Errors additive

By using an effective, distance-dependent dielectric constant, the ability of bulk water to reduce electrostatic interactions can be mimicked without the presence of explicit solvent molecules. One disadvantage of aU vacuum simulations, corrected for shielding effects or not, is the fact that they cannot account for the ability of water molecules to form hydrogen bonds with charged and polar surface residues of a protein. As a result, adjacent polar side chains interact with each other and not with the solvent, thus introducing additional errors. 

Note that the answers have been rounded to three significant digits. Since the even-tempered formula is only an approximation, this does not introduce any significant additional error. 

Data Limitations The process of measuring Xy t) adds additional error due to the random error of measurement. Or,... 

Additive and proportional errors. The absolute value of an additive error is independent of the amount of the constituent present in the determination. Examples of additive errors are loss in weight of a crucible in which a precipitate is ignited, and errors in weights. The presence of this error is revealed by taking samples of different weights. 

The efficiency of power generation is significantly reduced by any deposits formed on the turbine blades by BW carryover and severe turbine damage may also result. Tiirbine efficiency also is reduced by demands for output that exceed the rated maximum and by extended operation beyond the maintenance period or design life. Additionally, errors in steam flow meters, thermometers, and pressure gauges, and so forth cause the control system to regulate the generation of electricity at some further reduced level. 

The vector w is an additive error introduced to account for inaccuracies generated by approximations and reflects the expected degree of modeling errors. 

Let us state the measurement model for the ith observation as the sum of the true state being measured and an additive error, that is,... 

This is the most commonly misused test method, except in those few cases where one is truly only comparing two groups of data and the group sizes are roughly equivalent. Not valid for multiple comparisons (because of resulting additive errors) or where group sizes are very unequal. 

It should be noted that the accuracy of the determination of fluorescence quantum yields cannot be better than 5-10%, due to the small additive errors relevant to the absorbances at the excitation wavelength, the correction factors of the detection system and the quantum yield of the standard. 

Thus, y is related to a linear combination of the x-variables, plus an additive error term. The difference to simple regression is that for each additional a-variable a new regression coefficient is needed, resulting in the unknown coefficients b0, b, ..., bm for the m regressor variables. It is more convenient to formulate Equation 4.35 in matrix notation. Therefore, we use the vectors y and e like in Equation 4.19, but define a matrix X of size nx (m+ 1) which includes in its first column n values of 1,... 

The overflowing fluid is equivalent to the gas volume. If the measurement has to be more exact than about 3%, corrections concerning the actual atmospheric pressure, the decreased pressure due to the height Ah of the fluid and the vapor pressure of the fluid are possible [74]. Additional errors can occur if the gas is significantly soluble in the fluid. 

For those scientists who had to perform quantitation, the linearity of the A/D was also critical. Linearity is the condition in which the detector s response is directly proportional to the concentration or amount of a component over a specified range of component concentrations or amounts. It is imperative that the A/D not add any additional error or variability to the performance of the detector. The resulting calibration curve now becomes dependent on the combined linearity of the detector and the /VD. Accurate quantitation requires that the system is linear over the range of actual sample concentrations or amounts. Many pharmaceutical assays, like degradation and stability studies, require that the system be able to identify and quantitate very disparate levels of peaks. In many cases, this translates into a 3 to 4 order of magnitude difference between the main active component and the impurities that need to be quantitated. 

The experimental scheme for a three level reflected saturated fractional design for seven factors is shown in Table 5.15 ( note that one factor was retained as a dummy factor to be used as an additional error check). The experimental order of the scheme was sorted on acid type as this required long equilibration times, this ordering loses some of the features of the initial design but is a compromise that can be justified on the fact that... 

Interference is defined as an effect causing a systematic deviation in the measurement of the signal when a sample is nebulized, as compared with the measure that would be obtained for a solution of equal analyte concentration in the same solvent, but in the absence of concomitants. The interference may be due to a particular concomitant or to the combined effect of several concomitants. A concomitant causing an interference is called an interferent. Interference only causes an error if not adequately corrected for during an analysis. Uncorrected interferences may lead to either enhancements or depressions. Additionally, errors may arise in analytical methods in other ways, e g. in sample pretreatment via the... 

Assumptions (i) and (ii) justify the model in the form (3.2), with an additive error as the only random variable. By (iii) we assume that the model is correct and there are no systematic measurement errors, i.e.,... 

While in the first step the deviation from the exact solution stems only from approximating the solution curve by its tangent line, in further steps we calculate the slope at the current approximation y1 instead of the unknown true value (), thereby introducing additional errors. The solution of (5.2) is given by (5.3), and the total error Ei = y(t ) - y for this simple equation is... 

Uncertainty in sea-level C02 estimates. The calculation of unknown paleo-elevations hinges on the difference in C02 partial pressure between sea-level and the site of unknown elevation (Eqn. 1). Therefore, not knowing exact sea-level C02 concentrations will introduce a significant additional error into the estimation. This uncertainty could be minimized by estimating sea-level C02 using stomatal frequency analysis on the same species from a contemporaneous low-elevation flora. However, if such fossil material is not available, C02 estimates based on other plant species or other proxies have to be used for calibration. 

Stomatal density and index show great potential for paleoelevation reconstructions with low error margins, if additional error sources such as the presence of sun and shade morphotypes and especially uncertainty in sea-level C02 concentrations can be well constrained. Unlike other paleobotanical methods, stomatal frequency analysis is not restricted to angiosperm dominated floras, and has no requirements for a minimum amount of taxa present. The method will be most reliable when applied to fossil taxa that are closely related to extant species, and suitable taxa are most likely to be found for periods when C02 concentrations were not much higher than ambient (380 ppmV). 

The comparisons may take place every time a measurement is made (e.g., calibration of an analytical measurement using a standard solution), periodically (e.g., calibration of the balance), or infrequently (e.g., validation of a method). The reference value is used to either calibrate the process or to check its calibration or validity. The number of steps in the chain of comparisons should be kept to a minimum as each additional step introduces additional errors and increases the overall uncertainty. Interlaboratory comparisons provide evidence of comparability and provide confidence in traceability claims they do not, however, provide traceability directly. 

The uncertainty associated with a traceable value must be related to a specified measurand (analyte) and be related to stated references. The following example illustrates the effect the choice of stated reference has on the stated uncertainty for the measurement of lead in milk. The uncertainty of a measurement of lead in milk, measured using a standard method, could be small, if stated relative to that standard method, where the measurand (analyte) is implicitly defined by the standard method. However, the method is likely to contain some additional errors and uncertainties if it were to be related to a primary method traceable to the SI, and these would need to be included in the estimate of uncertainty, if the SI was quoted as the stated reference. The interrelationship between uncertainty and... 

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