INDEX coefficient matrix

MODIFY - addressing of members of the coefficient matrix are adjusted to allocate their row and column index in the banded matrix. 

In a computer program for the Wang-Henke bubble-point method, 10100 storage locations are wastefully set aside for the four indexed coefficients of the tridiagonal matrix solution of the component material balances for a 100-stage distillation column. 

In Equation 7.33 we have written out both the g-value and the zero-field coefficient of the basic S2 interaction term in the form of diagonal 3x3 matrices in which all off-diagonal elements are equal to zero. The diagonal elements were indexed with subscripts x, y, z, corresponding to the Cartesian axes of the molecular axes system. But how do we define a molecular axis system in a (bio)coordination complex that lacks symmetry The answer is that if we would have made a wrong choice, then the matrices would not be diagonal with zeros elsewhere. In other words, if the spin Hamiltonian would have been written out for a different axes system, then, for example, the g-matrix would not have three, but rather six, independent elements ... 

We start by creating a matrix. This matrix is based on the index of coefficients that are to be ultimately produced. Savitzky and Golay labeled the coefficients in relation to the central data point of the convolution, therefore a three-term set of coefficients are labeled -1, 0, 1. A five-term set is labeled -2, -1, 0, 1, 2 and so forth. 

Index L is given to GL to distinguish it from the Lyapunov function for closed systems. Strictly speaking, it is not the Lyapunov function, since it cannot be differentiated on the hyperplanes prescribed by the equations 2, = 2 . Therefore, instead of estimating its derivative by virtue of eqn. (152), let us determine its decrease for a finite period of time x. Actually, we will find an ergodicity coefficient [42] for the matrix exp xK... 

Consider first a series of eight views of the same data matrix for the intensity coefficient ii for a relative refractive index m of 1.200. Figures 1 through 8 represent different perspective viewpoints of the same three-dimensional matrix viewed from the front, right-hand side, back, etc., so as to reveal details of the simple behavior of complicated mathematical functions. 

We are still dealing with two species as in the uncoupled case and the same boundary conditions apply they are reformulated in the present matrix-vector form here. As noted above, there is a common condition for all experiments, the flux condition (6.30), generalised to include the normalised diffusion coefficients, to the gradient condition (6.32), and we now write out its discrete form fully, pairing the two species terms for each spatial index ... 

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