INDEX vector

The NSS concept corresponds to an operator attached to an arbitrary number of nested sums. In other words, a NSS represents a set of summation symbols where the number of them can be variable. In a general notation one can write a NSS as E (j=i,f,s,L) where the meaning of this convention corresponds to perform all the sums involved in the generation of all the possible values of the index vector j under the fulfillment of the set of logical expressions collected in the components of the vector L. The elements of the vector j have the following limits ... 

The term D(j) can be taken as a Slater determinant, formed by n functions chosen from a set of in available spinorbitals, and ordered following the actual internal values of the j index vectors. That is ... 

If the pure component samples were prepared in a transparent matrix, the spectra should be normalized to produce a pure spectrum at unit concentration. It is also common to estimate an offset or randomly varying linear or quadratic baseline when ming DCLS. To estimate an offset, a vector of ones is added to the S matrix as another component- For a linear baseline, a running index vector and a vector of ones are added to the S matrix. The multiplier for the running index accounts for the slope of the baseline and die vector of ones accounts for the offset. Finally, for a quadratic baseline, a running index squared vector, a running index vector, and a vector of ones arc added to the... 

Direct Cl methods often require an index vector which points to a list of all allowed excitations from a given iV-electron basis function. Using alpha and beta strings, the index vector need not be the length of the Cl vector—its size is dictated by the number of alpha or beta strings, which (for a full Cl) is approximately the square root of the number of determinants. This results from the fact that in determinant-based Cl, electrons in alpha spin-orbitals can be excited only to other alpha spin-orbitals, and electrons in beta spin-orbitals can be excited only to other beta spin-orbitals (because of the restriction to a single value of Ms). 

When the hypothesis of isotropy is invalid, the discretization has to be realized for the three components of the velocity vector. An alternative and more convenient notation with respect to that in Eq. (7.50) makes use of an index vector i = (hJiJs) and defines the discrete velocity as... 

Figure 3.82. Definition of Euier angies describing orientation and principai components of maximum absorption index vector, kmax-...

Furthermore, let I be an index vector containing loop iterators and let /(/) be an affine function on I. Then all variables of the program are of the form... 

The first step in the extraction process is to parse the MATLAB code and to convert it into a number of node domains. We create a node domain for every function-call statement separately. Its domain, the context of the function call, is derived from the expressions of the active loop and conditional statements. The index vector of a node domain is formed by the iterators of the active FOR-statements. For example, Floyd-Steinberg has one node domain, whereas the QR algorithm has two node domains. 

Fig. IV.l. Nonintegral index vectors (q) of carbon atoms of the orthorhombic...

A unit cell of a crystal lattice is denoted with an index vector L with integral components h, k, 1). The i-th atom of the L-iti cell may be denoted with a nonintegral index vector... 

The covariant (lower index) and contravariant (upper index) vectors in the above equations are related in the usual way through the metric tensor as... 

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