Duplications

READ STANDARD DEVIATIONS OF VLE MEASUREMENTS- ND IS THE NUMBER OF STANDARD DEVIATIONS WHICH ARE DUPLICATED (1.UE.NO.LE-NN). 

Figure Bl.9.8. Schematic diagram of the relationship between a particle distribution and the measured experimental scattering data. This figure is duplicated from [14],with pennission from Academic Press.

Figure Bl.9.9. Comparison of the distance distribution fiinction p(r) of a RNA-polymerase core enzyme from the experimental data (open circle) and the simulation data (using two different models). This figure is duplicated from [27], with pennission from Elsevier Science.

Since the periodic im iipes are exact copies oT Lh e original box, movements of atoms in the original box are duplicated in the images. When a particle leaves a box. its periodic image enters I rom the opposite box side and replaces it. This con serves the n limber or atom s in each box. 

In place of the conical flask G, a small Buchner flask may be used with the calcium chloride tube fitted to the side-arm, but in either case a duplicate flask for the second fraction should be available. 

Now distil the contents of C by heating carefully over a gauze. A small initial fraction of unchanged thionyl chloride boiling at 78-80° comes over, and the temperature then rises rapidly to 194°. Directly this happens, stop the distillation, allow the condenser to drain thoroughly, and then replace G by the duplicate receiver. Run the water out of the condenser so that it acts as an air-condenser, and then continue the distillation. Collect the benzoyl chloride as the fraction boiling at 194-198°. Yield, 19 g. 

Despite these similarities between the G2 calculations of Dg for H2 and Hj, there is a profound difference that is only hinted at in the single-point energies in Table 10-1. In the first group of results we see that all the calculations, with the exception of the last one, give the same answer. In the lower block of results, for H2, this is not the case. Some results are duplicated and some are not. The results are more mixed. 

Plot of the orthogonalized 3 s orbital probability density vs r note there are two nodes in the 0-5 bohr region but they are not distinguishable as such. A duplicate plot with this nodal region expanded follows. 

Gadolinium ethyl sulfate has extremely low noise characteristics and may find use in duplicating the performance of amplifiers, such as the maser. 

Structure-property relationships are qualitative or quantitative empirically defined relationships between molecular structure and observed properties. In some cases, this may seem to duplicate statistical mechanical or quantum mechanical results. However, structure-property relationships need not be based on any rigorous theoretical principles. 

Note A few symbols are duplicated. Although this is at times confusing, it does reflect common usage in the literature. Thus, it is an important notation for the reader to understand. Acronyms are defined in the glossary at the end of the book. 

It is possible to reduce thiazole carbonyl derivatives with aluminium isopropoxide (56, 57). For example, 4-methyl-5-acetylthiazole gives 4-methyl-5-(a-hydroxyethyl)thiazole. With aluminium amalgam one obtains a duplication like to the pinacol reaction, and the yield is genaally poor... 

Each cross peak has x and y coordinates One coordinate corresponds to the chem real shift of a proton the other to the chemical shift to a proton to which it is coupled Because the diagonal splits the 2D spectrum m half each cross peak is duplicated on the other side of the other diagonal with the same coordinates except m reverse order This redundancy means that we really need to examine only half of the cross peaks To illustrate start with the lowest field signal (8 2 4) of 2 hexanone We assign fhis signal a friplef fo fhe protons af C 3 on fhe basis of ifs chemical shifl and fhe spin fmg evidenf m fhe ID speefrum... 

Most of the SpartanView models on the CD have been constructed using quantum mechanical calculations although some simplifications have been used to accelerate the calculations This means that the models although closely resembling real molecules never precisely duplicate the properties of real molecules Even so the models are suf ficiently similar to real molecules that they can usually be treated as equivalent This is important because models can contain more types of information and models can be constructed for molecules that cannot be studied m the laboratory Also models can be joined together to make animations that show how molecules move... 

The water molecules used to solvate a solute comes from Jorgensen s Monte Carlo equilibrated box of 216 water molecules, described by the T1P3P potential function [W- L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983)]. This box is cubic and 18.70 A on a side. When the requested box fits into this, it is just carved out of the basic Jorgensen box. When a bigger box (more than 216 water molecules or perhaps an elongated box) is required, then the basic 216 molecule box is duplicated to create 3x3x3x216 water molecules in a box 56.10 Aon a side and the required box is carved out of this. 

The most useful methods for quality assessment are those that are coordinated by the laboratory and that provide the analyst with immediate feedback about the system s state of statistical control. Internal methods of quality assessment included in this section are the analysis of duplicate samples, the analysis of blanks, the analysis of standard samples, and spike recoveries. 

Analysis of Duplicate Samples An effective method for determining the precision of an analysis is to analyze duplicate samples. In most cases the duplicate samples are taken from a single gross sample (also called a split sample), although in some cases the duplicates must be independently collected gross samples. The results from the duplicate samples, Xi and X2, are evaluated by determining the difference, d, or the relative difference, d) between the samples... 

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