Matrix, defined

The native form of chromatin in cells assumes a higher order stmcture called the 30-nm filament, which adopts a solenoidal stmcture where the 10-nm filament is arranged in a left-handed cod (Fig. 5). The negative supercoiling of the DNA is manifested by writhing the hehcal axis around the nucleosomes. Chromatin stmcture is an example of toroidal winding whereas eukaryotic chromosomes are linear, the chromatin stmctures, attached to a nuclear matrix, define separate closed-circular topological domains. 

The sum of the product of MO coefficients and the occupation numbers is the density matrix defined in Section 3.5 (eq. (3.51)). The sum over the product of the density and overlap matrix elements is the number of electrons. 

This matrix C is essentially By5, B being the matrix defined in Section 9.5 by the equation By B-1 = yuT. The total charge operator... 

Rjj Matrix defining how a specific reaction contributes to a change in... 

The C matrix, the columns ofwhich, Cj(, are the eigenvectors of H, is normally not too different from the matrix defined above. However, the QDPT treatment, applied either to an adiabatic or to a diabatic zeroth-order basis, is necessary in order to prevent serious artefacts, especially in the case of avoided crossings [27]. The preliminary diabatisation makes it easier to interpolate the matrix elements of the hamiltonian and of other operators as functions of the nuclear coordinates and to calculate the nonadiabatic coupling matrix elements ... 

Mathematics texts use the term transpose conjugate for this matrix and apply the term adjoint to the adjugate matrix defined in equation (1.28). 

The output sensitivity matrix (dyT/dk)T is related to the sensitivity coefficient matrix defined as... 

To decouple the system equations, we require that GDGC be a diagonal matrix. Define G0 = GDGC, and the previous step can be solved for C ... 

This formula can be generalized to several reaction coordinates with little difficulty. In that case, is a matrix defined as the inverse of matrix Zc... 

The obvious way to form a similarity between the Wigner rotation matrix and the adiabatic-to-diabatic transformation matrix defined in Eqs. (28) is to consider the (unbreakable) multidegeneracy case that is based, just like Wigner rotation matrix, on a single axis of rotation. For this sake, we consider the particular set of x matrices as defined in Eq. (51) and derive the relevant adiabatic-to-diabatic transformation matrices. In what follows, the degree of similarity between the two types of matrices will be presented for three special cases, namely, the two-state case which in Wigner s notation is the case, j = j, the tri-state case (i.e.,j = 1) and the tetra-state case (i.e., j = ). 

To obtain the 7r-orbitals polyene model system and their orbital energies j one first diagonalizes the N x N matrix defined by equation 15, N being the number of basis functions ryy... 

Vectors are a special type of matrix, defined as having one column and n rows. For example in (A.2) x has n components... 

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