Formatting numbers using "Precision

The quantity s2/n, which represents the variability among arithmetic means (i.e., simple averages) of n repetitions, is known as the standard error of the mean, and is abbreviated either as SEM or SE. Results of assays involving n repetitions, such as the absorbance results reported earlier as x SD = 0.42 0.09 are also frequently reported as x SE, which in this case is 0.42 (0.09/V3) = 0.42 0.05. Confusion can arise if either this x SE or the x SD format is used without specific indication of whether it is SD or SE that follows the reported mean. The latter is preferable whenever the purpose is to represent the precision of the assay s summary result rather than the variability of the individual measurements that have contributed to it. This is almost always the case with chemical analyses, and we recommend the x SE notation, supplemented by the number of replicates, n, for general use. Thus, in the example, we would report an absorbance of 0.42 0.05 (SE), from three replications. 

Note that a number of complicating factors have been left out for clarity For instance, in the EMF equation, activities instead of concentrations should be used. Activities are related to concentrations by a multiplicative activity coefficient that itself is sensitive to the concentrations of all ions in the solution. The reference electrode necessary to close the circuit also generates a (diffusion) potential that is a complex function of activities and ion mobilities. Furthermore, the slope S of the electrode function is an experimentally determined parameter subject to error. The essential point, though, is that the DVM-clipped voltages appear in the exponent and that cheap equipment extracts a heavy price in terms of accuracy and precision (viz. quantization noise such an instrument typically displays the result in a 1 mV, 0.1 mV, 0.01 mV, or 0.001 mV format a two-decimal instrument clips a 345.678. .. mV result to 345.67 mV, that is it does not round up ... 78 to ... 8 ). 

The stereoselectivity of the Wittig reaction is believed to be the result of steric effects that develop as the ylide and carbonyl compound approach one another. The three phenyl substituents on phosphorus impose large steric demands that govern the formation of the diastereomeric adducts.240 Reactions of unstabilized phosphoranes are believed to proceed through an early TS, and steric factors usually make these reactions selective for the d.v-alkcnc.241 Ultimately, however, the precise stereoselectivity is dependent on a number of variables, including reactant structure, the base used for ylide formation, the presence of other ions, solvent, and temperature.242... 

Biotinylation may be done before or after liposome formation, but having a stock supply of biotin-modified PE is an advantage, since it can then be used to test a number of liposomal recipes. In addition, only a very small percent of the total lipid should be biotinylated to prevent avidin-induced aggregation in the absence of antigen. It is difficult to control precisely... 

I chose to use this software for reasons that extend beyond familiarity and prejudice the programs are interactive and take simple commands as input. As such, I can include within the text of this book scripts that in a few lines show the precise steps taken to calculate each result. Readers can, of course, reproduce the calculations by using any of a number of other modeling programs, such as those listed in Appendix 1. Following the steps shown in the text, they should be able to construct input in the format recognized by the chosen program. 

Figure 7. Relationship of oxidation and degree of polyunsaturation. Polyunsaturation is measured as the methylene bridge index (MBI), which is a more precise measure of extent of unsaturation and oxidizability than the double bond index. It is the mean number of 6is-allylic methylene bridge positions per fatty acid (or fatty acyl chain) in a lipid ensemble. The rate of lipid radical formation measures formation of an oxidative product, while O2 consumption (% O2 lost per sec) is a measure of utilization of a reactant. (Drawn using our data abstracted from Wagner, B.A., Buettner, G.R., and Bums, C.P. 1994, Biochemistry 33 4449-4453).

Efficient cross-link formation by a small number of wall polymer-bound phenolics requires great precision in the metabolic reactions involved. It is not sufficient to form cross-links the cross-links need to be formed in the proper place within the polymer molecule and within the cell wall. Evidence that cross-links form at all [albeit sometimes as a low percentage of the total wall phenolics] is presented elsewhere (1,2,13,16,30-32). Here we present evidence that sufficient molecular specificity exists to be compatible with useful cross-link formation. 

