Diagonal map

If the canonical illuminant is assumed to be white light, then each vertex of Ain describes a possible illuminant. Each vertex can be viewed to be a diagonal map m, which has the form... 

If a mixture is not ideal, the phase-equilibrium maps are not as symmetric as the maps in Figures 4.67 and 4.68. In fact, the equilibrium line may cross the diagonal. Maps of vapor-liquid equilibrium data for nonideal mixtures are shown in Exercises 4.21 and 4.26. 

Fig. 8.6. (A) Two-dimensional diagonal maps of carboxymethylated reduced BPTI (B) single disulfide peak isolated by ion-exchange...

Figure C3.6.2 (a) The (fi2,cf) Poincare surface of a section of the phase flow, taken at ej = 8.5 with cq < 0, for the WR chaotic attractor at k = 0.072. (b) The next-amplitude map constmcted from pairs of intersection coordinates. ..,(c2(n-l-l),C2(n-l-2),C2(n-l-l)),...j. The sequence of horizontal and vertical line segments, each touching the diagonal B and the map, comprise a discrete trajectory. The direction on the first four segments is indicated.

Let us illustrate this with the mapping of a system of 16 particles on 16 processors. The diagonal processor Pu computes interactions in the (1,1)-block, which are interactions among particles (1,2,3,4), processor P22 computes interactions among particles (5,6, 7, 8), processor P33 computes interactions among particles (9,10,11,12) and processor P44 computes interactions... 

This is eontinued n — 1 times until the entire eoeffieient maPix has been eonverted to an upper triangular matrix, that is, a maP ix with only zeros below the principal diagonal. The b veetor is operated on with exactly the same sequenee of operations as the eoeffieient matrix. The last equation at the very bottom of the triangle, aititXit = bn, is one equation in one unknown. It ean be solved for whieh is baek-substituted into the equation above it to obtain x i and so on, until the entire solution set has been generated. 

An option input of 1 can be used to alter the F maPix called the core matrix. Elements can be entered or altered off the diagonal or, for inclusion of heteroatoms, by designating on-diagonal elements. The prompts and response formats for the E maP ix are similar to those of the G maPix. This opPon is similar to heteroatom inclusion in HMO. We shall use option 1 in Part C below. After all options have been entered, the final option is 0, which causes the calculation to be carried out. In... 

The extent to which Equation 1 is valid and the accuracy of the map are graphically shown in Fig. 5. The vertical lines, representing A-values, should increase in height with the square of their distance from the diagonal. 

Fig. 5.—In this figure ordinates and abscissas represent loci on the electronegativity map, and the heavy vertical lines are drawn to the height A, the observed deviation from additivity of bonds, attributed to their ionic character. Equation 1 in the text requires that these heights increase with the square of the distance from the diagonal.

Figure 2. Right figure amplitude of the Miju coefficients of a real mirror. If the mirror were perfect, then only diagonal elements would be non-null. Left figure surface figure map of a Virgo mirror.

The structure was refined by block-diagonal least squares in which carbon and oxygen atoms were modeled with isotropic and then anisotropic thermal parameters. Although many of the hydrogen atom positions were available from difference electron density maps, they were all placed in ideal locations. Final refinement with all hydrogen atoms fixed converged at crystallographic residuals of R=0.061 and R =0.075. 

The remaining off-diagonal elements are zero by specification. Vectors d and t may be obtained from vec ( P) by premultiplying by the appropriate mapping matrices D and T, that is,... 

D matrix that maps diagonal elements of "if into d D+ matrix that maps vector d into the diagonal elements of matrix it / degrees of freedom... 

T matrix that maps off-diagonal elements of matrix

maps vector t into off-diagonal elements of (P u arbitrary weights... 

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