Four Columns of

The data given in the first four columns of Table 4-132 were recorded during... 

Equation 16.12 expresses a relation between q and B.This is not a universal relation, but it does apply to the sp-bonded elements of the first four columns of the Periodic Table. Using chemical hardness values given by Parr and Yang (1989), and atomic volumes from Kittel (1996), it has been shown that the bulk moduli of the Group I, II, III, and IV elements are proportional to the chemical hardness density (CH/atomic volume) (Gilman, 1997). The correlation lines pass nearly through the coordinate origins with correlation coefficients, r = 0.999. Thus physical hardness is proportional to chemical hardness (Pearson, 2004). 

The last four columns of this matrix contain coefficients that can be used to determine the volume proportions of quartz, plagioclase, alkali feldspar and biotite in the rock to be classified using its major element composition, as described above. The first two columns of this matrix can be added in any linear combination to any of the last four vectors to produce alternative coefficients that yield the same independent measures of the classifying mineral proportions. 

Microsoft Excel Program. It is usual to use PC software such as Microsoft Excel to perform repetitive calculations such as the above. This enables a tabular printout and the generation of charts. The layout of the data sheet is shown in Fig. 8.2. The first four columns of data are entered directly. The fifth column is a correction of the titration using the actual strength of the sodium hydroxide used compared to what the result would have been if the concentration had been exactly 0.05 M. Thus, the equation to be entered in the cell to convert the previous column s value is in our case ... 

Problem 5-16. Verify the information in the rightmost four columns of Table 5.2. 

There are four columns of data, one column for time and the other three for the voltage data for the selected traces. Once again we need to modify the first row so that the text labels fit within the columns. When we remove the leading spaces from the text labels and we change the column widths in the spreadsheet, the labels for the columns are easily seen ... 

The last four columns of the following output list the matrix of semi-logarithmic sensitivities consisting of nyxnt = 22 rows and np = 4 columns. This matrix is called normalized sensitivity matrix. 

First, the sample was examined by GPC, for which four columns of styragel of 106,10s, 104 and 103 A nominal pore size were used. The total number of theoretical plates as determined by acetone at a flow rate of 1 ml/min was ca. 26,000. The eluent was tetrahydrofuran. The chromatogram is shown in Figure 9, which indicates two peaks at ca. 21 and 24 counts. The former may be assigned to the tetra-chain, star-draped component, and the latter to the precursor. However, no complete separation of the two peaks was observed. For another comparison, velocity ultra-centrifugation was performed for the sample at 59,780 rpm using a 6-solvent for polystyrene, cyclohexane. The operation temperature was established at 35 °C, the 6-temperature, to minimize the concentration dependence of sedimentation velocity and other effects. A sedimentation pattern taken by UV-absorption is shown in Figure 10. It is seen that the separation of S-A sample into the two components was quite difficult even at a very low polymer concentration, 0.077 g/dl. 

The four columns of a matrix in SO(4) are mutually perpendicular and each has length one. The ordering of the columns is restricted by the determinant-one condition. 

Data were obtained on a paper pulp with specific gravity 1.3, and are given as the first four columns of the table. Shear stress x and deformation rate y are derived by the equations applying to this kind of viscometer (Skelland, 1967, p. 31 Van Wazer et al., 1963, p. 197) ... 

Table 19.1 shows the smallest possible p-vectors for 7 < b < 20, accordingly see Lemma 19.2.3 below. The first four columns of the table show the quantities b, ps, Pt (the number of 5-, h-gons) and the number of vertices v. The invariants ms, mb, 2, 3, and ks are described in Section 19.2. In the 5th column, the 7-fulleroids are indexed by their construction, while in the last column their names are given. These names are of the form Fstb(G), where G is the symmetry group, or Ffc(l), using the notation given in Theorem 19.1.1. See on Figure 19.3 six F(5, b)(Ih) with b > 8. 

For the reaction, A + B —> C, three rate experiments yielded the data shown in the first four columns of the table, where [A]0 and[A] are [A] values at the beginning and end of the experiment, repectively ... 

