Extraction error

And the end, various results have been compared detected defects (1), non detected defects (2) and errors (3). The following figures illustrate some factors which have been extracted from final data analysis. 

A linear dependence approximately describes the results in a range of extraction times between 1 ps and 50 ps, and this extrapolates to a value of Ws not far from that observed for the 100 ps extractions. However, for the simulations with extraction times, tg > 50 ps, the work decreases more rapidly with l/tg, which indicates that the 100 ps extractions still have a significant frictional contribution. As additional evidence for this, we cite the statistical error in the set of extractions from different starting points (Fig. 2). As was shown by one of us in the context of free energy calculations[12], and more recently again by others specifically for the extraction process [1], the statistical error in the work and the frictional component of the work, Wp are related. For a simple system obeying the Fokker-Planck equation, both friction and mean square deviation are proportional to the rate, and... 

The two sources of stochasticity are conceptually and computationally quite distinct. In (A) we do not know the exact equations of motion and we solve instead phenomenological equations. There is no systematic way in which we can approach the exact equations of motion. For example, rarely in the Langevin approach the friction and the random force are extracted from a microscopic model. This makes it necessary to use a rather arbitrary selection of parameters, such as the amplitude of the random force or the friction coefficient. On the other hand, the equations in (B) are based on atomic information and it is the solution that is approximate. For ejcample, to compute a trajectory we make the ad-hoc assumption of a Gaussian distribution of numerical errors. In the present article we also argue that because of practical reasons it is not possible to ignore the numerical errors, even in approach (A). 

The errors in the present stochastic path formalism reflect short time information rather than long time information. Short time data are easier to extract from atomically detailed simulations. We set the second moment of the errors in the trajectory - [Pg.274]

The easiest way to extract a set of objects from the basic dataset, in order to compile a test set, is to do so randomly. This means that one selects a certain number of compounds from the initial (primary) dataset without considering the nature of these compounds. As mentioned above, this approach can lead to errors. 

In the two-sample collaborative test, each analyst performs a single determination on two separate samples. The resulting data are reduced to a set of differences, D, and a set of totals, T, each characterized by a mean value and a standard deviation. Extracting values for random errors affecting precision and systematic differences between analysts is relatively straightforward for this experimental design. 

The period covered by the published accounts of a company is usually 1 year, but the details from which these accounts are compiled are entered daily in a journal. The journal is a chronological listing of every transaction of the business, with details of the corresponding income or expenditure. For the smallest businesses, this may provide sufficient documentation, but in most cases the unsystematic nature of the journal can lead to computational errors. Therefore, the usual practice is to keep accounts that are listings of transactions related to a specific topic such as purchase-of-oil account. This account would list the cost of each purchase of oil, together with the date of purchase, as extracted from the journal. 

Estimations based on statistics can be made for total accuracy, precision, and reproducibility of results related to the sampling procedure being applied. Statistical error is expressed in terms of variance. Total samphng error is the sum of error variance from each step of the process. However, discussions herein will take into consideration only step (I)—mechanical extraction of samples. Mechanical-extracdion accuracy is dependent on design reflecding mechanical and statistical factors in carrying out efficient and practical collection of representative samples S from a bulk quantity B,... 

Theoiy related to material characteristics states that a minimum quantity of sample is predicated as that amount required to achieve a specified limit of error in the sample-taking process. Theoiy of sampling in its apphcation acknowledges sample preparation and testing as additional contributions to total error, but these error sources are placed outside consideration of sampling accuracy in theoiy of sample extraction. 

The procedure of simultaneous extracting-spectrophotometric determination of nitrophenols in wastewater is proposed on the example of the analysis of mixtures of mono-, di-, and trinitrophenols. The procedure consists of extraction concentrating in an acid medium, and sequential back-extractions under various pH. Such procedures give possibility for isolation o-, m-, p-nitrophenols, a-, P-, y-dinitrophenols and trinitrophenol in separate groups. Simultaneous determination is carried out by summary light-absorption of nitrophenol-ions. The error of determination concentrations on maximum contaminant level in natural waters doesn t exceed 10%. The peculiarities of application of the sequential extractions under fixed pH were studied on the example of mixture of simplest phenols (phenol, o-, m-, />-cresols). The procedure of their determination is based on the extraction to carbon tetrachloride, subsequent back-extraction and spectrophotometric measurement of interaction products with diazo-p-nitroaniline. 

A Checklist on Procedures Extracted from the Short Guide to Reducing Human Error" (UK Atomic Energy Authority, 1987)... 

Note. Under the above conditions of determination the following elements interfere in the amount specified when the amount of Mo is 10 fig (error greater than 3 per cent) V, 0.4 mg, yellow colour [interference prevented by washing extract with tin(II) chloride solution] Cr(VI), 2 mg, purple colour W( VI), 0.15 mg, yellow colour Co, 12 mg, slight green colour Cu, 5 mg Pb, 10 mg Ti(III), 30 mg (in presence of sodium fluoride). 

It is difficult to estimate the magnitude of the error due to insufficiently low humidity when distillation methods are used with organic liquids such as toluene (6, 28), xylene (6, 28), or chloroform (12). With organic liquids essentially immiscible with water and of high boiling point the error is probably very small. When methanol is used as an extraction solvent, as in the Fischer reagent method, the amount of unextracted water is undoubtedly some function of the concentration of water in the alcohol, but the error might be small because of substitution of adsorbed water by adsorbed alcohol (23, 34). This seems to be borne out by experiments of Schroeder and Nair (31), who deliberately added water to the alcohol to form a 0.5% water solution and found that the results of their moisture determinations were essentially the same as with anhydrous methanol, which contained about 0.05% water. 

So, we can discard the third eigenvector and, along with it, that portion of the variance in our spectra that displaced the data out of the plane of the noise-free data. We are in fact, discarding a portion of the noise without significantly distorting the spectra The portion of the noise we discard is called the extracted error or the residuals. Remember that the noise we added also displaced the points to some extent within the plane of the noise-free data. This portion of the noise remains in the data because it is spanned by the eigenvectors that we must retain. The noise that remains is called the imbedded error. The total error is sometimes called the real error. The relationship among the real error (RE), the extracted error (XE), and the imbedded error (IE) is... 

The low TTA dependence at 35.0°C probably is attributable to dissolution of TTA in the aqueous phase. Observation of fourth-power dependence on acidity argues against any change in the extraction mechanism (e.g., Pu(IV) reduction or NO3 involvement). An aqueous Pu(TTA)3+ complex has been reported (14, 15) and this possibility has been considered in the error analysis of the Pu(IV)-sulfate stability constants. 

Figure 1 outlines the basic AO system. Wavefronts incoming from the telescope are shown to be corrugated implying that they have phase errors. Part of the light is extracted to a wavefront phase sensor (usually referred to as a wavefront sensor, WFS). The wavefront phase is estimated and a wavefront corrector is used to cancel the phase errors by introducing compensating optical paths. The most common wavefront compensator is a deformable mirror. The idea of adaptive optics was first published by Babcock (1953) and shortly after by Linnik (1957). 

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