Error negatives

Not only is this error negative, meaning that we overestimate the integral (C.l), but it also appears that the error decreases very rapidly with y, such that one is tempted to conclude that in the limit n —> oo (and hence y = nh oo) e[Pg.94]

According to equation 43, corrected for basis-set superposition error. Negative values indicate stabilization by die ion. 

Data are presented as mean standard deviation. When data from a given site were reported with several averages and standard deviations, the data were pooled for an overall site average and a new estimate of the standard deviation was calculated using propogation of errors. Negative rates indicate uptake by the sediment. Rates are confined to those measured in situ in papers published since 1990 for a summary of earlier rates see Burdige (2006). 

Positive Deviations from Mean between Number of Errors. Percentage Number of Errors. Negative Deviations from Mean between Number of Errors. Percentage Number of Errors. 

Integrated absolute error (lAE) essentially takes the absolute value of the error. Negative areas are accounted for when lAE is used, thus dismissing the problem encountered with IE regarding sinusoidal responses. 

These small positive and negative errors partially cancel each other. The result is that capital cost targets predicted by the methods described in this chapter are usually within 5 percent of the final design, providing heat transfer coefficients vary by less than one order of magnitude. If heat transfer coefficients vary by more than one order of magnitude, then a more sophisticated approach can sometimes be justified. ... 

A Hbasis functions provides K molecular orbitals, but lUJiW of these will not be occupied by smy electrons they are the virtual spin orbitals. If u c were to add an electron to one of these virtual orbitals then this should provide a means of calculating the electron affinity of the system. Electron affinities predicted by Konpman s theorem are always positive when Hartree-Fock calculations are used, because fhe irtucil orbitals always have a positive energy. However, it is observed experimentally that many neutral molecules will accept an electron to form a stable anion and so have negative electron affinities. This can be understood if one realises that electron correlation uDiild be expected to add to the error due to the frozen orbital approximation, rather ihan to counteract it as for ionisation potentials. 

Errors affecting the distribution of measurements around a central value are called indeterminate and are characterized by a random variation in both magnitude and direction. Indeterminate errors need not affect the accuracy of an analysis. Since indeterminate errors are randomly scattered around a central value, positive and negative errors tend to cancel, provided that enough measurements are made. In such situations the mean or median is largely unaffected by the precision of the analysis. 

Note that a negative determinate error introduced by failing to recover all the analyte is partially offset by a positive determinate error due to a failure to remove all the interferent. 

Ammonia is a volatile compound as evidenced by the strong smell of even dilute solutions. This volatility presents a possible source of determinate error. Will this determinate error be negative or positive ... 

Any ioss of NH3 is ioss of anaiyte and a negative determinate error. 

Accuracy Under normal conditions relative errors of 1-5% are easily obtained with UV/Vis absorption. Accuracy is usually limited by the quality of the blank. Examples of the type of problems that may be encountered include the presence of particulates in a sample that scatter radiation and interferents that react with analytical reagents. In the latter case the interferant may react to form an absorbing species, giving rise to a positive determinate error. Interferents also may prevent the analyte from reacting, leading to a negative determinate error. With care, it maybe possible to improve the accuracy of an analysis by as much as an order of magnitude. 

There are problems to be considered and avoided when using Hquid-in-glass thermometers. One type of these is pressure errors. The change in height of the mercury column is a function of the volume of the bulb compared to the volume of the capillary. An external pressure (positive or negative) which tends to alter the bulb volume causes an error of indication, which may be small for normal barometric pressure variations but large when, for example, using the thermometer in an autoclave or pressure vessel. 

Feedback Control In a feedback control loop, the controlled variable is compared to the set point R, with the difference, deviation, or error e acted upon by the controller to move m in such a way as to minimize the error. This ac tion is specifically negative feedback, in that an increase in deviation moves m so as to decrease the deviation. (Positive feedback would cause the deviation to expand rather than diminish and therefore does not regulate.) The action of the controller is selectable to allow use on process gains of both signs. 

By comparison with Eq. (2-1) the measured value in Fig. 2-3 is too negative by according to Eq. (2-33) and correspondingly is too positive in the case of the anodic current. The error can be calculated for uniform current flow lines from Ohm s Law ... 

Since the object to be protected represents a cell consisting of active and passive steel, considerable IR errors in the cell current must be expected in measuring the off potential. The considerations in Section 3.3.1 with reference to Eqs. (3-27) and (3-28) are relevant here. Since upon switching off the protection current, 7, the nearby cathodes lead to anodic polarization of a region at risk from corrosion, the cell currents and 7, have opposite signs. It follows from Eqs. (3-27) and (3-28) that the 77 -free potential must be more negative than the off potential. Therefore, there is greater certainty of the potential criterion in Eq. (2-39). 

Errors in advection may completely overshadow diffusion. The amplification of random errors with each succeeding step causes numerical instability (or distortion). Higher-order differencing techniques are used to avoid this instability, but they may result in sharp gradients, which may cause negative concentrations to appear in the computations. Many of the numerical instability (distortion) problems can be overcome with a second-moment scheme (9) which advects the moments of the distributions instead of the pollutants alone. Six numerical techniques were investigated (10), including the second-moment scheme three were found that limited numerical distortion the second-moment, the cubic spline, and the chapeau function. 

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