The change in thickness of the phases involved into the interaction after consecutive anneals of the specimen was followed by the photometric examination of the X-ray patterns (for details of the experimental procedure, see Ref. 144). Using this technique, B.Ya. Pines and E.F. Chaikov-skiy could determine both the total thickness of the AlSb layer at any given moment of time and the increases in thickness of the layer at its both interfaces. Their data obtained at a temperature of 620°C are represented in first four columns of Table 1.1, with xSbi being the distance from a marker to the Al-AlSb interface and xA12 to the AlSb-Sb interface. 

Table II presents the results of some wettability measurements on adsorbed monolayers prepared from molten Compound D on pure, polished, clean, chromium surfaces after solvent treatment had been used to remove all surplus solidified acid. A series of successive solvent treatments was applied to each coated specimen (see first four columns of Table II) using liquids which have been shown to be good solvents for Compound in the bulk (9). These liquids were either absolute ethyl alcohol or benzene at or above 20°C., or n-hexane at or above 60°C. In the remaining columns are listed the average values of the slowly advancing contact angles measured by the drop-buildup method on from three to five different drops. Measurements were made on sessile drops of water, thiodiglycol, and methylene iodide. These three diagnostic liquids were chosen because of their high surface tensions (72.8, 54.0,...

An orthogonal array is called regular if it can be constructed by using a defining relation . For example, the array displayed in Table 1 is regular and is constructed by the following method. Denote a row (factor-level combination) of the array by (xi,..., Xe). The first four columns of the array consist of all the 16 level combinations of factors 1 through 4, and the levels of factors 5 and 6 are defined via... 

The last four columns of Table 4 contain numerical data that largely support this contention. The entries represent the changes in the various quantities that arise when either the proton donor or acceptor molecule is rotated by 40° from the equilibrium geometry. For example, a 40° distortion of the donor molecule, when R=3.25 A, raises the energy of the system by 4.43 kcal/mol, hence diminishing the H-bond energy by this amount. The same distortion reduces the H-bond energy by 6.24 kcal/mol when the two waters are separated by 2.75 A. The last two columns indicate that the interaction is somewhat less sensitive to 40° rotations of the proton acceptor molecule. 

Each linear (Ag—F) + chain, with two Ag—F = 2.002(3), and 2.009(3) A) (violet AgFBF4), is surrounded by four columns of linearly close-packed BFj, and vice versa. Each Ag(II) atom in the chain is further coordinated by four F ligands of the anions in square array (Ag—F = 2.330(2) A), each from one of the four surrounding BF4 anions. The Ag(II) is essentially in the same plane as these four... 

As previously indicated, the determination of a drug concentrations in plasma specimens requires the construction of a calibration response curve. This curve is often constructed as a straight line from the measured peak response ratios (y,) plotted against their respective calibrator concentrations (x,). The drug concentration in a specimen or the apparent (back-calculated) calibrator concentration is obtained from a rearrangement of theequation for the calibration line (without error) x,- = (y,- — b)/m. An example of a calibration curve with back-calculated concentrations is given the first four columns of Table 10. 

The necessary values and summations are given in the last four columns of Table 9-2. Solving for the constants, we have... 

Note that the last four columns of the M matrix constitute the connectivity table of the molecules. 

The first four columns of numbers give the experimental results and the last two give the results of the ab initio calculations. The agreement between the shapes of the experimentally and theoretically determined potential energy curves was quite good. These systems are of particular interest from the point of view of reactive scattering because of the extensive studies that have been carried out on the corresponding ion-molecule reactions. 

In A6 D9 enter the numbers from the middle four columns of Table 6.2-1, in the order in which they appear there, i.e., with 1.6534 in cell A6, and 2.8288 in cell D9. 

In the stoichiometric tables presented on the preceding pages, it was not necessary to make assumptions concerning a volume change in the first four columns of the table (i.e.. the species, initial number of moles or molar feed... 

If we apply property (38) to the four solutions that are the four columns of the matrix A(f), we obtain the equation... 

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