Squares defined

In the following ratios in each paranthesis the numerator is the respective sum of squares defined in Eqs. 2-83 to 2-85 and the denominator is the corresponding degree of freedom.)... 

The Regression output gives three quantities that are helpful in judging the quality of the fit of the model to the data. The first of these is the correlation coefficient R Squared, defined as... 

Standard Deviation Error in Calculation, SDEC ( standard error in calculation, SEC). A function of the residual sum of squares, defined as ... 

Note that 3 and X4 are qualitative factors and their values are limited to 1. An optimization method that could distinguish between discrete and continuous variables and which would thus only search the space of permitted values of the qualitative, or discrete quantitative variables, would be preferred. It can also be seen that the maximum desirability, on the edge of the square defined by X X2] at 1, is actually just outside the cylindrical experimental domain. The optimum should, strictly speaking, be displaced very slightly to lie on the edge of the design space. 

Some molecules have several rotation axes. The axis ofhighest order is called the principal axis. The complex [PtCU] ", in which the platinum atom is located in the centre of the square defined by the four chlorine atoms (6-10), possesses a C4-axis, perpendicular to the plane of the square, and four C2-axes in the plane of the square two of these are co-linear with the bonds Cli—Pt—CI3 and CI2—Pt—CI4 (C0, and the two others bisect the angles Cl—Pt—Cl (C O- The principal axis is therefore four-fold (of order four). The existence of a four-fold rotation axis implies the presence of a co-linear two-fold axis, as the operation (a rotation of 2 x 27t/4) is identical to the operation C (a rotation of 1 X in/2). 

Molecular squares define cavities that are potential hosts for appropriate molecular guests. In methylene chloride as solvent, pyridine binds to the available Zn(II) sites of IZn with an association constant of 10 M Whether binding occurs on the square interior or exterior (or a combination of both) has not been established. Recall, however, that Zn porphyrins generally axially bind only one ligand. The free base form of the dipyridyl porphyrin used to assemble the squares binds to IZn with an equilibrium constant of 3 x 10 [7]. The stronger association is a consequence of... 

Fig.4. Schematic representation of the variation in free energy of mixing with volume fraction of polymer A in a binary mixtures of polymers A and B filled squares define compositions corresponding to the binodal and open squares the spinodal of the phase diagram...

However, free spaces remain between plane netwoik particles, called interstices or voids. In (a)-type arrangement, the void shape is a square, defined by joining the centers of the four spheres from successive parallel strings, with the surface ... 

Ferraris and Donati [73] reevaluated the data of Nielsen et al. using both the Temkin equation Eq. (112) modified by Dyson and Simon and Eq. (83) used by Nielsen et al. They used the same thermodynamic data as Dyson and Simon. A non-linear parameter estimation program was used to calculate the constants in the two equations minimizing the sum of squares defined by ... 

By 1939 Pauling was able to present a table of covalent radii for the hydrogen atom and the sixteen elements in the square defined by the positions of C, Sn, F, and I in the periodic table [37]. These radii were based on the bond distances in the crystalline elements of the Group 14 metals the Group 15 elements P, As, and Sb and the Group 16 elements S, Se, and Te, all determined by X-ray diffraction the bond distances in H2 and the dihalogen molecules determined by spectroscopic methods and finally by the bond distances in the gaseous methyl derivatives of all the seventeen elements except Sb, Se, and Te determined by gas electron diffraction. 

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