Standards refinement

Figure 9 Treating internal dynamics during the refinement process. Due to dynamics and the weighting of the NOE, the measured distance may appear much shorter than the average distance. This can be accounted for by using ensemble refinement techniques. In contrast to standard refinement, an average distance is calculated over an ensemble of C structures (ensemble refinement) or a trajectory (time-averaged refinement). The time-averaged distance is defined with an exponential window over the trajectory. T is the total length over the trajectory, t is the time, and x is a relaxation time characterizing the width of the exponential window.

Refine the spec using one of the standard refinements. Some refinements are one-to-one others are decompositions. The latter split the spec into several separate ones, each of which can be dealt with as a separate goal. 

Macromolecular crystallographic refinement is an example of a restrained optimization problem. Standard refinement programs adjust the atomic positions and, typically, also their atomic displacement parameters of a given model with the... 

Be Square special wax Victory wax Stanolind wax Standard Refined wax... 

The earliest attempts to account for the effect of spin diffusion relied on some iterative scheme wherein a full relaxation matrix analysis would be used to calculate distances from NOEs, and these distances could be used in a standard refinement procedure.59-64 Clearly a more elegant approach would be to base an energy term on the directly measured NOE intensity. 

Such refining of raw sugar cane is done on a tremendous scale most of it in this country is done in a dozen huge plants, one of which may spend 200,000 to refine 2,000 tons per day, of which 20,000 per day may be for fuel. Thus, all standard refining methods are expensive because of ... 

The most common liquid feedstocks are residues from petroleum refining. Like petroleum coke these tend to have a low ash content and a high sulfur content. Sodium compounds in the feedstock can lead to fouling of s mgas coolers, but most refinery residues have had it reduced to less than 30 ppmw as part of the standard refining process. 

The aim of crystallographic refinement is to determine a reliable atomic coordinate model and therefore reliable estimates of density, structure factors and phases. A standard refinement procedure consists of several cycles, with each cycle hopefully yielding a better match to observations and therefore a more reliable atomic model for the following refinement step. There are several functions available to be minimized (or maximized) during the refinement procedure. Which functions are used depends on the program and the user s input the interested reader is referred to standard text books and program manuals, which provide more information about this (e.g. Refs. [1, 3,48]). 

The great potential of the X-ray data for obtaining motional information has recently led to a molecular dynamics test197 of the standard refinement techniques that assume isotropic and harmonic motion. Since simulations have shown that the atomic fluctuations are highly anisotropic and, in some cases, anharmonic (see Chapt. VI.A.1), it is important to determine the errors introduced in the refinement process by their neglect. A direct experimental estimate of the errors resulting from the assumption of isotropic, harmonic temperature factors is difficult because sufficient data are not yet available for protein crystals. Moreover, any data set includes other errors that would obscure the analysis, and the specific correlation of temperature factors and motion is complicated by the need to account for static disorder in the crystal. As an alternative to an experimental analysis of the errors in the refinement of proteins, a purely theoretical approach has been used.197 The basic idea is to generate X-ray data from a molecular dynamics simulation... 

As in standard refinements of macromolecules, the modeling of ordered solvent molecules is an iterative process in which it is important to adhere to some mles in order to arrive at a consistent description and to avoid endless cycling ... 

When cathodes are lifted from the cells the head bars are removed for reuse and the lead cathodes are washed, then melted in a standard refining kettle. 

An extremely versatile computer program, POLYMIN, which is designed specifically for the structural refinement of crystalline polymers has been developed. It incorporates several features not found in standard refinement programs and thereby eliminates many of the difficulties encountered in their use. The main advantages of the program are that it ... 

The diffraction patterns are analysed by standard refinement methods developed for X-ray scattering one determines the atom position inside the unit-cell which gives the best fit between the experimental and the calculated spectrum. In the Rietveld method [11], the fit is done on the complete line profiles if the resolution of the spectrometer is not well known, or if the Bragg peaks are broadened for physical reasons, then only the integrated intensities of each peak can be used. 

Figure 27.16 X-ray diffraction anaiysis of a (Ca, PbjTiOs perovskite thin fiim (a) as-prepared on a Pt-coated siiicon substrate (i) experimentai pattern and (ii) perovskite peaks caicuiated by a standard refinement method ...

Standard refined lecithins take the largest share of the lecithin group of emulsifiers. The definition refining is mostly used for the exact adjustment of quality parameters of clear filtered lecithin with guaranteed AI, AV, colour and phospholipid composition. Thus it is a different definition compared to refining of oils. 

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