First Differences

Rule 2 If a decision can t be reached by ranking the first atoms in the substituent, look at the second, third, or fourth atoms away from the double-bond carbons until the first difference is found. A — CH2CH3 substituent and a -CH3 substituent are equivalent by rule 1 because both have carbon as the first atom. By rule 2, however, ethyl receives higher priority than methyl because ethyl has a carbon as its highest second atom, while methyl has only hydrogen as its second atom. Look at the following examples to see how the Tule works ... 

There are two main differences between the structure of the NH4NbOF4 chains and that of the Rb5Nb30Fi8 chains. The first difference is, that in the case ofRbjNbjOFu neighboring octahedrons along the chain are rotated by 7t/4 relative to one another (the rotation axis coincides with z-axis), as shown in Fig. 31. The second difference is that in the NbOF4 complexes, the niobium atoms are all shifted in the same direction, forming a polar structure. 

The first difference of normal stresses (tr, t) may serve as an indirect index of the highly elastic properties of polymeric systems [199]. C. D. Han [200] related (ru with the residual pressure at outlet Pt)dt. Han, who observed its reduction in polypropylene filled with calcium carbonate [201], concluded that filling decreases the normal stresses. Note that addition of fibrous fillers, vice versa, somewhat increases Pexi, [180]. 

Fillers with particles nearly spherical in shape usually dimish <7n under a fixed shear stress [178,181, 182,202] in comparison with the pure polymer. In contrast, scales tend to step up the first difference of normal stresses [181]. Fibrous fillers have little effect on a, x value [181], except in a few cases where the tendency for... 

Nuclear reactions differ in some important ways from chemical reactions. First, different isotopes of the same element undergo essentially the same chemical reactions, but their nuclei undergo very different nuclear reactions. Second, when a or 3 particles are emitted from the nucleus, they leave behind a nucleus with a different number of protons. The product, which is called the daughter nucleus... 

First, different organizations have very different organizational goals as well as diverging training/human resource... 

Furthermore, we replace the first derivative u (0) by the first difference derivative = (j/j — yo)/h and impose the boundary condition at the point X = 0 such as... 

It is worth mentioning here that the sign of r x) has had a significant impact on construction of monotone schemes. One way of providing a second-order approximation and taking care of this sign is connected with a monotone scheme with one-sided first difference derivatives for the equation with perturbed coefficients... 

There are a few more situations you should know how to deal with when numbering the four groups. If you are comparing two carbon atoms and you find that the three atoms on one side are the same as the three atoms on the other, then keep going farther out until you find the first difference ... 

The difference in catalytic activity between the La- and the Ba-based hexa-aluminates results from the following reasons the first difference is the valence of cation in the mirror pleuie between tri-valent lanthanum ion and di-valent barium ion. The second is the crystal structure between magnetoplumbite and P-alumina, which are different in the coordination of ions and concentration of Frenkel-type defect in mirror plane. The redox cycle of transition metal in hexa-aluminate lattice, which closely related with catalytic activity, is affected sensitively with these two factors. 

The OPMBS used a custom-written spreadsheet application, i.e., a workbook, in conjunction with laboratory automation systems to standardize data recording, calculations, and presentation of results. Devising this approach required careful differentiation between (a) the workbook used to calculate and report the results and (b) the data acquisition systems used in each laboratory. The laboratory systems were used to collect the raw chromatographic data, but the calculation modules in the laboratory systems were not used. Instead, all calculations were done in the workbook. Use of the laboratory systems to collate and output the final results was considered but was rejected for two reasons. First, different laboratories used different systems, and some laboratories used more than one system. The output characteristics of the various systems differed considerably and would have required extensive modification... 

As explained above, we compare four different reaction paths for the first step of the reaction catalyzed by 40T. The first difference between the paths was the method employed to determine the MEP for the paths. The first two paths (A and B), were determined by the combined procedure [27, 35], In both cases seven images were employed for the optimization of the path. Path C was calculated with the CD method. Finally, path D corresponds to the MEP obtained from our previous calculations [33],... 

Equation yx + l- yx = 4>(x) This equation states that the first difference of the unknown function is equal to the given function (p(x). The solution by analogy with solving the differential equation dy/dx = 0(x) by integration is obtained by finite integration or summation. When there are only a finite number of data points, this is easily accomplished by writing yx = y0 + X =i 0(f - 1), where the data points are numbered from 1 to x. This is the only situation considered here. 

Equally Spaced Forward Differences If the ordinates are equally spaced, i.e., x, — x . = Ax for all j, then the first differences... 

Can we explain all these effects Of course we can, and in fact the explanation is almost obvious. When spacings are small, the computed derivative is a good approximation to the true derivative. As long as this is the case, the exact value of AX used to compute the derivative is unimportant, because as we saw in Figure 55-5, the first difference AT increases almost linearly with AX, therefore all values of AX give the same result for the computation, because AT/AX is constant regardless of spacing. 

The above reactivity is different from that of rhodium porphyrins in two respects. The first difference is that lP)Rh is not... 

The first difference between these two batteries is the voltage they produce a watch battery produces about 3 V and a lead-acid cell about 2 V. The obvious cause of the difference in emf are the different half-cells. The electrode potential E is the energy, expressed as a voltage, when a redox couple is at equilibrium. 

The first difference is that non-cumulative data refer to amount of drug dissolved within a certain time period and not at a specific time point, i.e., in this case the observed variable is the amount dissolved, W(t, t2), between the time points t1 and t2 it2 > t ). Consequently, in contrast to their application to cumulative data (30) where the difference factor and the Rescigno index refer to area differences, for non-cumulative data these indices refer to the difference between the dissolved amount of the test and the reference product in a given time interval. 

Fenvalerate Data. Calibration data for the GC measurement of Fenvalerate were furnished by D. Kurtz (17). Average responses for five replicates at each of five standard concentrations are given in Table III. It should be noted that the stated responses are not raw observations, but rather on-line computer generated peak area estimates (cm ). (Had we started with the raw data [chromatograms], the problem would actually have been two-dimensional, including as variables retention time and concentration.) The stated uncertainties in the peak areas are based on a linear fit (o a+bx) of the replication standard deviations to concentration and the "local slopes" [first differences] in the last column of Table III are presented... 

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