The utilization of lAC in analytical methods has received increasing retention in recent years [23,24], Of particular interest is the use of immobilized antibody columns in performing immunoassays, a technique known as a chromatographic immunoassay or flow-injection immunoassay. This approach has already been reported in a number of formats such as those involving simple analyte adsorption/desorption, sandwich immunoassays, competitive binding immunoassays, and multianalyte methods (see Figure 13,9) [23,24,73,74], Typical advantages of these methods include decreased analysis times and improved precision versus manual immunoassays. 

While transition metals have been used extensive ) in C-gly coside construction, assigning a precise reactivity profile to C(l) can be difficult and this section will cover cases where nucleophilic character is apparent, albeit loosely defined. The use of palladium-mediated synthesis of C-glycosides has been reported and this topic, which involves an anomeric tin intermediate, has been covered in Sect. 2.2.2. The insertion of carbon monoxide into a carbon-metal (C(l)-metal) bond is, however, an important aspect of transition metal-mediated C-glycoside formation, and this process has been observed and exploited in a number of situations. 

A supramolecular complexation between avidin and biotin-labeled enzyme results in the formation of enzyme multilayers composed of avidin and enzyme monolayers, in which each monolayer is connected through avidin-biotin complexation with each other. The thickness of the multilayers can be precisely controlled by regulating the deposition number (the thickness of each avidin plus enzyme double layer is approximately 10 nm). The enzyme multilayers are useful in preparing high... 

The second edition CD-ROM contains 139 validation SOPs they are made available so that customers can input them into their computers and use their Microsoft Word programs to edit and print these documents. The contents of the procedures are written in simple and precise language to be in compliance with FDA regulation GMP and GLP requirements. The book ensures minimization of the number of documents to avoid the nightmare of the head of quality assurance at the time of FDA audit. The SOPs exclusively refer to the documents specially required for compliance however, specific formats are not included to ensure that the electronic templates can be easily used by pharmaceutical, bulk pharmaceutical, medical device, and biotechnology industries. 

Several additional studies were carried out to obtain information about the precise behavior of the various components in the model system. The interplay between the manganese porphyrin and the rhodium cofactor was found to be crucial for an efficient catalytic performance of the whole assembly and, hence, their properties were studied in detail at different pH values in vesicle bilayers composed of various types of amphiphiles, viz. cationic (DODAC), anionic (DHP), and zwitterionic (DPPC) [30]. At pH values where the reduced rhodium species is expected to be present as Rh only, the rate of the reduction of 13 by formate increased in the series DPPC < DHP < DODAC, which is in line with an expected higher concentration of formate ions at the surface of the cationic vesicles. The reduction rates of 12 incorporated in the vesicle bilayers catalyzed by 13-formate increased in the same order, because formation of the Rh-formate complex is the rate-determining step in this reduction. When the rates of epoxidation of styrene were studied at pH 7, however, the relative rates were found to be reversed DODAC DPPC < DHP. Apparently, for epoxidation to occur, an efficient supply of protons to the vesicle surface is essential, probably for the step in which the Mn -02 complex breaks down into the active epoxidizing Mn =0 species and water. Using a-pinene as the substrate in the DHP-based system, a turnover number of 360 was observed, which is comparable to the turnover numbers observed for cytochrome P450 itself. 

Modern quantitative spectroscopy of hot stars has two aspects the analysis of photospheric lines and stellar wind lines The first one is meanwhile established as an almost classical tool to determine stellar parameters. NLTE model atmosphere and line formation calculations yield Te , log g and abundances with high precision (see recent reviews by Husfeld (this meeting), Kudritzki (1987), Kudritzki and Hummer (1986), Kudritzki, (1985).) The second aspect, however, the quantitative analysis of stellar wind lines is still at its very beginning. For long time the stellar wind lines have been used to determine mass-loss rates M and terminal velocities v only. While these studies were pioneering and of enormous importance, it was also clear that very approximate calculations were done with respect to NLTE ionization and excitation and the radiative transfer in stellar winds. Thus, stellar wind lines could be used only in a more qualitative comparative sense, with no theory behind, which allowed the determination of precise and reliable numbers. 

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