of a factor group, spanned on functions L (0) and corresponding to an element R, is given by... 

In this expansion we begin to try to make a distinction amongst the increasing profusion of sub- and super-scripts by using the fauniliar integer indexing labels i, j, k, ,... to label MOs (or MO-related quantities) and the less familiar indexing quantities r, s, f, ,... to label the basis functions (and quantities related to basis functions). ... 

Single index labels (Mabels) for PW/m increments 2.5 Formulae for the PW/m asymptotic expansion coefficients of 161... 

Figure 28 Definition of the angle 6 from the Poincare section of a torus attractor derived from experimental data. The index labels the order with which points appear in this section as the trajectory winds its way over the surface of the torus. This definition can be generalized to a wrinkled or fractal torus.

FIG. 5. Criticality safety index label. The background colour of the label shall be white, the colour of the printing shall be black. 

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